Bare Demo of IEEEtran.cls for \textsc{Transactions on Magnetics
Giorgio~Battistelli
% ~\IEEEmembership{Member
~IEEE
....lastname \thanks{...
Michael~Shell
~\IEEEmembership{Member
~IEEE
....lastname \thanks{...
\IEEEauthorblockN{Michael Shell
\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1
\IEEEauthorblockN{Michael Shell
\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1
Michael~Shell
~\IEEEmembership{Member
~IEEE
....lastname \thanks{...
Michael~Shell
~\IEEEmembership{Member
~IEEE
....lastname \thanks{...
\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1
The abstract goes here.
DFEKF_-_arxiv.tex

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	\title{Decentralized consensus finite-element \\ Kalman filter for field estimation}
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	\author{Giorgio~Battistelli,
%		~\IEEEmembership{Member,~IEEE,}
		Luigi~Chisci,~\IEEEmembership{Senior~Member,~IEEE},
		Nicola~Forti,
		Stefano~Selleri,~\IEEEmembership{Senior~Member,~IEEE},
		and~Giuseppe~Pelosi
		~\IEEEmembership{Fellow,~IEEE}% <-this % stops a space
		\thanks{The authors are with the Dipartimento
			di Ingegneria dell'Informazione (DINFO), Universit\`a di Firenze, Firenze,
			Italy. e-mails: \{giorgio.battistelli,luigi.chisci,nicola.forti,stefano.selleri,giuseppe.pelosi\} @unifi.it.}% <-this % stops a space
%		\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
%		\thanks{Manuscript received April 19, 2005; revised September 17, 2014.}
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	{Battistelli  \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
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	% As a general rule, do not put math, special symbols or citations
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	\begin{abstract}
		The paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in-space-and-time noisy measurements provided by sensors deployed over the spatial domain of interest. 
		A fully scalable approach is pursued by decomposing the domain into overlapping subdomains assigned to
		different processing nodes interconnected to form a network.
		Each node runs a local 
		finite-dimensional Kalman filter 
		which exploits the finite element approach for spatial discretization and the parallel Schwarz method to iteratively enforce consensus on the estimates and covariances over the boundaries of adjacent subdomains.
		Stability of the proposed distributed consensus-based finite element Kalman filter is mathematically proved and its effectiveness is demonstrated via simulation experiments concerning the estimation of a bi-dimensional
		temperature field.
	\end{abstract}
	
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		Networked state estimation; distributed-parameter systems; finite element method; Kalman filtering; consensus.
	\end{IEEEkeywords}
	
	
	
	
	
	
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	\section{Introduction}
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	\IEEEPARstart{T}{he} recent breakthrough of wireless sensor network technology has made possible to cost-effectively monitor spatially distributed systems via deployment of
	multiple sensors over the area of interest. 
	This clearly paves the way for several important practical monitoring applications concerning, e.g., weather forecasting \cite{weather}, water flow regulation \cite{water}, fire detection, diffusion of pollutants \cite{pollution}, smart grids \cite{smart-grids}, vehicular traffic \cite{traffic}.
	The problem of fusing data from different sensors can be accomplished either in a \textit{centralized} way, i.e. when there is a single fusion center collecting data from all sensors and taking care of the overall spatial domain of interest, or in \textit{distributed} (decentralized) fashion with multiple intercommunicating fusion centers (nodes) each of which can only access part of the sensor data and take care of a sub-region of the overall domain.
	The decentralized approach is preferable in terms of scalability of computation with the problem size and will be, therefore, undertaken in this paper.
	
	Since spatially distributed processes are usually modeled as infinite-dimensional systems, governed by \textit{partial differential equations} (PDEs), distributed state estimation for such systems turns out to be a key issue to be addressed.
While a lot of work has dealt with distributed consensus-type filters for finite-dimensional, both linear  \cite{Olfati1,Xiao,Calafiore,automatica} and nonlinear \cite{spl},  systems as well as for multitarget tracking \cite{J-STSP}, considerably less attention has been devoted to the more difficult case of distributed-parameter systems. 
	
Recent work \cite{Khan08,Stank09,Farina10,zhang-moura-krogh,pasqualetti} has addressed the design of distributed state estimators/observers for large-scale systems formed by the sparse interconnection of many subsystems (compartments).
Such systems are possibly (but not necessarily) originated from spatial discretization of PDEs. 
In particular, \cite{Khan08} presents a fully scalable distributed Kalman filter based on a suitable spatial decomposition of a complex large-scale system as well as on appropriate observation fusion techniques among the local Kalman filters.
In \cite{Stank09}, non-scalable consensus-based multi-agent estimators are proposed wherein each agent aims to estimate the state of the whole large-scale system.
In \cite{Farina10}, a moving-horizon partition-based approach  is followed in order to estimate the state of a large-scale interconnected system and decentralization is achieved via suitable approximations of covariances.
Further, \cite{zhang-moura-krogh} deals  with dynamic field estimation by wireless sensor networks with special emphasis on sensor scheduling for trading off communication/energy efficiency versus estimation performance.
In \cite{pasqualetti}, design of distributed continuous-time observers for partitioned linear systems is addressed.
	
As for the specific case of distributed-parameter systems, interesting contributions have been provided in \cite{Deme10,Deme13}
which present consensus filters wherein each node of the network aims to estimate the system state on the whole spatial domain of interest. 	

In the present paper, as compared to \cite{Deme10,Deme13}, a different strategy is adopted in which each node is only responsible for estimating the state over a sub-domain of the overall domain. 
This setup allows for a solution which is \textit{scalable} with respect to the spatial domain (i.e., the computational complexity in each node does not depend on the size of the whole spatial domain
	but only of its region of competence).  
	In this context, the contribution of the present paper is essentially in three directions.
	First, we develop \textit{scalable} consensus filters for distributed parameter systems by suitably adapting the so called Schwarz domain decomposition methods \cite{Schwa890,Lions88,Gander08,Chan94,Tos05,Smith96}, originally conceived to solve a boundary value problem
	by splitting it into smaller subproblems on subdomains and iterating to achieve consensus among the solutions on adjacent subdomains.
	Secondly, we exploit the \textit{finite element} (FE) method \cite{Pelosi09,Brenner96,Lee95} in order to approximate the original infinite-dimensional filtering problem into a, possibly large-scale, finite-dimensional one.
	Combining these two ingredients, we propose a novel distributed \textit{finite element Kalman filter} which generalizes to the more challenging distributed case previous work on FE Kalman filtering \cite{jap1,jap2}.
	Third, we provide results on the numerical stability of the proposed space-time discretization scheme as well as on the  stability of the proposed distributed FE Kalman filter.
Preliminary ideas on the topic can be found in \cite{ECC2015}.
	
	The rest of the paper is structured as follows. Section II introduces the basic notation and problem formulation.
	Then Section III  presents the centralized FE Kalman filter for distributed-parameter systems.
	Section IV shows how to extend such a filter to the distributed setting by means of parallel Schwarz consensus and analyzes the numerical stability in terms of boundedness and convergence of the discretization errors.
	Then, section V provides results on the exponential stability of the proposed distributed FE Kalman filter
	while section VI demonstrates its effectiveness  via numerical examples related to the estimation of a bi-dimensional temperature field.
	Finally, section VII ends the paper with concluding remarks and perspectives for future work.
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	%\label{fig_first_case}}
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	%\subfloat[Case II]{\includegraphics[width=2.5in]{spy_AF_AD_tilde_new}%
	%\label{fig_second_case}}
	%\caption{Simulation results for the network.}
	%\label{fig_sim}
	%\end{figure*}
	%
	% Note that often IEEE papers with subfigures do not employ subfigure
	% captions (using the optional argument to \subfloat[]), but instead will
	% reference/describe all of them (a), (b), etc., within the main caption.
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	% captions serve much like titles, are usually capitalized except for words
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	% and up, which are usually not capitalized unless they are the first or
	% last word of the caption. Table text will default to \footnotesize as
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	% \extrarowheight as needed to properly center the text within the cells
	%\caption{An Example of a Table}
	%\label{table_example}
	%\centering
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	%% than the plain LaTeX2e tabular which is used here.
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	%\hline
	%One & Two\\
	%\hline
	%Three & Four\\
	%\hline
	%\end{tabular}
	%\end{table}
	
	
	% Note that the IEEE does not put floats in the very first column
	% - or typically anywhere on the first page for that matter. Also,
	% in-text middle ("here") positioning is typically not used, but it
	% is allowed and encouraged for Computer Society conferences (but
	% not Computer Society journals). Most IEEE journals/conferences use
	% top floats exclusively. 
	% Note that, LaTeX2e, unlike IEEE journals/conferences, places
	% footnotes above bottom floats. This can be corrected via the
	% \fnbelowfloat command of the stfloats package.
	
	\section{Problem Formulation}
	This paper addresses the estimation of a scalar, time-and-space-dependent, field from given discrete, in both time and space, measurements related to such a field
	provided by multiple sensors placed within the domain of interest.
	The scalar field to be estimated $x \left( \mb{p}, t \right)$ is defined over the space-time domain $\Omega \times \rr_+$, as the solution of a
	\textit{partial differential equation (PDE)} of the form
	\be
	\dfrac{\partial x}{\partial t} +  \mathcal{A}(x) ~=~ f
	\label{PDE}
	\ee
	with (possibly unknown) initial condition $x \left( \mb{p}, 0 \right) = x_0(\mb{p})$, $\mb{p} \in \Omega$, and homogeneous boundary conditions
	\be
	\mathcal B (x) ~=~ 0 \mbox{ on } \partial \Omega\, .
	\label{boundary}
	\ee
	The space domain $\Omega$ is supposed to be bounded and with smooth boundary $ \partial \Omega$.
	
	%subject to the boundary condition
	%\be
	% \alpha \, \mb{n}^T  \dfrac{\partial x}{\partial \mb{p}} + \beta x = g ~~~~~~\mbox{on}~ \partial \Omega.
	%\label{BC}
	%\ee
	The measurements
	\be
	y_{q,i} ~=~ h_i \left( x \left( \mb{s}_i, t_q \right) \right) + v_{q,i}
	\label{meas}
	\ee
	are provided by sensors $i \in \mathcal{S} \defi \{ 1, \dots, S \}$, located at positions $\mb{s}_i \in \Omega$, at discrete sampling instants $t_q$, $q \in
	\Z_+ = \{ 1, 2, \dots \}$, such that $0 < t_1 < t_2 < \cdots$.
	In (\ref{PDE})-(\ref{meas}): $\mb{p} \in \Omega$ denotes the $d$-dimensional ($d \in \{ 1, 2, 3 \}$) position vector; 
	$\mathcal{A}(\cdot)$ and $\mathcal{B}(\cdot)$ are linear operators over a suitable Hilbert space $V$, with $\mathcal A(\cdot)$ self-adjoint; 
	$f \left( \mb{p}, t \right)$ %and $g \left( \mb{p}, t \right)$ 
	is a forcing term possibly affected by process noise; 
	%$\alpha, \beta$ are known real constants;
	%$\mb{n}(\mb{p})$ denotes the unit vector normal to the boundary $\partial \Omega$ in point $\mb{p} \in \partial \Omega$; 
	$h_i(\cdot)$ is the measurement function of sensor $i$; $v_{q,1}, \dots, v_{q,N}$ are mutually independent white measurement noise sequences, also independent from the initial state 
	$x_0(\mb{p})=x \left( \mb{p}, 0 \right)$ for any $\mb{p} \in \Omega$.
	
	More precisely, the aim is to estimate $ x (\mb{p},t ) $ given the information set $Y^t \defi \left\{ y_{q,i}, \forall i \in \mathcal{S} ~\mbox{and}~
	\forall q: t_q \leq t \right\}$.
	This is clearly an infinite-dimensional filtering problem.
	In the next section, it will be shown how it can be approximated into a finite-dimensional filtering problem by exploiting the FE
	method \cite{Pelosi09}-\cite{Brenner96}.
	
	An example of the above general problem is the estimation of the temperature field $x$ over the spatial domain of 
	interest given point measurements of temperature sensors. In this case, $V$ is usually taken as the Sobolev space $H^1(\Omega)$, the measurement function is simply $h(x)=x$, while
	the PDE (\ref{PDE}) reduces to the well known \textit{heat equation} with
	$\mathcal{A}(x) = -  \nabla \cdot \left ( \lambda \nabla (x) \right )$ and  $\mathcal B (x) = \alpha \,  {\partial x}/{\partial \mb{n}} + \beta x$ 
	with $\alpha(\mb{p}) \beta(\mb{p}) \ge 0 $, $\alpha(\mb{p}) + \beta(\mb{p}) > 0 $, $ \forall \mb{p} \in \partial \Omega$.
	Here $\lambda(\mb{p})$ is the \textit{thermal  diffusivity}, $\cdot$ stands for scalar product,
	$\nabla  \defi \partial  / \partial \mb{p} $ denotes the gradient operator, $\mb{n}$ is the outward pointing unit normal vector of the boundary 
	$\partial \Omega$, and $ {\partial x}/{\partial \mb{n}} = \nabla x \cdot \mb{n}$. Clearly, when the thermal  diffusivity is space-independent,
	one has $\mathcal{A}(x) = - \lambda \nabla^2 (x) $, where $\nabla^2 = \nabla \cdot \nabla$ is the Laplacian operator.
	
	Notice that considering homogeneous boundary conditions as in (\ref{boundary}) is not restrictive, since the non-homogeneous case $\mathcal B (x) = g$ on $\partial \Omega$
	can be subsumed into the  homogeneous one by means of the change of variables $z = x-w$, where $w$ is any function belonging to $V$ and satisfying the non-homogeneous boundary conditions.
	
	\section{Centralized Finite Element Kalman Filter}
	In this section, it is shown how to approximate the continuous-time infinite-dimensional system (\ref{PDE}) into a
	discrete-time finite-dimensional linear dynamical system within the FE framework. 
	%In first place (\ref{PDE}) can be recast as a discrete marching-in-time finite difference (FD) equation by
	%substituting the partial derivative in time with its finite differences approximation over a 
	%discrete set of time instants $t_k=k\delta t$ with $k\in \mathbb{N}$
	%\be
	% x_{k+1} = x_k - \delta t \mathcal{A}(x_k) + u_k
	%\label{PDETD}
	%\ee
	%having assumed the simplest possible approach.
	
	By subdividing the domain $\Omega$ into a suitable set of non overlapping regions, or
	elements, and by defining a suitable set of basis functions $\phi_{j} (\mb{p}) \in V \, (j=1,\ldots,n)$ 
	on them, it is possible to write an approximation of the unknown function $x(\mb{p},t)$ as
	\be
	x(\mb{p},t) \approx \sum_{j=1}^{n} \phi_{j}(\mb{p}) \, x_j(t) ~=~ \boldsymbol{\phi}^T(\mb{p}) \, \mb{x}(t)
	\label{EXPA}
	\ee
	where: $x_j(t)$ is the unknown expansion coefficient of function $x(\mb{p},t)$ relative to time $t$ and 
	basis function $\phi_j(\mb{p})$; $\bs{\phi}(\mb{p})  \defi col \{ \phi_j (\mb{p} ) \}_{j=1}^n$ and $\mb{x}(t) \defi col \{ x_j(t) \}_{j=1}^n$.
	
	The choices of the basis functions $\phi_{j}$ and of the elements are key points of the FE method. Typically,
	the elements (triangles or quadrilaterals in 2D, tetrahedral or polyhedral in 3D) define a FE mesh with vertices $\mb{p}_j \in \Omega, j=1,\ldots,n $.
	Then each basis function $\phi_{j}$ is a piece-wise polynomial which vanishes outside the FEs around $\mb{p}_j$ and 
	such that $\phi_{j}(\mb{p}_i) = \delta_{ij}$, $\delta_{ij}$ denoting the Kronecker delta.
	
	In order to apply the Galerkin weighted residual method, let the PDE (\ref{PDE}) be recast in the  following (weak) integral form
	\begin{equation}
	\ba{l}
	\displaystyle{\int_\Omega} \dfrac{\partial x}{\partial t}  \, \psi \, d\mb{p}  + \displaystyle{\int_\Omega} \mathcal A(x) \, \psi \,  d\mb{p} = \displaystyle{\int_\Omega} f \, \psi d\mb{p} 
	\ea
	\label{PDE:weak}
	 \end{equation}
	 where $\psi (\mb{p})$ is a generic space-dependent weight function. The following assumption is now needed. \vspace{.3cm}
	 
	 \begin{enumerate}[\bf {A}1.]
	 \item Under the boundary conditions (\ref{boundary}), the quadratic form 
	 ${\int_\Omega} \mathcal A(\psi) \, \psi \,  d\mb{p} $ is bounded and coercive (i.e., positive definite).
	\end{enumerate}
	\vspace{.3cm}
	 
	 Then, by choosing the test function  $\psi (\mb{p})$ equal to the selected basis functions and exploiting the approximation (\ref{EXPA}) in (\ref{PDE:weak}),
	%applying the Galerkin weighted residual method, and 
	thanks to the linearity of operator $\mathcal{A}(\cdot)$ the 
	usual FE weak form is obtained \cite{Pelosi09}-\cite{Brenner96}
	\begin{equation}
	\ba{l}
	\underbrace{\left[ \displaystyle{\int_\Omega}  \bs{\phi}(\mb{p}) \bs{\phi}^T(\mb{p}) d\mb{p} \right]}_{\mb{M}} \dot{\mb{x}}(t) +
	\underbrace{\left[ \displaystyle{\int_\Omega} \bs{\phi}(\mb{p}) \left[ \mathcal{A} \left( \bs{\phi}(\mb{p}) \right) \right]^T d\mb{p} \right]}_{\mb{S}} \mb{x}(t) \vspace{2mm} \\
	=  \underbrace{\displaystyle{\int_\Omega} \bs{\phi}(\mb{p}) f(\mb{p},t) d\mb{p}}_{\mb{u}(t)}
	\ea
	%\sum_{j=1}^{M} x_{j,k} \iint_\Omega \alpha_{j}\alpha_{i} d\Omega - \\
	%\delta t \sum_{j=1}^{M} x_{j,k} \iint_\Omega \mathcal{A}(\alpha_{j})\alpha_{i} d\Omega + 
	%\iint_\Omega u_k \alpha_{i} d\Omega
	\label{WF}
	\end{equation}
	where $\mathcal{A} \left( \bs{\phi} \right) \defi col \, \{ \mathcal{A}(\phi_j) \}_{j=1}^n$.
	It is evident how the first two integrals in (\ref{WF}) depend only on basis functions and can 
	be computed {\em a priori}. In particular, the first integral yields the well known 
	\textit{mass} matrix  $\mb{M}$, while the second depends on the operator $\mathcal{A}(\cdot)$ and, in the thermal case, 
	is the stiffness matrix $\mb{S}$ \cite{Pelosi09}. The third integral depends on the forcing term $f$, which is assumed to be known, and can hence
	be computed {\em a priori}, leading to a time dependent vector contribution $\mb{u}(t)$.
	
	It is worth pointing out that, in the FE weak form (\ref{WF}), the boundary conditions (\ref{boundary}) can be accounted for in two different ways \cite{Pelosi09,Brenner96}. 
	The so-called {\em essential} boundary conditions
	are handled by imposing them on the solution, i.e., by choosing basis functions belonging to $V_0 = \{x \in V: \; \mathcal B(x) = 0 \mbox{ on }  \partial \Omega\}$. On the other hand, the so-called {\em natural}
	boundary conditions can be directly incorporated into the weak form (\ref{PDE:weak}). 
	%In the FE method, depending on the case, the boundary conditions (\ref{boundary}) can be accounted for in two different ways. e.g., either by explicitly imposing the boundary
	%conditions on the solution by choosing basis functions belonging to $V_0 = \{x \in V: \; \mathcal B(x) = 0 \mbox{ on }  \partial \Omega\}$, or by incorporating them into the weak form (\ref{WF}). 
	%Boundary conditions of the former type are usually referred to as \textit{essential}, while in the latter case we have \textit{natural} boundary conditions. 
	For example, in the case of the heat equation,
	the (isotherm) homogeneous Dirichlet boundary conditions $x = 0 \mbox{ on } \partial \Omega$ are essential, while the (adiabatic) homogeneous Neumann boundary conditions 
	$\partial x / \partial \mb{n} = 0$ are natural. Of course, by letting the functions $\alpha$ and $\beta$ vary on $\partial \Omega$, we can also have a problem with mixed essential/natural boundary conditions.
	In all the cases, the resulting linear differential equation is of the form
	\be \label{eq:diffeq}
	\mb{M} \, \dot{\mb{x}} + \mb{S} \, \mb{x} = \mb{u} + \bm{\epsilon}
	\ee
	where $\bm{\epsilon}$ arises from the approximation error\footnote{If $x$ is sufficiently smooth, then the FE approximation error is point-wise bounded and converges to zero as the size of the FE mesh tends to zero.}  in the finite-	dimensional representation (\ref{EXPA})  of $x$ in terms of basis functions. 
	Notice that $\mb{M}$ turns out to be positive definite by linear independence of the basis functions $\phi_j(\cdot)$. Further, $\mb{S}$ is positive definite as well thanks
	to the coercivity of the quadratic form in the left-hand side of (\ref{PDE:weak}).
	System (\ref{eq:diffeq}) can be discretized in time by different methods 
	(e.g., backward or forward Euler integration, or the zero-order-hold method)
	to provide the discrete-time state-space model
	\be
	\mb{x}_{k+1} = \mb{A}\mb{x}_{k} + \mb{B} \mb{u}_k + \mb{w}_k
	\label{DTM}
	\ee
	where the process noise $\mb{w}_k$ has been introduced to account for the various uncertainties and/or imprecisions (e.g. FE approximation, time discretization, and imprecise knowledge of boundary conditions).
	Specifically, the backward Euler method (here adopted for stability issues) leads to a marching in time FE implementation \cite{Lee95}
	%-\cite{Choi91} 
	which yields (\ref{DTM}) with
	$$
	\ba{l}
	\mb{A} = \left( \mb{I} + \Delta \mb{M}^{-1} \mb{S} \right)^{-1}, ~
	\mb{B} = \mb{A} \mb{M}^{-1} \Delta, \\
	\mb{u}_k \defi \mb{u}((k+1) \Delta), \mb{x}_k \defi \mb{x}(k \Delta) = col \{ x_j(k \Delta) \}_{j=1}^n
	\ea
	$$
	where $\Delta$ denotes the time integration interval. Notice that $\mb{A} $ is well defined for any $\Delta > 0$ since both $\mb{M}$ and $\mb{S}$ are positive definite.
	
