Model-based Prediction and Optimal Control of Pandemics by Non-pharmaceutical Interventions
Reza~Sameni$^\textnormal{*
A model-based signal processing framework is proposed for pandemic trend forecasting and control, by using non-pharmaceutical interventions (NPI) at regional and country levels worldwide. The control objective is to prescribe quantifiable NPI strategies at different levels of stringency, which balance between human factors (such as new cases and death rates) and cost of intervention per region/country. Due to infrastructural disparities and differences in priorities of regions and countries, strategists are given the flexibility to weight between different NPIs and to select the desired balance between the human factor and overall NPI cost. The proposed framework is based on a finite-horizon optimal control (FHOC) formulation of the bi-objective problem and the FHOC is numerically solved by using an ad hoc extended Kalman filtering/smoothing framework for optimal NPI estimation and pandemic trend forecasting. The algorithm enables strategists to select the desired balance between the human factor and NPI cost with a set of weights and parameters. The parameters of the model are partially selected by epidemiological facts from COVID-19 studies, and partially trained by using machine learning techniques. The developed algorithm is applied on ground truth data from the Oxford COVID-19 Government Response Tracker project, which has categorized and quantified the regional responses to the pandemic for more than 300 countries and regions worldwide, since January 2020. The dataset was used for NPI-based prediction and prescription during the XPRIZE Pandemic Response Challenge.
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\begin{document}

\title{Model-based Prediction and Optimal Control of Pandemics by Non-pharmaceutical Interventions}
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\author{Reza~Sameni$^\textnormal{*}$,~\IEEEmembership{Senior~Member,~IEEE}%
\thanks{Manuscript received May 30, 2021; revised October 19, 2021; accepted November 15, 2021.}%
\thanks{\textsuperscript{*}R.~Sameni is with the Department of Biomedical Informatics, Emory University, Atlanta, GA (e-mail: \url{rsameni@dbmi.emory.edu}).}%
\thanks{Copyright (c) 2021 IEEE. Personal use of this material is permitted.  However, permission to use this material for any other purposes must be obtained from the IEEE by sending an email to pubs-permissions@ieee.org.}%
}%\newline
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\markboth{Published in IEEE Journal of Selected Topics in Signal Processing: \url{https://doi.org/10.1109/JSTSP.2021.3129118}}{R. Sameni: Model-based Prediction and Control of Pandemics}
\maketitle
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\begin{abstract}
A model-based signal processing framework is proposed for pandemic trend forecasting and control, by using non-pharmaceutical interventions (NPI) at regional and country levels worldwide. The control objective is to prescribe quantifiable NPI strategies at different levels of stringency, which balance between human factors (such as new cases and death rates) and cost of intervention per region/country. Due to infrastructural disparities and differences in priorities of regions and countries, strategists are given the flexibility to weight between different NPIs and to select the desired balance between the human factor and overall NPI cost.

The proposed framework is based on a \textit{finite-horizon optimal control} (FHOC) formulation of the bi-objective problem and the FHOC is numerically solved by using an ad hoc \textit{extended Kalman filtering/smoothing} framework for optimal NPI estimation and pandemic trend forecasting. The algorithm enables strategists to select the desired balance between the human factor and NPI cost with a set of weights and parameters. The parameters of the model are partially selected by epidemiological facts from COVID-19 studies, and partially trained by using machine learning techniques. The developed algorithm is applied on ground truth data from the Oxford COVID-19 Government Response Tracker project, which has categorized and quantified the regional responses to the pandemic for more than 300 countries and regions worldwide, since January 2020. The dataset was used for NPI-based prediction and prescription during the XPRIZE Pandemic Response Challenge.
\end{abstract} % 
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\begin{IEEEkeywords}
COVID-19; pandemic forecasting; pandemic control; non-pharmaceutical interventions; compartmental modeling; extended Kalman filtering; finite-horizon optimal control.
\end{IEEEkeywords}
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\IEEEpeerreviewmaketitle
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\section{Introduction
\label{sec:introduction}}
The COVID-19 pandemic highlighted the fact that social life--- as a \textit{dynamic system}--- is always in a \textit{metastable} condition, which is continuously prone to pandemic outbreaks (regardless of the severity or geographical origin of pandemics). Parallel to medical solutions and vaccinations against known viruses, the rapid and effective response to future pandemics requires proactive planning and interdisciplinary collaborations between different scientific communities. Specifically, some of the prominent contributions, which can be made by the signal processing and data science communities include: 1) developing accurate spatio-temporal forecasting models at different levels of abstraction, which simulate pandemic outbreaks and trends, 2) identifying quantifiable \textit{non-pharmaceutical intervention} (NPI) plans, with fact-based estimates of the impact and cost of each NPI \cite{Hale2021}, and 3) simulated multi-objective pandemic response strategies, which balance between NPI cost and effectiveness, to help governments and policymakers in resource allocation and fact-based decision making to control new pandemic waves.

In this context, NPIs refer to actions and policies adopted by individuals, authorities or governments that help slowing down the spread of epidemic diseases. Enforcement of social distancing, face covering, restrictions on social events and public transportation, etc. were among the NPIs that were experienced during the COVID-19 pandemic. NPIs are among the best ways of controlling pandemic diseases when vaccines or medications are not yet available\footnote{See Centers for Disease Control and Prevention guidelines on NPIs: \url{ https://www.cdc.gov/nonpharmaceutical-interventions/}.}.

During the COVID-19 pandemic, several attempts were made to categorize and quantify the various NPIs of different regions and nations, which was essential for comparing the effectiveness of regional policies in containing the pandemic spread. By using signal processing and machine learning techniques, the quantified NPI can be used to forecast the future trends of the pandemic and to simulate \textit{``what if scenarios''} for the better management of human and medical resources, and to eventually prescribe appropriate NPI for controlling the pandemic \cite{miikkulainen2021prediction}. The overall pandemic monitoring, forecasting and control cycle can be seen as a closed-loop system consisting of social and algorithmic elements, as shown in Fig.~\ref{fig:NPISystem}.

\begin{figure*}
    \centering
    \includegraphics[angle = 90, trim=2.4in 1.5in 2.2in 0.5in,clip,width=1.4\columnwidth]{Figures/NPISystem}
    \caption{A closed-loop system representation for pandemic control via non-pharmaceutical interventions (NPIs). Social constraints imposed by governments, states, etc. is influenced by the pandemic trend and external political and economic factors. Beyond the level of social interactions, the pandemic spread is also influenced by external factors such as vaccination, new virus variants, etc. The NPIs \textit{imposed} by decision-makers practically differ from the actual \textit{effective} NPIs practiced by the society. The monitoring entities (healthcare system and other organizations) observe the ``ground truth'' effective NPIs, the number of new cases, hospitalized and death cases, which contain inevitable errors and uncertainties. Data analysts contribute to this loop by forecasting the future trend of the pandemic and providing fact-based prescriptions of future NPI to control the pandemic, while satisfying other socioeconomic objectives.}
    \label{fig:NPISystem}
\end{figure*}

The Oxford COVID-19 Government Response Tracker (OxCGRT) was one of the NPI tracking projects, which were launched and regularly updated during the COVID-19 pandemic \cite{OxCGRT2020}. OxCGRT has been used by the data science community for NPI-based prediction and prescription planning. Specifically, the XPRIZE Pandemic Response Challenge addressed the problem of predicting future trends of the pandemic in different regions and countries, and prescribing efficient NPIs that compromise between the number of new cases and a weighted-cost of intervention \cite{XPRIZEPandemicResponse2020,miikkulainen2021prediction}. The challenge was motivated by the fact that due to disparities in infrastructures, available resources and priorities, policymakers worldwide tend to give different weights to each NPI and are interested to know the impacts and consequences of each policy in advance. During this challenge, the Alphanumerics Team from the Department of Biomedical Informatics at Emory University, adopted a model-based signal processing approach, based on estimation theory and \textit{finite-horizon optimal control}, to address the problem of weighted NPI prescription. Our team was among the finalists of this challenge.

The notion of multi-objective finite-horizon pandemic control has also been considered by other researchers in simulated scenarios \cite{Mallela2020,GUAN2020394}, and also on real data \cite{Perkins2020}. The latter is closely related to the hereby developed bi-objective optimization via NPI. Over the past year, several other control-theoretical approaches have emerged for pandemic control \cite{Djidjou-Demasse2020, Patterson-Lomba2020, Shah2020}, which have been mainly tested in simulated scenarios or over regional data.

In order to develop a general framework, which is applicable for all regions worldwide, the OxCGRT dataset was used for the current study. Since the only globally registered NPIs in this dataset are the total confirmed cases, the total confirmed deaths and the daily NPIs, we adopted an extension of a generic \textit{susceptible-infected} (SI) compartmental model from our previous work, as the base model for all regions/countries \cite{sameni2020mathematical}. The proposed model parameters are trained on historic data and used to predict future trends from input NPI by using an extended Kalman filter. It is further shown that the forecasting model can be integrated with a finite-horizon optimal controller to find the optimal daily NPIs with arbitrary NPI cost weight vectors. It should be noted that since the XPRIZE Challenge was held before the global availability of COVID-19 vaccines, the interventions considered for all nations do not include vaccinations. This fact is also reflected in the compartmental model detailed in the sequel. Nevertheless, the proposed framework is generic and can be extended to other compartmental models, when more accurate data exist for a specific region/nation. 

While the majority of recent pandemic data analysis research--- including the winners of the XPRIZE Pandemic Response Challenge \cite{Lozano2021,Janko2021}--- are based on data-driven machine learning (ML) techniques and deep neural networks, this research demonstrates how classical signal processing and optimal control theories can be used and combined with ML techniques for solving pandemic trend forecasting and NPI prescription. The advantages of the proposed approach are manifold, including: theoretical support for the predictions/prescriptions, ease of interpretation through fact-based data models, quantitative performance bounds, and lower computational/training cost as compared with fully data-driven ML-based approaches.

In Section \ref{sec:dataset}, the OxCGRT NPI database is explained. Section \ref{sec:datamodel} details the data model. The developed finite-horizon optimal NPI prescription framework is elaborated in Section \ref{sec:finitehorizoncontrol}. This framework is combined with an extended Kalman filter/smoother for pandemic forecasting in Section \ref{sec:prediction_prescription}, followed by the details of model training and implementation in Section \ref{sec:modeltraining}. The results on real data from the COVID-19 pandemic and a detailed discussion on the proposed method are presented in Sections \ref{sec:results} and \ref{sec:discussion}, followed by concluding remarks and future directions. The source codes of the developed models and algorithms are provided online for reference \cite{EpidemicModelingCodesSameni2020}.

\section{The non-pharmaceutical interventions dataset}
\label{sec:dataset}
To date, the Oxford COVID-19 Government Response Tracker (OxCGRT) is an ongoing project \cite{Hale2021}, which categorizes and quantifies the NPI policies of different regions/nations since the beginning of the pandemic. The dataset was used in the XPRIZE Pandemic Response Challenge \cite{XPRIZEPandemicResponse2020}, which addressed the problem of pandemic trend forecasting in different regions/countries under social interventions (e.g., social distancing, mandatory mask wearing, social gathering prohibitions, closure of schools and public transportation limitations), and prescribing efficient NPIs that compromise between human factors (infection and death rates) and a weighted cost of intervention. The subset of OxCGRT NPI categories used by the XPRIZE Challenge and the current study are listed in Table~\ref{tab:OxCGRTNPI}. Note that the OxCGRT dataset uses the Johns Hopkins Coronavirus dataset for US states \cite{Dong2020}, which also provides state-level information for the US. 
In OxCGRT, the level of NPI stringency for different social activities are quantified by integer values ranging from zero (minimum or no stringency), to two or four (for a maximum stringency, depending on the index). The total social stringency can be considered as a weighted combination of the different indexes. Throughout the XPRIZE Challenge, the weight vector was considered as a design parameter, which enables strategists to prioritize certain NPIs over the others.

\begin{table*}[tb]
    \centering
\caption{Subset of NPI indexes from the Oxford COVID-19 Government Response Tracker project used in this study, adopted from \cite{Hale2021}}
    \begin{tabular}{|c|l|p{12cm}|}
    \hline
      Index & Description & Values\\\hline
       C1 & School closing & 0: no measures 
1: recommend closing or all schools open with alterations resulting in significant differences compared to non-COVID-19 operations, 2: require closing (only some levels or categories, e.g., only high school or public schools), 3: require closing all levels, Blank: no data\\\hline
       C2 & Workplace closing & 0: no measures, 1: recommend closing (or recommend work from home), 2: require closing (or work from home) for some sectors or categories of workers, 3: require closing (or work from home) for all-but-essential workplaces (e.g., grocery stores, doctors), Blank: no data\\\hline
       C3 & Cancel public events & 0: no measures, 1: recommend canceling, 2: require canceling, Blank: no data\\\hline
       C4 & Restrictions on gatherings & 0: no restrictions, 1: restrictions on very large gatherings (above 1000 people), 2: restrictions on gatherings (101--1000 people), 3: restrictions on gatherings (11--100 people), 4: restrictions on gatherings (up to 10 people), Blank: no data\\\hline
       C5 & Close public transport & 0: no measures, 1: recommend closing (or significantly reduce volume/route/means of transport available), 2: require closing (or prohibit most citizens from using it), Blank: no data\\\hline
       C6 & Stay at home requirements & 0: no measures, 1: recommend not leaving house, 2: require not leaving house with exceptions for daily exercise, grocery shopping, and `essential' travels, 3: require not leaving house with minimal exceptions (e.g., allowed to leave once a week, or only one person at a time), Blank: no data\\\hline
       C7 & Internal movement restrictions & 0: no measures, 1: recommend not to travel between regions/cities, 2: internal movement restrictions in place, Blank: no data\\\hline
       C8 & International travel controls & 0: no restrictions, 1: screening arrivals, 2: quarantine arrivals from some or all regions, 3: ban arrivals from some regions, 4: ban on all regions or total border closure, Blank: no data\\\hline
       H1 & Public information campaigns & 0: no COVID-19 public information campaign, 1: public officials urging caution about COVID-19, 2: coordinated public information campaign (e.g., across traditional and social media), Blank: no data\\\hline
       H2 & Testing policy & 0: no testing policy, 1: only those who have symptoms AND meet specific criteria (e.g., key workers, admitted to hospital, came into contact with a known case, returned from overseas), 2: testing all symptomatic people, 3: open public testing (e.g., ``drive through'' testing available to asymptomatic people), Blank: no data\\\hline
       H3 & Contact tracing & 0: no contact tracing, 1: limited contact tracing (not done for all cases), 2: comprehensive contact tracing (done for all identified cases)\\\hline
       H6 & Facial coverings & 0: no policy, 1: recommended, 2: required in some specified shared/public spaces outside the home with other people present, or some situations when social distancing not possible, 3: required in all shared/public spaces outside the home with other people present or all situations when social distancing not possible, 4: required outside the home at all times regardless of location or presence of other people\\\hline
    \end{tabular}
    \label{tab:OxCGRTNPI}
\end{table*}

\section{Data Model}
\label{sec:datamodel}
The two major classes of methods for epidemic disease spread modeling are: 
\begin{enumerate}[leftmargin=*]
    \item \textit{Compartmental models}, which split the total population of a region into various compartments (groups) such as susceptibles, exposed, infected, recovered, vaccinated, deceased, etc. These compartments are used to form parametric differential/difference equations, which are fit on real data and are analytically or numerically solved to predict future trends of the disease spread. 
    \item \textit{Agent-based models}, which model the behaviors of individuals and their interactions at a simplified level-of-abstraction. Using these models, large groups of agents are generated in stochastic simulated environments, as they randomly move, interact and probabilistically pass the infection to one another, recover, pass away, etc. The population-level properties are obtained by ensemble averaging over the entire population.
\end{enumerate}
Each approach has its advantages and limitations. For large population sizes at regional or national levels--- which is the scope of the current study--- the first approach is asymptotically accurate and is more advantageous as it can be analytically studied in a rigorous mathematical framework and combined with state estimation techniques for forecasting, and optimal control theories for NPI prescription. Therefore, the first approach was adopted for this study, by using a contact-controlled time-variant version of the so-called \textit{susceptible-infected (SI)} compartmental model shown in Fig.~\ref{fig:si_model}. This model is a simplified variant of the general multi-compartment models studied in our previous research \cite{sameni2020mathematical}. Apparently, more accurate models can be used for the regions that additional data such as the number of recovered, hospitalized, vaccinated, or the age pyramid of the population are available. However, for the current study, since the global data provided in the OxCGRT dataset were the number of daily confirmed cases, total death cases, and the regional NPIs, the same SI model is used for all regions and countries.

\begin{figure}[t]
     \centering
     \MediumPicture\VCDraw{\begin{VCPicture}{(0,-1)(5,0)}
 % states
 \ShowState
 \State[s]{(0,0)}{A} \State[i]{(3,0)}{B} \HideState
 \State[R]{(6,0)}{C}
 % initial--final
 %\Initial{A} \Final{B}
 % transitions
 \EdgeL{B}{C}{\beta}
 \EdgeL{A}{B}{\alpha(t) i}
 \end{VCPicture}}
     \caption{The base susceptible-infected compartmental model with NPI-controlled infection rate}
     \label{fig:si_model}
 \end{figure}

The nonlinear dynamic equations corresponding to the proposed compartmental model are:
\begin{equation}
\begin{array}{l}
\dot{s}(t) = -\alpha(t)s(t)i(t)\\
\dot{i}(t) = \alpha(t)s(t)i(t) - \beta i(t)\\
\dot{\alpha}(t) = -\gamma \alpha(t) + \gamma h[\mathbf{u}(t)]
\end{array}
\label{eq:dynamicmodel}
\end{equation}
where
\begin{itemize}[leftmargin=*]
    \item $s(t)$ is the fraction of population in a region/country that is susceptible at time $t$ (i.e., the susceptible population divided by the population size $N$);
    \item $i(t)$ is the fraction of population that is infected and contagious at $t$ (i.e., the infected contagious population divided by the regional population size $N$);
    \item $\mathbf{u}(t)\in\mathbb{R}^L$ is the NPI vector considered as an exogenous control input ($L=12$, for the list of NPIs in Table~\ref{tab:OxCGRTNPI}, used for the XPRIZE Challenge \cite{XPRIZEPandemicResponse2020}). The full description of the OxCGRT data NPI set is detailed in \cite{OxCGRT2020};
    \item $\alpha(t)$ is the time-variant contagion rate, with inverse time unit;
    \item $h[\mathbf{u}(t)]$ is a causal monotonic function of the NPI, which maps the NPI to the contagion rate;
    \item $\beta$ is the rate of elimination from the contagious group (through quarantine, recovery, or death), assumed to be constant in the simplified case;
    \item $\gamma$ is the \textit{action to effect rate} (or the inverse of the NPI lag to the inter-individual contact rate), which accounts for the delay between adopting an NPI policy and the onset of its practical effectiveness in the pandemic trend. The third equation in (\ref{eq:dynamicmodel}) is equivalent to $\alpha(t) = \gamma\exp[-\gamma (t - t_0)] * h[\mathbf{u}(t)]$ (for $t \geq t_0$), which is a smoothed version of $h[\mathbf{u}(t)]$. As a corner case, $\gamma \rightarrow \infty$ represents zero latency between action and effect, resulting in $\alpha(t) = h[\mathbf{u}(t)]$.
    % , which is a causal function of $\mathbf{u}(t)\in\mathbb{R}^L$ input impact on the  
\end{itemize}
The parameters $\beta$, $\gamma$ and the function $h[\mathbf{u}(t)]$ require learning using the observed variables, as detailed in Section \ref{sec:modeltraining}. Furthermore, in \cite{sameni2020mathematical} we showed how the infection \textit{reproduction rate} $\mathcal{R}_t$ can be calculated from $\alpha(t)$ and $\beta$. Specifically, using the eigenanalysis-based definition of the reproduction rate proposed in \cite{sameni2020mathematical}, during the pandemic outbreak, when only several percents of the population are infected and \textit{herd immunity} has not been reached, we have:
\begin{equation}
    \mathcal{R}_t \approx \exp[\Delta(\alpha(t) - \beta)]
\label{eq:ReproductionRate}    
\end{equation}
where $\Delta$ is the reproduction rate generation time-unit.

Finally, for estimation purposes, the dynamic equations in (\ref{eq:dynamicmodel}) can be related to real-world reports of the fractions of \textit{new cases}: 
\begin{equation}
    n(t) = \alpha(t)s(t)i(t) + v(t),
\label{eq:observationNewCases}
\end{equation}
or through the fraction of \textit{total confirmed cases}:
\begin{equation}
c(t) = s(t_0) - s(t) + v(t),
\label{eq:observationTotalCases}
\end{equation}
where $v(t)$ is measurement noise due to case report errors (which inevitably existed during the COVID-19 global reports in all regions/nations), and $s(t_0)$ is the initial susceptible population fraction at the beginning of the pandemic (very close or equal to 1, for an un-vaccinated initial population). 

\section{Finite-horizon optimal NPI control}
\label{sec:finitehorizoncontrol}
\subsection{Cost function and problem statement}
From (\ref{eq:dynamicmodel}), the total number of new infections over an arbitrary time window $[t_0, t_1]$ is:
\begin{equation}
    J_0(\mathbf{u}) = -\int_{t = t_0}^{t_1} \dot{s}(t)\,\mathrm{d}t = \int_{t = t_0}^{t_1} \alpha(t)s(t)i(t)\,\mathrm{d}t
\label{eq:newcasescost}
\end{equation}
and the total cost of NPIs over the same time period is
\begin{equation}
    J_1(\mathbf{u}) = \int_{t = t_0}^{t_1} \mathbf{w}(t)^T\mathbf{u}(t)\,\mathrm{d}t 
\label{eq:npicost}
\end{equation}
where $\mathbf{w}(t)$ is the NPI weight vector given as input. The motivation for the user-selected weight vector $\mathbf{w}(t)$ is that the cost of intervention is different across regions. A stereotypical example considered in the XPRIZE Challenge was that ``closing public transportation may be much costlier in London than it is in Los Angeles. Such preferences are expressed as weights associated with each intervention plan dimension, given to the prescriptor as input for each region \cite{XPRIZEPandemicResponse2020}.''

With these assumptions, the optimal NPI prescription problem can be formulated as a bi-objective optimization problem, with a total cost:
\begin{equation}
    J(\mathbf{u}) = (1 - \epsilon)J_0(\mathbf{u}) + \epsilon J_1(\mathbf{u})\,\, \text{ s.t. } \mathbf{u} \in \Gamma
\label{eq:totalnpicost}
\end{equation}
where $\epsilon\in[0, 1]$ is a free parameter that compromises between the human factor ($J_0$) and the NPI cost ($J_1$), and $\Gamma$ is the set of admissible inputs:
\begin{equation}
    \Gamma = \{\mathbf{u} | \mathbf{u}^{\min}\leq \mathbf{u}(t) \leq \mathbf{u}^{\max}, \forall t\in [t_0, t_1]\} 
\label{eq:admissibleinput}
\end{equation}
where the vectors $\mathbf{u}^{\min}$ and $\mathbf{u}^{\max}$ are (element-wise) the minimum and maximum ranges of the NPI indexes in the OxCGRT dataset (the ``values'' column in Table~\ref{tab:OxCGRTNPI}). Accordingly, $\mathbf{u}^{\min}=\mathbf{0}$ corresponding to no stringency, and $\mathbf{u}^{\max} = [3, 3, 2, 4, 2, 3, 2, 4, 2, 3, 2, 4]^T$ for the maximum stringency of each NPI index.

For a given pair of design parameters $\{\epsilon, \mathbf{w}(t)\}$, the objective is to find $\mathbf{u}^*(t)$ for all $t\in[t_0, t_1]$, such that:
\begin{equation}
    J(\mathbf{u}^*) = \min_{\Gamma}(J(\mathbf{u}))
    \label{eq:optsolution}
\end{equation}

\subsection{The Pareto optimal solution}
The problem (\ref{eq:optsolution}) can be solved by \textit{finite-horizon optimization} \cite{naidu2003optimal}. In optimal control theory, the inputs which satisfy this equation are known as \textit{Pareto optimal (efficient)}. In fact, for an arbitrary weight vector $\mathbf{w}(t)$, by sweeping $\epsilon$ over $[0, 1]$, the \textit{Pareto-optimal front} of the optimization problem is found, from which pandemic strategists can select the desired free parameter $\epsilon$ that determines the desired operation point to balance between NPI effectiveness and cost (and its corresponding optimal NPI $\mathbf{u}^*(t)$ to be adopted by the country/region).

To solve (\ref{eq:optsolution}), first the corresponding \textit{Hamiltonian} function is formed \cite[Ch. 2]{naidu2003optimal}:
\begin{equation}
\begin{array}{rl}
     \mathcal{H} = & (1 - \epsilon)\alpha(t)s(t)i(t) + \epsilon \mathbf{w}(t)^T\mathbf{u}(t) \\
     & -\lambda_1(t) \alpha(t)s(t)i(t)
     \\
     & + \lambda_2(t)[ \alpha(t)s(t)i(t) - \beta i(t)]\\
     & - \gamma\lambda_3(t)\{\alpha(t) - h[\mathbf{u}(t)]\}
\end{array}
\label{eq:generalhamiltonian}
\end{equation}
where $\lambda_1(t)$, $\lambda_2(t)$ and $\lambda_2(t)$ are known as \textit{co-states}. According to \textit{Pontryagin's minimum principle}, the co-states and the optimal solution $\mathbf{u}^*$ satisfy \cite[Ch. 6]{naidu2003optimal}:
\begin{equation}
\begin{array}{l}
\dot{\lambda}_1(t) = \displaystyle-\frac{\partial\mathcal{H}}{\partial s} = [\lambda_1(t) -\lambda_2(t)-1 + \epsilon]\alpha(t)i(t)\\
\dot{\lambda}_2(t) = \displaystyle-\frac{\partial\mathcal{H}}{\partial i} = [\lambda_1(t) -\lambda_2(t)-1 + \epsilon]\alpha(t)s(t) + \beta\lambda_2(t)\\
\dot{\lambda}_3(t) = \displaystyle-\frac{\partial\mathcal{H}}{\partial\alpha} = [\lambda_1(t) -\lambda_2(t)-1 + \epsilon]s(t)i(t) + \gamma\lambda_3(t)
\\
\mathcal{H}(\mathbf{u}^*) \leq \mathcal{H}(\mathbf{u}), \quad \forall \mathbf{u}\in \Gamma
\end{array}
\label{eq:PontryaginPrinciple}
\end{equation}
When the inputs are unconstrained, the Hamiltonian minimizer input $\mathbf{u}^*$, in the last condition of (\ref{eq:PontryaginPrinciple}), can be found by solving
\begin{equation}
\bm{\nabla}_{\mathbf{u}}\mathcal{H}(\mathbf{u}^*) = \mathbf{0},
\label{eq:hamiltonianminmsolution}
\end{equation}
where $\bm{\nabla}_\mathbf{u}\mathcal{H}$ denotes the Hamiltonian gradient with respect to the input vector $\mathbf{u}$, and the condition should hold element-wise. In this case, a sufficient condition for the existence of a solution is to have $\bm{\nabla}_{\mathbf{u}}^2\mathcal{H}(\mathbf{u}^*) \succ \mathbf{0}$ (where $\bm{\nabla}_{\mathbf{u}}^2$ denotes the Hessian operator with respect to the input vector $\mathbf{u}$ and $\succ \mathbf{0}$ denotes positive-definiteness). In the constrained-input case--- as in this problem--- where the inputs are confined to the admissible set (\ref{eq:admissibleinput}), while the global solution of (\ref{eq:hamiltonianminmsolution}) might not exist or belong to the admissible set (\ref{eq:admissibleinput}), a Hamiltonian minimizer optimal input still exists. In either case, the optimal input is found as a parametric function of the costate $\lambda_3(t)$ and the other model parameters.

The parametric optimal input found from (\ref{eq:hamiltonianminmsolution}) is next combined with (\ref{eq:PontryaginPrinciple}) and (\ref{eq:dynamicmodel}) to calculate the states, using the initial conditions and appropriate boundary conditions (also known as the \textit{transversality conditions}) on the co-states and the Hamiltonian. The desired boundary conditions, which satisfy the pandemic control problem are:
\begin{equation}
    \begin{array}{ccc}
        \lambda_1(t_1) = 0, & \lambda_2(t_1) = 0, & \lambda_3(t_1) = 0.
    \end{array}
\label{eq:transversalityconditions}    
\end{equation}
The conditions in (\ref{eq:transversalityconditions}) are the general free end-point conditions of finite-horizon optimization problems, which match the objectives of the pandemic control problem. Alternative transversality conditions that can be studied within the proposed framework are \cite[Section 2.7]{naidu2003optimal}:
\begin{enumerate}[leftmargin=*]
    \item When the end-time $t_1$ is not fixed, but we require that $i(t_1)$ reaches below $i_{\max}$ by the end of the control period (\textit{infinite-horizon} scenario). This requires the additional condition: $\mathcal{H}(t_1) = 0$.
    \item Assuming that the objective of any NPI policy over a reasonable time period $[t_0, t_1]$ (long enough to make the NPIs effective) is to bring the number of active cases down to $i(t_1) \leq i_{\max}$, where $i_{\max}$ is some target fraction of active cases (ideally zero). In this case, the second condition in (\ref{eq:transversalityconditions}) can be replaced by: $\lambda_2(t_1) [i(t_1) - i_{\max}] = 0$.
    \item We require that $i(t_1)$ drops below $i_{\max}$ any time before a maximum end time $t_f$, which requires $(t_1 - t_f)\mathcal{H}(t_1) = 0$.
\end{enumerate}

\subsection{The NPI to inter-human contact map}
\label{sec:NPIhumanInteraction}
The solution of the NPI optimization problem depends on the choice of $h[\mathbf{u}(t)]$, i.e. the NPI to inter-human contact mapping model. Intuitively, $h[\mathbf{u}(t)]$ is expected to be a monotonically decreasing function of the input NPI vector $\mathbf{u}(t)$. In other words, more strict restrictions on social contact (corresponding to the higher values in Table~\ref{tab:OxCGRTNPI}) should overall reduce the person-to-person contact rates at the population level (this was the globally accepted rationale behind the social restrictions during the COVID-19 pandemic). However, the exact shape of $h[\mathbf{u}(t)]$ generally requires learning from historic data, where the monotonic decreasing assumption acts as a constraint during learning.

Based on this intuitive assumption, we study the following two cases, which lead to closed form solutions for the optimal input as functions of the model co-states.
\subsubsection{Linear regression model}
Let us take
\begin{equation}
h[\mathbf{u}(t)] = b + \mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)]
\label{eq:linear_model}
\end{equation}
where $\mathbf{a}$ is a vector of \textit{input influence weights} and $b$ is a constant bias (intercept value). The \textit{least absolute shrinkage and selection operator} (LASSO) method falls into this category. In addition, adding the constraint $\mathbf{a} \geq \mathbf{0}$ guarantees the monotonically decreasing relationship between the NPI and $\alpha$. In other words, more stringent NPI policies have a non-increasing effect on the human interactions parameter $\alpha$ (i.e. the NPI do not have any counter-impacts on the contact rates). Inserting $h[\mathbf{u}(t)]$ in (\ref{eq:generalhamiltonian}) we find:
\begin{equation}
\bm{\nabla}_{\mathbf{u}}\mathcal{H}(\mathbf{u}) = \epsilon \mathbf{w}(t) - \gamma\lambda_3(t)\mathbf{a}
\label{eq:LinearHamiltonianGradient}    
\end{equation}
Now, since $\bm{\nabla}_{\mathbf{u}}\mathcal{H}(\mathbf{u})$ is independent of $\mathbf{u}$, depending on its sign, the Hamiltonian which is a linear function of $\mathbf{u}$, admits its minimum at one of the extreme ends of the admissible input ranges (\ref{eq:admissibleinput}). This eventually results in
\begin{equation}
u^*_k(t) = 
\left\{
\begin{array}{ll}
     u^{\min}_k: & \epsilon w_k(t) > \gamma \lambda_3(t)a_k\\
     u^{\max}_k: & \epsilon w_k(t) < \gamma \lambda_3(t)a_k \end{array}
\right.
\label{eq:optimalinputlinear}    
\end{equation}
for $k = 1, \ldots, L$.
    
\subsubsection{Quadratic regression}
In the second case, we assume
\begin{equation}
h[\mathbf{u}(t)] = b + \mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)] + \frac{1}{2}[\mathbf{u}^{\max} - \mathbf{u}(t)]^T \mathbf{S} [\mathbf{u}^{\max} - \mathbf{u}(t)]
\label{eq:quadratic_model}
\end{equation}
where $\mathbf{a} \geq \mathbf{0}$ and $\mathbf{S}\in\mathbb{R}^{L\times L}$ is a positive-definite matrix. These assumptions guarantee the monotonically decreasing relationship between the NPI and $\alpha(t)$. Multivariate constrained polynomial fitting can be used to find $\mathbf{S}$, $\mathbf{a}$ and $b$ from historic NPI and case-report data\footnote{Despite the quadratic form of (\ref{eq:quadratic_model}), since it is linear in parameters $\mathbf{S}$, $\mathbf{a}$ and $b$, multivariate constrained polynomial fitting is applicable to find the unknown parameters by using historic data, i.e. model fitting over previous NPI actions adopted by different nations/states.}. Therefore, the required constraint polynomial fitting is straightforward to implement by conventional least squares solvers. In this case, we have:
    \begin{equation}
    \bm{\nabla}_{\mathbf{u}}\mathcal{H}(\mathbf{u}) = \epsilon \mathbf{w}(t) - \gamma\lambda_3(t)\{\mathbf{a} + \mathbf{S}[\mathbf{u}^{\max} - \mathbf{u}(t)]\}
    \label{eq:QuadraticHamiltonianGradient} 
    \end{equation}
    and setting $\bm{\nabla}_{\mathbf{u}}\mathcal{H}(\tilde{\mathbf{u}})=\mathbf{0}$ gives
    \begin{equation}
        \tilde{\mathbf{u}} = \mathbf{u}^{\max} - \mathbf{S}^{-1}[\frac{\epsilon\mathbf{w}(t)}{\gamma\lambda_3(t)} - \mathbf{a}]
    \end{equation}
    From the \textit{second partial derivative test}, since $\bm{\nabla}_{\mathbf{u}}^2\mathcal{H}=\gamma\lambda_3(t)\mathbf{S}$, and the fact that $\mathbf{S}$ is assumed to be positive definite, three cases may occur: 1) if $\lambda_3(t) > 0$, $\tilde{\mathbf{u}}$ is a local minimum, 2) if $\lambda_3(t) < 0$, it is a local maximum, and 3) $\lambda_3(t) = 0$ results in a saddle point. Therefore, by applying Pontryagin's minimum principle and considering the admissible input range (\ref{eq:admissibleinput}), after some algebraic simplifications we find: 
    \begin{equation}
    u^*_k(t) =
        \!\left\{
        \begin{array}{ll}
             \!u^{\min}_k: &\! \epsilon w_k(t) > \gamma \lambda_3(t)(a_k + s_k)\\
             \!\tilde{u}_k: &\! \gamma \lambda_3(t)a_k < \epsilon w_k(t) < \gamma \lambda_3(t)(a_k + s_k) \\
            \!u^{\max}_k: &\! \epsilon w_k(t) < \gamma \lambda_3(t)a_k
        \end{array}
        \right.
    \label{eq:optimalinputquadratic}       
    \end{equation}    
where $\tilde{u}_k$ and $s_k$ are the $k$\textsuperscript{th} entries of the vectors $\tilde{\mathbf{u}}$ and $\mathbf{S}(\mathbf{u}^{\max} - \mathbf{u}^{\min})$, respectively. Comparing (\ref{eq:optimalinputquadratic}) and (\ref{eq:optimalinputlinear}), it is clear how the quadratic case simplifies to the linear case when $\mathbf{S} \rightarrow \mathbf{0}$. It is also seen that in the linear case, the ``optimal NPI'' is always one of the extreme cases $u^{\min}_k$ (no action) or $u^{\max}_k$ (maximum stringency). But when $h(\cdot)$ is nonlinear, intermediate interventions may also be in the optimal NPI set.  
\section{A unified pandemic trend predictor and NPI prescriptor}
\label{sec:prediction_prescription}
For an ideal deterministic model, the state and co-state dynamic equations detailed in Section \ref{sec:finitehorizoncontrol} can be solved with numerical toolboxes for finite-horizon optimal control (cf. \cite{wang2009solving} for a MATLAB-based solution). However, for the application of interest, there are major issues which limit the numerical performance, including: 1) model inaccuracies, 2) noisy observations (inaccurate case reports), 3) missing reports (during holidays), 4) unknown or variable parameters (which is inevitable for a highly dynamic complex system, such as a global pandemic), 5) the difficulty of incorporating the start- and end-point boundary conditions from (\ref{eq:transversalityconditions}).

Due to these issues, we propose a novel technique based on optimal state estimation. Accordingly, we integrate the finite-horizon NPI optimizer and the pandemic trend predictor in a classical extended Kalman filter (EKF) and extended Kalman smoother (EKS) \cite{AndersonMoore1979}. Using (\ref{eq:dynamicmodel}), (\ref{eq:observationNewCases}) and (\ref{eq:PontryaginPrinciple}), the state-augmented dynamic equations for the EKF are:
\begin{equation}
\begin{array}{l}
\dot{s}(t) = -\alpha(t)s(t)i(t) + w_s(t)\\
\dot{i}(t) = \alpha(t)s(t)i(t) - \beta i(t) + w_i(t)\\
\dot{\alpha}(t) = -\gamma \alpha(t) + \gamma h[\mathbf{u}^*(t)] + w_{\alpha}(t)\\
\dot{\lambda}_1(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]\alpha(t)i(t) + \eta_{1}(t)\\
\dot{\lambda}_2(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]\alpha(t)s(t) + \beta\lambda_2(t) + \eta_{2}(t)\\
\dot{\lambda}_3(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]s(t)i(t) + \gamma\lambda_3(t) + \eta_{3}(t)\\
n(t)=\alpha(t)s(t)i(t) + v(t)
\end{array}
\label{eq:EKF}
\end{equation}
where the first six equations are the state and co-state dynamics, the last equation is the observation equation and $h[\mathbf{u}^*(t)]$ is the impact of the optimal control calculated from (\ref{eq:optimalinputlinear}) or (\ref{eq:optimalinputquadratic}). The terms $w_s(t)$, $w_i(t)$, $w_\alpha(t)$, $\eta_1(t)$, $\eta_2(t)$ and $\eta_3(t)$ in (\ref{eq:EKF}) represent process noises (due to model inaccuracies), and $v(t)$ is observation noise. Note that for an estimation based on the total number of confirmed cases (instead of the new cases), the last observation equation in (\ref{eq:EKF}) can be replaced with (\ref{eq:observationTotalCases}). 
The dynamic system (\ref{eq:EKF}) may now be numerically solved by using standard EKF and EKS equations. The discretized version of (\ref{eq:EKF}), which is required for the discrete-dime implementation of the EKF and EKS is detailed in the Appendix.

With the above formulation, the finite-horizon optimal NPI prescription and the EKF/EKS-based forecasting problems are unified in a single model. The overall scheme is summarized in Algorithm \ref{alg:prescription}. % and depicted in Fig.\ref{???}.
The MATLAB implementation of this algorithm is available in our online repository \cite{EpidemicModelingCodesSameni2020}. Note however that the prediction and prescription schemes may still be used independently. Specifically, the proposed optimal NPI prescriptor may be combined with any reliable forecasting scheme, including the data-driven LSTM-based models developed during the XPRIZE Pandemic Response Challenge \cite{miikkulainen2021prediction,Lozano2021,Janko2021}.

\begin{algorithm}[tb]
\begin{flushleft}
\caption{Summary of the proposed algorithm
\label{alg:prescription}}
\begin{algorithmic}[1]
\REQUIRE{Historic case reports and NPIs (or an arbitrary scenario from any \textit{predictor model})}
\REQUIRE{The NPI weights $\mathbf{w}(t)$ per region/country}
\REQUIRE The Pareto front tuning parameter $\epsilon\in[0, 1]$. 
\FORALL{Regions}
\STATE Train the compartmental model parameters over historic NPI and case reports (or a predictor model).
\STATE Use EKF and EKS for prediction and prescription of finite-horizon optimal control inputs $\mathbf{u}^*(t)$.
\ENDFOR
\end{algorithmic}
\end{flushleft}
\end{algorithm}


\section{Model training}
\label{sec:modeltraining}
The model parameters $h[\mathbf{u}(t)]$, $\beta$, $\gamma$ and the EKF/EKS parameters require region-wise training or fact-based selection. For this study, we used classical techniques for \textit{Kalman filter engineering}, based on monitoring the properties of the \textit{innovations process} of the Kalman filter to select and automatically adapt the Kalman filter parameters (initial/final states and covariance matrices) over time \cite[Ch. 8]{grewal2007global}. The parameters related to the social and epidemic aspects of the model are explained in the sequel.

\begin{comment}
Add a table containing the initial values of the EKF/EKS parameters.
\end{comment}

The mapping $h[\mathbf{u}(t)]$ was trained over the OxCGRT dataset historic cases. For this, the developed filter was first applied to the historic data by neglecting the explicit relation between the NPI and contact rates (equivalent to $h[\mathbf{u}(t)] = 0$). Referring to (\ref{eq:EKF}), this assumption is equivalent to considering the input-driven fluctuations of $\alpha(t)$ in the process noise $w_\alpha(t)$. Therefore, the entry of the process noise covariance matrix, which corresponds to $w_\alpha(t)$ is increased (as compared with the expected $\alpha(t)$ error) to account for the inaccuracy of the model due to neglecting $h[\mathbf{u}(t)]$. The resulting EKS gives a primary estimate of $\alpha(t)$ over the training period, which in the next stage is given to a constrained LASSO or quadratic polynomial fitter (for the linear and quadratic forms presumed in Section~\ref{sec:NPIhumanInteraction}) to estimate $h[\mathbf{u}(t)]$ using the historic NPI data. Next, the trained model $h[\mathbf{u}(t)]$, together with the historic data is used in a second round of EKS, this time by using the historic NPI and apparently a smaller \textit{a priori} assumption for the variance of $w_\alpha(t)$ (as it no longer accounts for neglecting $h[\mathbf{u}(t)]$). After the secondary EKS, the new estimates of $\alpha(t)$ are once more used to refine the model parameters of $h[\mathbf{u}(t)]$. The refined parameters are stored per country/region for utilization during the prescription phase over real or synthetic scenarios.

The \textit{action-to-effect rate} parameter $\gamma$ was selected intuitively. From various social experiences, it is reasonable to expect a smooth transition in $\alpha(t)$ due to any change in the NPI. This is based on the social experience that imposing any policy on a complex social system is rarely abrupt. Although the transition is region and NPI dependent, in order to reduce the model complexity, we have fixed $\gamma$ to 1/(7\,days)=0.1429\,days$^{-1}$ for all regions/countries.

The recovery parameter $\beta$ was selected by educated guesses from the Centers for Disease Control and Prevention (CDC) reports regarding recovery and contagion periods\footnote{Refer to CDC guidelines for Interim Guidance on Ending Isolation and Precautions for Adults with COVID-19: \url{https://www.cdc.gov/coronavirus/2019-ncov/hcp/duration-isolation.html}}. Accordingly, multiple scientific studies worldwide have reported that an exposed subject is no longer \textit{infectious} after three to four weeks. Of course, this is a stochastic range. To clarify, with an exponential model such as the SI model, in absence of new infected cases ($\alpha = 0$), we find the ratio $i(t_0 + T)/i(t_0)=\exp(-\beta T)$, which can be considered as an exponential law for the \textit{probability of infectiousness after $T$ time-units (days)}. Combining the model with the CDC reports, we derive the following rule of thumb for setting $\beta$:
\begin{equation}
%\beta = \frac{-\log(\text{probability of contagion after $T$ time units})}{T}
\beta = -\log(\text{contagion probability after time $T$})/T
\end{equation}
For the later presented results, we have set the probability of contagion to 0.01 at $T$=21\,days, resulting in $\beta$=0.219\,days$^{-1}$.

Following recent studies \cite{Petersen2020}, the reproduction rate of the pandemic during outbreak was taken to be $\mathcal{R}_0$=2.5 with $\Delta$=1 day, which using (\ref{eq:ReproductionRate}) together with $\beta$ were used to initialize $\alpha(t_0)$, i.e. the contact rate during outbreak. Note that one of the advantages of the EKF/EKS framework is that the model parameters can also be considered as state variables and be \textit{state-augmented} with the other equations to be estimated (or updated over time). This approach can be used for both $\gamma$ and $\beta$ to refine the initial educated guesses.%, as detailed in Section \ref{sec:adaptivecontrol}.  

Finally, the regional/national population sizes, as required for normalizing the total and new contaminated cases to the normalized variables of the SI model were obtained from the United Nations' World Population Prospects 2019 dataset \cite{UNGlobalPopulation}, and was assumed to remain fix over the study, i.e. immigration, inter-border travels, natural birth/deaths have been neglected throughout the study.

\section{Performance monitoring}
\label{sec:performance_monitoring}
Kalman filters have intrinsic mechanisms for monitoring their performance and the consistency of their selected parameters. The so-called \textit{innovation process} is at the heart of performance monitoring. It is defined:
\begin{equation}
	\hat{v}(t) \stackrel{\Delta}{=} x(t) - \hat{x}(t)
	\label{eq:innovation}
\end{equation}
where $\hat{x}(t)$ is an estimate of the desired observation $x(t)$, corresponding to the total number of cases or the new cases, as defined in (\ref{eq:observationTotalCases}) or (\ref{eq:observationNewCases}), respectively. 
For a well-functioning Kalman filter with a single observation (the total number of cases or the new cases), the innovation process has the following properties \cite[Ch 5.3]{AndersonMoore1979}, \cite{GrewalAndrews01}:
\begin{enumerate}[label= P{{\arabic*}})]
\item $\mathbb{E}\{\hat{v}(t)\} = 0$,
\item $\mathbb{E}\{\hat{v}(t) \hat{v}(t') ^ T\} = 0$ for $t \neq t'$,
\item $\gamma(t) \stackrel{\Delta}{=} \mathbb{E}\{\hat{v}(t) \hat{v}(t) ^ T\} = \mathbf{c}(t)^T\bar{\mathbf{P}}(t)\mathbf{c}(t) + r(t)$,
\end{enumerate}
where $\bar{\mathbf{P}}(t)$ is the covariance matrix of the state vector estimation error before the $t$\textsuperscript{th} measurement, $\mathbf{c}(t)$ is the state-to-observation map Jacobian, and $r(t)$ is the observation noise variance (defined in Appendix \ref{sec:EKFEKS}). P1 and P2 guarantee that the process noise is zero-mean and spectrally white, and P3 assures that the Kalman filter's estimate of the observation noise is in accordance with the presumed model parameters. The violation of any of these properties is an indication of parameter mis-selection, e.g., the state or observation noise covariance/variance. Although the above properties originally belong to the linear Kalman filter, they can be equally used to monitor the well-functioning of the EKF/EKS. In other contexts, indexes have been proposed based on the above properties for tracking the performance of Kalman filters and the selection of their parameters \cite{GrewalAndrews01}, \cite[Ch. 6]{AndersonMoore1979},  \cite{JamshidianSameniJutten2019}. These monitoring indexes are provided in the open-source implementation of the hereby developed EKF \cite{EpidemicModelingCodesSameni2020}, and are useful for tuning the EKF/EKS model parameters per region/country.

\section{Results}
\label{sec:results}
\subsection{Forecasting}
Fig.~\ref{fig:EKSSampleResult} shows the smoothing result of the number of new cases using the proposed EKS on daily reported cases of the US from March 4\textsuperscript{th} 2020 (the 100\textsuperscript{th} case report date), until November 9\textsuperscript{th} 2020. These 250 days of smoothing is followed by 40 days of forecasting by using an EKF. The $\pm 3 \sigma$ standard deviation envelopes obtained from the error covariance matrix estimates of the EKF are also plotted on the trend estimates. It is seen that as we estimate the number of cases farther in the future, the confidence intervals enlarge, i.e. the forecasts become less reliable.
\begin{figure}[tb]
\includegraphics[trim=0.9in 0in 0.9in 0.0in,clip,width=0.9\columnwidth]{Figures/NewCasesEKSUSA-2}
\caption{New cases trend tracking using the proposed EKS on daily reported cases of the US, since Mar 4\textsuperscript{th} 2020 (the 100\textsuperscript{th} case report). The raw noisy daily reports have been adopted from the OxCGRT dataset \cite{OxCGRT2020}. The smoothing period is up to day 250 and used to forecast the trends thereafter.}
\label{fig:EKSSampleResult}	
\end{figure}

In order to show the forecasting accuracy, another experiment was conducted, in which the EKF/EKS NPI prescription model was trained by the real US new cases and NPI data from March 4\textsuperscript{th} 2020 through December 3\textsuperscript{rd} 2020. The trained model was applied to the ground truth data from December 4\textsuperscript{th} 2020 to March 4\textsuperscript{th} 2021, to forecast the number of new cases from 1 to 60 days ahead, having only the actual NPIs as the input. Fig.~\ref{fig:ForecastingErrors} shows the percentage of forecasting error for different start dates from December 3\textsuperscript{rd} 2020 to March 4\textsuperscript{th} 2021, versus the number of look-ahead forecasting days. As expected, the model is generally more accurate for short-term forecasting as compared to long-term forecasting. Note that although we can see that the look-ahead forecasting errors have slightly decreased beyond 30 days, the observation is not generalizable and may not be associated to the accuracy of the forecasting model, as it highly depends on the dynamics of the pandemic, ground-truth data, NPI policies adopted by a country, and many other socioeconomic factors. We further elaborate on this point in the discussion.
\begin{figure}[tb]
\includegraphics[trim=0.3in 0in 0in 0in,clip,width=\columnwidth]{Figures/ForecastingErrors}
\caption{New cases look-ahead forecasting error percentage for the US, with variable start dates from from Dec 3\textsuperscript{rd} 2020 to Mar 4\textsuperscript{th} 2021. Real data and NPI from Dec 3\textsuperscript{rd} 2020 to Mar 4\textsuperscript{th} 2021 have been used for model training.}
\label{fig:ForecastingErrors}	
\end{figure}

\subsection{NPI prescription}
The OxCGRT dataset has above 300 countries and regions (states). Due to inconsistencies in the reported COVID-19 cases, some of the countries/regions were omitted from the study during the XPRIZE Challenge and the proposed prediction-prescription algorithm was trained and applied to a total number of 235 regions/countries, with arbitrary NPI cost weights. The training period for the model was from January 1\textsuperscript{st} 2020 to Feb 7\textsuperscript{th} 2021, and the test phase was from February 8\textsuperscript{th} 2021 up to May 7\textsuperscript{th} 2021 (the preparation date of the manuscript). As proof of concept, the bi-objective optimization space of the NPI cost $J_1$ vs the human factor cost $J_0$ are shown in Fig.~\ref{fig:paretofronts}, for several countries worldwide. Accordingly, each point in this figure corresponds to a $(J_0, J_1)$ pair for a sequence of NPI scenarios over the test phase. In Fig.~\ref{fig:paretofronts}, the red points are the result of the proposed method for different values of $\epsilon$ (the bi-objective optimization free parameter). The black crosses correspond to the scenario of continuing the latest NPI policy of each government at the end of the training date, up to the end of the testing date. Finally the blue points correspond to a pool of \textit{random constant} stringencies $\mathbf{u}(t) = \bm{\kappa}$, $\bm{\kappa}\sim U[\mathbf{u}^{\min}, \mathbf{u}^{\max}]$, and \textit{random variable} stringencies $\mathbf{u}(t)\sim U[\mathbf{u}^{\min}, \mathbf{u}^{\max}]$, i.e. uniformly distributed between $\mathbf{u}^{\min}$ and $\mathbf{u}^{\max}$. In all cases, the user defined NPI weight vector was chosen to be equal for all NPI ($\mathbf{w}(t) = \mathbf{1}$), i.e., the NPI were considered equally important for the policymaker.

As a bi-objective problem, the Pareto efficient front comprises of the NPI points which either have a smaller value of $J_0$ or $J_1$, while the non-efficient solutions are the ones for which there exists at least a point that gives a smaller cost of both $J_0$ and $J_1$. In other words, a Pareto efficient solution should outperform any other solution either in its cost or efficiency. As trivial cases, the maximum stringency case $\epsilon = 0$ (maximal enforcement of social limitations, to minimize human cost) and the minimum stringency case $\epsilon = 1$ (no social constraints, to minimize costs of intervention) are both Pareto efficient; the former minimizes the human losses and the latter minimizes the socioeconomic cost of intervention. Apparently, policymakers prefer a balance between these two objectives. Therefore, the Pareto efficient NPI policies should be close to the origin or along one of the left or bottom axes. From Fig.~\ref{fig:paretofronts}, it is seen that none of the NPI policies adopted by countries/regions were optimal (assuming equal NPI weights), and despite the significant disparities between the studied countries, the Pareto optimal points all belong to the proposed algorithm. Note that the ``optimal point'' is clearly a function of the bi-objective parameter $\epsilon$, eventually selected by policymakers.

\begin{figure*}[tb]
    \centering
\subfigure[Afghanistan]{\label{fig:Afghanistan}\includegraphics[trim=0.8in 0in 1.1in 0in,clip,width=.23\textwidth]{Figures/Afghanistan.eps}}
\subfigure[Argentina]{\label{fig:Argentina}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Argentina.eps}}
\subfigure[Brazil]{\label{fig:Brazil}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Brazil.eps}}
\subfigure[China]{\label{fig:China}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/China.eps}}
\subfigure[France]{\label{fig:France}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/France.eps}}
\subfigure[Iran]{\label{fig:Iran}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Iran.eps}}
\subfigure[Italy]{\label{fig:Italy}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Italy.eps}}
\subfigure[Germany]{\label{fig:Germany}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Germany.eps}}
\subfigure[South Africa]{\label{fig:SouthAfrica}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/SouthAfrica.eps}}
\subfigure[Spain]{\label{fig:Spain}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/Spain.eps}}
\subfigure[UK]{\label{fig:UK}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/UK.eps}}
\subfigure[US]{\label{fig:US}\includegraphics[trim=0.8in 0in 1.1in 0in,clip, width=.23\textwidth]{Figures/US.eps}\label{fig:USnpiBiObjective}}
\caption{Biobjective optimization space for sample countries. Black cross: fixed NPI (continuing current policies); Blue: random NPI inputs (both constant and variable over time); Red: finite-horizon optimal input for 250 $\epsilon\in[0, 1]$. $h[\mathbf{u}(t)]$ was found by linear regression over historic NPI from Jan 1\textsuperscript{st} 2020 to Feb 7\textsuperscript{th} 2021, using a LASSO with positive coefficients constraint.}
\label{fig:paretofronts}
\end{figure*}

A similar performance was obtained for all the 235 studied countries and regions. As a case study, Fig.~{\ref{fig:US_NPI_Scenarios}} demonstrates the estimates number of new case in the US for different NPI scenarios, by using seven-day averages of official reports from March 4\textsuperscript{th} 2020 (the US 100\textsuperscript{th} case report date) through January 15\textsuperscript{th} 2021 for NPI model training. The trained model was applied to the ground-truth data from January 16\textsuperscript{th} 2021 to March 15\textsuperscript{th} 2021 for test. Apparently, the hypothesized NPI scenarios may only be evaluated by simulation using our trained EKF forecasting model or other models. The compared scenarios are: A) optimal NPIs corresponding to 500 random $\epsilon \in[0, 1]$, B) fixed NPI (no changes in the NPI after January 15\textsuperscript{th} 2021), C) maximum stringency, D) zero stringency, and E) a compromised NPI on the bi-objective space Pareto front corresponding to the NPI scenario with the smallest normalized distance from the US bi-objective plane origin in Fig.~\ref{fig:USnpiBiObjective}. The latter point is a compromise between NPI cost and human factors, and was numerically found to correspond to $\epsilon = 8.235\times10^{-8}$. In Fig.~\ref{fig:US_NPI_Scenarios}, the ground-truth new number of cases (the result of the actual US NPI policy over the test period) is also shown for comparison. Accordingly, the human cost of the last scenario, which is Pareto efficient is very close to the full-stringency case, without imposing the maximum stringency socioeconomic cost.
\begin{figure}[tb]
\includegraphics[trim=0.8in 0.05in 1.1in 0.3in,clip,width=0.93\columnwidth]{Figures/US_NPI_Scenarios2}
\caption{The number of new case estimates in the US for different NPI scenarios: optimal NPIs corresponding to 500 random $\epsilon \in[0, 1]$, fixed NPI (no changes in the last training date NPI), full NPI (maximum stringency), no NPI (no stringency), and optimal NPI (numerically found to be $\epsilon = 8.235\times10^{-8}$ corresponding to the NPI scenario with closest normalized distance from the bi-objective origin in Fig.~\ref{fig:USnpiBiObjective}, which is a compromise between NPI cost and human factors), compared to the ground-truth (official reports). Seven-day averages of official reports from Mar 4\textsuperscript{th} 2020 (the US 100\textsuperscript{th} case report date) through Jan 15\textsuperscript{th} 2021 have been used for NPI model training and applied to ground-truth data until Mar 15\textsuperscript{th} 2021. Notice the scenarios that result in the catastrophic extreme case of total population contamination (\textit{herd immunity} by infection) in a short period after NPI removal.}
\label{fig:US_NPI_Scenarios}	
\end{figure}

\subsection{Processing load}
Since the Pareto front solutions are found by mathematical derivation (rather than trial and error or cumbersome searches), the proposed framework is extremely computationally efficient and the run-time for testing arbitrary scenarios is minimal. The MATLAB version of the codes applied to all regions and countries (235 in total), takes less than 30\,s to train over the historic cases, on a MacBook~Pro laptop with 2.3\,GHz Quad-Core Intel Core\,i7 and 32\,GB of memory, without notable optimizations. The run-time on the test scenarios takes about 15\,s in total for all regions, as it contains only one EKS stage during the test period, per region/country.


