<p>There are many neuroscientists who use the techniques of advanced mathematics and statistics to analyze actual neural data for patterns.</p>
<p><a href="https://web.archive.org/web/20180626182016/http://mulab.physiol.upenn.edu:80/" rel="nofollow noreferrer">George Gerstein</a>, who is now retired, has been a pioneer in applying &quot;particle&quot; methods in analyzing neuronal interactions.  The originator of the <a href="https://web.archive.org/web/20180409183300/http://mulab.physiol.upenn.edu:80/gravity.html" rel="nofollow noreferrer">Gravity transform</a>, he used this tool to untangle some of the stochastic processes that were underlying the firing patterns.  He also brought into widespread use tools like the <a href="https://web.archive.org/web/20180520215041/http://mulab.physiol.upenn.edu:80/jpst.html" rel="nofollow noreferrer">joint peristimulus time histogram</a>, which allow an &quot;at a glance&quot; view of co-firings.</p>
<p><a href="https://sleep.hms.harvard.edu/" rel="nofollow noreferrer">Emery Brown</a> is both an anesthesiologist and academic statistician who has done a lot of modeling with actual hippocampal place cell data in a Bayesian framework, as well as modeling firing patterns with point processes.  He, along with some other groups, have successfully used tools like Granger Causality to reveal connectivity among cells and subcircuits.</p>
<p><a href="http://www.pitt.edu/%7Ephase/" rel="nofollow noreferrer">G. Bard Ermentrout</a> is a bit more theoretical, as he is a mathematician, but has done a lot with determining the phase space relationships and coupling in neuronal firing patterns, and has often tested his models with <a href="https://pubmed.ncbi.nlm.nih.gov/17928562/" rel="nofollow noreferrer">neural data</a>.  He has &quot;written the book&quot; on the <a href="https://rads.stackoverflow.com/amzn/click/com/038787707X" rel="nofollow noreferrer" rel="nofollow noreferrer">subject</a>.</p>
<p>There are hundreds more examples, but these are the first three that sprang to mind.  Neuroscientists are eager and willing to collaborate with mathematicians, statisticians, and others of the theoretical ilk (as you're seeing), so doing a quick Pubmed search on areas that are of particular interest to you is probably the best way to seek out these subfields.</p>

CC BY-SA 4.0
2012-07-05T09:04:36.057Z
2022-04-15T00:24:51.443Z
2022-04-15T00:24:51.443Z
Chuck Sherrington
<p>The use of neural-networks in the cognitive sciences has been around <a href="https://cogsci.stackexchange.com/q/1263/29">since Turing</a>. However, many of the networks common in connectionism suffer from a lack of biological plausibility. Of these abstract ones, even the ones that try to capture some properties of biological neural networks only do some metaphorically. See for instance the <a href="https://cogsci.stackexchange.com/q/214/29">limitations of cascade correlation as a metaphor for neurogenesis</a>. However, these abstract networks are still used because they provide a great bridge between theory in neuroscience and psychology. The networks are abstract and powerful enough to deal with questions in psychology (say learning or developmental-psychology) but still try to ground themselves in some way (at least by analogy) in biological network. I will give two examples from this abstract working down towards biology point of view.</p>

<p>Most of the early approaches to neural nets, represented activation as real-valued outputs that were multiplied by the weights of interneuron connections. This approach is being replaced by more reasonable <a href="http://en.wikipedia.org/wiki/Spiking_neural_network" rel="nofollow noreferrer">spiking neuron models</a> that incorporate a more realistic coding medium (rate of action potentials) while still maintaining a relatively abstract level that is usable in psychology and machine learning applications. However, these models still tend to be too abstract to realistically model specific organisms.</p>

<p>Chris Eliasmith and his students have pushed a little further in the gap between abstract psychology-useful models and concrete biologically-useful models by proposing the <a href="http://ctnsrv.uwaterloo.ca/cnrglab/node/215" rel="nofollow noreferrer">neural engineering framework</a>. This computational model allows users to run a <a href="http://ctnsrv.uwaterloo.ca/cnrglab/node/219" rel="nofollow noreferrer">range of simulations</a> from close-to-biology studies like translational vestibular ocular reflex in monkeys and recognition of song by zebra finch to psychology-studies like parametric working memory and other kinds of cognitive models.</p>