	In the following, for the sake of notational simplicity, it will be assumed that each sampling instant is a multiple of $\Delta$,
	i.e., $t_q = T_q \Delta$ with $T_q \in \mathbb Z_+$, and we let $\mathcal T =\{T_1, T_2, \ldots \}$; irregular sampling could, however, be easily dealt with. This amounts to assuming that the numerical integration
	rate of the PDE (\ref{PDE}) in the filter can be higher than the measurement collection rate, which can be useful in order to reduce  numerical errors.
	In a centralized setting where all sensor measurements are available to the filter, the measurement equation (\ref{meas}) takes the discrete-time form
	\be
	\mb{y}_k ~=~  \mb{h} \left( \mb{x}_k \right) + \mb{v}_k
	\label{DTmeas}
	\ee
	for any $k = T_q \in \mathcal T$,
	where
	$$
	\ba{l}
	\mb{y}_k \defi col \left\{ y_{q,i} \right\}_{i\in \mathcal{S}},  \, \mb{h} \left( \mb{x} \right) \defi col \left\{ h_i \left( \bs{\phi}^T(\mb{s}_i) \mb{x} \right) \right\}_{i \in \mathcal{S}}, \\
	\mb{v}_k \defi col \left\{ v_{q,i} \right\}_{i \in \mathcal{S}}
	\ea
	$$
	In particular, in the case wherein all sensors directly measure the target field $x$, i.e. $h_i(x) = x$ for all $i \in \mathcal{S}$, the measurement equation
	(\ref{DTmeas}) turns out to be linear with $\mb{h}(\mb{x})= \mb{C} \mb{x}$, where
	\be
	\mb{C} = col \left\{ \bs{\phi}^T(\mb{s}_i) \right\}_{i \in \mathcal{S}}
	\label{outm}
	\ee
	Summarizing, the original infinite-dimensional continuous-time problem has been reduced to a much simpler finite-dimensional (possibly large-scale) discrete time filtering problem
	(a linear one provided that all sensor measurement functions are linear) to which the \textit{Kalman filter}, or \textit{extended Kalman filter} when sensor
	nonlinearities are considered, can be readily applied.
	The resulting centralized filter recursion becomes:
	\begin{eqnarray}
	&& \hspace{-.8cm} \mb{\hat{x}}_{k|k} = \left \{
	\ba{ll}
	\mb{\hat{x}}_{k|k-1} + \mb{L}_k
	\left( \mb{y}_k - \mb{h} \left( \mb{\hat{x}}_{k|k-1} \right) \right) & \mbox{ if } k \in \mathcal T \\
	\mb{\hat{x}}_{k|k-1}  & \mbox{ otherwise }
	\ea \right . \nonumber \\
	&&  \hspace{-.8cm} \mb{P}_{k|k} = \left \{
	\ba{ll}
	\mb{P}_{k|k-1} - \mb{L}_k  
	\mb{C}_k^T \mb{P}_{k|k-1} \quad \quad \quad \quad & \mbox{ if } k \in \mathcal T \\
	\mb{P}_{k|k-1}   & \mbox{ otherwise }
	\ea \right . \nonumber \\
	&& \hspace{-.8cm} \mb{\hat{x}}_{k+1|k}  =  \mb{A} \mb{\hat{x}}_{k|k} + \mb{B} \mb{u}_k \nonumber \\
	&& \hspace{-.8cm} \mb{P}_{k+1|k}  =  \mb{A} \mb{P}_{k|k} \mb{A}^T + \mb{Q}_k \label{KF}
	\end{eqnarray}
	where
	\begin{eqnarray*}
		&& \mb{C}_k  =  \dfrac{\partial \mb{h}}{\partial \mb{x}} \left( \mb{\hat{x}}_{k|k-1} \right)  \\
		&& \mb{L}_k  =  \mb{P}_{k|k-1} \mb{C}_k \left( \mb{R}_k + \mb{C}_k \mb{P}_{k|k-1} \mb{C}_k^T \right)^{-1}
	\end{eqnarray*}
	for $k \in \mathcal T$. The recursion is initialized from suitable $\mb{\hat{x}}_{1|0}$ and $\mb{P}_{1|0} = \mb{P}_{1|0}^T > \mb{0}$.
	In (\ref{KF}), $\mb{Q}_k$ and $\mb{R}_k$ denote the covariance matrices of the process noise $\mb{w}_k$ and, respectively, measurement noise $\mb{v}_k$, which are assumed as usual to be white, zero-mean, mutually uncorrelated and also uncorrelated with the initial state $\mb{x}_1$.
	
	
	%or, by inverting $\mb{T}$ and renaming $\mb{A}=\mb{I}-\delta t \mb{T}^{-1}\mb{S}$ and
	%$\mb{b}_k = \mb{T}^{-1}\mb{u}_k$, the following state equation is obtained:
	%\color{black} 
	%\be
	%\mb{x}_{k+1} ~=~ \mb{A}_k \mb{x}_k + \mb{B}_k \mb{u}_k + \mb{w}_k
	%\label{state-eq}
	%\ee
	%%\textcolor{red}{$\mb{A}$ non dipende dal tempo $k$ a meno che le caratteristiche del materiale non 
	%%siano tempovarianti}
	%for a state vector $\mb{x}_k = col \left\{ x ( \mb{p}_j, t_k ) \right\}_{j \in \mathcal{M}}$ defined over a suitably built \textit{mesh} $\mathcal{M}$, by exploiting
	%the FE and Euler methods for space and, respectively, time discretisation.
	
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	\section{Distributed Finite Element Kalman Filter}
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	
	%\subsection{Parallel Schwarz Consensus}
	%The Schwarz method  has been originally conceived \cite{Schwa890} for an iterative solution of boundary value problems.
	%Subsequently, it has received renewed interest \cite{Lions88,Gander08} in connection with the parallelisation of PDE solvers.
	%It turns out that the \textit{parallel Schwarz method} (PSM) \cite{Lions88} is especially useful for the distributed filtering problem considered in this work.
	%In loose terms, the idea of the PSM is to decompose the original PDE problem on the overall domain of interest into problems concerning smaller sub-domains, and then to solve in parallel such sub-problems via iterations in which previous solutions concerning neighboring sub-domains are used as boundary conditions.
	In order to develop a scalable distributed filter for monitoring the target field, the idea is to decompose the original problem on the whole domain
	of interest into estimation subproblems concerning smaller subdomains, and then to assign such subproblems to different \textit{nodes} which can locally process and exchange data.
	To this end, let us consider the set of nodes $\mathcal{N} = \{ 1, \dots, N \}$, subdivide the domain $\Omega$ into possibly overlapping subdomains $\Omega_m$, $m \in \mathcal{N}$, such that $\Omega = \bigcup_{m \in \mathcal{N}} \Omega_m$, 
	and assign the task ``estimation of $x$ over $\Omega_m$'' to node $m$.
	Further, let 
	$\mb{y}_q^m \defi col \left\{ y_{q,i} : \mb{s}_i \in \Omega_m \right\}$ denote the vector of local measurements available to node $m$ at time $t_q$.
	
	Hence, the idea is to run in each node $m \in \mathcal{N}$ a field estimator for the region $\Omega_m$ exploiting local measurements
	$\mb{y}_q^m$, information from the nodes assigned to neighboring subdomains, as well as the PDE model (\ref{PDE}) properly discretized in time and space.
	Taking inspiration from the Schwarz method \cite{Schwa890,Lions88,Gander08}, neighboring local estimators should iteratively find a \textit{consensus}
	on the estimates concerning the common parts. The Schwarz method  has been originally conceived \cite{Schwa890} for an iterative solution of boundary value problems.
	Subsequently, it has received renewed interest \cite{Lions88,Gander08} in connection with the parallelization of PDE solvers.
	In loose terms, the idea of the \textit{parallel Schwarz method} is to decompose the original PDE problem on the overall domain of interest into subproblems concerning smaller subdomains, and then to solve in parallel such subproblems via iterations in which previous solutions concerning neighboring 
	subdomains are used as boundary conditions.
	As shown below, such an idea turns out to be especially useful for the distributed filtering problem considered in this work.
	
	To formalize the consensus let us define, for any $m \in \mathcal{N}$, a partition $\left\{ \Gamma_{mj} \right\}_{j \in \mathcal{N}_m}$ of $\partial\Omega_m$ (the boundary of $\Omega_m$) such that
	\be
	\ba{l}
	\Gamma_{mm} = \partial \Omega \cap \partial \Omega_m \vspace{1mm} \\
	\partial \Omega_m = \displaystyle{\bigcup_{j \in \mathcal{N}_m}} \Gamma_{mj} \vspace{1mm} \\
	\Gamma_{mj} \subset \Omega_j ,~~~ \forall j \neq m \vspace{1mm} \\
	\Gamma_{mj} \cap \Gamma_{mh} = \emptyset,~~~ \forall j \neq h
	\ea
	\label{part}
	\ee
	In this way, each piece $\Gamma_{mj}$ of $\partial \Omega_m$ for any $j \in \mathcal{N}_m \backslash \{ m \}$ is uniquely assigned to node $j$. 
	Notice that in the above definitions,  for each node $m$, $\mathcal{N}_m$ indicates the in-neighborhood of node $m$, where $j$ is called an in-neighbor of node $m$ whenever $ \Gamma_{mj} \ne \emptyset$
	(by definition, $\mathcal{N}_m$ includes the node $m$.) This clearly originates a directed network (graph)
	$\mathcal{G} = \left( \mathcal{N}, \mathcal{L} \right)$
	with node set $\mathcal{N}$ and link set $\mathcal{L} \defi \{ (j,m) \in \mathcal{N} \times \mathcal{N}: \Gamma_{mj} \ne \emptyset \}$.
	\begin{figure}[h!]
		\centering
		\includegraphics[width=.7\columnwidth]{./interfaces.pdf}
		\caption{Definition of interfaces $\Gamma_{mj}$ in two different configurations with three overlapping subdomains.}
		\label{fig:interfaces}
	\end{figure}
	
	In order to describe the filtering cycle to be implemented in node $m$ within the sampling interval $[t_q,t_{q+1})$, let us assume that at time $t_q^-$, before the
	acquisition of $\mb{y}_q^m$, such a node is provided with a prior estimate ${\hat{x}}_{q|q-1}^m$ %and relative covariance $\mb{P}_{q|q-1}^m$
	as the result of the previous filtering cycles.
	Let $\delta$ be the time interval necessary for performing one consensus step, i.e., information exchange between neighbors and related computations. Then,
	$L_q \defi  \left( t_{q+1} - t_q \right) / \delta$ represents the number of consensus steps  (equal to the number of allowed data exchanges) in the $q$-th
	sampling interval. Note that, for the sake of notational simplicity, hereafter it is supposed that $ t_{q+1} - t_q$ is an integer multiple of $\delta$, i.e., $L_q \in \mathbb Z_+$.
	Anyway, the method could easily encompass the general case.
	%Let $L \geq 1$ denote the number of consensus steps during a sampling interval) and let
	%$\delta _q \defi \left( t_{q+1} - t_q \right) / L $.
	Then, the above mentioned filtering cycle for the proposed distributed estimation algorithm essentially consists of:
	\begin{enumerate}
		\item \textbf{Correction}, i.e. incorporation (assimilation) of the last measurement $\mb{y}_q^m$ into the current estimate;
		\item \textbf{Consensus}, i.e. alternate exchanges of estimates with the neighborhood $\mathcal{N}_m$ and predictions over the time sub-intervals
		$[t_q + (\ell-1) \delta, t_{q} + \ell \delta]$ for  $\ell = 1, \dots, L_q$, i.e. $L_q$ times.
	\end{enumerate}
	The proposed \textit{Parallel Schwarz Consensus} filter is detailed hereafter. \vspace{.3cm}
	
	{\bf Algorithm 1.}
	\begin{enumerate}
		\item Given $\mb{y}_q^m$, update the prior estimate ${\hat{x}}_{q|q-1}^m$ %and covariance $\mb{P}_{q|q-1}^m$ 
		into ${\hat{x}}_{q|q}^m$. %and $\mb{P}_{q|q}^m$. 
		\item Initialize the consensus with ${\hat{x}}_{q,0}^m = {\hat{x}}_{q|q}^m$ %$\mb{P}_{q,0}^m =\mb{P}_{q|q}^m$ 
		and ${\hat{x}}_{q,-1}^m ={\hat{x}}_{q|q}^m$. %, $\mb{P}_{q,-1}^m =\mb{P}_{q|q}^m$.
		\item For $\ell = 1, \dots, L_q$ proceed as follows
		\begin{enumerate}
			\item Exchange data with the neighborhood; specifically send to neighbor $j$ the data ${\hat{x}}_{q,\ell-1}^m$ %, \mb{P}^m_{q,\ell-1}$ 
			concerning the sub-boundary $\Gamma_{jm} \subset \partial \Omega_j$ , and
			get from neighbor $j$ the data ${\hat{x}}_{q,\ell-1}^j$ %, \mb{P}^j_{q,\ell-1}$ 
			concerning the sub-boundary $\Gamma_{mj} \subset \partial \Omega_m$.
			\item Solve the problem
			\be
			\dfrac{\hat{x}^m_{q,\ell} - \hat{x}_{q,\ell-1}^m}{\delta} + \mathcal{A} \left( \hat{x}_{q,\ell}^m \right) ~=~ f_{q,\ell}  ~~~\mbox{in} ~ \Omega_m
			\label{PDE2}
			\ee
			subject to the Dirichlet boundary conditions
			\be
			\hat{x}_{q,\ell}^m = \hat{x}^j_{q,\ell-1} ~~~\mbox{on}~ \Gamma_{mj} ~~~~ \forall j \in \mathcal{N}_m \backslash \{m \}
			\label{DBC}
			\ee
			and the linear boundary conditions
			\be
			\mathcal B (\hat{x}_{q,\ell}^m) = 0 \mbox{ on } \Gamma_{mm} \, .
			\label{BC}
			\ee
			where $f_{q,\ell}(\mb{p}) \defi f \left( \mb{p}, t_q + \ell \delta \right)$.
		\end{enumerate}
		\item Set ${\hat{x}}_{q+1|q}^m = {\hat{x}}_{q,L_q}^m$  %and $\mb{P}_{q+1|q}^m =\mb{P}_{q,L_q}^m$ 
		for the next cycle.
	\end{enumerate}
	\vspace{.3cm}
	
	Some remarks concerning the above reported algorithm are in order.  As it can be seen from step 3b), the information received
	by neighboring nodes is taken into account by explicitly imposing the non-homogeneous Dirichlet interface conditions (\ref{DBC}) on $\Gamma_{mj}, j \in \mathcal{N}_m \setminus \{m\}$.
	Clearly, a delay is introduced in those terms concerning neighboring nodes which makes the algorithm well-suited for distributed computation.
	With this respect, it is worth pointing out that the proposed consensus algorithm is based on the parallel Schwarz method for evolution problems,
	which, as well known, enjoys nice convergence properties to the centralized solution as the time discretization step $\delta$ tends to zero \cite{Lions88}-\cite{Gander08}.
	Hence, it seems a sensible and promising approach to spread the information through the network. 
	Finally, notice that the prediction step of each local filter is directly incorporated into the consensus algorithm.

	
	\subsection{Implementation via the finite-element method}
	
	In practice, the algorithm, and in particular the solution of the boundary value problem (\ref{PDE2})-(\ref{BC}), has to be implemented
	via a finite dimensional approximation. In particular, we follow the same approach described in Section III for the centralized case
	by constructing a FE mesh for the global domain $\Omega$, and then decomposing such a grid into $N$ overlapping sub-meshes, according to the domain decomposition. 
	%Then the Galerkin weighted residual method is applied for each subdomain in order to derive a local discrete-time discrete-space model. 
	For the sequel, it is important to distinguish vertices lying on the boundary between neighbors (\textit{interface}) from the other vertices of the subdomain. 
	To this end, let ${\rm int} (S)$ denote the interior of a generic set $S$. 
	Then, we introduce the sets of indices $\mathfrak{I}_m \defi \{ i: \mb{p}_i \in {\rm int} (\Omega_m) \cup \Gamma_{mm} \}$ 
	%of the basis functions corresponding to
	and $\mathfrak{I}_{mj} \defi \{ i: \mb{p}_i \in \Gamma_{mj} \}$
	of the basis functions corresponding to \textit{internal} and, respectively, \textit{interface} vertices of subdomain $\Omega_m$.
	In particular, let 
	%$\mb{x}^m \defi col \{ x_j \}, \, m = 1,\dots, N$ of field values in vertices $\mb{p}_j \in \Omega_m$.
	%$\mb{x}^m \defi col \{ x_i : \mb{p}_i \in \Omega_m \cup \, \Gamma_{mm} \}, \, m = 1,\dots, N$
	$\mb{x}^m \defi col \{ x_i : i \in \mathfrak{I}_m \}, \, m = 1,\dots, N$,
	denote the vector of field values in vertices belonging to $ {\rm int} (\Omega_m) \cup \Gamma_{mm} $,
	%of the FE mesh not involved in the consensus procedure, 
	i.e. the \textit{internal} state of subsystem $m$.
	Then, it is possible to extract from (\ref{eq:diffeq}) the rows relative to states $\mb{x}^m$ so that
	%\be
	%\small{ \mb{M}^{mm} \dot{\mb{x}}^m + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{M}^{m j} \dot{\mb{x}}^j + \mb{S}^{mm} \dot{\mb{x}}^m + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{S}^{m j} \dot{\mb{x}}^j = 
	%\mb{u}^m \mb{\epsilon}^m  } 
	%\label{localaugsys}
	%\ee
	\begin{eqnarray}
	&\mb{M}^{mm}& \dot{\mb{x}}^m + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{M}^{m j} \dot{\mb{x}}^j 
	+ \mb{S}^{mm} \mb{x}^m \nonumber \\ && {}  + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{S}^{m j} \mb{x}^j =   
	\mb{u}^m + \bm{\epsilon}^m
	\label{localaugsys}
	\end{eqnarray}
	where the matrices $\mb{M}^{mj}$ and $\mb{S}^{mj}$ take into account the contribution of state variables in vertices $\mb{p}_j \in \Gamma_{mj}$, and $\bm{\epsilon}^m$ accounts for the approximation error in the finite-dimensional 
	representation \eqref{EXPA} of $x$ in terms of basis functions.	
	Notice that both $\mb{M}^{mm}$ and $\mb{S}^{mm}$ are positive definite because so are $\mb{M}$ and $\mb{S}$.
	As a result, the ODE (\ref{eq:diffeq}) can be written %in terms of $\mb{\tilde{x}}$ 
	as the interconnection of $N$ subsystems of the form (\ref{localaugsys}).	 
		
	Each of the subsystems (\ref{localaugsys}) can be discretized in time in the interval $[t_q,t_{q+1}]$
	using a modified backward Euler technique wherein a delay is introduced in those terms concerning neighboring nodes, so that at time $t_q + \ell \delta$ 
	we obtain the following discrete-time linear descriptor system 
	\begin{eqnarray}
	&&{\mb{M}}^{mm} \left(\frac{{\mb{x}}^m_{q,\ell+1}-{\mb{x}}^m_{q,\ell}}{\delta}\right) 
	+ {\mb{S}}^{mm} \, {\mb{x}}^m_{q,\ell+1} \nonumber \\ && {} 
	+  \sum_{j \in \mathcal N_m \setminus \{m\}}   \left[ {\mb{M}}^{mj} \, \left(\frac{{\mb{x}}^j_{q,\ell}-{\mb{x}}^j_{q,\ell-1}}{\delta}\right) + {\mb{S}}^{mj} \, {\mb{x}}_{q,\ell}^j  \right ]\nonumber \\ && {} 
	=  
	{\mb{u}}^m_{q,\ell+1} + {\bm{\epsilon}}^m_{q,\ell+1} + \bm{\tau}^m_{q,\ell}
	\label{time-discr:m}
	\end{eqnarray}
	where ${\mb{x}}^m_{q,\ell} \defi {\mb{x}}^m (t_q + \ell \delta)$, for $\ell = 1 \, \ldots, L$, and $\bm{\tau}_{q,\ell}^m$ denotes the time discretization error at time $t_q + \ell \delta$. The recursion (\ref{time-discr:m}) is 
	initialized at time $t_q$ by setting
	\begin{equation}
	\ba{l}
	{\mb{x}}^m_{q,0} =  {\mb{x}}^m (t_q) , 
	\\ {\mb{x}}^j_{q,0} =  {\mb{x}}^j (t_q), \quad {\mb{x}}^j_{q,-1} =  {\mb{x}}^j (t_q) , \quad j \in \mathcal N_m \setminus \{m\}
	\ea
	\label{eq:init}
	\end{equation}
	The well-posedness of the discretization scheme resulting from (\ref{time-discr:m})-(\ref{eq:init}) will be analyzed in Section IV-B.
	
	It can be readily seen that such a hybrid Euler time discretization implements 
	the Parallel Schwarz method, described earlier. In fact, it is equivalent to approximate $x$ in $\Omega_m$ at time $t_q + \ell \delta$ as
		\begin{eqnarray}
		x(\mb{p}, t_q + \ell \delta) &\approx& \displaystyle \sum_{i \in \mathfrak{I}_m} \phi_{i}^m(\mb{p}) \, x_{q,\ell}^{m,i}     \\ && {} 
		+ \displaystyle \sum_{j \in \mathcal{N}_m \setminus \{m\}}  \displaystyle \sum_{i \in \mathfrak{I}_{mj}} \phi_{i}^j(\mb{p}) \, x_{q,\ell-1}^{j,i} \nonumber
		%\mathfrak{I}_m \defi \{ i: \mb{p}_i \in \Omega_m \cup \Gamma_{mm} \} \\
		%\mathfrak{I}_{mj} \defi \{ i: \mb{p}_i \in \Gamma_{mj} \}
		\label{approx_Dirich}
		\end{eqnarray}
	which in turn corresponds to explicitly imposing non-homogeneous Dirichlet interface conditions on $\Gamma_{mj}, j \in \mathcal{N}_m \setminus \{m\}$ taken from neighboring nodes (like in  (\ref{DBC})).