\section{Discussion}
\label{sec:discussion}
The proposed algorithm for predicting pandemic trends and prescribing Pareto optimal NPI policies has multiple advantages over mere data-driven machine learning algorithms. The highlights of this algorithm include: 
    \begin{itemize}[leftmargin=*]
    \item The method is based on theoretical derivations and within the scope of the proposed compartmental model accuracy (which is asymptotically accurate for region/country-level population sizes), it gives accurate \textit{Pareto efficient} solutions.
    \item The operation point on the Pareto front can be tuned by a single parameter $\epsilon\in[0, 1]$ selected by the policymaker, where the corner case $\epsilon=0$ neglects the NPI cost (in favor of the human factor) and $\epsilon=1$ neglects the human factor (in favor of intervention cost).
    \item The prediction and prescription problems are integrated in a unified framework. Nevertheless, the method is applicable to both real-world data and any other machine-learning based technique, which accurately predicts pandemic trends from historic data (see for example \cite{miikkulainen2021prediction}).
    \item This framework can be used for \textit{targeted pandemic control}, where strategists can target specific infection bounds that match the medical resources of a country/region, over a fixed or maximally bounded period of time. Therefore, apart from the optimal NPI and fatality rate objectives, such scenarios can also be considered: \textit{``how to bring the pandemic reproduction rate below 0.8 by a specific time?''}, or \textit{``how to bring the new cases below 200 per day in less than two months?''} The training phase of the pandemic over historic data together with the forecasting model can be used to study the feasibility of such scenarios and the prescription of the required NPI policies that would achieve such goals.
    \item Both the model parameters and NPI cost weights can be updated over time. Therefore, unprecedented events such as vaccination or virus mutation effects can be integrated in the model with appropriate training. According to the so-called \textit{principle of optimality}, ``any portion of an optimal control trajectory is optimal \cite[Sec 6.4]{naidu2003optimal},'' which implies that optimality of future actions is independent of the past. Therefore, the prescribed optimal control strategy may be adopted at any point, regardless of the past actions of a region/nation. 
    \item The computational efficiency of this algorithm permits its combination with other machine learning methods to reduce the search space and to improve the accuracy on other datasets and under more complicated models such as the \textit{long short-term memory} (LSTM), as in \cite{miikkulainen2021prediction}. This feature is specifically useful for training the NPI to inter-human contact map $h(\cdot)$, which requires learning.
    \item The predictor part of the model gives confidence intervals during both the prediction and prescription steps of the algorithm. Therefore, the performance and well-function of the algorithm can be continuously monitored and adapted by using the innovation process, as detailed in Section~\ref{sec:performance_monitoring}.
    \item The proposed framework is extendable to pharmaceutical intervention plans and vaccinations, whenever sufficient data is available to design and train alternative compartmental models for these factors.
\end{itemize}

As a point of reservation, we should note that the scope of algorithmic and machine learning-based pandemic trend forecasts and prescriptions should not be overestimated or exaggerated. As an extreme case, consider a forecasting model which predicts that the daily new cases will reach below a certain threshold in several years. We can debate that such long-term speculations are neither scientific nor of any practical use. Because the intrinsic dynamics of pandemics (with or without NPIs, vaccination or herd immunity), guarantee that at some point in the future, there will no longer be any susceptible groups (neglecting the virus mutations). It is therefore essential to demonstrate that any forecasting is fact-based, nontrivial, and predictable from previous observations (in the causal sense).%%Similarly, in global data challenges where hundreds or thousands of groups compete}

\section{Conclusion and future work}
In this research, a model-based approach was used for the prediction and prescription of NPIs that best balance between an arbitrary weighted-cost of interventions and the human factors (number of new cases) during a pandemic. The proposed algorithm and the prescribed NPIs were proved to be Pareto optimal, within the scope of the utilized compartmental model accuracy. Software implementations of the proposed algorithms are online available at \cite{EpidemicModelingCodesSameni2020}. In future studies, different aspects of this framework can be extended and improved. Specifically, advanced ML algorithms can be used for training the NPI to contact rate function $\mathbf{h}(\cdot)$. The LSTM is specifically a promising approach for this purpose.

For regions which have access to additional data (e.g., the number of hospitalized, number of vaccinated, fatality rate of the virus, the population age pyramid, etc.), more accurate models such as the fatal \textit{susceptible-exposed-infected-recovered} (SEIR) can be used \cite{sameni2020mathematical}. Other indexes such as the daily death reports can be augmented as additional observation equations in the dynamic model (\ref{eq:EKF}), and will help to increase the EKF/EKS accuracies. Theoretical aspects of the proposed EKF/EKS frameworks, including stability conditions, parameter identifiability and robustness to parameter and modeling errors also require further studies.

\begin{comment}
\newpage
\subsection{Linear causal input dependency}
As the first model, we assume that the infection rate is the linear mixture of the inputs $\mathbf{u}(t)$, passed through a low-pass filter. In the simplest case, we can take $\alpha(t) = \gamma\exp[-\gamma (t - t_0)] * u_e(t)$ (for $t \geq t_0$), where $u_e(t) = \mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)] + b$ is a linear mixture of the NPI inputs, $\mathbf{a}$ is a vector of \textit{input influence weights} (different from the \textit{input cost weights} $\mathbf{w}(t)$), $b$ is a constant bias, and $\gamma \geq 0$ is the \textit{action to effect rate} (or the inverse of the NPI to contact rate lag). As a corner case, $\gamma \rightarrow \infty$ represents zero latency between action and effect, resulting in $\alpha(t) = \mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)] + b$. In practice $\mathbf{a}$, $b$ and $\gamma$ require learning, e.g., with a LASSO or LSTM model, as detailed in Section \ref{sec:???}.

This model is equivalent to the following state-space form:
\begin{equation}
    \dot{\alpha}(t) = -\gamma \alpha(t) + \gamma(\mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)] + b)
\label{eq:LinearCausalAlphaModel}    
\end{equation}
%%%% They can be found by applying LASSO and cross correlation between empirical values of $\alpha(\cdot)$. In a more advanced scheme, they are found by an LSTM or other advanced learning algorithms.

Now applying Pontryagin's minimum principle necessary conditions (\ref{eq:PontryaginPrinciple}) on (\ref{eq:generalhamiltonian}) and (\ref{eq:LinearCausalAlphaModel}) results in:
\begin{equation}
\begin{array}{l}
\dot{s}(t) = -\alpha(t)s(t)i(t)\\
\dot{i}(t) = \alpha(t)s(t)i(t) - \beta i(t)\\
\dot{\alpha}(t) = -\gamma \alpha(t) + \gamma(\mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)] + b)\\
\dot{\lambda}_1(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]\alpha(t)i(t)\\
\dot{\lambda}_2(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]\alpha(t)s(t) + \beta\lambda_2(t)\\
\dot{\lambda}_3(t) = [\lambda_1(t) -\lambda_2(t)-(1 - \epsilon)]s(t)i(t) + \gamma\lambda_3(t)\\
\bm{\nabla}_{\mathbf{u}}{\mathcal{H}} = \epsilon \mathbf{w}(t) - \gamma\lambda_3(t)\mathbf{a}
\end{array}
\label{eq:LinearCausalAlphaModelDynamics____}
\end{equation}
The last condition in (\ref{eq:LinearCausalAlphaModelDynamics}) can not be identical to zero (except for trivial zero weights). Therefore, the Hamiltonian admits its minima at the boundaries. The following result applies to each entry of the optimal input $\mathbf{u}^*$:
\begin{equation}
u^*_k(t) = 
    \left\{
    \begin{array}{ll}
         u^{\min}_k: & \text{if } \lambda_3(t) \leq \displaystyle\frac{\epsilon w_k(t)}{\gamma a_k}\\%\epsilon w_k(t) \geq \gamma \lambda_3(t) a_k\\
         u^{\max}_k: & \text{if } \lambda_3(t) > \displaystyle\frac{\epsilon w_k(t)}{\gamma a_k}%\epsilon w_k(t) < \gamma \lambda_3(t) a_k
    \end{array}
    \right.
\label{eq:optimalinputlinear000}    
\end{equation}
which means that the optimal inputs at each point are one of the extreme minimum or maximum values, depending on the costate $\lambda_3(t)$. For later use, in order to make the transition between the inputs smooth we can approximate the step transition with a steep sigmoid function, resulting in:
\begin{equation}
u^{\max}_k - u^*_k(t) = (u^{\max}_k - u^{\min}_k)\frac{\exp[-\sigma(\lambda_3(t) - \frac{\epsilon w_k(t)}{\gamma a_k})]}{1 + \exp[-\sigma(\lambda_3(t) - \frac{\epsilon w_k(t)}{\gamma a_k})]}
\end{equation}
which while being differentiable in $\lambda_3(t)$, reduces to (\ref{eq:optimalinputlinear}) at $\sigma\rightarrow\infty$.  

\subsection{Solving only the co-states backward in time}


\subsection{Quadratic causal input dependency}
See: \url{https://en.wikipedia.org/wiki/Levenberg–Marquardt_algorithm}

Use constrained LASSO with monotonic constraint to avoid inaccurate relationship between control input and alpha: \url{https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6320228/} and \url{https://www.tandfonline.com/doi/abs/10.1080/00401706.2015.1079245?journalCode=utch20}.

\subsection{Parameter selection}
According to CDC (\url{https://www.cdc.gov/coronavirus/2019-ncov/hcp/duration-isolation.html}) it is reasonable that an exposed subject is no longer \textit{infectious} (not necessarily \textit{infected}) after 3 to 4 weeks. Assuming an exponential model as we have, in absence of new infected cases, we have: $I(t)=\exp(-\beta t) I(t_0)$. So we have:
\begin{equation}
\beta = \frac{-\log(\text{prob. of contagion after $T$ days})}{T}
\end{equation}

In order to make the model more flexible, we next update the infection rate dynamics with a quadratic term
\begin{equation}
\begin{array}{rl}
    \dot{\alpha}(t) = &  -\gamma \alpha(t) + \gamma b + \gamma\mathbf{a}^T [\mathbf{u}^{\max} - \mathbf{u}(t)]\\
     & + \gamma[\mathbf{u}^{\max} - \mathbf{u}(t)]^T\mathbf{S}[\mathbf{u}^{\max} - \mathbf{u}(t)]
\end{array}
\label{eq:QuadraticCausalAlphaModel}    
\end{equation}
Where $\mathbf{S}$ is generally a positive definite matrix. Applying Pontryagin's minimum principle to the resulting model gives a set of dynamic equations similar to (\ref{eq:LinearCausalAlphaModelDynamics}), except by replacing the infection rate dynamics with (\ref{eq:QuadraticCausalAlphaModel}) and the Hamiltonian gradient as follows:

....
Quadratic


which results in
\begin{equation}
\mathbf{u}^*(t) = \max(\mathbf{u}^{\min}, \min(\mathbf{u}^{\max}, \mathbf{u}^{\max} - \mathbf{S}^{-1}[\frac{\epsilon}{\gamma\lambda_3(t)}\mathbf{w} - \mathbf{a}]))
\end{equation}
where the $\max$ and $\min$ operators are applied element-wise on the vectors.

\section{The finite-interval extended Kalman smoother}
\begin{equation}
\begin{array}{l}
\dot{s}(t) = -\alpha(t)s(t)i(t)  \textcolor{blue}{\,+\,w_s(t)}\\
\dot{i}(t) = \alpha(t)s(t)i(t) - \beta i(t)  \textcolor{blue}{\,+\,w_i(t)}\\
n(t) = \alpha(t)s(t)i(t) \textcolor{blue}{\,+\,v(t)}
\end{array}
\label{eq:dynamicmodel__}
\end{equation}
where $\alpha(t)$ with inverse time unit, is a causal function of the NPI vector $\mathbf{u}(t)\in\mathbb{R}^L$ (considered as the control input). The blue terms in $(\ref{eq:dynamicmodel})$ represent modeling and observation noises, which we neglect in this section and we will restudy in Section \ref{sec:???}, during the algorithm design.

\subsection{The general case}
As demonstrated above, in the proposed scheme $\alpha(t)$ is the only part of the model that requires learning or fact-based presumptions.

\subsection{Other findings}
Another problem that can be addressed in the proposed formulation is to minimize the time of reaching the optimal points. See Chapter 7 of Optimal Control textbook (2003) for details.

\textcolor{blue}{An important feature of our model is that the weights can be changed over time dynamically (based on the theory of optimal input that future optimality is independent of past actions).}



\section{A closed loop controller}

\section{Extensions and future work}
\begin{itemize}
    \item Numerous `gauges' for monitoring the performance and well-function of the predictor and prescriptors
    \item The proposed model can be used for both average and worse-case scenarios, by using the so called H-infinity filtering schemes. 
    \item Gives the reproduction rate of the pandemic
    \item Can be extended to LSTM model using the derivatives of the LSTM gradient
    \item Possibility of improving the performance for regions/countries that have access to further data such as active cases, hospitalizations or more granular intervention plans.
\end{itemize}
\section{Prescription Algorithm}
The proposed prescription algorithm is highlighted in Algorithm \ref{alg:prescription}.

Our prediction consists of two phases: the \textit{endogenous} part in absence of any NPI, and the \textit{exogenous} part due to the NPIs.
\subsection{Endogenous prediction}
In absence of NPIs, we assume $h(\mathbf{p}(t)) = 0$ (or constant) in (\ref{eq:dynamicmodel}). Defining the state vector $\bm{s}(t) = [x(t), \lambda(t)]^T$, the first two equations in (\ref{eq:dynamicmodel}) serve as smooth differentiable nonlinear state equations and the third equation is the linear observation equation. In our online Git repository, we have implemented an extended Kalman filter (EKF) and a fixed-interval extended Kalman smoother (EKS) based on this endogenous model. The algorithm is summarized in the Appendix. During the training phase, the EKS is used for smoothing the noisy daily reports and to estimate the exponential rate $\lambda(t)$. The same model is used in an EKF during the prediction phase of the challenge, but without having any new case reports. The EKF and EKS may even be used for estimating the missing dates (such as weekends and holidays that countries do not report exact cases). The entries of the covariance matrices of the EKF/EKS, which are integral elements of all Bayesian estimators including the EKF/EKS are also used to calculate confidence intervals for the estimated values.

% \section{Innovations}
% \section{Generality}
% \section{Collaborative Contributions}
% \section{Consistency}


% \section{Addressing the Challenge}
% , , , , , and 



%Further details regarding the proposed model and prior contributions of our team in the field of pandemic modeling and estimation are provided online in our detailed technical reports and open-source repositories.

%In summary, the instability of the model is indeed worrying for global healthcare; but it's good to emphasize that the above property
%In this study we considered some of the properties of epidemic diseases from a mathematical and signal processing perspective, by using a compartmental model for the propagation of the epidemic disease. It was shown that the model is not stable around its fixed-point (the no-infection case). %A fundamental question is whether or not we should be worried about the instability of our societies to such epidemic outbreaks?
%We should indeed be proactively worried about the instability of our societies to such epidemic outbreaks; since a fatal virus with an initial seed as small as a single subject worldwide can trigger the avalanche of pandemic waves, killing many people worldwide, as the COVID-19 coronavirus has shown. Note however that from the modeling and dynamics perspective, there is nothing specific to the coronavirus, apart from its specific parameters. In fact, humans have always been living in such a metastable condition and researchers from all domains need to synergize to think a way through this condition.


%It is too early to draw any fact-based conclusion from this study.
The research is currently continued and extended from various aspects including the extension of the EKF/EKS algorithm to the post-vaccination period; the utilization of second-order EKF/EKS for higher accuracy and better convergence; improving the LSTM model for predicting the impact of the NPIs on the exponential rate; extending the model as regions/countries approach herd immunity. 

%%Specifically, by fitting the model over real data, the prediction of infection and mortality rates under quarantine and vaccination, and the study of the recurrent pattern of the epidemic disease over time. Non-exponential law infection distributions have also been considered in the literature \cite{feng2007epidemiological}. This can be an interesting track of research for the study of epidemic diseases, including the family of coronaviruses. %  are of primary interest

\end{comment}

\appendices

\section{The discrete-time model\label{sec:discretized}}
%\appendix[The discrete-time model\label{sec:discretized}]
For a discrete-time implementation of the EKF/EKS, the discrete form of the dynamic system (\ref{eq:EKF}) is required. Accordingly, we define the discrete variables
\begin{equation*}
    \begin{array}{l}
         \!\!\bm{s}_k\!=\![s(k\Delta), i(k\Delta), \alpha(k\Delta)]^T  \\
         \!\!\bm{w}_k\!=\![w_s(k\Delta), w_i(k\Delta), w_\alpha(k\Delta), \eta_1(k\Delta), \eta_2(k\Delta), \eta_3(k\Delta)]^T\\
         \!\!n_k\!=\!n(k\Delta), \quad c_k\!=\!c(k\Delta), \quad v_k\!=\!v(k\Delta)\\
    \end{array}
\end{equation*}
where $\Delta$ is the discretization time unit. Assuming that $\Delta$ is small as compared with the variations of the pandemic trends, a first order discrete approximation of (\ref{eq:EKF}) is found as follows:
\begin{equation}
\begin{array}{l}
\!\!s_{k+1}\!=\!s_k -\Delta\alpha_k s_k i_k + \Delta w_{sk}\\
\!\!i_{k+1}\!=\!i_k + \Delta\alpha_k s_k i_k - \Delta\beta i_k  + \Delta w_{ik}\\
\!\!\alpha_{k+1}\!=\!\alpha_k -\Delta\gamma \alpha_k + \Delta\gamma h[\mathbf{u}^*_k]+ \Delta w_{\alpha k}\\
\!\!\lambda_{1,k+1}\!=\!\lambda_{1k} + \Delta[\lambda_{1k}\!-\!\lambda_{2k}\!-1\!+\!\epsilon]\alpha_k i_k + \Delta\eta_{1k}\\
\!\!\lambda_{2,k+1}\!=\!\lambda_{2k} + \Delta[\lambda_{1k}\! -\!\lambda_{2k}\!-1\!+\!\epsilon]\alpha_k s_k + \Delta\beta\lambda_{2k} + \Delta\eta_{2k}\\
\!\!\lambda_{3,k+1}\!=\!\lambda_{3k} + \Delta[\lambda_{1k}\! -\!\lambda_{2k}\!-1\!+\!\epsilon]s_k i_k + \Delta\gamma\lambda_{3k} + \Delta\eta_{3k}\\
\!\!n_k=\alpha_k s_k i_k + v_k
\end{array}
\label{eq:EKFDiscrete}
\end{equation}
which can be formulated in a compact form:
\begin{equation}
    \begin{array}{l}
    \bm{s}_{k+1} = \mathbf{f}(\bm{s}_{k}, \bm{w}_k ; h(\mathbf{u}_k))\\
    n_k = g(\bm{s}_{k}) + v_k
    \end{array}
    \label{eq:statespacemodel}
\end{equation}
where $\mathbf{f}(\cdot)$ and $g(\cdot)$ represent the nonlinear equations in (\ref{eq:EKFDiscrete}). Following (\ref{eq:observationTotalCases}), if the number of confirmed cases is used as the observation, the second equation in (\ref{eq:statespacemodel}) is replaced by
\begin{equation}
c_k = s_0 - s_k + v_k = g(\bm{s}_{k}) + v_k
\label{eq:TotalCaseObservationsDiscrete}  
\end{equation}
which is a linear function of the state vector.

It is straightforward to linearize the discrete-time dynamic model (\ref{eq:EKFDiscrete}) by calculating its Jacobian matrices, as required for the implementation of the EKF/EKS. An alternative approach is to use a \textit{continuous-dynamics discrete-observations} approach, which is a classical method in optimal state estimation \cite{Gel74,AndersonMoore1979}. Accordingly, to implement the EKF/EKS, the state equations are updated by using the continuous version of the dynamic model (\ref{eq:EKF}), while the observations are only updated on discrete-time intervals (e.g., on a daily basis).

%\appendix[The Extended Kalman Filter Algorithm\label{sec:jacobians}]
%We define the discrete-time version of the dynamic model (\ref{eq:EKF}) variables as: $n_k = n(k\Delta)$, $s_k = s(k\Delta)$, $i_k = i(k\Delta)$ and $\alpha_k = \alpha(k\Delta)$, where $\Delta$ is the discretization time unit. Using a similar notation for the process and observation noises,
%The discretized version of the dynamic equations () can 
\section{The extended Kalman filter}
\label{sec:EKFEKS}
With the state vectors and discretized dynamic models defined in Appendix \ref{sec:discretized}, defining the noisy regular reports $x_k$ (number of new cases $n_k$, or alternatively the total confirmed cases $c_k$) with observation noise variance $r_k$, process noise covariance matrix $\mathbf{Q}_k$, initial state estimate $\hat{\bm{s}}_{0}^+$ with covariance $\mathbf{P}_{0}^+$, the recursive equations for the EKF are listed in Algorithm \ref{alg:EKF}. In this algorithm, $\mathbf{A}_k = \left.\partial \mathbf{f}/\partial \bm{s}_k\right|_{\bm{s} = \hat{\bm{s}}_{k}^+}$ and $\mathbf{c}_k = \left.\partial g/\partial \bm{s}_k\right|_{\bm{s} = \hat{\bm{s}}_{k}^-}$ are the linearized forms of the system's dynamics equations, and $\bar{\bm{w}}_k=\mathbb{E}\{\bm{w}_k\}$. Step\,10 of the algorithm corresponds to enforcing hard constraints on the estimated variables (e.g. positiveness or range) and Step\,11 corresponds to Kalman filter sanity checks (cf. Section~\ref{sec:performance_monitoring}).

\begin{algorithm}[tbh]
\begin{flushleft}
\caption{An extended Kalman filter for simultaneous compartment variable and model parameter tracking
\label{alg:EKF}}
\begin{algorithmic}[1]
\REQUIRE{The noisy regular reports $x_k$ (number of new cases $n_k$, or alternatively the total confirmed cases $c_k$)}
\REQUIRE Initial conditions: $\mathbf{Q}$, $\mathbf{R}$, $\hat{\bm{x}}_{0}^+$, $\mathbf{P}_{0}^+$
\ENSURE{$\hat{\bm{s}}_{k}^+$ (vector of state and model parameter estimates)}
\FOR{$k=0,\cdots, T$}
\STATE \textit{State prediction:}
\STATE $\hat{\bm{s}}_{k+1}^- = \mathbf{f}(\hat{\bm{s}}_{k}^+, \bar{\bm{w}}_k ; h(\mathbf{u}_k))$ 
\STATE $\mathbf{P}_{k+1}^- = \mathbf{A}_{k}\mathbf{P}_{k}^+\mathbf{A}_{k}^{T} + \mathbf{Q}_k$
\STATE \textit{Measurement update:}
\STATE $\mathbf{k}_{k} = \mathbf{P}_{k}^- \mathbf{c}_{k}[\mathbf{c}_{k}^T\mathbf{P}_{k}^-\mathbf{c}_{k} + r_k]^{-1}$
\STATE $\hat{v}_{k} = x_{k} - g(\hat{\bm{s}}_{k}^-)$
\STATE $\hat{\bm{s}}_{k}^+ = \hat{\bm{s}}_{k}^- + \mathbf{k}_{k}\hat{v}_{k}$
\STATE $\mathbf{P}_{k}^+ = [\mathbf{I} - \mathbf{k}_{k}\mathbf{c}_{k}^T]\mathbf{P}_{k}^-$
\STATE \textit{Check and enforce variable and parameter ranges using hard-constraints}
\STATE \textit{Performance monitoring}
\ENDFOR
\end{algorithmic}
\end{flushleft}
\end{algorithm}

\section*{Acknowledgment}
The author sincerely thanks Prof. Christian Jutten, Emeritus Professor of Universit\'e Grenoble Alpes (UGA) for the very insightful and motivating comments on the first versions of this work. The author also acknowledges the SEEPIA COVID-19 working group at UGA, directed by Prof. Didier Georges, for the fruitful (virtual) scientific meetings during the pandemic.  
%///////////////////////////////////////////////////////
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% Encoding: Cp1252


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  Keywords                 = {cardiology, medical signal processing, time-frequency analysis, algorithm, burst-type structures, complex energy structures, continuous activity, fetal heart-rate variability, matching pursuits, power-spectrum analysis, time-frequency analysis approach, wavelet transforms},
  Owner                    = {sameni},
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  Month                    = {August},
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  Abstract                 = {Combined EEG/fMRI recording has been used to localize the generators of EEG events and to identify subject state in cognitive studies and is of increasing interest. However, the large EEG artifacts induced during fMRI have precluded simultaneous EEG and fMRI recording, restricting study design. Removing this artifact is difficult, as it normally exceeds EEG significantly and contains components in the EEG frequency range. We have developed a recording system and an artifact reduction method that reduce this artifact effectively. The recording system has large dynamic range to capture both low-amplitude EEG and large imaging artifact without distortion (resolution 2 microV, range 33.3 mV), 5-kHz sampling, and low-pass filtering prior to the main gain stage. Imaging artifact is reduced by subtracting an averaged artifact waveform, followed by adaptive noise cancellation to reduce any residual artifact. This method was validated in recordings from five subjects using periodic and continuous fMRI sequences. Spectral analysis revealed differences of only 10 to 18\% between EEG recorded in the scanner without fMRI and the corrected EEG. Ninety-nine percent of spike waves (median 74 microV) added to the recordings were identified in the corrected EEG compared to 12\% in the uncorrected EEG. The median noise after artifact reduction was 8 microV. All these measures indicate that most of the artifact was removed, with minimal EEG distortion. Using this recording system and artifact reduction method, we have demonstrated that simultaneous EEG/fMRI studies are for the first time possible, extending the scope of EEG/fMRI studies considerably.}
}

@Article{Allen98,
  Title                    = {{Identification of EEG Events in the MR Scanner: The Problem of Pulse Artifact and a Method for Its Subtraction}},
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  Year                     = {1998},

  Month                    = {October},
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  Pages                    = {229--239},
  Volume                   = {8},

  Abstract                 = {Triggering functional MRI (fMRI) image acquisition immediately after an EEG event can provide information on the location of the event generator. However, EEG artifact associated with pulsatile blood flow in a subject inside the scanner may obscure EEG events. This pulse artifact (PA) has been widely recognized as a significant problem, although its characteristics are unpredictable. We have investigated the amplitude, distribution on the scalp, and frequency of occurrence of this artifact. This showed large interindividual variations in amplitude, although PA is normally largest in the frontal region. In five of six subjects, PA was greater than 50 µV in at least one of the temporal, parasagittal, and central channels analyzed. Therefore, we developed and validated a method for removing PA. This subtracts an averaged PA waveform calculated for each electrode during the previous 10 s. Particular attention has been given to reliable ECG peak detection and ensuring that the average PA waveform is free of other EEG artifacts. Comparison of frequency spectra for EEG recorded outside and inside the scanner, with and without PA subtraction, showed a clear reduction in artifact after PA subtraction for all four frequency ranges analyzed. As further validation, lateralized epileptiform spikes were added to recordings from inside and outside the scanner: PA subtraction significantly increased the proportion of these spikes that were correctly identified and decreased the number of false spike detections. We conclude that in some subjects, EEG/fMRI studies will be feasible only using PA subtraction.}
}

@Book{allen2004signal,
  Title                    = {{Signal analysis: time, frequency, scale, and structure}},
  Author                   = {R. L. Allen and D. W. Mills},
  Publisher                = {IEEE Press},
  Year                     = {2004},

  ISBN                     = {9780471234418},
  Lccn                     = {2004298648}
}

@Article{Almasi2013214,
  Title                    = {Bayesian denoising framework of phonocardiogram based on a new dynamical model},
  Author                   = {A. Almasi and M. Bagher Shamsollahi and L. Senhadji},
  Journal                  = {\{IRBM\} },
  Year                     = {2013},
  Number                   = {3},
  Pages                    = {214 - 225},
  Volume                   = {34},

  Doi                      = {http://dx.doi.org/10.1016/j.irbm.2013.01.017},
  ISSN                     = {1959-0318},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S1959031813000559}
}

@Article{Amer-Wahlin2001,
  Title                    = {Cardiotocography only versus cardiotocography plus ST analysis of fetal electrocardiogram for intrapartum fetal monitoring: a Swedish randomised controlled trial},
  Author                   = {Amer-Wahlin, I and Hellsten, C and Noren, H and Hagberg, H and Herbst, A and Kjellmer, I and Lilja, H and Lindoff, C and Mansson, M and Martensson, L and Olofsson, P and Sundstrom, A and Marsal, K},
  Journal                  = {Lancet},
  Year                     = {2001},
  Pages                    = {534--538},
  Volume                   = {358},

  Doi                      = {10.1016/S0140-6736(01)05703-8},
  Owner                    = {sameni},
  Pubmedid                 = {11520523},
  Timestamp                = {2012.10.22}
}

@Article{Amer-Wahlin2005,
  Title                    = {Implementation of new medical techniques: experience from the Swedish randomized controlled trial on fetal ECG during labor},
  Author                   = {Amer-Wahlin, I and Kallen, K and Herbst, A and Rydhstroem, H and Sundstrom, AK and Marsal, K},
  Journal                  = {J Matern Fetal Neonatal Med},
  Year                     = {2005},
  Pages                    = {93--100},
  Volume                   = {18},

  Doi                      = {10.1080/14767050500233191},
  Owner                    = {sameni},
  Pubmedid                 = {16203593},
  Timestamp                = {2012.10.22}
}

@InProceedings{Amini08,
  Title                    = {{MR Artifact Reduction in the Simultaneous Acquisition of EEG and fMRI of Epileptic Patients}},
  Author                   = {L. Amini and R. Sameni and C. Jutten and G.A. Hossein-Zadeh and H. Soltanian-Zadeh},
  Booktitle                = {{EUSIPCO2008 - 16th European Signal Processing Conf.}},
  Year                     = {2008},

  Address                  = {Lausanne, Switzerland},
  Month                    = {August 25-29},

  Owner                    = {sameni},
  Timestamp                = {2008.04.22}
}

@Article{Anastassiou2001,
  Title                    = {Genomic signal processing},
  Author                   = {Anastassiou, D.},
  Journal                  = {Signal Processing Magazine, IEEE},
  Year                     = {2001},

  Month                    = {jul.},
  Number                   = {4},
  Pages                    = {8 -20},
  Volume                   = {18},

  Doi                      = {10.1109/79.939833},
  ISSN                     = {1053-5888},
  Keywords                 = {DNA;DSP;Fourier transforms;agriculture;alphabet size;biomolecular sequence analysis;biomolecular sequences;character strings;color spectrograms;digital filtering;digital signal processing;genomes sequences;genomic information science;genomic information technology;genomic signal processing;living organisms;local texture;medicine;numerical sequences;phase magnitude;protein coding regions;proteins;simulations;DNA;Fourier transforms;digital filters;digital simulation;medical signal processing;molecular biophysics;proteins;sequences;}
}

@Book{AndersonMoore1979,
  Title                    = {{Optimal Filtering}},
  Author                   = {Brian D. O. Anderson and John B. Moore},
  Publisher                = {{Dover Publications, Inc.}},
  Year                     = {1979},

  Owner                    = {sameni},
  Timestamp                = {2009.02.14}
}

@Article{AndeSS98,
  Title                    = {Multivariate autoregressive models for classification of spontaneous electroencephalographic signals during mental tasks.},
  Author                   = {C. W. Anderson and E. A. Stolz and S. Shamsunder},
  Journal                  = {IEEE Trans. Biomed. Eng.},
  Year                     = {1998},

  Month                    = {Mar},
  Number                   = {3},
  Pages                    = {277--286},
  Volume                   = {45},

  Abstract                 = {This article explores the use of scalar and multivariate autoregressive (AR) models to extract features from the human electroencephalogram ({EEG}) with which mental tasks can be discriminated. This is part of a larger project to investigate the feasibility of using {EEG} to allow paralyzed persons to control a device such as a wheelchair. {EEG} signals from four subjects were recorded while they performed two mental tasks. Quarter-second windows of six-channel {EEG} were transformed into four different representations: scalar AR model coefficients, multivariate AR coefficients, eigenvalues of a correlation matrix, and the Karhunen-LoÃ¨ve transform of the multivariate AR coefficients. Feature vectors defined by these representations were classified with a standard, feedforward neural network trained via the error backpropagation algorithm. The four representations produced similar results, with the multivariate AR coefficients performing slightly better and more consistently with an average classification accuracy of 91.4\% on novel, untrained, {EEG} signals.},
  File                     = {AndeSS98.pdf:AndeSS98.pdf:PDF},
  Institution              = {Department of Computer Science, Colorado State University, Fort Collins 80523, USA. anderson@cs.colostate.edu},
  Keywords                 = {Electroencephalography; Feasibility Studies; Humans; Mental Processes; Models, Statistical; Multivariate Analysis; Neural Networks (Computer); Regression Analysis},
  Owner                    = {Cedric Gouy-Pailler},
  Pmid                     = {9509744},
  Timestamp                = {2008.01.17}
}

@Article{Andreao2006,
  Title                    = {{ECG signal analysis through hidden Markov models}},
  Author                   = {Andreao, R.V. and Dorizzi, B. and Boudy, J.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2006},

  Month                    = {aug. },
  Number                   = {8},
  Pages                    = {1541 -1549},
  Volume                   = {53},

  Abstract                 = {This paper presents an original hidden Markov model (HMM) approach for online beat segmentation and classification of electrocardiograms. The HMM framework has been visited because of its ability of beat detection, segmentation and classification, highly suitable to the electrocardiogram (ECG) problem. Our approach addresses a large panel of topics some of them never studied before in other HMM related works: waveforms modeling, multichannel beat segmentation and classification, and unsupervised adaptation to the patient's ECG. The performance was evaluated on the two-channel QT database in terms of waveform segmentation precision, beat detection and classification. Our waveform segmentation results compare favorably to other systems in the literature. We also obtained high beat detection performance with sensitivity of 99.79% and a positive predictivity of 99.96%, using a test set of 59 recordings. Moreover, premature ventricular contraction beats were detected using an original classification strategy. The results obtained validate our approach for real world application},
  Doi                      = {10.1109/TBME.2006.877103},
  ISSN                     = {0018-9294},
  Keywords                 = {ECG signal analysis;beat detection;electrocardiogram;hidden Markov model;multichannel beat segmentation;online beat segmentation;signal classification;two-channel QT database;waveform modeling;electrocardiography;hidden Markov models;medical signal detection;medical signal processing;signal classification;waveform analysis;}
}

@Book{Arce2004,
  Title                    = {{Nonlinear Signal Processing: A Statistical Approach}},
  Author                   = {Gonzalo R. Arce},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2004},

  Address                  = {New York},

  Owner                    = {sameni},
  Timestamp                = {2008.01.30}
}

@Book{arfken2005mathematical,
  Title                    = {Mathematical Methods For Physicists International Student Edition},
  Author                   = {Arfken, G.B. and Weber, H.J. and Harris, F.E.},
  Publisher                = {Elsevier Science},
  Year                     = {2005},

  ISBN                     = {9780080470696}
}

@Article{ABAC99,
  Title                    = {{Improved Estimation of Pericardial Potentials From Body-Surface Maps Using Individualized Torso Models}},
  Author                   = {R. M. Arthur and D. G. Beetner and H. D. Ambos and M. E. Cain},
  Journal                  = {J. of Electrocardiology},
  Year                     = {1999},
  Pages                    = {106--113},
  Volume                   = {31(supp.)}
}

@Article{Astrom00,
  Title                    = {Vectorcardiographic loop alignment and the measurement of morphologic beat-to-beat variability in noisy signals},
  Author                   = {Astrom, M. and Santos, E.C. and Sornmo, L. and Laguna, P. and Wohlfart, B.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {April },
  Number                   = {4},
  Pages                    = {497-506},
  Volume                   = {47},

  Abstract                 = {The measurement of subtle morphologic beat-to-beat variability in the electrocardiogram (ECG)/vectorcardiogram (VCG) is complicated by the presence of noise which is caused by, e.g., respiration and muscular activity. A method was recently presented which reduces the influence of such noise by performing spatial and temporal alignment of VCG loops. The alignment is performed in terms of scaling, rotation and time synchronization of the loops. Using an ECG simulation model based on propagation of action potentials in cardiac tissue, the ability of the method to separate morphologic variability of physiological origin from respiratory activity was studied. Morphologic variability was created by introducing a random variation in action potential propagation between different compartments. The results indicate that the separation of these two activities can be done accurately at low to moderate noise levels (less than 10 /spl mu/V). At high noise levels, the estimation of the rotation angles was found to break down in an abrupt manner. It was also shown that the breakdown noise level is strongly dependent on loop morphology; a planar loop corresponds to a lower breakdown noise level than does a nonplanar loop.},
  Doi                      = {10.1109/10.828149},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, medical signal processing, noise, physiological models10 muV, ECG signal processing, ECG simulation model, action potential propagation, cardiac tissue, electrodiagnostics, morphologic beat-to-beat variability measurement, noisy signals, random variation, respiratory activity, rotation, scaling, time synchronization, vectorcardiographic loop alignment}
}

@Article{audoly2001global,
  Title                    = {Global identifiability of nonlinear models of biological systems},
  Author                   = {Audoly, Stefania and Bellu, Giuseppina and D'Angio, Leontina and Saccomani, Maria Pia and Cobelli, Claudio},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2001},
  Number                   = {1},
  Pages                    = {55--65},
  Volume                   = {48},

  Publisher                = {IEEE}
}

@Article{Avendano-Valencia2007b,
  Title                    = {Reduction of power line interference on ECG signals using Kalman filtering and Delta operator},
  Author                   = {Avenda{\~{n}}o-Valencia, Luis David and Avenda{\~{n}}o, Luis Enrique and Castellanos-Dom{\'{\i}}nguez, C{\'{e}}sar Germ{\'{a}}n and Villegas-Jaramillo, Eduardo Jos{\'{e}}},
  Year                     = {2007},

  Booktitle                = {23rd ISPE International Conference on CAD/CAM robotics and factories of the future 2007},
  Owner                    = {DavidAVN},
  Timestamp                = {2010.08.23}
}

@InProceedings{Avendano-Valencia-2007,
  Title                    = {Improvement of an extended Kalman filter power line interference suppressor for {ECG} signals},
  Author                   = {Avenda{\~{n}}o-Valencia, Luis David and Avenda{\~{n}}o, Luis Enrique and Ferrero, J.M. and Castellanos-Dom{\'{\i}}nguez, C{\'{e}}sar Germ{\'{a}}n},
  Booktitle                = {Computers in Cardiology, 2007},
  Year                     = {2007},
  Month                    = {30 2007-oct. 3},
  Pages                    = {553 -556},

  Abstract                 = {The powerline interference reduction in ECG records is a challenging problem which is still open for research. The powerline signal, measured directly from the transmission line may have amplitude, phase and frequency variations. These reasons make the classical filtering methods sub-optimal in the powerline interference reduction. We propose a tracking method based on Kalman filtering which uses an state space model for the noisy signal and allows adequate discrimination between the ECG signal and the perturbation, even during non-stationarities. The parameters of this algorithm are optimized via genetic algorithms, obtaining a set of values that give it a mean correlation index on the QT database over 0,99.},
  Doi                      = {10.1109/CIC.2007.4745545},
  ISSN                     = {0276-6547},
  Keywords                 = {ECG signals;QT database;extended Kalman filter;filtering methods;genetic algorithms;power line interference suppressor;transmission line;Kalman filters;electrocardiography;genetic algorithms;medical signal processing;}
}

@InProceedings{Azzerboni2005,
  Title                    = {A new approach based on wavelet-ICA algorithms for fetal electrocardiogram extraction.},
  Author                   = {Bruno Azzerboni and Fabio {La Foresta} and Nadia Mammone and Francesco Carlo Morabito},
  Booktitle                = {Proceedings of the 13th European Symposium on Artificial Neural Networks (ESANN 2005)},
  Year                     = {2005},
  Pages                    = {193--198},

  Bibsource                = {DBLP, http://dblp.uni-trier.de},
  Ee                       = {http://www.dice.ucl.ac.be/Proceedings/esann/esannpdf/es2005-63.pdf},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@article{Hale2021,
  doi = {10.1038/s41562-021-01079-8},
  url = {https://doi.org/10.1038/s41562-021-01079-8},
  year = {2021},
  month = mar,
  publisher = {Springer Science and Business Media {LLC}},
  author = {Thomas Hale and Noam Angrist and Rafael Goldszmidt and Beatriz Kira and Anna Petherick and Toby Phillips and Samuel Webster and Emily Cameron-Blake and Laura Hallas and Saptarshi Majumdar and Helen Tatlow},
  title = {{A global panel database of pandemic policies (Oxford {COVID}-19 Government Response Tracker)}},
  journal = {Nature Human Behaviour}
}

@article{Dong2020,
  doi = {10.1016/s1473-3099(20)30120-1},
  url = {https://doi.org/10.1016/s1473-3099(20)30120-1},
  year = {2020},
  month = may,
  publisher = {Elsevier {BV}},
  volume = {20},
  number = {5},
  pages = {533--534},
  author = {Ensheng Dong and Hongru Du and Lauren Gardner},
  title = {An interactive web-based dashboard to track {COVID}-19 in real time},
  journal = {The Lancet Infectious Diseases}
}

@Manual{B.DeMoor,
  Title                    = {{Database for the Identification of Systems (DaISy)}},
  Author                   = {{B. De Moor}},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://homes.esat.kuleuven.be/~smc/daisy/}
}

@Manual{OxCGRT2020,
  Title                    = {{Oxford COVID-19 Government Response Tracker}},
  Author                   = {{Thomas Hale and Sam Webster and Anna Petherick and Toby Phillips and Beatriz Kira}},
  Year                = {2020},
  Note = {{Blavatnik School of Government}},
  Url                      = {https://github.com/OxCGRT/covid-policy-tracker}
}

@Manual{XPRIZEPandemicResponse2020,
  Title                    = {{The XPRIZE Pandemic Response Challenge}},
  Author                   = {{XPRIZE}},
  Year                = {Oct 2020 -- Feb 2021},
  Url                      = {https://xprize.org/pandemicresponse}
}

@article {Patterson-Lomba2020,
	author = {Patterson-Lomba, Oscar},
	title = {Optimal timing for social distancing during an epidemic},
	elocation-id = {2020.03.30.20048132},
	year = {2020},
	doi = {10.1101/2020.03.30.20048132},
	publisher = {Cold Spring Harbor Laboratory Press},
	abstract = {Social distancing is an effective way to contain the spread of a contagious disease, particularly when facing a novel pathogen and no pharmacological interventions are available. In such cases, conventional wisdom suggests that social distancing measures should be introduced as soon as possible after the beginning of an outbreak to more effectively mitigate the spread of the disease. Using a simple epidemiological model we show that, however, there is in fact an optimal time to initiate a temporal social distancing intervention if the goal is to reduce the final epidemic size or {\textquotedblleft}flatten{\textquotedblright} the epidemic curve. The optimal timing depends strongly on the effective reproduction number (R0) of the disease, such that as the R0 increases, the optimal time decreases non-linearly. Additionally, if pharmacological interventions (e.g., a vaccine) become available at some point during the epidemic, the sooner these interventions become available the sooner social distancing should be initiated to maximize its effectiveness. Although based on a simple model, we hope that these insights inspire further investigations within the context of more complex and data-driven epidemiological models, and can ultimately help decision makers to improve temporal social distancing policies to mitigate the spread of epidemics.Competing Interest StatementThe authors have declared no competing interest.Clinical TrialNAFunding StatementNo external funding was received for the present work.Author DeclarationsAll relevant ethical guidelines have been followed; any necessary IRB and/or ethics committee approvals have been obtained and details of the IRB/oversight body are included in the manuscript.YesAll necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesNo empirical data was used in this manuscript. Results are based on analytical derivations and numerical simulations.},
	URL = {https://www.medrxiv.org/content/early/2020/04/07/2020.03.30.20048132},
	eprint = {https://www.medrxiv.org/content/early/2020/04/07/2020.03.30.20048132.full.pdf},
	journal = {medRxiv}
}

@InProceedings{Lozano2021,
author="Lozano, Miguel Angel
and Orts, {\`O}scar Garibo i.
and Pi{\~{n}}ol, Eloy
and Rebollo, Miguel
and Polotskaya, Kristina
and Garcia-March, Miguel Angel
and Conejero, J. Alberto
and Escolano, Francisco
and Oliver, Nuria",
editor="Dong, Yuxiao
and Kourtellis, Nicolas
and Hammer, Barbara
and Lozano, Jose A.",
title={{Open Data Science to Fight COVID-19: Winning the 500k XPRIZE Pandemic Response Challenge}},
booktitle="Machine Learning and Knowledge Discovery in Databases. Applied Data Science Track",
year="2021",
publisher="Springer International Publishing",
address="Cham",
pages="384--399",
  doi = {10.1007/978-3-030-86514-6_24},
  url = {https://doi.org/10.1007/978-3-030-86514-6_24},
abstract="In this paper, we describe the deep learning-based COVID-19 cases predictor and the Pareto-optimal Non-Pharmaceutical Intervention (NPI) prescriptor developed by the winning team of the 500k XPRIZE Pandemic Response Challenge, a four-month global competition organized by the XPRIZE Foundation. The competition aimed at developing data-driven AI models to predict COVID-19 infection rates and to prescribe NPI Plans that governments, business leaders and organizations could implement to minimize harm when reopening their economies. In addition to the validation performed by XPRIZE with real data, the winning models were validated in a real-world scenario thanks to an ongoing collaboration with the Valencian Government in Spain. We believe that this experience contributes to the necessary transition to more evidence-driven policy-making, particularly during a pandemic.",
isbn="978-3-030-86514-6"
}

@article {Mallela2020,
	author = {Mallela, Abhishek},
	title = {Optimal Control applied to a SEIR model of 2019-nCoV with social distancing},
	elocation-id = {2020.04.10.20061069},
	year = {2020},
	doi = {10.1101/2020.04.10.20061069},
	publisher = {Cold Spring Harbor Laboratory Press},
	abstract = {Does the implementation of social distancing measures have merit in controlling the spread of the novel coronavirus? In this study, we develop a mathematical model to explore the effects of social distancing on new disease infections. Mathematical analyses of our model indicate that successful eradication of the disease is strongly dependent on the chosen preventive measure. Numerical computations of the model solution demonstrate that the ability to flatten the curve becomes easier as social distancing is strictly enforced. Based on our model, we also formulate an optimal control problem and solve it using Pontryagin{\textquoteright}s Maximum Principle and an efficient numerical iterative method. Our numerical results of an optimal 2019-nCoV treatment protocol that yields a minimum disease burden from this disease indicates that social distancing is vitally important.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThe author received no specific funding for this work.Author DeclarationsAll relevant ethical guidelines have been followed; any necessary IRB and/or ethics committee approvals have been obtained and details of the IRB/oversight body are included in the manuscript.YesAll necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesAll relevant data are within the manuscript.},
	URL = {https://www.medrxiv.org/content/early/2020/04/22/2020.04.10.20061069},
	eprint = {https://www.medrxiv.org/content/early/2020/04/22/2020.04.10.20061069.full.pdf},
	journal = {medRxiv}
}


@article {Djidjou-Demasse2020,
	author = {Djidjou-Demasse, R. and Michalakis, Y. and Choisy, M. and Sofonea, M. T. and Alizon, S.},
	title = {Optimal COVID-19 epidemic control until vaccine deployment},
	elocation-id = {2020.04.02.20049189},
	year = {2020},
	doi = {10.1101/2020.04.02.20049189},
	publisher = {Cold Spring Harbor Laboratory Press},
	abstract = {Since Dec 2019, the COVID-19 epidemic has spread over the globe creating one of the greatest pandemics ever witnessed. This epidemic wave will only begin to roll back once a critical proportion of the population is immunised, either by mounting natural immunity following infection, or by vaccination. The latter option can minimise the cost in terms of human lives but it requires to wait until a safe and efficient vaccine is developed, a period estimated to last at least 18 months. In this work, we use optimal control theory to explore the best strategy to implement while waiting for the vaccine. We seek a solution minimizing deaths and costs due to the implementation of the control strategy itself. We find that such a solution leads to an increasing level of control with a maximum reached near the 16th month of the epidemics and a steady decrease until vaccine deployment. The average containment level is approximately 50\% during the 25-months period for vaccine deployment. This strategy strongly out-performs others with constant or cycling allocations of the same amount of resources to control the outbreak. This work opens new perspectives to mitigate the effects of the ongoing COVID-19 pandemics, and be used as a proof-of-concept in using mathematical modelling techniques to enlighten decision making and public health management in the early times of an outbreak.Competing Interest StatementThe authors have declared no competing interest.Funding StatementNo external funding was receivedAuthor DeclarationsAll relevant ethical guidelines have been followed; any necessary IRB and/or ethics committee approvals have been obtained and details of the IRB/oversight body are included in the manuscript.YesAll necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesAll data pertaining to this study are available within the manuscript},
	URL = {https://www.medrxiv.org/content/early/2020/05/15/2020.04.02.20049189},
	eprint = {https://www.medrxiv.org/content/early/2020/05/15/2020.04.02.20049189.full.pdf},
	journal = {medRxiv}
}


@Article{Perkins2020,
  author    = {T. Alex Perkins and Guido Espa{\~{n}}a},
  title     = {Optimal Control of the {COVID}-19 Pandemic with Non-pharmaceutical Interventions},
  year      = {2020},
  journal   = {Bulletin of Mathematical Biology},
  month     = {sep},
  number    = {9},
  volume    = {82},
  doi       = {10.1007/s11538-020-00795-y},
  url       = {https://doi.org/10.1007/s11538-020-00795-y},

  publisher = {Springer Science and Business Media {LLC}},
}

@Manual{EpidemicModelingCodesSameni2020,
  Title                    = {{Open-access codes for the mathematical modeling of epidemic diseases}},
  Author                   = {{Reza Sameni}},
  Year                = {2021},
  Url                      = {https://github.com/alphanumericslab/EpidemicModeling.git}
}

@misc{miikkulainen2020prediction,
      title={{From Prediction to Prescription: Evolutionary Optimization of Non-Pharmaceutical Interventions in the COVID-19 Pandemic}}, 
      author={Risto Miikkulainen and Olivier Francon and Elliot Meyerson and Xin Qiu and Elisa Canzani and Babak Hodjat},
      year={2020},
      eprint={2005.13766},
      archivePrefix={arXiv},
      primaryClass={cs.NE},
      url = {https://arxiv.org/abs/2005.13766}
}

@article{miikkulainen2021prediction,
  title={From Prediction to Prescription: Evolutionary Optimization of Nonpharmaceutical Interventions in the COVID-19 Pandemic},
  author={Miikkulainen, Risto and Francon, Olivier and Meyerson, Elliot and Qiu, Xin and Sargent, Darren and Canzani, Elisa and Hodjat, Babak},
  journal={IEEE Transactions on Evolutionary Computation},
  volume={25},
  number={2},
  pages={386--401},
  year={2021},
  publisher={IEEE}
}

@book{naidu2003optimal,
  title={Optimal control systems},
  author={Naidu, D Subbaram},
  year={2003},
  publisher={CRC press}
}

@Article{bach03beyond,
  Title                    = {Beyond independent components: trees and clusters},
  Author                   = {F. Bach and M. Jordan},
  Journal                  = {Journal of Machine Learning Research},
  Year                     = {2003},
  Pages                    = {1205--1233},
  Volume                   = {4},

  Url                      = {http://cmm.ensmp.fr/~bach/bach03a.pdf}
}

@Article{Bailey1990,
  Title                    = {{Recommendations for standardization and specifications in automated electrocardiography{:} bandwidth and digital signal processing.}},
  Author                   = {J. J. Bailey and A. S. Berson and A. J. Garson},
  Journal                  = {Circulation},
  Year                     = {1990},
  Pages                    = {730--739},
  Volume                   = {81},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Baker1995,
  Title                    = {Measurement of fetal liver, brain and placental volumes with echo-planar magnetic resonance imaging.},
  Author                   = {P. N. Baker and I. R. Johnson and P. A. Gowland and J. Hykin and V. Adams and P. Mansfield and B. S. Worthington},
  Journal                  = {Br J Obstet Gynaecol},
  Year                     = {1995},

  Month                    = {Jan},
  Number                   = {1},
  Pages                    = {35--39},
  Volume                   = {102},

  Abstract                 = {OBJECTIVE: To quantify accurately in utero fetal liver, brain and placental volumes using echo planar imaging, and to assess whether the technique has the potential to enhance intrauterine fetal assessment. DESIGN: Thirty-two singleton, complicated pregnancies were scanned using echo planar imaging, a form of magnetic resonance imaging. Pregnancies were subdivided on the basis of whether the fetus was found subsequently to have an individualised birthweight ratio above (n = 21) or below (n = 11) the 10th centile. Comparisons of the organ volumes of these two groups were made. RESULTS: The first quantitative in utero measurement of fetal liver volume showed a linear relation between liver volume and gestational age in fetuses where the individualised birthweight ratio was above the 10th centile (the normal growth group). Ten of the 11 liver volume measurements of fetuses subsequently found to have an individualised birthweight ratio below the 10th centile fell on or outside the 95\% confidence limits established for the normal growth group. In contrast, no such differences were demonstrated when the brain and placental volumes were considered, with 10 of the 11 brain measurements and all of the 11 placental measurements falling within the 95\% confidence limits of the normal growth group. CONCLUSIONS: A single measurement of fetal liver volume using echo planar imaging enabled accurate identification of fetuses subsequently found to have individualised birthweight ratios below the 10th centile. If these findings are repeated in larger, more representative studies, this suggests that the technique has the potential to contribute to intrauterine fetal assessment.},
  Institution              = {Department of Obstetrics and Gynaecology, University of Nottingham, UK.},
  Keywords                 = {Adult; Brain; Echo-Planar Imaging; Female; Fetus; Gestational Age; Humans; Liver; Placenta; Pregnancy},
  Owner                    = {sameni},
  Pmid                     = {7833308},
  Timestamp                = {2008.05.09}
}