<p>Thus these approaches allow you to understand certain properties of biological neural networks by looking at the essential features of abstract models</p>

<p>Of course, you can push things closer to biology, and @ChuckSherrington's answer gives some great examples of this.</p>

CC BY-SA 3.0
2012-07-05T12:45:14.473Z
2012-07-05T13:03:37.367Z
2017-04-13T12:56:16.167Z
Artem Kaznatcheev
<p>I'd like to add to Chuck's excellent answer; the computational approach is very well-represented in neuroscience, and actually involves a large number of very heterogeneous methods.  Thus, a very different set of neuroscientists and examples have sprung to mind for me.</p>

<p>To my mind, the best single example of the utility of a computational approach to interpreting neural data is the reward prediction error hypothesis of dopamine function.  Early investigations in machine learning led to the development of the temporal difference reinforcement learning algorithm.  Subsequently it was noticed, by Wolfram Schulz, that the pattern of firing in dopaminergic cells appeared to closely correspond to what would be expected of a temporal difference error signal - the very core of this form of reinforcement learning. Subsequently, similar reinforcement learning algorithms (e.g., Q-learning) have been applied to a variety of neural data - albeit at the much coarser scale of fMRI - and provided a variety of evidence that is strongly supportive of this hypothesis. This work has been absolutely crucial to progress in the last 10-15 years in cognitive and systems neuroscience.</p>

<p>The second example that springs to mind also pertains to dopamine; in this case, the utility of the computational approach was in understanding the pattern of effects produced by release of dopamine, rather than in characterizing the pattern of dopamine release itself.  At the cellular level Jeremy Seaman's work is a great example of this approach; he has used Fisher discriminant analysis and other multivariate techniques to better characterize multi-unit activity recorded in prefrontal cortex, under various dopamine conditions.  Ultimately his work has been the primary computational approach contributing to what is now the modal understanding of dopamine's effect in the prefrontal cortex, which is to enhance signal to noise ratio.</p>

<p>A third example has to do with the application of graph theory to neural networks, and in particular our understanding of small-world connected graphs.  The implication of this work for neuroscience was not lost on the mathematicians that originally pursued this line of work, but its actual utility for neuroscience has been most famously demonstrated by Olaf Sporns in understanding what is coming to be called the "connectome" - that is, the graph of structurally- and functionally-connected neural systems.  Although this is still an active line of research, small-world connectivity appears to be a ubiquitous feature of cortex.</p>

<p>I would be remiss not to mention the work of a large group of researchers trained in the "parallel distributed processing" or connectionism tradition, including Matt Botvinick, Jon Cohen, Michael Frank, Ken Norman, Yuko Munakata, Randy O'Reilly. There are too many excellent examples from their work to name, but all of these researchers have used behavioral and neural data to build neural network models of cortical and subcortical processing, at varying levels of biological detail; validated these models in terms of their fit to existing behavioral and neural data; and used these models to derive predictions that have subsequently been tested using a variety of approaches. The following is a woefully incomplete, but at least representative, list of the progress made by these researchers: the discovery of parallels between the dimensionality-reduction or "abstraction" techniques that can be useful in reinforcement learning to cortical processing (in the case of Matt Botvinick); the discovery of parallels between the exploration/exploitation dilemma in reinforcement learning and the function of the locus coereleus/norepinephrine system (in the case of Jon Cohen); the understanding of fine-grained functional consequences of differences in dopamine receptor subtypes, as well as prefrontal/striatal interactions (in the case of Michael Frank), the discovery of the large-scale consequences of cellular-level long-term depression and potentiation phenomena for hemodynamic patterns in memory tasks (in the case of Ken Norman), the discovery of the role of prefrontal inhibitory neurotransmission in tasks requiring "selection" of information under competition (in the case of Yuko Munakata), and the discovery of the computational underpinnings of the tri-partite division of labor between hippocampus, posterior cortex, and prefrontal cortex (in the case of Randy O'Reilly).  Jay McClelland, David Rumelhart, David Seidenberg, Geoff Hinton, and many others laid the groundwork for much of this progress, although their contact with detailed neural phenomena was more limited than that made by their trainees (and their trainees' trainees), above.</p>