	Thanks to the positive definiteness of ${\mb{M}}^{mm}$ and ${\mb{S}}^{mm}$, each discretized-model (\ref{time-discr:m}) can be easily transformed into a state-space model of the form
	\begin{eqnarray} \label{statespace_local}
	{\mb{x}}^m_{q,\ell} &=& \mb{A}^m {\mb{x}}^m_{q,\ell-1} + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{A}^{m j} \hat{\mb{x}}^j_{q,\ell-1}      \\ && {} 
	+ \sum_{j \in \mathcal N_m \setminus \{m\}} \bar{\mb{A}}^{m j} {\mb{x}}^j_{q,\ell-2}
	+ \mb{B}^{m} \mb{u}_{q,\ell}^m + {\mb{w}}_{q,\ell}^m  \nonumber
	\end{eqnarray}
	where
	\begin{equation}
	\begin{aligned}
	\mb{A}^m & = \left( \mb{M}^{mm} + \delta \mb{S}^{mm} \right)^{-1} \mb{M}^{mm} \\
	\mb{A}^{m j} &= \left( \mb{M}^{mm} + \delta \mb{S}^{mm} \right)^{-1} \left( - \delta \mb{S}^{mj} - \mb{M}^{mj} \right)  \\
	\bar{\mb{A}}^{m j} &= \left( \mb{M}^{mm} + \delta \mb{S}^{mm} \right)^{-1} \mb{M}^{mj}     \\
	\mb{B}^m &= \left( \mb{M}^{mm} + \delta \mb{S}^{mm} \right)^{-1} \delta 
	\end{aligned} \nonumber
	\end{equation}
	and 
	${\mb{w}}_{q,\ell}^m = ({\mb{M}}^{mm} + \delta  \, {\mb{S}}^{mm} )^{-1} \delta \left( 
	\tilde{\bm{\epsilon}}_{q,\ell+1}^m + \bm{\tau}_{q,\ell}^m \right)$ 
	is the error combining the effects of both spatial and temporal discretizations. 

	Such interconnected models can be exploited so as to derive a FE approximation of the distributed-state estimation algorithm with Parallel Schwarz Consensus (Algorithm 1). In particular, 
	the numerical solution of (\ref{PDE2})-(\ref{BC}) takes the form of the local one-step-ahead predictor for model (\ref{statespace_local}) at time $t_q + (\ell-1) \delta$, 
	whereas the correction step of the local filtering cycle is the usual (extended) Kalman filter update step for the local
	subsystem. The resulting distributed finite-element (extended) Kalman filter is as follows. \vspace{.3cm}
	
	{\bf Algorithm 2.}
		\begin{enumerate}
		\item Given $\mb{y}_q^m$, update the prior estimate $\mb{\hat{x}}_{q|q-1}^m$ and covariance $\mb{P}_{q|q-1}^m$ into
		$\mb{\hat{x}}_{q|q}^m$ and $\mb{P}_{q|q}^m$ as follows
			\begin{eqnarray}
	\mb{\hat{x}}_{q|q}^m &=& \mb{\hat{x}}^m_{q|q-1} + \mb{L}_q^m
	\left( \mb{y}_q^m - \mb{h}^m \left( \mb{\hat{x}}^m_{q|q-1} \right) \right)
	\nonumber \\
	\mb{P}_{q|q}^m &=& \mb{P}_{q|q-1}^m - \mb{L}_q^m  
	(\mb{C}_q^m)^T \mb{P}^m_{q|q-1}  \nonumber \\
	\mb{C}_q^m  &=&  \dfrac{\partial \mb{h}^m}{\partial \mb{x}} \left( \mb{\hat{x}}^m_{q|q-1} \right) \nonumber  \\
	\mb{L}_q^m  &=&  \mb{P}_{q|q-1}^m \mb{C}_q^m \left( \mb{R}_q^m + \mb{C}_q^m \mb{P}_{q|q-1}^m (\mb{C}_q^m)^T \right)^{-1} \nonumber 
	\end{eqnarray}
	where $\mb{h}^m \defi col \left\{ h_{i} : \mb{s}_i \in \Omega_m \right\}$ denote the local measurement function at node $m$.
		
		\item Initialize the consensus with $\mb{\hat{x}}_{q,0}^m =\mb{\hat{x}}_{q|q}^m$, $\mb{P}_{q,0}^m =\mb{P}_{q|q}^m$ and $\mb{\hat{x}}_{q,-1}^m =\mb{\hat{x}}_{q|q}^m$, $\mb{P}_{q,-1}^m =\mb{P}_{q|q}^m$.
		\item For $\ell = 1, \dots, L_q$ proceed as follows
		\begin{enumerate}
			\item Exchange data with the neighborhood; specifically send to neighbor $j$ the data $\mb{\hat{x}}_{q,\ell-1}^m, \mb{P}^m_{q,\ell-1}$ concerning the 
			sub-boundary $\Gamma_{jm} \subset \partial \Omega_j$ , and
			get from neighbor $j$ the data $\mb{\hat{x}}_{q,\ell-1}^j, \mb{P}^j_{q,\ell-1}$ concerning the sub-boundary $\Gamma_{mj} \subset \partial \Omega_m$.
			\item set
			\begin{eqnarray}   \nonumber 
			\hat{\mb{x}}^m_{q,\ell} &=& \mb{A}^m \hat{\mb{x}}^m_{q,\ell-1} + \sum_{j \in \mathcal N_m \setminus \{m\}} \mb{A}^{m j} \hat{\mb{x}}^j_{q,\ell-1}      \\ && {}  \hspace{-1cm}
			+ \sum_{j \in \mathcal N_m \setminus \{m\}} \bar{\mb{A}}^{m j} \hat{\mb{x}}^j_{q,\ell-2}
			+ \mb{B}^{m} \mb{u}_{q,\ell}^m \label{statespace_local:pred} \\ 
		\mb{P}_{q,\ell}^m &=& \gamma^2 \, \mb{A}^m \mb{P}_{q,\ell-1}^m \left ( \mb{A}^m  \right )^T + \mb{Q}^m 
		\label{LDTM-cov}
		\end{eqnarray}
		with $\gamma \ge 1$.
		\end{enumerate}
		\item Set $\mb{\hat{x}}_{q+1|q}^m =\mb{\hat{x}}_{q,L_q}^m$  and $\mb{P}_{q+1|q}^m =\mb{P}_{q,L_q}^m$ for the next cycle.
	\end{enumerate}
	\vspace{.3cm}

	As previously shown, the additional terms $\sum_{j \in \mathcal N_m \setminus \{m\}} \mb{A}^{m j} \hat{\mb{x}}^j_{q,\ell-1}$ and $\sum_{j \in \mathcal N_m \setminus \{m\}} \bar{\mb{A}}^{m j} \hat{\mb{x}}^j_{q,\ell-2}$ 
	in equation (\ref{statespace_local}) arise from the non-homogeneous Dirichlet boundary conditions (\ref{DBC}). In this respect, it is worth noting that the matrices $\mb{A}^{m j}$ and $\bar{\mb{A}}^{m j}$ are 
	sparse since only the components of the neighbor estimates $\mb{\hat  x}^j_{q,\ell-1}$ and $\mb{\hat  x}^j_{q,\ell-2}$ concerning the sub-boundary $\Gamma_{mj}$ are involved.
	The positive real $\gamma > 1 $ is a covariance boosting factor whose role, as will be discussed in the stability analysis of the distributed FE-KF, is that of guaranteeing convergence of the estimates. 	
	The covariance boosting factor is also necessary in order to compensate for the additional uncertainty associated with the boundary conditions at the interfaces, i.e., for the uncertainty associated 
	with the estimates $\sum_{j \in \mathcal N_m \setminus \{m\}} \mb{A}^{m j} \hat{\mb{x}}^j_{q,\ell-1}$ and $\sum_{j \in \mathcal N_m \setminus \{m\}} \bar{\mb{A}}^{m j} \hat{\mb{x}}^j_{q,\ell-2}$ .
	In fact, such an uncertainty is not explicitly accounted for in (\ref{LDTM-cov}) due to the fact that the correlation between the estimates of neighboring nodes is not precisely known.
	The interested reader is referred to  \cite{Farina10} for additional insights on this issue  in the context of distributed estimation of 
	large-scale interconnected systems. As in the centralized context, the positive definite matrix $ \mb{Q}^m$ accounts for the various uncertainties and imprecisions (i.e., discretization errors, imprecise knowledge of the exogenous
	input $f$ and of the boundary conditions (\ref{BC})).

%The additional term $\sum_{j \in \mathcal N_m \setminus \{m\}} \mb{A}^{m j} \mb{P}_{q,\ell-1}^j \left ( \mb{A}^{m j} \right )^T$, which instead is peculiar of the decentralised case, accounts for the fact that each neighbor estimate $\mb{\hat  x}^j_{q,\ell-1}$ is affected by an estimation error with estimated covariance equal to $\mb{P}_{q,\ell-1}^j$.
		%It is worth noting that equation (\ref{LDTM-cov}) is based on the idea (already proposed in \cite{Farina10} in the context of distributed estimation of 
		%large-scale interconnected systems) 
		%of treating each neighbor state as an unknown stochastic input with mean $\mb{\hat  x}^j_{q,\ell-1}$ and covariance $\mb{P}_{q,\ell-1}^j$.
	
		
	\subsection{Numerical stability}
	
	As previously shown, in the FE-based implementation the Parallel Schwarz consensus amounts to performing a hybrid Euler discretization on the interconnection of the $N$ subsystems
	(\ref{localaugsys}). Hence, as a preliminary analysis step, it is important to verify the well-posedness of such a modified discretization method in terms of numerical stability (i.e., in terms of boundedness and convergence 
	of the time-discretization errors). To this end, it is convenient to consider the global dynamics of the interconnection.
	
	Let us consider the augmented global state $\mb{\tilde{x}} \defi col \{ \mb{x}^m, \, m = 1,\dots, N \}$, which clearly contains repeated components of the state due to the overlapping nature of the decomposition.
	Let the vectors $\tilde{\mb{u}}  $ and $\tilde{\bm{\epsilon}}$ be defined in a similar way.
	In terms of $\mb{\tilde{x}}$ the interconnection of the $N$ subsystems of the form (\ref{localaugsys}) gives rise to a global augmented system which obeys the following continuous-time 	linear dynamics 
	\be \label{eq:diffeqtilde}
	\tilde{\mb{M}} \, \dot{ \tilde{\mb{x}} } + \tilde{\mb{S}} \, \tilde{\mb{x}} = \tilde{\mb{u}} + \tilde{\bm{\epsilon}}
	\ee
	Note that the only difference between (\ref{eq:diffeq}) and (\ref{eq:diffeqtilde}) is the presence of duplicated states in the latter linear ODE. Nevertheless, the two systems originate an identical state evolution.
	According to the divide-and-conquer strategy, matrices $\tilde{\mb{M}}$ and $\tilde{\mb{S}}$ can be decomposed as
	\begin{eqnarray} \label{Mdecomp}
	\tilde{\mb{M}}  &=&  \tilde{\mb{M}}_D + \tilde{\mb{M}}_F 
	%\nonumber  
	\\ \tilde{\mb{S}}  &=&  \tilde{\mb{S}}_D + \tilde{\mb{S}}_F \label{Sdecomp}
	\end{eqnarray} 
	with $ \tilde{\mb{M}}_D =$ block-diag($\mb{M}^{11},\dots,\mb{M}^{NN}$), $\tilde{\mb{S}}_D =$ block-diag($\mb{S}^{11},\dots,\mb{S}^{NN}$), whereas $\tilde{\mb{M}}_F$ and $\tilde{\mb{S}}_F$ take into account
	the FE interconnection structure among neighboring subsystems.
	By substituting (\ref{Mdecomp})-(\ref{Sdecomp}) into (\ref{eq:diffeqtilde}), one obtains
	\be \label{eq:diffeqtilde2}
	\tilde{\mb{M}}_D \, \dot{ \tilde{\mb{x}} } + \tilde{\mb{S}}_D \, \tilde{\mb{x}} + \tilde{\mb{M}}_F \, \dot{ \tilde{\mb{x}} } + \tilde{\mb{S}}_F \, \tilde{\mb{x}} = \tilde{\mb{u}} + \tilde{\bm{\epsilon}} \, .
	\ee
	Then, by applying the hybrid Euler time discretization (\ref{time-discr:m}), the time-discretized augmented system takes the form
	\begin{eqnarray}
	&&\hspace{-.5cm} \tilde{\mb{M}}_D \left(\frac{\tilde{\mb{x}}_{q,\ell+1}-\tilde{\mb{x}}_{q,\ell}}{\delta}\right) 
	+ \tilde{\mb{S}}_D\tilde{\mb{x}}_{q,\ell+1} 
	+ \tilde{\mb{M}}_F \left(\frac{\tilde{\mb{x}}_{q,\ell}-\tilde{\mb{x}}_{q,\ell-1}}{\delta}\right) \nonumber \\ && {} 
	+ \tilde{\mb{S}}_F\tilde{\mb{x}}_{q,\ell} =  
	\tilde{\mb{u}}_{q,\ell+1} + \tilde{\bm{\epsilon}}_{q,\ell+1} + \bm{\tau}_{q,\ell}
	\label{time-discr}
	\end{eqnarray}
	 for $\ell = 0, \ldots, L-1$, where $\tilde{\mb{x}}_{q,\ell} \defi \tilde{\mb{x}} (t_q + \ell \delta)$, and, as previously, $\bm{\tau}_{q,\ell}$ denotes the time discretization error at time $t_q + \ell \delta$. Further, the initialization
	(\ref{eq:init}) can be simply rewritten as
	\be
	\ba{l}
	\tilde{\mb{x}}_{q,0} = \tilde{\mb{x}} (t_q) \\
	\tilde{\mb{x}}_{q,-1} = \tilde{\mb{x}} (t_q) 
	\ea
	\label{eq:init:tilde}
	\ee
	
	The following result can now be stated which summarizes the numerical stability properties\footnote{The interested reader is referred to chapter 12 of \cite{num:stab} 
	for an introduction on the concepts of consistency, zero-stability, and convergence of time-discretization methods.} of (\ref{time-discr})-(\ref{eq:init:tilde}). \vspace{.3 cm}
	
	\begin{theorem} 
	The  hybrid Euler time-discretization scheme (\ref{time-discr})-(\ref{eq:init:tilde}) is {\em consistent} with local truncation error of order $1$. Further, it is {\em zero-stable} provided that the following condition holds
	\be\label{eq:rho}
	\rho ( \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F) < 1
	\ee
	where $\rho (\cdot)$ denotes the spectral radius.
	\end{theorem} \vspace{.3cm}
	{\em Proof:} Let $\mathcal{D}$ denote the differential operator in the left-hand side of (\ref{eq:diffeqtilde2}), i.e., 
	\[ 
	\mathcal{D} (\bm{\xi},t) = \tilde{\mb{M}}_D \, \dot{\bm{\xi}}(t)  +  \tilde{\mb{S}}_D \, \bm{\xi} (t) 
	+ \tilde{\mb{M}}_F \, \dot{\bm{\xi}}(t) +  \tilde{\mb{S}}_F \, \bm{\xi} (t)  
	\] 
	for any smooth time-function $\bm{\xi}$. Further, let $\mathcal{D}_\delta$ denote the discrete-time operator in the left-hand side of
	(\ref{time-discr}), i.e.,  
	\begin{eqnarray*}
	\mathcal{D}_\delta (\bm{\xi},t) &=&  \tilde{\mb{M}}_D   \left(\frac{\bm{\xi} (t+\delta) -  \bm{\xi} (t)}{\delta} \right ) +  \tilde{\mb{S}}_D \, \bm{\xi} (t+\delta) \\
	&& {} +  \tilde{\mb{M}}_F   \left(\frac{\bm{\xi} (t) -  \bm{\xi} (t-\delta)}{\delta} \right ) + \tilde{\mb{S}}_F \, \bm{\xi} (t) \, . 
	\end{eqnarray*}
	As well known, the time-discretization scheme (\ref{time-discr})  is consistent
	when, for any smooth time-function $\bm{\xi}$ and for any time $t$,  $\mathcal{D}_\delta (\bm{\xi},t)$ converges to $\mathcal{D} (\bm{\xi},t)$ as $\delta$ goes to $0$. By taking the Taylor expansion
	of $\bm{\xi}$ in $t$, we can write $ \bm{\xi} (t+\delta) = \bm{\xi} (t) + \delta \,  \dot{\bm{\xi}}(t)  + \delta^2 \,  \ddot{\bm{\xi}}(t)  + O(\delta^3)$ and $ \bm{\xi} (t-\delta) = \bm{\xi} (t) - \delta \,  \dot{\bm{\xi}}(t) 
	 + \delta^2 \,  \ddot{\bm{\xi}}(t)   + O(\delta^3)$.
	Hence, after some algebra, we have
	\begin{eqnarray*}
	\mathcal{D}_\delta (\bm{\xi},t) &=& \mathcal{D} (\bm{\xi},t) + \tilde{\mb{M}}_D \, \delta \, \ddot{\bm{\xi}}(t)  + \tilde{\mb{S}}_D \, \delta \, \dot{\bm{\xi}}(t) - \tilde{\mb{M}}_F \, \delta \, \ddot{\bm{\xi}}(t) \\
	&& {} + O (\delta^2)
	\end{eqnarray*}
	which shows that the scheme is consistent and the local truncation error has order $1$.
	
	In order to study zero-stability, we start by considering the limit for $\delta$ going to zero of the time-difference equation (\ref{time-discr}), which is given by
	\be\label{eq:zero:stability}
	\tilde{\mb{M}}_D  \left({\tilde{\mb{x}}_{q,\ell+1}-\tilde{\mb{x}}_{q,\ell}}{}\right) 
	+ \tilde{\mb{M}}_F \left({\tilde{\mb{x}}_{q,\ell}-\tilde{\mb{x}}_{q,\ell-1}}{}\right)  = 0 \, .
	\ee
	In fact, zero-stability of the time-discretization scheme (\ref{time-discr}) corresponds to the asymptotic stability of the discrete-time system (\ref{eq:zero:stability}).
	Then the proof can be concluded by noting that, by defining $\bm{\zeta}_{q,\ell+1}= \tilde{\mb{x}}_{q,\ell+1}-\tilde{\mb{x}}_{q,\ell}$, system  (\ref{eq:zero:stability}) can be rewritten as
	\[
	\left [ \begin{array}{c}
	\tilde{\mb{x}}_{q,\ell+1} \\ \bm{\zeta}_{q,\ell+1} 
	\end{array}
	\right ]
	=
	\left [ \begin{array}{cc}
	\mb{I} & - \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F\\
	\mb{0} & - \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F
	\end{array}
	\right ]
	\left [ \begin{array}{c}
	\tilde{\mb{x}}_{q,\ell} \\ \bm{\zeta}_{q,\ell}
	\end{array}
	\right ]
	\]
	which is stable if and only if condition (\ref{eq:rho}) holds.	
	\qed \vspace{.3cm}

       	Recall that, in view of the {\em Dahlquist's Equivalence Theorem}, zero-stability is necessary and sufficient for convergence of a 
	consistent time-discretization scheme \cite{num:stab}. Hence, under condition (\ref{eq:rho}), the hybrid Euler time-discretization scheme (\ref{time-discr:m}) turns out to be convergent.
	For instance, this means that in each interval $[t_q, t_{q+1}]$ the predicted estimates obtained via the Parallel Schwarz Consensus step (\ref{statespace_local:pred}) converge to the solution
	of a centralized prediction equation of the form
	\[
		\tilde{\mb{M}} \, \dot{ \hat{\mb{x}} } + \tilde{\mb{S}} \, \hat{\mb{x}} = \tilde{\mb{u}} 
	\]
	as the time-discretization step $\delta$ goes to $0$, or equivalently as the number $L$ of consensus steps goes to infinity. \vspace{.3cm}
	
	\begin{remark}
	Taking into account the particular structure of the FE mass matrix $\mb{M}$, which is reflected in the sparse structure of  $\tilde{\mb{M}}$, the numerical stability condition (\ref{eq:rho})
	is usually satisfied in practice (see, for instance, the simulation example of Section VI). In addition, in the unlikely case in which condition (\ref{eq:rho}) does not hold, 
	it is possible to modify the hybrid Euler time-discretization scheme (\ref{time-discr})
	(and hence the implementation of the Parallel Schwarz Consensus) so as to retrieve zero-stability. Specifically, by introducing a suitable  scalar $\omega \in ( 0, 1]$, one can replace (\ref{time-discr})
	with
	\begin{eqnarray}
	&&\tilde{\mb{M}}_D \left(\frac{\tilde{\mb{x}}_{q,\ell+1} - ( 2 - \omega )\, \tilde{\mb{x}}_{q,\ell} + (1-\omega) \,  \tilde{\mb{x}}_{q,\ell-1}  }{\omega \, \delta}\right) 
	\nonumber \\ && {} + \tilde{\mb{S}}_D\tilde{\mb{x}}_{q,\ell+1}  + \tilde{\mb{M}}_F \left(\frac{\tilde{\mb{x}}_{q,\ell}-\tilde{\mb{x}}_{q,\ell-1}}{\delta}\right) + \tilde{\mb{S}}_F\tilde{\mb{x}}_{q,\ell}  \nonumber \\ && {} =  
	\tilde{\mb{u}}_{q,\ell+1} + \tilde{\bm{\epsilon}}_{q,\ell+1} + \bm{\tau}_{q,\ell}
	\label{time-discr:omega}
	\end{eqnarray}
	which is still well-suited for distributed implementation.  Notice that such a modified scheme coincides with (\ref{time-discr}) for $\omega = 1$. Further,
	along the lines of Theorem 1, it is possible to show that (\ref{time-discr:omega}) is consistent for any value of $\omega \in (0,1]$, and zero-stable provided that
	\be
	\rho ( \omega \, \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F - (1 -\omega) \, \mb{I} )  <1 \, .
	\label{eq:rho:omega}
	\ee
	In turn, since 
	\[
	\rho ( \omega \, \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F - (1 -\omega) \, \mb{I} )  \le \max \{ \omega \,  \rho ( \tilde{\mb{M}}_D^{-1} \, \tilde{\mb{M}}_F ) , \,  1-\omega\}
	\]
	for any $\omega \in (0,1]$, condition (\ref{eq:rho:omega}) can be always satisfied
	for suitably small values of $\omega$ even 
	when condition (\ref{eq:rho}) does not hold. The price to be paid for the
	improved numerical stability is a slow-down of the information spread.
	\end{remark}

	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	\section{Stability analysis}
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
	
	
	In this section, the stability of the estimation error dynamics resulting from application of the distributed finite-element Kalman filter of Algorithm 2 is analyzed
	by supposing the measurement equation in each domain to be linear (as it happens when the sensors directly measure the target field like in (\ref{outm})). 
	Further, in order to simplify the notation, the interval $t_{q+1}-t_{q}$ between consecutive measurements is supposed to be constant, 
	so that in each sampling interval $[t_q , t_{q+1})$ a fixed number $L$ of consensus steps is performed.	
	With this respect,
	we make the following assumption. \vspace{.3cm}
	
	\begin{enumerate}[\bf {A}1.]
	\setcounter{enumi}{1}
	\item For each $m \in \mathcal N$, the local measurement function is linear, i.e., $\mb{h}^m (\mb{x}^m) = \mb{C}^m \mb{x}^m$. 
	Further, local observability holds in the sense that the pair $(({\mb A}^m)^L, \mb{C}^m)$ is observable for any $m \in \mathcal N$.
	\end{enumerate}
	\vspace{.3cm}
	
	Notice that the observability condition can be satisfied by choosing each subdomain large enough so that a sufficient number of sensors is included inside.
		