@Article{Barbati2004,
  Title                    = {Optimization of an independent component analysis approach for artifact identification and removal in magnetoencephalographic signals},
  Author                   = {G. Barbati and C. Porcaro and F. Zappasodi and P.M. Rossini and F. Tecchio},
  Journal                  = {Clin Neurophysiol},
  Year                     = {2004},
  Pages                    = {1220-1232},
  Volume                   = {115},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InCollection{Barr89,
  Title                    = {Genesis of the Electrocardiogram},
  Author                   = {R.C. Barr},
  Booktitle                = {Comprehensive Electrocardiology},
  Publisher                = {Pergamon Press},
  Year                     = {1989},

  Address                  = {Oxford},
  Chapter                  = {5},
  Editor                   = {Macfarlane, P. W. and Lawrie, T. T. V.},
  Pages                    = {129--151},

  Vol                      = {{I}}
}

@Article{Barros1998,
  Title                    = {Removing Artifacts From {ECG} Signals Using Independent Components Analysis},
  Author                   = {Barros, AK and Mansour, A. and Ohnishi, N.},
  Journal                  = {Neurocomputing},
  Year                     = {1998},
  Pages                    = {173--186},
  Volume                   = {22},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Vol                      = {22}
}

@Article{Barros2001,
  Title                    = {Extraction of specific signals with temporal structure.},
  Author                   = {A. K. Barros and A. Cichocki},
  Journal                  = {Neural Comput},
  Year                     = {2001},

  Month                    = {Sep},
  Number                   = {9},
  Pages                    = {1995--2003},
  Volume                   = {13},

  Abstract                 = {In this work we develop a very simple batch learning algorithm for semiblind extraction of a desired source signal with temporal structure from linear mixtures. Although we use the concept of sequential blind extraction of sources and independent component analysis, we do not carry out the extraction in a completely blind manner; neither do we assume that sources are statistically independent. In fact, we show that the a priori information about the autocorrelation function of primary sources can be used to extract the desired signals (sources of interest) from their linear mixtures. Extensive computer simulations and real data application experiments confirm the validity and high performance of the proposed algorithm.},
  Doi                      = {10.1162/089976601750399272},
  Institution              = {Bio-mimetic Control Research Center, RIKEN, Moriyama-ku, Shimoshidami, Nagoya 463-0003, Japan.},
  Keywords                 = {Algorithms; Computer Simulation; Electrocardiography; Female; Fetal Heart; Heart; Humans; Models, Biological; Normal Distribution; Pregnancy; Reproducibility of Results},
  Owner                    = {sameni},
  Pmid                     = {11516354},
  Timestamp                = {2008.04.30},
  Url                      = {http://dx.doi.org/10.1162/089976601750399272}
}

@Article{Bartelmaos2008,
  Title                    = {Fast Principal Component Extraction Using Givens Rotations},
  Author                   = {Bartelmaos, S. and Abed-Meraim, K.},
  Journal                  = {Signal Processing Letters, IEEE},
  Year                     = {2008},

  Month                    = { },
  Pages                    = {369 -372},
  Volume                   = {15},

  Doi                      = {10.1109/LSP.2008.920006},
  ISSN                     = {1070-9908},
  Keywords                 = {Givens rotation;PCA;adaptive estimation;eigenvector;iterative method;orthogonal projection approximation;positive Hermitian covariance matrix;principal component extraction;singular value decomposition;subspace tracking;weight matrix;Hermitian matrices;adaptive estimation;adaptive signal processing;approximation theory;covariance matrices;eigenvalues and eigenfunctions;iterative methods;principal component analysis;tracking;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{Batzel2007,
  Title                    = {Cardiovascular and Respiratory Systems Modeling, Analysis, and Control},
  Author                   = {Jerry J. Batzel and Franz Kappel and Daniel Schneditz and Hien T. Iran},
  Publisher                = {SIAM},
  Year                     = {2007},

  ISBN                     = {9780898716177}
}

@Article{Bednar84,
  Title                    = {Alpha-trimmed means and their relationship to median filters},
  Author                   = {Bednar, J. and Watt, T.},
  Journal                  = {Acoustics, Speech, and Signal Processing, IEEE Transactions on},
  Year                     = {1984},

  Month                    = {February},
  Number                   = {1},
  Pages                    = {145--153},
  Volume                   = {32},

  ISSN                     = {0096-3518 }
}

@ARTICLE{JamshidianSameniJutten2019,
  author={Fahimeh {Jamshidian-Tehrani} and Reza {Sameni} and Christian {Jutten}},
  journal={IEEE Transactions on Biomedical Engineering}, 
  title={{Temporally Nonstationary Component Analysis; Application to Noninvasive Fetal Electrocardiogram Extraction}}, 
  year={2020},
  volume={67},
  number={5},
  pages={1377--1386},
  url={http://dx.doi.org/10.1109/TBME.2019.2936943}
  }
  
@Conference{BeharAJOG2013,
  Title                    = {{Evaluation of the fetal QT interval using non-invasive fetal ECG technology}},
  Author                   = {Joachim Behar and Adam Wolfberg and Tingting Zhu and Julian Oster and Alisa Niksch and Douglas Mah and Terrence Chun and James Greenberg and Cassandre Tanner and Jessica Harrop and Alexander Van Esbroeck and Amy Alexander and Michele McCarroll and Timothy Drake and Angela Silber and Reza Sameni and Jay Ward and Gari Clifford},
  Booktitle                = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {2014},

  Address                  = {New Orleans, LA},
  Month                    = {February },
  Number                   = {1},
  Organization             = {{Society for Maternal-Fetal Medicine}},
  Pages                    = {S283--S284},
  Volume                   = {210}
}

@Article{BehrensScharf1994,
  Title                    = {Signal processing applications of oblique projection operators},
  Author                   = {R. T. Behrens and L. L. Scharf},
  Journal                  = IEEE_J_SP,
  Year                     = {1994},
  Pages                    = {1413--1424},
  Volume                   = {42},

  Owner                    = {sameni},
  Timestamp                = {2009.02.14}
}

@Book{Bellman57,
  Title                    = {Dynamic Programming},
  Author                   = {Bellman, R.E.},
  Publisher                = {Princeton University Press, Princeton, NJ.},
  Year                     = {1957},
  Note                     = {Republished 2003: Dover},

  Owner                    = {sameni},
  Timestamp                = {2008.04.11}
}

@Article{Belouchrani1997,
  Title                    = {{A Blind Source Separation Technique Using Second-Order Statistics}},
  Author                   = {A. Belouchrani and K. Abed-Meraim and J-F. Cardoso and Eric Moulines},
  Journal                  = IEEE_J_SP,
  Year                     = {1997},

  Month                    = {Feb.},
  Pages                    = {434--444},
  Volume                   = {45},

  No                       = {2}
}

@Article{bb16291,
  Title                    = {Nonorthogonal Representation of Signals by {G}aussians and {G}abor Functions},
  Author                   = {Ben-Arie, J. and Rao, K.R.},
  Journal                  = IEEE_J_CASII,
  Year                     = {1995},

  Month                    = {June},
  Number                   = {6},
  Pages                    = {402-413},
  Volume                   = {42}
}

@Article{BV03,
  Title                    = {{On the Kernel Widths in Radial-Basis Function Networks}},
  Author                   = {N. Benoudjit and M. Verleysen},
  Journal                  = {Neural Processing Letters},
  Year                     = {2003},

  Month                    = {Oct.},
  Pages                    = {139--154},
  Volume                   = {18},

  No                       = {2}
}

@Article{Bergveld1981,
  Title                    = {{A New Technique for the Suppression of the MECG}},
  Author                   = {Bergveld, Piet and Meijer, Wietze J. H.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1981},

  Month                    = {April},
  Number                   = {4},
  Pages                    = {348--354},
  Volume                   = {BME-28},

  Abstract                 = {After a review of the different techniques in use up to now for the detection of an interference-free abdominal fetal electrocardiogram (FECG), with the limitations of these techniques indicated, a new technique is described which does not suffer from these limitations. This technique is based on an optimization procedure applied to the multiplication coefficients of six independent abdominal signals which are added together. The theoretical background of this method is given, as well as the required operational conditions and electrode positions, leading to an FECG reading guaranteed free of maternal electrocardiogram (MECG).},
  Doi                      = {10.1109/TBME.1981.324803},
  ISSN                     = {0018-9294},
  Keywords                 = {Electrocardiography;Female;Fetal Heart;Heart Rate;Humans;Pregnancy;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{Bienati2001,
  Title                    = {An adaptive blind signal separation based on the joint optimization of Givens rotations},
  Author                   = {Bienati, N. and Spagnolini, U. and Zecca, M.},
  Booktitle                = {Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on},
  Year                     = {2001},
  Pages                    = {2809 -2812 vol.5},
  Volume                   = {5},

  Abstract                 = {Blind signal separation (BSS) is a recurrent problem in many multi-sensors applications where observations can be modelled as mixtures of N statistical independent source signals. We propose the estimation of the orthonormal transformation matrix Q in the case of whitened observations and a cost function based on the fourth-order moments. Q is described as combination of elementary Givens rotations and the optimization is carried out jointly for all the rotations. When sub-sets of angles are optimized separately the method reduces to the deflation approach which has been proved to be globally convergent. The joint estimation of Givens rotation matrices has a computational complexity O(7N2) and, compared to other adaptive BSS, simulations demonstrate that it converges faster and achieves a better crosstalk attenuation},
  Doi                      = {10.1109/ICASSP.2001.940230},
  ISSN                     = {1520-6149},
  Keywords                 = {Givens rotation matrices;adaptive blind signal separation;adaptive estimation;angle quantization;blind signal separation;computational complexity;cost function;crosstalk attenuation;deflation approach;fourth-order moments;globally convergent method;joint optimization of Givens rotations;multisensors applications;orthonormal transformation matrix;statistical independent source signals;whitened observations;adaptive estimation;adaptive signal processing;computational complexity;convergence of numerical methods;crosstalk;matrix algebra;optimisation;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{bishop95,
  Title                    = {Neural Networks for Pattern Recognition},
  Author                   = {Bishop, C.},
  Publisher                = {Oxford University Press},
  Year                     = {1995},

  Address                  = {New York}
}

@Article{Bjorck1973,
  Title                    = {Numerical Methods for Computing Angles between Linear Subspaces},
  Author                   = {{\AA}. Bj{\"o}rck and G. H. Golub},
  Journal                  = {Math. Comp.},
  Year                     = {1973},
  Pages                    = {579--594},
  Volume                   = {27},
  Kwds                     = {csd},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Blankertz2008,
  Title                    = {{Optimizing Spatial filters for Robust EEG Single-Trial Analysis}},
  Author                   = {Blankertz, B. and Tomioka, R. and Lemm, S. and Kawanabe, M. and Muller, K.-R.},
  Journal                  = {Signal Processing Magazine, IEEE},
  Year                     = {2008},

  Month                    = { },
  Number                   = {1},
  Pages                    = {41-56},
  Volume                   = {25},

  Doi                      = {10.1109/MSP.2008.4408441},
  ISSN                     = {1053-5888},
  Keywords                 = {electroencephalography, learning (artificial intelligence), medical signal processing, neurophysiology, spatial filters, user interfacesBerlin BCI project, brain activity, brain-computer interface, common spatial pattern algorithm, electroencephalogram, machine learning, robust EEG analysis, signal processing, signal-to-noise ratio, single-trial analysis, spatial filters, spatiotemporal filters, volume conduction multichannel EEG}
}

@Misc{Blomhoj2014,
  Title                    = {{Compartment models}},

  Author                   = {M. Blomh{\o}j and T.H. Kjeldsen and J. Ottesen},
  Month                    = {January},
  Year                     = {2014},

  Url                      = {http://www4.ncsu.edu/$~$msolufse/Compartmentmodels.pdf}
}

@Article{Bloom06,
  Title                    = {Fetal Pulse Oximetry and Cesarean Delivery},
  Author                   = {Bloom, Steven L. and Spong, Catherine Y. and Thom, Elizabeth and Varner, Michael W. and Rouse, Dwight J. and Weininger, Sandy and Ramin, Susan M. and Caritis, Steve N. and Peaceman, Alan and Sorokin, Yoram and Sciscione, Anthony and Carpenter, Marshall and Mercer, Brian and Thorp, John and Malone, Fergal and Harper, Margaret and Iams, Jay and Anderson, Garland},
  Journal                  = {N Engl J Med},
  Year                     = {2006},
  Note                     = {For the National Institute of Child Health and Human Development Maternal-Fetal Medicine Units Network},
  Number                   = {21},
  Pages                    = {2195-2202},
  Volume                   = {355},

  Abstract                 = {Background Knowledge of fetal oxygen saturation, as an adjunct to electronic fetal monitoring, may be associated with a significant change in the rate of cesarean deliveries or the infant's condition at birth. Methods We randomly assigned 5341 nulliparous women who were at term and in early labor to either "open" or "masked" fetal pulse oximetry. In the open group, fetal oxygen saturation values were displayed to the clinician. In the masked group, the fetal oxygen sensor was inserted and the values were recorded by computer, but the data were hidden. Labor complicated by a nonreassuring fetal heart rate before randomization was documented for subsequent analysis. Results There was no significant difference in the overall rates of cesarean delivery between the open and masked groups (26.3% and 27.5%, respectively; P=0.31). The rates of cesarean delivery associated with the separate indications of a nonreassuring fetal heart rate (7.1% and 7.9%, respectively; P=0.30) and dystocia (18.6% and 19.2%, respectively; P=0.59) were similar between the two groups. Similar findings were observed in the subgroup of 2168 women in whom a nonreassuring fetal heart rate was detected before randomization. The condition of the infants at birth did not differ significantly between the two groups. Conclusions Knowledge of the fetal oxygen saturation is not associated with a reduction in the rate of cesarean delivery or with improvement in the condition of the newborn. (ClinicalTrials.gov number, NCT00098709 .)},
  Doi                      = {10.1056/NEJMoa061170},
  Eprint                   = {http://content.nejm.org/cgi/reprint/355/21/2195.pdf},
  Url                      = {http://content.nejm.org/cgi/content/abstract/355/21/2195}
}

@Article{Blum1985,
  Title                    = {First magnetoencephalographic recordings of the brain activity of a human fetus},
  Author                   = {T. Blum and E. Saling and R. Bauer},
  Journal                  = {Br J Obstet Gynaecol.},
  Year                     = {1985},
  Pages                    = {1224--1229},
  Volume                   = {92},

  No                       = {12},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Bogaerts2009,
  Title                    = {Automated threshold detection for auditory brainstem responses: comparison with visual estimation in a stem cell transplantation study},
  Author                   = {S. Bogaerts and J. D. Clements and J. M. Sullivan and S. Oleskevich},
  Journal                  = {BMC Neuroscience},
  Year                     = {2009},
  Number                   = {104},
  Pages                    = {1--7},
  Volume                   = {10},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Bonmassar02,
  Title                    = {Motion and ballistocardiogram artifact removal for interleaved recording of {EEG} and {EP}s during {MRI}},
  Author                   = {Bonmassar, G. and Purdon, P. L. and Jaaskelainen, I. P. and Chiappa, K. and Solo, V. and Brown, E. N. and Belliveau, J. W.},
  Journal                  = {NeuroImage},
  Year                     = {2002},
  Number                   = {4},
  Pages                    = {1127--1141},
  Volume                   = {16}
}

@Article{PTB1,
  Title                    = {{Nutzung der EKG-Signaldatenbank CARDIODAT der PTB uber das Internet}},
  Author                   = {R. Bousseljot and D. Kreiseler and A. Schnabel},
  Journal                  = {Biomedizinische Technik},
  Year                     = {1995},
  Number                   = {1},
  Pages                    = {S317-S318},
  Volume                   = {40}
}

@Article{Brace1989,
  Title                    = {Normal amniotic fluid volume changes throughout pregnancy.},
  Author                   = {R. A. Brace and E. J. Wolf},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {1989},

  Month                    = {Aug},
  Number                   = {2},
  Pages                    = {382--388},
  Volume                   = {161},

  Abstract                 = {The purpose of this study was to provide a quantitative characterization of the changes in amniotic fluid volume that occur throughout gestation. From 705 published amniotic volumes for normal pregnancies, we found that after log transformation, amniotic fluid volume had a uniform variability over 8 to 43 weeks' gestation. Thus the 95\% confidence interval covered the range of 1/2.57 to 2.57 times the mean volume at any given gestational age. Contrary to expected trends, mean amniotic fluid volume did not change significantly between 22 and 39 weeks and averaged 777 ml, with the 95\% confidence interval ranging from 302 to 1997 ml. The data are summarized in nomograms covering 8 to 43 weeks' gestation.},
  Institution              = {Department of Reproductive Medicine, University of California, San Diego, La Jolla 92093.},
  Keywords                 = {Amniotic Fluid; Female; Gestational Age; Humans; Pregnancy; Reference Values; Regression Analysis},
  Owner                    = {sameni},
  Pii                      = {0002-9378(89)90527-9},
  Pmid                     = {2764058},
  Timestamp                = {2008.05.09}
}

@Article{Broomhead86,
  Title                    = {Extracting qualitative dynamics from experimental data},
  Author                   = {D S Broomhead and G P King},
  Journal                  = {Physica D},
  Year                     = {1986},
  Number                   = {2-3},
  Pages                    = {217--236},
  Volume                   = {20},

  Address                  = {Amsterdam, The Netherlands, The Netherlands},
  Doi                      = {http://dx.doi.org/10.1016/0167-2789(86)90031-X},
  ISSN                     = {0167-2789},
  Publisher                = {Elsevier Science Publishers B. V.}
}

@Misc{BrunLMSP08,
  Title                    = {{BCI} Competion 2008 -- {Graz} Dataset {A}},

  Author                   = {Clemens Brunner and Robert Leeb and Gernot R. M\"uller-Putz and Alois Schl\"ogl and Gert Pfurtscheller},
  Month                    = {Jul},
  Year                     = {2008},

  Owner                    = {Cedric Gouy-Pailler},
  Timestamp                = {2008.11.03},
  Url                      = {http://ida.first.fraunhofer.de/projects/bci/competition\_iv/desc\_2a.pdf}
}

@Article{KHO02,
  Title                    = {{The principles of software QRS detection. Review and comparing algorithms for detecting this important ECG waveform}},
  Author                   = {{B-U K\"{o}hler} and C Hennig and R. Orglmeister},
  Journal                  = IEEE_M_EMB,
  Year                     = {2002},

  Month                    = {Jan/Feb},
  Pages                    = {42-57},
  Volume                   = {21}
}

@Article{Buxton2004S220,
  Title                    = {Modeling the hemodynamic response to brain activation},
  Author                   = {Richard B. Buxton and Kâmil Uludag and David J. Dubowitz and Thomas T. Liu},
  Journal                  = {NeuroImage},
  Year                     = {2004},
  Note                     = {Mathematics in Brain Imaging},
  Number                   = {Supplement 1},
  Pages                    = {S220 - S233},
  Volume                   = {23},

  Abstract                 = {Neural activity in the brain is accompanied by changes in cerebral blood flow (CBF) and blood oxygenation that are detectable with functional magnetic resonance imaging (fMRI) techniques. In this paper, recent mathematical models of this hemodynamic response are reviewed and integrated. Models are described for: (1) the blood oxygenation level dependent (BOLD) signal as a function of changes in cerebral oxygen extraction fraction (E) and cerebral blood volume (CBV); (2) the balloon model, proposed to describe the transient dynamics of CBV and deoxy-hemoglobin (Hb) and how they affect the BOLD signal; (3) neurovascular coupling, relating the responses in CBF and cerebral metabolic rate of oxygen (CMRO2) to the neural activity response; and (4) a simple model for the temporal nonlinearity of the neural response itself. These models are integrated into a mathematical framework describing the steps linking a stimulus to the measured BOLD and CBF responses. Experimental results examining transient features of the BOLD response (post-stimulus undershoot and initial dip), nonlinearities of the hemodynamic response, and the role of the physiologic baseline state in altering the BOLD signal are discussed in the context of the proposed models. Quantitative modeling of the hemodynamic response, when combined with experimental data measuring both the BOLD and CBF responses, makes possible a more specific and quantitative assessment of brain physiology than is possible with standard BOLD imaging alone. This approach has the potential to enhance numerous studies of brain function in development, health, and disease.},
  Doi                      = {DOI: 10.1016/j.neuroimage.2004.07.013},
  ISSN                     = {1053-8119},
  Keywords                 = {Hemodynamic response}
}

@PhdThesis{Callaerts89,
  Title                    = {Signal Separation Methods based on Singular Value Decomposition and their Application to the Real-Time Extraction of the Fetal Electrocardiogram from Cutaneous Recordings},
  Author                   = {Dirk Callaerts},
  School                   = {K.U.Leuven - E.E. Dept.},
  Year                     = {Dec. 1989},

  Owner                    = {sameni},
  Timestamp                = {2010.03.07}
}

@Article{0143-0815-10-4B-001,
  Title                    = {Description of a real-time system to extract the fetal electrocardiogram},
  Author                   = {D Callaerts and W Sansen and J Vandewalle and G Vantrappen and J Janssens},
  Journal                  = {Clinical Physics and Physiological Measurement},
  Year                     = {1989},
  Number                   = {4B},
  Pages                    = {7-10},
  Volume                   = {10},

  Abstract                 = {An overview is given of the FEMME-project (Fetal Electrocardiogram Measuring Method and Equipment). The project started in 1981 and is close to producing a prototype personal computer-based system. This records simultaneously a number of cutaneous potential signals and derives from this set one or more maternal electrocardiogram-free fetal heart signals, by combining linearly the recorded signals. An on-line adaptive algorithm based on the Singular Value Decomposition (SVD) has been designed to compute the coefficients in these linear combinations. This algorithm will be implemented on a DSP board that can be plugged into the real-time recording system. The system will be very useful in studies of the fetal electrocardiogram during pregnancy but also in all other studies such as fetal heart rate variability, fetal movements, etc., where a precise trigger of the electrical signal from the fetal heart is required. },
  Url                      = {http://stacks.iop.org/0143-0815/10/7}
}

@Article{Call86,
  Title                    = {An adaptive on-line method for the extraction of the complete fetal electrocardiogram from cutaneous multilead recordings},
  Author                   = {Callaerts, D. and Vanderschoot, J. and Vandewalle, J. and Sansen, W. and Vantrappen, G. and Janssens, J.},
  Journal                  = {J Perinatal Medicine},
  Year                     = {1986},
  Pages                    = {421--432},
  Volume                   = {14}
}

@Book{Candy2005,
  Title                    = {{Model-Based Signal Processing}},
  Author                   = {James V. Candy},
  Publisher                = {Wiley-IEEE Press},
  Year                     = {2005}
}

@Article{Mees-00,
  Title                    = {Deterministic Structure in Mutli-channel Physiological Data},
  Author                   = {Cao, L. and Mees, A.},
  Journal                  = {Int. J. Bif. Chaos},
  Year                     = {2000},

  Month                    = {December},
  Number                   = {12},
  Pages                    = {2767-2780},
  Volume                   = {10}
}

@InProceedings{Cardoso1994,
  Title                    = {{On the performance of orthogonal source separation algorithms}},
  Author                   = {J.F. Cardoso},
  Booktitle                = {Proc. EUSIPCO},
  Year                     = {1994},
  Pages                    = {776--779},

  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@Article{Cardoso1993b,
  Title                    = {{Blind beamforming for non Gaussian signals}},
  Author                   = {J. F. Cardoso and A. Souloumiac},
  Journal                  = {IEE Proceedings-F},
  Year                     = {1993},
  Number                   = {6},
  Pages                    = {362--370},
  Volume                   = {140},

  Added-at                 = {2008-02-26T11:58:58.000+0100},
  Biburl                   = {http://www.bibsonomy.org/bibtex/219569ee68a675c25590abf6299700683/schaul},
  Citeulike-article-id     = {2381055},
  Description              = {idsia},
  Interhash                = {f814b05a3eeedd3cd182cb7950b47a93},
  Intrahash                = {19569ee68a675c25590abf6299700683},
  Keywords                 = {juergen},
  Owner                    = {sameni},
  Priority                 = {2},
  Timestamp                = {2008-02-26T11:58:58.000+0100}
}

@Manual{Cardoso,
  Title                    = {{Blind Source Separation and Independent Component Analysis}},
  Author                   = {J-F Cardoso},
  Year                     = {2005},

  Url                      = {http://www.tsi.enst.fr/~cardoso/guidesepsou.html}
}

@Article{Cardoso99,
  Title                    = {High-order contrasts for independent component analysis},
  Author                   = {J.-F. Cardoso},
  Journal                  = {Neural Comput.},
  Year                     = {1999},
  Number                   = {1},
  Pages                    = {157--192},
  Volume                   = {11},

  Address                  = {Cambridge, MA, USA},
  Doi                      = {http://dx.doi.org/10.1162/089976699300016863},
  ISSN                     = {0899-7667},
  Publisher                = {MIT Press}
}

@InProceedings{Car98,
  Title                    = {{Multidimensional independent component analysis}},
  Author                   = {J.-F. Cardoso},
  Booktitle                = {Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '98)},
  Year                     = {1998},
  Month                    = {May},
  Pages                    = {1941--1944},
  Volume                   = {4}
}

@Article{Cardoso1998,
  Title                    = {Blind signal separation: statistical principles},
  Author                   = {Cardoso, J.-F.},
  Journal                  = IEEE_J_PROC,
  Year                     = {1998},
  Number                   = {10},
  Pages                    = {2009--2025},
  Volume                   = {86},

  Doi                      = {10.1109/5.720250},
  ISSN                     = {0018-9219},
  Keywords                 = {adaptive signal processing, array signal processing, estimation theory, higher order statistics, BSS, ICA, array processing, blind signal separation, data analysis, independent component analysis, mixtures, mutual independence, statistical principles, unobserved signals, unobserved sources},
  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@InProceedings{Cardoso1990,
  Title                    = {Eigen-structure of the fourth-order cumulant tensor with application to the blind source separation problem},
  Author                   = {Jean-Fran\c{c}ois Cardoso},
  Booktitle                = {{Proc. ICASSP}},
  Year                     = {1990},
  Pages                    = {2655--2658},

  Html                     = {ftp://sig.enst.fr/pub/jfc/Papers/icassp90.ps.gz},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{Cardoso1996a,
  Title                    = {Independent Component Analysis, a survey of some algebraic methods},
  Author                   = {Jean-Fran\c{c}ois Cardoso and Pierre Comon},
  Booktitle                = {Proc. ISCAS'96},
  Year                     = {1996},
  Pages                    = {93--96},
  Volume                   = {2},

  Html                     = {ftp://sig.enst.fr/pub/jfc/Papers/iscas96_algebra.ps.gz},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Cardoso1996,
  Title                    = {Equivariant adaptive source separation},
  Author                   = {Cardoso, J.-F. and Laheld, B.H.},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {1996},

  Month                    = {dec},
  Number                   = {12},
  Pages                    = {3017 -3030},
  Volume                   = {44},

  Abstract                 = {Source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed. This paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence (EASI). The EASI algorithms are based on the idea of serial updating. This specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures. Most importantly, the performance of an EASI algorithm does not depend on the mixing matrix. In particular, convergence rates, stability conditions, and interference rejection levels depend only on the (normalized) distributions of the source signals. Closed-form expressions of these quantities are given via an asymptotic performance analysis. The theme of equivariance is stressed throughout the paper. The source separation problem has an underlying multiplicative structure. The parameter space forms a (matrix) multiplicative group. We explore the (favorable) consequences of this fact on implementation, performance, and optimization of EASI algorithms},
  Doi                      = {10.1109/78.553476},
  ISSN                     = {1053-587X},
  Keywords                 = {EASI algorithms;adaptive algorithms;asymptotic performance analysis;closed-form expressions;complex mixtures;convergence rates;equivariant adaptive separation via independence;equivariant adaptive source separation;equivariant estimation;independent signals;interference rejection levels;matrix group;matrix updates;multiplicative group;multiplicative structure;normalized distributions;optimization;parameter space;real mixtures;serial updating;source signals;stability conditions;adaptive estimation;adaptive signal processing;convergence of numerical methods;matrix algebra;parameter estimation;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Cardoso1996b,
  Title                    = {Jacobi angles for simultaneous diagonalization},
  Author                   = {Jean-Fran\c{c}ois Cardoso and Antoine Souloumiac},
  Journal                  = {{SIAM} J. Mat. Anal. Appl.},
  Year                     = {1996},

  Month                    = jan,
  Number                   = {1},
  Pages                    = {161--164},
  Volume                   = {17},

  Html                     = {ftp://sig.enst.fr/pub/jfc/Papers/siam_note.ps.gz},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Cardoso1993,
  Title                    = {{Blind beamforming for non Gaussian signals}},
  Author                   = {J.-F. Cardoso and A. Souloumiac},
  Journal                  = {{IEE - Proceedings -F}},
  Year                     = {1993},
  Pages                    = {362--370},
  Volume                   = {140},

  No                       = {6}
}

@Book{carson2001,
  Title                    = {Modeling Methodology for Physiology and Medicine},
  Author                   = {Carson, E.R. and Cobelli, C.},
  Publisher                = {Acad. Press},
  Year                     = {2001},
  Series                   = {Academic Press Series in Biomedical Engineering},

  ISBN                     = {9780121602451},
  Lccn                     = {00104369}
}

@Article{Champagne1998,
  Title                    = {{Plane Rotation-Based EVD Updating Schemes for Efficient Subspace Tracking}},
  Author                   = {B. Champagne and Q-G. Liu},
  Journal                  = {IEEE transacation on signal processing},
  Year                     = {1998},

  Month                    = { July},
  Pages                    = {1886-1998},
  Volume                   = {46},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Chen2001,
  Title                    = {Eigenvector based spatial filtering of fetal biomagnetic signals.},
  Author                   = {M. Chen and R. T. Wakai and B. Van Veen},
  Journal                  = {J Perinat Med},
  Year                     = {2001},
  Number                   = {6},
  Pages                    = {486--496},
  Volume                   = {29},

  Abstract                 = {In this paper we demonstrate the usefulness of an eigenvector based spatial filtering method for signal processing of multi-channel fetal magnetocardiogram (fMCG) and fetal magnetoencephalogram (fMEG) recordings. This method of filtering can separate signal and interference by exploiting the considerable spatial information contained in multi-channel recordings. Typically, fMCGs and fMEGs suffer from large cardiac interference and low signal-to-noise ratio. To isolate the signal from the interference, we identify their respective subspaces using one portion of the record dominated by the signal and another dominated by the interference. Each subspace is approximately rank two since the sources of the signal and interference can be modeled as current dipoles. The spatial filter consists of a linear transformation that preserves the signal subspace and annihilates the interference subspace. It is easier to implement than a matched filter, preserves the morphology and topography of the fetal signal, and effectively removes maternal cardiac interference, even when the maternal and fetal complexes overlap strongly in time or when small maternal movements or maternal arrhythmias alter the temporal character of the interference.},
  Institution              = {Department of Medical Physics, University of Wisconsin-Madison, Madison, Wisconsin, USA.},
  Keywords                 = {Evoked Potentials, Auditory; Female; Fetal Monitoring; Filtration; Heart Function Tests; Humans; Magnetics; Magnetoencephalography; Pregnancy},
  Owner                    = {sameni},
  Pmid                     = {11776679},
  Timestamp                = {2008.04.30}
}

@Article{CCA96,
  Title                    = {{Regularized Orthogonal Least Squares Algorithm for Constructing Radial Basis Function Networks}},
  Author                   = {S. Chen and E. S. Chng and K. Alkadhimi},
  Journal                  = {Int J. Control},
  Year                     = {1996},
  Pages                    = {829--837},
  Volume                   = {64},

  No                       = {5}
}

@Unpublished{CH05,
  Title                    = {Bayesian Filtering{:} From Kalman Filters to Particle Filters, and Beyond},
  Author                   = {Zhe Chen},
  Note                     = {Adaptive Syst. Lab., McMaster Univ., Hamilton, ON, Canada},
  Year                     = {2003},

  Citeulike-article-id     = {1412789},
  Institution              = {McMaster University},
  Keywords                 = {bayesian-filters, kalman-filters, particle-filters, probability},
  Posted-at                = {2007-06-26 02:39:20},
  Priority                 = {2},
  Url                      = {http://soma.crl.mcmaster.ca/~zhechen/ieee_bayes.ps}
}

@Book{Cheng1989,
  Title                    = {{Field and Wave Electromagnetics}},
  Author                   = {D. K. Cheng},
  Publisher                = {Addison-Wesley, Reading, Mass.},
  Year                     = {1989},
  Edition                  = {Second}
}

@Misc{Chitnis2011,
  Title                    = {{Introduction to Mathematical Epidemiology: Deterministic Compartmental Models}},

  Author                   = {Nakul Chitnis},
  HowPublished             = {Universit{\"a}t Basel, Mathematisches Institut, Swiss Tropical and Public Health Institute},
  Month                    = {Autumn},
  Year                     = {2011},

  Owner                    = {sameni},
  Url                      = {http://www.luchsinger-mathematics.ch/ME-DeterministicCompartmentalModels.pdf}
}

@Article{Christov1999,
  Title                    = {{Filtering of electromyogram artifacts from the electrocardiogram}},
  Author                   = {I. I. Christov and I. K. Daskalov},
  Journal                  = {Medical Engineering and Physics},
  Year                     = {1999},
  Pages                    = {731--736},
  Volume                   = {21},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{CichockiAmari2002,
  Title                    = {Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications},
  Author                   = {Cichocki, Andrzej and Amari, Shun-ichi},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2002},

  ISBN                     = {0470845899}
}

@Article{GDC06,
  Title                    = {A Novel Framework for Signal Representation and Source Separation},
  Author                   = {Clifford, G.D.},
  Journal                  = {Journal of Biological Systems},
  Year                     = {2006},

  Month                    = {June},
  Number                   = {2},
  Pages                    = {169-183},
  Volume                   = {14}
}

@Book{CliffordBook2006,
  Title                    = {Advanced methods and tools for ECG data analysis},
  Author                   = {Clifford, G.D. and Azuaje, F. and McSharry, P.E.},
  Publisher                = {Artech House},
  Year                     = {2006},
  Series                   = {Artech House engineering in medicine \& biology series},

  ISBN                     = {9781580539661}
}

@Article{CNS2010,
  Title                    = {{An Artificial Vector Model for Generating Abnormal Electrocardiographic Rhythms}},
  Author                   = {G.D. Clifford and S. Nemati and R. Sameni},
  Journal                  = {{Physiological Measurements}},
  Year                     = {2010},

  Month                    = {May},
  Number                   = {5},
  Pages                    = {595--609},
  Volume                   = {31},

  Owner                    = {sameni},
  Timestamp                = {2010.03.17}
}

@InProceedings{CliffordSameni2008,
  Title                    = {{An Artificial Multi-Channel Model for Generating Abnormal Electrocardiographic Rhythms}},
  Author                   = {G.D. Clifford and S. Nemati and R. Sameni},
  Booktitle                = {Computers in Cardiology, 2008},
  Year                     = {2008},

  Address                  = {Bologna, Italy},
  Month                    = {September 14--17},
  Pages                    = {773--776},

  Abstract                 = {We present generalizations of our previously published artificial models for generating multi-channel ECG so that the simulation of abnormal rhythms is possible. Using a three-dimensional vectorcardiogram (VCG) formulation, we generate the normal cardiac dipole for a patient using a sum of Gaussian kernels, fitted to real VCG recordings. Abnormal beats are then specified either as new dipoles, or as perturbations of the existing dipole. Switching between normal and abnormal beat types is achieved using a hidden Markov model (HMM). Probability transitions can be learned from real data or modeled by coupling to heart rate and sympathovagal balance. Natural morphology changes form beat-to-beat are incorporated as before from varying the angular frequency of the dipole as a function of the inter-beat (RR) interval. The RR interval time series is generated using our previously described model whereby time-and frequency-domain heart rate (HR) and heart rate variability (HRV) characteristics can be specified. QT-HR hysteresis is simulated by coupling the Gaussian kernels associated with the T-wave in the model with a nonlinear factor related to the local HR (determined from the last N RR intervals). Morphology changes due to respiration are simulated by coupling the RR interval to the angular frequency of the dipole. We demonstrate an example of the use of this model by simulating T-Wave Alternans (TWA). The magnitude of the TWA effect is modeled as a disturbance on the T-loop of the dipole with a magnitude that differs in each of the three VCG planes. The effect is then turned on or off using a HMM. The values of the transition matrix are determined by the local heart rate, such that when the HR ramps up towards 100 BPM, the probability of a TWA effect rapidly but smoothly increases. In this way, no 'sudden' switching from non-TWA to TWA is observed, and the natural tendency for TWA to be associated with a critical HR-related activation level is simulated. Finally, to generate multi-lead signals, the VCG is mapped to any set of clinical leads using a Dower-like transform derived from a least-squares optimization between known VCGs and known lead morphologies. ECGs with calibrated amounts of TWA were generated by this model and included in the PhysioNet/CinC Challenge 2008 data set.}
}

@Article{AJOG2011,
  Title                    = {{Clinically accurate fetal ECG parameters acquired from maternal abdominal sensors}},
  Author                   = {Gari Clifford and Reza Sameni and Jay Ward and Julian Robinson and Adam John Wolfberg},
  Journal                  = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {2011},

  Month                    = {July},
  Number                   = {1},
  Pages                    = {47.e1--47.e5},
  Volume                   = {205},

  Owner                    = {sameni},
  Timestamp                = {2011.02.23}
}

@Article{cliffordSPIE04,
  Title                    = {A realistic coupled nonlinear artificial {{ECG}}, {BP}, and respiratory signal generator for assessing noise performance of biomedical signal processing algorithms},
  Author                   = {Clifford, G. D. and McSharry, P. E.},
  Journal                  = {Proc of SPIE International Symposium on Fluctuations and Noise},
  Year                     = {2004},
  Number                   = {34},
  Pages                    = {290-301},
  Volume                   = {5467}
}

@Conference{CliffordAJOG2009,
  Title                    = {{Comparing the fetal ST-segment acquired using a FSE and abdominal sensors}},
  Author                   = {Gari D. Clifford and Reza Sameni and Jay Ward and Jim Robertson and Courtenay Pettigrew and Adam J. Wolfberg},
  Booktitle                = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {2009},

  Address                  = {Chicago, IL},
  Month                    = {December},
  Number                   = {6},
  Organization             = {{Society for Maternal-Fetal Medicine}},
  Pages                    = {S242--S242},
  Volume                   = {201},

  Owner                    = {sameni},
  Timestamp                = {2011.02.09}
}

@InProceedings{CSMJ05a,
  Title                    = {{Model-based filtering, compression and classification of the ECG}},
  Author                   = {G. D. Clifford and A. Shoeb and P. E. McSharry and B. A. Janz },
  Booktitle                = {Proceedings of Bioelectromagnetism and 5th International Symposium on Noninvasive Functional Source Imaging within the Human Brain and Heart (BEM \& NFSI)},
  Year                     = {2005},

  Address                  = {Minnesota, USA},
  Month                    = {May}
}

@Article{CSMJ05b,
  Title                    = {{Model-based Filtering, Compression and Classification of the ECG}},
  Author                   = {Clifford, G. D. and Shoeb, A. and McSharry, P. E. and Janz, B. A.},
  Journal                  = {International Journal of Bioelectromagnetism},
  Year                     = {2005},
  Number                   = {1},
  Pages                    = {158-161},
  Volume                   = {7}
}

@Article{clifford01,
  Title                    = {One-pass training of optimal architecture auto-associative neural network for detecting ectopic beats},
  Author                   = {Clifford, G. D. and Tarassenko, L.},
  Journal                  = {IEE Electronic Letters},
  Year                     = {2001},

  Month                    = {Aug},
  Number                   = {18},
  Pages                    = {1126--1127},
  Volume                   = {37}
}

@Conference{Comon95,
  Title                    = {Supervised Classification, a Probabilistic Approach},
  Author                   = {P. Comon},
  Booktitle                = {ESANN-European Symposium on Artificial Neural Networks},
  Year                     = {1995},

  Address                  = {Brussels},
  Editor                   = {Verleysen},
  Month                    = {Apr 19-21},
  Note                     = {[invited paper]},
  Pages                    = {111--128},
  Publisher                = {D~facto Publ.}
}

@InProceedings{Comon1991,
  Title                    = {Independent {C}omponent {A}nalysis},
  Author                   = {P. Comon},
  Booktitle                = {Proc. Int. Sig. Proc. Workshop on Higher-Order Statistics},
  Year                     = {1991},

  Address                  = {Chamrousse, France},
  Month                    = {July 10-12},
  Pages                    = {111--120},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{ComonJutten2010handbook,
  Title                    = {Handbook of Blind Source Separation: Independent Component Analysis and Applications},
  Author                   = {Comon, P. and Jutten, C.},
  Publisher                = {Elsevier Science},
  Year                     = {2010},
  Series                   = {Independent Component Analysis and Applications Series},

  ISBN                     = {9780080884943}
}

@InProceedings{CongJSG08,
  Title                    = {{A new General Weighted Least-Squares Algorithm for Approximate Joint Diagonalization}},
  Author                   = {M. Congedo and C. Jutten and R. Sameni and C. Gouy-Pailler},
  Booktitle                = {Proceedings of the 4th International BCI Workshop},
  Year                     = {2008},

  Address                  = {Graz, Austria},

  Owner                    = {Cedric Gouy-Pailler},
  Timestamp                = {2008.06.25}
}

@Article{Gratta2001,
  Title                    = {Magnetoencephalography - a noninvasive brain imaging method with 1 ms time resolution},
  Author                   = {Cosimo Del Gratta, Vittorio Pizzella, Franca Tecchio and Gian Luca Romani},
  Journal                  = {Reports on Progress in Physics},
  Year                     = {2001},
  Number                   = {12},
  Pages                    = {1759-1814},
  Volume                   = {64},

  Url                      = {http://stacks.iop.org/0034-4885/64/1759}
}

@Article{Cremer1906,
  Title                    = {{\"Uber die Direkte Ableitung der Aktionstrome des Menschlichen Herzens vom Oesophagus und \"Uber das Elektrokardiogramm des Fetus}},
  Author                   = {M. Cremer},
  Journal                  = {{M\"unchener Medizinische Wochenschrift}},
  Year                     = {1906},

  Month                    = {April},
  Pages                    = {811--813},
  Volume                   = {53},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Article{Dos00,
  Title                    = {Inverse problem of electro- and magnetocardiography: Review and recent progress},
  Author                   = {O. D\"{o}ssel},
  Journal                  = {Int. J. Bioelectromagnetism},
  Year                     = {2000},
  Number                   = {2},
  Volume                   = {2},

  Url                      = {http://www.ijbem.org/volume2/number2/doessel/paper.htm}
}

@Article{Damen82,
  Title                    = {{The use of the singular value decomposition in electrocardiography}},
  Author                   = {A. A. Damen and J. {Van Der Kam}},
  Journal                  = {{Med Biol Eng Comput}},
  Year                     = {1982},

  Month                    = {July},
  Number                   = {4},
  Pages                    = {473-82},
  Volume                   = {20},

  Owner                    = {sameni},
  Timestamp                = {2008.07.18}
}

@Article{Dash2000,
  Title                    = {An extended complex Kalman filter for frequency measurement of distorted signals},
  Author                   = {Dash, P.K. and Jena, R.K. and Panda, G. and Routray, A.},
  Journal                  = {Instrumentation and Measurement, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {aug},
  Number                   = {4},
  Pages                    = {746 -753},
  Volume                   = {49},

  Doi                      = {10.1109/19.863918},
  ISSN                     = {0018-9456},
  Keywords                 = {amplitude;complex model;covariance setting;distorted signal;distorted signals;extended complex Kalman filter;floating point processor;frequency measurement;phase;power system frequency;real extended Kalman filter;real-time applications;standard test signals;worst-case measurement;Kalman filters;computerised instrumentation;covariance matrices;frequency estimation;frequency measurement;interference suppression;nonlinear filters;power system measurement;real-time systems;signal processing;}
}

@Article{Davies04,
  Title                    = {{Identifiability Issues in Noisy ICA}},
  Author                   = {M. Davies},
  Journal                  = IEEE_J_SPL,
  Year                     = {2004},
  Number                   = {5},
  Pages                    = {470--473},
  Volume                   = {11}
}

@Article{DeBoer1987,
  Title                    = {Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model},
  Author                   = {De Boer, R. W. and Karemaker, J. M. and Strackee, J.},
  Journal                  = {Am. J. Physiol.},
  Year                     = {1987},
  Pages                    = {680--689},
  Volume                   = {253},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{LMV00,
  Title                    = {{Fetal electrocardiogram extraction by blind source subspace separation}},
  Author                   = {De Lathauwer, L. and De Moor, B. and Vandewalle, J.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {May},
  Pages                    = {567-572},
  Volume                   = {47},

  No                       = {5}
}

@Manual{DeMoor,
  Title                    = {{Database for the Identification of Systems (DaISy)}},
  Author                   = {De Moor, B.},
  Year                     = {1997},

  Url                      = {http://homes.esat.kuleuven.be/~smc/daisy/}
}

@InCollection{DeGroat1998,
  Title                    = {Subspace Tracking},
  Author                   = {R. D. DeGroat and E. M. Dowling and D. A. Linebarger},
  Booktitle                = {The Digital Signal Processing Handbook},
  Publisher                = {CRC and IEEE Press},
  Year                     = {1998},
  Chapter                  = {66},
  Pages                    = {66.1--66.15},

  Date-modified            = {2010-01-06 14:26:06 -0500},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Demartines1997,
  Title                    = {Curvilinear component analysis: a self-organizing neural network for nonlinear mapping of data sets},
  Author                   = {Demartines, P. and Herault, J.},
  Journal                  = {Neural Networks, IEEE Transactions on},
  Year                     = {Jan 1997},
  Number                   = {1},
  Pages                    = {148-154},
  Volume                   = {8},

  Doi                      = {10.1109/72.554199},
  ISSN                     = {1045-9227},
  Keywords                 = {data structures, pattern matching, self-organising feature maps, vector quantisationbackward mapping, curvilinear component analysis, data sets, dimensionality reduction, dimensionality representation, interactive data exploration, learning, nonlinear mapping, nonlinear projection, self-organizing neural network, vector quantization}
}

@Article{Deng2000,
  Title                    = {{New aspects to event-synchronous cancellation of ECG interference: an application of the method in diaphragmatic EMG signals}},
  Author                   = {Yuancheng Deng and Wolf, W. and Schnell, R. and Appel, U.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {Sept. },
  Number                   = {9},
  Pages                    = {1177-1184},
  Volume                   = {47},

  Abstract                 = {An "event-synchronous interference canceller" (ESC) for cancellation of electrocardiographic (ECG) interference in diaphragmatic electromyographic (EMGdi) signals is addressed in this paper, ESC pursues the concept of the "event synchronous adaptive interference canceller" (ESAIC), which was proposed in P. Strobach et al., ibid., vol. 41, p. 343-50 (1994) as a specific application of the well known "adaptive noise canceller" (ANC) paradigm, but ESC uses a simple adaptive gain control (AGC) instead of the complex adaptive filter of the ANC. The proposed ESC method is evaluated using both computer simulations and real EMGdi data, and its efficiency in interference cancellation is compared to that of ESAIC. Of particular interest is the result that the ESC can replace the ESAIC providing better performance as well as a considerable reduction of computational costs.},
  Doi                      = {10.1109/10.867924},
  ISSN                     = {0018-9294},
  Keywords                 = {adaptive filters, adaptive signal processing, electrocardiography, electromyography, interference (signal), medical signal processingECG interference, complex adaptive filter, computational costs reduction, computer simulations, diaphragmatic EMG signals, electrodiagnostics, event-synchronous cancellation, event-synchronous interference canceller, simple adaptive gain control}
}

@Article{dennis1983numerical,
  Title                    = {Numerical Methods for Unconstrained Optimization and Nonlinear Equations},
  Author                   = {Dennis, J.E. and Schnabel, R.B.},
  Year                     = {1983},

  ISBN                     = {9780898713640},
  Lccn                     = {lc95051776},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Series                   = {Classics in Applied Mathematics}
}

@Article{Devedeux1993,
  Title                    = {Uterine electromyography: a critical review.},
  Author                   = {D. Devedeux and C. Marque and S. Mansour and G. Germain and J. Duchêne},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {1993},

  Month                    = {Dec},
  Number                   = {6},
  Pages                    = {1636--1653},
  Volume                   = {169},

  Abstract                 = {On the basis of a literature review, this work summarizes uterine animal and human electromyographic information obtained at cellular, myometrial, and abdominal levels during gestation and parturition. We show that both internal and external electromyograms occur in phase with intrauterine pressure increase and exhibit similar spectra, including a slow wave (0.01 < frequency < 0.03 Hz) probably because of mechanical artifacts and a fast wave whose frequency content can be subdivided into a low-frequency band always present in every contraction and a high-frequency band related to efficient parturition contractions. Application of classic spectral techniques to electromyogram envelopes has identified group propagation but not pacemaker areas. However, no time delay or classic propagation has been demonstrated by applying the same spectral techniques to the electromyogram itself, probably because of the nonlinearity and three-dimensional nature of the propagating process.},
  Institution              = {Unité de Recherche Associée, Centre National de Recherche Scientifique 858, Université de Technologie de Compiègne, France.},
  Keywords                 = {Animals; Electromyography; Electrophysiology; Female; Humans; Labor, Obstetric; Pregnancy; Pregnancy, Animal; Uterine Contraction; Uterus},
  Owner                    = {sameni},
  Pii                      = {0002-9378(93)90456-S},
  Pmid                     = {8267082},
  Timestamp                = {2008.05.12}
}

@Article{do2008expectation,
  Title                    = {What is the expectation maximization algorithm?},
  Author                   = {Do, Chuong B and Batzoglou, Serafim},
  Journal                  = {Nature biotechnology},
  Year                     = {2008},
  Number                   = {8},
  Pages                    = {897--899},
  Volume                   = {26},

  Publisher                = {Nature Publishing Group}
}

@Article{Donoho1995,
  Title                    = {{De-noising by soft-thresholding}},
  Author                   = {D. L. Donoho},
  Journal                  = IEEE_J_IT,
  Year                     = {1995},
  Pages                    = {613--627},
  Volume                   = {41},

  No                       = {3},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Doron2007,
  Title                    = {{Cram\'er-Rao-Induced Bound for Blind Separation of Stationary Parametric Gaussian Sources}},
  Author                   = {Doron, E. and Doron, E. and Yeredor, A. and Tichavsky, P.},
  Journal                  = IEEE_J_SPL,
  Year                     = {2007},
  Number                   = {6},
  Pages                    = {417--420},
  Volume                   = {14},

  Doi                      = {10.1109/LSP.2006.888425},
  Editor                   = {Yeredor, A.},
  ISSN                     = {1558-2361},
  Keywords                 = {Gaussian processes, autoregressive moving average processes, blind source separation, matrix algebra, ARMA, Cramer-Rao-induced bound, autoregressive moving-average process, blind source separation algorithm, mixing matrix estimation, stationary parametric Gaussian sources, Auto-regressive (AR), Cramer&ndash, Rao bound, auto-regressive moving average (ARMA), blind source separation (BSS), independent component analysis (ICA), interference-to-signal ratio (ISR), moving average (MA)},
  Owner                    = {sameni},
  Timestamp                = {2008.05.15}
}

@Article{Dougherty2005,
  Title                    = {Research issues in genomic signal processing},
  Author                   = {Dougherty, E.R. and Datta, A. and Sima, C.},
  Journal                  = {Signal Processing Magazine, IEEE},
  Year                     = {2005},

  Month                    = {nov.},
  Number                   = {6},
  Pages                    = { 46 - 68},
  Volume                   = {22},

  Abstract                 = { Genomic signal processing (GSP) concerns the processing of genomic signals. It may be defined as the analysis, processing, and use of genomic signals to gain biological knowledge and the translation of that knowledge into systems-based applications. In this article, the authors discuss the key research issues for GSP. It is important to recognize that "genomic signal processing" is not a name for genomic bioinformatics nor for the application of signal processing methods in genomics. We note that the research issues pertaining to GSP fit within the overall challenges confronting research in the area of multimodal biomedical systems.},
  Doi                      = {10.1109/MSP.2005.1550189},
  ISSN                     = {1053-5888},
  Keywords                 = { biological knowledge; genetic regulatory network; genomic signal processing; network inference; signal classification; genetics; medical signal processing; signal classification;}
}

@Article{Dougherty2007,
  Title                    = {Signal Processing in Genomics [From The Guest Editors]},
  Author                   = {Dougherty, E.R. and Stolovitzky, G.A. and Tabus, L. and Wang, X.},
  Journal                  = {Signal Processing Magazine, IEEE},
  Year                     = {2007},

  Month                    = {jan.},
  Number                   = {1},
  Pages                    = {16 -16},
  Volume                   = {24},

  Abstract                 = {Genomic signal processing has been defined as the analysis, processing, and use of genomic signals for gaining biological knowledge and the translation of that knowledge into systems-based applications.},
  Doi                      = {10.1109/MSP.2007.273047},
  ISSN                     = {1053-5888}
}

@InProceedings{Douglas2000,
  Title                    = {{Combined Subspace Tracking, Prewhitening, and Contrast Optimization for Noisy Blind Signal Separation }},
  Author                   = {S.C. Douglas},
  Booktitle                = {Proc. 2nd IEEE Int. Workshop on Independent Component Analysis and Source Separation, Helsinki, Finland},
  Year                     = {2000},
  Month                    = {June },
  Pages                    = {579-584},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Douglas2000a,
  Title                    = {{Combined Subspace Tracking, Prewhitening, and Contrast Optimization for Noisy Blind Signal Separation }},
  Author                   = {S.C. Douglas},
  Journal                  = { Proc. 2nd IEEE Int. Workshop on Independent Component Analysis and Source Separation, Helsinki, Finlan},
  Year                     = {2000},

  Month                    = {June },
  Pages                    = {579-584},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{DMO80,
  Title                    = {{On deriving the electrocardiogram from vectorcardiographic leads}},
  Author                   = {G. E. Dower and H. B. Machado and J. A. Osborne},
  Journal                  = {Clin. Cardiol.},
  Year                     = {1980},
  Pages                    = {87},
  Volume                   = {3},

  Abstract                 = {The issue of whether a traditional or scientifically based system for applying electrodes to the body for routine electrocardiography may be resolved by deriving the 12-lead ECG from the Frank XYZ signals. The result, the ECGD, is sufficiently close to the ECG for serial comparisons to be valid. Reducing data acquisition to the XYZ signals alone has several technical advantages. These have been realized with the introduction of a computer system employing the ECGD at a large general hospital. Plotting the lead vectors of the ECGD on Aitoff's projection of the sphere brings out important relationships between the leads, one to another, and to the spatial directions of the QRS and T vectors. Reversing the polarity of a VR enhances the sequential relationship between the limb leads; this is taken advantage of in an educational display generated by the computer.}
}

@Article{Dower1980,
  Title                    = {On deriving the electrocardiogram from vectorcardiographic leads},
  Author                   = {G. E. Dower and H. B. Machado and J. A. Osborne},
  Journal                  = {Clin. Cardiol.},
  Year                     = {1980},
  Pages                    = {87},
  Volume                   = {3},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Dragosevic1995,
  Title                    = {An adaptive notch filter with improved tracking properties},
  Author                   = {Dragosevic, M.V. and Stankovic, S.S.},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {1995},

  Month                    = {sep},
  Number                   = {9},
  Pages                    = {2068 -2078},
  Volume                   = {43},

  Abstract                 = {An analysis of the properties of an adaptive notch filter (ANF) applied to time-varying frequency tracking is presented. Starting from the derivation of an expression for ANF output power, asymptotically optimal values for the pole contraction and forgetting factors are derived for recursive prediction error (RPE) type ANF algorithms. Based on the obtained results, a new ANF algorithm that includes adaptation of both pole contraction and forgetting factors is proposed. The given experimental results confirm the theoretical conclusions and show that the proposed algorithm is highly efficient in practice},
  Doi                      = {10.1109/78.414768},
  ISSN                     = {1053-587X},
  Keywords                 = { adaptive notch filter; asymptotically optimal values; forgetting factors; output power; pole contraction; recursive prediction error; time-varying frequency tracking; tracking properties; adaptive filters; error analysis; notch filters; optimisation; poles and zeros; prediction theory; recursive filters; tracking filters;}
}