	Let us first rewrite (\ref{time-discr})
	into the state-space form
	\begin{eqnarray}
	\tilde{\mb{x}}_{q,\ell+1} &=& \underbrace{ \left( \tilde{\mb{M}}_D + \delta  \tilde{\mb{S}}_D \right)^{-1} \tilde{\mb{M}}_D }_{\tilde{\mb{A}}_D} \tilde{\mb{x}}_{q,\ell}    \nonumber \\ && {} 
	+ \underbrace{ \left( \tilde{\mb{M}}_D + \delta  \tilde{\mb{S}}_D \right)^{-1}
		\left( - \delta \tilde{\mb{S}}_F - \tilde{\mb{M}}_F \right) }_{\tilde{\mb{A}}_F} \tilde{\mb{x}}_{q,\ell}   \nonumber \\ && {} 
	+ \underbrace{ \left( \tilde{\mb{M}}_D + \delta  \tilde{\mb{S}}_D \right)^{-1} \tilde{\mb{M}}_F }_{\bar{\mb{A}}_F}  \tilde{\mb{x}}_{q,\ell-1} \nonumber \\ && {} 
	+ \underbrace{ \left( \tilde{\mb{M}}_D + \delta  \tilde{\mb{S}}_D \right)^{-1} \delta }_{\tilde{\mb{B}}} \, \tilde{\mb{u}}_{q,\ell+1} + \tilde{\mb{w}}_{q,\ell}
	\label{statespace_tilde}
	\end{eqnarray}
	where, clearly, $\tilde{\mb{A}}_D = {\rm block-diag} ( \mb{A}^{1},\dots,\mb{A}^{N} )$ is the block diagonal matrix of state transition matrices, representing the $N$ isolated subsystems.
	
	Recalling that, in each interval $[t_q, t_{q+1})$, the recursion (\ref{statespace_tilde}) is initialized with the initial conditions (\ref{eq:init:tilde}), it can be easily noticed that
	at the last consensus step $\ell = L$ one obtains
	\be
		\tilde{\mb{x}}_{q,L} = \tilde{\mb{A}}_D^{L} \, \tilde{\mb{x}}_{q,0} +  \tilde{\mb{A}}_{F,L} \tilde{\mb{x}}_{q,0} +  \tilde{\mb{B}}_{L} \tilde{\mb{U}}_{q} +
		 \tilde{\mb{D}}_{L} \tilde{\mb{W}}_{q} 
	\ee
	where $\tilde{\mb{U}}_{q} \defi col \{ \mb{u}_{q,\ell}, \, \ell = 1,\dots, L \}$,  $\tilde{\mb{W}}_{q} \defi col \{ \mb{w}_{q,\ell}, \, \ell = 1,\dots, L \}$
	and $\tilde{\mb{B}}_{L}$, $\tilde{\mb{D}}_{L}$, and $\tilde{\mb{A}}_{F,L}$ are suitable matrices 
	with the latter defining the interconnection couplings between subsystems. Noting that, by definition, $\tilde{\mb{x}}_{q,L} = \tilde{\mb{x}}_{q+1,0} = \tilde{\mb{x}} (T_{q+1} \Delta)$, the latter equation
	can be rewritten as 
	\be
		\tilde{\mb{x}}_{q+1} = \tilde{\mb{A}}_D^{L} \, \tilde{\mb{x}}_{q} +  \tilde{\mb{A}}_{F,L} \tilde{\mb{x}}_{q} +  \tilde{\mb{B}}_{L} \tilde{\mb{U}}_{q} +
		 \tilde{\mb{D}}_{L} \tilde{\mb{W}}_{q} 
	\ee
	where $\tilde{\mb{x}}_{q} \defi  \tilde{\mb{x}} (T_{q} \Delta)$.

	Similarly, application of step 3 of Algorithm 2 yields, at the last consensus step $\ell = L$,
	\be \label{eq:est1}
		\hat{\mb{x}}_{q,L} = \tilde{\mb{A}}_D^{L} \, \hat{\mb{x}}_{q,0} +  \tilde{\mb{A}}_{F,L} \hat{\mb{x}}_{q,0} +  \tilde{\mb{B}}_{L} \tilde{\mb{U}}_{q} \, .	
	\ee
	where $\hat{\mb{x}}_{q,\ell}  \defi col \{ \hat{\mb{x}}^m_{q,\ell} , \, m \in \mathcal N \}$. Further, by defining $\hat{\mb{x}}_{q|q}  \defi col \{ \hat{\mb{x}}^m_{q|q} , \, m \in \mathcal N \}$
	and $\hat{\mb{x}}_{q|q-1}  \defi col \{ \hat{\mb{x}}^m_{q|q-1} , \, m \in \mathcal N \}$, the global correction step of Algorithm 2 at time $t_{q+1}$ can be
	written as 
	\be \label{eq:est2}
	\hat{\mb{x}}_{q+1|q+1} = \hat{\mb{x}}_{q+1|q} + \tilde{\mb{L}}_{q+1} (  \tilde{\mb{y}}_{q+1} -  \tilde{\mb{C}}  \,   \hat{\mb{x}}_{q+1|q}     )
	\ee
	where $\tilde{{\mb{y}}}_{q+1}  \defi col \{ {\mb{y}}^m_{q+1} , \, m \in \mathcal N \}$, 
		   $\tilde{\mb{L}}_{q+1} = {\rm block-diag} ( \mb{L}^{1}_{q+1},\dots,\mb{L}^{N}_{q+1} )$, and
		   $ \tilde{{\mb{C}}}  \defi col \{ {\mb{C}}^m , \, m \in \mathcal N \} $.
		   
	Recalling that $\hat{\mb{x}}_{q,L} = \hat{\mb{x}}_{q+1|q}$ and $\hat{\mb{x}}_{q,0} = \hat{\mb{x}}_{q|q} $, equations (\ref{eq:est1}) and (\ref{eq:est2})  can be easily combined so as to write 
	$\hat{\mb{x}}_{q+1|q+1}$ as a function of $\hat{\mb{x}}_{q|q}$ so as to obtain a recursive expression for the global estimate. In addition, noting that the global output vector can be written as
	$\tilde{\mb{y}}_{q+1} = \tilde{\mb{C}}  \tilde{\mb{x}}_{q+1}  + \tilde{\mb{v}}_{q+1}$
	with $\tilde{{\mb{v}}}_{q+1}  \defi col \{ {\mb{v}}^m_{q+1} , \, m \in \mathcal N \}$, 
	we can also write a recursive expression for  the dynamics of the global estimation error $\tilde{\mb{e}}_{q} \defi col \{  \tilde{\mb{x}}_{q} - \hat{\mb{x}}_{q|q} , \, m \in \mathcal N \} $. Specifically,
	standard calculations yield
	\be \label{eq:est-err}
	\tilde{\mb{e}}_{q+1} = \left ( \mb{I} - \tilde{\mb{L}}_{q+1} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right )  \tilde{\mb{e}}_{q} + \tilde{\bm{\nu}}_q
	\ee
	where the term $\tilde{\bm{\nu}}_q =  ( \mb{I} - \tilde{\mb{L}}_{q+1} \tilde{\mb{C}}  )  \tilde{\mb{D}}_{L} \tilde{\mb{W}}_{q}  + \tilde{\mb{v}}_{q+1}$  accounts for the time/space discretization errors, for the
	measurement noise, and for all the other possible uncertainties.
	
	As for the time evolution of the global covariance matrix $ \tilde{\mb{P}}_{q|q} \defi {\rm block-diag} ( \mb{P}^{1}_{q|q},\dots,\mb{P}^{N}_{q|q} ) $, with similar reasoning as above
	it is an easy matter to see that application of Algorithm 2 leads to the following recursion
	\begin{eqnarray}
		\tilde{\mb{P}}_{q+1|q+1} &=& \left ( \mb{I}  - \tilde{\mb{L}}_{q+1} \tilde{\mb{C}}^T \right ) \tilde{\mb{P}}_{q+1|q} \nonumber \\
		&& \left ( \mb{I}  - \tilde{\mb{L}}_{q+1} \tilde{\mb{C}}^T \right ) \left [ \gamma^{2 L}  \tilde{\mb{A}}_D^{L} \tilde{\mb{P}}_{q|q} (\tilde{\mb{A}}_D^{L}  )^T +  \tilde{\mb{\Phi}} \right ] \nonumber \\
		\label{eq:cov}
	\end{eqnarray}
	where $ \tilde{\mb{\Phi}} \defi \sum_{i=0}^{L-1}  \gamma^{2 i}  \tilde{\mb{A}}_D^{i} \tilde{\mb{Q}} (\tilde{\mb{A}}_D^{i}  )^T $ and  $ \tilde{\mb{Q}} \defi {\rm block-diag} ( \mb{Q}^{1},\dots,\mb{Q}^{N} ) $.
	
	The following stability result can now be stated.
	 \vspace{.3 cm}
	
	\begin{theorem}
	Let assumptions A1 and A2 hold and let the matrices $\tilde{\mb{Q}}$ and $\tilde{\mb{R}} \defi {\rm block-diag} ( \mb{R}^{1},\dots,\mb{R}^{N} ) $ be positive definite. 
	Then, the global covariance matrix asymptotically converges to the the unique positive solution $\tilde{\mb{P}}$ of the
	algebraic Riccati equation
	\[
	\tilde{\mb{P}}^{-1} = \left [ \gamma^{2 L}  \tilde{\mb{A}}_D^{L} \tilde{\mb{P}} (\tilde{\mb{A}}_D^{L}  )^T +  \tilde{\mb{\Phi}} \right ]^{-1} + \tilde{\mb{C}}^T \, \tilde{\mb{R}}^{-1} \, \tilde{\mb{C}} \, .
	\]
	
	In addition, if the scalar $\gamma$ is chosen so that
	\be \label{eq:stab}
	\gamma^L > \left \| \mb{I} + \left ( \tilde{\mb{A}}_D^{L} \right )^{-1}  \tilde{\mb{A}}_{F,L}  \right \|_{\tilde{\mb{P}}} \, ,
	\ee
	where $\| \cdot \|_{\mb{M}}$ denotes the matrix norm induced by the vector norm 
	$\| \mb{x} \|_{\mb{M}} \defi \sqrt{\mb{x}^T
	\mb{M} \mb{x}}$,
	then the dynamics (\ref{eq:est-err}) of the estimation error is exponentially stable.
	\end{theorem} \vspace{.3cm}
	{\em Proof:} Notice first that assumption A2 implies observability of the pair $(\tilde{\mb{A}}_D^L, \tilde{\mb{C}} )$ which, as it can be easily verified through the PBH test, also implies observability of 
	$(\gamma^L \tilde{\mb{A}}_D^L, \tilde{\mb{C}} )$ for any real $\gamma >0$.	
	Then, the convergence of  $\tilde{\mb{P}}_{q|q}$ to $\tilde{\mb{P}} >0$ follows from well known results on discrete-time Kalman filtering, since (\ref{eq:cov}) is
	the standard Kalman filter covariance recursion for a linear system with state matrix $\gamma^L \tilde{\mb{A}}_D^L$ and output matrix $\tilde{\mb{C}}$.
	
	Let now $\tilde{\mb{L}}$ be the steady-state global Kalman gain associated with the steady-state covariance $\tilde{\mb{P}}$. With standard manipulations, it can be seen that $\tilde{\mb{L}}$ and $\tilde{\mb{P}}$
	satisfy the relationship
	\[
	\tilde{\mb{P}} =  ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}}^T  ) \left [ \gamma^{2 L}  \tilde{\mb{A}}_D^{L} \tilde{\mb{P}} (\tilde{\mb{A}}_D^{L}  )^T +  \tilde{\mb{\Phi}} \right ] 
	( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}}^T  )^T + \tilde{\mb{L}}  \tilde{\mb{R}} \tilde{\mb{L}}^T
	\]
	so that
	\[
	( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}}^T  ) \left [ \gamma^{2 L}  \tilde{\mb{A}}_D^{L} \tilde{\mb{P}} (\tilde{\mb{A}}_D^{L}  )^T  \right ]  ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}}^T )^T \le   \tilde{\mb{P}} 
	\]
	and, hence, 
	\be \label{eq:proof:stab}
	\left \| ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}}^T  )  \tilde{\mb{A}}_D^{L}  \right \|_{\tilde{\mb{P}}}  \le 1/ \gamma^L \, .
	\ee
	Notice now that the matrix $ \left ( \mb{I} - \tilde{\mb{L}}_{q+1} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right ) $, which determines the dynamics of the estimation error,
	exponentially converges to $ \left ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right ) $, so that the estimation error dynamics is exponentially stable
	if and only if $ \left ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right ) $ is Schur stable.
	Hence, in order to complete the proof, it is sufficient to observe that
	\begin{eqnarray*}
	\lefteqn{ \left \|  \left ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right ) \right \|_{\tilde{\mb{P}}} } \\ 
	&& {} \le
	\bigg \|  \left ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}} \right ) \, \tilde{\mb{A}}_D^{L}  \bigg  \|_{\tilde{\mb{P}}} \,
	\bigg \|  \mb{I} + \left ( \tilde{\mb{A}}_D^{L} \right )^{-1}  \tilde{\mb{A}}_{F,L}  \bigg \|_{\tilde{\mb{P}}} \\
	&&  {} \le  \bigg \|  \mb{I} + \left ( \tilde{\mb{A}}_D^{L} \right )^{-1}  \tilde{\mb{A}}_{F,L}  \bigg \|_{\tilde{\mb{P}}} \,  /\gamma^L
	\end{eqnarray*} 
	where the latter inequality follows from (\ref{eq:proof:stab}). In fact, this implies that 
	$\left \|  \left ( \mb{I} - \tilde{\mb{L}} \tilde{\mb{C}} \right ) \left ( \tilde{\mb{A}}_D^{L} + \tilde{\mb{A}}_{F,L}  \right ) \right \|_{\tilde{\mb{P}}}  < 1$ whenever (\ref{eq:stab}) holds.
	\qed \vspace{.3cm}
	
	
	\section{Simulation Experiments}
	
	This section provides numerical examples and relative results illustrating the effectiveness of the proposed distributed \textit{finite element Kalman filter} presented in section IV. Consider the transient \textit{heat conduction} problem, introduced in section II as a particular example of \eqref{PDE}, in a thin polygonal metal plate with constant, homogeneous, and isotropic properties. Assuming the thickness of the slab is considerably smaller than the planar dimensions, then the temperature can be assumed to be constant along the width direction, and the problem is reduced to two dimensions.
	Hence, the diffusion process in a thin plate is modelled by the 2D parabolic PDE $\, {\partial x} / {\partial t} - \lambda \left ( {\partial^2 x} / {\partial \xi^2} + {\partial^2 x} / {\partial \eta^2} \right ) = 0$ with boundary condition $\mathcal B (x) = \alpha(\xi,\eta) \,  {\partial x}/{\partial \mb{n}} + \beta(\xi,\eta) x$ such that $\alpha(\xi,\eta) \,\beta(\xi,\eta) \ge 0 $, $\alpha(\xi,\eta) + \beta(\xi,\eta) > 0, \, \forall (\xi,\eta) \in \partial \Omega$. Notice that, $x(\xi,\eta,t)$ denotes the temperature as a function of time $t$ and spatial variables $(\xi,\eta) \in \Omega$, $f = 0$ stands for no inner heat-generation, whereas $\lambda = 1.11 \times 10^{-4} \left[m^2/s\right]$ is the \textit{thermal diffusivity} of copper at $25 \, [\degree C]$ (Table 12, Appendix 2 in \cite{Kreith10}), assumed to be constant in time and space.
	
	A network of $S = 23$ sensors (Fig. \ref{fig:subdomains}) located in the known positions $\mb{s}_i = \left[ \xi_i,\eta_i \right]^T$ is assumed to collect point temperature measurements at regularly time-spaced instants $t_q = q\,T_s$, with $T_s = 100 \, [s]$ and standard deviation of measurement noise $\sigma_v = 0.1 \, [K]$. The considered sensor network has been chosen to guarantee local observability (assumption A2).
	
	The MATLAB PDE Toolbox is used to generate the triangular mesh (252 vertices, 436 elements) shown in Fig. \ref{fig:subdomains} of size $b = 0.2 [m]$ (defined as the length of the longest edge of the element), over the global 2D domain $\Omega$.
	Next, as can be seen from Fig. \ref{fig:subdomains}, the domain under consideration is decomposed into $N = 8$ overlapping subdomains $\Omega_m$, i.e. 
	$\mathcal{N} = \{ 1, \dots, 8 \}$, each being assigned to a \textit{node} with local processing and communication capabilities. 
	%Notice that, for simplicity, it has been assumed that $N=S$ and that there is only a single sensor within each subdomain $\Omega_m$. 
	%The communication topology defining neighboring nodes is shown in Fig. \ref{fig:subdomains}.
	It is worth pointing out that domain decomposition comes with an appropriate partitioning of the original global mesh so that the resulting local grids actually match on the regions of overlap between subdomains.
	%which implements a Delaunay triangulation algorithm. 
	\begin{figure}[!t]
					\centering
					%	\includegraphics[width=\columnwidth]{./subdomains_start_sensors.pdf}
					\includegraphics[width=.5\columnwidth]{./subdomains_start_sensors2.pdf}
					\caption{Global FE mesh (grid of solid lines) generated over $\Omega$ and domain decomposition into 8 overlapping subdomains (dashed polygons). The position of each sensor is denoted by $\ast$.}
					\label{fig:subdomains}
	\end{figure}
	
	Domain triangulation allows for a simple construction of basis functions $\{\phi_{j} (\xi,\eta)\}_{j=1}^n$, %in \eqref{EXPA}
	which are continuous piecewise polynomial functions, such that their value is unity in vertex $j$ and vanishes at the remaining vertices, i.e.
	\begin{eqnarray*}
		&& \hspace{-.8cm} \phi_j(\xi_i,\eta_i) = \left \{
		\ba{ll}
		1 & \mbox{ if } i = j ~~~~~~~~~~~~~~~i,j = 1,2,...,n\\
		0   & \mbox{ if } i \neq j \\
		\ea \right . \nonumber \\
	\end{eqnarray*}
	Here we use continuous piecewise linear functions defined on each element as $\psi_{\mathcal{E}}(\xi,\eta) = c_0 + c_1\xi + c_2\eta$ with $(\xi,\eta) \in \mathcal{E}$ and $c_0, c_1, c_2 \in \rr$, so that each function is uniquely determined by its three nodal values $x_i = \psi_{\mathcal{E}}(\xi_i,\eta_i)$, $i \in {\mathcal{E}}$.
	
	Basis functions are used off-line by the FE centralized filter and in the distributed setup for the element-by-element construction of matrices $\mb{S}$ and $\mb{M}$, introduced in \eqref{WF}.
	Then, the state dynamics of the centralized filter can be directly computed, whereas local estimators first need to extract matrices $\mb{M}^{mm}, \mb{S}^{mm}$ and $\mb{M}^{mj}$, $\mb{S}^{mj}$ in order to calculate $\mb{A}^m, \mb{A}^{m j}$ and $\bar{\mb{A}}^{m j}$ which finally provide the finite-dimensional model of temperature evolution in $\Omega_m$ through \eqref{statespace_local}. 
	Notice that these matrices are evaluated for a fixed sampling interval $\delta = T_s / L$, where $L$ denotes the number of consensus iterations $L_q$ introduced in Section IV, here assumed constant in each sampling interval $q$.
	For a fair comparison between centralized and distributed approaches, a constant time integration interval $\Delta = 10 \, [s]$ has been chosen for the centralised filter.
	
	Notice that, being $\{\phi_{j} (\xi,\eta)\}_{j=1}^n$ functions with a small support defined by the set of triangles sharing node $j$, the resulting \textit{mass} and \textit{stiffness} matrices will be sparse, with the same pattern shown in Fig. \ref{fig:S_centr}.
	In Fig. \ref{fig:SD_SF} it can be seen how the structure of the stiffness matrix changes when considering the augmented system \eqref{eq:diffeqtilde}.
	The distributed pattern of the networked system is highlighted in Fig. \ref{fig:AD_AF}, where $\tilde{\mb{A}}_D$ represents each subsystem as isolated, though affected by the evolution of neighbors through $\tilde{\mb{A}}_F$.
	%Figs. \ref{fig:meshcentr} and \ref{fig:meshdistr} show the mesh generated by the centralised filter and, respectively, the local estimator in $\Omega_6$. 
	%The initial temperature field of the plate is $293 \, [K]$, and the bottom edge is set to $298 \, [K]$. Furthermore, the a-priori estimate taken as first guess of the field of interest is $296 \, [K]$, with diagonal covariance $\mb{P}_{1|0} = 20 \, \mb{I}$. A zero-mean white noise process has been assumed, with covariance 
	%$\mb{Q} = \sigma_w^2 \mb{I}$, where $\sigma_{w} = 3 \, [K]$.  
	%\begin{figure}[h!]
	%	\centering
	%	\includegraphics[width=\columnwidth]{./domain_graph.pdf}
	%	\caption{Graph structure of the distributed scenario considered in experiments 1 and 2. 
	%	In this case, the network originated by nodes $m \in \{ 1, \dots, 16 \}$ is undirected.}
	%	\label{fig:domgraph}
	%\end{figure}
    		\begin{figure}[!t] 
    			\centering 
    			\subfloat[$\mb{S}$: 1626 nonzero elements]{\includegraphics[width=.5\columnwidth]{spy_Stiff_centr_new}%
    				\label{fig:S_centr}}
    			\hfil
    			\subfloat[$\tilde{\mb{S}}_D$: 1632 nonzero elements (red); $\tilde{\mb{S}}_F$: 223 nonzero elements (blue)]{\includegraphics[width=.5\columnwidth]{spy_SD_SF_tilde_new}%
    				\label{fig:SD_SF}}
    			\caption{Sparsity pattern of $252 \times 252$ matrix $\mb{S}$ (a), and $286 \times 286$ matrix $\tilde{\mb{S}} = \tilde{\mb{S}}_D + \tilde{\mb{S}}_F$ (b).}
    			\label{fig_spyS}
    		\end{figure}
    		
    			\begin{figure}[!t]
    				\centering
    				\includegraphics[width=.5\columnwidth]{./spy_AF_AD_tilde_new.pdf}
    				\caption{Sparsity pattern of $\tilde{\mb{A}}_D$ (red) and $\tilde{\mb{A}}_F$ (black).}
    				\label{fig:AD_AF}
    			\end{figure}
     	
	In the following experiments, both FE filters assume the initial temperature field of the plate uniform at $x_0(\xi,\eta) = 300 \, [K]$, and the a-priori estimate taken as first guess $\hat{x}_{1|0}(\xi,\eta) = 305 \, [K]$, with diagonal covariance $\mb{P}_{1|0} = 20 \, \mb{I}$. Moreover, a zero-mean white noise process has been assumed, with covariance $\mb{Q} = \sigma_w^2 \, \mb{I}$, where $\sigma_{w} = 3 \, [K]$.
	Taking into consideration model uncertainty, the \textit{ground truth} of the experiments is represented by a real process simulator implementing a finer mesh (915 vertices, 1695 elements) of size $b = 0.1$ instead of $b=0.2$, running at a higher sample rate ($1 \, Hz$), and aware of the possibly time-varying boundary conditions of the system.
	On the other hand, both distributed and centralised filters have no knowledge of the real system boundary conditions, so they simply assume the plate adiabatic on each side.
	
	The performance of the novel distributed \textit{FE Kalman filter} has been evaluated in terms of Root Mean Square Error (RMSE) of the estimated temperature field, averaged over a set of about 300 sampling points uniformly spread within the domain $\Omega$, and 500 independent Monte Carlo realizations.
		\begin{figure}[!t]
			\centering
			\includegraphics[width=\columnwidth]{./RMSE_bf107_exp1.pdf}
			%	\caption{Scenario 1: RMSE of the cFE-KF and of the dFE-KF as a function of the number of consensus iterations $L$, for $\gamma_1 = 1.07$.}
			\caption{Scenario 1: Comparison of performance of centralised and distributed FE-KF ($\gamma = 1.1$).}
			\label{fig:rmse1}
		\end{figure}
		\begin{figure}[t!]
			\centering
			\includegraphics[width=\columnwidth]{./subplots_fields_scenario1_bf1_1_q50_200}
			\caption{Scenario 1: \textit{True} and estimated temperature fields at time steps $q = 50$ (a,b,c) and $q = 200$ (d,e,f).}
			\label{fig:field1}
		\end{figure}  
	\subsection*{Scenario 1}
	In the first example, transient analysis is performed on a thin adiabatic L-shaped plate (seen in Fig. \ref{fig:subdomains}) with a fixed temperature along the bottom edge. This is a problem with mixed boundary conditions, namely a non-homogeneous Dirichlet condition on the bottom edge of the plate $\partial \Omega_1$, i.e. 
	\be
	x = T_1 \,\,\,\,\,\,\, \mbox{ on } \partial \Omega_1,
	\label{Dbc}
	\ee
	where $T_1 = 315 \, [K]$, and natural homogeneous Neumann boundary conditions on the remaining insulated sides $\partial \Omega_2 = \partial \Omega \setminus \partial \Omega_1$, so that
	\be
	{\partial x}/{\partial \mb{n}} = 0 \,\,\,\,\,\,\, \mbox{ on } \partial \Omega_2.
	\label{Nbc}
	\ee
					\begin{figure}[!t]
						\centering
						\includegraphics[width=\columnwidth]{./RMSE_bf107_exp2.pdf}
						\caption{Scenario 2: Comparison of performance of centralised and distributed FE-KF ($\gamma = 1.1$).}
						\label{fig:rmse2}
					\end{figure}
					\begin{figure}[t!]
						\centering
						\includegraphics[width=\columnwidth]{./subplots_fields_scenario2_bf1_07_q350_900}
						\caption{Scenario 2: \textit{True} and estimated temperature fields at time steps $q = 350$ (a,b,c) and $q = 900$ (d,e,f).}
						\label{fig:field2}
					\end{figure} 
	The duration of each Monte Carlo run is fixed to $3 \times 10^4 \, [s]$ (300 samples).  
	Fig. \ref{fig:rmse1} illustrates the performance comparison between centralized (cFE-KF) and distributed (dFE-KF) filters for $\gamma = 1.1$ and for three different values of the parameter $L$ adopted in the distributed framework. 
	First of all, it can be seen that both FE algorithms succeed in reconstructing the \textit{true} field of the system based on fixed, point-wise temperature observations.
	Moreover, the performance of the distributed FE filters is very close, even for $L = 1$, to that of the centralized filter, which collects all the data in a central node. 
	Last but not least, in the distributed setting the RMSE behaviour improves by increasing the number of consensus steps. 
	This is true for certain values of $\gamma$, whereas for others the difference in performance is considerably reduced, as clearly presented in Fig. \ref{fig:rmse_gamma}.  
	Note that the covariance boosting factor used in (\ref{LDTM-cov}) is set to 
	$\gamma_L = \sqrt[L]{\gamma}, \, \forall L = 1,2,10$, in order to obtain a fairly comparable effect of covariance inflation after $L$ consensus steps for different distributed filters.   
	Further insight on the performance of the proposed FE estimators is provided in Fig. \ref{fig:field1}, which shows the \textit{true} and estimated temperature fields at two different time steps $q = 50$ and $q = 200$, obtained in a single Monte Carlo experiment by using cFE-KF and dFE-KF with $L=10$. 
	
	\subsection*{Scenario 2}
	
	In the second experiment, two time-varying disturbances have been added in order to test the robustness of the proposed FE estimators in a more challenging scenario. To this end, different boundary conditions are considered. Specifically, a time-dependent Dirichlet condition \eqref{Dbc} with $T_1 = 310 \, [K]$ for time steps $q \in \{0,...,299\}$, and $T_2 = 320 \, [K]$ for $q \in \{300,...,1000\}$, is set on all nodes of the bottom edge $\partial \Omega_1$. The top edge of the plate $\partial \Omega_3$ is first assumed adiabatic for $q \in \{0,...,699\}$, then the inhomogeneous Robin boundary condition 
	\be
	\lambda \, {\partial x}/{\partial \mb{n}} + \nu \, x = \nu \, x_e \,\,\,\, \mbox{ on } \partial \Omega_3
	\label{Rbc}
	\ee
	is applied for $q \in \{700,...,1000\}$. This models a sudden exposure of the surface to a fluid, fixed at an external temperature $x_e = 300 \, [K]$, through a
	uniform and constant convection heat transfer coefficient $\nu = 10 \,[W/m^2 K]$. 
	The remaining edges $\partial \Omega_2$ where \eqref{Nbc} holds, are assumed thermally insulated for the duration of the whole experiment, lasting $10^5 \, [s]$ ($1000$ samples).
	%In addition, we consider the initial temperature field on the plate uniform at $293 \, [K]$. 
	%As previously assumed in experiment 1, the centralised and distributed filters have no knowledge of boundary conditions. 
	%\textit{True} and estimated temperature fields are shown for time instants $q = 88$ and $q = 150$ in Fig. \ref{fig:contour}, where isothermal curves correspond to different temperatures spaced of $0.01 [K]$. 
	
%	\begin{table*}[t]
%		\caption{Comparison of the mean value of the RMSE for different values of $\gamma$ used in Algorithm 2.}
%		\begin{center}
%			{
%				\begin{tabular}{|c||c|c|c|c|c|c|c|c|}\hline
%					$\gamma$&1.02&1.04&1.06&1.08&1.10&1.20&1.50&2.00\\\hline\hline
%					dFE-KF ($L = 1$)&0.7906 & 0.7692 & 0.7478 & 0.7262 & 0.7051   & 0.6075 & 0.4531 & 0.5759\\\hline
%					dFE-KF ($L = 2$)&0.7004 & 0.6877 & 0.6751 & 0.6621 & 0.6491 & 0.5847 & 0.4562 & 0.4801\\\hline
%					dFE-KF ($L = 10$)&0.6207 & 0.6138& 0.6069 & 0.5995 & 0.5922 & 0.5531& 0.4564 & 0.4501\\\hline
%					\hline
%					cFE-KF &0.5625&0.5625&0.5625&0.5625&0.5625&0.5625&0.5625&0.5625 \\\hline
%				\end{tabular}
%			}
%			
%			
%			
%		\end{center}
%	\end{table*}
	
				\begin{figure}[!t]
					\centering
					\includegraphics[width=\columnwidth]{./mRMSEdvsmRMSEc2.pdf}
					\caption{Scenario 1: Comparison of the mean value of the RMSE for different values of $\gamma$.}
					\label{fig:rmse_gamma}
				\end{figure}
	
	Performance of the proposed distributed filter has been evaluated for different values of $L$ over 500 independent Monte Carlo runs and compared to the behavior of the centralized FE Kalman filter. Simulation results, in Fig. \ref{fig:rmse2}, show that the proposed FE estimators provide comparable performance to the centralized filter, moreover the gap reduces as $L$ increases. It is worth pointing out that the peaks appearing in the RMSE plot, displayed in Fig. \ref{fig:rmse2}, are due to the abrupt changes of the unknown boundary conditions, which cause considerable jumps of the estimation errors at time steps $300$ and $700$.
	Nevertheless, the filters under consideration manage to compensate for the lack of knowledge and effectively reduce the error, even if, due to persistent and cumulative disturbances on the inferred field profile, errors do not converge to zero.
	The original \textit{ground truth} and the reconstructed fields are depicted in Fig. \ref{fig:field2} for $q = 350$ and $q = 900$.
	
	%\begin{figure}[!t]
	%	\centerline{\subfigure[Ground truth.]{\includegraphics[width =1in]{contour_ex2_simulator_88less}
	%			\label{fig:contourS88}}
	%		\hfil
	%		\subfigure[cFE-KF.]{\includegraphics[width=1in]{contour_ex2_centralised_88less}
	%			\label{fig:contourC88}}
	%		\hfil
	%		\subfigure[dFE-KF ($L = 10$).]{\includegraphics[width=1in]{contour_ex2_distributed_88less}
	%			\label{fig:contourD88}}}
	%	\label{fig_sim}
	%\end{figure}
	%\begin{figure}[!t]
	%	\centerline{\subfigure[Ground truth.]{\includegraphics[width =1in]{contour_ex2_simulator_150less}
	%			\label{fig:contourS150}}
	%		\hfil
	%		\subfigure[cFE-KF.]{\includegraphics[width=1in]{contour_ex2_centralised_150less}
	%			\label{fig:contourC150}}
	%		\hfil
	%		\subfigure[dFE-KF ($L = 10$).]{\includegraphics[width=1in]{contour_ex2_distributed_150less}
	%			\label{fig:contourD150}}}
	%	\caption{\textit{True} and estimated temperature fields in experiment 2 at time steps $q = 88$ (a,b,c) and $q = 150$ (d,e,f).}
	%	\label{fig:contour}
	%\end{figure} 
	%\vspace{0.05cm}
	%\begin{figure}[h!]
	%	\centering
	%	\includegraphics[scale=.28]{./RMSE_ex2.pdf}
	%	\caption{RMSE of the FE filters in the second experiment.}
	%	\label{fig:rmse2}
	%\end{figure} 
	
	
	\section{Conclusions}
	The paper has dealt with the decentralised estimation of a time-evolving and space-dependent field governed by a linear partial differential equation, given point-in space measurements of multiple sensors deployed over the area of interest.
	The originally infinite-dimensional filtering problem has been approximated into a finite-dimensional large-scale one via the \textit{finite element} method and, further, a consensus approach inspired by the parallel Schwarz method for domain decomposition has allowed to nicely scale the
	overall problem complexity with respect to the number of used processing nodes.
	Combining these two ingredients, a novel computationally efficient consensus finite-element Kalman filter has been proposed to solve in a decentralized and scalable fashion filtering problems involving distributed-parameter systems.
Both numerical stability of the finite-element approximation and exponential stability of the proposed consensus finite-element Kalman filter have been analysed.
Simulation experiments have been presented in order to demonstrate the validity of the proposed approach.

The results of this work can be extended to the estimation of fields governed by more general partial differential equations and also
be applied to the estimation/localization of diffusive sources.

	%Future work on the consensus finite element Kalman filter will concern
	%extension to nonlinear partial differential equations and
	%replacement of the currently adopted data exchange with data fusion for the consensus on boundary estimates-covariances.
	
	
	
	% if have a single appendix:
	%\appendix[Proof of the Zonklar Equations]
	% or
	%\appendix  % for no appendix heading
	% do not use \section anymore after \appendix, only \section*
	% is possibly needed
	
	% use appendices with more than one appendix
	% then use \section to start each appendix
	% you must declare a \section before using any
	% \subsection or using \label (\appendices by itself
	% starts a section numbered zero.)
	%
	
	
	%\appendices
	%\section{Proof of the stability result}
	%Appendix one text goes here.
	
	% you can choose not to have a title for an appendix
	% if you want by leaving the argument blank
	%\section{}
	%Appendix two text goes here.
	
	
	
	% Can use something like this to put references on a page
	% by themselves when using endfloat and the captionsoff option.
	\ifCLASSOPTIONcaptionsoff
	\newpage
	\fi
	
	
	
	% trigger a \newpage just before the given reference
	% number - used to balance the columns on the last page
	% adjust value as needed - may need to be readjusted if
	% the document is modified later
	%\IEEEtriggeratref{8}
	% The "triggered" command can be changed if desired:
	%\IEEEtriggercmd{\enlargethispage{-5in}}
	
	% references section
	
	% can use a bibliography generated by BibTeX as a .bbl file
	% BibTeX documentation can be easily obtained at:
	% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
	% The IEEEtran BibTeX style support page is at:
	% http://www.michaelshell.org/tex/ieeetran/bibtex/
	%\bibliographystyle{IEEEtran}
	% argument is your BibTeX string definitions and bibliography database(s)
	%\bibliography{IEEEabrv,../bib/paper}
	%
	% <OR> manually copy in the resultant .bbl file
	% set second argument of \begin to the number of references
	% (used to reserve space for the reference number labels box)
	
	\begin{thebibliography}{99}
		
		%\bibitem{IEEEhowto:kopka}
		%H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
		%  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
% weather forecasting
\bibitem{weather}
M. Fisher, J. Nocedal, Y. Tremolet and S.J. Wright,
``Data assimilation in weather forecasting: A case study in PDE-constrained optimization'', 
\emph{ Optimization and Engineering},  vol. 10, no. 3, pp. 409-426, 2009.

% regulation of water flow
\bibitem{water}
J. de Halleux, C. Prieur, J.M. Coron, B. d'Andr\'ea-Novel and G. Bastin, 
``Boundary feedback control in networks of open channels'',
\emph{Automatica}, vol. 39, no. 8, pp. 1365-1376, 2003.

% pollution monitoring
\bibitem{pollution}
M. Ortner, A. Nehorai and A. Jeremic, 
``Biochemical transport modeling and Bayesian source estimation in realistic environments'',
\emph{IEEE Trans. on Signal Processing}, vol. 55, no. 6, pp. 2520-2532, 2007.

% monitoring of thermostatically controlled loads in smart grids
\bibitem{smart-grids}
S. Moura, J. Bendtsen and V. Ruiz, 
``Observer design for boundary coupled PDEs: application to thermostatically controlled loads in smart grids,''
\emph{Proc. of the IEEE Conference on Decision and Control}, pp. 6286-6291, Florence, Italy, 2013

%reconstruction of highway traffic flow
\bibitem{traffic}
C. G. Claudel and A. M. Bayen, 
``Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: Theory'',
\emph{ IEEE Trans.  on Automatic Control}, vol. 55, no. 6, pp. 1142-1157, 2010

% Consensus filters for finite-dimensional systems
	
\bibitem{Olfati1} R. Olfati-Saber, J.A. Fax and R. Murray, \textquotedblleft
 Consensus and cooperation in networked multi-agent
 systems,\textquotedblright\ \textit{Proc. of the IEEE}, vol. 95, no. 1, pp.
215-233, 2007.

\bibitem{Xiao} L. Xiao, S. Boyd and S. Lall, \textquotedblleft A scheme for
robust distributed sensor fusion based on average
consensus,\textquotedblright\ \textit{Proc. 4th Int. Symp. on Information
Processing in Sensor Networks}, pp. 63-70, Los Angeles, CA, 2005.

\bibitem{Calafiore} 
G.C. Calafiore and F. Abrate, \textquotedblleft
Distributed linear estimation over sensor networks,\textquotedblright\
\textit{Int. J. of Control}, vol. 82, no. 5, pp. 868-882, 2009.

\bibitem{automatica}
G. Battistelli and L. Chisci, 
``Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability'', \emph{Automatica}, 
vol. 5, no. 3, pp. 707-718, 2014.
		
\bibitem{spl}
G. Battistelli, L. Chisci, and C. Fantacci, ``Parallel consensus on likelihoods and priors for networked nonlinear filtering'', 
\emph{IEEE Signal Processing Letters}, vol. 21, no. 7, pp. 787-791, 2014.

% Consensus filter for multi-object estimation	
				
		\bibitem{J-STSP}
		G. Battistelli, L. Chisci, C. Fantacci, A. Farina and A. Graziano, ``Consensus CPHD filter for distributed multitarget tracking'',
		\emph{IEEE Journal of Selected Topics in Signal Processing}, vol. 7, no. 3, pp. 508-520, 2013.
		
% Distributed estimation for large-scale systems
				
		\bibitem{Khan08}
		U.A. Khan and J. Moura, ``Distributing the Kalman filter for
		large-scale systems", \emph{ IEEE Trans. on Signal Processing}, \relax vol. 66, no. 10, 
		pp. 4919--4935, 2008.
		
		\bibitem{Stank09}
		S. Stankovic, M.S. Stankovic and D.M. Stepanovic, ``Consensus based
		overlapping decentralized estimation with missing observations and
		communication faults", \emph{Automatica}, \relax vol. 45, no. 6, 
		pp. 1397--1406, 2009.
		
		\bibitem{Farina10}
		M. Farina, G. Ferrari-Trecate and R. Scattolini, ``Moving-horizon
		partition-based state estimation of large-scale systems", \emph{Automatica},
		\relax vol. 46,  no. 5, pp. 910--918, 2010.
		
% centralised estimation of a spatially distributed, time-varying random field from noisy measurements collected by a wireless sensor network, with % bandwidth and energy constraints
\bibitem{zhang-moura-krogh}
H. Zhang, J. Moura and B. Krogh, 
``Dynamic field estimation using wireless sensor networks: Tradeoffs between estimation error and communication cost'',
\emph{IEEE Trans. on Signal Processing}, vol. 57, no. 6, pp. 2383-2395, 2009.

% distributed algorithm for observer design for linear continuous-time systems
\bibitem{pasqualetti}
F. D\"{o}rfler, F. Pasqualetti and F. Bullo, “
``Continuous-time distributed observers with discrete communication'',
\textit{IEEE Journal of Selected Topics in Signal Processing}, vol. 7, no. 2, pp. 296-304, 2013.		



% Consensus filters for PDE systems
		
		\bibitem{Deme10}
		M.A. Demetriou, ``Design of consensus and adaptive consensus filters for
		distributed parameter systems", \emph{Automatica}, \relax vol. 46, no. 2, 
		pp. 300--311, 2010.
		
		\bibitem{Deme13}
		M.A. Demetriou, ``Adaptive consensus filters of spatially distributed systems with limited connectivity'', \textit{Proc, 52nd IEEE Conference on Decision and Control}, pp. 442-447, Firenze, Italy, 2013.
		
		
		% Schwarz decomposition methods
		
		\bibitem{Schwa890}
		H.A. Schwarz, \emph{Gesammelte mathematische abhandlungen. Band I, II},
		\relax AMS Chelsea Publishing, Bronx, NY, 1890.
		
		\bibitem{Lions88}
		P.L. Lions, \emph{On the Schwarz alternating method. I}, \relax in First
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		Equations, R.~Glowinski et al., SIAM, Philadelphia, PA, pp. 1--42, 1988,.
		
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		M.J. Gander, ``Schwarz methods over the course of time", \emph{Electronic
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		T.F. Chan and T.P. Mathew, ``Domain decomposition algorithms'', \emph{Acta Numerica}, vol. 3, pp. 61--143, 1994.
		
		\bibitem{Tos05}
		A. Toselli and O. Widlund, \emph{Domain decomposition methods -- Algorithms
			and theory}, \relax Springer--Verlag, Berlin, Germany, 2005.
		
		\bibitem{Smith96}
		B. Smith, P. Bjorstad and W. Gropp, \emph{Domain decomposition: parallel
			multilevel methods for elliptic partial differential equations}, \relax
		Cambridge University Press, New York, NY, 1996.
		
		%% Testi FEM
		%%
		\bibitem{Pelosi09}
		G. Pelosi, R. Coccioli and S. Selleri, \emph{Quick finite elements for
			electromagnetic waves}, \relax Artech House, Norwood, MA, 2009.
		
		\bibitem{Brenner96}
		S.C. Brenner and L.R. Scott, \emph{The mathematical theory of finite
			element methods}, \relax Springer--Verlag, New York, NY, 1996.
		%%
		%% Articoli FEM temporale calore
		%%
		\bibitem{Lee95}
		J.-F. Lee, J.-F. and Z. Sacks, ``Whitney elements time domain {(WETD)} methods'', 
		\emph{IEEE Trans. on Magnetics.}, vol. 31, no. 3, pp. 1325-1329, 1995.
		