@Book{Drose98,
  Title                    = {Fetal Echocardiography},
  Author                   = {Julia A. Drose},
  Publisher                = {Saunders W B Co},
  Year                     = {1998},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@InProceedings{Dubois2009,
  Title                    = {Efficient modeling of ECG waves for morphology tracking},
  Author                   = {Dubois, R. and Roussel, P. and Vaglio, M. and Extramiana, F. and Badilini, F. and Maison-Blanche, P. and Dreyfus, G.},
  Booktitle                = {Computers in Cardiology, 2009},
  Year                     = {2009},
  Pages                    = {313-316},

  Abstract                 = {We propose a new approach to fully automatic ECG wave extraction and morphology tracking. It is based on Generalized Orthogonal Forward Regression (GOFR), which allows decomposing a one-dimensional signal into a set of appropriate parameterized functions. Two applications of GOFR to ECG modeling are presented. First, in order to delineate ECG characteristic waves, we make use of a specific function, called the Gaussian Mesa function (GMF). Secondly, we track the evolution of the T-wave morphology by introducing a Bi-Gaussian function (BGF). The approach was validated on three experimental settings; the results confirm that the combination of GOFR and of an appropriate parametric function is remarkably efficient for ECG wave modeling.},
  ISSN                     = {0276-6547},
  Keywords                 = {electrocardiography;medical signal processing;physiological models;regression analysis;ECG modeling;ECG morphology tracking;ECG wave modeling;Gaussian Mesa function;T-wave morphology;bi-Gaussian function;generalized orthogonal forward regression;morphology tracking;one-dimensional signal decomposion;wave extraction;Algorithm design and analysis;Biomedical signal processing;Databases;Electrocardiography;Iterative algorithms;Libraries;Morphology;Signal analysis;Signal processing algorithms;Vectors}
}

@Book{dym2004,
  Title                    = {Principles of Mathematical Modeling, 2e},
  Author                   = {Dym, C.L.},
  Publisher                = {Academic Press},
  Year                     = {2004},
  Series                   = {Principles of Mathematical Modeling},

  ISBN                     = {9780122265518},
  Lccn                     = {2004046996}
}

@Article{EP88,
  Title                    = {Vectorcardiogram synthesized from a 12-lead {ECG}: Superiority of the inverse {D}ower matrix},
  Author                   = {L. Edenbrandt and O Pahlm},
  Journal                  = {J. Electrocardiol.},
  Year                     = {1988},
  Pages                    = {361},
  Volume                   = {21}
}

@Article{Einthoven1895,
  Title                    = {{\"Uber die Form des menschlichen electrocardiogramms}},
  Author                   = {W Einthoven},
  Journal                  = {Arch Gesamte Physiol.},
  Year                     = {1895},
  Pages                    = {101--123},
  Volume                   = {60},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.11}
}

@Article{Espy03,
  Title                    = {{SQUID noise as a function of temperature: a survey of three SQUID's}},
  Author                   = {Espy, M.A. and Matlachov, A.N. and Kraus, R.H. and Betts, J.B.},
  Journal                  = {Applied Superconductivity, IEEE Transactions on},
  Year                     = {2003},

  Month                    = {june},
  Number                   = {2},
  Pages                    = {731 - 734},
  Volume                   = {13},

  Abstract                 = {The temperature dependence of SQUID noise was tested over a temperature range from 0.3-4 K for SQUID's of three different manufactures, two designed for user supplied pick-up coils and one a magnetometer. A SQUID-based picovoltmeter, designed to reduce noise contributions for cables and electronics was used to read out the signal from the SQUID being investigated. The data were taken in support of a physics experiment which will use SQUID's to measure the precession frequency of spin polarized 3He, acting as a comagnetometer with spin polarized ultra cold neutrons (UCN). The final aim of the experiment is to measure the neutron electric dipole moment to 4 times;10-28 ecm. The 3He and UCN will be in a bath at temperatures <0.5 K. The noise performance of the SQUID's at these temperatures must be well understood before the experiment. The results of the noise studies as a function of temperature are presented for the three SQUID's and their behavior is compared to theoretical predictions based on SQUID parameters.},
  Doi                      = {10.1109/TASC.2003.814019},
  ISSN                     = {1051-8223},
  Keywords                 = { 0.3 to 4 K; He; SQUID noise; comagnetometer; magnetometer; neutron electric dipole moment; pick-up coil; picovoltmeter; precession frequency; spin polarized ultra cold neutrons; temperature dependence;spin polarized 3He; SQUID magnetometers; superconducting device noise;}
}

@Article{Eswaran2005,
  Title                    = {Fetal magnetoencephalographyâ€”a multimodal approach},
  Author                   = {Hari Eswaran and Curtis L. Lowery and James D. Wilson and Pam Murphy and Hubert Preissl},
  Journal                  = {Developmental Brain Research},
  Year                     = {2005},
  Number                   = {1},
  Pages                    = {57 - 62},
  Volume                   = {154},

  Doi                      = {10.1016/j.devbrainres.2004.10.003},
  ISSN                     = {0165-3806},
  Keywords                 = {Magnetoencephalography},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0165380604003062}
}

@Article{Eswaran2002,
  Title                    = {Short-term serial magnetoencephalography recordings of fetal auditory evoked responses},
  Author                   = {H. Eswaran and H. Preissl and J. D. Wilson and P. Murphy and S. E. Robinson and D. Rose and J. Vrba and C. Lowery},
  Year                     = {2002},
  Pages                    = {128--132},
  Volume                   = {331},

  Booktitle                = {{Neurosci. Lett.}},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Misc{Evans,
  Title                    = {{An Introduction to Stochastic Differential Equations}},

  Author                   = {Lawrence C. Evans},
  Note                     = {{Lecture notes, v 1.2}},

  Publisher                = {{Department of Mathematics, UC Berkeley}},
  Url                      = {http://math.berkeley.edu/~evans/}
}

@Article{Farvet1968,
  Title                    = {{Computer Matched Filter Location of Fetal R-Waves}},
  Author                   = {A. G. Farvet},
  Journal                  = {Medical \& Biological Engineering},
  Year                     = {1968},

  Month                    = {September},
  Number                   = {5},
  Pages                    = {467--475},
  Volume                   = {6},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@InProceedings{FatemiCINC2013,
  Title                    = {{A Robust Framework for Noninvasive Extraction of Fetal Electrocardiogram Signals}},
  Author                   = {Marzieh Fatemi and Mohammad Niknazar and Reza Sameni},
  Booktitle                = {Proceedings of the 40th Annual International Conference on Computersin Cardiology},
  Year                     = {2013},

  Address                  = {Zaragoza, Spain},
  Month                    = {September 22-25},
  Pages                    = {201--204},

  Vol                      = {40}
}

@Article{Fatemi2012,
  Title                    = {{An Online Subspace Denoising Algorithm for Maternal ECG Removal from Fetal ECG Signals}},
  Author                   = {Marzieh Fatemi and Reza Sameni},
  Journal                  = {{Submitted to IEEE Trans Biomed Eng.}},
  Year                     = {September 2012},

  Owner                    = {sameni},
  Timestamp                = {2012.10.21}
}

@Article{Ferdjallah94,
  Title                    = {{Adaptive digital notch filter design on the unit circle for the removal of powerline noise from biomedical signals}},
  Author                   = {Ferdjallah, M. and Barr, R.E.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1994},

  Month                    = {June},
  Number                   = {6},
  Pages                    = {529-536},
  Volume                   = {41},

  Doi                      = {10.1109/10.293240},
  ISSN                     = {0018-9294},
  Keywords                 = {adaptive filters, biomedical electronics, interference (signal), medical signal processing, notch filters60 Hz, adaptive digital notch filter design, biomedical signals, center frequency variation, constrained least mean-squared algorithm, frequency variation distribution, noisy EEG, pole-zero placement, powerline noise removal, powerline noise sample, predefined attenuation level, unit circle}
}

@Article{Ferreol2000,
  Title                    = {{On the Behavior of Current Second and Higher Order Blind Source Separation Methods for Cyclostationary Sources}},
  Author                   = {A. Ferreol and P. Chevalier},
  Journal                  = IEEE_J_SP,
  Year                     = {2000},

  Month                    = {June},
  Pages                    = {1712--1725},
  Volume                   = {48},

  No                       = {6}
}

@Book{FinkBeaty06,
  Title                    = {{Standard Handbook for Electrical Engineers},, 1978, ISBN 0-07-020974-X, page 16-15, 16-16},
  Author                   = {Donald G. Fink and H. Wayne Beaty},
  Publisher                = {McGraw-Hill},
  Year                     = {2006},
  Edition                  = {15th},

  Owner                    = {sameni},
  Timestamp                = {2010.07.07}
}

@Book{fishwick2007,
  Title                    = {Handbook of Dynamic System Modeling},
  Author                   = {Fishwick, P.A.},
  Publisher                = {Taylor \& Francis},
  Year                     = {2007},
  Series                   = {Chapman \& Hall/CRC Computer and Information Science Series},

  ISBN                     = {9781420010855}
}

@Book{Flandrin1999,
  Title                    = {{Time-Frequency/Time-Scale Analysis, Volume 10 (Wavelet Analysis and Its Applications)}},
  Author                   = {Patrick Flandrin},
  Publisher                = {Academic Press},
  Year                     = {1999},

  Owner                    = {sameni},
  Timestamp                = {2012.12.01}
}

@Book{flandrin1999time,
  Title                    = {Time-frequency/time-scale analysis},
  Author                   = {Flandrin, P.},
  Publisher                = {Academic Press},
  Year                     = {1999},
  Series                   = {Wavelet analysis and its applications},

  ISBN                     = {9780122598708},
  Lccn                     = {98038814}
}

@Article{GeraldFFletcher07042001,
  Title                    = {{Exercise Standards : A Statement for Healthcare Professionals From the American Heart Association}},
  Author                   = {Fletcher, Gerald F. and Balady, Gary and Froelicher, Victor F. and Hartley, L. Howard and Haskell, William L. and Pollock, Michael L.},
  Journal                  = {Circulation},
  Year                     = {2001},
  Number                   = {2},
  Pages                    = {580-615},
  Volume                   = {91},

  Url                      = {http://circ.ahajournals.org}
}

@TechReport{Fodor2002,
  Title                    = {A survey of dimension reduction techniques},
  Author                   = {I. K. Fodor},
  Institution              = {U.S. Department of Energy},
  Year                     = {2002},
  Month                    = {June},

  Owner                    = {sameni},
  Timestamp                = {2008.04.30},
  Url                      = {https://e-reports-ext.llnl.gov/pdf/240921.pdf}
}

@Article{ERNESTFRANK05011956,
  Title                    = {{An Accurate, Clinically Practical System For Spatial Vectorcardiography}},
  Author                   = {Frank, Ernest},
  Journal                  = {Circulation},
  Year                     = {1956},
  Number                   = {5},
  Pages                    = {737-749},
  Volume                   = {13},

  Abstract                 = {This paper describes a news improved system of spatial vectorcardiography that is practical for clinical use. It represents an optimum compromise among such factors as soundness of theoretic basis, accuracy, reproducibility, signal-to-noise ratio, and speed of application. Some of its advantages over currently employed systems include a rational physical basis, corrections for torso shape, avoidance of left arm, insensitivity to individual variability of ventricle location, and accuracy comparable to applicability of 3-dimensional torso-model data to the human subject. Detailed description of electrode placement, practical procedures, and useful technics is included.},
  Eprint                   = {http://circ.ahajournals.org/cgi/reprint/13/5/737.pdf},
  Url                      = {http://circ.ahajournals.org/cgi/content/abstract/13/5/737}
}

@Book{franklin1998digital,
  Title                    = {{Digital control of dynamic systems}},
  Author                   = {Franklin, G. F. and Powell, J. D. and Workman, M. L.},
  Publisher                = {Addison-Wesley},
  Year                     = {1998},

  ISBN                     = {9780201820546},
  Lccn                     = {97035994}
}

@Book{Freeman91,
  Title                    = {Fetal heart rate monitoring},
  Author                   = {Roger K. Freeman and Thomas J. Garite and Michael P. Nageotte},
  Editor                   = {2nd},
  Publisher                = {Williams \& Wilkins},
  Year                     = {1991},

  Owner                    = {sameni},
  Timestamp                = {2009.06.01}
}

@Article{Frenkel99,
  Title                    = {{Recursive Expectation-Maximization (EM) Algorithms for Time-varying Parameters with Applications to Multiple Target Tracking}},
  Author                   = {Frenkel, L. and Feder, M. },
  Journal                  = {IEEE Transactions on Signal Processing},
  Year                     = {1999},

  Month                    = Feb,
  Pages                    = {306-320},
  Volume                   = {47},

  No                       = {2}
}

@Article{friesen90,
  Title                    = {{A comparison of the noise sensitivity of nine QRS detection algorithms}},
  Author                   = {Friesen, G. M. and Jannett, T. C. and Jadallah, M. A. and Yates, S. L. and Quint, S. R. and Nagle, H. T.},
  Journal                  = {{IEEE} Trans. Biomed. Eng.},
  Year                     = {1990},
  Number                   = {1},
  Pages                    = {85-98},
  Volume                   = {37}
}

@Book{Fukunaga1990,
  Title                    = {Introduction to Statistical Pattern Recognition},
  Author                   = {K. Fukunaga},
  Publisher                = {Academic Press, New York},
  Year                     = {1990},
  Edition                  = {Second},

  Owner                    = {sameni},
  Timestamp                = {2008.05.23}
}

@Manual{FastICA,
  Title                    = {{The FastICA package for MATLAB - Version 2.1}},
  Author                   = {Hugo G\"avert and Jarmo Hurri and Jaakko S\"arel\"a and Aapo Hyv\"arinen},
  Year                     = {2001},

  Url                      = {http://www.cis.hut.fi/projects/ica/fastica/}
}

@Manual{UNGlobalPopulation,
  Title                    = {{World Population Prospects}},
  Author                   = {{United Nations, Department of Economic and Social Affairs, Population Dynamics}},
  Year                     = {2019},
  Url                      = {https://population.un.org/wpp/Download/Standard/Population/}
}

@Article{GaborNelson1954,
  Title                    = {{Determination of the Resultant Dipole of the Heart from Measurements on the Body Surface}},
  Author                   = {D. Gabor and C. V. Nelson},
  Journal                  = {J. Appl. Phys.},
  Year                     = {1954},
  Number                   = {4},
  Pages                    = {413--416},
  Volume                   = {25},

  Abstract                 = {By means of the vector calculus, it is proved that the magnitude, orientation, and location of the resultant dipole of a system of sources and sinks inside a finite volume conductor is given by an integration over the bounding surface. The method is applied to finding the ``heart vector,'' or the resultant dipole moment of the human heart. The theory was checked in two- and three-dimensional electrolytic tank models of the human thorax. Journal of Applied Physics is copyrighted by The American Institute of Physics.},
  Doi                      = {10.1063/1.1721655},
  Owner                    = {sameni},
  Timestamp                = {2008.07.18}
}

@InProceedings{PG03,
  Title                    = {{Blind Separation of Fetal {ECG} from Single Mixture using SVD and ICA}},
  Author                   = {P. Gao and E-C Chang and L Wyse},
  Booktitle                = {{Proceedings of ICICS-PCM 2003}},
  Year                     = {2003},
  Month                    = {December},
  Pages                    = {1418-1422}
}

@Article{Genevier95,
  Title                    = {{Separation of fetal and maternal ECG complexes from a mixed signal using an algorithm based on linear regression}},
  Author                   = {E.S.G. Genevier and A.C. Deans and M.C. Carter and P.J. Steer},
  Journal                  = {Medical Engineering \& Physics},
  Year                     = {1995},

  Month                    = {October},
  Number                   = {7},
  Pages                    = {514-522},
  Volume                   = {17},

  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Ges89,
  Title                    = {{On the Theory of the Electrocardiogram}},
  Author                   = {D. B. Geselowitz},
  Journal                  = IEEE_J_PROC,
  Year                     = {1989},

  Month                    = {Jun.},
  Pages                    = {857--876},
  Volume                   = {77},

  No                       = {6}
}

@Article{Ges67,
  Title                    = {{On bioelectric potentials in an inhomogeneous volume conductor}},
  Author                   = {D. B. Geselowitz},
  Journal                  = {{Biophys J}},
  Year                     = {1967},
  Pages                    = {1--11},
  Volume                   = {7}
}

@Book{Ghanem2003,
  Title                    = {{Stochastic finite elements: a spectral approach}},
  Author                   = {Roger G. Ghanem and Pol D. Spanos},
  Publisher                = {Courier Dover Publications},
  Year                     = {2003},

  Owner                    = {sameni},
  Timestamp                = {2009.04.22}
}

@Book{giordano2008,
  Title                    = {First Course in Mathematical Modeling},
  Author                   = {Giordano, F.R.},
  Publisher                = {Simon \& Schuster},
  Year                     = {2008},

  ISBN                     = {9780495558774},
  Lccn                     = {2008921546}
}

@Article{Glover1977,
  Title                    = {{Adaptive Noise Canceling Applied to Sinusoidal Interferences}},
  Author                   = {Glover, J., Jr.},
  Journal                  = {Acoustics, Speech and Signal Processing, IEEE Transactions on},
  Year                     = {1977},

  Month                    = {dec},
  Number                   = {6},
  Pages                    = { 484 - 491},
  Volume                   = {25},

  Abstract                 = { This paper investigates a new method for eliminating sinusoidal or other periodic interference corrupting a signal. This task is typically accomplished by explicitly measuring the frequency of the interference and implementing a notch filter at that frequency. The method proposed herein uses an adaptive filter to eliminate the interference. The procedure is called adaptive noise canceling and is applicable when an auxiliary reference input is available containing the interference alone. The reference input is filtered in such a way that it closely matches the interfering sinusoid, and is then subtracted from the primary input leaving the signal alone. The results of this research show that when a sum of sinusoids is applied to an adaptive filter, the filter converges to a dynamic solution in which the weights of the filter are time varying. This time-varying solution implements a tunable notch filter, with a notch located at each of the reference frequencies. When used in noise-canceling applications, this adaptive notch filter provides a simple alternative to other methods of tracking and eliminating sinusoidal interferences.},
  ISSN                     = {0096-3518}
}

@Article{PhysioNet,
  Title                    = {{PhysioBank, PhysioToolkit, and PhysioNet}: Components of a New Research Resource for Complex Physiologic Signals},
  Author                   = {Goldberger, A. L. and Amaral, L. A. N. and Glass, L. and Hausdorff, J. M. and Ivanov, P. Ch. and Mark, R. G. and Mietus, J. E. and Moody, G. B. and Peng, C.-K. and Stanley, H. E.},
  Journal                  = {Circulation},
  Year                     = {2000},

  Month                    = {June},
  Note                     = {Circulation Electronic Pages: http://circ.ahajournals.org/cgi/content/full/101/23/e215},
  Number                   = {23},
  Pages                    = {e215--e220},
  Volume                   = {101}
}

@Book{Golub96,
  Title                    = {{Matrix Computations}},
  Author                   = {G.H Golub and C.F van Loan},
  Publisher                = {The Johns Hopkins University Press},
  Year                     = {1996},
  Edition                  = {Third}
}

@Article{Goodyer42,
  Title                    = {Clinical Fetal Elecrocardiography},
  Author                   = {Goodyer, A. V. N. and Geiger, A. J. and Monroe, W. M.},
  Journal                  = {Yale J. Biol. Med.},
  Year                     = {1942},
  Number                   = {15},
  Pages                    = {1--19}
}

@InProceedings{GNE01,
  Title                    = {{Improving the transform domain ECG denoising performance by applying interbeat and intra-beat decorrelating transforms}},
  Author                   = {A. Gotchev and N. Nikolaev and K. Egiazarian},
  Booktitle                = {Proc. of the 2001 IEEE International Symposium on Circuits and Systems; IEEE Circuits and Systems Society 2001},
  Year                     = {2001},

  Address                  = {Sydney, Australia},
  Pages                    = {17-20}
}

@InProceedings{GouyPailler09,
  Title                    = {{Iterative Subspace Decomposition for Ocular Artifact Removal from EEG Recordings}},
  Author                   = {C. Gouy-Pailler and R. Sameni and M. Congedo and C. Jutten},
  Booktitle                = {Proc. of the 8th Intl. Conf. on Independent Component (ICA 2009)},
  Year                     = {2009},

  Address                  = {Paraty, Brazil},
  Pages                    = {419--426},

  Owner                    = {sameni},
  Timestamp                = {2008.04.22}
}

@InProceedings{Graupe2007,
  Title                    = {Extracting fetal from maternal ECG for early diagnosis: theoretical problems and solutions - BAF and ICA},
  Author                   = {Graupe, Daniel and Zhong, Yunde and Graupe, Menachem H.},
  Booktitle                = {Proceedings of the fifth IASTED International Conference: biomedical engineering},
  Year                     = {2007},

  Address                  = {Anaheim, CA, USA},
  Pages                    = {352--356},
  Publisher                = {ACTA Press},
  Series                   = {BIEN '07},

  Acmid                    = {1295558},
  Keywords                 = {ICA, P-Wave, T-Wave, beat-wise ECG, blind adaptive filter, fetal ECG},
  Location                 = {Innsbruck, Austria},
  Numpages                 = {5},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://dl.acm.org/citation.cfm?id=1295494.1295558}
}

@Article{Greene89,
  Title                    = {Long-term ST waveform changes in the ovine fetal electrocardiogram: the relationship to spontaneous labour and intrauterine death},
  Author                   = {K R Greene and K G Rosen},
  Journal                  = {Clinical Physics and Physiological Measurement},
  Year                     = {1989},
  Number                   = {4B},
  Pages                    = {33-40},
  Volume                   = {10},

  Abstract                 = {The present data, obtained from chronically instrumented fetal lambs, includes three fetuses monitored throughout spontaneous labour, six fetuses with spontaneously developed long-term ST waveform changes and another three fetuses which died in the post-operative period. Uterine contractions could by themselves cause an increase in T wave height (T/QRS ratio$>$0.30). If the ST elevation was normalised between contractions the fetus seemed to compensate to a moderate degree of hypoxia. When oxygenation was further reduced the T wave remained elevated between contractions and a progressive increase occurred in the T/QRS ratio ($>$0.60) during the final stages of labour, in parallel with increasing blood lactate levels. Death in utero, whatever the cause (bleeding, infection or spontaneous hypoxia), was always preceded by marked ST waveform changes. It is concluded that ST elevation with high peaked T waves can appear on a long-term basis in fetuses with intrauterine complications.},
  Url                      = {http://stacks.iop.org/0143-0815/10/33}
}

@Book{GrewalAndrews01,
  Title                    = {{Kalman Filtering: Theory and Practice Using MATLAB}},
  Author                   = {M. S. Grewal and A. P. Andrews},
  Publisher                = {John Wiley \& Sons, Inc.},
  Year                     = {2001},
  Edition                  = {2nd},

  Owner                    = {sameni},
  Timestamp                = {2010.06.19}
}

@InProceedings{ICA03:Gribonval,
  Title                    = {{Proposals for Performance Measurement in Source Separation}},
  Author                   = {R. Gribonval and L. Benaroya and E. Vincent and C. F{\'e}votte},
  Booktitle                = {Proc. 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003)},
  Year                     = {2003},

  Address                  = {Nara, Japan},
  Month                    = apr,
  Pages                    = {763--768}
}

@Article{Grimm2003,
  Title                    = {{Recommended standards for fetal magnetocardiography}},
  Author                   = {B. Grimm and J. Haueisen and M. Huotilainen and S. Lange and P. {van Leeuwen} and T. Menendez and M. J. Peters and E. Schleussner and U. Schneider},
  Journal                  = {{Pacing Clin. Electrophysiol.}},
  Year                     = {2003},
  Pages                    = {2121--2126},
  Volume                   = {26}
}

@Article{Grouiller2007,
  Title                    = {{A comparative study of different artefact removal algorithms for EEG signals acquired during functional MRI}},
  Author                   = {F. Grouiller and L. Vercueil and A. Krainik and C. Segebarth and P Kahane and O David},
  Journal                  = {NeuroImage},
  Year                     = {2007},
  Number                   = {1},
  Pages                    = {124--37},
  Volume                   = {38}
}

@Article{Gulrajani98,
  Title                    = {The forward and inverse problems of electrocardiography},
  Author                   = {Gulrajani, R.M.},
  Journal                  = {Engineering in Medicine and Biology Magazine, IEEE},
  Year                     = {Sep/Oct 1998},
  Number                   = {5},
  Pages                    = {84-101, 122},
  Volume                   = {17},

  Abstract                 = {This article summarizes the theoretical underpinnings of both the forward and inverse problems of electrocardiography. Space limitations prohibit describing all of the research work done in these areas, and the author apologizes in advance for any omissions on this account or due to oversight. The article should enable one to gain a better qualitative and quantitative understanding of the heart's electrical activity},
  Doi                      = {10.1109/51.715491},
  ISSN                     = {0739-5175},
  Keywords                 = {electrocardiography, inverse problems, reviewsECG forward problem, ECG inverse problem, cardiac electrophysiology, heart electrical activity, theoretical underpinnings}
}

@Book{Gumbel58,
  Title                    = {Statistics of Extremes},
  Author                   = {Gumbel, E. J.},
  Publisher                = {Columbia University Press},
  Year                     = {1958}
}

@Book{Har01,
  Title                    = {Frequency-warped autoregressive modeling and filtering},
  Author                   = {A. H\"{a}rm\"{a}},
  Publisher                = {Helsinki University of Technology, Espoo, Finland},
  Year                     = {2001},

  Url                      = {http://lib.tkk.fi/Diss/2001/isbn9512254603/}
}

@Book{haberman1998elementary,
  Title                    = {Elementary Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems},
  Author                   = {Haberman, R.},
  Publisher                = {Prentice Hall},
  Year                     = {1998},

  ISBN                     = {9780132638074},
  Lccn                     = {97019521}
}

@Article{HBV04,
  Title                    = {{A novel mobile transtelephonic system with synthesized 12-lead {ECG}}},
  Author                   = {L. Hadzievski and B. Bojovic and V. Vukcevic and P. Belicev and S. Pavlovic and Z. Vasiljevic-Pokrajcic and M. Ostojic},
  Journal                  = IEEE_J_ITBM,
  Year                     = {2004},

  Month                    = {Dec.},
  Pages                    = {428-438},
  Volume                   = {8},

  No                       = {4}
}

@Book{haefner2005,
  Title                    = {Modeling Biological Systems: Principles and Applications},
  Author                   = {Haefner, J.W.},
  Publisher                = {Springer},
  Year                     = {2005},

  ISBN                     = {9780387250113},
  Lccn                     = {05042543}
}

@InProceedings{HMM03,
  Title                    = {{Analysing ICA components by injecting noise}},
  Author                   = {S. Hamerling and F. Meinecke and K.-R. {M\"{u}ller}},
  Booktitle                = {Proceedings of the 4th Int. Symp. on Independent Component Analysis and Blind Source Separation (ICA2003)},
  Year                     = {2003},

  Address                  = {Nara, Japan},
  Month                    = {April 1-4},
  Pages                    = {149-154},

  Url                      = {http://www.lis.inpg.fr/pages_perso/bliss/deliverables/d19.html}
}

@Article{Hamilton96,
  Title                    = {{A comparison of adaptive and nonadaptive filters for reduction of power line interference in the ECG}},
  Author                   = {Hamilton, P.S.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1996},

  Month                    = {January},
  Number                   = {1},
  Pages                    = {105-109},
  Volume                   = {43},

  Abstract                 = {We have investigated the relative performance of an adaptive and nonadaptive 60-Hz notch filter applied to an ECG signal. We evaluated the performance of the two implementations with respect to adaptation rate (or transient response time), signal distortion, and implementation complexity. We also investigated the relative effect of adaptive and nonadaptive 60-Hz filtering on ECG data compression. With a 360 Hz sample rate and an adaptation time of approximately 0.3 s for a 1 mV 60-Hz signal, the adaptive implementation is less complex and introduces less noise, particularly in the ST-segment, into a typical ECG signal. When applied to ECG signals, prior to data compression by average beat subtraction and residual differencing, the residual signal resulting from the adaptively filtered signal had an average entropy 0.31 bits per sample (bps) lower than the unfiltered signal. The nonadaptive 60-Hz filter produced an average entropy decrease of 0.08 bps relative to the unfiltered ECG},
  Doi                      = {10.1109/10.477707},
  ISSN                     = {0018-9294},
  Keywords                 = {adaptive filters, adaptive signal processing, data compression, electrocardiography, entropy, interference suppression, medical signal processing, notch filters0.3 s, 1 mV, 360 Hz, 60 Hz, ECG, ECG data compression, ST-segment, adaptation rate, adaptation time, adaptive filters, adaptive implementation, average beat subtraction, average entropy, implementation complexity, noise, nonadaptive filters, notch filter, power line interference, residual differencing, residual signal, sample rate, signal distortion, transient response time}
}

@InProceedings{Hassani2012,
  Title                    = {{Using matched filters for similarity search in genomic data}},
  Author                   = {Hassani Saadi, Hamed and Sameni, Reza},
  Booktitle                = {{Proceedings of the 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISP)}},
  Year                     = {2012},

  Address                  = {Shiraz, Iran},
  Month                    = {2-3 May 2012},
  Pages                    = {469--472},

  Owner                    = {sameni},
  Timestamp                = {2012.10.23}
}

@Article{He05,
  Title                    = {Application of {ICA} in removing artefacts from the {ECG}},
  Author                   = {He, T. and Clifford, G. D. and Tarassenko, L.},
  Journal                  = {Neural Processing Letters},
  Year                     = {2006},
  Note                     = {In Press},
  Number                   = {2},
  Pages                    = {105-116},
  Volume                   = {15}
}

@Book{Hilborn2000,
  Title                    = {Chaos and Nonlinear Dynamics},
  Author                   = {R. C. Hilborn},
  Publisher                = {Oxford University Press},
  Year                     = {2000},
  Edition                  = {Second}
}

@Article{HANC07,
  Title                    = {Performance comparison of six independent components analysis algorithms for fetal signal extraction from real {fMCG} data},
  Author                   = {Kenneth E Hild and Giovanna Alleva and Srikantan Nagarajan and Silvia Comani},
  Journal                  = {Phys. Med. Biol.},
  Year                     = {2007},
  Pages                    = {449-462},
  Volume                   = {512},

  Url                      = {doi:10.1088/0031-9155/52/2/010}
}

@Article{Hodges97,
  Title                    = {{Rate Correction of the QT Interval}},
  Author                   = {Morrison Hodges},
  Journal                  = {Cardiac Electrophysiology Review},
  Year                     = {1997},
  Pages                    = {360--363},
  Volume                   = {3},

  Owner                    = {a},
  Timestamp                = {2009.01.13}
}

@Book{Holmes1998,
  Title                    = {{Turbulence, Coherent Structures, Dynamical Systems and Symmetry}},
  Author                   = {Philip Holmes and John L. Lumley and Gal Berkooz},
  Publisher                = {Cambridge University Press},
  Year                     = {1998},

  Owner                    = {sameni},
  Timestamp                = {2009.04.22}
}

@Article{hon60,
  Title                    = {The instrumentation of fetal heart rate and fetal electrocardiography I. A fetal heart rate monitor},
  Author                   = {Hon, E. H.},
  Journal                  = {Conn Med},
  Year                     = {1960},
  Pages                    = {289--293},
  Volume                   = {24}
}

@Article{Horimoto04,
  Title                    = {Does maternal blood cortisol entrain fetal diurnal rhythm?},
  Author                   = {Horimoto, N. and Morokuma, S. and Nakano, H.},
  Journal                  = {Early Human Development},
  Year                     = {2004},
  Number                   = {1},
  Pages                    = {55-64},
  Volume                   = {76}
}

@Article{Hornberger2007,
  Title                    = {Rhythm abnormalities of the fetus.},
  Author                   = {Lisa K Hornberger and David J Sahn},
  Journal                  = {Heart},
  Year                     = {2007},

  Month                    = {Oct},
  Number                   = {10},
  Pages                    = {1294--1300},
  Volume                   = {93},

  Doi                      = {10.1136/hrt.2005.069369},
  Institution              = { Fetal Treatment Center, University of California, San Francisco, California, USA.},
  Keywords                 = {Arrhythmias, Cardiac; Echocardiography; Female; Fetal Diseases; Humans; Pregnancy; Ultrasonography, Prenatal},
  Owner                    = {Reza Sameni},
  Pii                      = {93/10/1294},
  Pmid                     = {17890709},
  Timestamp                = {2008.05.11},
  Url                      = {http://dx.doi.org/10.1136/hrt.2005.069369}
}

@Article{HuX06,
  Title                    = {{A single-lead {ECG} enhancement algorithm using a regularized data-driven filter}},
  Author                   = {Hu, X. and Nenov, V.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2006},

  Month                    = Feb,
  Pages                    = {347-351},
  Volume                   = {53},

  No                       = {2}
}

@Article{Huotilainen2005,
  Title                    = {Short-term memory functions of the human fetus recorded with magnetoencephalography},
  Author                   = {M. Huotilainen and A. Kujala and M. Hotakainen and L. Parkkonen and S. Taulu and J. Simola and J. Nenonen and M. Karjalainen and R. Naatanen},
  Journal                  = NeuroReport,
  Year                     = {2005},
  Pages                    = {81--84},
  Volume                   = {19},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Hurst1998,
  Title                    = {{Naming of the waves in the ECG, with a brief account of their genesis}},
  Author                   = {J. W. Hurst},
  Journal                  = {Circulation},
  Year                     = {1998},

  Month                    = {Nov},
  Number                   = {18},
  Pages                    = {1937--1942},
  Volume                   = {98},

  Institution              = {Division of Cardiology, Department of Medicine, University of Medicine Atlanta, GA 30322, USA.},
  Keywords                 = {Cardiology; Electrocardiography; History, 16th Century; History, 17th Century; History, 19th Century; Humans; Portraits as Topic},
  Owner                    = {Reza Sameni},
  Pmid                     = {9799216},
  Timestamp                = {2008.05.11}
}

@Article{hyv00emergence,
  Title                    = {Emergence of phase and shift invariant features by decomposition of natural images into independent feature subspaces},
  Author                   = {A. Hyv{\"a}rinen and P. Hoyer},
  Journal                  = {Neural Computation},
  Year                     = {2000},
  Number                   = {7},
  Pages                    = {1705--1720},
  Volume                   = {12},

  Url                      = {citeseer.ist.psu.edu/hyv00emergence.html}
}

@Book{HKO01,
  Title                    = {Independent Component Analysis},
  Author                   = {A. Hyv\"{a}rinen and J. Karhunen and E. Oja},
  Publisher                = {Wiley-Interscience},
  Year                     = {2001}
}

@InProceedings{HSV99,
  Title                    = {{Spikes and bumps: Artefacts generated by independent component analysis with insufficient sample size}},
  Author                   = {A. {Hyv\"{a}rinen} and J. {S\"{a}rel\"{a}} and R. {Vig\'{a}rio}},
  Booktitle                = {Int. Workshop on Independent Component Analysis and Signal Separation (ICA'99)},
  Year                     = {1999},

  Address                  = {Aussois, France},
  Pages                    = {425--429},

  Url                      = {http://citeseer.ist.psu.edu/513307.html}
}

@Book{HyvaeKO01,
  Title                    = {Independent Component Analysis},
  Author                   = {A. HyvÃ¤rinen and J. Karhunen and E. Oja},
  Publisher                = {Wiley-Interscience},
  Year                     = {2001},

  Owner                    = {Cedric Gouy-Pailler},
  Timestamp                = {2008.02.11}
}

@Book{Hyvarinen2001,
  Title                    = {Independent Component Analysis},
  Author                   = {A. Hyvarinen and J. Karhunen and E. Oja},
  Publisher                = {Wiley-Interscience},
  Year                     = {2001},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Ihar06,
  Title                    = {{Atrial repolarization as observable during the PQ interval}},
  Author                   = {Ihara, Z. and van Oosterom, A. and Hoekema, R.},
  Journal                  = {{Journal of Electrocardiology}},
  Year                     = {2006},
  Pages                    = {290--297},
  Volume                   = {39}
}

@Article{IlleBS02,
  Title                    = {Artifact correction of the ongoing {EEG} using spatial filters based on artifact and brain signal topographies.},
  Author                   = {Nicole Ille and Patrick Berg and Michael Scherg},
  Journal                  = {J. Clin. Neurophysiol.},
  Year                     = {2002},

  Month                    = {Apr},
  Number                   = {2},
  Pages                    = {113--124},
  Volume                   = {19},

  Abstract                 = {Review and analysis of continuous EEG recordings may be impeded by physiological artifacts such as blinks, eye movements, or cardiac activity. Spatial filters based on artifact and brain signal topographies can remove artifacts completely without distortion of relevant brain activity. The authors describe the basic principle of artifact correction by spatial filtering and they review different approaches to estimate artifact and brain signal topographies. The main focus is on the preselection approach, which is fast enough to be applied while paging through the segments of a digital EEG recording. Examples of real EEG segments, containing epileptic seizure activity or interictal spikes contaminated by artifacts, show that spatial filtering by preselection can be a useful tool during EEG review. Advantages and disadvantages of the different spatial filter approaches are discussed.},
  File                     = {IlleBS02.pdf:IlleBS02.pdf:PDF},
  Institution              = {Section of Biomagnetism, Department of Neurology, University of Heidelberg, Germany.},
  Keywords                 = {Artifacts; Brain; Brain Mapping; Computer Simulation; Electroencephalography; Humans},
  Owner                    = {Cedric Gouy-Pailler},
  Pmid                     = {11997722},
  Timestamp                = {2008.02.11}
}

@Article{In2006,
  Title                    = {Ballistocardiogram artifact removal from EEG signals using adaptive filtering of EOG signals},
  Author                   = {Myung H In and Soo Y Lee and Tae S Park and Tae-S Kim and Min H Cho and Young B Ahn},
  Journal                  = {Physiological Measurement},
  Year                     = {2006},
  Number                   = {11},
  Pages                    = {1227-1240},
  Volume                   = {27},

  Url                      = {http://stacks.iop.org/0967-3334/27/1227}
}

@Book{Ingalls2012,
  Title                    = {An Introduction to Mathematical Modelling in Molecular Systems Biology},
  Author                   = {Brian Ingalls},
  Publisher                = {Department of Applied Mathematics, University of Waterloo},
  Year                     = {2012}
}

@Book{Jackson1999,
  Title                    = {{Classical Electrodynamics}},
  Author                   = {J. D. Jackson},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {1999},
  Edition                  = {Third}
}

@Article{Jafari2005,
  Title                    = {Fetal electrocardiogram extraction by sequential source separation in the wavelet domain.},
  Author                   = {Maria G Jafari and Jonathon A Chambers},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2005},

  Month                    = {Mar},
  Number                   = {3},
  Pages                    = {390--400},
  Volume                   = {52},

  Abstract                 = {This paper addresses the problem of fetal electrocardiogram extraction using blind source separation (BSS) in the wavelet domain. A new approach is proposed, which is particularly advantageous when the mixing environment is noisy and time-varying, and that is shown, analytically and in simulation, to improve the convergence rate of the natural gradient algorithm. The distribution of the wavelet coefficients of the source signals is then modeled by a generalized Gaussian probability density, whereby in the time-scale domain the problem of selecting appropriate nonlinearities when separating mixtures of both sub- and super-Gaussian signals is mitigated, as shown by experimental results.},
  Doi                      = {10.1109/TBME.2004.842958},
  Institution              = {Centre for Digital Music, Department of Electronic Engineering, Queen Mary University of London, London, E1 4NS, UK. maria.jafari@elec.qmul.ac.uk},
  Keywords                 = {Algorithms; Body Surface Potential Mapping; Diagnosis, Computer-Assisted; Electrocardiography; Female; Fetal Monitoring; Humans; Models, Cardiovascular; Models, Neurological; Models, Statistical; Pregnancy; Signal Processing, Computer-Assisted; Stochastic Processes},
  Owner                    = {sameni},
  Pmid                     = {15759569},
  Timestamp                = {2008.04.30},
  Url                      = {http://dx.doi.org/10.1109/TBME.2004.842958}
}

@InProceedings{Jafari03,
  Title                    = {{Adaptive Noise Cancellation and Blind Source Separation}},
  Author                   = {M. G. Jafari and J. A. Chambers},
  Booktitle                = {Proceedings of the 4th Int. Symp. on Independent Component Analysis and Blind Source Separation (ICA2003)},
  Year                     = {2003},

  Address                  = {Nara, Japan},
  Month                    = {April 1-4},
  Pages                    = {627-632},

  Url                      = {www.kecl.ntt.co.jp/icl/signal/ica2003/cdrom/data/0012.pdf}
}

@Article{Jafari2006,
  Title                    = {{Sequential blind source separation based exclusively on second-order statistics developed for a class of periodic signals}},
  Author                   = {M. G. Jafari and W. Wang and J. A. Chambers and T. Hoya and A. Cichocki},
  Journal                  = IEEE_J_SP,
  Year                     = {2006},

  Month                    = {March},
  Pages                    = {1028--1040},
  Volume                   = {54},

  No                       = {3}
}

@Article{Jalaleddine90,
  Title                    = {ECG data compression techniques-a unified approach},
  Author                   = {Jalaleddine, S.M.S. and Hutchens, C.G. and Strattan, R.D. and Coberly, W.A.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1990},

  Month                    = {april },
  Number                   = {4},
  Pages                    = {329 -343},
  Volume                   = {37},

  Abstract                 = {Electrocardiogram (ECG) compression techniques are compared, and a unified view of these techniques is established. ECG data compression schemes are presented in two major groups: direct data compression and transformation methods. The direct data compression techniques are ECG differential pulse code modulation (DPCM) and entropy coding, AZTEC, Turning-point, CORTES, Fan and SAPA algorithms, peak-picking, and cycle-to-cycle compression methods. The transformation methods include Fourier, Walsh, and Karhunen-Loeve transforms. The theoretical bases behind the direct ECG data compression schemes are presented and classified into three categories: tolerance-comparison compression, DPCM, and entropy coding methods. A framework for evaluation and comparison of ECG compression schemes is presented.},
  Doi                      = {10.1109/10.52340},
  ISSN                     = {0018-9294},
  Keywords                 = {AZTEC;CORTES;ECG data compression techniques;Fan algorithms;Fourier transforms;Karhunen-Loeve transforms;SAPA algorithms;Turning-point;Walsh transforms;cycle-to-cycle compression;differential pulse code modulation;direct data compression;entropy coding;peak-picking;tolerance-comparison compression;transformation methods;Fourier transforms;Walsh functions;computerised signal processing;data compression;electrocardiography;encoding;medical computing;pulse-code modulation;reviews;transforms;Algorithms;Electrocardiography;Signal Processing, Computer-Assisted;}
}

@Manual{Jan04,
  Title                    = {Early Fetal Heart Development: 0-9 Weeks},
  Author                   = {L. Jana},
  Organization             = {The Dr. Spock Company},
  Year                     = {2004},

  Owner                    = {sameni},
  Timestamp                = {2008.05.07},
  Url                      = {http://www.drspock.com/article/0,1510,5287,00.html}
}

@Book{jones2003,
  Title                    = {Differential Equations and Mathematical Biology},
  Author                   = {Jones, D.D.S. and SLEEMAN, B.D.A.},
  Publisher                = {Taylor \& Francis Group},
  Year                     = {2003},
  Series                   = {Hall/CRC Mathematical Biology \& Medicine Series},

  ISBN                     = {9781584882961},
  Lccn                     = {2002191159}
}

@Article{JUD00,
  Title                    = {{A new method for the nonlinear transformation of means and covariances in filters and estimators}},
  Author                   = {S. Julier and J. Uhlmann and H.F. Durrant-Whyte},
  Journal                  = IEEE_J_AC,
  Year                     = {2000},

  Month                    = Mar,
  Pages                    = {477-482},
  Volume                   = {45},

  No                       = {3}
}

@InProceedings{JUD95,
  Title                    = {{A New Approach for Filtering Nonlinear Systems}},
  Author                   = {S. J. Julier and J. K. Uhlmann and H. F. Durrant-Whyte},
  Booktitle                = {Proceedings of the Ameriacan Control Conference},
  Year                     = {1995},
  Month                    = {21-23 June},
  Pages                    = {1628-1632},
  Volume                   = {3}
}

@Article{jung2000,
  Title                    = {{Removing electroencephalographic artifacts by blind source separation}},
  Author                   = {T. Jung and C. Humphries and T. Lee and M. McKeown and V. Iragui and S. Makeig and T. Sejnowski},
  Journal                  = {{Journal of Psychophysiology}},
  Year                     = {2000},
  Pages                    = {163--178},
  Volume                   = {37}
}

@Article{JungHLMIMS00,
  Title                    = {{Removing electroencephalographic artifacts by blind source separation}},
  Author                   = {T. Jung and C. Humphries and T. Lee and M. McKeown and V. Iragui and S. Makeig and T. Sejnowski},
  Journal                  = {J. Psychophysiol.},
  Year                     = {2000},
  Pages                    = {163--178},
  Volume                   = {37},

  Owner                    = {Cedric Gouy-Pailler},
  Timestamp                = {2008.02.11}
}

@Article{JuttenHerault1991,
  Title                    = {Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture},
  Author                   = {C. Jutten and J. Herault},
  Journal                  = {Signal Processing},
  Year                     = {1991},
  Pages                    = {1--10},
  Volume                   = {24},

  Owner                    = {a},
  Timestamp                = {2008.11.26}
}

@InProceedings{JSH06,
  Title                    = {{On the Relevance of Independent Components}},
  Author                   = {C. Jutten and R. Sameni and H. Hauksd\'{o}ttir},
  Booktitle                = {Proc. of the ICA Research Network International Workshop (ICArn 2006)},
  Year                     = {2006},

  Address                  = {Liverpool, UK},
  Month                    = {September 18-19},
  Pages                    = {1--8}
}

@Book{KadisonRingrose83,
  Title                    = {{Fundamentals of the Theory of Operator Algebras}},
  Author                   = {Richard Y. Kadison and John R. Ringrose},
  Publisher                = {{Academic Press}},
  Year                     = {1983},
  Volume                   = {I \& II},

  Owner                    = {sameni},
  Timestamp                = {2009.10.07}
}

@Book{Kailath1980,
  Title                    = {{Linear Systems}},
  Author                   = {Thomas Kailath},
  Publisher                = {Prentice Hall},
  Year                     = {1980}
}

@Book{Kailath2000,
  Title                    = {{Linear Estimation}},
  Author                   = {T. Kailath and A. H. Sayed and B. Hassibi},
  Publisher                = {Prentice Hall},
  Year                     = {2000},

  Owner                    = {sameni},
  Timestamp                = {2010.06.19}
}

@Article{Kaipio1997,
  Title                    = {Estimation of event-related synchronization changes by a new TVAR method},
  Author                   = {Kaipio, J.P. and Karjalainen, P.A.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1997},

  Month                    = aug.,
  Number                   = {8},
  Pages                    = {649 -656},
  Volume                   = {44},

  Abstract                 = {The modeling of nonstationary electroencephalogram (EEG) with time-varying autoregressive (TVAR) models is discussed. The classical least squares TVAR approach is modified so that prior assumptions about the signal can be taken into account in an optimal way. The method is then applied to the estimation of event-related synchronization changes in the EEG. The results show that the new approach enables effective estimation of the parameter evolution of the time-varying EEG with better time resolution compared to previous methods. The new method also allows single-trial analysis of the event-related synchronization.},
  Doi                      = {10.1109/10.605421},
  ISSN                     = {0018-9294},
  Keywords                 = {electrodiagnostics;event-related synchronization;event-related synchronization changes estimation;parameter evolution;single-trial analysis;time resolution;time-varying EEG;autoregressive processes;electroencephalography;medical signal processing;physiological models;Algorithms;Electroencephalography;Evoked Potentials, Visual;Female;Humans;Least-Squares Analysis;Models, Neurological;Reference Values;Time Factors;}
}

@Article{Kanjilal1997,
  Title                    = {Fetal ECG extraction from single-channel maternal ECG using singular value decomposition},
  Author                   = {Kanjilal, P.P. and Kanjilal, P.P. and Palit, S. and Saha, G.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1997},
  Number                   = {1},
  Pages                    = {51--59},
  Volume                   = {44},

  Doi                      = {10.1109/10.553712},
  Editor                   = {Palit, S.},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, medical signal processing, singular value decomposition, spectral analysis, abdominal lead, appropriately configured data matrices, composite maternal ECG signal, computationally efficient method, fetal ECG extraction, numerically robust method, single-channel maternal ECG, singular value ratio spectrum},
  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Article{KPS97,
  Title                    = {{Fetal {ECG} extraction from single-channel maternal {ECG} using singular value decomposition}},
  Author                   = {P. P Kanjilal and S. Palit and G. Saha},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1997},

  Month                    = {Jan.},
  Pages                    = {51-59},
  Volume                   = {44},

  No                       = {1}
}

@InProceedings{KS98,
  Title                    = {Human {ECG}: nonlinear deterministic versus stochastic aspects},
  Author                   = {Kantz, H. and Schreiber, T.},
  Year                     = {Nov 1998},
  Number                   = {6},
  Pages                    = {279-284},
  Volume                   = {145},

  Abstract                 = {The authors discuss aspects of randomness and determinism in electrocardiographic signals. In particular, they take a critical look at attempts to apply methods of nonlinear time series analysis derived from the theory of deterministic dynamical systems. It is argued that deterministic chaos is not a likely explanation for the short-time variability of the inter-beat interval times, except for certain pathologies. Conversely, densely sampled full ECG recordings possess properties typical of deterministic signals. In the last-mentioned case, methods of deterministic nonlinear time-series analysis can yield new insights},
  ISSN                     = {1350-2344},
  Journal                  = {Science, Measurement and Technology, IEE Proceedings -},
  Keywords                 = {chaos, electrocardiography, interference suppression, medical signal processing, nonlinear systems, random processes, stochastic processes, time seriesHuman ECG, chaos, deterministic dynamical systems, deterministic signals, electrocardiographic signal, foetal ECG, inter-beat interval times, noise, nonlinear deterministic processes, nonlinear time series analysis, nonlinear time-series analysis, randomness, short-time variability, stochastic processes}
}

@Article{KarHuk1977,
  Title                    = {Quantification of fetal heart rate variability by magnetocardiography and direct electrocardiography},
  Author                   = {V. Kariniemi and K. Hukkinen},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {1977},

  Month                    = {July},
  Number                   = {5},
  Pages                    = {526--30},
  Volume                   = {128},

  Abstract                 = {A computer method for quantification of fetal heart rate (FHR) variability from fetal magnetocardiography during pregnancy and from direct fetal electrocardiography during labor is presented. It is based on statistical analysis of the QRS interval sequences. Beat-to-beat variation is characterized by a differential index (DI) and long-term variation by an interval index (II). The effect of the sample time on the DI is minimal, and hence the DI can be calculated from rather short samples. The II is more sensitive to FHR trends and should be calculated from longer samples, but between the periodic changes, accelerations, and decelerations. Variable amounts of detection pulses are lost in both methods. The DI is sensitive to the missing intervals; no analysis result should be accepted if the number of lost intervals exceeds 10 per cent. The II is less sensitive to the number of missing intervals. The means and standard deviations of the variability indices for eight fetuses during pregnancy and for five fetuses during labor are presented.},
  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Article{Kautz01,
  Title                    = {{Jim Zimmerman and the SQUID}},
  Author                   = {Kautz, R.L.},
  Journal                  = {{Applied Superconductivity, IEEE Transactions on}},
  Year                     = {2001},

  Month                    = {March},
  Number                   = {1},
  Pages                    = {1026 -1031},
  Volume                   = {11},

  Abstract                 = {The career of Jim Zimmerman, beginning with a solid foundation in electronics and cryogenics, reached a turning point in 1965 when he became coinventor of the rf SQUID (Superconducting QUantum Interference Device), while working at the Scientific Laboratory of the Ford Motor Company in Dearborn, Michigan. Recognizing the exquisite sensitivity of the SQUID as an amplifier and magnetometer, Zimmerman devoted the remainder of his career, at Ford and later at the National Bureau of Standards, to the further development of the SQUID and its applications. In 1969, Zimmerman also helped found SHE Corporation, which marketed the first commercially successful SQUID. While at NBS, Zimmerman introduced two variations, the SQUID gradiometer and the fractional-turn SQUID, to enhance the sensitivity of SQUIDs in special situations. He also developed an improved understanding of SQUID dynamics by exploring the pendulum analog using carefully made models, work that has benefited a generation of students. Putting the SQUID to work, Zimmerman investigated applications in metrology, biomagnetism, and geophysics. Notably, he participated in collaborations that recorded the first magnetocardiogram made with a SQUID and the first magnetoencephalogram of an evoked auditory response. Later, Zimmerman explored closed-cycle refrigeration as a means of making SQUIDs more useful outside the laboratory environment, and in 1977 he demonstrated an operating SQUID cooled to 8.5 K by a Stirling-cycle refrigerator made largely of plastic. Zimmerman is remembered for his keen physical insight, the elegance and simplicity of his experiments, and his willingness to question conventional wisdom in all aspects of life},
  Doi                      = {10.1109/77.919524},
  ISSN                     = {1051-8223},
  Keywords                 = {Jim Zimmerman;RF SQUID;SQUID;SQUID amplifier;SQUID gradiometer;SQUID magnetometer;Stirling-cycle refrigerator;closed-cycle refrigeration;cryogenic electronics;fractional-turn SQUID;magnetocardiogram;magnetoencephalogram;obituary;pendulum model;SQUIDs;biographies;}
}

@Book{Kay93,
  Title                    = {{Fundamentals of Statistical Signal Processing{:} Estimation Theory}},
  Author                   = {S. M. Kay},
  Publisher                = {Prentice Hall PTR},
  Year                     = {1993}
}

@Article{Kay81,
  Title                    = {{Efficient Generation of Colored Noise}},
  Author                   = {S. M. Kay},
  Journal                  = IEEE_J_PROC,
  Year                     = {1981},

  Month                    = Apr,
  Pages                    = {480-481},
  Volume                   = {69},

  No                       = {4}
}

@InProceedings{Kazinnik1997,
  Title                    = {{Orthogonal decomposition of non-uniform B-spline spaces using wavelets}},
  Author                   = {Kazinnik, R. and Elber, G.},
  Booktitle                = {{EUROGRAPHICS 1997, Computer Graphics Forum}},
  Year                     = {1997},
  Pages                    = {27--38},

  Owner                    = {sameni},
  Timestamp                = {2011.04.19}
}

@Book{keener1998,
  Title                    = {Mathematical Physiology: With 360 Illustrations},
  Author                   = {Keener, J.P. and Sneyd, J.},
  Publisher                = {Springer Verlag},
  Year                     = {1998},
  Series                   = {Interdisciplinary applied mathematics: Mathematical biology},

  ISBN                     = {9780387983813},
  Lccn                     = {98014499}
}

@InProceedings{Kestler1998,
  Title                    = {{Denoising of High-Resolution ECG-Signals by Combining the Discrete Wavelet Transform with the Wiener Filter}},
  Author                   = {H. A. Kestler and M. Haschka and W. Kratz and F. Schwenker and G. Palm and V. Hombach and M. {H\"{o}her}},
  Booktitle                = {Proceedings IEEE Conference on Computers in Cardiology},
  Year                     = {1998},
  Pages                    = {233-236},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@book{diekmann2012mathematical,
  title={Mathematical tools for understanding infectious disease dynamics},
  author={Diekmann, Odo and Heesterbeek, Hans and Britton, Tom},
  volume={7},
  year={2012},
  publisher={Princeton University Press}
}