		
		%\bibitem{Choi91}
		%C.T.M. Choi and A. Konrad, ``Finite element modeling of the RF heating process'',
		%\emph{IEEE Trans. on Magnetics}, vol. 27, pp. 4227-4230, 1991.
		
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		%O. C.~Zienkiewicz, \emph{The Finite Element Method in Engineering Science},
		%\relax McGraw-Hill, New York, NY, 1971.
		%
		%\bibitem{Zienk05}
		%O. C.~Zienkiewicz, R. L.~Taylor, and J. Z.~Zhu \emph{The Finite Element
		%Method: Its Basis and Fundamentals}, \relax Elsevier, Burlington, MA, 2005.
		%
		%\bibitem{Hughes87}
		%T. J.~Hughes, \emph{The Finite Element Method - Linear Static and Dynamic
		%Finite Element Analysis}, \relax Prentice-Hall, Englewood Cliffs, NJ, 1987.
		%
		%\bibitem{John88}
		%C.~Johnson, \emph{Numerical Solution of Partial Differential Equations by
		%the Finite Element Method}, \relax Cambridge University Press, Cambridge,
		%UK, 1988.
		%
		%\bibitem{Axel84}
		%O.~Axelsson and V. A.~Barker, \emph{Finite Element Solution of Boundary
		%Value Problems: Theory and Computation}, \relax  Academic Press, London, UK,
		%1984.
		%
		%\bibitem{Brenner96}
		%S. C.~Brenner and L. R.~Scott, \emph{The Mathematical Theory of Finite
		%Element Methods}, \relax Springer--Verlag, New York, NY, 1996.
		%
		%\bibitem{Larson13}
		%M. G.~Larson and F.~Bengzon, \emph{The Finite Element Method: Theory,
		%Implementation, and Applications}, \relax Springer, Heidelberg, Germany,
		%2013.
		%
		%\bibitem{Ciarlet78}
		%T.~Ciarlet, \emph{The Finite Element Method for Elliptic Problems in Applied
		%Mathematics}, \relax North-Holland, Amsterdam, The Netherlands, 1978.
		%
		%\bibitem{Pelosi09}
		%G.~Pelosi, R.~Coccioli, and S.~Selleri, \emph{Quick Finite Elements for
		%Electromagnetic Waves}, \relax Artech House, Norwood, MA, 2009.
		
		\bibitem{jap1}
		R. Suga and M. Kawahara, ``Estimation of tidal current using Kalman filter finite-element method'', \emph{Computers \& Mathematics with Applications}, vol. 52, no. 8-9, pp. 1289-1298, 2006.
		
		\bibitem{jap2}
		Y. Ojima and M. Kawahara, ``Estimation of river current using reduced Kalman filter finite element method'', \emph{Computer Methods in Applied Mechanics and Engineering}, vol. 198, no. 9-12, pp. 904-911, 2009.
		
				\bibitem{ECC2015}
		G. Battistelli, L. Chisci, N. Forti, G. Pelosi and. S. Selleri, ``Distributed finite element Kalman filter'',
		\emph{Proc. of the European Control Conference 2015}, pp. 3700-3705, Linz, Austria, 2015.
		
		\bibitem{num:stab}
		 E. {S\"uli} and D.F. Mayers, \emph{An introduction to numerical analysis}, \relax Cambridge University Press, Cambridge, UK, 2003.
		
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		F. Kreith, R.M. Manglik and M.S. Bohn, \emph{Principles of heat transfer}, \relax Springer--Verlag, New York, NY, 1996.
		
	\end{thebibliography}
	
	
%	% biography section
%	% 
%	% If you have an EPS/PDF photo (graphicx package needed) extra braces are
%	% needed around the contents of the optional argument to biography to prevent
%	% the LaTeX parser from getting confused when it sees the complicated
%	% \includegraphics command within an optional argument. (You could create
%	% your own custom macro containing the \includegraphics command to make things
%	% simpler here.)
%	%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
%	% or if you just want to reserve a space for a photo:
%	
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\end{document}



bare_adv.tex

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%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/


% IEEEtran V1.7 and later provides for these CLASSINPUT macros to allow the
% user to reprogram some IEEEtran.cls defaults if needed. These settings
% override the internal defaults of IEEEtran.cls regardless of which class
% options are used. Do not use these unless you have good reason to do so as
% they can result in nonIEEE compliant documents. User beware. ;)
%
%\newcommand{\CLASSINPUTbaselinestretch}{1.0} % baselinestretch
%\newcommand{\CLASSINPUTinnersidemargin}{1in} % inner side margin
%\newcommand{\CLASSINPUToutersidemargin}{1in} % outer side margin
%\newcommand{\CLASSINPUTtoptextmargin}{1in}   % top text margin
%\newcommand{\CLASSINPUTbottomtextmargin}{1in}% bottom text margin




%
\documentclass[10pt,journal,compsoc]{IEEEtran}
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[10pt,journal,compsoc]{../sty/IEEEtran}


% For Computer Society journals, IEEEtran defaults to the use of 
% Palatino/Palladio as is done in IEEE Computer Society journals.
% To go back to Times Roman, you can use this code:
%\renewcommand{\rmdefault}{ptm}\selectfont





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)



% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
  % IEEE Computer Society needs nocompress option
  % requires cite.sty v4.0 or later (November 2003)
  \usepackage[nocompress]{cite}
\else
  % normal IEEE
  \usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society  papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later.





% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%\usepackage{acronym}
% acronym.sty was written by Tobias Oetiker. This package provides tools for
% managing documents with large numbers of acronyms. (You don't *have* to
% use this package - unless you have a lot of acronyms, you may feel that
% such package management of them is bit of an overkill.)
% Do note that the acronym environment (which lists acronyms) will have a
% problem when used under IEEEtran.cls because acronym.sty relies on the
% description list environment - which IEEEtran.cls has customized for
% producing IEEE style lists. A workaround is to declared the longest
% label width via the IEEEtran.cls \IEEEiedlistdecl global control:
%
% \renewcommand{\IEEEiedlistdecl}{\IEEEsetlabelwidth{SONET}}
% \begin{acronym}
%
% \end{acronym}
% \renewcommand{\IEEEiedlistdecl}{\relax}% remember to reset \IEEEiedlistdecl
%
% instead of using the acronym environment's optional argument.
% The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/acronym/


%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


%\usepackage{mdwmath}
%\usepackage{mdwtab}
% Also highly recommended is Mark Wooding's extremely powerful MDW tools,
% especially mdwmath.sty and mdwtab.sty which are used to format equations
% and tables, respectively. The MDWtools set is already installed on most
% LaTeX systems. The lastest version and documentation is available at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/mdwtools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.


%\usepackage{eqparbox}
% Also of notable interest is Scott Pakin's eqparbox package for creating
% (automatically sized) equal width boxes - aka "natural width parboxes".
% Available at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/eqparbox/




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=footnotesize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a sans serif font rather
% than the serif font used in traditional IEEE formatting and thus the need
% to invoke different subfig.sty package options depending on whether
% compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/


%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and 
% Axel Sommerfeldt. This package may be useful when used in conjunction with 
% IEEEtran.cls'  captionsoff option. Some IEEE journals/societies require that
% submissions have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.4.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a 
% page by themselves.





% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.


% NOTE: PDF thumbnail features are not required in IEEE papers
%       and their use requires extra complexity and work.
%\ifCLASSINFOpdf
%  \usepackage[pdftex]{thumbpdf}
%\else
%  \usepackage[dvips]{thumbpdf}
%\fi
% thumbpdf.sty and its companion Perl utility were written by Heiko Oberdiek.
% It allows the user a way to produce PDF documents that contain fancy
% thumbnail images of each of the pages (which tools like acrobat reader can
% utilize). This is possible even when using dvi->ps->pdf workflow if the
% correct thumbpdf driver options are used. thumbpdf.sty incorporates the
% file containing the PDF thumbnail information (filename.tpm is used with
% dvips, filename.tpt is used with pdftex, where filename is the base name of
% your tex document) into the final ps or pdf output document. An external
% utility, the thumbpdf *Perl script* is needed to make these .tpm or .tpt
% thumbnail files from a .ps or .pdf version of the document (which obviously
% does not yet contain pdf thumbnails). Thus, one does a:
% 
% thumbpdf filename.pdf 
%
% to make a filename.tpt, and:
%
% thumbpdf --mode dvips filename.ps
%
% to make a filename.tpm which will then be loaded into the document by
% thumbpdf.sty the NEXT time the document is compiled (by pdflatex or
% latex->dvips->ps2pdf). Users must be careful to regenerate the .tpt and/or
% .tpm files if the main document changes and then to recompile the
% document to incorporate the revised thumbnails to ensure that thumbnails
% match the actual pages. It is easy to forget to do this!
% 
% Unix systems come with a Perl interpreter. However, MS Windows users
% will usually have to install a Perl interpreter so that the thumbpdf
% script can be run. The Ghostscript PS/PDF interpreter is also required.
% See the thumbpdf docs for details. The latest version and documentation
% can be obtained at.
% http://www.ctan.org/tex-archive/support/thumbpdf/


% NOTE: PDF hyperlink and bookmark features are not required in IEEE
%       papers and their use requires extra complexity and work.
% *** IF USING HYPERREF BE SURE AND CHANGE THE EXAMPLE PDF ***
% *** TITLE/SUBJECT/AUTHOR/KEYWORDS INFO BELOW!!           ***
\newcommand\MYhyperrefoptions{bookmarks=true,bookmarksnumbered=true,
pdfpagemode={UseOutlines},plainpages=false,pdfpagelabels=true,
colorlinks=true,linkcolor={black},citecolor={black},urlcolor={black},
pdftitle={Bare Demo of IEEEtran.cls for Computer Society Journals},%<!CHANGE!
pdfsubject={Typesetting},%<!CHANGE!
pdfauthor={Michael D. Shell},%<!CHANGE!
pdfkeywords={Computer Society, IEEEtran, journal, LaTeX, paper,
             template}}%<^!CHANGE!
%\ifCLASSINFOpdf
%\usepackage[\MYhyperrefoptions,pdftex]{hyperref}
%\else
%\usepackage[\MYhyperrefoptions,breaklinks=true,dvips]{hyperref}
%\usepackage{breakurl}
%\fi
% One significant drawback of using hyperref under DVI output is that the
% LaTeX compiler cannot break URLs across lines or pages as can be done
% under pdfLaTeX's PDF output via the hyperref pdftex driver. This is
% probably the single most important capability distinction between the
% DVI and PDF output. Perhaps surprisingly, all the other PDF features
% (PDF bookmarks, thumbnails, etc.) can be preserved in
% .tex->.dvi->.ps->.pdf workflow if the respective packages/scripts are
% loaded/invoked with the correct driver options (dvips, etc.). 
% As most IEEE papers use URLs sparingly (mainly in the references), this
% may not be as big an issue as with other publications.
%
% That said, Vilar Camara Neto created his breakurl.sty package which
% permits hyperref to easily break URLs even in dvi mode.
% Note that breakurl, unlike most other packages, must be loaded
% AFTER hyperref. The latest version of breakurl and its documentation can
% be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/breakurl/
% breakurl.sty is not for use under pdflatex pdf mode.
%
% The advanced features offer by hyperref.sty are not required for IEEE
% submission, so users should weigh these features against the added
% complexity of use.
% The package options above demonstrate how to enable PDF bookmarks
% (a type of table of contents viewable in Acrobat Reader) as well as
% PDF document information (title, subject, author and keywords) that is
% viewable in Acrobat reader's Document_Properties menu. PDF document
% information is also used extensively to automate the cataloging of PDF
% documents. The above set of options ensures that hyperlinks will not be
% colored in the text and thus will not be visible in the printed page,
% but will be active on "mouse over". USING COLORS OR OTHER HIGHLIGHTING
% OF HYPERLINKS CAN RESULT IN DOCUMENT REJECTION BY THE IEEE, especially if
% these appear on the "printed" page. IF IN DOUBT, ASK THE RELEVANT
% SUBMISSION EDITOR. You may need to add the option hypertexnames=false if
% you used duplicate equation numbers, etc., but this should not be needed
% in normal IEEE work.
% The latest version of hyperref and its documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/hyperref/





% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Advanced Demo of IEEEtran.cls\\ for Computer Society Journals}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
%
%\IEEEcompsocitemizethanks is a special \thanks that produces the bulleted
% lists the Computer Society journals use for "first footnote" author
% affiliations. Use \IEEEcompsocthanksitem which works much like \item
% for each affiliation group. When not in compsoc mode,
% \IEEEcompsocitemizethanks becomes like \thanks and
% \IEEEcompsocthanksitem becomes a line break with idention. This
% facilitates dual compilation, although admittedly the differences in the
% desired content of \author between the different types of papers makes a
% one-size-fits-all approach a daunting prospect. For instance, compsoc 
% journal papers have the author affiliations above the "Manuscript
% received ..."  text while in non-compsoc journals this is reversed. Sigh.

\author{Michael~Shell,~\IEEEmembership{Member,~IEEE,}
        John~Doe,~\IEEEmembership{Fellow,~OSA,}
        and~Jane~Doe,~\IEEEmembership{Life~Fellow,~IEEE}% <-this % stops a space
\IEEEcompsocitemizethanks{\IEEEcompsocthanksitem M. Shell is with the Department
of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta,
GA, 30332.\protect\\
% note need leading \protect in front of \\ to get a newline within \thanks as
% \\ is fragile and will error, could use \hfil\break instead.
E-mail: see http://www.michaelshell.org/contact.html
\IEEEcompsocthanksitem J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
\thanks{Manuscript received April 19, 2005; revised September 17, 2014.}}

% note the % following the last \IEEEmembership and also \thanks - 
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
% 
% \author{....lastname \thanks{...} \thanks{...} }
%                     ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
% line to be shifted left slightly. This is one of those "LaTeX things". For
% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.



% The paper headers
\markboth{Journal of \LaTeX\ Class Files,~Vol.~13, No.~9, September~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Advanced Demo of IEEEtran.cls for Journals}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
% 
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.



% The publisher's ID mark at the bottom of the page is less important with
% Computer Society journal papers as those publications place the marks
% outside of the main text columns and, therefore, unlike regular IEEE
% journals, the available text space is not reduced by their presence.
% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2014 IEEE}
% or like this to get the Computer Society new two part style.
%\IEEEpubid{\makebox[\columnwidth]{\hfill 0000--0000/00/\$00.00~\copyright~2014 IEEE}%
%\hspace{\columnsep}\makebox[\columnwidth]{Published by the IEEE Computer Society\hfill}}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark (Computer Society journal
% papers don't need this extra clearance.)



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}



% for Computer Society papers, we must declare the abstract and index terms
% PRIOR to the title within the \IEEEtitleabstractindextext IEEEtran
% command as these need to go into the title area created by \maketitle.
% As a general rule, do not put math, special symbols or citations
% in the abstract or keywords.
\IEEEtitleabstractindextext{%
\begin{abstract}
The abstract goes here.
\end{abstract}

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
Computer Society, IEEEtran, journal, \LaTeX, paper, template.
\end{IEEEkeywords}}


% make the title area
\maketitle


% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEtitleabstractindextext text will
% not be used in maketitle, but will appear (i.e., to be "transported")
% here as \IEEEdisplaynontitleabstractindextext when compsoc mode
% is not selected <OR> if conference mode is selected - because compsoc
% conference papers position the abstract like regular (non-compsoc)
% papers do!
\IEEEdisplaynontitleabstractindextext
% \IEEEdisplaynontitleabstractindextext has no effect when using
% compsoc under a non-conference mode.


% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle


\ifCLASSOPTIONcompsoc
\IEEEraisesectionheading{\section{Introduction}\label{sec:introduction}}
\else
\section{Introduction}
\label{sec:introduction}
\fi
% Computer Society journal (but not conference!) papers do something unusual
% with the very first section heading (almost always called "Introduction").
% They place it ABOVE the main text! IEEEtran.cls does not automatically do
% this for you, but you can achieve this effect with the provided
% \IEEEraisesectionheading{} command. Note the need to keep any \label that
% is to refer to the section immediately after \section in the above as
% \IEEEraisesectionheading puts \section within a raised box.




% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps (small caps for compsoc).
% 
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
% 
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
% 
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
% 
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{his} demo file is intended to serve as a ``starter file''
for IEEE Computer Society journal papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.

% needed in second column of first page if using \IEEEpubid
%\IEEEpubidadjcol

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.
% However, the Computer Society has been known to put floats at the bottom.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.





% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


\appendices
\section{Proof of the First Zonklar Equation}
Appendix one text goes here.

% you can choose not to have a title for an appendix
% if you want by leaving the argument blank
\section{}
Appendix two text goes here.


% use section* for acknowledgment
\ifCLASSOPTIONcompsoc
  % The Computer Society usually uses the plural form
  \section*{Acknowledgments}
\else
  % regular IEEE prefers the singular form
  \section*{Acknowledgment}
\fi


The authors would like to thank...


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to {\LaTeX}}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}



bare_conf.tex

%% bare_conf.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8a or later) with an IEEE
%% conference paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



\documentclass[conference]{IEEEtran}
% Some Computer Society conferences also require the compsoc mode option,
% but others use the standard conference format.
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[conference]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
%\usepackage{cite}
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.






% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a larger sans serif font
% than the serif footnote size font used in traditional IEEE formatting
% and thus the need to invoke different subfig.sty package options depending
% on whether compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.




% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls for Conferences}


% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\author{\IEEEauthorblockN{Michael Shell}
\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\
Georgia Institute of Technology\\
Atlanta, Georgia 30332--0250\\
Email: http://www.michaelshell.org/contact.html}
\and
\IEEEauthorblockN{Homer Simpson}
\IEEEauthorblockA{Twentieth Century Fox\\
Springfield, USA\\
Email: homer@thesimpsons.com}
\and
\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
\IEEEauthorblockA{Starfleet Academy\\
San Francisco, California 96678--2391\\
Telephone: (800) 555--1212\\
Fax: (888) 555--1212}}

% conference papers do not typically use \thanks and this command
% is locked out in conference mode. If really needed, such as for
% the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
% after \documentclass

% for over three affiliations, or if they all won't fit within the width
% of the page, use this alternative format:
% 
%\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
%Homer Simpson\IEEEauthorrefmark{2},
%James Kirk\IEEEauthorrefmark{3}, 
%Montgomery Scott\IEEEauthorrefmark{3} and
%Eldon Tyrell\IEEEauthorrefmark{4}}
%\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
%Georgia Institute of Technology,
%Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
%\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
%Email: homer@thesimpsons.com}
%\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
%Telephone: (800) 555--1212, Fax: (888) 555--1212}
%\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}




% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

% As a general rule, do not put math, special symbols or citations
% in the abstract
\begin{abstract}
The abstract goes here.
\end{abstract}

% no keywords




% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{Introduction}
% no \IEEEPARstart
This demo file is intended to serve as a ``starter file''
for IEEE conference papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.


\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.




% conference papers do not normally have an appendix


% use section* for acknowledgment
\section*{Acknowledgment}


The authors would like to thank...





% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}




% that's all folks
\end{document}



bare_conf_compsoc.tex

%% bare_conf_compsoc.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8s or later) with an IEEE Computer
%% Society conference paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



\documentclass[conference,compsoc]{IEEEtran}
% Some/most Computer Society conferences require the compsoc mode option,
% but others may want the standard conference format.
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[conference,compsoc]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
  % IEEE Computer Society needs nocompress option
  % requires cite.sty v4.0 or later (November 2003)
  \usepackage[nocompress]{cite}
\else
  % normal IEEE
  \usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society  papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later.





% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=footnotesize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a sans serif font rather
% than the serif font used in traditional IEEE formatting and thus the need
% to invoke different subfig.sty package options depending on whether
% compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.




% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls for Computer Society Conferences}


% author names and affiliations
% use a multiple column layout for up to three different
% affiliations
\author{\IEEEauthorblockN{Michael Shell}
\IEEEauthorblockA{School of Electrical and\\Computer Engineering\\
Georgia Institute of Technology\\
Atlanta, Georgia 30332--0250\\
Email: http://www.michaelshell.org/contact.html}
\and
\IEEEauthorblockN{Homer Simpson}
\IEEEauthorblockA{Twentieth Century Fox\\
Springfield, USA\\
Email: homer@thesimpsons.com}
\and
\IEEEauthorblockN{James Kirk\\ and Montgomery Scott}
\IEEEauthorblockA{Starfleet Academy\\
San Francisco, California 96678-2391\\
Telephone: (800) 555--1212\\
Fax: (888) 555--1212}}

% conference papers do not typically use \thanks and this command
% is locked out in conference mode. If really needed, such as for
% the acknowledgment of grants, issue a \IEEEoverridecommandlockouts
% after \documentclass

% for over three affiliations, or if they all won't fit within the width
% of the page (and note that there is less available width in this regard for
% compsoc conferences compared to traditional conferences), use this
% alternative format:
% 
%\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
%Homer Simpson\IEEEauthorrefmark{2},
%James Kirk\IEEEauthorrefmark{3}, 
%Montgomery Scott\IEEEauthorrefmark{3} and
%Eldon Tyrell\IEEEauthorrefmark{4}}
%\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering\\
%Georgia Institute of Technology,
%Atlanta, Georgia 30332--0250\\ Email: see http://www.michaelshell.org/contact.html}
%\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA\\
%Email: homer@thesimpsons.com}
%\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, California 96678-2391\\
%Telephone: (800) 555--1212, Fax: (888) 555--1212}
%\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, California 90210--4321}}




% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

% As a general rule, do not put math, special symbols or citations
% in the abstract
\begin{abstract}
The abstract goes here.
\end{abstract}

% no keywords




% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{Introduction}
% no \IEEEPARstart
This demo file is intended to serve as a ``starter file''
for IEEE conference papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.


\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.




% conference papers do not normally have an appendix



% use section* for acknowledgment
\ifCLASSOPTIONcompsoc
  % The Computer Society usually uses the plural form
  \section*{Acknowledgments}
\else
  % regular IEEE prefers the singular form
  \section*{Acknowledgment}
\fi


The authors would like to thank...





% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}




% that's all folks
\end{document}



bare_jrnl.tex

%% bare_jrnl.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% see http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8a or later) with an IEEE
%% journal paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



\documentclass[journal]{IEEEtran}
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[journal]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
%\usepackage{cite}
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.






% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex





% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a larger sans serif font
% than the serif footnote size font used in traditional IEEE formatting
% and thus the need to invoke different subfig.sty package options depending
% on whether compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and 
% Axel Sommerfeldt. This package may be useful when used in conjunction with 
% IEEEtran.cls'  captionsoff option. Some IEEE journals/societies require that
% submissions have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.4.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a 
% page by themselves.




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.




% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls for Journals}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%

\author{Michael~Shell,~\IEEEmembership{Member,~IEEE,}
        John~Doe,~\IEEEmembership{Fellow,~OSA,}
        and~Jane~Doe,~\IEEEmembership{Life~Fellow,~IEEE}% <-this % stops a space
\thanks{M. Shell is with the Department
of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta,
GA, 30332 USA e-mail: (see http://www.michaelshell.org/contact.html).}% <-this % stops a space
\thanks{J. Doe and J. Doe are with Anonymous University.}% <-this % stops a space
\thanks{Manuscript received April 19, 2005; revised September 17, 2014.}}

% note the % following the last \IEEEmembership and also \thanks - 
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
% 
% \author{....lastname \thanks{...} \thanks{...} }
%                     ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
% line to be shifted left slightly. This is one of those "LaTeX things". For
% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.



% The paper headers
\markboth{Journal of \LaTeX\ Class Files,~Vol.~13, No.~9, September~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
% 
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.




% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2014 IEEE}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark.



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}




% make the title area
\maketitle

% As a general rule, do not put math, special symbols or citations
% in the abstract or keywords.
\begin{abstract}
The abstract goes here.
\end{abstract}

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
IEEEtran, journal, \LaTeX, paper, template.
\end{IEEEkeywords}






% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{Introduction}
% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps.
% 
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
% 
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
% 
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
% 
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{his} demo file is intended to serve as a ``starter file''
for IEEE journal papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.

% needed in second column of first page if using \IEEEpubid
%\IEEEpubidadjcol

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.





% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


\appendices
\section{Proof of the First Zonklar Equation}
Appendix one text goes here.

% you can choose not to have a title for an appendix
% if you want by leaving the argument blank
\section{}
Appendix two text goes here.


% use section* for acknowledgment
\section*{Acknowledgment}


The authors would like to thank...


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}



bare_jrnl_compsoc.tex

%% bare_jrnl_compsoc.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% See:
%% http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8a or later) with an IEEE
%% Computer Society journal paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/


\documentclass[10pt,journal,compsoc]{IEEEtran}
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[10pt,journal,compsoc]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
\ifCLASSOPTIONcompsoc
  % IEEE Computer Society needs nocompress option
  % requires cite.sty v4.0 or later (November 2003)
  \usepackage[nocompress]{cite}
\else
  % normal IEEE
  \usepackage{cite}
\fi
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.
%
% Note that some packages require special options to format as the Computer
% Society requires. In particular, Computer Society  papers do not use
% compressed citation ranges as is done in typical IEEE papers
% (e.g., [1]-[4]). Instead, they list every citation separately in order
% (e.g., [1], [2], [3], [4]). To get the latter we need to load the cite
% package with the nocompress option which is supported by cite.sty v4.0
% and later. Note also the use of a CLASSOPTION conditional provided by
% IEEEtran.cls V1.7 and later.





% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex






% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=footnotesize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a sans serif font rather
% than the serif font used in traditional IEEE formatting and thus the need
% to invoke different subfig.sty package options depending on whether
% compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/




% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and 
% Axel Sommerfeldt. This package may be useful when used in conjunction with 
% IEEEtran.cls'  captionsoff option. Some IEEE journals/societies require that
% submissions have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.4.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a 
% page by themselves.




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.





% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls\\ for Computer Society Journals}
%
%
% author names and IEEE memberships
% note positions of commas and nonbreaking spaces ( ~ ) LaTeX will not break
% a structure at a ~ so this keeps an author's name from being broken across
% two lines.
% use \thanks{} to gain access to the first footnote area
% a separate \thanks must be used for each paragraph as LaTeX2e's \thanks
% was not built to handle multiple paragraphs
%
%
%\IEEEcompsocitemizethanks is a special \thanks that produces the bulleted
% lists the Computer Society journals use for "first footnote" author
% affiliations. Use \IEEEcompsocthanksitem which works much like \item
% for each affiliation group. When not in compsoc mode,
% \IEEEcompsocitemizethanks becomes like \thanks and
% \IEEEcompsocthanksitem becomes a line break with idention. This
% facilitates dual compilation, although admittedly the differences in the
% desired content of \author between the different types of papers makes a
% one-size-fits-all approach a daunting prospect. For instance, compsoc 
% journal papers have the author affiliations above the "Manuscript
% received ..."  text while in non-compsoc journals this is reversed. Sigh.

\author{Michael~Shell,~\IEEEmembership{Member,~IEEE,}
        John~Doe,~\IEEEmembership{Fellow,~OSA,}
        and~Jane~Doe,~\IEEEmembership{Life~Fellow,~IEEE}% <-this % stops a space
\IEEEcompsocitemizethanks{\IEEEcompsocthanksitem M. Shell is with the Department
of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta,
GA, 30332.\protect\\
% note need leading \protect in front of \\ to get a newline within \thanks as
% \\ is fragile and will error, could use \hfil\break instead.
E-mail: see http://www.michaelshell.org/contact.html
\IEEEcompsocthanksitem J. Doe and J. Doe are with Anonymous University.}% <-this % stops an unwanted space
\thanks{Manuscript received April 19, 2005; revised September 17, 2014.}}

% note the % following the last \IEEEmembership and also \thanks - 
% these prevent an unwanted space from occurring between the last author name
% and the end of the author line. i.e., if you had this:
% 
% \author{....lastname \thanks{...} \thanks{...} }
%                     ^------------^------------^----Do not want these spaces!
%
% a space would be appended to the last name and could cause every name on that
% line to be shifted left slightly. This is one of those "LaTeX things". For
% instance, "\textbf{A} \textbf{B}" will typeset as "A B" not "AB". To get
% "AB" then you have to do: "\textbf{A}\textbf{B}"
% \thanks is no different in this regard, so shield the last } of each \thanks
% that ends a line with a % and do not let a space in before the next \thanks.
% Spaces after \IEEEmembership other than the last one are OK (and needed) as
% you are supposed to have spaces between the names. For what it is worth,
% this is a minor point as most people would not even notice if the said evil
% space somehow managed to creep in.



% The paper headers
\markboth{Journal of \LaTeX\ Class Files,~Vol.~13, No.~9, September~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Computer Society Journals}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
% 
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.



% The publisher's ID mark at the bottom of the page is less important with
% Computer Society journal papers as those publications place the marks
% outside of the main text columns and, therefore, unlike regular IEEE
% journals, the available text space is not reduced by their presence.
% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2014 IEEE}
% or like this to get the Computer Society new two part style.
%\IEEEpubid{\makebox[\columnwidth]{\hfill 0000--0000/00/\$00.00~\copyright~2014 IEEE}%
%\hspace{\columnsep}\makebox[\columnwidth]{Published by the IEEE Computer Society\hfill}}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark (Computer Society jorunal
% papers don't need this extra clearance.)



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}



% for Computer Society papers, we must declare the abstract and index terms
% PRIOR to the title within the \IEEEtitleabstractindextext IEEEtran
% command as these need to go into the title area created by \maketitle.
% As a general rule, do not put math, special symbols or citations
% in the abstract or keywords.
\IEEEtitleabstractindextext{%
\begin{abstract}
The abstract goes here.
\end{abstract}

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
Computer Society, IEEEtran, journal, \LaTeX, paper, template.
\end{IEEEkeywords}}


% make the title area
\maketitle


% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEtitleabstractindextext text will
% not be used in maketitle, but will appear (i.e., to be "transported")
% here as \IEEEdisplaynontitleabstractindextext when the compsoc 
% or transmag modes are not selected <OR> if conference mode is selected 
% - because all conference papers position the abstract like regular
% papers do.
\IEEEdisplaynontitleabstractindextext
% \IEEEdisplaynontitleabstractindextext has no effect when using
% compsoc or transmag under a non-conference mode.



% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\IEEEraisesectionheading{\section{Introduction}\label{sec:introduction}}
% Computer Society journal (but not conference!) papers do something unusual
% with the very first section heading (almost always called "Introduction").
% They place it ABOVE the main text! IEEEtran.cls does not automatically do
% this for you, but you can achieve this effect with the provided
% \IEEEraisesectionheading{} command. Note the need to keep any \label that
% is to refer to the section immediately after \section in the above as
% \IEEEraisesectionheading puts \section within a raised box.




% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps (small caps for compsoc).
% 
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
% 
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
% 
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
% 
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{his} demo file is intended to serve as a ``starter file''
for IEEE Computer Society journal papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.

% needed in second column of first page if using \IEEEpubid
%\IEEEpubidadjcol

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.
% However, the Computer Society has been known to put floats at the bottom.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.





% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


\appendices
\section{Proof of the First Zonklar Equation}
Appendix one text goes here.

% you can choose not to have a title for an appendix
% if you want by leaving the argument blank
\section{}
Appendix two text goes here.


% use section* for acknowledgment
\ifCLASSOPTIONcompsoc
  % The Computer Society usually uses the plural form
  \section*{Acknowledgments}
\else
  % regular IEEE prefers the singular form
  \section*{Acknowledgment}
\fi


The authors would like to thank...


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}



bare_jrnl_transmag.tex

%% bare_jrnl_transmag.tex
%% V1.4a
%% 2014/09/17
%% by Michael Shell
%% see http://www.michaelshell.org/
%% for current contact information.
%%
%% This is a skeleton file demonstrating the use of IEEEtran.cls
%% (requires IEEEtran.cls version 1.8a or later) with an IEEE 
%% Transactions on Magnetics journal paper.
%%
%% Support sites:
%% http://www.michaelshell.org/tex/ieeetran/
%% http://www.ctan.org/tex-archive/macros/latex/contrib/IEEEtran/
%% and
%% http://www.ieee.org/

%%*************************************************************************
%% Legal Notice:
%% This code is offered as-is without any warranty either expressed or
%% implied; without even the implied warranty of MERCHANTABILITY or
%% FITNESS FOR A PARTICULAR PURPOSE! 
%% User assumes all risk.
%% In no event shall IEEE or any contributor to this code be liable for
%% any damages or losses, including, but not limited to, incidental,
%% consequential, or any other damages, resulting from the use or misuse
%% of any information contained here.
%%
%% All comments are the opinions of their respective authors and are not
%% necessarily endorsed by the IEEE.
%%
%% This work is distributed under the LaTeX Project Public License (LPPL)
%% ( http://www.latex-project.org/ ) version 1.3, and may be freely used,
%% distributed and modified. A copy of the LPPL, version 1.3, is included
%% in the base LaTeX documentation of all distributions of LaTeX released
%% 2003/12/01 or later.
%% Retain all contribution notices and credits.
%% ** Modified files should be clearly indicated as such, including  **
%% ** renaming them and changing author support contact information. **
%%
%% File list of work: IEEEtran.cls, IEEEtran_HOWTO.pdf, bare_adv.tex,
%%                    bare_conf.tex, bare_jrnl.tex, bare_conf_compsoc.tex,
%%                    bare_jrnl_compsoc.tex, bare_jrnl_transmag.tex
%%*************************************************************************


% *** Authors should verify (and, if needed, correct) their LaTeX system  ***
% *** with the testflow diagnostic prior to trusting their LaTeX platform ***
% *** with production work. IEEE's font choices and paper sizes can       ***
% *** trigger bugs that do not appear when using other class files.       ***                          ***
% The testflow support page is at:
% http://www.michaelshell.org/tex/testflow/



\documentclass[journal,transmag]{IEEEtran}
%
% If IEEEtran.cls has not been installed into the LaTeX system files,
% manually specify the path to it like:
% \documentclass[journal]{../sty/IEEEtran}





% Some very useful LaTeX packages include:
% (uncomment the ones you want to load)


% *** MISC UTILITY PACKAGES ***
%
%\usepackage{ifpdf}
% Heiko Oberdiek's ifpdf.sty is very useful if you need conditional
% compilation based on whether the output is pdf or dvi.
% usage:
% \ifpdf
%   % pdf code
% \else
%   % dvi code
% \fi
% The latest version of ifpdf.sty can be obtained from:
% http://www.ctan.org/tex-archive/macros/latex/contrib/oberdiek/
% Also, note that IEEEtran.cls V1.7 and later provides a builtin
% \ifCLASSINFOpdf conditional that works the same way.
% When switching from latex to pdflatex and vice-versa, the compiler may
% have to be run twice to clear warning/error messages.






% *** CITATION PACKAGES ***
%
%\usepackage{cite}
% cite.sty was written by Donald Arseneau
% V1.6 and later of IEEEtran pre-defines the format of the cite.sty package
% \cite{} output to follow that of IEEE. Loading the cite package will
% result in citation numbers being automatically sorted and properly
% "compressed/ranged". e.g., [1], [9], [2], [7], [5], [6] without using
% cite.sty will become [1], [2], [5]--[7], [9] using cite.sty. cite.sty's
% \cite will automatically add leading space, if needed. Use cite.sty's
% noadjust option (cite.sty V3.8 and later) if you want to turn this off
% such as if a citation ever needs to be enclosed in parenthesis.
% cite.sty is already installed on most LaTeX systems. Be sure and use
% version 5.0 (2009-03-20) and later if using hyperref.sty.
% The latest version can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/cite/
% The documentation is contained in the cite.sty file itself.






% *** GRAPHICS RELATED PACKAGES ***
%
\ifCLASSINFOpdf
  % \usepackage[pdftex]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../pdf/}{../jpeg/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.pdf,.jpeg,.png}
\else
  % or other class option (dvipsone, dvipdf, if not using dvips). graphicx
  % will default to the driver specified in the system graphics.cfg if no
  % driver is specified.
  % \usepackage[dvips]{graphicx}
  % declare the path(s) where your graphic files are
  % \graphicspath{{../eps/}}
  % and their extensions so you won't have to specify these with
  % every instance of \includegraphics
  % \DeclareGraphicsExtensions{.eps}
\fi
% graphicx was written by David Carlisle and Sebastian Rahtz. It is
% required if you want graphics, photos, etc. graphicx.sty is already
% installed on most LaTeX systems. The latest version and documentation
% can be obtained at: 
% http://www.ctan.org/tex-archive/macros/latex/required/graphics/
% Another good source of documentation is "Using Imported Graphics in
% LaTeX2e" by Keith Reckdahl which can be found at:
% http://www.ctan.org/tex-archive/info/epslatex/
%
% latex, and pdflatex in dvi mode, support graphics in encapsulated
% postscript (.eps) format. pdflatex in pdf mode supports graphics
% in .pdf, .jpeg, .png and .mps (metapost) formats. Users should ensure
% that all non-photo figures use a vector format (.eps, .pdf, .mps) and
% not a bitmapped formats (.jpeg, .png). IEEE frowns on bitmapped formats
% which can result in "jaggedy"/blurry rendering of lines and letters as
% well as large increases in file sizes.
%
% You can find documentation about the pdfTeX application at:
% http://www.tug.org/applications/pdftex




% *** MATH PACKAGES ***
%
%\usepackage[cmex10]{amsmath}
% A popular package from the American Mathematical Society that provides
% many useful and powerful commands for dealing with mathematics. If using
% it, be sure to load this package with the cmex10 option to ensure that
% only type 1 fonts will utilized at all point sizes. Without this option,
% it is possible that some math symbols, particularly those within
% footnotes, will be rendered in bitmap form which will result in a
% document that can not be IEEE Xplore compliant!
%
% Also, note that the amsmath package sets \interdisplaylinepenalty to 10000
% thus preventing page breaks from occurring within multiline equations. Use:
%\interdisplaylinepenalty=2500
% after loading amsmath to restore such page breaks as IEEEtran.cls normally
% does. amsmath.sty is already installed on most LaTeX systems. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/amslatex/math/





% *** SPECIALIZED LIST PACKAGES ***
%
%\usepackage{algorithmic}
% algorithmic.sty was written by Peter Williams and Rogerio Brito.
% This package provides an algorithmic environment fo describing algorithms.
% You can use the algorithmic environment in-text or within a figure
% environment to provide for a floating algorithm. Do NOT use the algorithm
% floating environment provided by algorithm.sty (by the same authors) or
% algorithm2e.sty (by Christophe Fiorio) as IEEE does not use dedicated
% algorithm float types and packages that provide these will not provide
% correct IEEE style captions. The latest version and documentation of
% algorithmic.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithms/
% There is also a support site at:
% http://algorithms.berlios.de/index.html
% Also of interest may be the (relatively newer and more customizable)
% algorithmicx.sty package by Szasz Janos:
% http://www.ctan.org/tex-archive/macros/latex/contrib/algorithmicx/




% *** ALIGNMENT PACKAGES ***
%
%\usepackage{array}
% Frank Mittelbach's and David Carlisle's array.sty patches and improves
% the standard LaTeX2e array and tabular environments to provide better
% appearance and additional user controls. As the default LaTeX2e table
% generation code is lacking to the point of almost being broken with
% respect to the quality of the end results, all users are strongly
% advised to use an enhanced (at the very least that provided by array.sty)
% set of table tools. array.sty is already installed on most systems. The
% latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/required/tools/


% IEEEtran contains the IEEEeqnarray family of commands that can be used to
% generate multiline equations as well as matrices, tables, etc., of high
% quality.




% *** SUBFIGURE PACKAGES ***
%\ifCLASSOPTIONcompsoc
%  \usepackage[caption=false,font=normalsize,labelfont=sf,textfont=sf]{subfig}
%\else
%  \usepackage[caption=false,font=footnotesize]{subfig}
%\fi
% subfig.sty, written by Steven Douglas Cochran, is the modern replacement
% for subfigure.sty, the latter of which is no longer maintained and is
% incompatible with some LaTeX packages including fixltx2e. However,
% subfig.sty requires and automatically loads Axel Sommerfeldt's caption.sty
% which will override IEEEtran.cls' handling of captions and this will result
% in non-IEEE style figure/table captions. To prevent this problem, be sure
% and invoke subfig.sty's "caption=false" package option (available since
% subfig.sty version 1.3, 2005/06/28) as this is will preserve IEEEtran.cls
% handling of captions.
% Note that the Computer Society format requires a larger sans serif font
% than the serif footnote size font used in traditional IEEE formatting
% and thus the need to invoke different subfig.sty package options depending
% on whether compsoc mode has been enabled.
%
% The latest version and documentation of subfig.sty can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/subfig/



% *** FLOAT PACKAGES ***
%
%\usepackage{fixltx2e}
% fixltx2e, the successor to the earlier fix2col.sty, was written by
% Frank Mittelbach and David Carlisle. This package corrects a few problems
% in the LaTeX2e kernel, the most notable of which is that in current
% LaTeX2e releases, the ordering of single and double column floats is not
% guaranteed to be preserved. Thus, an unpatched LaTeX2e can allow a
% single column figure to be placed prior to an earlier double column
% figure. The latest version and documentation can be found at:
% http://www.ctan.org/tex-archive/macros/latex/base/


%\usepackage{stfloats}
% stfloats.sty was written by Sigitas Tolusis. This package gives LaTeX2e
% the ability to do double column floats at the bottom of the page as well
% as the top. (e.g., "\begin{figure*}[!b]" is not normally possible in
% LaTeX2e). It also provides a command:
%\fnbelowfloat
% to enable the placement of footnotes below bottom floats (the standard
% LaTeX2e kernel puts them above bottom floats). This is an invasive package
% which rewrites many portions of the LaTeX2e float routines. It may not work
% with other packages that modify the LaTeX2e float routines. The latest
% version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/sttools/
% Do not use the stfloats baselinefloat ability as IEEE does not allow
% \baselineskip to stretch. Authors submitting work to the IEEE should note
% that IEEE rarely uses double column equations and that authors should try
% to avoid such use. Do not be tempted to use the cuted.sty or midfloat.sty
% packages (also by Sigitas Tolusis) as IEEE does not format its papers in
% such ways.
% Do not attempt to use stfloats with fixltx2e as they are incompatible.
% Instead, use Morten Hogholm'a dblfloatfix which combines the features
% of both fixltx2e and stfloats:
%
% \usepackage{dblfloatfix}
% The latest version can be found at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/dblfloatfix/




%\ifCLASSOPTIONcaptionsoff
%  \usepackage[nomarkers]{endfloat}
% \let\MYoriglatexcaption\caption
% \renewcommand{\caption}[2][\relax]{\MYoriglatexcaption[#2]{#2}}
%\fi
% endfloat.sty was written by James Darrell McCauley, Jeff Goldberg and 
% Axel Sommerfeldt. This package may be useful when used in conjunction with 
% IEEEtran.cls'  captionsoff option. Some IEEE journals/societies require that
% submissions have lists of figures/tables at the end of the paper and that
% figures/tables without any captions are placed on a page by themselves at
% the end of the document. If needed, the draftcls IEEEtran class option or
% \CLASSINPUTbaselinestretch interface can be used to increase the line
% spacing as well. Be sure and use the nomarkers option of endfloat to
% prevent endfloat from "marking" where the figures would have been placed
% in the text. The two hack lines of code above are a slight modification of
% that suggested by in the endfloat docs (section 8.4.1) to ensure that
% the full captions always appear in the list of figures/tables - even if
% the user used the short optional argument of \caption[]{}.
% IEEE papers do not typically make use of \caption[]'s optional argument,
% so this should not be an issue. A similar trick can be used to disable
% captions of packages such as subfig.sty that lack options to turn off
% the subcaptions:
% For subfig.sty:
% \let\MYorigsubfloat\subfloat
% \renewcommand{\subfloat}[2][\relax]{\MYorigsubfloat[]{#2}}
% However, the above trick will not work if both optional arguments of
% the \subfloat command are used. Furthermore, there needs to be a
% description of each subfigure *somewhere* and endfloat does not add
% subfigure captions to its list of figures. Thus, the best approach is to
% avoid the use of subfigure captions (many IEEE journals avoid them anyway)
% and instead reference/explain all the subfigures within the main caption.
% The latest version of endfloat.sty and its documentation can obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/endfloat/
%
% The IEEEtran \ifCLASSOPTIONcaptionsoff conditional can also be used
% later in the document, say, to conditionally put the References on a 
% page by themselves.