@article{dietz1975transmission,
  title={Transmission and control of arbovirus diseases},
  author={Dietz, Klaus},
  journal={Epidemiology},
  volume={104},
  pages={104--121},
  year={1975},
  publisher={SIAM Philadelphia}
}

@article{jones2007notes,
  title={Notes on R0},
  author={Jones, James Holland},
  journal={Califonia: Department of Anthropological Sciences},
  url = {https://web.stanford.edu/~jhj1/teachingdocs/Jones-Epidemics050308.pdf},
  year={2007}
}

@article{van2002reproduction,
  title={Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission},
  author={Van den Driessche, Pauline and Watmough, James},
  journal={Mathematical biosciences},
  volume={180},
  number={1-2},
  pages={29--48},
  year={2002},
  publisher={Elsevier}
}

@article{kamgang2008computation,
  title={Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE)},
  author={Kamgang, Jean Claude and Sallet, Gauthier},
  journal={Mathematical biosciences},
  volume={213},
  number={1},
  pages={1--12},
  year={2008},
  publisher={Elsevier}
}

@article{hethcote2000mathematics,
  title={The mathematics of infectious diseases},
  author={Hethcote, Herbert W},
  journal={SIAM review},
  volume={42},
  number={4},
  pages={599--653},
  year={2000},
  publisher={SIAM}
}

@InProceedings{KHKS98,
  Title                    = {Denoising of High-Resolution {ECG}-Signals by Combining the Discrete Wavelet Transform with the {W}iener Filter},
  Author                   = {H. A. Kestler and M. Haschka and W. Kratz and F. Schwenker and G. Palm and V. Hombach and M. {H\"{o}her}},
  Booktitle                = {Proceedings IEEE Conference on Computers in Cardiology},
  Year                     = {1998},

  Address                  = {September 13-1 6, 1998 Cleveland, Ohio, USA},
  Pages                    = {233-236}
}

@Article{Khamene2000,
  Title                    = {A new method for the extraction of fetal ECG from the composite abdominal signal},
  Author                   = {Khamene, A. and Negahdaripour, S.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {April},
  Number                   = {4},
  Pages                    = {507--516},
  Volume                   = {47},

  Doi                      = {10.1109/10.828150},
  ISSN                     = {0018-9294},
  Keywords                 = {composite abdominal signal;fetal ECG extraction;modulus maxima locations;recursive reconstruction method;singularities detection;thoracic signal;wavelet transform-based method;electrocardiography;medical signal processing;obstetrics;signal reconstruction;wavelet transforms;Abdomen;Algorithms;Electrocardiography;Female;Fetal Heart;Fetal Monitoring;Humans;Pregnancy;Signal Processing, Computer-Assisted;Thorax;}
}

@Book{khan2011digital,
  Title                    = {Digital Design of Signal Processing Systems: A Practical Approach},
  Author                   = {Khan, S.A.},
  Publisher                = {Wiley},
  Year                     = {2011},

  ISBN                     = {9780470975251},
  Lccn                     = {2010026285}
}

@InProceedings{Kharabian2009,
  Title                    = {{Fetal R-wave detection from multichannel abdominal ECG recordings in low SNR}},
  Author                   = {Kharabian, S. and Shamsollahi, M.B. and Sameni, R.},
  Booktitle                = {Proc. of the 31st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2009)},
  Year                     = {2009},

  Address                  = {Minneapolis, Minnesota, USA},
  Month                    = {Sep.},
  Pages                    = {344--347},

  Doi                      = {10.1109/IEMBS.2009.5333578},
  ISSN                     = {1557-170X},
  Journal                  = {Engineering in Medicine and Biology Society, 2009. EMBC 2009. Annual International Conference of the IEEE},
  Keywords                 = {Hilbert transform;ICA;SNR;fetal ECG extraction algorithm;fetal R-wave detection;fetal repositioning;independent component analysis;maternal ECG cancellation;multichannel abdominal ECG recordings;signal-to-noise ratio;source separation;Hilbert transforms;electrocardiography;feature extraction;independent component analysis;medical signal detection;medical signal processing;obstetrics;source separation;}
}

@Article{Knyazev2002,
  Title                    = {Principal angles between subspaces in an A-based scalar product: Algorithms and perturbation estimates},
  Author                   = {Andrew V. Knyazev and Merico and E. Argentati},
  Journal                  = {SIAM J. Sci. Comput},
  Year                     = {2002},
  Pages                    = {2009--2041},
  Volume                   = {23},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{Kogan2009,
  Title                    = {Introduction to Computational Cardiology: Mathematical Modeling and Computer Simulation},
  Author                   = {Kogan, B.J.},
  Publisher                = {Springer},
  Year                     = {2009},

  ISBN                     = {9780387766850},
  Lccn                     = {2009942421}
}

@InProceedings{Koldovsky2006,
  Title                    = {{Methods of Fair Comparison of Performance of Linear ICA Techniques in Presence of Additive Noise}},
  Author                   = {Z. Koldovsky and P. Tichavsky},
  Booktitle                = {Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on},
  Year                     = {2006},
  Month                    = {May},
  Pages                    = {873--876},
  Volume                   = {5},

  Abstract                 = {Linear ICA model with additive Gaussian noise is frequently considered in many practical applications, because it approaches the reality often much better than the noise-free alternate. In this paper, a number important differences between noisy and noiseless ICA are discussed. It is shown that estimation of the mixing/demixing matrix should not be the main goal, in the noisy case. Instead, it is proposed to compare the outcome of ICA algorithms with a minimum mean square (MMSE) separation, derived for known mixing model. The signal-to-interference-plus-noise ratio is suggested as the most meaningful performance criterion. A simulation study that compares a few well known ICA algorithms applied to noise data is included},
  Doi                      = {10.1109/ICASSP.2006.1661415}
}

@Article{Kole91,
  Title                    = {The quantitative extraction and topographic mapping of the abnormal components in the clinical {EEG}.},
  Author                   = {Koles, Z J},
  Journal                  = {Electroencephalogr. Clin. Neurophysiol.},
  Year                     = {1991},
  Pages                    = {440--447},
  Volume                   = {79},

  Owner                    = {Cedric Gouy-Pailler},
  Timestamp                = {2009.01.02}
}

@Article{Kotas2004,
  Title                    = {Projective filtering of time-aligned {ECG} beats},
  Author                   = {Kotas, M.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2004},
  Number                   = {7},
  Pages                    = {1129--1139},
  Volume                   = {51},

  Doi                      = {10.1109/TBME.2004.826592},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, filtering theory, medical signal processing, principal component analysis, state-space methods, electrocardiographic signal, nonlinear state-space projections, orthogonal basis functions, principal component analysis, projective filtering, time synchronization, time-aligned ECG beats},
  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Kovacs2000,
  Title                    = {A rule-based phonocardiographic method for long-term fetal heart rate monitoring},
  Author                   = {Kovacs, F. and Torok, M. and Habermajer, I.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},
  Number                   = {1},
  Pages                    = {124--130},
  Volume                   = {47},

  Doi                      = {10.1109/10.817627},
  Editor                   = {Torok, M.},
  ISSN                     = {0018-9294},
  Keywords                 = {acoustic signal processing, adaptive signal processing, bioacoustics, cardiology, medical signal processing, obstetrics, patient monitoring, acoustic method, adaptive time pattern analysis, algorithm, artefact, clinical tests, heartbeats analysis, long-term fetal heart rate monitoring, long-term fetal surveillance, low-power portable electronic instrument, reference ultrasound method, rule-based phonocardiographic method, tolerance limit, ultrasound cardiotocography},
  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Article{PTB2,
  Title                    = {{Automatisierte EKG-Auswertung mit Hilfe der EKG-Signaldatenbank CARDIODAT der PTB}},
  Author                   = {D. Kreiseler and R. Bousseljot},
  Journal                  = {Biomedizinische Technik},
  Year                     = {1995},
  Number                   = {1},
  Pages                    = {S319-S320},
  Volume                   = {40}
}

@Article{Kwee04,
  Title                    = {STAN S21 fetal heart monitor for fetal surveillance during labor: an observational study in 637 patients},
  Author                   = {Kwee, A and van der Hoorn-van den Beld CW and Veerman, J and Dekkers, AH and Visser, GH},
  Journal                  = {J Matern Fetal Neonatal Med},
  Year                     = {2004},
  Pages                    = {400-407},
  Volume                   = {15},

  Doi                      = {10.1080/14767050410001727404},
  Pubmedid                 = {15280112}
}

@Article{Laguna1992,
  Title                    = {{Adaptive filter for event-related bioelectric signals using an impulse correlated reference input}},
  Author                   = {P. Laguna and R. Jane and O. Meste and P. W. Poon and P. Caminal and H. Rix and N. V. Thakor},
  Journal                  = IEEE_J_BME,
  Year                     = {1992},
  Pages                    = {1032-1044},
  Volume                   = {39},

  No                       = {10},
  Owner                    = {sameni},
  Timestamp                = {2014.02.16}
}

@Article{LJMP92,
  Title                    = {{Adaptive filter for event-related bioelectric signals using an impulse correlated reference input}},
  Author                   = {P. Laguna and R. Jane and O. Meste and P. W. Poon and P. Caminal and H. Rix and N. V. Thakor},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1992},
  Pages                    = {1032-1044},
  Volume                   = {39},

  No                       = {10}
}

@Article{LMM98,
  Title                    = {{Power spectral density of unevenly sampled data by least-square analysis{:} performance and application to heart rate signals}},
  Author                   = {P. Laguna and G. B. Moody and R. G. Mark},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1998},

  Month                    = Jun,
  Pages                    = {698-715},
  Volume                   = {45}
}

@Article{Lai2002,
  Title                    = {A successive cancellation algorithm for fetal heart-rate estimation using an intrauterine {ECG} signal},
  Author                   = {Lai, Kuei-Chiang and Shynk, J.J.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2002},
  Number                   = {9},
  Pages                    = {943--954},
  Volume                   = {49},

  Doi                      = {10.1109/TBME.2002.802010},
  Editor                   = {Shynk, J.J.},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, medical signal detection, medical signal processing, obstetrics, physiological models, computer simulation results, counting mechanism, electrodiagnostics, fetal heart-rate estimation, interference cancellation, intrauterine ECG signal, maternal QRS complexes, noise events, peak detection, successive cancellation algorithm, template matching},
  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Lamarque2011,
  Title                    = {A New Concept of Virtual Patient for Real-Time ECG Analyzers},
  Author                   = {Lamarque, G. and Ravier, P. and Dumez-Viou, C.},
  Journal                  = {Instrumentation and Measurement, IEEE Transactions on},
  Year                     = {2011},

  Month                    = march,
  Number                   = {3},
  Pages                    = {939 -946},
  Volume                   = {60},

  Doi                      = {10.1109/TIM.2010.2064610},
  ISSN                     = {0018-9456},
  Keywords                 = {Holter manufacturers;analog signals;data processing algorithm;electrical heart activity;electrocardiogram analyzer;real-time ECG analyzer;real-time system;virtual patient;biomedical equipment;data acquisition;electrocardiography;medical diagnostic computing;medical signal processing;patient diagnosis;virtual reality;}
}

@Article{Lander1997,
  Title                    = {{Time frequency plane Wiener filtering of the high resolution ECG{:} background and time frequency representations}},
  Author                   = {P. Lander and E. J. Berbari},
  Journal                  = IEEE_J_BME,
  Year                     = {1997},
  Pages                    = {247-255},
  Volume                   = {44},

  No                       = {4},
  Owner                    = {sameni},
  Timestamp                = {2014.02.16}
}

@Article{Lander1997a,
  Title                    = {{Time frequency plane Wiener filtering of the high resolution ECG{:} development and applications}},
  Author                   = {P. Lander and E. J. Berbari},
  Journal                  = IEEE_J_BME,
  Year                     = {1997},
  Pages                    = {256-265},
  Volume                   = {44},

  No                       = {4},
  Owner                    = {sameni},
  Timestamp                = {2014.02.16}
}

@Article{LB97a,
  Title                    = {{Time frequency plane Wiener filtering of the high resolution ECG{:} development and applications}},
  Author                   = {P. Lander and E. J. Berbari},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1997},
  Pages                    = {256-265},
  Volume                   = {44},

  No                       = {4}
}

@Article{LB97b,
  Title                    = {{Time frequency plane Wiener filtering of the high resolution ECG{:} background and time frequency representations}},
  Author                   = {P. Lander and E. J. Berbari},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1997},
  Pages                    = {247-255},
  Volume                   = {44},

  No                       = {4}
}

@Article{Landqvist2005,
  Title                    = {{Novel Application of Projection Approximation Subspace Tracking Algorithm for Whitening in Wireless Communications}},
  Author                   = {Ronnie Landqvist and Abbas Mohammed},
  Journal                  = {{In Proc. Radio Communications Conference}},
  Year                     = {2005},

  Month                    = {June},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Larks1962,
  Title                    = {Present Status of Fetal Electrocardiography},
  Author                   = {Larks, Saul D.},
  Journal                  = {Bio-Medical Electronics, IRE Transactions on},
  Year                     = {1962},

  Month                    = {July},
  Number                   = {3},
  Pages                    = {176-180},
  Volume                   = {9},

  Abstract                 = {Fetal electrocardiography, an infant but vigorous young discipline, seems to be rapidly emerging as a useful tool for that biological research and medical practice which concerns the unborn heart. Based upon wide experience, it will be useful to survey the status of fetal electrocardiography, pointing out the possibilities as well as limitations. The significance in terms of capability for early study of the developing heart, the diagnosis of fetal life, multiple pregnancy, origins of congenital heart disease, as well as the study of intrauterine difficulties as in labor is presented and discussed in detail. On the basis of a discussion of present-day instruments and the types of "noise" encountered, it is suggested that improved low-noise amplifiers are desirable; it is suggested further that the use of averaging, correlation, and other computer-based techniques may hold substantial promise. 9152.},
  Doi                      = {10.1109/TBMEL.1962.4322994},
  ISSN                     = {0096-1884}
}

@Article{Lasserre1997,
  Title                    = {{Tight bounds for the trace of a matrix product}},
  Author                   = {J.B. Lasserre},
  Journal                  = IEEE_J_AC,
  Year                     = {1997},
  Pages                    = {578--581},
  Volume                   = {42},

  No                       = {4},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Lasserre95,
  Title                    = {{A trace inequality for matrix product}},
  Author                   = {J.B. Lasserre},
  Journal                  = IEEE_J_AC,
  Year                     = {1995},
  Pages                    = {1500--1501},
  Volume                   = {40},

  No                       = {8}
}

@Article{Lasserre97,
  Title                    = {{Tight Bounds for the Trace of a Matrix Product}},
  Author                   = {J. B. Lasserre},
  Journal                  = IEEE_J_AC,
  Year                     = {1997},

  Month                    = {April},
  Number                   = {4},
  Pages                    = {578--581},
  Volume                   = {42},

  Doi                      = {10.1109/5.720250},
  ISSN                     = {0018-9219},
  Keywords                 = {adaptive signal processing, array signal processing, estimation theory, higher order statistics, BSS, ICA, array processing, blind signal separation, data analysis, independent component analysis, mixtures, mutual independence, statistical principles, unobserved signals, unobserved sources},
  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@Article{Lathauwer2000,
  Title                    = {Fetal electrocardiogram extraction by blind source subspace separation},
  Author                   = {de Lathauwer, L. and de Moor, B. and Vandewalle, J.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {may },
  Number                   = {5},
  Pages                    = {567 -572},
  Volume                   = {47},

  Abstract                 = {We propose the emerging technique of independent component analysis, also known as blind source separation, as an interesting tool for the extraction of the antepartum fetal electrocardiogram from multilead cutaneous potential recordings. The technique is illustrated by means of a real-life example.},
  Doi                      = {10.1109/10.841326},
  ISSN                     = {0018-9294},
  Keywords                 = {antepartum fetal electrocardiogram;blind source subspace separation;fetal electrocardiogram extraction;independent component analysis;multilead cutaneous potential recordings;real-life example;electrocardiography;feature extraction;medical signal processing;paediatrics;signal reconstruction;statistical analysis;Algorithms;Electrocardiography;Female;Fetal Monitoring;Heart Rate, Fetal;Humans;Linear Models;Mathematics;Pregnancy;Signal Processing, Computer-Assisted;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Manual{Lawrence95,
  Title                    = {Fetal Heart Development},
  Author                   = {C. D. Lawrence},
  Year                     = {1995},

  Owner                    = {sameni},
  Timestamp                = {2008.05.07},
  Url                      = {http://user.gru.net/clawrence/vccl/chpt1/embryo.htm}
}

@PhdThesis{Lee03,
  Title                    = {Analysis of high-dimensional numerical data : from principal component analysis to non-linear dimensionality reduction and blind source separation},
  Author                   = {John A. Lee},
  School                   = {Louvain-la-Neuve, UCL, Belgium},
  Year                     = {2003},

  Editor                   = {John A. Lee},
  Publisher                = {Ph.D. dissertation, Louvain-la-Neuve, UCL, Belgium}
}

@Book{LeeVerleysen2007,
  Title                    = {{Nonlinear Dimensionality Reduction}},
  Author                   = {J. A. Lee and M. Verleysen},
  Publisher                = {Springer Science},
  Year                     = {2007},

  Owner                    = {sameni},
  Timestamp                = {2008.05.20}
}

@Book{lee2003verilog,
  Title                    = {Verilog coding for logic synthesis},
  Author                   = {Lee, W.F.},
  Publisher                = {Wiley-Interscience},
  Year                     = {2003},

  ISBN                     = {9780471429760},
  Lccn                     = {2002032433}
}

@Article{Lengle2001,
  Title                    = {{Improved neuromagnetic detection of fetal and neonatal auditory evoked response}},
  Author                   = {J.M. Lengle and M. Chen and R.T. Wakai},
  Journal                  = {{Clin. Neurophysiol.}},
  Year                     = {2001},
  Pages                    = {785--792 pp},
  Volume                   = {112},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{LeongaLiubMandic2008,
  Title                    = {{Blind source extraction: Standard approaches and extensions to noisy and post-nonlinear mixing}},
  Author                   = {Wai Yie Leonga and Wei Liub and Danilo P. Mandic},
  Journal                  = {Neurocomputing},
  Year                     = {2008},
  Pages                    = {2344--2355},
  Volume                   = {71},

  Owner                    = {sameni},
  Timestamp                = {2009.02.21}
}

@Article{Leski2002,
  Title                    = {Robust weighted averaging [of biomedical signals]},
  Author                   = {Leski, J.M.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2002},
  Number                   = {8},
  Pages                    = {796--804},
  Volume                   = {49},

  Doi                      = {10.1109/TBME.2002.800757},
  ISSN                     = {0018-9294},
  Keywords                 = {Gaussian noise, electrocardiography, filtering theory, impulse noise, mean square error methods, medical signal processing, minimisation, Gaussian noise, aggregation operation, biomedical signals, criterion function minimization, dissimilarity measure, electrocardiographic signal, impulsive noise, late potentials extraction, muscle noise, outliers, quadratic function, robust weighted averaging, root mean-square error, signal averaging, time-misalignment of cycles, variable power},
  Owner                    = {sameni},
  Timestamp                = {2008.01.29}
}

@Article{Leski2004,
  Title                    = {{Computationally effective algorithm for robust weighted averaging}},
  Author                   = {Leski, J.M. and Gacek, A.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2004},
  Number                   = {7},
  Pages                    = {1280--1284},
  Volume                   = {51},

  Doi                      = {10.1109/TBME.2004.827953},
  Editor                   = {Gacek, A.},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, medical signal processing, obstetrics, /spl epsiv/-insensitive loss function, fetal ECG, noise reduction, weighted signal averaging method},
  Owner                    = {sameni},
  Timestamp                = {2008.01.29}
}

@InProceedings{Li2011,
  Title                    = {{Activity recognition using dynamic subspace angles}},
  Author                   = {Binlong Li and Mustafa Ayazoglu and Teresa Mao and O.I. Camps and Mario Sznaier},
  Booktitle                = {Computer Vision and Pattern Recognition (CVPR), 2011 IEEE Conference on},
  Year                     = {2011},
  Month                    = {june},
  Pages                    = {3193 -3200},

  Abstract                 = {Cameras are ubiquitous everywhere and hold the promise of significantly changing the way we live and interact with our environment. Human activity recognition is central to understanding dynamic scenes for applications ranging from security surveillance, to assisted living for the elderly, to video gaming without controllers. Most current approaches to solve this problem are based in the use of local temporal-spatial features that limit their ability to recognize long and complex actions. In this paper, we propose a new approach to exploit the temporal information encoded in the data. The main idea is to model activities as the output of unknown dynamic systems evolving from unknown initial conditions. Under this framework, we show that activity videos can be compared by computing the principal angles between subspaces representing activity types which are found by a simple SVD of the experimental data. The proposed approach outperforms state-of-the-art methods classifying activities in the KTH dataset as well as in much more complex scenarios involving interacting actors.},
  Doi                      = {10.1109/CVPR.2011.5995672},
  ISSN                     = {1063-6919},
  Keywords                 = {KTH dataset;SVD;activity types;dynamic subspace angles;elderly assisted living;human activity recognition;principal angles;security surveillance;singular value decomposition;video gaming;object recognition;singular value decomposition;video signal processing;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Li95,
  Title                    = {{Detection of ECG characteristic points using wavelet transforms}},
  Author                   = {Cuiwei Li and Chongxun Zheng and Changfeng Tai},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1995},

  Month                    = {January},
  Number                   = {1},
  Pages                    = {21-28},
  Volume                   = {42},

  Abstract                 = {An algorithm based on wavelet transforms (WT's) has been developed for detecting ECG characteristic points. With the multiscale feature of WT's, the QRS complex can be distinguished from high P or T waves, noise, baseline drift, and artifacts. The relation between the characteristic points of ECG signal and those of modulus maximum pairs of its WT's is illustrated. By using this method, the detection rate of QRS complexes is above 99.8% for the MIT/BIH database and the P and T waves can also be detected, even with serious base line drift and noise },
  Doi                      = {10.1109/10.362922},
  ISSN                     = {0018-9294},
  Keywords                 = {medical signal processing, wavelet transformsECG characteristic points detection, P waves, QRS complexes, T waves, artifacts, baseline drift, modulus maximum pairs, multiscale feature, wavelet transform-based algorithm}
}

@Article{Li09,
  Title                    = {Artificial arterial blood pressure artifact models and an evaluation of a robust blood pressure and heart rate estimator},
  Author                   = {Li, Q. and Mark, R. G. and Clifford, G. D.},
  Journal                  = {BioMedical Engineering OnLine},
  Year                     = {2009},
  Number                   = {1},
  Pages                    = {13},
  Volume                   = {8},

  Abstract                 = {BACKGROUND:Within the intensive care unit (ICU), arterial blood pressure (ABP) is typically recorded at different (and sometimes uneven) sampling frequencies, and from different sensors, and is often corrupted by different artifacts and noise which are often non-Gaussian, nonlinear and nonstationary. Extracting robust parameters from such signals, and providing confidences in the estimates is therefore difficult and requires an adaptive filtering approach which accounts for artifact types.METHODS:Using a large ICU database, and over 6000 hours of simultaneously acquired electrocardiogram (ECG) and ABP waveforms sampled at 125 Hz from a 437 patient subset, we documented six general types of ABP artifact. We describe a new ABP signal quality index (SQI), based upon the combination of two previously reported signal quality measures weighted together. One index measures morphological normality, and the other degradation due to noise. After extracting a 6084-hour subset of clean data using our SQI, we evaluated a new robust tracking algorithm for estimating blood pressure and heart rate (HR) based upon a Kalman Filter (KF) with an update sequence modified by the KF innovation sequence and the value of the SQI. In order to do this, we have created six novel models of different categories of artifacts that we have identified in our ABP waveform data. These artifact models were then injected into clean ABP waveforms in a controlled manner. Clinical blood pressure (systolic, mean and diastolic) estimates were then made from the ABP waveforms for both clean and corrupted data. The mean absolute error for systolic, mean and diastolic blood pressure was then calculated for different levels of artifact pollution to provide estimates of expected errors given a single value of the SQI.RESULTS:Our artifact models demonstrate that artifact types have differing effects on systolic, diastolic and mean ABP estimates. We show that, for most artifact types, diastolic ABP estimates are less noise-sensitive than mean ABP estimates, which in turn are more robust than systolic ABP estimates. We also show that our SQI can provide error bounds for both HR and ABP estimates.CONCLUSION:The KF/SQI-fusion method described in this article was shown to provide an accurate estimate of blood pressure and HR derived from the ABP waveform even in the presence of high levels of persistent noise and artifact, and during extreme bradycardia and tachycardia. Differences in error between artifact types, measurement sensors and the quality of the source signal can be factored into physiological estimation using an unbiased adaptive filter, signal innovation and signal quality measures.},
  Doi                      = {10.1186/1475-925X-8-13},
  ISSN                     = {1475-925X},
  Pubmedid                 = {19586547},
  Url                      = {http://www.biomedical-engineering-online.com/content/8/1/13}
}

@Article{LiPM08,
  Title                    = {Robust heart rate estimation from multiple asynchronous noisy sources using signal quality indices and a {K}alman Filter},
  Author                   = {Li, Q. and Mark, R. G. and Clifford, G. D.},
  Journal                  = {IOP Physiol Meas},
  Year                     = {2008},

  Month                    = {Jan},
  Number                   = {1},
  Pages                    = {15-32},
  Volume                   = {29}
}

@Article{Li2007,
  Title                    = {{Sequential Blind Extraction Adopting Second-Order Statistics}},
  Author                   = {Li, Xi-Lin and Zhang, Xian-Da},
  Journal                  = IEEE_J_SPL,
  Year                     = {2007},
  Number                   = {1},
  Pages                    = {58--61},
  Volume                   = {14},

  Doi                      = {10.1109/LSP.2006.881519},
  Editor                   = {Zhang, Xian-Da},
  ISSN                     = {1070-9908},
  Keywords                 = {approximation theory, blind source separation, correlation methods, electrocardiography, feature extraction, higher order statistics, matrix algebra, medical signal processing, ECG data, a priori knowledge, approximation, autocorrelation matrix, electrocardiography, joint diagonalization, second-order statistics, sequential blind extraction algorithm, Approximate joint diagonalization (AJD), blind extraction, second-order statistics (SOS)},
  Owner                    = {sameni},
  Timestamp                = {2008.01.29}
}

@Article{Li2006,
  Title                    = {Underdetermined blind source separation based on sparse representation},
  Author                   = {Yuanqing Li and Amari, S. and Cichocki, A. and Ho, D.W.C. and Shengli Xie},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {2006},

  Month                    = {Feb.},
  Number                   = {2},
  Pages                    = { 423-437},
  Volume                   = {54},

  Abstract                 = { This paper discusses underdetermined (i.e., with more sources than sensors) blind source separation (BSS) using a two-stage sparse representation approach. The first challenging task of this approach is to estimate precisely the unknown mixing matrix. In this paper, an algorithm for estimating the mixing matrix that can be viewed as an extension of the DUET and the TIFROM methods is first developed. Standard clustering algorithms (e.g., K-means method) also can be used for estimating the mixing matrix if the sources are sufficiently sparse. Compared with the DUET, the TIFROM methods, and standard clustering algorithms, with the authors' proposed method, a broader class of problems can be solved, because the required key condition on sparsity of the sources can be considerably relaxed. The second task of the two-stage approach is to estimate the source matrix using a standard linear programming algorithm. Another main contribution of the work described in this paper is the development of a recoverability analysis. After extending the results in , a necessary and sufficient condition for recoverability of a source vector is obtained. Based on this condition and various types of source sparsity, several probability inequalities and probability estimates for the recoverability issue are established. Finally, simulation results that illustrate the effectiveness of the theoretical results are presented.},
  Doi                      = {10.1109/TSP.2005.861743},
  ISSN                     = {1053-587X},
  Keywords                 = { blind source separation, linear programming, signal representation, sparse matrices clustering algorithms, linear programming algorithm, mixing matrix, recoverability analysis, sparse representation approach, two-stage approach, undetermined blind source separation}
}

@Article{LiYi2008,
  Title                    = {An algorithm for extracting fetal electrocardiogram},
  Author                   = {Yunxia Li and Zhang Yi},
  Journal                  = {Neurocomput.},
  Year                     = {2008},
  Number                   = {7-9},
  Pages                    = {1538--1542},
  Volume                   = {71},

  Address                  = {Amsterdam, The Netherlands, The Netherlands},
  Doi                      = {http://dx.doi.org/10.1016/j.neucom.2007.05.001},
  ISSN                     = {0925-2312},
  Publisher                = {Elsevier Science Publishers B. V.}
}

@Article{LiMa2005,
  Title                    = {{ECG Modeling with DFG}},
  Author                   = {Zheying Li and Minjie Ma},
  Year                     = {2005},

  Month                    = jan.,
  Pages                    = {2691 -2694},

  Abstract                 = {ECG signals model described by data flow graph (DFG) is addressed in this paper. The model is built on the time processing. The principle of DFG modeling method for ECG signal is based on the idea of ECG time interval. According to the data processing flow, the each wave could be considered as a piece of ECG signal and the pieces could be processed in time sequence. According to the model, the time characters and parameters could be processed by the algorithm. And the model is also useful for the design of ECG signal generator},
  Booktitle                = {Engineering in Medicine and Biology Society, 2005. IEEE-EMBS 2005. 27th Annual International Conference of the},
  Doi                      = {10.1109/IEMBS.2005.1617025},
  Keywords                 = {DFG;ECG modeling;ECG signal generator;data flow graph;data processing flow;time processing;time sequence;data flow graphs;electrocardiography;medical signal processing;physiological models;}
}

@Article{Lindsley1942,
  Title                    = {{Heart and Brain Potentials of Human Fetuses in Utero}},
  Author                   = {D. B. Lindsley},
  Journal                  = {The American Journal of Psychology},
  Year                     = {1942},

  Month                    = {July},
  Number                   = {3},
  Pages                    = {412-416},
  Volume                   = {55},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@InProceedings{Liu03,
  Title                    = {{Blind Source Separation Based on Dual Adaptive Control}},
  Author                   = {D. Liu and X. Liu and F. Qian and H. Liu},
  Booktitle                = {Proceedings of the 4th Int. Symp. on Independent Component Analysis and Blind Source Separation (ICA2003)},
  Year                     = {2003},

  Address                  = {Nara, Japan},
  Month                    = {April 1-4},
  Pages                    = {445-450},

  Url                      = {www.kecl.ntt.co.jp/icl/signal/ica2003/cdrom/data/0069.pdf}
}

@Book{ljung1994,
  Title                    = {Modeling of Dynamic Systems},
  Author                   = {Ljung, L. and Torkel Glad},
  Publisher                = {Prentice Hall},
  Year                     = {1994},
  Series                   = {Prentice Hall Information \& System Sciences Series},

  ISBN                     = {9780135970973},
  Lccn                     = {94000862}
}

@Article{Luca2008,
  Title                    = {{P300-Based BCI Mouse with Genetically-Optimized Analogue Control}},
  Author                   = {Luca, C. and Riccardo, P. and Caterina, C. and Francisco S. and Tarassenko, L.},
  Journal                  = {IEE Electronic Letters},
  Year                     = {2008},

  Month                    = {Feb.},
  Number                   = {1},
  Pages                    = {51--61},
  Volume                   = {16},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Lunshof1998,
  Title                    = {{Fetal and maternal diurnal rhythms during the third trimester of normal pregnancy: Outcomes of computerized analysis of continuous twenty-four-hour fetal heart rate recordings}},
  Author                   = {S. Lunshof and K. Boer and H. Wolf and G. {van Hoffen} and N. Bayram and M. Mirmiran},
  Journal                  = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {1998},
  Pages                    = {247--254},
  Volume                   = {178},

  Owner                    = {sameni},
  Timestamp                = {2009.12.07}
}

@Unpublished{Maa03,
  Title                    = {{Estimation Theory and Optimal Filtering, [Lecture Notes]}},
  Author                   = {M. A. Maasoumnia},
  Note                     = {{Sharif University of Technology, Tehran, Iran}},
  Year                     = {2003}
}

@Article{Magann1997,
  Title                    = {Amniotic fluid volume in normal singleton pregnancies.},
  Author                   = {E. F. Magann and J. D. Bass and S. P. Chauhan and R. A. Young and N. S. Whitworth and J. C. Morrison},
  Journal                  = {Obstet Gynecol},
  Year                     = {1997},

  Month                    = {Oct},
  Number                   = {4 Pt 1},
  Pages                    = {524--528},
  Volume                   = {90},

  Abstract                 = {OBJECTIVE: To evaluate the amniotic fluid (AF) volume in normal singleton pregnancies from 15 to 40 weeks. METHODS: This prospective study evaluated the AF volume in singleton pregnancies undergoing amniocentesis for genetic assessment of fetal karyotype, preterm labor, or fetal lung maturity. Amniotic fluid volume was determined using a dye dilution technique. To assess the relationship between AF volume and estimated gestational age, a nonlinear regression model was applied. RESULTS: One hundred forty-four normal singleton pregnancies had AF volume evaluated. There was wide variability in the measured AF volumes with a significant (P < .01) increase in AF volume as a function of gestational age. Growth curve modeling estimated that AF volume continued to increase until 40 weeks' gestation. Analyses of the observed AF volume indicated that AF volume nearly doubled after 30 weeks' gestation. CONCLUSION: In contrast to other reports indicating that maximal AF volume in singleton gestations is expected early in the third trimester, we observed the attainment of maximal AF volume near term.},
  Institution              = {Department of Obstetrics and Gynecology, University of Mississippi Medical Center, Jackson, USA.},
  Keywords                 = {Adult; Amniotic Fluid; Female; Gestational Age; Humans; Pregnancy; Prospective Studies; Regression Analysis},
  Owner                    = {sameni},
  Pmid                     = {9380309},
  Timestamp                = {2008.05.09}
}

@Article{Maggioni05,
  Title                    = {Circadian rhythm of maternal blood pressure and fetal growth},
  Author                   = {Maggioni, C. and Cornelissen, G. and Otsuka, K. and Halberg, F. and Consonni, D. and Nicolini, U.},
  Journal                  = {Biomed Pharmacother},
  Year                     = {2005},

  Month                    = {October},
  Number                   = {1},
  Pages                    = {S86-S91},
  Volume                   = {59}
}

@Article{Makeig96,
  Title                    = {{Independent component analysis of electroencephalographic data}},
  Author                   = {S. Makeig and A.J. Bell and T-P. Jung and T.J. Sejnowski},
  Journal                  = {{Advances in Neural Information Processing Systems}},
  Year                     = {1996},
  Pages                    = {145--151},
  Volume                   = {8},

  Owner                    = {sameni},
  Timestamp                = {2010.08.01}
}

@Book{mallat2008wavelet,
  Title                    = {A Wavelet Tour of Signal Processing: The Sparse Way},
  Author                   = {S. Mallat},
  Publisher                = {Elsevier Science},
  Year                     = {2008}
}

@Book{MP95,
  Title                    = {{Bioelectromagnetism, Principles and Applications of Bioelectric and Biomagnetic Fields}},
  Author                   = {J. A. Malmivuo and R. Plonsey},
  Publisher                = {Oxford University Press},
  Year                     = {1995},

  Url                      = {http://butler.cc.tut.fi/~malmivuo/bem/bembook}
}

@Article{MHAC06,
  Title                    = {Performance comparison of independent component analysis algorithms for fetal cardiac signal reconstruction: a study on synthetic {fMCG} data},
  Author                   = {D Mantini and K E Hild II and G Alleva and S Comani},
  Journal                  = {Phys. Med. Biol.},
  Year                     = {2006},
  Pages                    = {1033-1046},
  Volume                   = {51},

  Url                      = {doi:10.1088/0031-9155/51/4/018}
}

@Article{Mantini07,
  Title                    = {Complete artifact removal for {EEG} recorded during continuous {fMRI} using independent component analysis},
  Author                   = {D. Mantini and M.G Perrucci and S. Cugini and A. Ferretti and G.L Romani and C. Del Gratta},
  Journal                  = {Neuroimage},
  Year                     = {2007},

  Month                    = {Jan},
  Number                   = {2},
  Pages                    = {598--607},
  Volume                   = {34},

  Abstract                 = {The simultaneous recording of EEG and fMRI is a promising method for combining the electrophysiological and hemodynamic information on cerebral dynamics. However, EEG recordings performed in the MRI scanner are contaminated by imaging, ballistocardiographic (BCG) and ocular artifacts. A number of processing techniques for the cancellation of fMRI environment disturbances exist: the most popular is averaged artifact subtraction (AAS), which performs well for the imaging artifact, but has some limitations in removing the BCG artifact, due to the variability in cardiac wave duration and shape; furthermore, no processing method to attenuate ocular artifact is currently used in EEG/fMRI, and contaminated epochs are simply rejected before signal analysis. In this work, we present a comprehensive method based on independent component analysis (ICA) for simultaneously removing BCG and ocular artifacts from the EEG recordings, as well as residual MRI contamination left by AAS. The ICA method has been tested on event-related potentials (ERPs) obtained from a visual oddball paradigm: it is very effective in attenuating artifacts in order to reconstruct clear brain signals from EEG acquired in the MRI scanner. It performs significantly better than the AAS method in removing the BCG artifact. Furthermore, since ocular artifacts can be completely suppressed, a larger number of trials is available for analysis. A comparison of ERPs inside the magnetic environment with those obtained out of the MRI scanner confirms that no systematic bias in the ERP waveform is produced by the ICA method.}
}

@Article{Martens06,
  Title                    = {{An Improved Adaptive Power Line Interference Canceller for Electrocardiography}},
  Author                   = {Martens, S.M.M. and Mischi, M. and Oei, S.G. and Bergmans, J.W.M.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2006},

  Month                    = {November},
  Number                   = {11},
  Pages                    = {2220-2231},
  Volume                   = {53},

  Abstract                 = {Power line interference may severely corrupt a biomedical recording. Notch filters and adaptive cancellers have been suggested to suppress this interference. We propose an improved adaptive canceller for the reduction of the fundamental power line interference component and harmonics in electrocardiogram (ECG) recordings. The method tracks the amplitude, phase, and frequency of all the interference components for power line frequency deviations up to about 4 Hz. A comparison is made between the performance of our method, former adaptive cancellers, and a narrow and a wide notch filter in suppressing the fundamental power line interference component. For this purpose a real ECG signal is corrupted by an artificial power line interference signal. The cleaned signal after applying all methods is compared with the original ECG signal. Our improved adaptive canceller shows a signal-to-power-line-interference ratio for the fundamental component up to 30 dB higher than that produced by the other methods. Moreover, our method is also effective for the suppression of the harmonics of the power line interference},
  Doi                      = {10.1109/TBME.2006.883631},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, harmonics suppression, interference (signal), medical signal processing, notch filtersECG, adaptive cancellers, electrocardiography, harmonics suppression, improved adaptive power line interference canceller, interference components, interference harmonics, notch filters}
}

@Article{Martens2007,
  Title                    = {{A robust fetal ECG detection method for abdominal recordings}},
  Author                   = {Suzanna M M Martens and Chiara Rabotti and Massimo Mischi and Rob J Sluijter},
  Journal                  = {Physiol Meas},
  Year                     = {2007},

  Month                    = {Apr},
  Number                   = {4},
  Pages                    = {373--388},
  Volume                   = {28},

  Abstract                 = {In this paper, we propose a new method for FECG detection in abdominal recordings. The method consists of a sequential analysis approach, in which the a priori information about the interference signals is used for the detection of the FECG. Our method is evaluated on a set of 20 abdominal recordings from pregnant women with different gestational ages. Its performance in terms of fetal heart rate (FHR) detection success is compared with that of independent component analysis (ICA). The results show that our sequential estimation method outperforms ICA with a FHR detection rate of 85\% versus 60\% of ICA. The superior performance of our method is especially evident in recordings with a low signal-to-noise ratio (SNR). This indicates that our method is more robust than ICA for FECG detection.},
  Doi                      = {10.1088/0967-3334/28/4/004},
  Institution              = {Department of Electrical Engineering, University of Technology Eindhoven, Eindhoven, The Netherlands. smm.martens@gmail.com},
  Keywords                 = {Abdomen; Algorithms; Artificial Intelligence; Diagnosis, Computer-Assisted; Electrocardiography; Fetal Monitoring; Humans; Pattern Recognition, Automated; Principal Component Analysis; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted},
  Owner                    = {sameni},
  Pii                      = {S0967-3334(07)38126-4},
  Pmid                     = {17395993},
  Timestamp                = {2008.05.02},
  Url                      = {http://dx.doi.org/10.1088/0967-3334/28/4/004}
}

@Book{marvasti2001nonuniform,
  Title                    = {Nonuniform Sampling: Theory and Practice},
  Author                   = {Marvasti, F.A.},
  Publisher                = {Kluwer Academic/Plenum Publishers},
  Year                     = {2001},
  Series                   = {Information Technology: Transmission, Processing, and Storage},

  ISBN                     = {9780306464454},
  Lccn                     = {00062213}
}

@Book{marvasti1987unified,
  Title                    = {A unified approach to zero-crossings and nonuniform sampling of single and multidimensional signals and systems},
  Author                   = {Marvasti, F.A.},
  Publisher                = {Nonuniform},
  Year                     = {1987},

  ISBN                     = {9780961816704},
  Lccn                     = {90162001}
}

@Article{McCubbin2007,
  Title                    = {{Validation of flash evoked response from fetal MEG}},
  Author                   = {J. McCubbin and P. Murphy and H. Eswaran and H. Preissl and T. Yee and S.E. Robinson and J. Vrba},
  Journal                  = {{Phys Med Biol}},
  Year                     = {2007},
  Pages                    = {5803--5813},
  Volume                   = {52},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Conference{McDonnellAJOG2011,
  Title                    = {{Comparison of abdominal sensors to a fetal scalp electrode for fetal ST analysis during labor}},
  Author                   = {Caitlin McDonnell and Gari Clifford and Reza Sameni and Jay Ward and Jim Robertson and Adam Wolfberg},
  Booktitle                = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {2011},
  Month                    = {January},
  Number                   = {1},
  Organization             = {{Society for Maternal-Fetal Medicine}},
  Pages                    = {S256--S256},
  Volume                   = {204},

  Owner                    = {sameni},
  Timestamp                = {2011.02.09}
}

@Manual{ecggenPhysionet,
  Title                    = {{ECGSYN - A realistic ECG waveform generator}},
  Author                   = {P. E. McSharry and G. D. Clifford},

  Url                      = {http://www.physionet.org/physiotools/ecgsyn/}
}

@Article{mcsharrySPIE04,
  Title                    = {A comparison of nonlinear noise reduction and independent component analysis using a realistic dynamical model of the electrocardiogram},
  Author                   = {McSharry, P. E. and Clifford, G. D.},
  Journal                  = {Proc of SPIE International Symposium on Fluctuations and Noise},
  Year                     = {2004},
  Number                   = {09},
  Pages                    = {78-88},
  Volume                   = {5467}
}

@Article{McSharry2003,
  Title                    = {{A Dynamic Model for Generating Synthetic Electrocardiogram Signals}},
  Author                   = {P. E. McSharry and G. D. Clifford and L. Tarassenko and L. A. Smith},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2003},

  Month                    = {mar},
  Pages                    = {289-294},
  Volume                   = {50},

  No                       = {3},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{MB81,
  Title                    = {{The Simulation of the Abdominal {MECG}}},
  Author                   = {W. J. H. Meijer and P. Bergveld},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1981},

  Month                    = {Apr.},
  Pages                    = {354--357},
  Volume                   = {BME-28},

  No                       = {4}
}

@Article{Meinecke2002,
  Title                    = {A resampling approach to estimate the stability of one-dimensional or multidimensional independent components.},
  Author                   = {Frank Meinecke and Andreas Ziehe and Motoaki Kawanabe and Klaus-Robert {M\"{u}ller}},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2002},
  Number                   = {12 Pt 2},
  Pages                    = {1514-25},
  Volume                   = {49}
}

@InProceedings{Min2009,
  Title                    = {Blind Sources Separation Algorithm Based on Adaptive Givens Rotations},
  Author                   = {Zhao Min and Li Weijun and Zhou Guoxu and Zhou Zhiheng},
  Booktitle                = {Natural Computation, 2009. ICNC '09. Fifth International Conference on},
  Year                     = {2009},
  Month                    = {aug.},
  Pages                    = {95 -99},
  Volume                   = {1},

  Doi                      = {10.1109/ICNC.2009.14},
  Keywords                 = {adaptive Givens rotations;blind sources separation algorithm;natural gradient algorithms;optimization model;blind source separation;gradient methods;optimisation;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Minino2007,
  Title                    = {Deaths: Final Data for 2004},
  Author                   = {A. M. Minino and M. P. Heron and S. L. Murphy and K. D. Kochanek},
  Journal                  = {National Vital Statistics Reports},
  Year                     = {2007},

  Month                    = {August},
  Number                   = {19},
  Pages                    = {1--120},
  Volume                   = {55},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.04}
}

@Manual{MMO05,
  Title                    = {{Matlab\textregistered\, Wavelet Toolbox User's guide version 3}},
  Author                   = {M. Misiti and Y. Misiti and G. Oppenheim and J-M Poggi},
  Year                     = {2005},

  Url                      = {http://www.mathworks.com/access/helpdesk/help/toolbox/wavelet/}
}

@Book{Mitra2005,
  Title                    = {{Digital Signal Processing: A Computer Based Approach}},
  Author                   = {S. K. Mitra},
  Publisher                = {McGraw-Hill },
  Year                     = {2005},
  Edition                  = {Third}
}

@Article{moody89,
  Title                    = {{QRS} morphology representation and noise estimation using the {K}arhunen-Lo\`{e}ve transform},
  Author                   = {Moody, G.B. and Mark, R.G.},
  Journal                  = {Computers in Cardiology},
  Year                     = {1989},
  Pages                    = {269-272},
  Volume                   = {16}
}

@Misc{nstdb,
  Title                    = {The {MIT-BIH} {N}oise {S}tress {T}est {D}atabase},

  Author                   = {Moody, G.B. and Muldrow, W.E. and Mark, R.G.},
  HowPublished             = {http://www.physionet.org/physiobank/database/nstdb/}
}

@InProceedings{Moody84,
  Title                    = {A noise stress test for arrhythmia detectors},
  Author                   = {Moody, G.B. and Muldrow, W.E. and Mark, R.G.},
  Booktitle                = {Computers in Cardiology},
  Year                     = {1984},
  Pages                    = {381-384},

  Vol                      = {11}
}

@Article{moon1996expectation,
  Title                    = {The expectation-maximization algorithm},
  Author                   = {Moon, Todd K},
  Journal                  = {Signal processing magazine, IEEE},
  Year                     = {1996},
  Number                   = {6},
  Pages                    = {47--60},
  Volume                   = {13},

  Publisher                = {IEEE}
}

@Article{Moon96,
  Title                    = {{The expectation-maximization algorithm}},
  Author                   = {T. K. Moon},
  Journal                  = IEEE_M_SP,
  Year                     = {1996},

  Month                    = {Nov.},
  Pages                    = {47--60},
  Volume                   = {13},

  No                       = {6}
}

@Article{Moraru2011,
  Title                    = {{Validation of fetal auditory evoked cortical responses to enhance the assessment of early brain development using fetal MEG measurements}},
  Author                   = {Liviu Moraru and Reza Sameni and Uwe Schneider and Jens Haueisen and Ekkehard Schleu{\ss}ner and Dirk Hoyer},
  Journal                  = {Physiological Measurements},
  Year                     = {2011},

  Month                    = {October},
  Number                   = {11},
  Pages                    = {1847--1868},
  Volume                   = {32},

  Abstract                 = {The maturation of fetal auditory evoked cortical responses (fAECRs) is an important aspect of developmental medicine, but their reliable identification is limited due to the technical restrictions in prenatal diagnosis. The signal-to-noise ratio of the fAECRs extracted exclusively from fetal magnetoencephalography is a known issue which limits their analysis as markers of brain development. The objective of this work was to develop a signal analysis strategy to address these problems and find appropriate processing steps. In this study, a group of 147 normal fetuses with gestations between 26 and 41 weeks underwent auditory evoked response testing. We combine different approaches that address data cleaning, fAECR determination and statistical fAECR validation to reduce the uncertainty in the detection of the auditory evoked responses. For the statistical validation of the evoked responses, we use parameters computed from bootstrap-based test statistics and the correlation between different averaging modes. Appropriate thresholds for those parameters are identified using linear regression analyses by looking at the maximum correlation coefficients. The results show that by using different validation parameters, the selected fAECRs conduct to similar regression slopes with an average of âˆ’13.6 ms/week gestational age which agree with previous studies. Our novel processing framework provides an objective way to identify and eliminate non-physiological variation in the data induced by artifacts. This approach has the potential to produce more reliable data needed in clinical studies for fetal brain maturation as well as extending the investigations to high-risk groups.},
  Doi                      = {10.1088/0967-3334/32/11/002},
  Owner                    = {sameni},
  Timestamp                = {2011.10.01}
}

@InProceedings{Moraru08,
  Title                    = {Identification of fetal auditory evoked cortical responses using a denoising method based on periodic component analysis},
  Author                   = {L. Moraru and R. Sameni and U. Schneider and C. Jutten and J. Haueisen and D. Hoyer},
  Booktitle                = {Proceedings of the 4th European Conference of the International Federation for Medical and Biological Engineering (ECIFMBE 2008)},
  Year                     = {2008},

  Address                  = {Antwerp, Belgium},
  Pages                    = {1390--1393},

  Mounth                   = {23--27 November}
}

@Article{Muceli2007,
  Title                    = {Real-time foetal ECG extraction with JADE on floating point DSP},
  Author                   = {Muceli, S. and Pani, D. and Raffo, L.},
  Journal                  = {Electronics Letters},
  Year                     = {2007},

  Month                    = {31},
  Number                   = {18},
  Pages                    = {963 -965},
  Volume                   = {43},

  Doi                      = {10.1049/el:20071331},
  ISSN                     = {0013-5194},
  Keywords                 = {JADE algorithm;TMS320C6713;block-on-line version;floating point DSP;foetal ECG extraction;mixing process variation;digital signal processing chips;electrocardiography;medical signal processing;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Muro04,
  Title                    = {{Changes in diurnal variations in the fetal heart rate baseline with advancing gestational age}},
  Author                   = {Masami Muro and Hideaki Shono and Mayumi Shono and Akira Uchiyama and Tsuyoshi Iwasaka},
  Journal                  = {{Sleep and Biological Rhythms}},
  Year                     = {2004},
  Pages                    = {83--85},
  Volume                   = {2:1},

  Owner                    = {sameni},
  Timestamp                = {2009.12.07}
}

@Article{Murphy06,
  Title                    = {{Endocrine Regulation of Human Fetal Growth: The Role of the Mother, Placenta, and Fetus}},
  Author                   = {Murphy, Vanessa E. and Smith, Roger and Giles, Warwick B. and Clifton, Vicki L.},
  Journal                  = {Endocr Rev},
  Year                     = {2006},
  Number                   = {2},
  Pages                    = {141-169},
  Volume                   = {27},

  Abstract                 = {The environment in which the fetus develops is critical for its survival and long-term health. The regulation of normal human fetal growth involves many multidirectional interactions between the mother, placenta, and fetus. The mother supplies nutrients and oxygen to the fetus via the placenta. The fetus influences the provision of maternal nutrients via the placental production of hormones that regulate maternal metabolism. The placenta is the site of exchange between mother and fetus and regulates fetal growth via the production and metabolism of growth-regulating hormones such as IGFs and glucocorticoids. Adequate trophoblast invasion in early pregnancy and increased uteroplacental blood flow ensure sufficient growth of the uterus, placenta, and fetus. The placenta may respond to fetal endocrine signals to increase transport of maternal nutrients by growth of the placenta, by activation of transport systems, and by production of placental hormones to influence maternal physiology and even behavior. There are consequences of poor fetal growth both in the short term and long term, in the form of increased mortality and morbidity. Endocrine regulation of fetal growth involves interactions between the mother, placenta, and fetus, and these effects may program long-term physiology.},
  Doi                      = {10.1210/er.2005-0011},
  Eprint                   = {http://edrv.endojournals.org/cgi/reprint/27/2/141.pdf},
  Url                      = {http://edrv.endojournals.org/cgi/content/abstract/27/2/141}
}

@Article{Mydlarczyk2001,
  Title                    = {{A Volterra inequality with the power type nonlinear kernel}},
  Author                   = {W. Mydlarczyk},
  Journal                  = {Journal of Inequalities and Applications},
  Year                     = {2001},
  Number                   = {6},
  Pages                    = {625-631},
  Volume                   = {6},

  Doi                      = {doi:10.1155/S1025583401000376},
  Owner                    = {sameni},
  Timestamp                = {2008.05.28}
}

@Manual{Nor01,
  Title                    = {{The Kalman Filter Toolbox}},
  Author                   = {M. N{\o}rgaard},

  Url                      = {http://www.iau.dtu.dk/research/control/kalmtool.html}
}

@Article{NadakuditiEdelman2008,
  Title                    = {Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples},
  Author                   = {Nadakuditi, R.R. and Edelman, A.},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {2008},

  Month                    = {july },
  Number                   = {7},
  Pages                    = {2625 -2638},
  Volume                   = {56},

  Abstract                 = {The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a mathematically justifiable, computationally simple, sample-eigenvalue-based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a sample-eigenvalue-based scheme is the computational simplicity and the robustness to eigenvector modelling errors which can adversely impact the performance of estimators that exploit information in the sample eigenvectors. There is, however, a price we pay by discarding the information in the sample eigenvectors; we highlight a fundamental asymptotic limit of sample-eigenvalue-based detection of weak or closely spaced high-dimensional signals from a limited sample size. This motivates our heuristic definition of the effective number of identifiable signals which is equal to the number of ldquosignalrdquo eigenvalues of the population covariance matrix which exceed the noise variance by a factor strictly greater than . The fundamental asymptotic limit brings into sharp focus why, when there are too few samples available so that the effective number of signals is less than the actual number of signals, underestimation of the model order is unavoidable (in an asymptotic sense) when using any sample-eigenvalue-based detection scheme, including the one proposed herein. The analysis reveals why adding more sensors can only exacerbate the situation. Numerical simulations are used to demonstrate that the proposed estimator, like Wax and Kailath's MDL-based estimator, consistently estimates the true number of signals in the dimension fixed, large sample size limit and the effective number of identifiable signals, unlike Wax and Kailath's MDL-based estimator, in the large dimension, (relatively) large sample size limit.},
  Doi                      = {10.1109/TSP.2008.917356},
  ISSN                     = {1053-587X},
  Keywords                 = {covariance matrix;eigenvector error modelling;high-dimensional signal detection;noise variance;sample-eigenvalue-based procedure;signal estimation;white noise;covariance matrices;eigenvalues and eigenfunctions;estimation theory;signal detection;signal sampling;white noise;}
}

@Article{NaeeBLGP06,
  Title                    = {Seperability of four-class motor imagery data using independent components analysis.},
  Author                   = {M. Naeem and C. Brunner and R. Leeb and B. Graimann and G. Pfurtscheller},
  Journal                  = {J. Neural Eng.},
  Year                     = {2006},

  Month                    = {Sep},
  Number                   = {3},
  Pages                    = {208--216},
  Volume                   = {3},