% *** PDF, URL AND HYPERLINK PACKAGES ***
%
%\usepackage{url}
% url.sty was written by Donald Arseneau. It provides better support for
% handling and breaking URLs. url.sty is already installed on most LaTeX
% systems. The latest version and documentation can be obtained at:
% http://www.ctan.org/tex-archive/macros/latex/contrib/url/
% Basically, \url{my_url_here}.




% *** Do not adjust lengths that control margins, column widths, etc. ***
% *** Do not use packages that alter fonts (such as pslatex).         ***
% There should be no need to do such things with IEEEtran.cls V1.6 and later.
% (Unless specifically asked to do so by the journal or conference you plan
% to submit to, of course. )


% correct bad hyphenation here
\hyphenation{op-tical net-works semi-conduc-tor}


\begin{document}
%
% paper title
% Titles are generally capitalized except for words such as a, an, and, as,
% at, but, by, for, in, nor, of, on, or, the, to and up, which are usually
% not capitalized unless they are the first or last word of the title.
% Linebreaks \\ can be used within to get better formatting as desired.
% Do not put math or special symbols in the title.
\title{Bare Demo of IEEEtran.cls for \textsc{Transactions on Magnetics}}



% author names and affiliations
% transmag papers use the long conference author name format.

\author{\IEEEauthorblockN{Michael Shell\IEEEauthorrefmark{1},
Homer Simpson\IEEEauthorrefmark{2},
James Kirk\IEEEauthorrefmark{3}, 
Montgomery Scott\IEEEauthorrefmark{3}, and
Eldon Tyrell\IEEEauthorrefmark{4},~\IEEEmembership{Fellow,~IEEE}}
\IEEEauthorblockA{\IEEEauthorrefmark{1}School of Electrical and Computer Engineering,
Georgia Institute of Technology, Atlanta, GA 30332 USA}
\IEEEauthorblockA{\IEEEauthorrefmark{2}Twentieth Century Fox, Springfield, USA}
\IEEEauthorblockA{\IEEEauthorrefmark{3}Starfleet Academy, San Francisco, CA 96678 USA}
\IEEEauthorblockA{\IEEEauthorrefmark{4}Tyrell Inc., 123 Replicant Street, Los Angeles, CA 90210 USA}% <-this % stops an unwanted space
\thanks{Manuscript received December 1, 2012; revised September 17, 2014. 
Corresponding author: M. Shell (email: http://www.michaelshell.org/contact.html).}}



% The paper headers
\markboth{Journal of \LaTeX\ Class Files,~Vol.~13, No.~9, September~2014}%
{Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for Journals}
% The only time the second header will appear is for the odd numbered pages
% after the title page when using the twoside option.
% 
% *** Note that you probably will NOT want to include the author's ***
% *** name in the headers of peer review papers.                   ***
% You can use \ifCLASSOPTIONpeerreview for conditional compilation here if
% you desire.




% If you want to put a publisher's ID mark on the page you can do it like
% this:
%\IEEEpubid{0000--0000/00\$00.00~\copyright~2014 IEEE}
% Remember, if you use this you must call \IEEEpubidadjcol in the second
% column for its text to clear the IEEEpubid mark.



% use for special paper notices
%\IEEEspecialpapernotice{(Invited Paper)}


% for Transactions on Magnetics papers, we must declare the abstract and
% index terms PRIOR to the title within the \IEEEtitleabstractindextext
% IEEEtran command as these need to go into the title area created by
% \maketitle.
% As a general rule, do not put math, special symbols or citations
% in the abstract or keywords.
\IEEEtitleabstractindextext{%
\begin{abstract}
The abstract goes here.
\end{abstract}

% Note that keywords are not normally used for peerreview papers.
\begin{IEEEkeywords}
IEEEtran, journal, \LaTeX, magnetics, paper, template.
\end{IEEEkeywords}}



% make the title area
\maketitle


% To allow for easy dual compilation without having to reenter the
% abstract/keywords data, the \IEEEtitleabstractindextext text will
% not be used in maketitle, but will appear (i.e., to be "transported")
% here as \IEEEdisplaynontitleabstractindextext when the compsoc 
% or transmag modes are not selected <OR> if conference mode is selected 
% - because all conference papers position the abstract like regular
% papers do.
\IEEEdisplaynontitleabstractindextext
% \IEEEdisplaynontitleabstractindextext has no effect when using
% compsoc or transmag under a non-conference mode.







% For peer review papers, you can put extra information on the cover
% page as needed:
% \ifCLASSOPTIONpeerreview
% \begin{center} \bfseries EDICS Category: 3-BBND \end{center}
% \fi
%
% For peerreview papers, this IEEEtran command inserts a page break and
% creates the second title. It will be ignored for other modes.
\IEEEpeerreviewmaketitle



\section{Introduction}
% The very first letter is a 2 line initial drop letter followed
% by the rest of the first word in caps.
% 
% form to use if the first word consists of a single letter:
% \IEEEPARstart{A}{demo} file is ....
% 
% form to use if you need the single drop letter followed by
% normal text (unknown if ever used by IEEE):
% \IEEEPARstart{A}{}demo file is ....
% 
% Some journals put the first two words in caps:
% \IEEEPARstart{T}{his demo} file is ....
% 
% Here we have the typical use of a "T" for an initial drop letter
% and "HIS" in caps to complete the first word.
\IEEEPARstart{T}{his} demo file is intended to serve as a ``starter file''
for IEEE \textsc{Transactions on Magnetics} journal papers produced under \LaTeX\ using
IEEEtran.cls version 1.8a and later.
% You must have at least 2 lines in the paragraph with the drop letter
% (should never be an issue)
I wish you the best of success.

\hfill mds
 
\hfill September 17, 2014

\subsection{Subsection Heading Here}
Subsection text here.

% needed in second column of first page if using \IEEEpubid
%\IEEEpubidadjcol

\subsubsection{Subsubsection Heading Here}
Subsubsection text here.


% An example of a floating figure using the graphicx package.
% Note that \label must occur AFTER (or within) \caption.
% For figures, \caption should occur after the \includegraphics.
% Note that IEEEtran v1.7 and later has special internal code that
% is designed to preserve the operation of \label within \caption
% even when the captionsoff option is in effect. However, because
% of issues like this, it may be the safest practice to put all your
% \label just after \caption rather than within \caption{}.
%
% Reminder: the "draftcls" or "draftclsnofoot", not "draft", class
% option should be used if it is desired that the figures are to be
% displayed while in draft mode.
%
%\begin{figure}[!t]
%\centering
%\includegraphics[width=2.5in]{myfigure}
% where an .eps filename suffix will be assumed under latex, 
% and a .pdf suffix will be assumed for pdflatex; or what has been declared
% via \DeclareGraphicsExtensions.
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure}

% Note that IEEE typically puts floats only at the top, even when this
% results in a large percentage of a column being occupied by floats.


% An example of a double column floating figure using two subfigures.
% (The subfig.sty package must be loaded for this to work.)
% The subfigure \label commands are set within each subfloat command,
% and the \label for the overall figure must come after \caption.
% \hfil is used as a separator to get equal spacing.
% Watch out that the combined width of all the subfigures on a 
% line do not exceed the text width or a line break will occur.
%
%\begin{figure*}[!t]
%\centering
%\subfloat[Case I]{\includegraphics[width=2.5in]{box}%
%\label{fig_first_case}}
%\hfil
%\subfloat[Case II]{\includegraphics[width=2.5in]{box}%
%\label{fig_second_case}}
%\caption{Simulation results for the network.}
%\label{fig_sim}
%\end{figure*}
%
% Note that often IEEE papers with subfigures do not employ subfigure
% captions (using the optional argument to \subfloat[]), but instead will
% reference/describe all of them (a), (b), etc., within the main caption.
% Be aware that for subfig.sty to generate the (a), (b), etc., subfigure
% labels, the optional argument to \subfloat must be present. If a
% subcaption is not desired, just leave its contents blank,
% e.g., \subfloat[].


% An example of a floating table. Note that, for IEEE style tables, the
% \caption command should come BEFORE the table and, given that table
% captions serve much like titles, are usually capitalized except for words
% such as a, an, and, as, at, but, by, for, in, nor, of, on, or, the, to
% and up, which are usually not capitalized unless they are the first or
% last word of the caption. Table text will default to \footnotesize as
% IEEE normally uses this smaller font for tables.
% The \label must come after \caption as always.
%
%\begin{table}[!t]
%% increase table row spacing, adjust to taste
%\renewcommand{\arraystretch}{1.3}
% if using array.sty, it might be a good idea to tweak the value of
% \extrarowheight as needed to properly center the text within the cells
%\caption{An Example of a Table}
%\label{table_example}
%\centering
%% Some packages, such as MDW tools, offer better commands for making tables
%% than the plain LaTeX2e tabular which is used here.
%\begin{tabular}{|c||c|}
%\hline
%One & Two\\
%\hline
%Three & Four\\
%\hline
%\end{tabular}
%\end{table}


% Note that the IEEE does not put floats in the very first column
% - or typically anywhere on the first page for that matter. Also,
% in-text middle ("here") positioning is typically not used, but it
% is allowed and encouraged for Computer Society conferences (but
% not Computer Society journals). Most IEEE journals/conferences use
% top floats exclusively. 
% Note that, LaTeX2e, unlike IEEE journals/conferences, places
% footnotes above bottom floats. This can be corrected via the
% \fnbelowfloat command of the stfloats package.




\section{Conclusion}
The conclusion goes here.





% if have a single appendix:
%\appendix[Proof of the Zonklar Equations]
% or
%\appendix  % for no appendix heading
% do not use \section anymore after \appendix, only \section*
% is possibly needed

% use appendices with more than one appendix
% then use \section to start each appendix
% you must declare a \section before using any
% \subsection or using \label (\appendices by itself
% starts a section numbered zero.)
%


\appendices
\section{Proof of the First Zonklar Equation}
Appendix one text goes here.

% you can choose not to have a title for an appendix
% if you want by leaving the argument blank
\section{}
Appendix two text goes here.


% use section* for acknowledgment
\section*{Acknowledgment}


The authors would like to thank...


% Can use something like this to put references on a page
% by themselves when using endfloat and the captionsoff option.
\ifCLASSOPTIONcaptionsoff
  \newpage
\fi



% trigger a \newpage just before the given reference
% number - used to balance the columns on the last page
% adjust value as needed - may need to be readjusted if
% the document is modified later
%\IEEEtriggeratref{8}
% The "triggered" command can be changed if desired:
%\IEEEtriggercmd{\enlargethispage{-5in}}

% references section

% can use a bibliography generated by BibTeX as a .bbl file
% BibTeX documentation can be easily obtained at:
% http://www.ctan.org/tex-archive/biblio/bibtex/contrib/doc/
% The IEEEtran BibTeX style support page is at:
% http://www.michaelshell.org/tex/ieeetran/bibtex/
%\bibliographystyle{IEEEtran}
% argument is your BibTeX string definitions and bibliography database(s)
%\bibliography{IEEEabrv,../bib/paper}
%
% <OR> manually copy in the resultant .bbl file
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
\begin{thebibliography}{1}

\bibitem{IEEEhowto:kopka}
H.~Kopka and P.~W. Daly, \emph{A Guide to \LaTeX}, 3rd~ed.\hskip 1em plus
  0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.

\end{thebibliography}

% biography section
% 
% If you have an EPS/PDF photo (graphicx package needed) extra braces are
% needed around the contents of the optional argument to biography to prevent
% the LaTeX parser from getting confused when it sees the complicated
% \includegraphics command within an optional argument. (You could create
% your own custom macro containing the \includegraphics command to make things
% simpler here.)
%\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{mshell}}]{Michael Shell}
% or if you just want to reserve a space for a photo:

\begin{IEEEbiography}{Michael Shell}
Biography text here.
\end{IEEEbiography}

% if you will not have a photo at all:
\begin{IEEEbiographynophoto}{John Doe}
Biography text here.
\end{IEEEbiographynophoto}

% insert where needed to balance the two columns on the last page with
% biographies
%\newpage

\begin{IEEEbiographynophoto}{Jane Doe}
Biography text here.
\end{IEEEbiographynophoto}

% You can push biographies down or up by placing
% a \vfill before or after them. The appropriate
% use of \vfill depends on what kind of text is
% on the last page and whether or not the columns
% are being equalized.

%\vfill

% Can be used to pull up biographies so that the bottom of the last one
% is flush with the other column.
%\enlargethispage{-5in}



% that's all folks
\end{document}



1604.02392.extracted_bib
{IEEEhowto:kopka %H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus % 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999. % weather forecasting
1604.02392.extracted_bib
{weather M. Fisher, J. Nocedal, Y. Tremolet and S.J. Wright, ``Data assimilation in weather forecasting: A case study in PDE-constrained optimization'', Optimization and Engineering, vol. 10, no. 3, pp. 409-426, 2009. % regulation of water flow
1604.02392.extracted_bib
{water J. de Halleux, C. Prieur, J.M. Coron, B. d'Andr\'ea-Novel and G. Bastin, ``Boundary feedback control in networks of open channels'', Automatica, vol. 39, no. 8, pp. 1365-1376, 2003. % pollution monitoring
1604.02392.extracted_bib
{pollution M. Ortner, A. Nehorai and A. Jeremic, ``Biochemical transport modeling and Bayesian source estimation in realistic environments'', IEEE Trans. on Signal Processing, vol. 55, no. 6, pp. 2520-2532, 2007. % monitoring of thermostatically controlled loads in smart grids
1604.02392.extracted_bib
{smart-grids S. Moura, J. Bendtsen and V. Ruiz, ``Observer design for boundary coupled PDEs: application to thermostatically controlled loads in smart grids,'' Proc. of the IEEE Conference on Decision and Control, pp. 6286-6291, Florence, Italy, 2013 %reconstruction of highway traffic flow
1604.02392.extracted_bib
{traffic C. G. Claudel and A. M. Bayen, ``Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: Theory'', IEEE Trans. on Automatic Control, vol. 55, no. 6, pp. 1142-1157, 2010 % Consensus filters for finite-dimensional systems
1604.02392.extracted_bib
{Olfati1 R. Olfati-Saber, J.A. Fax and R. Murray, \textquotedblleft Consensus and cooperation in networked multi-agent systems,\textquotedblright\ Proc. of the IEEE, vol. 95, no. 1, pp. 215-233, 2007.
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{Xiao L. Xiao, S. Boyd and S. Lall, \textquotedblleft A scheme for robust distributed sensor fusion based on average consensus,\textquotedblright\ Proc. 4th Int. Symp. on Information Processing in Sensor Networks, pp. 63-70, Los Angeles, CA, 2005.
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{Calafiore G.C. Calafiore and F. Abrate, \textquotedblleft Distributed linear estimation over sensor networks,\textquotedblright\ Int. J. of Control, vol. 82, no. 5, pp. 868-882, 2009.
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{automatica G. Battistelli and L. Chisci, ``Kullback-Leibler average, consensus on probability densities, and distributed state estimation with guaranteed stability'', Automatica, vol. 5, no. 3, pp. 707-718, 2014.
1604.02392.extracted_bib
{spl G. Battistelli, L. Chisci, and C. Fantacci, ``Parallel consensus on likelihoods and priors for networked nonlinear filtering'', IEEE Signal Processing Letters, vol. 21, no. 7, pp. 787-791, 2014. % Consensus filter for multi-object estimation
1604.02392.extracted_bib
{J-STSP G. Battistelli, L. Chisci, C. Fantacci, A. Farina and A. Graziano, ``Consensus CPHD filter for distributed multitarget tracking'', IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 3, pp. 508-520, 2013. % Distributed estimation for large-scale systems
1604.02392.extracted_bib
{Khan08 U.A. Khan and J. Moura, ``Distributing the Kalman filter for large-scale systems", IEEE Trans. on Signal Processing, \relax vol. 66, no. 10, pp. 4919--4935, 2008.
1604.02392.extracted_bib
{Stank09 S. Stankovic, M.S. Stankovic and D.M. Stepanovic, ``Consensus based overlapping decentralized estimation with missing observations and communication faults", Automatica, \relax vol. 45, no. 6, pp. 1397--1406, 2009.
1604.02392.extracted_bib
{Farina10 M. Farina, G. Ferrari-Trecate and R. Scattolini, ``Moving-horizon partition-based state estimation of large-scale systems", Automatica, \relax vol. 46, no. 5, pp. 910--918, 2010. % centralised estimation of a spatially distributed, time-varying random field from noisy measurements collected by a wireless sensor network, with % bandwidth and energy constraints
1604.02392.extracted_bib
{zhang-moura-krogh H. Zhang, J. Moura and B. Krogh, ``Dynamic field estimation using wireless sensor networks: Tradeoffs between estimation error and communication cost'', IEEE Trans. on Signal Processing, vol. 57, no. 6, pp. 2383-2395, 2009. % distributed algorithm for observer design for linear continuous-time systems
1604.02392.extracted_bib
{pasqualetti F. D\"{orfler, F. Pasqualetti and F. Bullo, “ ``Continuous-time distributed observers with discrete communication'', IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 2, pp. 296-304, 2013. % Consensus filters for PDE systems
1604.02392.extracted_bib
{Deme10 M.A. Demetriou, ``Design of consensus and adaptive consensus filters for distributed parameter systems", Automatica, \relax vol. 46, no. 2, pp. 300--311, 2010.
1604.02392.extracted_bib
{Deme13 M.A. Demetriou, ``Adaptive consensus filters of spatially distributed systems with limited connectivity'', Proc, 52nd IEEE Conference on Decision and Control, pp. 442-447, Firenze, Italy, 2013. % Schwarz decomposition methods
1604.02392.extracted_bib
{Schwa890 H.A. Schwarz, Gesammelte mathematische abhandlungen. Band I, II, \relax AMS Chelsea Publishing, Bronx, NY, 1890.
1604.02392.extracted_bib
{Lions88 P.L. Lions, On the Schwarz alternating method. I, \relax in First Int. Symp. on Domain Decomposition Methods for Partial Differential Equations, R.~Glowinski et al., SIAM, Philadelphia, PA, pp. 1--42, 1988,.
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{Gander08 M.J. Gander, ``Schwarz methods over the course of time", Electronic Trans. on Numerical Analysis, vol. 31, pp. 228--255, 2008.
1604.02392.extracted_bib
{Chan94 T.F. Chan and T.P. Mathew, ``Domain decomposition algorithms'', Acta Numerica, vol. 3, pp. 61--143, 1994.
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{Tos05 A. Toselli and O. Widlund, Domain decomposition methods -- Algorithms and theory, \relax Springer--Verlag, Berlin, Germany, 2005.
1604.02392.extracted_bib
{Smith96 B. Smith, P. Bjorstad and W. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, \relax Cambridge University Press, New York, NY, 1996. %% Testi FEM %%
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{Pelosi09 G. Pelosi, R. Coccioli and S. Selleri, Quick finite elements for electromagnetic waves, \relax Artech House, Norwood, MA, 2009.
1604.02392.extracted_bib
{Brenner96 S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, \relax Springer--Verlag, New York, NY, 1996. %% %% Articoli FEM temporale calore %%
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{Lee95 J.-F. Lee, J.-F. and Z. Sacks, ``Whitney elements time domain {(WETD) methods'', IEEE Trans. on Magnetics., vol. 31, no. 3, pp. 1325-1329, 1995. %
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{Choi91 %C.T.M. Choi and A. Konrad, ``Finite element modeling of the RF heating process'', %IEEE Trans. on Magnetics, vol. 27, pp. 4227-4230, 1991. %
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{Zienk71 %O. C.~Zienkiewicz, The Finite Element Method in Engineering Science, %\relax McGraw-Hill, New York, NY, 1971. % %
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{Zienk05 %O. C.~Zienkiewicz, R. L.~Taylor, and J. Z.~Zhu The Finite Element %Method: Its Basis and Fundamentals, \relax Elsevier, Burlington, MA, 2005. % %
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{Hughes87 %T. J.~Hughes, The Finite Element Method - Linear Static and Dynamic %Finite Element Analysis, \relax Prentice-Hall, Englewood Cliffs, NJ, 1987. % %
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{John88 %C.~Johnson, Numerical Solution of Partial Differential Equations by %the Finite Element Method, \relax Cambridge University Press, Cambridge, %UK, 1988. % %
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{Axel84 %O.~Axelsson and V. A.~Barker, Finite Element Solution of Boundary %Value Problems: Theory and Computation, \relax Academic Press, London, UK, %1984. % %
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{Brenner96 %S. C.~Brenner and L. R.~Scott, The Mathematical Theory of Finite %Element Methods, \relax Springer--Verlag, New York, NY, 1996. % %
1604.02392.extracted_bib
{Larson13 %M. G.~Larson and F.~Bengzon, The Finite Element Method: Theory, %Implementation, and Applications, \relax Springer, Heidelberg, Germany, %2013. % %
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{Ciarlet78 %T.~Ciarlet, The Finite Element Method for Elliptic Problems in Applied %Mathematics, \relax North-Holland, Amsterdam, The Netherlands, 1978. % %
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{Pelosi09 %G.~Pelosi, R.~Coccioli, and S.~Selleri, Quick Finite Elements for %Electromagnetic Waves, \relax Artech House, Norwood, MA, 2009.
1604.02392.extracted_bib
{jap1 R. Suga and M. Kawahara, ``Estimation of tidal current using Kalman filter finite-element method'', Computers \& Mathematics with Applications, vol. 52, no. 8-9, pp. 1289-1298, 2006.
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{jap2 Y. Ojima and M. Kawahara, ``Estimation of river current using reduced Kalman filter finite element method'', Computer Methods in Applied Mechanics and Engineering, vol. 198, no. 9-12, pp. 904-911, 2009.
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{ECC2015 G. Battistelli, L. Chisci, N. Forti, G. Pelosi and. S. Selleri, ``Distributed finite element Kalman filter'', Proc. of the European Control Conference 2015, pp. 3700-3705, Linz, Austria, 2015.
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{num:stab E. {S\"uli and D.F. Mayers, An introduction to numerical analysis, \relax Cambridge University Press, Cambridge, UK, 2003.
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{Kreith10 F. Kreith, R.M. Manglik and M.S. Bohn, Principles of heat transfer, \relax Springer--Verlag, New York, NY, 1996.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to {\LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.
1604.02392.extracted_bib
{IEEEhowto:kopka H.~Kopka and P.~W. Daly, A Guide to \LaTeX, 3rd~ed.\hskip 1em plus 0.5em minus 0.4em\relax Harlow, England: Addison-Wesley, 1999.