  Abstract                 = {This paper compares different ICA preprocessing algorithms on cross-validated training data as well as on unseen test data. The {EEG} data were recorded from 22 electrodes placed over the whole scalp during motor imagery tasks consisting of four different classes, namely the imagination of right hand, left hand, foot and tongue movements. Two sessions on different days were recorded for eight subjects. Three different independent components analysis (ICA) algorithms (Infomax, FastICA and SOBI) were studied and compared to common spatial patterns (CSP), Laplacian derivations and standard bipolar derivations, which are other well-known preprocessing methods. Among the ICA algorithms, the best performance was achieved by Infomax when using all 22 components as well as for the selected 6 components. However, the performance of Laplacian derivations was comparable with Infomax for both cross-validated and unseen data. The overall best four-class classification accuracies (between 33\% and 84\%) were obtained with CSP. For the cross-validated training data, CSP performed slightly better than Infomax, whereas for unseen test data, CSP yielded significantly better classification results than Infomax in one of the sessions.},
  Doi                      = {10.1088/1741-2560/3/3/003},
  File                     = {NaeeBLGP06.pdf:NaeeBLGP06.pdf:PDF},
  Keywords                 = {Adult; Algorithms; Artificial Intelligence; Diagnosis, Computer-Assisted; Electroencephalography; Evoked Potentials, Motor; Female; Humans; Imagination; Male; Movement; Pattern Recognition, Automated; Principal Component Analysis; Reproducibility of Results; Sensitivity and Specificity},
  Owner                    = {Cedric Gouy-Pailler},
  Pii                      = {S1741-2560(06)17554-0},
  Pmid                     = {16921204},
  Timestamp                = {2007.01.09},
  Url                      = {http://dx.doi.org/10.1088/1741-2560/3/3/003}
}

@Article{Naik2006,
  Title                    = {Limitations and Applications of {ICA} for Surface Electromyogram},
  Author                   = {Naik, G.R. and Kumar, D.K. and Arjunan, S.P. and Palaniswami, M. and Begg, R.},
  Journal                  = {Engineering in Medicine and Biology Society, 2006. EMBS '06. 28th Annual International Conference of the IEEE},
  Year                     = {2006},

  Month                    = {30 2006-Sept. 3},
  Number                   = {5},
  Pages                    = {5739--5742},
  Volume                   = {46},

  Abstract                 = {This paper reports research conducted to evaluate the use of sparse ICA for the separation of muscle activity from SEMG. It discusses some of the conditions that could affect the reliability of the separation and evaluates issues related to the properties of the signals and number of sources. The paper reports tests using Zibulevsky's method of temporal plotting to identify number of independent sources in SEMG recordings. The theoretical analysis and experimental results demonstrate that sparse ICA is not suitable for SEMG signals. The results identify that the technique is unable to identify finite number of active muscles. The work demonstrates that even at extremely low level of muscle contraction, and with filtering using wavelets and band pass filters, it is not possible to get the data sparse enough to identify number of independent sources using Zibulevsky's sparse decomposition technique},
  Doi                      = {10.1109/IEMBS.2006.259844},
  ISSN                     = {1557-170X},
  Keywords                 = {band-pass filters, biomechanics, electromyography, independent component analysis, medical signal processing, wavelet transformsICA, Zibulevsky method, band pass filters, muscle activity, muscle contraction, sparse decomposition technique, surface EMG, surface electromyogram, temporal plotting, wavelet filtering}
}

@Book{clifford2006advancedCh7,
  Title                    = {Advanced methods and tools for ECG data analysis, Chapter 7},
  Author                   = {Sanjiv M. Narayan},
  Publisher                = {Artech House, Inc.},
  Year                     = {2006},

  Editors                  = {Clifford, Gari D and Azuaje, Francisco and McSharry, Patrick}
}

@Article{Nelson96,
  Title                    = {{Uncertain Value of Electronic Fetal Monitoring in Predicting Cerebral Palsy}},
  Author                   = {Nelson, Karin B. and Dambrosia, James M. and Ting, Tricia Y. and Grether, Judith K.},
  Journal                  = {N Engl J Med},
  Year                     = {1996},
  Number                   = {10},
  Pages                    = {613-619},
  Volume                   = {334},

  Abstract                 = {Background Electronic monitoring of the fetal heart rate is commonly performed, in part to detect hypoxia during delivery that may result in brain injury. It is not known whether specific abnormalities on electronic fetal monitoring are related to the risk of cerebral palsy. Methods Among 155,636 children born from 1983 through 1985 in four California counties, we identified singleton infants with birth weights of at least 2500 g who survived to three years of age and had moderate or severe cerebral palsy. The children with cerebral palsy were compared with randomly selected control children with respect to characteristics noted in the birth records. Results Seventy-eight of 95 children with cerebral palsy and 300 of 378 controls underwent intrapartum fetal monitoring. Characteristics found to be associated with an increased risk of cerebral palsy were multiple late decelerations in the heart rate, commonly defined as slowing of the heart rate well after the onset of uterine contractions (odds ratio, 3.9; 95 percent confidence interval, 1.7 to 9.3), and decreased beat-to-beat variability of the heart rate (odds ratio, 2.7; 95 percent confidence interval, 1.1 to 5.8); there was no association between the highest or lowest fetal heart rate recorded for each child and the risk of cerebral palsy. Even after adjustment for other risk factors, the association of abnormalities on fetal monitoring with an increased risk of cerebral palsy persisted (adjusted odds ratio, 2.7; 95 percent confidence interval, 1.4 to 5.4). The 21 children with cerebral palsy who had multiple late decelerations or decreased variability in heart rate on fetal monitoring represented only 0.19 percent of singleton infants with birth weights of 2500 g or more who had these fetal-monitoring findings, for a false positive rate of 99.8 percent. Conclusions Specific abnormal findings on electronic monitoring of the fetal heart rate were associated with an increased risk of cerebral palsy. However, the false positive rate was extremely high. Since cesarean section is often performed when such abnormalities are noted and is associated with risk to the mother, our findings arouse concern that, if these indications were widely used, many cesarean sections would be performed without benefit and with the potential for harm.},
  Doi                      = {10.1056/NEJM199603073341001},
  Eprint                   = {http://content.nejm.org/cgi/reprint/334/10/613.pdf},
  Url                      = {http://content.nejm.org/cgi/content/abstract/334/10/613}
}

@InProceedings{NG00,
  Title                    = {{ECG signal denoising using wavelet domain Wiener filtering}},
  Author                   = {N. Nikolaev and A. Gotchev},
  Booktitle                = {Proc. European Signal Processing Conf. EUSIPCO-2000},
  Year                     = {2000},

  Address                  = {Tampere, Finland},
  Month                    = {September},
  Pages                    = {51-54}
}

@Electronic{Norman2017,
  Title                    = {Normal Regulation of Blood Glucose},
  Author                   = {James Norman},
  Note                     = {https://www.endocrineweb.com/conditions/diabetes/normal-regulation-blood-glucose},
  Url                      = {https://www.endocrineweb.com/conditions/diabetes/normal-regulation-blood-glucose},
  Year                     = {2017},

  Owner                    = {sameni},
  Timestamp                = {2017.06.12}
}

@Article{OGrady2005,
  Title                    = {{Survey of sparse and non-sparse methods in source separation}},
  Author                   = {P. D. O'Grady and B. A. Pearlmutter and S. T. Rickard},
  Journal                  = {International Journal of Imaging Systems and Technology},
  Year                     = {2005},
  Number                   = {1},
  Pages                    = {18--33},
  Volume                   = {15},

  Owner                    = {sameni},
  Timestamp                = {2009.05.30}
}

@Misc{Oleary,
  Title                    = {{QR Factorizations using a Restricted Set of Rotations}},

  Author                   = {Dianne P. O'Leary and Stephen and S. Bullock},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{OSL02,
  Title                    = {{Block adaptive filters with deterministic reference inputs for event related signals; BLMS and BRLS}},
  Author                   = {S. Olmos and L. {S\"{o}rnmo} and P. Laguna},
  Journal                  = IEEE_J_SP,
  Year                     = {2002},
  Pages                    = {1102-1112},
  Volume                   = {50},

  No                       = {5}
}

@Book{Oostendorp1989,
  Title                    = {Modeling the Fetal {ECG}},
  Author                   = {T. Oostendorp},
  Publisher                = {Ph.D. dissertation, K. U. Nijmegen, The Netherlands},
  Year                     = {1989},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Oos89a,
  Title                    = {{Electrical properties of tissues involved in the conduction of fetal ECG}},
  Author                   = {T.F. Oostendorp and A. van Oosterom and H.W. Jongsma},
  Journal                  = {Biomed Eng Comput},
  Year                     = {1989},
  Pages                    = {322--324},
  Volume                   = {27},

  Owner                    = {sameni},
  Timestamp                = {2008.07.17}
}

@misc{sameni2020mathematical,
      title={{Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus}}, 
      author={Reza Sameni},
      year={2020},
      eprint={2003.11371},
      archivePrefix={arXiv},
      primaryClass={q-bio.PE},
      url = {https://arxiv.org/abs/2003.11371}
}

@Article{Oost89d,
  Title                    = {The fetal {ECG} throughout the second half of gestation},
  Author                   = {T. F. Oostendorp and A. van Oosterom and H. W. Jongsma},
  Journal                  = {Clin Phys physiol Meas.},
  Year                     = {1989},
  Number                   = {2},
  Pages                    = {147--160},
  Volume                   = {10}
}

@Article{Oost89e,
  Title                    = {The effect of changes in the conductive medium on the fetal {ECG} throughout gestation},
  Author                   = {T. F. Oostendorp and A. van Oosterom and H. W. Jongsma},
  Journal                  = {Clin. Phys. physiol Meas.},
  Year                     = {1989},
  Pages                    = {11--20},
  Volume                   = {10 Sup. {B}}
}

@Article{Oos02,
  Title                    = {Beyond the Dipole; Modeling the Genesis of the Electrocardiogram},
  Author                   = {A. van Oosterom},
  Journal                  = {100 years Einthoven},
  Year                     = {2002},
  Note                     = {The Einthoven Foundation, Leiden},
  Pages                    = {7-15},

  Editors                  = {M.J Schalij and M. C Janse and A. van Oosterom and H. J. J Wellens and E. van der Wal.}
}

@Article{Oosterom86,
  Title                    = {Spatial filtering of the fetal electrocardiogram},
  Author                   = {A. van Oosterom},
  Journal                  = {J. Perinat Med.},
  Year                     = {1986},
  Number                   = {6},
  Pages                    = {411--419},
  Volume                   = {14},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Book{oppenheim1999discrete,
  Title                    = {{Discrete-time signal processing}},
  Author                   = {Oppenheim, A.V. and Schafer, R.W. and Buck, J.R.},
  Publisher                = {Prentice Hall},
  Year                     = {1999},
  Series                   = {Prentice-Hall signal processing series},

  ISBN                     = {9780137549207},
  Lccn                     = {98050398}
}

@Book{Oppenheim1997,
  Title                    = {Signals and Systems},
  Author                   = {Alan V. Oppenheim and Alan S. Willsky and Hamid Nawab},
  Publisher                = {Prentice Hall International, Inc.},
  Year                     = {1997},

  Owner                    = {a},
  Timestamp                = {2009.01.12}
}

@Article{Osei1999,
  Title                    = {Fetal position and size data for dose estimation.},
  Author                   = {E. K. Osei and K. Faulkner},
  Journal                  = {Br J Radiol},
  Year                     = {1999},

  Month                    = {Apr},
  Number                   = {856},
  Pages                    = {363--370},
  Volume                   = {72},

  Abstract                 = {In order to establish both positional and size data for estimation of fetal absorbed dose from radiological examinations, the depth from the mother's anterior surface to the mid-line of the fetal head and abdomen were measured from ultrasound scans in 215 pregnant women. Depths were measured along a ray path projected in the anteroposterior (AP) direction from the mother's abdomen. The fetal size was estimated from measurements of the fetal abdominal and head circumference, femur length and the biparietal diameter. The effects of fetal presentation, maternal bladder volume, placenta location, gestational age and maternal AP thickness on fetal depth and size were analysed. The fetal position from the anterior surface of the mother's abdomen is shorter for posterior placenta and empty bladder volume, but longer for anterior placenta and full bladder volume. Mean fetal depth (MFD) observed for all bladder volumes, fetal presentations and placenta locations increased from 6.5 +/- 0.5 cm to 10.2 +/- 0.7 cm over the duration of pregnancy. Similarly, mean fetal skull depth (FSD) increased from 6.6 +/- 0.6 cm to 9.8 +/- 0.6 cm over the period of pregnancy, but only from about 6.6 cm to 7.8 cm over the period (8-25 weeks) when damage to the developing brain has been observed to result in mental retardation. Using the range of mean fetal depth (4.7-13.9 cm) observed in this study and depth dose data at 75 kVp and 3.0 mmAl half value thickness (HVT), fetal absorbed dose would be overestimated by up to 66\% or underestimated by up to 77\% if the mean value of MFD (8.1 cm) is used rather than actual individual values. These errors increase with lower tube potential and filtration up to over 90\% overestimation and up to 100\% underestimation at 60 kVp and 1.0 mmAl filtration.},
  Institution              = {Regional Medical Physics Department, Newcastle General Hospital, Newcastle Upon Tyne, UK.},
  Keywords                 = {Anthropometry; Body Height; Body Weight; Female; Fetus; Gestational Age; Humans; Labor Presentation; Maternal Exposure; Placenta; Pregnancy; Radiation Dosage; Ultrasonography, Prenatal; Urinary Bladder},
  Owner                    = {sameni},
  Pmid                     = {10474497},
  Timestamp                = {2008.05.09}
}

@Book{ottesen2004,
  Title                    = {Applied Mathematical Models in Human Physiology},
  Author                   = {Ottesen, J.T. and Olufsen, M.S. and Larsen, J.K.},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Year                     = {2004},
  Series                   = {Monographs on Mathematical Modeling and Computation},

  ISBN                     = {9780898715392},
  Lccn                     = {03067274}
}

@InProceedings{Outram95,
  Title                    = {Techniques for Optimal Enhancement and Feature Extraction of Fetal Electrocardiogram},
  Author                   = {N. J. Outram and E. C. Ifeachor and P. W. J. Van Eetvelt and J. S. H. Curnow},
  Booktitle                = {IEE Proc.-Sci. Meas. Technol.},
  Year                     = {1995},
  Month                    = {November},
  Number                   = {6},
  Pages                    = {482--489},
  Volume                   = {142},

  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Pajkrt2004,
  Title                    = {Fetal cardiac anomalies and genetic syndromes.},
  Author                   = {Eva Pajkrt and Boaz Weisz and Helen V Firth and Lyn S Chitty},
  Journal                  = {Prenat Diagn},
  Year                     = {2004},

  Month                    = {Dec},
  Number                   = {13},
  Pages                    = {1104--1115},
  Volume                   = {24},

  Abstract                 = {Cardiac anomalies may occur in isolation or can be part of a genetic syndrome. In this article, we describe some of the genetic syndromes commonly associated with cardiac anomalies where there are other sonographic features that may aid accurate prenatal diagnosis.},
  Doi                      = {10.1002/pd.1067},
  Institution              = {Institute of Child Health, University College London Hospital, London, UK.},
  Keywords                 = {Chromosome Aberrations; Fetal Diseases; Fetal Heart; Genetic Diseases, Inborn; Heart Defects, Congenital; Humans; Hydrops Fetalis; Mass Screening; Musculoskeletal Abnormalities; Nuchal Translucency Measurement; Syndrome; Teratogens; Ultrasonography, Prenatal},
  Owner                    = {Reza Sameni},
  Pmid                     = {15614851},
  Timestamp                = {2008.05.04},
  Url                      = {http://dx.doi.org/10.1002/pd.1067}
}

@Book{palnitkar2003verilog,
  Title                    = {Verilog Hdl: A Guide to Digital Design and Synthesis},
  Author                   = {Palnitkar, S.},
  Publisher                = {SunSoft Press},
  Year                     = {2003},

  ISBN                     = {9780130449115},
  Lccn                     = {2003269714}
}

@Article{Pan1985,
  Title                    = {{A Real-Time QRS Detection Algorithm}},
  Author                   = {Pan, Jiapu and Tompkins, Willis J.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1985},
  Number                   = {3},
  Pages                    = {230--236},
  Volume                   = {BME-32},

  Doi                      = {10.1109/TBME.1985.325532},
  Editor                   = {Tompkins, Willis J.},
  ISSN                     = {0018-9294},
  Owner                    = {sameni},
  Timestamp                = {2008.01.30}
}

@InProceedings{Pani2008,
  Title                    = {A DSP algorithm and system for real-time fetal ECG extraction},
  Author                   = {Pani, D. and Argiolas, S. and Raffo, L.},
  Booktitle                = {Computers in Cardiology, 2008},
  Year                     = {2008},
  Month                    = {sept.},
  Pages                    = {1065 -1068},

  Abstract                 = {Fetal ECG (FECG) extraction from maternal abdominal potential recordings is a task of paramount importance for pediatric cardiologists, but there is a lack of established solutions for it. In this paper the real-time implementation of a block-on-line independent component analysis (ICA) algorithm for FECG extraction is presented and evaluated over real long lasting recordings. The problem of the signals permutation, typical of ICA algorithms and particularly severe for block-on-line ones, is analyzed in detail. The comparison with batch approaches applied to different segments of the signals demonstrates the quality of the proposed solution. The performances of the real-time implementation enable further developments of the system to automatically provide other interesting clinical parameters.},
  Doi                      = {10.1109/CIC.2008.4749229},
  ISSN                     = {0276-6547},
  Keywords                 = {DSP algorithm;ICA algorithm;block-on-line independent component analysis;maternal abdominal potential recording;pediatric cardiologist;real-time fetal ECG extraction;signal permutation;signal segmentation;digital signal processing chips;electrocardiography;feature extraction;independent component analysis;medical signal processing;obstetrics;paediatrics;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{Pap91,
  Title                    = {{Probability, random variables, and stochastic processes}},
  Author                   = {A. Papoulis},
  Publisher                = {McGraw-Hill},
  Year                     = {1991},
  Edition                  = {Third}
}

@Book{Pap2002,
  Title                    = {{Probability, random variables, and stochastic processes}},
  Author                   = {Athanasios Papoulis and S. Unnikrishana Pillai},
  Publisher                = {McGraw-Hill},
  Year                     = {2002},
  Edition                  = {Fourth}
}

@Article{Park92,
  Title                    = {{On detecting the presence of fetal R-wave using the moving averaged magnitude difference algorithm}},
  Author                   = {Park, Y.C. and Lee, K.Y. and Youn, D.H. and Kim, N.H. and Kim, W.K. and Park, S.H.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1992},

  Month                    = {August},
  Number                   = {8},
  Pages                    = {868-871},
  Volume                   = {39},

  Doi                      = {10.1109/10.148396},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, signal processingexponential averaging, fetal ECG signal, fetal QRS complex, fetal R-wave, moving averaged magnitude difference algorithm, slowly varying signal shape, template signal}
}

@Article{Parra2003,
  Title                    = {{Blind Source Separation via Generalized Eigenvalue Decomposition}},
  Author                   = {L. Parra and P. Sajda},
  Journal                  = {{Journal of Machine Learning Research}},
  Year                     = {2003},
  Pages                    = {1261--1269},
  Volume                   = {4},

  No                       = {4}
}

@Article{Pelliccia87,
  Title                    = {{Idiopathic dilated cardiomyopathy: T/R ratio as an ECG index of ventricular volume and function}},
  Author                   = {F. Pelliccia and M. Ciavolella and A. Gaspardone and F. Tomai and F. Romeo and A. Nigri and P. A. Gioffr\'e and Reale A},
  Journal                  = {{Cardiologia}},
  Year                     = {1987},

  Month                    = {March},
  Number                   = {3},
  Pages                    = {281--286},
  Volume                   = {32},

  Owner                    = {sameni},
  Timestamp                = {2011.04.24}
}

@Article{Peters2001,
  Title                    = {{Monitoring the fetal heart non-invasively: a review of methods}},
  Author                   = {Maria Peters and John Crowe and Jean-Francois Pi\'eri and Hendrik Quartero and Barrie Hayes-Gill and David James and Jeroen Stinstra and Simon Shakespeare},
  Journal                  = {J. Perinat. Med.},
  Year                     = {2001},
  Pages                    = {408--416},
  Volume                   = {29},

  Owner                    = {sameni},
  Timestamp                = {2008.05.02}
}

@Article{Pham1997,
  Title                    = {Blind separation of mixture of independent sources through a quasi-maximum likelihood approach},
  Author                   = {Pham, Dinh Tuan and Garat, P.},
  Journal                  = IEEE_J_SP,
  Year                     = {1997},
  Number                   = {7},
  Pages                    = {1712--1725},
  Volume                   = {45},

  Doi                      = {10.1109/78.599941},
  ISSN                     = {1053-587X},
  Keywords                 = {correlation methods, filtering theory, matrix algebra, maximum likelihood estimation, probability, signal processing, spectral analysis, blind separation, correlated sources, experiments, independent sources mixture, linear separating filters, maximum likelihood solution, nonlinear separating functions, numerical results, performance, probability distribution, quasimaximum likelihood approach, simulation results, simultaneous diagonalization, spectral analysis, symmetric matrices, temporally independent nonGaussian sources},
  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@Article{PhamCardoso2001,
  Title                    = {Blind separation of instantaneous mixtures of nonstationary sources },
  Author                   = {Dinh-Tuan Pham and Cardoso, J.-F.},
  Journal                  = {Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]},
  Year                     = {Sep 2001},
  Number                   = {9},
  Pages                    = {1837--1848},
  Volume                   = {49},

  Abstract                 = {Most source separation algorithms are based on a model of stationary sources. However, it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation. This paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information. These principles are exploited by efficient algorithms in both the off-line case (via a new joint diagonalization procedure) and in the on-line case (via a Newton-like procedure). Some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented: their ability to achieve a kind of super-efficiency. The paper concludes with a discussion contrasting separating methods for non-Gaussian and nonstationary models and emphasizing that, as a matter of fact, “what makes the algorithms work” is-strictly speaking-not the nonstationarity itself but rather the property that each realization of the source signals has a time-varying envelope},
  Doi                      = {10.1109/78.942614},
  ISSN                     = {1053-587X},
  Keywords                 = {maximum likelihood estimation, signal processing, time-varying systemsNewton-like procedure, blind separation, instantaneous mixtures, joint diagonalization procedure, maximum likelihood, minimum mutual information, nonGaussian models, nonstationary models, nonstationary sources, off-line case, on-line case, performance, source separation algorithms, super-efficiency, time-varying envelope}
}

@Manual{MIT-BIH2,
  Title                    = {{The MIT-BIH Noise Stress Test Database}},
  Author                   = {PhysioNet},
  Organization             = {National Institutes of Health},

  Url                      = {http://www.physionet.org/physiobank/database/nstdb/}
}

@Manual{MIT-BIH5,
  Title                    = {MIT-BIH Arrhythmia Database},
  Author                   = {PhysioNet},
  Organization             = {National Institutes of Health},

  Url                      = {http://www.physionet.org/physiobank/database/mitdb/}
}

@Manual{MIT-BIH4,
  Title                    = {{MIT-BIH Polysomnographic Database}},
  Author                   = {PhysioNet},
  Organization             = {National Institutes of Health},
  Year                     = {1999},

  Url                      = {http://www.physionet.org/physiobank/database/slpdb/}
}

@Manual{MIT-BIH,
  Title                    = {{The MIT-BIH Normal Sinus Rhythm Database}},
  Author                   = {PhysioNet},
  Organization             = {National Institutes of Health},
  Year                     = {1991},

  Url                      = {http://www.physionet.org/physiobank/database/nsrdb/}
}

@Article{JPolich1995,
  Title                    = {{Cognitive and biological determinants of P300: An integrative review}},
  Author                   = {J. Polich and A. Kok},
  Journal                  = {Biol. Psychol},
  Year                     = {1995},
  Number                   = {2},
  Pages                    = {103--146},
  Volume                   = {41},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{PCB98,
  Title                    = {{High Resolution ECG Filtering Using Adaptive Bayesian Wavelet Shrinkage}},
  Author                   = {M. Popescu and P. Cristea and A. Bezerianos},
  Booktitle                = {Proc. Computers in Cardiology 1998 Conference},
  Year                     = {1998},

  Address                  = {Cleveland, Ohio, USA},
  Month                    = {September 13-16},
  Pages                    = {401-404},

  Vol                      = {25}
}

@Article{Porcaro2006,
  Title                    = {Fetal auditory responses to external sounds and mother's heart beat : Detection improved by Independent Component Analysis},
  Author                   = {C. Porcaro and F. Zappasodi and G. Barbati and C. Salustri and V. Pizzella and P. M. Rossini and F. Tecchio},
  Journal                  = {{Brain Research}},
  Year                     = {2006},
  Pages                    = {51 - 58},
  Volume                   = {1101},

  No                       = {1},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@TechReport{ACOG09,
  Title                    = {Intrapartum Fetal Heart Rate Monitoring: Nomenclature, Interpretation, and General Management Principles},
  Author                   = {Practice, Bulletin, A. C. O. G.},
  Institution              = {American College of Obstetricians and Gynecologists},
  Year                     = {2009},
  Number                   = {109}
}

@Book{Press92,
  Title                    = {{Numerical Recipes in C: The Art of Scientific Computing}},
  Author                   = {William H. Press and Saul A. Teukolsky and William T. Vetterling},
  Publisher                = {Cambridge University Press},
  Year                     = {1992},
  Edition                  = {2nd},

  Owner                    = {sameni},
  Timestamp                = {2008.01.30}
}

@Article{Rajapakse1998,
  Title                    = {Modeling hemodynamic response for analysis of functional MRI time-series},
  Author                   = {Rajapakse, Jagath C. and Kruggel, Frithjof and Maisog, Jose M. and Yves von Cramon, D.},
  Journal                  = {Human Brain Mapping},
  Year                     = {1998},
  Number                   = {4},
  Pages                    = {283--300},
  Volume                   = {6},

  Abstract                 = {Abstract The standard Gaussian function is proposed for the hemodynamic modulation function (HDMF) of functional magnetic resonance imaging (fMRI) time-series. Unlike previously proposed parametric models, the Gaussian model accounts independently for the delay and dispersion of the hemodynamic responses and provides a more flexible and mathematically convenient model. A suboptimal noniterative scheme to estimate the hemodynamic parameters is presented. The ability of the Gaussian function to represent the HDMF of brain activation is compared with Poisson and Gamma models. The proposed model seems valid because the lag and dispersion values of hemodynamic responses rendered by the Gaussian model are in the ranges of their previously reported values in recent optical and fMR imaging studies.An extension of multiple regression analysis to incorporate the HDMF is presented. The detected activity patterns exhibit improvements with hemodynamic correction. The proposed model and efficient parameter estimation scheme facilitated the investigation of variability of hemodynamic parameters of human brain activation. The hemodynamic parameters estimated over different brain regions and across different stimuli showed significant differences. Measurement of hemodynamic parameters over the brain during sensory or cognitive stimulation may reveal vital information on physiological events accompanying neuronal activation and functional variability of the human brain, and should lead to the investigation of more accurate and complex models. Hum. Brain Mapping 6:283â€“300, 1998. Â© 1998 Wiley-Liss, Inc.},
  ISSN                     = {1097-0193},
  Keywords                 = {brain imaging, blood-oxygen-level-dependent contrast, functional magnetic resonance imaging, hemodynamic response function, multiple regression},
  Publisher                = {John Wiley \& Sons, Inc.}
}

@InProceedings{RaoJones1999,
  Title                    = {A denoising approach to multichannel signal estimation},
  Author                   = {A. M. Rao and D. L. Jones},
  Booktitle                = {{Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference}},
  Year                     = {1999},
  Pages                    = {2869--2872},
  Volume                   = {05},

  Owner                    = {sameni},
  Timestamp                = {2009.02.14}
}

@Article{Ravier2007,
  Title                    = {Redefining Performance Evaluation Tools for Real-Time QRS Complex Classification Systems},
  Author                   = {Ravier, P. and Leclerc, F. and Dumez-Viou, C. and Lamarque, G.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2007},

  Month                    = sept.,
  Number                   = {9},
  Pages                    = {1706 -1710},
  Volume                   = {54},

  Doi                      = {10.1109/TBME.2007.902594},
  ISSN                     = {0018-9294},
  Keywords                 = {QRS complex waveforms;heartbeat classification procedure;heartbeat extraction function;neural-network classifier;performance evaluation tools;real-time QRS complex classification systems;electrocardiography;medical signal detection;neural nets;Algorithms;Arrhythmias, Cardiac;Artificial Intelligence;Computer Systems;Diagnosis, Computer-Assisted;Electrocardiography;Heart Rate;Humans;Pattern Recognition, Automated;Sensitivity and Specificity;Software;}
}

@InProceedings{RazavipourCINC2013,
  Title                    = {{Fetal QRS Complex Detection using Semi-Blind Source Separation Framework}},
  Author                   = {Fatemeh Razavipour and Masoumeh Haghpanahi and Reza Sameni},
  Booktitle                = {Proceedings of the 40th Annual International Conference on Computersin Cardiology},
  Year                     = {2013},

  Address                  = {Zaragoza, Spain},
  Month                    = {September 22-25},
  Pages                    = {181--184},

  Vol                      = {40}
}

@Article{Razavipour2013,
  Title                    = {{A General Framework for Extracting Fetal Magnetoencephalogram and Audio-Evoked Responses}},
  Author                   = {Razavipour, Fatemeh and Sameni, Reza},
  Journal                  = {J Neurosci Methods},
  Year                     = {2013},

  Month                    = {January},
  Number                   = {2},
  Pages                    = {283--296},
  Volume                   = {212},

  Doi                      = {10.1016/j.jneumeth.2012.10.021},
  Owner                    = {sameni},
  Timestamp                = {2013.01.15}
}

@Article{Reif99,
  Title                    = {{Stochastic stability of the discrete-time extended Kalman filter}},
  Author                   = {K. Reif and S. Gunther and E. Yaz and R. Unbehauen},
  Journal                  = IEEE_J_AC,
  Year                     = {1999},
  Number                   = {4},
  Pages                    = {714--728},
  Volume                   = {44}
}

@Article{RSK98,
  Title                    = {{Fetal ECG Extraction with Nonlinear State-Space Projections}},
  Author                   = {M. Richter and T. Schreiber and D. T. Kaplan},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1998},

  Month                    = {January},
  Number                   = {1},
  Pages                    = {133-137},
  Volume                   = {45},

  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Book{Rideout1991,
  Title                    = {Mathematical and Computer Modeling of Physiological Systems},
  Author                   = {Vincent C. Rideout},
  Publisher                = {Prentice Hall},
  Year                     = {1991},

  Owner                    = {sameni},
  Timestamp                = {2012.12.18}
}

@Article{Riera06,
  Title                    = {A theoretical formulation of the electrophysiological inverse problem on the sphere},
  Author                   = {J. J. Riera and P. A. Valdes and K. Tanabe and R. Kawashima},
  Journal                  = {Physics in Medicine and Biology},
  Year                     = {2006},
  Number                   = {7},
  Pages                    = {1737-1758},
  Volume                   = {51},

  Abstract                 = {The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.},
  Url                      = {http://stacks.iop.org/0031-9155/51/1737}
}

@Article{RJ.Ilmoniemi1997,
  Title                    = {Signal-space projection method for separating MEG or EEG into components},
  Author                   = { RJ.Ilmoniemi and MA.Uusitalo},
  Journal                  = {{IEEE Trans Biomed Eng}},
  Year                     = {1997},
  Pages                    = {135-140},
  Volume                   = {35},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InBook{Robinson2002,
  Title                    = {Biomag 2002},
  Author                   = {S. E. Robinson and J. Vrba and J. McCubbin},
  Chapter                  = {{Separating fetal MEG signals from the noise}},
  Editor                   = {Nowak H, et al.},
  Pages                    = {665-667 pp},
  Publisher                = {Berlin: VDE Verlag Gmbh},
  Year                     = {2002},

  Booktitle                = {{in Biomag.}},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Robinson2002a,
  Title                    = {{Separating fetal MEG signals from the noise}},
  Author                   = {S. E. Robinson and J. Vrba and J. McCubbin},
  Year                     = {2002},
  Pages                    = {665-667 pp},

  Booktitle                = {{in Biomag.}},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{ROCHE1965,
  Title                    = {{The fetal electrocardiogram. V. Comparison of lead systems}},
  Author                   = {J. B. Roche and E. H. Hon},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {1965},

  Month                    = {Aug},
  Pages                    = {1149--1159},
  Volume                   = {92},

  Keywords                 = {Abdominal Wall; Amniotic Fluid; Body Weight; Electrocardiography; Extraembryonic Membranes; Fetal Heart; Infant, Newborn; Labor Presentation; Placenta; Pregnancy; Umbilical Cord},
  Owner                    = {sameni},
  Pmid                     = {14337039},
  Timestamp                = {2008.05.09}
}

@Article{RomeMB08,
  Title                    = {{A comparative study of automatic techniques for ocular artifact reduction in spontaneous {EEG} signals based on clinical target variables: A simulation case}},
  Author                   = {Sergio Romero and Miguel A Ma\~{n}anas and Manel J Barbanoj},
  Journal                  = {Comput. Biol. Med.},
  Year                     = {2008},

  Month                    = {Jan},
  Number                   = {3},
  Pages                    = {348--60},
  Volume                   = {38},

  Abstract                 = {Eye movement artifacts represent a critical issue for quantitative electroencephalography ({EEG}) analysis and a number of mathematical approaches have been proposed to reduce their contribution in {EEG} recordings. The aim of this paper was to objectively and quantitatively evaluate the performance of ocular filtering methods with respect to spectral target variables widely used in clinical and functional {EEG} studies. In particular the following methods were applied: regression analysis and some blind source separation (BSS) techniques based on second-order statistics (PCA, AMUSE and SOBI) and on higher-order statistics (JADE, INFOMAX and FASTICA). Considering blind source decomposition methods, a completely automatic procedure of BSS based on logical rules related to spectral and topographical information was proposed in order to identify the components related to ocular interference. The automatic procedure was applied in different montages of simulated {EEG} and electrooculography (EOG) recordings: a full montage with 19 {EEG} and 2 EOG channels, a reduced one with only 6 {EEG} leads and a third one where EOG channels were not available. Time and frequency results in all of them indicated that AMUSE and SOBI algorithms preserved and recovered more brain activity than the other methods mainly at anterior regions. In the case of full montage: (i) errors were lower than 5\% for all spectral variables at anterior sites; and (ii) the highest improvement in the signal-to-artifact (SAR) ratio was obtained up to 40dB at these anterior sites. Finally, we concluded that second-order BSS-based algorithms (AMUSE and SOBI) provided an effective technique for eye movement removal even when EOG recordings were not available or when data length was short.},
  Doi                      = {10.1016/j.compbiomed.2007.12.001},
  File                     = {RomeMB08.pdf:RomeMB08.pdf:PDF},
  Institution              = {Department of Automatic Control (ESAII), Biomedical Engineering Research Center, Technical University of Catalonia (UPC), 08028 Barcelona, Spain.},
  Owner                    = {Cedric Gouy-Pailler},
  Pii                      = {S0010-4825(07)00185-0},
  Pmid                     = {18222418},
  Timestamp                = {2008.02.03},
  Url                      = {http://dx.doi.org/10.1016/j.compbiomed.2007.12.001}
}

@Article{Kheirati20131453,
  Title                    = {Morphological modeling of cardiac signals based on signal decomposition
},
  Author                   = {Ebadollah Kheirati Roonizi and Reza Sameni},
  Journal                  = {Computers in Biology and Medicine},
  Year                     = {2013},

  Month                    = {October},
  Number                   = {10},
  Pages                    = {1453--1461},
  Volume                   = {43},

  Abstract                 = {Abstract In this paper a general framework is presented for morphological modeling of cardiac signals from a signal decomposition perspective. General properties of a desired morphological model are presented and special cases of the model are studied in detail. The presented approach is studied for modeling the morphology of electrocardiogram (ECG) signals. Specifically, three types of \{ECG\} modeling techniques, including polynomial spline models, sinusoidal model and a model previously presented by McSharry et al., are studied within this framework. The proposed method is applied to datasets from the PhysioNet \{ECG\} database for compression and modeling of normal and abnormal \{ECG\} signals. Quantitative and qualitative results of these applications are also presented and discussed. },
  Doi                      = {http://dx.doi.org/10.1016/j.compbiomed.2013.06.017},
  ISSN                     = {0010-4825}
}

@Article{Rosen84,
  Title                    = {The relationship between circulating catecholamines and ST waveform in the fetal lamb electrocardiogram during hypoxia 3},
  Author                   = {Rosen, KG and Dagbjartsson, A and Henriksson, BA and Lagercrantz, H and Kjellmer, I},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {1984},
  Pages                    = {190-195},
  Volume                   = {149},

  Pubmedid                 = {6720798}
}

@Article{Routray2002,
  Title                    = {A novel Kalman filter for frequency estimation of distorted signals in power systems},
  Author                   = {Routray, A. and Pradhan, A.K. and Rao, K.P.},
  Journal                  = {Instrumentation and Measurement, IEEE Transactions on},
  Year                     = {2002},

  Month                    = {jun},
  Number                   = {3},
  Pages                    = {469 -479},
  Volume                   = {51},

  Doi                      = {10.1109/TIM.2002.1017717},
  ISSN                     = {0018-9456},
  Keywords                 = {distorted signals;extended Kalman filter;filter stability;frequency estimation;harmonics;measurement uncertainty;noisy conditions;nonlinear filter;power system frequency;power system measurement;real-time applications;Kalman filters;electric distortion;filtering theory;frequency estimation;frequency measurement;measurement uncertainty;nonlinear filters;power system harmonics;power system measurement;stability;}
}

@Manual{Sar04,
  Title                    = {{Exploratory source separation in biomedical systems}},
  Author                   = {J. {S\"{a}rel\"{a}}},
  Month                    = {October},
  Note                     = {{PhD Thesis, Helsinki University of Technology}},
  Year                     = {2004},

  Url                      = {http://lib.tkk.fi/Diss/2004/isbn9512273438/}
}

@Article{SV03,
  Title                    = {{Overlearning in marginal distribution-based ICA: analysis and solutions}},
  Author                   = {J. {S\"{a}rel\"{a}} and R. {Vig\'{a}rio}},
  Journal                  = {Journal of machine learning research},
  Year                     = {2003},
  Pages                    = {1447--1469},
  Volume                   = {4},

  Url                      = {http://jmlr.csail.mit.edu/papers/volume4/sarela03a/sarela03a.pdf}
}

@Unpublished{SV03b,
  Title                    = {{A bayesian approach to overlearning in ICA: a comparison study}},
  Author                   = {J. {S\"{a}rel\"{a}} and R. {Vig\'{a}rio}},
  Note                     = {{Technical Report, Helsinki University of Technology}},
  Year                     = {2003},

  Url                      = {www.cis.hut.fi/jaakkos/papers/techrepA70.pdf }
}

@InProceedings{Sameni2012,
  Title                    = {{A Linear Kalman Notch Filter for Power-Line Interference Cancellation}},
  Author                   = {Reza Sameni},
  Booktitle                = {{Proceedings of the 16th CSI International Symposium on Artificial Intelligence and Signal Processing (AISP)}},
  Year                     = {2012},

  Address                  = {Shiraz, Iran},
  Month                    = {2-3 May 2012},
  Pages                    = {604--610},

  Owner                    = {sameni},
  Timestamp                = {2012.10.23}
}

@book{jazwinski1970stochastic,
  title = {Stochastic Processes and Filtering Theory},
  author = {Jazwinski, A.H.},
  publisher = {Elsevier Science},
  year = {1970},
  series = {Mathematics in Science and Engineering},
  isbn = {9780080960906}
}

@Manual{OSET2.1,
  Title                    = {{The Open-Source Electrophysiological Toolbox (OSET), version 2.1}},
  Author                   = {Reza Sameni},
  Year                     = {2010},

  Url                      = {http://www.oset.ir}
}

@Manual{EpidemicModelingCodes,
  Title                    = {{Mathematical Modeling of Epidemic Diseases}},
  Author                   = {Reza Sameni},
  Year                     = {2020},
  Url                      = {https://github.com/rsameni/EpidemicModeling.git}
}

@Manual{OSET,
  Title                    = {{Open-Source ECG Toolbox (OSET)}},
  Author                   = {R. Sameni},
  Note                     = {2nd version},
  Year                     = {2008},

  Url                      = {http://ecg.sharif.ir/}
}

@PhdThesis{Sameni2008,
  Title                    = {{Extraction of Fetal Cardiac Signals from an Array of Maternal Abdominal Recordings}},
  Author                   = {Reza Sameni},
  School                   = {Sharif University of Technology -- Institut National Polytechnique de Grenoble},
  Year                     = {2008},
  Month                    = {July},

  Owner                    = {sameni},
  Timestamp                = {2008.05.08},
  Url                      = {http://www.sameni.info/Publications/Thesis/PhDThesis.pdf}
}

@Unpublished{Sameni2007c,
  Title                    = {{Removing ECG Contaminants from Multichannel Recordings by Deation}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {September},
  Year                     = {2007},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Unpublished{Sameni2007d,
  Title                    = {{Primary Results on Multichannel Fetal ECG Recordings}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {June},
  Year                     = {2007},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Unpublished{Sameni2007e,
  Title                    = {{Multipole Expansion of Body Surface Potentials: An ICA Oriented Formulation (Part I)}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {November},
  Year                     = {2007},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@TechReport{SameniReport151007,
  Title                    = {{A Kalman Notch Filter for Removing Power-Line Noise from Biomedical Signals}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2007},
  Month                    = {October}
}

@TechReport{SameniReport161107,
  Title                    = {{Multipole Expansion of Body Surface Potentials: An ICA Oriented Formulation (Part I)}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2007},
  Month                    = {November},
  Note                     = {{Technical Report}}
}

@TechReport{SameniReport260607,
  Title                    = {{Primary Results on Multichannel Fetal ECG Recordings}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2007},
  Month                    = {June},
  Note                     = {{Technical Report}}
}

@TechReport{SameniReport270907,
  Title                    = {{Removing ECG Contaminants from Multichannel Recordings by Deflation}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2007},
  Month                    = {September}
}

@TechReport{Sameni2006,
  Title                    = {{Writing Efficient Matlab Codes}},
  Author                   = {Reza Sameni},
  Institution              = {{Lecture Notes, Sharif University of Technology}},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2010.03.17}
}

@Unpublished{Sameni2006d,
  Title                    = {{Removing ECG Artifacts from EEG Recordings}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {May},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Unpublished{Sameni2006e,
  Title                    = {{Model-Based Multichannel ECG Filtering}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {December},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Unpublished{Sameni2006f,
  Title                    = {{Primary Results on Multichannel Magnetocardiograms}},
  Author                   = {R. Sameni},
  Note                     = {{Technical Report}},

  Month                    = {November},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Manual{Sameni2006g,
  Title                    = {{Open Source ECG Toolbox (OSET)}},
  Author                   = {R. Sameni},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://ecg.sharif.ir/}
}

@TechReport{SameniReport111106,
  Title                    = {{Primary Results on Multichannel Magnetocardiograms}},
  Author                   = {R. Sameni},
  Institution              = {Sharif University of Technology},
  Year                     = {2006},
  Month                    = {November},
  Note                     = {{Technical Report}}
}

@TechReport{SameniReport201206,
  Title                    = {{Model-Based Multichannel ECG Filtering}},
  Author                   = {R. Sameni},
  Institution              = {Sharif University of Technology},
  Year                     = {2006},
  Month                    = {December},
  Note                     = {{Technical Report}}
}

@TechReport{SameniReport270506,
  Title                    = {{Removing ECG Artifacts from EEG Recordings}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2006},
  Month                    = {May},
  Note                     = {{Technical Report}}
}

@TechReport{Sameni2004,
  Title                    = {{Discrimination of EEG Patterns during the Performance of Different Mental Activities}},
  Author                   = {Reza Sameni},
  Institution              = {{Research Project Report, Sharif University of Technology}},
  Year                     = {2004},

  Owner                    = {sameni},
  Timestamp                = {2010.03.17}
}

@Unpublished{Sameni2004b,
  Title                    = {{Analysis of Iterative Approaches of Interpolation-Distortion Compensation}},
  Author                   = {R. Sameni},
  Note                     = {{DSPII course term paper, Sharif University of Technology}},

  Month                    = {March},
  Year                     = {2004},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@TechReport{SameniTermPaperDSPII,
  Title                    = {{Analysis of Iterative Approaches of Interpolation-Distortion Compensation}},
  Author                   = {R. Sameni},
  Institution              = {GIPSA-LAB, INP-Grenoble},
  Year                     = {2004},
  Month                    = {March},
  Note                     = {{DSPII course term paper, Sharif University of Technology}}
}

@MastersThesis{Sameni2003,
  Title                    = {{Discrimination of EEG Signals during the Performance of Different Mental Tasks}},
  Author                   = {R. Sameni},
  School                   = {Sharif University of Technology},
  Year                     = {2003},

  Owner                    = {sameni},
  Publisher                = {M.Sc. dissertation, Sharif University of Technology},
  Timestamp                = {2012.10.22}
}

@TechReport{Sameni2001,
  Title                    = {{Design and Implementation of a Portable Hotwire Anemometer}},
  Author                   = {Reza Sameni},
  Institution              = {{IROST}},
  Year                     = {2001},
  Month                    = {November},

  Owner                    = {sameni},
  Timestamp                = {2010.03.17}
}

@Article{SameniClifford2010,
  Title                    = {{A Review of Fetal ECG Signal Processing; Issues and Promising Directions}},
  Author                   = {Reza Sameni and Gari D. Clifford},
  Journal                  = {{The Open Pacing, Electrophysiology \& Therapy Journal (TOPETJ)}},
  Year                     = {2010},

  Month                    = {November},
  Pages                    = {4--20},
  Volume                   = {3},

  Doi                      = {10.2174/1876536X01003010004},
  Owner                    = {sameni},
  Timestamp                = {2010.04.10}
}

@Article{SCJS06,
  Title                    = {{Multichannel ECG and Noise Modeling: Application to Maternal and Fetal ECG Signals}},
  Author                   = {R Sameni and G. D. Clifford and C. Jutten and M. B. Shamsollahi},
  Journal                  = {{EURASIP Journal on Advances in Signal Processing}},
  Year                     = {2007},
  Note                     = {{ISSN 1687-6172, doi:10.1155/2007/43407}},
  Pages                    = {{Article ID 43407, 14 pages}},
  Volume                   = {2007}
}

@Conference{SameniAJOG2009,
  Title                    = {{Accuracy of fetal heart rate acquired from sensors on the maternal abdomen compared to a fetal scalp electrode}},
  Author                   = {Reza Sameni and Gari D. Clifford and Jay Ward and Jim Robertson and Courtenay Pettigrew and Adam J. Wolfberg},
  Booktitle                = {{American Journal of Obstetrics and Gynecology}},
  Year                     = {2009},

  Address                  = {Chicago, IL},
  Month                    = {December},
  Number                   = {6},
  Organization             = {{Society for Maternal-Fetal Medicine}},
  Pages                    = {S241--S241},
  Volume                   = {201},

  Owner                    = {sameni},
  Timestamp                = {2011.02.09}
}

@Article{SameniGouyPailler2014,
  Title                    = {{An Iterative Subspace Denoising Algorithm for Removing Electroencephalogram Ocular Artifacts}},
  Author                   = {Reza Sameni and Cedric Gouy-Pailler},
  Journal                  = {Journal of Neuroscience Methods},
  Year                     = {2014},

  Month                    = {March},
  Note                     = {[In Press]},
  Pages                    = {97--105},
  Volume                   = {225},

  Address                  = {l},
  Booktitle                = {Proc. },
  Doi                      = {10.1016/j.jneumeth.2014.01.024},
  Owner                    = {sameni},
  Timestamp                = {2014}
}

@InProceedings{Sameni2012b,
  Title                    = {{An Iterative Subspace Denoising algorithm for Removing Electrocardiogram Ocular Artifact}},
  Author                   = {R. Sameni and C. Gouy-Pailler},
  Booktitle                = {Proc. },
  Year                     = {2012},

  Address                  = {l},

  Owner                    = {sameni},
  Timestamp                = {2012}
}

@TechReport{GouyPailler08,
  Title                    = {{Iterative Subspace Decomposition for Ocular Artifact Removal from EEG Recordings}},
  Author                   = {R. Sameni and C. Gouy-Pailler},
  Institution              = {GIPSA-lab, INP-Grenoble},
  Year                     = {2008},

  Owner                    = {sameni},
  Timestamp                = {2008.04.22}
}

@Patent{patentSameni1_Published,
  Title                    = {{Extraction of Fetal Cardiac Signals}},
  Nationality              = {U.S.},
  Number                   = {{US 2010/0137727 A1}},
  Year                     = {2010},
  Yearfiled                = {2010},
  Author                   = {R. Sameni and C. Jutten and M.B. Shamsollahi and G.D. Clifford},
  Day                      = {3},
  Dayfiled                 = {3},
  Month                    = {June},
  Monthfiled               = {June},

  Owner                    = {sameni},
  Timestamp                = {2009.09.12}
}

@Article{SJS2010,
  Title                    = {{A Deflation Procedure for Subspace Decomposition}},
  Author                   = {R. Sameni and C. Jutten and M. B. Shamsollahi},
  Journal                  = {IEEE Transactions on Signal Processing},
  Year                     = {2010},

  Month                    = {April},
  Number                   = {4},
  Pages                    = {2363--2374},
  Volume                   = {58},

  Owner                    = {sameni},
  Timestamp                = {2009.12.17}
}

@Article{Sameni2008a,
  Title                    = {{Multichannel Electrocardiogram Decomposition using Periodic Component Analysis}},
  Author                   = {R. Sameni and C. Jutten and M. B. Shamsollahi},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2008},

  Month                    = {Aug},
  Number                   = {8},
  Pages                    = {1935--1940},
  Volume                   = {55},

  Abstract                 = {In this letter, we propose the application of the generalized eigenvalue decomposition for the decomposition of multichannel electrocardiogram (ECG) recordings. The proposed method uses a modified version of a previously presented measure of periodicity and a phase-wrapping of the RR-interval, for extracting the “most periodic” linear mixtures of a recorded dataset. It is shown that the method is an improved extension of conventional source separation techniques, specifically customized for ECG signals. The method is therefore of special interest for the decomposition and compression of multichannel ECG, and for the removal of maternal ECG artifacts from fetal ECG recordings. },
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{SJS06,
  Title                    = {{What ICA Provides for {ECG} Processing: Application to Noninvasive Fetal {ECG} Extraction}},
  Author                   = {R. Sameni and C. Jutten and M. B. Shamsollahi},
  Booktitle                = {{Proc. of the International Symposium on Signal Processing and Information Technology (ISSPIT'06)}},
  Year                     = {2006},

  Address                  = {{Vancouver, Canada}},
  Month                    = {August},
  Pages                    = {656--661}
}

@Unpublished{Sameni00,
  Title                    = {{Designing a Training Board for the 8x51 Microcontroller Series}},
  Author                   = {Reza Sameni and Sharifoddin Mansouri},
  Note                     = {{Bachlor's final project, Shiraz University}},

  Month                    = {September},
  Year                     = {2000},

  Owner                    = {sameni},
  Timestamp                = {2010.03.16}
}

@InProceedings{SaSh03,
  Title                    = {{Discrimination of EEG Signals during the Performance of Different Mental Tasks}},
  Author                   = {R. Sameni and M.B Shamsollahi},
  Booktitle                = {Proc. of the World Congress on Medical Physics and Biomedical Engineering},
  Year                     = {2003},

  Address                  = {Sydney, Australia},
  Month                    = {August 24-29},
  Note                     = {[CD-ROM] ISBN 1877040142, Poster Paper No. 4251}
}

@InProceedings{SSJ06,
  Title                    = {{Multi-Channel Electrocardiogram Denoising Using a Bayesian Filtering Framework}},
  Author                   = {R. Sameni and M.B Shamsollahi and C. Jutten},
  Booktitle                = {Proc. of the 33$^{\text{rd}}$ Annual International Conference on Computers in Cardiology},
  Year                     = {2006},

  Address                  = {Valencia, Spain},
  Month                    = {September 17-20},
  Pages                    = {185--188},

  Url                      = {http://cinc.mit.edu/archives/2006/},
  Vol                      = {33}
}

@InProceedings{SSS04,
  Title                    = {{Processing Polysomnographic Signals, using Independent Component Analysis}},
  Author                   = {R. Sameni and M.B Shamsollahi and L. Senhadji},
  Booktitle                = {Proc. Of the International Conference on Biomedical Engineering (BIOMED 2004)},
  Year                     = {2004},

  Address                  = {Innsbruck, Austria},
  Month                    = {February},
  Pages                    = {193-196}
}

@Article{SSJ08,
  Title                    = {{Model-based Bayesian filtering of cardiac contaminants from biomedical recordings}},
  Author                   = {R. Sameni and M. B. Shamsollahi and C. Jutten},
  Journal                  = {Physiological Measurement},
  Year                     = {2008},

  Month                    = {May},
  Number                   = {5},
  Pages                    = {595--613},
  Volume                   = {29},

  Abstract                 = {Electrocardiogram (ECG) and magnetocardiogram (MCG) signals are among the most considerable sources of noise for other biomedical signals. In some recent works, a Bayesian filtering framework has been proposed for denoising the ECG signals. In this paper, it is shown that this framework may be effectively used for removing cardiac contaminants such as the ECG, MCG and ballistocardiographic artifacts from different biomedical recordings such as the electroencephalogram, electromyogram and also for canceling maternal cardiac signals from fetal ECG/MCG. The proposed method is evaluated on simulated and real signals.},
  Doi                      = {10.1088/0967-3334/29/5/006}
}

@InProceedings{SSJ05,
  Title                    = {{Filtering Electrocardiogram Signals Using the Extended Kalman Filter}},
  Author                   = {R. Sameni and M. B. Shamsollahi and C. Jutten},
  Booktitle                = {Proceedings of the 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS)},
  Year                     = {2005},

  Address                  = {Shanghai, China},
  Month                    = {September 1-4},
  Pages                    = {5639--5642}
}

@InProceedings{SSJB05,
  Title                    = {{Filtering Noisy {ECG} Signals Using the Extended {K}alman Filter Based on a Modified Dynamic {ECG} Model}},
  Author                   = {R. Sameni and M. B. Shamsollahi and C. Jutten and M. Babaie-Zadeh},
  Booktitle                = {Proceedings of the 32nd Annual International Conference on Computersin Cardiology},
  Year                     = {2005},

  Address                  = {Lyon, France},
  Month                    = {September 25-28},
  Pages                    = {1017-1020},

  Vol                      = {32}
}

@Article{SSJC06,
  Title                    = {A Nonlinear Bayesian Filtering Framework for {ECG} Denoising},
  Author                   = {R. Sameni and M. B. Shamsollahi and C. Jutten and G. D. Clifford},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2007},

  Month                    = {December},
  Number                   = {12},
  Pages                    = {2172--2185},
  Volume                   = {54},

  No                       = {12},
  Vol                      = {54}
}

@InProceedings{SVPH06,
  Title                    = {{Electrode Selection for Noninvasive Fetal Electrocardiogram Extraction using Mutual Information Criteria}},
  Author                   = {R. Sameni and F. Vrins and F. Parmentier and C. H\'erail and V. Vigneron and M. Verleysen and C. Jutten and M.B Shamsollahi},
  Booktitle                = {Proc. of the 26$^{\text{th}}$ International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2006)},
  Year                     = {2006},

  Address                  = {CNRS, Paris, France},
  Month                    = {July 8-13},
  Pages                    = {97--104},
  Volume                   = {872}
}

@Article{Samonas1997,
  Title                    = {Identification and elimination of cardiac contribution in single-trial magnetoencephalographic signals.},
  Author                   = { M. Samonas and M. Petrou and A. A. Ioannides},
  Journal                  = {{IEEE Trans Biomed Eng}},
  Year                     = {1997},
  Pages                    = {386-393},
  Volume                   = {44},

  No                       = {5},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{SaulA00,
  Title                    = {{Periodic Component Analysis: An Eigenvalue Method for Representing Periodic Structure in Speech}},
  Author                   = {Lawrence K. Saul and Jont B. Allen},
  Booktitle                = {NIPS},
  Year                     = {2000},
  Pages                    = {807-813},

  Url                      = {http://www.cs.cmu.edu/Groups/NIPS/00papers-pub-on-web/SaulAllen.pdf}
}

@Article{SavitzkyGolay1964,
  Title                    = {Smoothing and Differentiation of Data by Simplified Least Squares Procedures.},
  Author                   = {Savitzky, Abraham. and Golay, M. J. E.},
  Journal                  = {Analytical Chemistry},
  Year                     = {1964},
  Number                   = {8},
  Pages                    = {1627-1639},
  Volume                   = {36},

  Doi                      = {10.1021/ac60214a047}
}

@InProceedings{Sayadi2007,
  Title                    = {{ECG Denoising Using Parameters of ECG Dynamical Model as the States of an Extended Kalman Filter}},
  Author                   = {Sayadi, O. and Sameni, R. and Shamsollahi, M.B.},
  Booktitle                = {Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE},
  Year                     = {2007},
  Month                    = {Aug.},
  Pages                    = {2548--2551},

  Abstract                 = {In this paper an efficient filtering procedure based on the extended Kalman filter (EKF) has been proposed. The method is based on a modified nonlinear dynamic model, previously introduced for the generation of synthetic ECG signals. We have suggested simple dynamics as the governing equations for the model parameters. Since we have not any observation for these new state variables, they are considered as hidden states. Quantitative evaluation of the proposed algorithm on the MIT-BIH signals shows that an average SNR improvement of 12 dB is achieved for a signal of -5 dB. The results show improved output SNRs compared to the EKF outputs in the absence of these new dynamics.},
  Doi                      = {10.1109/IEMBS.2007.4352848},
  ISSN                     = {1557-170X},
  Keywords                 = {Biomedical measurements;Electrocardiography;Equations;Filtering;Noise measurement;Noise reduction;Nonlinear dynamical systems;Nonlinear systems;Pollution measurement;Signal generators;Kalman filters;electrocardiography;medical signal processing;signal denoising;ECG denoising;ECG dynamical model;electrocardiogram;extended Kalman filter;hidden states;modified nonlinear dynamic model;ECG dynamical model;Extended Kalman filter;Hidden state variable;}
}

@Article{Sayadi2008,
  Title                    = {ECG Denoising and Compression Using a Modified Extended Kalman Filter Structure},
  Author                   = {Sayadi, O. and Shamsollahi, M.B.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2008},

  Month                    = {sept. },
  Number                   = {9},
  Pages                    = {2240 -2248},
  Volume                   = {55},

  Abstract                 = {This paper presents efficient denoising and lossy compression schemes for electrocardiogram (ECG) signals based on a modified extended Kalman filter (EKF) structure. We have used a previously introduced two-dimensional EKF structure and modified its governing equations to be extended to a 17-dimensional case. The new EKF structure is used not only for denoising, but also for compression, since it provides estimation for each of the new 15 model parameters. Using these specific parameters, the signal is reconstructed with regard to the dynamical equations of the model. The performances of the proposed method are evaluated using standard denoising and compression efficiency measures. For denosing, the SNR improvement criterion is used, while for compression, we have considered the compression ratio (CR), the percentage area difference (PAD), and the weighted diagnostic distortion (WDD) measure. Several Massachusetts Institute of Technology-Beth Israel Deaconess Medical Center (MIT-BIH) ECG databases are used for performance evaluation. Simulation results illustrate that both applications can contribute to and enhance the clinical ECG data denoising and compression performance. For denoising, an average SNR improvement of 10.16 dB was achieved, which is 1.8 dB more than the next benchmark methods such as MAB WT or EKF2. For compression, the algorithm was extended to include more than five Gaussian kernels. Results show a typical average CR of 11.37:1 with WDD lt; 1.73 %. Consequently, the proposed framework is suitable for a hybrid system that integrates these algorithmic approaches for clean ECG data storage or transmission scenarios with high output SNRs, high CRs, and low distortions.},
  Doi                      = {10.1109/TBME.2008.921150},
  ISSN                     = {0018-9294},
  Keywords                 = {ECG denoising;EKF structure;Massachusetts Institute of Technology-Beth Israel Deaconess Medical Center;electrocardiogram signals;hybrid system;lossy image compression;modified extended Kalman filter structure;performance evaluation;weighted diagnostic distortion;Kalman filters;data compression;electrocardiography;image denoising;medical image processing;Algorithms;Artifacts;Data Compression;Diagnosis, Computer-Assisted;Electrocardiography;Models, Neurological;Signal Processing, Computer-Assisted;}
}

@Article{Sayadi2010,
  Title                    = {Robust Detection of Premature Ventricular Contractions Using a Wave-Based Bayesian Framework},
  Author                   = {Sayadi, O. and Shamsollahi, M.B. and Clifford, G.D.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2010},

  Month                    = {feb. },
  Number                   = {2},
  Pages                    = {353 -362},
  Volume                   = {57},

  Doi                      = {10.1109/TBME.2009.2031243},
  ISSN                     = {0018-9294},
  Keywords                 = {ECG;Holter monitoring;MIT-BIH arrhythmia database;aggregate positive predictivity;aggregate sensitivity;characteristic waveforms;clinical PVC detection;covariance matrix;critical care patient monitoring;dangerous heart condition diagnosis;extended Kalman filter;life-threatening arrhythmias;model-based dynamic algorithm;normal sinus beats;polar envelope;polar signal representation;polargram;premature ventricular contractions;signal fidelity;ventricular complex classification;ventricular complex detection;wave-based Bayesian framework;Kalman filters;belief networks;cardiovascular system;covariance matrices;electrocardiography;patient care;patient monitoring;physiological models;waveform analysis;}
}

@Article{ScharfMcCloud2002,
  Title                    = {Blind adaptation of zero forcing projections and oblique pseudo-inverses for subspace detection and estimation when interference dominates noise},
  Author                   = {Scharf, L.L. and McCloud, M.L.},
  Journal                  = IEEE_J_SP,
  Year                     = {2002},

  Month                    = {December},
  Number                   = {12},
  Pages                    = {2938 -- 2946},
  Volume                   = {50},

  Abstract                 = {In much of modern radar, sonar, and wireless communication, it seems more reasonable to model "measurement noise" as subspace interference-plus-broadband noise than as colored noise. This observation leads naturally to a variety of detection and estimation problems in the linear statistical model. To solve these problems, one requires oblique pseudo-inverses, oblique projections, and zero-forcing orthogonal projections. The problem is that these operators depend on knowledge of signal and interference subspaces, and this information is often not at hand. More typically, the signal subspace is known, but the interference subspace is unknown. We prove a theorem that allows these operators to be estimated directly from experimental data, without knowledge of the interference subspace. As a byproduct, the theorem shows how signal subspace covariance may be estimated. When the strict identities of the theorem are approximated, then the detectors, estimators, and beamformers of this paper take on the form of adaptive subspace estimators, detectors, and Capon beamformers, all of which are reduced in rank. The fundamental operator turns out to be a certain reduced-rank Wiener filter, which we clarify in the course of our derivations. The results of this paper form a foundation for the rapid adaptation of receivers that are then used for detection and estimation. They may be applied to detection and estimation in radar, sonar, and hyperspectral imaging and to data decoding in multiuser communication receivers.},
  Owner                    = {sameni},
  Timestamp                = {2009.02.14}
}

@Book{schiff2008cellular,
  Title                    = {Cellular automata: a discrete view of the world},
  Author                   = {Schiff, Joel L},
  Publisher                = {John Wiley \& Sons},
  Year                     = {2008}
}

@Article{SchlKZSLP07,
  Title                    = {A fully automated correction method of {EOG} artifacts in {EEG} recordings.},
  Author                   = {A. Schl\"{o}gl and C. Keinrath and D. Zimmermann and R. Scherer and R. Leeb and G. Pfurtscheller},
  Journal                  = {Clin. Neurophysiol.},
  Year                     = {2007},

  Month                    = {Jan},
  Number                   = {1},
  Pages                    = {98--104},
  Volume                   = {118},

  Abstract                 = {OBJECTIVE: A fully automated method for reducing EOG artifacts is presented and validated. METHODS: The correction method is based on regression analysis and was applied to 18 recordings with 22 channels and approx. 6 min each. Two independent experts scored the original and corrected EEG in a blinded evaluation. RESULTS: The expert scorers identified in 5.9\% of the raw data some EOG artifacts; 4.7\% were corrected. After applying the EOG correction, the expert scorers identified in another 1.9\% of the data some EOG artifacts, which were not recognized in the uncorrected data. CONCLUSIONS: The advantage of a fully automated reduction of EOG artifacts justifies the small additional effort of the proposed method and is a viable option for reducing EOG artifacts. The method has been implemented for offline and online analysis and is available through BioSig, an open source software library for biomedical signal processing. SIGNIFICANCE: Visual identification and rejection of EOG-contaminated EEG segments can miss many EOG artifacts, and is therefore not sufficient for removing EOG artifacts. The proposed method was able to reduce EOG artifacts by 80\%.},
  Doi                      = {10.1016/j.clinph.2006.09.003},
  File                     = {SchlKZSLP07.pdf:SchlKZSLP07.pdf:PDF},
  Institution              = {Institute of Human-Computer Interfaces, Graz University of Technology, Krenngasse 37/IV, A-8010 Graz, Austria. alois.schloegl@tugraz.at},
  Keywords                 = {Adolescent; Adult; Artifacts; Brain; Brain Mapping; Electroencephalography; Electrooculography; Female; Humans; Male; Reproducibility of Results; Signal Processing, Computer-Assisted},
  Owner                    = {Cedric Gouy-Pailler},
  Pii                      = {S1388-2457(06)01431-3},
  Pmid                     = {17088100},
  Timestamp                = {2008.02.19},
  Url                      = {http://dx.doi.org/10.1016/j.clinph.2006.09.003}
}

@Conference{Schneider2004,
  Title                    = {{libRASCH: a programming framework for signal handling}},
  Author                   = {Schneider, R. and Bauer, A. and Barthel, P. and Schmidt, G.},
  Booktitle                = {Computers in Cardiology, 2004},
  Year                     = {19-22 Sept. 2004},
  Pages                    = {53-56},

  Doi                      = {10.1109/CIC.2004.1442869},
  ISSN                     = { },
  Keywords                 = { C language, Linux, Web sites, electrocardiography, libraries, medical information systems, medical signal processing, programming languages, user interfaces ECG, EDF(+), Linux, MIT-BIH, Windows, computer program, continuous blood pressure recording, data formats, file formats, libRASCH, mandatory, physiological signal, plugin mechanism, processed data, programming framework, programming languages, programming library, raw signal data, signal handling, source code, web-site, www.librasch.org}
}

@Article{Schneider2001,
  Title                    = {Signal analysis of auditory evoked cortical fields in fetal magnetoencephalography.},
  Author                   = {Schneider, U. and Schleussner, E. and Haueisen, J. and Nowak, H. and Seewald, H.J.},
  Journal                  = {Brain Topogr},
  Year                     = {2001},
  Number                   = {1},
  Pages                    = {69-80},
  Volume                   = {14},

  Abstract                 = {Magnetoencephalography (MEG) using auditory evoked cortical fields (AEF) is an absolutely non-invasive method of passive measurement which utilizes magnetic fields caused by specific cortical activity. By applying the exceptionally sensitive SQUID technology to record these fields of dipolar configuration produced by the fetal brain, MEG as an investigational tool could provide new insights into the development of the human brain in utero. The major constraint to this application is a very low signal-to-noise ratio (SNR) that has to be attributed to a variety of factors including the magnetic signals generated by the fetal and maternal hearts which inevitably obscure a straightforward signal analysis. By applying a new algorithm of specific heart artefact reduction based on the relative regularity of the heart signals, we were able to increase the chance of extracting a fetal AEF from the raw data by the means of averaging techniques and principle component analysis. Results from 27 pregnant, healthy women (third trimester of their uncomplicated pregnancy) indicate an improved detection rate and the reproducibility of the fetal MEG. We evaluate and discuss a-priori criteria for signal analyses which will enable us to systematically analyze additional limiting factors, to further enhance the efficiency of this method and to promote the assessment of its possible clinical value in the future.},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{schreiberk96,
  Title                    = {Nonlinear noise reduction for electrocardiograms},
  Author                   = {Schreiber, T. and Kaplan, D. T..},
  Journal                  = {Chaos},
  Year                     = {1996},
  Number                   = {1},
  Pages                    = {87-92},
  Volume                   = {6}
}

@Article{SK96a,
  Title                    = {{Signal separation by nonlinear projections: The fetal electrocardiogram}},
  Author                   = {T. Schreiber and D. T. Kaplan},
  Journal                  = {Phys. Rev. E.},
  Year                     = {1996},
  Pages                    = {R4326- R4329},
  Volume                   = {53},

  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Sedlacek2004,
  Title                    = {Low uncertainty power-line frequency estimation for distorted and noisy harmonic signals},
  Author                   = {M. Sedlacek and J. Blaska},
  Journal                  = {Measurement},
  Year                     = {2004},
  Number                   = {1},
  Pages                    = {97 - 107},
  Volume                   = {35},

  Abstract                 = {The paper presents a comparison of four methods of instantaneous power-line frequency estimation. Comparison is performed from the point-of-view of the methodsâ€™ sensitivity to higher-order harmonic content and to the additive noise and from the point-of-view of their response time. The compared methods are zero crossing with pre-filtration, integrated zero crossing, windowed and interpolated FFT, and dynamic parameter estimation with pre-filtration. Comparison is based on computer simulations.},
  Doi                      = {10.1016/j.measurement.2003.08.013},
  ISSN                     = {0263-2241},
  Keywords                 = {Power-line frequency measurement},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0263224103000952}
}

@Article{Sekihara1996,
  Title                    = {{Generalized Wiener estimation of three-dimensional current distribution from biomagnetic measurements}},
  Author                   = {Sekihara, K. and Scholz, B.},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {1996},
  Number                   = {3},
  Pages                    = {281-91},
  Volume                   = {43},

  Abstract                 = {This paper proposes a method for estimating three-dimensional (3-D) biocurrent distribution from spatio-temporal biomagnetic data. This method is based on the principle of generalized Wiener estimation, and it is formulated based on the assumption that current sources are uncorrelated. Computer simulation demonstrates that the proposed method can reconstruct a 3-D current distribution where the conventional least-squares minimum-norm method fails. The influence of noise is also simulated, and the results indicate that a signal-to-noise ratio of more than 20 for the uncorrelated sensor noise is needed to implement the proposed method. The calculated point spread function shows that the proposed method has very high spatial resolution compared to the conventional minimum norm method. The results of computer simulation of the distributed current sources are also presented, including cases where current sources are correlated. These results suggest that no serious errors arise if the source correlation is weak.},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Manual{Sexton2005,
  Title                    = {{Fetal blood flow}},
  Author                   = {M. J. Sexton and L. A. Latson},
  Month                    = {October},
  Organization             = {Healthwise, Inc.},
  Year                     = {2005},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.10},
  Url                      = {http://www.memorialhermann.org/}
}

@Article{Shao2004,
  Title                    = {{An interference cancellation algorithm for noninvasive extraction of transabdominal fetal electroencephalogram (TaFEEG)}},
  Author                   = {Shao, Min and Barner, K.E. and Goodman, M.H.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2004},
  Number                   = {3},
  Pages                    = {471--483},
  Volume                   = {51},

  Doi                      = {10.1109/TBME.2003.821011},
  Editor                   = {Barner, K.E.},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, electroencephalography, interference (signal), iterative methods, obstetrics, FECG, cerebral function, cerebral palsy, electroencephalogram, fetal electroencephalogram, interference cancellation algorithm, interfering baseline wander, maternal ECG, mental retardation syndromes, multistep extraction procedure, noninvasive extraction, transabdominal fetal electroencephalogram},
  Owner                    = {sameni},
  Timestamp                = {2008.04.30}
}

@Article{Shao2004a,
  Title                    = {An interference cancellation algorithm for noninvasive extraction of transabdominal fetal electroencephalogram (TaFEEG) },
  Author                   = {Min Shao and K.E.Barner and M.H.Goodman},
  Journal                  = {{IEEE Trans Biomed Eng}},
  Year                     = {2004},
  Pages                    = {471-483},
  Volume                   = {51},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Shepovalnikov2006,
  Title                    = {{Investigation of time, amplitude, and frequency parameters of a direct fetal ECG signal during labor and delivery}},
  Author                   = {R. A. {Shepoval'nikov} and A. P. Nemirko and A. N. Kalinichenko and V. V. Abramchenko},
  Journal                  = {{Pattern Recognition and Image Analysis}},
  Year                     = {2006},

  Month                    = {January},
  Number                   = {1},
  Pages                    = {74--76},
  Volume                   = {16},

  Doi                      = {10.1134/S1054661806010238},
  Owner                    = {sameni},
  Timestamp                = {2009.06.06}
}

@Article{Shono94,
  Title                    = {{Fetal heart rate recorder for long-duration use in active full-term pregnant women}},
  Author                   = {Hideaki Shono and Masami Muro and Mayumi Kohara and Yuji Ito and Takashi Nagasawa and Hajime Sugimori},
  Journal                  = {{Obstetrics \& Gynecology}},
  Year                     = {1994},
  Pages                    = {301--6},
  Volume                   = {83},

  Owner                    = {sameni},
  Timestamp                = {2009.12.07}
}

@Article{Signorini2003,
  Title                    = {Linear and nonlinear parameters for the analysis of fetal heart rate signal from cardiotocographic recordings.},
  Author                   = {Maria G Signorini and Giovanni Magenes and Sergio Cerutti and Domenico Arduini},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2003},

  Month                    = {Mar},
  Number                   = {3},
  Pages                    = {365--374},
  Volume                   = {50},

  Abstract                 = {Antepartum fetal monitoring based on the classical cardiotocography (CTG) is a noninvasive and simple tool for checking fetal status. Its introduction in the clinical routine limited the occurrence of fetal problems leading to a reduction of the precocious child mortality. Nevertheless, very poor indications on fetal pathologies can be inferred from the even automatic CTG analysis methods, which are actually employed. The feeling is that fetal heart rate (FHR) signals and uterine contractions carry much more information on fetal state than is usually extracted by classical analysis methods. In particular, FHR signal contains indications about the neural development of the fetus. However, the methods actually adopted for judging a CTG trace as "abnormal" give weak predictive indications about fetal dangers. We propose a new methodological approach for the CTG monitoring, based on a multiparametric FHR analysis, which includes spectral parameters from autoregressive models and nonlinear algorithms (approximate entropy). This preliminary study considers 14 normal fetuses, eight cases of gestational (maternal) diabetes, and 13 intrauterine growth retarded fetuses. A comparison with the traditional time domain analysis is also included. This paper shows that the proposed new parameters are able to separate normal from pathological fetuses. Results constitute the first step for realizing a new clinical classification system for the early diagnosis of most common fetal pathologies.},
  Doi                      = {10.1109/TBME.2003.808824},
  Institution              = {Dipartimento di Bioingegneria, University Politecnico di Milan, 20133 Milano, Italy. signorini@biomed.polimi.it},
  Keywords                 = {Algorithms; Cardiotocography; Diabetes, Gestational; Diagnosis, Computer-Assisted; Female; Fetal Growth Retardation; Fetal Monitoring; Fetal Movement; Heart Rate; Heart Rate, Fetal; Humans; Linear Models; Models, Cardiovascular; Nonlinear Dynamics; Pregnancy; Quality Control; Regression Analysis; Reproducibility of Results; Retrospective Studies; Sensitivity and Specificity},
  Owner                    = {sameni},
  Pmid                     = {12669993},
  Timestamp                = {2008.04.30},
  Url                      = {http://dx.doi.org/10.1109/TBME.2003.808824}
}

@InProceedings{MoodyCINC2013,
  Title                    = {{Noninvasive Fetal ECG: the PhysioNet/Computing in Cardiology Challenge 2013}},
  Author                   = {Ikaro Silva and Joachim Behar and Reza Sameni and Tingting Zhu and Julien Oster and Gari D. Clifford and George B. Moody},
  Booktitle                = {Proceedings of the 40th Annual International Conference on Computersin Cardiology},
  Year                     = {2013},

  Address                  = {Zaragoza, Spain},
  Month                    = {September 22-25},
  Pages                    = {149--152},

  Vol                      = {40}
}

@Book{SIMON2006,
  Title                    = {{Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches}},
  Author                   = {Dan Simon},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2006}
}

@Article{Snowden2001,
  Title                    = {A digital system for recording the electrical activity of the uterus.},
  Author                   = {S. Snowden and N. A. Simpson and J. J. Walker},
  Journal                  = {Physiol Meas},
  Year                     = {2001},

  Month                    = {Nov},
  Number                   = {4},
  Pages                    = {673--679},
  Volume                   = {22},

  Abstract                 = {The ability to identify true pre-term labour would be of considerable clinical benefit as electrical signals from the uterus, recorded using surface electrodes, may discriminate between labouring and non-labouring states in human pregnancy. A digital recording system for recording the electrical activity of the uterus has been developed and is described in this paper. A pilot study in which entire recordings in 21 women were subjected to power spectral analysis suggests that the relative power in two frequency bands (0.2-0.45 Hz and 0.8-3 Hz) changes as pregnancy progresses into early labour.},
  Institution              = {Department of Medical Physics and Engineering, Leeds Teaching Hospitals, UK. s.snowden@leeds.ac.uk},
  Keywords                 = {Adult; Algorithms; Amplifiers; Data Collection; Electrodes; Electromyography; Electrophysiology; Female; Fourier Analysis; Humans; Labor, Obstetric; Obstetric Labor, Premature; Pregnancy; Signal Processing, Computer-Assisted; Uterus},
  Owner                    = {sameni},
  Pmid                     = {11761075},
  Timestamp                = {2008.05.12}
}

@Article{Sornmo1998,
  Title                    = {Vectorcardiographic loop alignment and morphologic beat-to-beat variability},
  Author                   = {Sornmo, L.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1998},

  Month                    = {December},
  Number                   = {12},
  Pages                    = {1401-1413},
  Volume                   = {45},

  Abstract                 = {The measurement of subtle morphologic beat-to-beat variations in the electrocardiogram is complicated by the presence of respiration-induced movements of the heart. A statistical signal model is developed which accounts for such movements by means of scaling, rotation, and time synchronization of vector-cardiographic loops. The maximum-likelihood estimator of the parameters describing these three transformations is presented and is extended to the case of multiple loop alignment. The performance of the method is assessed by measuring morphologic variability before and after loop alignment. It is shown that the effects of respiration on morphologic variability can be considerably reduced by the new method. Measurements on morphologic variability were typically reduced by a factor of 0.53 after loop alignment. The results show also that beat-to-beat measurements are strongly dependent on the selected sampling rate and that a rate of 1 kHz is too low},
  Doi                      = {10.1109/10.730434},
  ISSN                     = {0018-9294},
  Keywords                 = {electrocardiography, maximum likelihood estimation, medical signal processing, physiological models1 kHz, ECG analysis, electrodiagnostics, maximum-likelihood estimator, morphologic QRS variability, respiration effects, respiration-induced heart movements, rotation, sampling rate, scaling, subtle morphologic beat-to-beat variations, time synchronization, vectorcardiographic loop alignment}
}

@Article{Spencer1992,
  Title                    = {Adaptive filters for monitoring localized brain activity from surface potential time series},
  Author                   = {Spencer,M. E. and Leahy,R. M. and Mosher,J. C. and Lewis,P. S.},
  Journal                  = {26th Asilomar Conf. Signals, Systems, and Computers},
  Year                     = {1992},
  Pages                    = {156â€“161},
  Volume                   = {1},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Srivastava05,
  Title                    = {{ICA-based procedures for removing ballistocardiogram artifacts from EEG data acquired in the MRI scanner}},
  Author                   = {G. Srivastava and S. Crottaz-Herbette K.M Lau and G.H Glover and V. Menon},
  Journal                  = {Neuroimage},
  Year                     = {2005},

  Month                    = {Jan},
  Number                   = {1},
  Pages                    = {50--60},
  Volume                   = {24},

  Abstract                 = {Electroencephalogram (EEG) data acquired in the MRI scanner contains significant artifacts, one of the most prominent of which is ballistocardiogram (BCG) artifact. BCG artifacts are generated by movement of EEG electrodes inside the magnetic field due to pulsatile changes in blood flow tied to the cardiac cycle. Independent Component Analysis (ICA) is a statistical algorithm that is useful for removing artifacts that are linearly and independently mixed with signals of interest. Here, we demonstrate and validate the usefulness of ICA in removing BCG artifacts from EEG data acquired in the MRI scanner. In accordance with our hypothesis that BCG artifacts are physiologically independent from EEG, it was found that ICA consistently resulted in five to six independent components representing the BCG artifact. Following removal of these components, a significant reduction in spectral power at frequencies associated with the BCG artifact was observed. We also show that our ICA-based procedures perform significantly better than noise-cancellation methods that rely on estimation and subtraction of averaged artifact waveforms from the recorded EEG. Additionally, the proposed ICA-based method has the advantage that it is useful in situations where ECG reference signals are corrupted or not available.}
}

@Article{SDMS98,
  Title                    = {{{ECG} analysis using nonlinear PCA neural networks for ischemia detection}},
  Author                   = {T. Stamkopoulos and K. Diamantaras and N. Maglaveras and M. Strintzis},
  Journal                  = IEEE_J_SP,
  Year                     = {1998},

  Month                    = {Nov.},
  Pages                    = {3058-3067},
  Volume                   = {46},

  No                       = {11}
}

@PhdThesis{Stinstra2001,
  Title                    = {Reliability of the fetal magnetocardiogram},
  Author                   = {J.G. Stinstra},
  School                   = {University of Twente, Enschede, The Netherlands},
  Year                     = {2001},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29},
  Url                      = {http://doc.utwente.nl/35964/}
}

@Article{stogbauer-2004-70,
  Title                    = {Least Dependent Component Analysis Based on Mutual Information},
  Author                   = {Harald Stogbauer and Alexander Kraskov and Sergey A. Astakhov and Peter Grassberger},
  Journal                  = {Physical Review E},
  Year                     = {2004},
  Pages                    = {066123},
  Volume                   = {70},

  Url                      = {doi:10.1103/PhysRevE.70.066123}
}

@Book{Strang1988,
  Title                    = {Linear Algebra and Its Applications},
  Author                   = {Gilbert Strang},
  Publisher                = {Brooks/Cole},
  Year                     = {1988},
  Edition                  = {3},

  Keywords                 = {MATHtext}
}

@Book{Stratton1941,
  Title                    = {{Electromagnetic Theory}},
  Author                   = {J.A. Stratton},
  Publisher                = {McGraw-Hill Book Company Inc.},
  Year                     = {1941}
}

@Article{Strobach1994,
  Title                    = {Event-synchronous cancellation of the heart interference in biomedical signals},
  Author                   = {Strobach, P. and Abraham-Fuchs, K. and Harer, W.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1994},

  Month                    = {april },
  Number                   = {4},
  Pages                    = {343 -350},
  Volume                   = {41},

  Abstract                 = {A two-pass adaptive filtering algorithm is proposed for cancellation of recurrent interferences such as the heart interference in biomedical signals. In the first pass, an average waveform in one period of the interference is estimated by event-synchronous (QRS-synchronous) averaging of the corrupted signal. In a second pass, an adaptive Schur recursive least squares (RLS) lattice filter is used to cancel the interference by using the event synchronously repeated estimated average waveform of the interference as an artificial reference signal. One key feature of this approach is that the ECG is only used for QRS synchronization and not directly as a reference signal for adaptive filtering. Thus the proposed algorithm can be applied to interference problems where ECG and true interference are almost synchronous but show considerably different waveforms. This is usually the case with the heart interference in biomedical signals. Both off-line and real-time implementations of the event synchronous interference canceller are described. The method is applied to the cancellation of the heart interference in magnetoencephalogram (MEG) signals and to the effective isolation of ventricular extrasystoles (VES) in magnetocardiogram (MCG) signals. Experimental results are shown. The new method typically attenuates the amplitudes of R-wave and T-wave interference components by an amplitude factor of 30 without influencing the MEG events of interest.},
  Doi                      = {10.1109/10.284962},
  ISSN                     = {0018-9294},
  Keywords                 = {2-pass adaptive filtering algorithm;QRS synchronization;R-wave interference;T-wave interference;adaptive Schur recursive least squares lattice filter;artificial reference signal;biomedical signals;event-synchronous averaging;event-synchronous cancellation;heart interference;magnetocardiogram;magnetoencephalogram;ventricular extrasystoles isolation;biomagnetism;brain;cardiology;electrocardiography;interference (signal);medical signal processing;Algorithms;Artifacts;Electrocardiography;Humans;Least-Squares Analysis;Magnetoencephalography;Models, Cardiovascular;Signal Processing, Computer-Assisted;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Misc{CharlesSullivan,
  Title                    = {{Systems Course (ENGS 22)}},

  Author                   = {Charles Sullivan},
  Year                     = {2014},

  Publisher                = {{Thayer School of Engineering, Dartmouth College}},
  Url                      = {http://www.dartmouth.edu/~sullivan/engs22.html}
}

@Article{Sureau60,
  Title                    = {Electrocardiographie foetale humaine normale},
  Author                   = {Sureau, C.},
  Journal                  = {Bull. Soc. Roy. Belg. Gynec. Obstet.},
  Year                     = {1960},
  Number                   = {2},
  Pages                    = {123--151},
  Volume                   = {30}
}

@Article{Sur97,
  Title                    = {{Additive noise effect in digital phase detection}},
  Author                   = {Y. Surrel},
  Journal                  = {Applied Optics},
  Year                     = {1997},
  Pages                    = {271-276},
  Volume                   = {36},

  No                       = {1}
}

@Article{Swami94,
  Title                    = {{Multichannel ARMA processes}},
  Author                   = {Swami, A. and Giannakis, G. and Shamsunder, S.},
  Journal                  = {Signal Processing, IEEE Transactions on [see also Acoustics, Speech, and Signal Processing, IEEE Transactions on]},
  Year                     = {1994},

  Month                    = {April},
  Number                   = {4},
  Pages                    = {898-913},
  Volume                   = {42},

  Doi                      = {10.1109/78.285653},
  ISSN                     = {1053-587X},
  Keywords                 = {linear systems, matrix algebra, parameter estimation, signal processing, stochastic processes, time seriesKronecker product formulation, causal ARMA models, colored Gaussian noise, cumulant matching algorithm, frequency-domain methods, higher order statistics, linear equations, multichannel ARMA processes, multichannel time series, multiminimum phase assumption, nonparametric system identification, observed nonGaussian data, parameter estimation, parametric modeling, permutation matrix, postmultiplication, vector processes}
}

@Book{Szirtes2007,
  Title                    = {Applied Dimensional Analysis and Modeling},
  Author                   = {Szirtes, T.},
  Publisher                = {Elsevier Science},
  Year                     = {2007},

  ISBN                     = {9780080555454},
  Owner                    = {sameni},
  Timestamp                = {2014.02.16}
}

@Article{TGR06,
  Title                    = {{Time-varying analysis of heart rate variability signals with a {K}alman smoother algorithm}},
  Author                   = {M. P. Tarvainen and S. D. Georgiadis and P. O. Ranta-aho and P. A. Karjalainen},
  Journal                  = {Physiol. Meas.},
  Year                     = {2006},

  Month                    = {Mar.},
  Pages                    = {225-239},
  Volume                   = {27},

  No                       = {3}
}

@InProceedings{Tavakoli2006,
  Title                    = {{Audio Watermarking for Covert Communication through Telephone System}},
  Author                   = {Tavakoli, E. and Vahdat, B.V. and Shamsollahi, M.B. and Sameni, R.},
  Booktitle                = {IEEE International Symposium on Signal Processing and Information Technology, 2006},
  Year                     = {2006},
  Month                    = {Aug.},
  Pages                    = {955--959},

  Doi                      = {10.1109/ISSPIT.2006.270935},
  Journal                  = {Signal Processing and Information Technology, 2006 IEEE International Symposium on}
}

@Article{TST03,
  Title                    = {{Non-invasive fetal electrocardiography in singleton and multiple pregnancies}},
  Author                   = {M. J. O. Taylor and M. J. Smith and M. Thomas and A. R. Green and F. Cheng and S. Oseku-Afful and L. Y. Wee and N. M. Fisk and H. M. Gardiner},
  Journal                  = {BJOG: an International Journal of Obstetrics and Gynaecology},
  Year                     = {2003},

  Month                    = {Jul.},
  Pages                    = {668--678},
  Volume                   = {110}
}

@Article{terBrake2002,
  Title                    = {{Fetal magnetocardiography: clinical relevance and feasibility}},
  Author                   = {H.J.M. {ter Brake} and A.P. Rijpma and J.G. Stinstra and J. Borgmann and H.J. Holland and H.J.G. Krooshoop and M.J. Peters and J. Flokstra and H.W.P. Quartero and H. Rogalla},
  Journal                  = {Physica C},
  Year                     = {2002},

  Month                    = {March},
  Pages                    = {10--17},
  Volume                   = {368},

  Doi                      = {doi:10.1016/S0921-4534(01)01132-7},
  Url                      = {http://www.ingentaconnect.com/content/els/09214534/2002/00000368/00000001/art01132}
}

@Article{Thakor1991,
  Title                    = {{Application of adaptive filtering to ECG analysis{:} noise cancellation and arrhythmia detection}},
  Author                   = {N. V. Thakor and Y. S. Zhu},
  Journal                  = IEEE_J_BME,
  Year                     = {1991},
  Pages                    = {785-794},
  Volume                   = {38},

  No                       = {8},
  Owner                    = {sameni},
  Timestamp                = {2014.02.16}
}

@Article{TZ91,
  Title                    = {{Application of adaptive filtering to ECG analysis{:} noise cancellation and arrhythmia detection}},
  Author                   = {N. V. Thakor and Y. S. Zhu},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1991},
  Pages                    = {785-794},
  Volume                   = {38},

  No                       = {8}
}

@InProceedings{Thameri2012,
  Title                    = {{New Algorithm For Adaptive BSS}},
  Author                   = {Thameri, M. and AbedMeraim, K. and Belouchrani, A.},
  Booktitle                = {Proceedings of the 11th International Conference on Information Science, Signal Processing and their Applications (ISSPA), 2012},
  Year                     = {2012},
  Pages                    = {590--594},

  Journal                  = {ISSPI},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InProceedings{Thameri2011,
  Title                    = {Fast principal component analysis and data whitening algorithms},
  Author                   = {Thameri, M. and Kammoun, A. and Abed-Meraim, K. and Belouchrani, A.},
  Booktitle                = {Systems, Signal Processing and their Applications (WOSSPA), 2011 7th International Workshop on},
  Year                     = {2011},
  Month                    = {may},
  Pages                    = {139 -142},

  Doi                      = {10.1109/WOSSPA.2011.5931434},
  Keywords                 = {PCA algorithm;data whitening algorithms;fast principal component analysis;fast-convergent algorithm;principal component extraction;principal subspace;signal processing technique;principal component analysis;signal processing;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@InCollection{Theis2010,
  Title                    = {Robust Second-Order Source Separation Identifies Experimental Responses in Biomedical Imaging},
  Author                   = {Theis, Fabian and M{\"u}ller, Nikola and Plant, Claudia and B{\"o}hm, Christian},
  Booktitle                = {Latent Variable Analysis and Signal Separation},
  Publisher                = {Springer Berlin / Heidelberg},
  Year                     = {2010},
  Editor                   = {Vigneron, Vincent and Zarzoso, Vicente and Moreau, Eric and Gribonval, RÃ©mi and Vincent, Emmanuel},
  Pages                    = {466-473},
  Series                   = {Lecture Notes in Computer Science},
  Volume                   = {6365},

  Abstract                 = {Multidimensional biomedical imaging requires robust statistical analyses. Corresponding experiments such as EEG or FRAP commonly result in multiple time series. These data are classically characterized by recording response patterns to any kind of stimulation mixed with any degree of noise levels. Here, we want to detect the underlying signal sources such as these experimental responses in an unbiased fashion, and therefore extend and employ a source separation technique based on temporal autodecorrelation. Our extension first centers the data using a multivariate median, and then separates the sources based on approximate joint diagonalization of multiple sign autocovariance matrices.},
  Affiliation              = {IBIS, Helmholtz Zentrum Munich, Germany},
  ISBN                     = {978-3-642-15994-7},
  Keyword                  = {Computer Science}
}

@Article{ThulGRWZX04,
  Title                    = {Effect of ocular artifact removal in brain computer interface accuracy.},
  Author                   = {M. Thulasidas and C. Guan and S. Ranganatha and J. Wu and X. Zhu and W. Xu},
  Journal                  = {Conf. Proc. IEEE Eng. Med. Biol. Soc.},
  Year                     = {2004},
  Pages                    = {4385--4388},
  Volume                   = {6},

  Abstract                 = {We report the effect of removing ocular artifacts on the performance of a word-processing application based on the event related potential P300. Various methods of removing artifacts have been reported. The efficiency of these algorithms are usually done by subjective visual comparisons. Noting that there is a direct correlation of artifact rectifying algorithms to the accuracy in a brain computer interface system's accuracy, we present this work as a means to compare different algorithms.},
  Doi                      = {10.1109/IEMBS.2004.1404220},
  File                     = {ThulGRWZX04.pdf:ThulGRWZX04.pdf:PDF},
  Owner                    = {Cedric Gouy-Pailler},
  Pmid                     = {17271277},
  Timestamp                = {2007.02.09},
  Url                      = {http://dx.doi.org/10.1109/IEMBS.2004.1404220}
}

@Article{Tichavsky06,
  Title                    = {Performance Analysis of the FastICA Algorithm and Cramer-Rao Bounds for Linear Independent Component Analysis},
  Author                   = {P. Tichavsky and Z. Koldovsky and E. Oja},
  Journal                  = IEEE_J_SP,
  Year                     = {2006},
  Number                   = {4},
  Pages                    = {1189--1203},
  Volume                   = {54}
}

@Article{TichavskyNehorai1997,
  Title                    = {Comparative study of four adaptive frequency trackers},
  Author                   = {Tichavsky, P. and Nehorai, A.},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {1997},

  Month                    = {jun},
  Number                   = {6},
  Pages                    = {1473 -1484},
  Volume                   = {45},

  Doi                      = {10.1109/78.599971},
  ISSN                     = {1053-587X},
  Keywords                 = {SNR;adaptive estimation;adaptive frequency trackers;adaptive notch filter;adaptive retrieval;algorithms;comparative study;computer simulations;equilibrium state;high signal-to-noise ratio;hyperstable adaptive line enhancer;large data sample;linear filter approximation;local behavior;multiple frequency tracker;noise;single-cisoid;slowly time-varying multiple cisoids;adaptive estimation;adaptive filters;adaptive signal processing;approximation theory;filtering theory;notch filters;signal sampling;tracking filters;}
}

@Article{Tong1991,
  Title                    = {{Indeterminacy and identifiability of blind identification}},
  Author                   = {L. Tong and R.-W. Liu and V.C. Soon and Y.-F. Huang},
  Journal                  = IEEE_J_CAS,
  Year                     = {1991},

  Month                    = {May},
  Pages                    = {499--509},
  Volume                   = {38},

  No                       = {5}
}

@Book{VanTrees2002arrayprocessing,
  Title                    = {Detection, Estimation, and Modulation Theory, Part IV, Optimum Array Processing},
  Author                   = {H. van-Trees},
  Publisher                = {John Wiley \& Sons},
  Year                     = {2002}
}

@Book{VanTrees2001detection,
  Title                    = {{Detection, Estimation, and Modulation Theory. Part I}},
  Author                   = {H. van-Trees},
  Publisher                = {John Wiley \& Sons},
  Year                     = {2001}
}

@Unpublished{Tsakalis,
  Title                    = {{Stability, controllability, observability}},
  Author                   = {K. S. Tsakalis},
  Note                     = {{Lecture Notes}},

  Month                    = {June},
  Year                     = {2001},

  Url                      = {http://tsakalis.faculty.asu.edu/notes/sco.pdf}
}

@Article{Tsalaile2008,
  Title                    = {{Sequential Blind Source Extraction For Quasi-Periodic Signals With Time-Varying Period}},
  Author                   = {Thato Tsalaile and Reza Sameni and Saeid~Sanei and Christian Jutten and Jonathon Chambers},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2009},

  Month                    = {March},
  Number                   = {3},
  Pages                    = {646--655},
  Volume                   = {56},

  Abstract                 = {A novel second-order-statistics-based sequential blind extraction algorithm for blind extraction of quasi-periodic signals, with time-varying period, is introduced in this paper. Source extraction is performed by sequentially converging to a solution that effectively diagonalizes autocorrelation matrices at lags corresponding to the time-varying period, which thereby explicitly
exploits a key statistical nonstationary characteristic of the desired source. The algorithm is shown to have fast convergence and yields significant improvement in signal-to-interference ratio as compared to when the algorithm assumes a fixed period. The algorithm is further evaluated on the problem of separation of a heart sound signal from real-world lung sound recordings. Separation results confirm the utility of the introduced approach, and listening tests are employed to further corroborate the results.}
}

@InProceedings{Turqueti2010,
  Title                    = {Real-time Independent Component Analysis Implementation and applications},
  Author                   = {Turqueti, M. and Saniie, J. and Oruklu, E.},
  Booktitle                = {Real Time Conference (RT), 2010 17th IEEE-NPSS},
  Year                     = {2010},
  Month                    = {may},
  Pages                    = {1 -7},

  Abstract                 = {A common problem in disciplines such as high energy physics, biomedicine and acoustic signal processing is finding a suitable representation of multivariate data. Independent Component Analysis (ICA) is a recently developed mathematical tool that can recover independent source signals and is now mature enough to be implemented in real-time applications such as photomultipliers signal processing, magnetic resonance imaging and acoustic arrays. This technique is based on the assumption that signals from different sources are statistically independent and statistically independent signals can be extracted from mixture signals. ICA defines a model for the observed data that requires a large number of samples in order to establish the necessary statistics. The model assumes that the data variables are linear combination of unknown variables, the unknown variables are assumed to be non-Gaussian and independent. The goal then becomes to find a transformation in which the components are as statistical independent as possible from each other. This technique is related with methods such as principal component analysis and factor analysis. The ICA algorithm is computing intensive since it must accumulate and go through the signal samples performing complex operations. Efficient versions of the algorithm have being already deployed using different techniques such as the FastICA that can be implemented efficiently in hardware platforms such as DSP processors and FPGA's. In this paper, we present the ICA principles, implementation and current applications.},
  Doi                      = {10.1109/RTC.2010.5750336},
  Keywords                 = {DSP processors;FPGA;FastICA;acoustic arrays;acoustic signal processing;biomedicine;blind source separation;energy physics;factor analysis;magnetic resonance imaging;mathematical tool;multivariate data representation;photomultipliers signal processing;principal component analysis;real-time independent component analysis;acoustic arrays;blind source separation;data structures;independent component analysis;principal component analysis;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Ungureanu2006,
  Title                    = {Basic Aspects Concerning the Event-Synchronous Interference Canceller},
  Author                   = {Ungureanu, M. and Wolf, W.M.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2006},

  Month                    = {nov. },
  Number                   = {11},
  Pages                    = {2240 -2247},
  Volume                   = {53},

  Abstract                 = {The adaptive noise canceller (ANC) is a commonly used linear system method for noise reduction in cases where the disturbing noise can be separately recorded (reference signal) and is not correlated with the signal of interest. In case of a periodic disturbing signal, special solutions are described in literature. Problems, however, arise when the propagation of the noise from the source to the recording sensors passes nonlinear structures. An ANC modification proposed for this case by Strobach and applied by several other researchers, thus, uses an artificial reference signal, based on event triggered averaging of segments of the recorded wanted (but disturbed) signal in order to obtain a template for the repetitive distortion sequence and to construct the artificial reference signal. The effect of the averaging and the error introduced by this approximation of the real disturbing signal was not addressed in literature until now, thus, this paper presents some basic theoretical considerations on this topic. Methods are demonstrated in simulations and real biosignal processing, and application aspects are discussed},
  Doi                      = {10.1109/TBME.2006.877119},
  ISSN                     = {0018-9294},
  Keywords                 = {adaptive noise canceller;artificial reference signal;biosignal processing;disturbing noise;event-synchronous interference canceller;linear system method;noise reduction;periodic disturbing signal;repetitive distortion sequence;adaptive filters;electrocardiography;electromyography;medical signal processing;noise;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{VaradyWBH03,
  Title                    = {An advanced method in fetal phonocardiography},
  Author                   = {P{\'e}ter V{\'a}rady and Ludwig Wildt and Zolt{\'a}n Beny{\'o} and Achim Hein},
  Journal                  = {Computer Methods and Programs in Biomedicine},
  Year                     = {2003},
  Number                   = {3},
  Pages                    = {283--296},
  Volume                   = {71},

  Bibsource                = {DBLP, http://dblp.uni-trier.de},
  Ee                       = {http://dx.doi.org/10.1016/S0169-2607(02)00111-6}
}

@Conference{Vahabzadeh2012,
  Title                    = {{The Notion of Cardiac Phase and its Applications in Electrophysiological Studies}},
  Author                   = {Bahman Vahabzadeh and Reza Sameni},
  Booktitle                = {Biomedical Engineering (BioMed 2012)},
  Year                     = {2012},

  Address                  = {Innsbruck, Austria},
  Month                    = {February 15--17},

  Abstract                 = {In this paper the cardiac phase is calculated using different methods based on time warping theory. The estimated phase is used for calculation of the heart rate (HR) signal. The results show that the estimated HR is similar to the HR calculated by using the RR-interval sequence. Unlike the RR-interval signal which is non-uniformly sampled, the proposed method for HR calculation is continuous in time. Therefore, conventional signal processing methods can be used to study the HR signal easily and without any preprocessing techniques like resampling and interpolations used in previous method.},
  Doi                      = {10.2316/P.2012.764-127},
  Owner                    = {sameni},
  Timestamp                = {2012.07.10}
}

@Book{vaidyanathan1993multirate,
  Title                    = {Multirate Systems and Filter Banks},
  Author                   = {Vaidyanathan, P.P.},
  Publisher                = {Prentice Hall},
  Year                     = {1993},
  Series                   = {Prentice Hall Signal Processing Series}
}

@InProceedings{Valizadeh2007,
  Title                    = {A novel algorithm for signal subspace tracking based on a new subspace information criterion},
  Author                   = {Valizadeh, A. and Mohammadian, R. and Rafiei, A. and Rafati, A.},
  Booktitle                = {Information, Communications Signal Processing, 2007 6th International Conference on},
  Year                     = {2007},
  Month                    = {dec.},
  Pages                    = {1 -4},

  Abstract                 = {In this paper, we present a new algorithm for tracking the signal subspace recursively. It is based on a new interpretation of the signal subspace. We introduce a novel information criterion for signal subspace estimation. We show that the solution of the proposed constrained optimization problem results the signal subspace. In addition, we introduce three adaptive algorithms which can be used for real time implementation of the signal subspace tracking. The computational complexity of the proposed signal subspace tracking algorithms are O(nr 2) which is much less than the direct computation of singular value decomposition or even some algorithms. Simulation results in the direction of arrival (DOA) tracking context depict excellent performance of the proposed algorithm.},
  Doi                      = {10.1109/ICICS.2007.4449774},
  Keywords                 = {adaptive algorithm;computational complexity;constrained optimization problem;direction of arrival tracking;recursive signal subspace tracking algorithm;signal subspace estimation;signal subspace interpretation;singular value decomposition;subspace information criterion;computational complexity;information theory;signal processing;singular value decomposition;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Geijn96,
  Title                    = {{Developments in CTG analysis}},
  Author                   = {H. P. {van Geijn}},
  Journal                  = {{Baillieres Clin Obstet Gynaecol.}},
  Year                     = {1996},

  Month                    = {June},
  Number                   = {2},
  Pages                    = {185--209},
  Volume                   = {10},

  Abstract                 = {FHR monitoring has been the subject of many debates. The technique, in itself, can be considered to be accurate and reliable both in the antenatal period, when using the Doppler signal in combination with autocorrelation techniques, and during the intrapartum period, in particular when the FHR signal can be obtained from a fetal ECG electrode placed on the presenting part. The major problems with FHR monitoring relate to the reading and interpretation of the CTG tracings.

Since the FHR pattern is primarily an expression of the activity of the control by the central and peripheral nervous system over cardiovascular haemodynamics, it is possibly too indirect a signal. In other specialities such as neonatology, anaesthesiology and cardiology, monitoring and graphic display of heart rate patterns have not gained wide acceptance among clinicians. Digitized archiving, numerical analysis and even more advanced techniques, as described in this chapter, have primarily found a place in obstetrics. This can be easily explained, since the obstetrician is fully dependent on indirectly collected information regarding the fetal condition, such as (a) movements experienced by the mother, observed with ultrasound or recorded with kinetocardiotocography (Schmidt, 1994), (b) perfusion of various vessels, as assessed by Doppler velocimetry, (c) the amount of amniotic fluid or (d) changes reflected in the condition of the mother, such as the development of gestation-induced hypertension and (e) the easily, continuously obtainable FHR signal.

It is of particular comfort to the obstetrician that a normal FHR tracing reliably predicts the birth of the infant in a good condition, which makes cardiotocography so attractive for widespread application. However, in the intrapartum period, many traces cannot fulfil the criteria of normality, especially in the second stage. In this respect, cardiotocography remains primarily a screening and not so much a diagnostic method. As long as continuous monitoring of fetal acid-base balance has not been extensively tested in clinical practice, microblood sampling of the fetal presenting part (Saling, 1994) is a useful adjunct. The problem with non-normal tracings is that their significance is very often unclear. They may indicate serious fetal distress, finally resulting in preventable destruction of critical areas in the fetal brain and damage to various organs; or, on the contrary, they may indicate temporary changes in cardiovascular control as a reaction to the intermittent effects on fetal haemodynamics of, for example, uterine contractions, whether or not in combination with partial or complete compression of umbilical cord vessels or the vessels on the chorionic plate (van Geijn, 1994). Many factors influence the FHR and its variability, which further complicates the interpretation of FHR patterns; some have been discussed here in some detail. Undoubtedly, there is a need for quantitative and objective FHR analysis, as long as it does not lead to erroneous results. Close collaboration between engineers and clinicians is a prerequisite for further advances in this field. Decision support systems certainly have a future but only if they are able to take into account a large set of clinical data and can combine it with data obtained from FHR signals and other parameters referring to the fetal condition, such as fetal growth, Doppler velocimetry, amniotic fluid volume and biochemical and biophysical data obtained from the mother. Basic technical concepts inherent in computerized CTG analysis, such as sampling rate (Chang et al, 1995), signal loss, artefact detection (van Geijn et al, 1980), further processing of intervals, archiving in digitized format and monitor display, should receive considerable attention. There is still a long way to go until decision support systems find their way into obstetric practice. Further developments can only be achieved thanks to efforts of many basic and clinical researchers, working in a harmonious environment with adequate funding.},
  Owner                    = {sameni},
  Timestamp                = {2010.03.07}
}

@Article{Leeuwen1999,
  Title                    = {Fetal heart rate variability and complexity in the course of pregnancy},
  Author                   = {P. {van Leeuwen} and S. Lange and H. Bettermann and D. Grönemeyer and W. Hatzmann},
  Journal                  = {Early Hum Dev},
  Year                     = {1999},

  Month                    = {Apr},
  Number                   = {3},
  Pages                    = {259--269},
  Volume                   = {54},

  Abstract                 = {Aim of this study was the examination of fetal heart rate variability and complexity measures during pregnancy using fetal magnetocardiography. We registered 80 fetal magnetocardiograms in 19 healthy fetuses between the 16th and 41st week of gestation. On the basis of beat to beat intervals, mean RR interval (mRR), its standard deviation (SD), root mean square of successive differences (RMSSD), as well as complexity variables such as dimension (ApD1), entropy (ApEn), Lyapunov exponent (ApML) and trajectory divergence rate (p) were calculated for each recording. Dependency of these variables on gestational age was evaluated with correlation analysis. All variables changed consistently over time. RMSSD showed the strongest dependency on gestational age, followed closely by ApEn, SD and p. ApD1 and mRR showed only weak dependency. We conclude that magnetocardiography is well suited to register fetal cardiac activity with sufficient accuracy to permit detailed analysis of various heart rate variables during the second and third trimester of pregnancy. The observed increases in heart rate variability and complexity of fetuses most likely reflect differing but overlapping aspects of fetal development. They may be linked to the maturation of the autonomic nervous system and could aid in the timely identification of pathological conditions.},
  Institution              = {Department of Biomagnetism, Research and Development Center for Microtherapy (EFMT), Bochum, Germany. petervl@microtherapy.de},
  Keywords                 = {Adult; Female; Fetal Monitoring; Gestational Age; Heart Function Tests; Heart Rate, Fetal; Humans; Magnetics; Pregnancy; Sensitivity and Specificity},
  Owner                    = {Reza Sameni},
  Pii                      = {S0378378298001029},
  Pmid                     = {10321792},
  Timestamp                = {2008.05.11}
}

@Article{null2004,
  Title                    = {{Dependency of magnetocardiographically determined fetal cardiac time intervals on gestational age, gender and postnatal biometrics in healthy pregnancies}},
  Author                   = {P. {van Leeuwen} and S. Lange and A. Klein and D. Geue and D. HW Gr\"unemeyer},
  Journal                  = {{BMC Pregnancy Childbirth}},
  Year                     = {2004},
  Number                   = {6},
  Volume                   = {4},

  Doi                      = {10.1186/1471-2393-4-6},
  Owner                    = {sameni},
  Timestamp                = {2008.05.07}
}

@Article{vanLeeuwen2004,
  Title                    = {{Dependency of magnetocardiographically determined fetal cardiac time intervals on gestational age, gender and postnatal biometrics in healthy pregnancies}},
  Author                   = {P. {van Leeuwen} and S. Lange and A. Klein and D. Geue and D. HW Gr\"unemeyer},
  Journal                  = {{BMC Pregnancy Childbirth}},
  Year                     = {2004},
  Number                   = {1},
  Pages                    = {6},
  Volume                   = {4},

  Doi                      = {10.1186/1471-2393-4-6},
  Owner                    = {sameni},
  Timestamp                = {2008.05.07}
}

@InProceedings{VanVeen1992,
  Title                    = {Localization of intra-cerebral sources of electrical activity via linearly constrained minimum variance spatial filtering},
  Author                   = {Van Veen, B. and Joseph, J. and Hecox, K.},
  Booktitle                = {IEEE Sixth SP Workshop on Statistical Signal and Array Processing},
  Year                     = {1992},
  Month                    = {7-9 Oct 1992},
  Pages                    = {526--529},

  Journal                  = {Proc. of 6th SP IEEE Workshop Statistical Signal and Array Processing},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{VanVeen1997,
  Title                    = {Localization of brain electrical activity via linearly constrained minimum variance spatial filtering},
  Author                   = {Van Veen,B. D. and Van Drongelen,W. and Yuchtman,M. and Suzuki,A.},
  Journal                  = {IEEE Trans. Biomed. Eng},
  Year                     = {1997},
  Pages                    = {867â€“880},
  Volume                   = {44},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Zaen2010,
  Title                    = {Adaptive tracking of {EEG} oscillations},
  Author                   = {{van} Zaen, J\'er\^ome and Uldry, Laurent and Duch\^ene, C\'edric and Prudat, Yann and Meuli, Reto A. and Murray, Micah M. and Vesin, Jean-Marc},
  Journal                  = {Journal of {N}euroscience {M}ethods},
  Year                     = {2010},
  Number                   = {1},
  Pages                    = {97--106},
  Volume                   = {186},

  Abstract                 = {Neuronal oscillations are an important aspect of EEG recordings. These oscillations are supposed to be involved in several cognitive mechanisms. For instance, oscillatory activity is considered a key component for the top-down control of perception. However, measuring this activity and its influence requires precise extraction of frequency components. This processing is not straightforward. Particularly, difficulties with extracting oscillations arise due to their time-varying characteristics. Moreover, when phase information is needed, it is of the utmost importance to extract narrow-band signals. This paper presents a novel method using adaptive filters for tracking and extracting these time-varying oscillations. This scheme is designed to maximize the oscillatory behavior at the output of the adaptive filter. It is then capable of tracking an oscillation and describing its temporal evolution even during low amplitude time segments. Moreover, this method can be extended in order to track several oscillations simultaneously and to use multiple signals. These two extensions are particularly relevant in the framework of EEG data processing, where oscillations are active at the same time in different frequency bands and signals are recorded with multiple sensors. The presented tracking scheme is first tested with synthetic signals in order to highlight its capabilities. Then it is applied to data recorded during a visual shape discrimination experiment for assessing its usefulness during EEG processing and in detecting functionally relevant changes. This method is an interesting additional processing step for providing alternative information compared to classical time-frequency analyses and for improving the detection and analysis of cross-frequency couplings.},
  Affiliation              = {EPFL},
  Details                  = {http://infoscience.epfl.ch/record/146703},
  Doi                      = {10.1016/j.jneumeth.2009.10.018},
  Extra-id                 = {000274761200015},
  Keywords                 = {Adaptive tracking; Neuronal oscillations; Cross-frequency couplings; EEG},
  Oai-id                   = {oai:infoscience.epfl.ch:146703},
  Oai-set                  = {article},
  Review                   = {REVIEWED},
  Status                   = {PUBLISHED},
  Unit                     = {ASPG}
}

@Article{Vand87,
  Title                    = {{Two methods for optimal MECG elimination and FECG detection from skin electrode signals}},
  Author                   = {Vanderschoot, J. and Callaerts, D. and Sansen, W. and Vandewalle, J. and Vantrappen, G. and Janssens, J.},
  Journal                  = {{IEEE} Trans Biomed Eng},
  Year                     = {1987},
  Pages                    = {233--243},
  Volume                   = {BME-34}
}

@Misc{Vas2014,
  Title                    = {{Mathematical Modeling}},

  Author                   = {Lia Vas},
  HowPublished             = {Lecture Notes},
  Year                     = {2014},

  Owner                    = {sameni},
  Timestamp                = {2014.02.16},
  Url                      = {http://www.usciences.edu/~lvas/}
}

@Article{VigaSJHO00,
  Title                    = {Independent component approach to the analysis of {EEG} and {MEG} recordings.},
  Author                   = {R. Vigario and J. Sarela and V. Jousmaki and M. Hamalainen and E. Oja},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2000},

  Month                    = {May},
  Number                   = {5},
  Pages                    = {589--593},
  Volume                   = {47},

  Abstract                 = {Multichannel recordings of the electromagnetic fields emerging from neural currents in the brain generate large amounts of data. Suitable feature extraction methods are, therefore, useful to facilitate the representation and interpretation of the data. Recently developed independent component analysis (ICA) has been shown to be an efficient tool for artifact identification and extraction from electroencephalographic ({EEG}) and magnetoencephalographic (MEG) recordings. In addition, ICA has been applied to the analysis of brain signals evoked by sensory stimuli. This paper reviews our recent results in this field.},
  File                     = {VigaSJHO00.pdf:VigaSJHO00.pdf:PDF},
  Keywords                 = {Algorithms; Artifacts; Electroencephalography; Evoked Potentials, Auditory; Evoked Potentials, Somatosensory; Humans; Magnetoencephalography; Signal Processing, Computer-Assisted},
  Owner                    = {Cedric Gouy-Pailler},
  Pmid                     = {10851802},
  Timestamp                = {2007.01.09}
}

@Article{Vigneron2003,
  Title                    = {{Fetal electrocardiogram extraction based on non-stationary ICA and wavelet denoising}},
  Author                   = {Vigneron, V. and Paraschiv-Ionescu, A. and Azancot, A. and Sibony, O. and Jutten, C.},
  Journal                  = {Signal Processing and Its Applications, 2003. Proceedings. Seventh International Symposium on},
  Year                     = {1-4 July 2003},
  Pages                    = { 69--72 vol.2},
  Volume                   = {2},

  Doi                      = {10.1109/ISSPA.2003.1224817},
  ISSN                     = { },
  Keywords                 = { electrocardiography, independent component analysis, medical signal processing, obstetrics, signal denoising, wavelet transforms fetal electrocardiogram monitoring, fetal heart, fetus, higher order statistical tools, measuring electrical signals, mother body surface, nonstationary ICA, pregnancy, wavelet denoising}
}

@Article{Vintzileos95,
  Title                    = {Intrapartum electronic fetal heart rate monitoring versus intermittent auscultation: a meta-analysis},
  Author                   = {Vintzileos, A. M. and Nochimson, D.J. and Guzman, E. R. and Knuppel, R. A. and Lake, M. and Schifrin, B. S.},
  Journal                  = {Obstet Gynecol},
  Year                     = {1995},
  Number                   = {1},
  Pages                    = {149-55},
  Volume                   = {85},

  Optvolume                = {85}
}

@InBook{Vrba2000,
  Title                    = {{Applications of Superconductivity}},
  Author                   = {J. Vrba},
  Chapter                  = {{Multichannel SQUID biomagnetic systems}},
  Editor                   = {H. Weinstock},
  Pages                    = {61--138},
  Publisher                = {{Kluwer Academic Publishers}},
  Year                     = {2000},

  Owner                    = {sameni},
  Timestamp                = {2012.10.23}
}

@Article{Vrba2004,
  Title                    = {{Fetal MEG redistribution by projection operators}},
  Author                   = {J. Vrba and S.E. Robinson and J. McCubbin and C.L. Lowery and H. Eswaran and J.D. Wilson and P. Murphy and H. Preissl},
  Journal                  = {{IEEE Trans Biomed Eng}},
  Year                     = {2004},
  Pages                    = {1207--1218},
  Volume                   = {51},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{vrba2004hum,
  Title                    = {Human fetal brain imaging by magnetoencephalography: verification of fetal brain signals by comparison with fetal brain models.},
  Author                   = {Vrba, J. and Robinson, S.E. and McCubbin, J. and Murphy, P. and Eswaran, H. and Wilson, J.D. and Preissl, H. and Lowery, C.L.},
  Journal                  = {Neuroimage},
  Year                     = {2004},
  Number                   = {3},
  Pages                    = {1009-20},
  Volume                   = {21}
}

@Book{deVries2006,
  Title                    = {A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods},
  Author                   = {de Vries, G. and Hillen, T. and Lewis, M. and Sch{\~o}nfisch, B. and Muller, J.},
  Publisher                = {Society for Industrial and Applied Mathematics},
  Year                     = {2006},
  Series                   = {Monographs on Mathematical Modeling and Computation},

  ISBN                     = {9780898716122},
  Lccn                     = {06044305}
}

@InProceedings{Vrins04b,
  Title                    = {Sensor Array and Electrode Selection for Non-Invasive Fetal Electrocardiogram Extraction by Independent Component Analysis},
  Author                   = {F. Vrins and C. Jutten and M. Verleysen},
  Booktitle                = {Independent Componenent Analysis and Blind Signal Separation},
  Year                     = {2004},
  Editor                   = {C.G. Puntonet , A. Prieto},
  Pages                    = {1017--1024},
  Publisher                = {Springer},
  Series                   = {Lecture Notes in Computer Science (LNCS 3195)},

  ISBN                     = {3-540-23056-4}
}

@InProceedings{Vrins03,
  Title                    = {Improving Independent Component Analysis Performances by Variable Selection},
  Author                   = {F. Vrins and J. A. Lee and M. Verleysen and V. Vigneron and C. Jutten},
  Booktitle                = {NNSP 2003, 13th IEEE Signal Processing Workshop on Neural Networks for Signal Processing},
  Year                     = {2003},

  Address                  = {Toulouse (France)},
  Pages                    = {359--368},

  Date                     = {September 17-19}
}

@InProceedings{Vrins04a,
  Title                    = {Abdominal Electrodes Analysis by Statistical Processing for Fetal Electrocardiogram Extraction},
  Author                   = {F. Vrins and V. Vigneron and C. Jutten and M. Verleysen},
  Booktitle                = {BioMed 2004, 2nd IASTED Int. Conf. on Biomedical Engineering},
  Year                     = {2004},

  Address                  = {Innsbruck (Austria)},
  Pages                    = {244--249},

  Date                     = {February 16-18}
}

@InProceedings{VVJV04,
  Title                    = {{Abdominal Electrodes Analysis by Statistical Processing for Fetal Electrocardiogram Extraction}},
  Author                   = {F. Vrins and V. Vigneron and C. Jutten and M. Verleysen},
  Booktitle                = {Proc. 2nd IASTED Int. Conf. on Biomedical Engineering (BioMed 2004)},
  Year                     = {2004},

  Address                  = {Innsbruck , Austria},
  Month                    = {February 16-18},
  Pages                    = {244-249}
}

@InProceedings{Vullings2007,
  Title                    = {Artifact reduction in maternal abdominal ECG recordings for fetal ECG estimation},
  Author                   = {Vullings, R. and Peters, C. and Mischi, M. and Sluijter, R. and Oei, G. and Bergmans, J.},
  Booktitle                = {Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE},
  Year                     = {2007},
  Month                    = {aug.},
  Pages                    = {43 -46},

  Abstract                 = {Monitoring the fetal electrocardiogram (1ECG) is currently one of the most promising methods to assess fetal health. However, the main problem associated with this method is that the signals recorded from the maternal abdomen are affected by noise and interferences: the maternal electrocardiogram (mECG) being the dominant interference. In this paper a mECG removal technique is described, which is based on dynamic segmentation of the mECG and subsequent linear prediction of the mECG segments. Moreover, as the linear prediction is significantly affected by artifacts, a signal validation technique is presented to suppress the effect of artifacts on the mECG prediction. The performance of the presented technique is evaluated by comparison to the performance of three other mECG removal techniques: the presented technique outperforms the other techniques for all recordings.},
  Doi                      = {10.1109/IEMBS.2007.4352218},
  ISSN                     = {1557-170X},
  Keywords                 = {artifact reduction;dominant interference suppression;dynamic segmentation;fetal electrocardiogram monitoring;fetal health;linear prediction;mECG removal technique;maternal abdominal ECG recordings;signal validation technique;bioelectric phenomena;electrocardiography;interference suppression;medical signal processing;obstetrics;patient monitoring;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Vullings2009,
  Title                    = {Dynamic segmentation and linear prediction for maternal ECG removal in antenatal abdominal recordings.},
  Author                   = {Vullings, R and Peters, C H L and Sluijter, R J and Mischi, M and Oei, S G and Bergmans, J W M},
  Journal                  = {Physiol Meas},
  Year                     = {2009},
  Number                   = {3},
  Pages                    = {291-307},
  Volume                   = {30},

  ISSN                     = {0967-3334},
  Owner                    = {sameni},
  Pubmedid                 = {19223679},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.biomedsearch.com/nih/Dynamic-segmentation-linear-prediction-maternal/19223679.html}
}

@Article{Wakai2006,
  Title                    = {{Linear minimum mean-square error filtering for evoked responses: application to fetal MEG}},
  Author                   = {R.T. Wakai and M. Chen and B.D. {van Veen}},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2006},
  Pages                    = {959 - 963 },
  Volume                   = {53},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Wakai2002,
  Title                    = {Matched-filter template generation via spatial filtering: application to fetal biomagnetic recordings },
  Author                   = {R.T. Wakai and W.J. Lutter},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2002},
  Pages                    = {1214 - 1217 },
  Volume                   = {49},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Wakai2004,
  Title                    = {Assessment of fetal neurodevelopment via fetal magnetocardiography.},
  Author                   = {Ronald T Wakai},
  Journal                  = {Exp Neurol},
  Year                     = {2004},

  Month                    = {Nov},
  Pages                    = {S65--S71},
  Volume                   = {190 Suppl 1},

  Abstract                 = {Fetal magnetocardiography (fMCG) offers unique capabilities for assessment of fetal heart rate (FHR) and fetal behavior, which are fundamental aspects of neurodevelopment. The most important attribute of fMCG for FHR monitoring is its high precision, which allows accurate assessment of beat-to-beat fetal heart rate variability (FHRV), including respiratory sinus arrhythmia. Using mathematical indices to assess FHRV, we find that short- and long-term FHRV both increase during gestation but not in the same manner. The largest increases in short-term FHRV occur during the last trimester, while the largest increases in long-term FHRV occur early on, with smaller changes occurring during the last trimester. The fMCG also allows assessment of fetal activity. This results from the high sensitivity of the signal to the position and orientation of the fetal heart. FMCG actograms are therefore specific for fetal trunk movement, which are thought to be more important than isolated extremity movements and other small fetal movements. The ability to assess FHR, FHRV, and fetal trunk movement simultaneously makes fMCG a valuable tool for neurodevelopment research.},
  Doi                      = {10.1016/j.expneurol.2004.04.019},
  Institution              = {Department of Medical Physics, University of Wisconsin-Madison, Madison, WI 53706, USA. rtwakai@wisc.edu},
  Keywords                 = {Electrocardiography; Female; Fetal Development; Fetal Movement; Fetus; Gestational Age; Heart Rate, Fetal; Humans; Magnetics; Nervous System; Nervous System Physiology; Pregnancy; Pregnancy Trimester, Second; Pregnancy Trimester, Third; Sensitivity and Specificity},
  Owner                    = {sameni},
  Pii                      = {S0014488604001694},
  Pmid                     = {15498544},
  Timestamp                = {2008.05.13},
  Url                      = {http://dx.doi.org/10.1016/j.expneurol.2004.04.019}
}

@Article{Wakai2002a,
  Title                    = {{Matched-filter template generation via spatial filtering: Application to fetal biomagnetic recordings}},
  Author                   = {R. T. Wakai and W. J. Lutter},
  Journal                  = {IEEE Trans Biomed Eng},
  Year                     = {2002},

  Month                    = {Octobr},
  Pages                    = {1214--1217},
  Volume                   = {49},

  Booktitle                = {{IEEE Trans. Biomed. Eng.}},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Manual{Wan05,
  Title                    = {{ReBEL{:} Recursive Bayesian Estimation Library}},
  Author                   = {E. {Wan \textit{et al.}}},

  Url                      = {http://choosh.ece.ogi.edu/rebel/}
}

@Article{Wan06,
  Title                    = {Artifact reduction for simultaneous {EEG/fMRI} recording: Adaptive FIR reduction of imaging artifacts},
  Author                   = {Wan, Xiaohong and Iwata, Kazuki and Riera, Jorge and Kitamura, Masaharu and Kawashima, Ryuta},
  Journal                  = {Clinical Neurophysiology},
  Year                     = {2006},

  Month                    = {March},
  Number                   = {3},
  Pages                    = {681--692},
  Volume                   = {117},

  Abstract                 = {Objective We present a new method of effectively removing imaging artifacts of electroencephalography (EEG) and extensively conserving the time-frequency features of EEG signals during simultaneous functional magnetic resonance imaging (fMRI) scanning under conventional conditions.Methods Under the conventional conditions of a 5000 Hz EEG sampling rate, but in the absence of the MRI slice-timing signals, the imaging artifact during each slice scanning is theoretically inferred to be a linear combination of the average artifact waveform and its derivatives, deduced by band-limited Taylor's expansion. Technically, the imaging artifact reduction algorithm is equivalent to an adaptive finite impulse response (FIR) filter.Results The capability of this novel method removing the imaging artifacts of EEG recording during fMRI scanning has been demonstrated by a phantom experiment. Moreover, the effectiveness of this method in conserving the time-frequency features of EEG activity has been evaluated by both visually evoked experiments and alpha waves.Conclusions The adaptive FIR method is an effective method of removing the imaging artifacts under conventional conditions, and also conserving the time-frequency EEG signals.Significance The proposed adaptive FIR method, removing the imaging artifacts, combined with the wavelet-based non-linear noise reduction (WNNR) method [Wan X, Iwata K, Riera J, Ozaki T, Kitamura M, Kawashima R. Artifact reduction for EEG/fMRI recording: Nonlinear reduction of ballistocardiogram artifacts. Clin Neurophysiol 2006;117:668-80], reducing the ballistocardiogram artifacts (BAs), makes it feasible to obtain accurate EEG signals from the simultaneous EEG recordings during fMRI scanning.},
  Citeulike-article-id     = {1076299},
  Doi                      = {10.1016/j.clinph.2005.07.025},
  Keywords                 = {eeg fmri},
  Priority                 = {2},
  Url                      = {http://dx.doi.org/10.1016/j.clinph.2005.07.025}
}

@Manual{FetalPositions,
  Title                    = {{Fetal Positions, WebMD Inc.}},
  Author                   = {WebMD},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.webmd.com/content/tools/1/slide_fetal_pos.htm}
}

@article{GUAN2020394,
title = {Transport effect of COVID-19 pandemic in France},
journal = {Annual Reviews in Control},
volume = {50},
pages = {394-408},
year = {2020},
issn = {1367-5788},
doi = {https://doi.org/10.1016/j.arcontrol.2020.09.009},
url = {https://www.sciencedirect.com/science/article/pii/S1367578820300663},
author = {Lina Guan and Christophe Prieur and Liguo Zhang and Clémentine Prieur and Didier Georges and Pascal Bellemain},
keywords = {COVID-19, Pandemic model, Optimization, Network model},
abstract = {An extension of the classical pandemic SIRD model is considered for the regional spread of COVID-19 in France under lockdown strategies. This compartment model divides the infected and the recovered individuals into undetected and detected compartments respectively. By fitting the extended model to the real detected data during the lockdown, an optimization algorithm is used to derive the optimal parameters, the initial condition and the epidemics start date of regions in France. Considering all the age classes together, a network model of the pandemic transport between regions in France is presented on the basis of the regional extended model and is simulated to reveal the transport effect of COVID-19 pandemic after lockdown. Using the measured values of displacement of people between cities, the pandemic network of all cities in France is simulated by using the same model and method as the pandemic network of regions. Finally, a discussion on an integro-differential equation is given and a new model for the network pandemic model of each age class is provided.}
}

@article{wang2009solving,
  title={{Solving optimal control problems with MATLAB: Indirect methods}},
  author={Wang, Xuezhong},
  journal={ISE Dept., NCSU, Raleigh, NC},
  volume={27695},
  year={2009},
  url = {http://solmaz.eng.uci.edu/Teaching/MAE274/SolvingOptContProb_MATLAB.pdf}
}

@Manual{WebMD,
  Title                    = {{Fetal Positions, WebMD Inc.}},
  Author                   = {WebMD},
  Year                     = {2005},

  Url                      = {http://www.webmd.com/content/tools/1/slide_fetal_pos.htm}
}

@InProceedings{weiss99segmentation,
  Title                    = {Segmentation using Eigenvectors: A Unifying View},
  Author                   = {Yair Weiss},
  Booktitle                = {Proc. IEEE Int. Conf. Computer Vision (2)},
  Year                     = {1999},
  Pages                    = {975-982},

  Url                      = {citeseer.ist.psu.edu/weiss99segmentation.html}
}

@Article{Weixue96,
  Title                    = {{Computer simulation of epicardial potentials using a heart-torso model with realistic geometry}},
  Author                   = {Weixue, L. and Ling, X.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1996},

  Month                    = Feb,
  Pages                    = {211-217},
  Volume                   = {43},

  No                       = {2}
}

@Article{Westerhuis07,
  Title                    = {A randomised clinical trial on cardiotocography plus fetal blood sampling versus cardiotocography plus ST-analysis of the fetal electrocardiogram (STAN(R)) for intrapartum monitoring},
  Author                   = {Westerhuis, Michelle and Moons, Karel and van Beek, Erik and Bijvoet, Saskia and Drogtrop, Addy and van Geijn, Herman and van Lith, Jan and Mol, Ben and Nijhuis, Jan and Oei, S Guid and Porath, Martina and Rijnders, Robbert and Schuitemaker, Nico and van der Tweel, Ingeborg and Visser, Gerard and Willekes, Christine and Kwee, Anneke},
  Journal                  = {BMC Pregnancy and Childbirth},
  Year                     = {2007},
  Number                   = {1},
  Pages                    = {13},
  Volume                   = {7},

  Abstract                 = {BACKGROUND:Cardiotocography (CTG) is worldwide the method for fetal surveillance during labour. However, CTG alone shows many false positive test results and without fetal blood sampling (FBS), it results in an increase in operative deliveries without improvement of fetal outcome. FBS requires additional expertise, is invasive and has often to be repeated during labour. Two clinical trials have shown that a combination of CTG and ST-analysis of the fetal electrocardiogram (ECG) reduces the rates of metabolic acidosis and instrumental delivery. However, in both trials FBS was still performed in the ST-analysis arm, and it is therefore still unknown if the observed results were indeed due to the ST-analysis or to the use of FBS in combination with ST-analysis.METHODS/DESIGN:We aim to evaluate the effectiveness of non-invasive monitoring (CTG + ST-analysis) as compared to normal care (CTG + FBS), in a multicentre randomised clinical trial setting. Secondary aims are: 1) to judge whether ST-analysis of fetal electrocardiogram can significantly decrease frequency of performance of FBS or even replace it; 2) perform a cost analysis to establish the economic impact of the two treatment options.Women in labour with a gestational age [greater than or equal to] 36 weeks and an indication for CTG-monitoring can be included in the trial.Eligible women will be randomised for fetal surveillance with CTG and, if necessary, FBS or CTG combined with ST-analysis of the fetal ECG.The primary outcome of the study is the incidence of serious metabolic acidosis (defined as pH < 7.05 and Bdecf > 12 mmol/L in the umbilical cord artery). Secondary outcome measures are: instrumental delivery, neonatal outcome (Apgar score, admission to a neonatal ward), incidence of performance of FBS in both arms and cost-effectiveness of both monitoring strategies across hospitals.The analysis will follow the intention to treat principle. The incidence of metabolic acidosis will be compared across both groups. Assuming a reduction of metabolic acidosis from 3.5% to 2.1 %, using a two-sided test with an alpha of 0.05 and a power of 0.80, in favour of CTG plus ST-analysis, about 5100 women have to be randomised. Furthermore, the cost-effectiveness of CTG and ST-analysis as compared to CTG and FBS will be studied.DISCUSSION:This study will provide data about the use of intrapartum ST-analysis with a strict protocol for performance of FBS to limit its incidence. We aim to clarify to what extent intrapartum ST-analysis can be used without the performance of FBS and in which cases FBS is still needed.TRIAL REGISTRATION NUMBER:ISRCTN95732366},
  Doi                      = {10.1186/1471-2393-7-13},
  ISSN                     = {1471-2393},
  Pubmedid                 = {17655764},
  Url                      = {http://www.biomedcentral.com/1471-2393/7/13}
}

@Article{Westgate01,
  Title                    = {ST waveform changes during repeated umbilical cord occlusions in near-term fetal sheep},
  Author                   = {Westgate, JA and Bennet, L and Brabyn, C and Williams, CE and Gunn, AJ},
  Journal                  = {Am J Obstet Gynecol},
  Year                     = {2001},
  Pages                    = {743-751},
  Volume                   = {184},

  Doi                      = {10.1067/mob.2001.111932},
  Pubmedid                 = {11262482}
}

@Article{Westgate92,
  Title                    = {Randomised trial of cardiotocography alone or with ST waveform analysis for intrapartum monitoring},
  Author                   = {J. Westgate and M. Harris and J. S. H. Curnow and K. R. Greene},
  Journal                  = {The Lancet},
  Year                     = {1992},
  Number                   = {8813},
  Pages                    = {194 - 198},
  Volume                   = {340},

  Doi                      = {DOI: 10.1016/0140-6736(92)90465-F},
  ISSN                     = {0140-6736},
  Url                      = {http://www.sciencedirect.com/science/article/B6T1B-49K5G3B-7H/2/821ed8d2f7a9e29f6c095caeae5df4ea}
}

@Article{Widrow75,
  Title                    = {{Adaptive Noise Cancelling: Principles and Applications}},
  Author                   = {B. Widrow and J. Glover and J.M. McCool and J. Kaunitz and C.S. Williams and H.R. Hearn and J.R. Zeidler and E. Dong and R.C. Goodlin},
  Journal                  = IEEE_J_PROC,
  Year                     = {1975},
  Number                   = {12},
  Pages                    = {1692--1716},
  Volume                   = {63}
}

@Article{XIA2007,
  Title                    = {Online Wavelet Denoising via a Moving Window},
  Author                   = {Rui Xia and Ke Meng and Feng Qian and Zhen-Lei Wang},
  Journal                  = {Acta Automatica Sinica},
  Year                     = {2007},
  Number                   = {9},
  Pages                    = {897 - 901},
  Volume                   = {33},

  Doi                      = {10.1360/aas-007-0897},
  ISSN                     = {1874-1029},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S1874102907600421}
}

@Article{Xu2007,
  Title                    = {{Marginal Fisher Analysis and Its Variants for Human Gait Recognition and Content Based Image Retrieval}},
  Author                   = {D. Xu and S. Yan and D. Tao and S. Lin and H. Zhang},
  Journal                  = IEEE_J_IP,
  Year                     = {2007},

  Month                    = {November},
  Number                   = {11},
  Pages                    = {2811-2821},
  Volume                   = {16},

  Url                      = {www.ntu.edu.sg/home/dongxu/TIP-MFASingle.pdf}
}

@Article{Petersen2020,
  author    = {Eskild Petersen and Marion Koopmans and Unyeong Go and Davidson H Hamer and Nicola Petrosillo and Francesco Castelli and Merete Storgaard and Sulien Al Khalili and Lone Simonsen},
  journal   = {The Lancet Infectious Diseases},
  title     = {Comparing {SARS}-{CoV}-2 with {SARS}-{CoV} and influenza pandemics},
  year      = {2020},
  month     = {sep},
  number    = {9},
  pages     = {e238--e244},
  volume    = {20},
  doi       = {10.1016/s1473-3099(20)30484-9},
  publisher = {Elsevier {BV}},
}

@Article{Janko2021,
  author    = {Vito Janko and Ga{\v{s}}per Slapni{\v{c}}ar and Erik Dovgan and Nina Re{\v{s}}{\v{c}}i{\v{c}} and Tine Kolenik and Martin Gjoreski and Maj Smerkol and Matja{\v{z}} Gams and Mitja Lu{\v{s}}trek},
  title     = {{Machine Learning for Analyzing Non-Countermeasure Factors Affecting Early Spread of {COVID}-19}},
  year      = {2021},
  month     = {jun},
  number    = {13},
  pages     = {6750},
  volume    = {18},
  journal = {International Journal of Environmental Research and Public Health},
  doi       = {10.3390/ijerph18136750},
  publisher = {{MDPI} {AG}},
}

@Article{Xu2007a,
  Title                    = {{Marginal Fisher Analysis and Its Variants for Human Gait Recognition and Content Based Image Retrieval}},
  Author                   = {D. Xu and S. Yan and D. Tao and S. Lin and H. Zhang},
  Journal                  = IEEE_J_IP,
  Year                     = {2007},
  Note                     = {to appear},
  Pages                    = {2811--2821},
  Volume                   = {16},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {www.ntu.edu.sg/home/dongxu/TIP-MFASingle.pdf}
}

@Article{Yilmaz2004,
  Title                    = {Blind separation of speech mixtures via time-frequency masking},
  Author                   = {Y{\i}lmaz, O. and Rickard, S.},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {2004},

  Month                    = {July},
  Number                   = {7},
  Pages                    = { 1830-1847},
  Volume                   = {52},

  Doi                      = {10.1109/TSP.2004.828896},
  ISSN                     = {1053-587X},
  Keywords                 = { blind source separation, maximum likelihood estimation, speech processing, time-frequency analysis W-disjoint orthogonality, blind separation, demixing, maximum likelihood mixing parameter estimators, power weighted two-dimensional histogram, speech mixtures, speech signals, time-frequency masking, time-frequency representations}
}

@InProceedings{DBLPconfeccvYanT06,
  Title                    = {{Trace Quotient Problems Revisited}},
  Author                   = {Shuicheng Yan and Xiaoou Tang},
  Booktitle                = {ECCV (2)},
  Year                     = {2006},
  Pages                    = {232--244},

  Bibsource                = {DBLP, http://dblp.uni-trier.de},
  Ee                       = {http://dx.doi.org/10.1007/11744047_18}
}

@Article{Yang1995,
  Title                    = {Projection approximation subspace tracking},
  Author                   = {Bin Yang},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {1995},

  Month                    = {jan},
  Number                   = {1},
  Pages                    = {95 -107},
  Volume                   = {43},

  Doi                      = {10.1109/78.365290},
  ISSN                     = {1053-587X},
  Keywords                 = {algorithms;computational complexity;eigencomponents;high-resolution methods;input vector dimension;projection approximation subspace tracking;recursive least squares;signal processing applications;signal subspace;simulation results;subspace estimation;subspace tracking methods;unconstrained minimization problem;computational complexity;least squares approximations;minimisation;recursive estimation;signal resolution;tracking;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Yang2006,
  Title                    = {RLS-based adaptive algorithms for generalized eigen-decomposition},
  Author                   = {Jian Yang and Hongsheng Xi and Feng Yang and Yu Zhao},
  Journal                  = {Signal Processing, IEEE Transactions on},
  Year                     = {2006},

  Month                    = {april},
  Number                   = {4},
  Pages                    = { 1177 - 1188},
  Volume                   = {54},

  Abstract                 = { The aim of this paper is to develop efficient online adaptive algorithms for the generalized eigen-decomposition problem which arises in a variety of modern signal processing applications. First, we reinterpret the generalized eigen-decomposition problem as an unconstrained minimization problem by constructing a novel cost function. Second, by applying projection approximation method and recursive least-square (RLS) technique to the cost function, a parallel adaptive algorithm for a basis for the r-dimensional (r>0) dominant generalized eigen-subspace and a sequential algorithm based on deflation technique for the first r-dominant generalized eigenvectors are derived. These algorithms can be viewed as counterparts of the extended projection approximation subspace tracking (PAST) and PASTd algorithms, respectively. Furthermore, we modify the parallel algorithm to explicitly estimate the first r-generalized eigenvectors in parallel, not the generalized eigen-subspace. More important, the modified parallel algorithm can be used to extract multiple generalized eigenvectors of two nonstationary sequences, while the proposed sequential algorithm lacks this ability because of slow convergence of minor generalized eigenvectors due to error propagation of the deflation technique. Third, following convergence analysis methods for PAST and PASTd, we prove the asymptotic convergence properties of the proposed algorithms. Finally, computer simulations are performed to investigate the accuracy and the speed advantages of the proposed algorithms.},
  Doi                      = {10.1109/TSP.2005.863040},
  ISSN                     = {1053-587X},
  Keywords                 = { RLS-based adaptive algorithms; convergence analysis methods; cost function; deflation technique; generalized eigen-decomposition; nonstationary sequences; online adaptive algorithms; projection approximation subspace tracking; recursive least-square technique; sequential algorithm; adaptive signal processing; convergence of numerical methods; eigenvalues and eigenfunctions; least squares approximations; recursive estimation;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Yellin1999,
  Title                    = {{Multichannel system identification and deconvolution: performance bounds}},
  Author                   = {Yellin, D. and Friedlander, B.},
  Journal                  = IEEE_J_SP,
  Year                     = {1999},
  Number                   = {5},
  Pages                    = {1410--1414},
  Volume                   = {47},

  Doi                      = {10.1109/78.757233},
  ISSN                     = {1053-587X},
  Keywords                 = {MIMO systems, deconvolution, parameter estimation, probability, signal reconstruction, CRLB, Cramer-Rao lower bound, MIMO linear system, closed-form asymptotic expressions, deconvolution, input probability density functions, input signals observation, location parameter, mean, multi-input multi-output linear system, multichannel system identification, nonGaussian system inputs, parameter estimation, performance bounds, scale parameter, signal reconstruction performance, standard deviation},
  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@Article{Shah2020,
  author    = {Nita H. Shah and Ankush H. Suthar and Ekta N. Jayswal},
  title     = {Control Strategies to Curtail Transmission of {COVID}-19},
  year      = {2020},
  month     = {may},
  pages     = {1--12},
  volume    = {2020},
  doi       = {10.1155/2020/2649514},
  journal   = {International Journal of Mathematics and Mathematical Sciences},
  publisher = {Hindawi Limited},
}

@InProceedings{Yellin1996,
  Title                    = {Blind multi-channel system identification and deconvolution: performance bounds},
  Author                   = {Yellin, D. and Friedlander, B.},
  Booktitle                = {Proc. No.96TB10004 th IEEE Signal Processing Workshop on (Cat Statistical Signal and Array Processing},
  Year                     = {1996},
  Pages                    = {582--585},

  Doi                      = {10.1109/SSAP.1996.534944},
  Keywords                 = {MIMO systems, deconvolution, equalisers, linear systems, parameter estimation, probability, signal reconstruction, telecommunication channels, CRLB, Cramer-Rao lower bound, MIMO linear system, blind multichannel system identification, block diagonal structure, closed-form asymptotic expressions, deconvolution performance, diagonal elements equalization, identification performance, input probability density functions, input recovery, location parameters, lower bounds, multichannel system deconvolution, multiinput multioutput linear system, parameter estimation, performance bounds, signal reconstruction performance, signal separation, system output observations, system parameters},
  Owner                    = {sameni},
  Timestamp                = {2008.07.23}
}

@Article{Young1963,
  Title                    = {On the Representation of Electrocardiograms},
  Author                   = {Young, T. Y. and Huggins, W. H.},
  Journal                  = {Bio-medical Electronics, IEEE Transactions on},
  Year                     = {1963},

  Month                    = july,
  Number                   = {3},
  Pages                    = {86 -95},
  Volume                   = {10},

  Doi                      = {10.1109/TBMEL.1963.4322805},
  ISSN                     = {0096-0616}
}

@Article{Zappasodi2001,
  Title                    = {Detection of fetal auditory evoked responses by means of magnetoencephalography},
  Author                   = {Filippo Zappasodi and Franca Tecchio and Vittorio Pizzella and Emanuele Cassetta and Giuseppe V Romano and Giancarlo Filligoi and Paolo M Rossini},
  Journal                  = {Brain Research},
  Year                     = {2001},
  Number                   = {2},
  Pages                    = {167 - 173},
  Volume                   = {917},

  Doi                      = {10.1016/S0006-8993(01)02901-8},
  ISSN                     = {0006-8993},
  Keywords                 = {Magnetoencephalography},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.sciencedirect.com/science/article/pii/S0006899301029018}
}

@Article{Zarzoso01,
  Title                    = {Noninvasive fetal electrocardiogram extraction: blind separation versus adaptive noise cancellation},
  Author                   = {Zarzoso, V. and Nandi, A.K.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2001},

  Month                    = {January},
  Number                   = {1},
  Pages                    = {12-18},
  Volume                   = {48},

  Abstract                 = {The problem of the fetal electrocardiogram (FECG) extraction from maternal skin electrode measurements can be modeled from the perspective of blind source separation (BSS). Since no comparison between BSS techniques and other signal processing methods has been made, the authors compare a BSS procedure based on higher-order statistics and Widrow's multireference adaptive noise cancelling approach. As a best-case scenario for this latter method, optimal Wiener-Hopf solutions are considered. Both procedures are applied to real multichannel ECG recordings obtained from a pregnant woman. The experimental outcomes demonstrate the more robust performance of the blind technique and, in turn, verify the validity of the BSS model in this important biomedical application},
  Doi                      = {10.1109/10.900244},
  ISSN                     = {0018-9294},
  Keywords                 = {adaptive signal processing, electrocardiography, feature extraction, medical signal processing, noise, obstetricsWidrow's multireference adaptive noise cancelling approach, blind separation, electrodiagnostics, higher-order statistics, maternal skin electrode measurements, noninvasive fetal electrocardiogram extraction, optimal Wiener-Hopf solutions, pregnant woman, real multichannel ECG recordings, signal processing methods}
}

@InProceedings{Zarzoso99,
  Title                    = {Comparison between blind separation and adaptive noise cancellation techniques for fetal electrocardiogram extraction},
  Author                   = {V. Zarzoso and A. K. Nandi},
  Booktitle                = {IEE Colloq. Medical Applications for Signal Processing},
  Year                     = {1999},
  Pages                    = {1/1-1/6},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Article{Zarzoso97,
  Title                    = {{Maternal and fetal ECG separation using blind source separation methods}},
  Author                   = {V. Zarzoso and A. K. Nandi and E. Bacharakis},
  Journal                  = {IMA J. Math. Appl. Med. Biol},
  Year                     = {1997},
  Pages                    = {207--225},
  Volume                   = {14},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@InProceedings{Zhang2005,
  Title                    = {A new pretreatment approach of eliminating abnormal data in discrete time series},
  Author                   = {Zhang, Jun and Zhang, Jun and Wang, Hong},
  Booktitle                = {Proc. IEEE International Geoscience and Remote Sensing Symposium IGARSS '05},
  Year                     = {2005},
  Editor                   = {Wang, Hong},
  Pages                    = {4 pp.--},
  Volume                   = {1},

  Doi                      = {10.1109/IGARSS.2005.1526263},
  Keywords                 = {data analysis, geophysical signal processing, geophysical techniques, remote sensing, time series, abnormal data elimination, cluster abnormal data, discrete time series, iterative calculation procedure, pretreatment approach, robust estimation, robust weighted average},
  Owner                    = {sameni},
  Timestamp                = {2008.01.29}
}

@Article{Zhang2006,
  Title                    = {Extraction of temporally correlated sources with its application to non-invasive fetal electrocardiogram extraction},
  Author                   = {Zhi-Lin Zhang and Zhang Yi},
  Journal                  = {Neurocomputing},
  Year                     = {2006},
  Number                   = {7-9},
  Pages                    = {894--899},
  Volume                   = {69},

  Bibsource                = {DBLP, http://dblp.uni-trier.de},
  Ee                       = {http://dx.doi.org/10.1016/j.neucom.2005.08.004}
}

@InProceedings{Zhao2008,
  Title                    = {{Incremental Common Spatial Pattern algorithm for BCI}},
  Author                   = {Qibin Zhao and Liqing Zhang and A. Cichocki and Jie Li},
  Booktitle                = {Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence). IEEE International Joint Conference on},
  Year                     = {2008},
  Month                    = {june},
  Pages                    = {2656 -2659},

  Abstract                 = {A major challenge in applying machine learning methods to Brain-Computer Interfaces (BCIs) is to overcome the on-line non-stationarity of the data blocks. An effective BCI system should be adaptive to and robust against the dynamic variations in brain signals. One solution to it is to adapt the model parameters of BCI system online. However, CSP is poor at adaptability since it is a batch type algorithm. To overcome this, in this paper, we propose the Incremental Common Spatial Pattern (ICSP) algorithm which performs the adaptive feature extraction on-line. This method allows us to perform the online adjustment of spatial filter. This procedure helps the BCI system robust to possible non-stationarity of the EEG data. We test our method to data from BCI motor imagery experiments, and the results demonstrate the good performance of adaptation of the proposed algorithm.},
  Doi                      = {10.1109/IJCNN.2008.4634170},
  ISSN                     = {1098-7576},
  Keywords                 = {EEG data;adaptive feature extraction;batch type algorithm;brain signals;brain-computer interfaces;incremental common spatial pattern algorithm;machine learning methods;spatial filter online adjustment;brain-computer interfaces;electroencephalography;feature extraction;learning (artificial intelligence);pattern classification;},
  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Article{Zigel2000,
  Title                    = {ECG signal compression using analysis by synthesis coding},
  Author                   = {Zigel, Y. and Cohen, A. and Katz, A.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {2000},

  Month                    = {oct. },
  Number                   = {10},
  Pages                    = {1308 -1316},
  Volume                   = {47},

  Abstract                 = {An electrocardiogram (ECG) compression algorithm, called analysis by synthesis ECG compressor (ASEC), is introduced. The ASEC algorithm is based on analysis by synthesis coding, and consists of a beat codebook, long and short-term predictors, and an adaptive residual quantizer. The compression algorithm uses a defined distortion measure in order to efficiently encode every heartbeat, with minimum bit rate, while maintaining a predetermined distortion level. The compression algorithm was implemented and tested with both the percentage rms difference (PRD) measure and the recently introduced weighted diagnostic distortion (WDD) measure. The compression algorithm has been evaluated with the MIT-BIH Arrhythmia Database. A mean compression rate of approximately 100 bits/s (compression ratio of about 30:1) has been achieved with a good reconstructed signal quality (WDD below 4% and PRD below 8%). The ASEC was compared with several well-known ECG compression algorithms and was found to be superior at all tested bit rates. A mean opinion score (MOS) test was also applied. The testers were three independent expert cardiologists. As In the quantitative test, the proposed compression algorithm was found to be superior to the other tested compression algorithms.},
  Doi                      = {10.1109/10.871403},
  ISSN                     = {0018-9294},
  Keywords                 = {ECG signal compression;MIT-BIH Arrhythmia Database;adaptive residual quantizer;analysis by synthesis coding;beat codebook;bit rate;electrodiagnostics;percentage rms difference measure;reconstructed signal quality;adaptive signal processing;data compression;electrocardiography;encoding;medical signal processing;Algorithms;Arrhythmias, Cardiac;Databases as Topic;Electrocardiography;Humans;Signal Processing, Computer-Assisted;}
}

@Article{Zuckerwar1993,
  Title                    = {Development of a piezopolymer pressure sensor for a portable fetal heart rate monitor},
  Author                   = {Zuckerwar, A.J. and Pretlow, R.A. and Stoughton, J.W. and Baker, D.A.},
  Journal                  = {Biomedical Engineering, IEEE Transactions on},
  Year                     = {1993},
  Number                   = {9},
  Pages                    = {963--969},
  Volume                   = {40},

  Doi                      = {10.1109/10.245618},
  Editor                   = {Pretlow, R.A.},
  ISSN                     = {0018-9294},
  Keywords                 = {acoustic signal processing, biomedical equipment, biomedical measurement, biomedical ultrasonics, calibration, cardiology, patient monitoring, piezoelectric transducers, polymer films, portable instruments, pressure sensors, acceleration cancellation, acoustic signature, acoustical isolation, electrical isolation, electrical shielding, frequency spectrum, in vitro sensor calibration, localization, nonstress test recordings, phonography, piezopolymer pressure sensor, portable fetal heart rate monitor, sensitivity, signal amplitude, signal detection},
  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.04}
}

@Book{Bro00,
  Title                    = {{The Biomedical Engineering Handbook}},
  Editor                   = {J. Bronzino},
  Publisher                = {CRC Press, Inc.},
  Year                     = {2000},
  Edition                  = {Second}
}

@Book{CA03,
  Title                    = {{Adaptive Blind Signal and Image Processing}},
  Editor                   = {A. Cichocki and S. Amari},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2003}
}

@Book{CRE01,
  Title                    = {{Geometric Modeling with Splines}},
  Editor                   = {E. Cohen and R. F. Riesenfeld and G. Elber},
  Publisher                = {A K Peters Ltd.},
  Year                     = {2001}
}

@Book{Gel74,
  Title                    = {{Applied Optimal Estimation}},
  Editor                   = {A. Gelb},
  Publisher                = {MIT Press},
  Year                     = {1974}
}

@Book{GWA01,
  Title                    = {{Global Positioning Systems, Inertial Navigation, and Integration}},
  Editor                   = {M. S. Grewal and L. R. Weill and A. P. Andrews},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2001}
}

@book{grewal2007global,
  title={Global positioning systems, inertial navigation, and integration},
  author={Grewal, Mohinder S and Weill, Lawrence R and Andrews, Angus P},
  year={2007},
  publisher={John Wiley \& Sons}
}

@Book{Guy96,
  Title                    = {{Textbook of Medical Physiology}},
  Editor                   = {A. C Guyton and J.E Hall},
  Publisher                = {W. B. Saunders Co.},
  Year                     = {1996},
  Edition                  = {Ninth}
}

@Book{Hay01,
  Title                    = {{Kalman Filtering and Neural Networks}},
  Editor                   = {S. Haykin},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2001}
}

@Book{Malmivuo1995,
  Title                    = {{Bioelectromagnetism, Principles and Applications of Bioelectric and Biomagnetic Fields}},
  Editor                   = {J. A. Malmivuo and R. Plonsey},
  Publisher                = {Oxford University Press},
  Year                     = {1995},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://butler.cc.tut.fi/~malmivuo/bem/bembook}
}

@Book{Simon2006,
  Title                    = {{Optimal State Estimation}},
  Editor                   = {Dan Simon},
  Publisher                = {John Wiley \& Sons Inc.},
  Year                     = {2006},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22}
}

@Book{Tomkins93,
  Title                    = {Biomedical Digital Signal Processing: C Language Examples and Laboratory Experiments for the IBM PC},
  Editor                   = {W. J. Tompkins},
  Publisher                = {Prentice Hall},
  Year                     = {1993},

  Address                  = {Englewood Cliffs, NJ}
}

@Book{Webster1998,
  Title                    = {{Medical Instrumentation: Application and Design}},
  Editor                   = {J. G. Webster},
  Publisher                = {John Wiley \& Sons},
  Year                     = {1998},
  Edition                  = {Third},

  Owner                    = {sameni},
  Timestamp                = {2008.05.12}
}

@Book{Wladimiroff96,
  Title                    = {{Ultrasound and the Fetal Heart}},
  Editor                   = {J.W. Wladimiroff and G. Pilu},
  Publisher                = {Parthenon Publishing},
  Year                     = {1996},

  Address                  = {New York, NY},

  Owner                    = {sameni},
  Timestamp                = {2008.04.29}
}

@Manual{MIT-BIH3,
  Title                    = {{The PTB Diagnostic ECG Database}},
  Organization             = {Physikalisch-Technische Bundesanstalt (PTB)},

  Url                      = {http://www.physionet.org/physiobank/database/ptbdb/}
}

@Manual{MIT-BIHNoiseStress,
  Title                    = {{The MIT-BIH Noise Stress Test Database}},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.physionet.org/physiobank/database/nstdb/}
}

@Manual{MIT-BIHNormalSinus,
  Title                    = {{The MIT-BIH Normal Sinus Rhythm Database}},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.physionet.org/physiobank/database/nsrdb/}
}

@Manual{MIT-BIHPTB,
  Title                    = {{The MIT-BIH PTB Diagnosis Database}},

  Owner                    = {sameni},
  Timestamp                = {2012.10.22},
  Url                      = {http://www.physionet.org/physiobank/database/ptbdb/}
}

@Manual{SCII,
  Title                    = {{Scientific Computing and Imaging Institute}},

  Url                      = {http://www.sci.utah.edu/index.html}
}

@Manual{WikipediaCoD,
  Title                    = {Curse of dimensionality},
  Organization             = {Wikipedia},

  Owner                    = {sameni},
  Timestamp                = {2008.04.11},
  Url                      = {http://en.wikipedia.org/wiki/Curse_of_dimensionality}
}

@Manual{WikipediaCTG,
  Title                    = {Cardiotocograph},
  Organization             = {Wikipedia},

  Owner                    = {sameni},
  Timestamp                = {2008.04.11},
  Url                      = {http://en.wikipedia.org/wiki/Cardiotocograph}
}

@Manual{WikipediaSQUID,
  Title                    = {Superconducting Quantum Interference Devices (SQUID)},
  Organization             = {Wikipedia},

  Url                      = {http://en.wikipedia.org/wiki/SQUID}
}

@Misc{PauliMiettinen,
  Title                    = {{Pauli Miettinen's Homepage}},
  Year                     = {2010},

  Owner                    = {sameni},
  Timestamp                = {2010.09.27},
  Url                      = {http://www.cs.helsinki.fi/u/pamietti/}
}

@Manual{AHA2008,
  Title                    = {Congenital Heart Defects in Children Fact Sheet},
  Organization             = {American Heart Association},
  Year                     = {2008},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.04},
  Url                      = {http://www.americanheart.org/children}
}

@Manual{Britannica,
  Title                    = {{Phonocardiography}},
  Organization             = {Encyclopaedia Britannica, Inc.},
  Year                     = {2008},

  Owner                    = {sameni},
  Timestamp                = {2008.04.11},
  Url                      = {http://www.britannica.com/}
}

@Manual{PubMed,
  Title                    = {{PubMed}},
  Note                     = {{A service of the U.S. National Library of Medicine and the National Institutes of Health}},
  Organization             = {The U.S. National Library of Medicine and the National Institutes of Health},
  Year                     = {2008},

  Url                      = {http://www.pubmed.gov/}
}

@Manual{CadioCons2006,
  Title                    = {Physiology},
  Organization             = {{Cardiovascular Consultants}},
  Year                     = {2006},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.11},
  Url                      = {http://www.cardioconsult.com/Physiology/}
}

@Manual{Mar05,
  Title                    = {Congenital Heart Defects},
  Organization             = {March of Dimes},
  Year                     = {2005},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.04},
  Url                      = {http://www.marchofdimes.com/professionals/14332_1212.asp}
}

@Manual{CancerWEB,
  Title                    = {CancerWEB},
  Organization             = {Centre for Cancer Education, University of Newcastle upon Tyne},
  Year                     = {1998},

  Owner                    = {Reza Sameni},
  Timestamp                = {2008.05.24},
  Url                      = {http://cancerweb.ncl.ac.uk/}
}

@article{stolwijk1974regulation,
  title={Regulation and control in physiology},
  author={Stolwijk, JAJ and Hardy, JD},
  journal={Medical physiology},
  volume={2},
  pages={1343--1358},
  year={1974},
  publisher={CV Mosby St. Louis}
}

@article{bergman1979quantitative,
  title={Quantitative estimation of insulin sensitivity.},
  author={Bergman, Richard N and Ider, Y Ziya and Bowden, Charles R and Cobelli, Claudio},
  journal={American Journal of Physiology-Endocrinology And Metabolism},
  volume={236},
  number={6},
  pages={E667},
  year={1979},
  publisher={Am Physiological Soc}
}

@article{de2000mathematical,
  title={Mathematical modelling of the intravenous glucose tolerance test},
  author={De Gaetano, Andrea and Arino, Ovide},
  journal={Journal of mathematical biology},
  volume={40},
  number={2},
  pages={136--168},
  year={2000},
  publisher={Springer}
}

@article{steil2005modeling,
  title={Modeling insulin action for development of a closed-loop artificial pancreas},
  author={Steil, GM and Clark, Bud and Kanderian, Sami and Rebrin, K},
  journal={Diabetes technology \& therapeutics},
  volume={7},
  number={1},
  pages={94--108},
  year={2005},
  publisher={Mary Ann Liebert, Inc. 2 Madison Avenue Larchmont, NY 10538 USA}
}

@inproceedings{friis2007modeling,
  title={Modeling and simulation of glucose-insulin metabolism},
  author={Friis-Jensen, Esben},
  booktitle={Congress Lyngby},
	url = {http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/5312/pdf/imm5312.pdf},
  year={2007}
}

@article{pascual1994low,
  title={Low resolution electromagnetic tomography: a new method for localizing electrical activity in the brain},
  author={Pascual-Marqui, Roberto D and Michel, Christoph M and Lehmann, Dietrich},
  journal={International Journal of psychophysiology},
  volume={18},
  number={1},
  pages={49--65},
  year={1994},
  publisher={Elsevier}
}

@article{pascual2002standardized,
  title={Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details},
  author={Pascual-Marqui, Roberto Domingo and others},
  journal={Methods Find Exp Clin Pharmacol},
  volume={24},
  number={Suppl D},
  pages={5--12},
  year={2002}
}

@article{andrianantoandro2006synthetic,
  title={Synthetic biology: new engineering rules for an emerging discipline},
  author={Andrianantoandro, Ernesto and Basu, Subhayu and Karig, David K and Weiss, Ron},
  journal={Molecular systems biology},
  volume={2},
  number={1},
  year={2006},
  publisher={EMBO Press}
}

@article{gabor2015robust,
  title={Robust and efficient parameter estimation in dynamic models of biological systems},
  author={G{\'a}bor, Attila and Banga, Julio R},
  journal={BMC systems biology},
  volume={9},
  number={1},
  pages={74},
  year={2015},
  publisher={Springer}
}

@book{moeller2003mathematical,
  title={Mathematical and computational modeling and simulation},
  author={Moeller, Dietmar PF},
  year={2003},
  publisher={Springer}
}

@article{miller2019distribution,
  title={Distribution of outbreak sizes for SIR disease in finite populations},
  author={Miller, Joel C},
  journal={arXiv preprint arXiv:1907.05138},
  year={2019}
}

@article{pellis2012reproduction,
  title={{Reproduction numbers for epidemic models with households and other social structures. I. Definition and calculation of R0}},
  author={Pellis, Lorenzo and Ball, Frank and Trapman, Pieter},
  journal={Mathematical biosciences},
  volume={235},
  number={1},
  pages={85--97},
  year={2012},
  publisher={Elsevier}
}

@article{britton2010stochastic,
  title={Stochastic epidemic models: a survey},
  author={Britton, Tom},
  journal={Mathematical biosciences},
  volume={225},
  number={1},
  pages={24--35},
  year={2010},
  publisher={Elsevier}
}

@article{feng2007final,
  title={Final and peak epidemic sizes for SEIR models with quarantine and isolation},
  author={Feng, Zhilan},
  journal={Mathematical Biosciences \& Engineering},
  volume={4},
  number={4},
  pages={675},
  year={2007},
  publisher={American Institute of Mathematical Sciences}
}

@article{de2005modified,
  title={Modified AIC and MDL model selection criteria for short data records},
  author={De Ridder, Fjo and Pintelon, Rik and Schoukens, Johan and Gillikin, David Paul},
  journal={IEEE Transactions on Instrumentation and Measurement},
  volume={54},
  number={1},
  pages={144--150},
  year={2005},
  publisher={IEEE}
}

@article{burnham2004multimodel,
  title={Multimodel inference: understanding AIC and BIC in model selection},
  author={Burnham, Kenneth P and Anderson, David R},
  journal={Sociological methods \& research},
  volume={33},
  number={2},
  pages={261--304},
  year={2004},
  publisher={Sage Publications Sage CA: Thousand Oaks, CA}
}

@article{yang2014comparison,
  title={Comparison of filtering methods for the modeling and retrospective forecasting of influenza epidemics},
  author={Yang, Wan and Karspeck, Alicia and Shaman, Jeffrey},
  journal={PLoS computational biology},
  volume={10},
  number={4},
  year={2014},
  publisher={Public Library of Science}
}

@book{azar2020control,
  title={Control Applications for Biomedical Engineering Systems},
  author={Azar, A.T.},
  isbn={9780128174623},
  year={2020},
  publisher={Elsevier Science}
}

@article{gonccalves2011oscillations,
  title={Oscillations in SIRS model with distributed delays},
  author={Gon{\c{c}}alves, Sebasti{\'a}n and Abramson, Guillermo and Gomes, Marcelo FC},
  journal={The European Physical Journal B},
  volume={81},
  number={3},
  pages={363},
  year={2011},
  publisher={Springer}
}

@Manual{OSET3.14,
  Title                    = {{The Open-Source Electrophysiological Toolbox (OSET), version 3.14}},
  Author                   = {Reza Sameni},
  Year                     = {2018},
  Url                      = {https://gitlab.com/rsameni/OSET/}
}

@book{terrell2009stability,
  title={Stability and stabilization: an introduction},
  author={Terrell, William J},
  year={2009},
  publisher={Princeton University Press}
}

@book{brauer2012mathematical,
  title={Mathematical models in population biology and epidemiology},
  author={Brauer, Fred and Castillo-Chavez, Carlos and Castillo-Chavez, Carlos},
  volume={2},
  year={2012},
  publisher={Springer}
}

@article{feng2007epidemiological,
  title={Epidemiological models with non-exponentially distributed disease stages and applications to disease control},
  author={Feng, Zhilan and Xu, Dashun and Zhao, Haiyun},
  journal={Bulletin of mathematical biology},
  volume={69},
  number={5},
  pages={1511--1536},
  year={2007},
  publisher={Springer}
}

@article{anderson1979population,
  title={Population biology of infectious diseases: Part I},
  author={Anderson, Roy M and May, Robert M},
  journal={Nature},
  volume={280},
  number={5721},
  pages={361--367},
  year={1979},
  publisher={Nature Publishing Group}
}

@article{may1979population,
  title={Population biology of infectious diseases: Part II},
  author={May, Robert M and Anderson, Roy M},
  journal={Nature},
  volume={280},
  number={5722},
  pages={455--461},
  year={1979},
  publisher={Nature Publishing Group}
}

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