<p>I would conclude by seconding Chuck's suggestion to do a PubMed search.  Your question is too broad for a comprehensive answer conveyed in anything shorter than a book!</p>

CC BY-SA 3.0
2012-07-05T12:28:57.050Z
Schultz is an excellent example! (I'm sure many of the others are, too, but I haven't heard of any but the superhuman names like Cohen (met him very very briefly about 10-11 years ago), and the PDP power hitters (McClelland, Rumelhart, Hinton)).  I was trying to find those with mathematical might while preserving experimental bent, as even Ermentrout is getting a bit theoretical for some experimentalists' tastes.
Chuck Sherrington
CC BY-SA 3.0
2012-07-06T07:29:59.700Z
Thanks for the great answer, and to the other answerers!  This is plenty to get me going.
Douglas S. Stones
CC BY-SA 3.0
2012-07-05T12:22:13.190Z
2012-07-05T12:22:13.190Z
CHCH
<p>In an upcoming postdoc, I'm going to be looking through biological neural network data in the hopes of finding some interesting "patterns".  I'm coming at this field from a mathematics/computer science point of view, and am quite new to the biological side of things.  I'm hoping that by looking at some examples in which computational methods were successfully used in understanding biological neural networks, it might help me understand more about what I should be looking for, and what approaches are likely to be successful.</p>

<blockquote>
  <p><strong>Question</strong>:  What are some key examples in which computational methods were used on biological neural networks to gain important insights into these networks?</p>
</blockquote>

CC BY-SA 3.0
2012-07-07T16:01:13.237Z
This is rather tangential, but you might find it helpful, or at least interesting, [openworm -- A simulation platform to build digital in silico living systems -- starting with a c. elegans worm virtual organism simulation](https://code.google.com/p/openworm/)
William B Swift
<neuroscience><computational-modeling><neural-network><theoretical-neuroscience>
What are the key examples of the use of computational methods in the study of biological neural networks?
Douglas S. Stones
# What are the key examples of the use of computational methods in the study of biological neural networks?

(Asked by: username_0 on 2012-07-05)

In an upcoming postdoc, I'm going to be looking through biological neural network data in the hopes of finding some interesting "patterns". I'm coming at this field from a mathematics/computer science point of view, and am quite new to the biological side of things. I'm hoping that by looking at some examples in which computational methods were successfully used in understanding biological neural networks, it might help me understand more about what I should be looking for, and what approaches are likely to be successful.

> **Question**: What are some key examples in which computational methods were used on biological neural networks to gain important insights into these networks?

**Tags:** neuroscience, computational-modeling, neural-network, theoretical-neuroscience

> **Comments:**
> **username_1**: This is rather tangential, but you might find it helpful, or at least interesting, [openworm -- A simulation platform to build digital in silico living systems -- starting with a c. elegans worm virtual organism simulation](https://code.google.com/p/openworm/)  

---

## 3 answers

### Answer by username_4 on 2012-07-05. Score: 12 | Accepted answer

I'd like to add to Chuck's excellent answer; the computational approach is very well-represented in neuroscience, and actually involves a large number of very heterogeneous methods. Thus, a very different set of neuroscientists and examples have sprung to mind for me.

To my mind, the best single example of the utility of a computational approach to interpreting neural data is the reward prediction error hypothesis of dopamine function. Early investigations in machine learning led to the development of the temporal difference reinforcement learning algorithm. Subsequently it was noticed, by Wolfram Schulz, that the pattern of firing in dopaminergic cells appeared to closely correspond to what would be expected of a temporal difference error signal - the very core of this form of reinforcement learning. Subsequently, similar reinforcement learning algorithms (e.g., Q-learning) have been applied to a variety of neural data - albeit at the much coarser scale of fMRI - and provided a variety of evidence that is strongly supportive of this hypothesis. This work has been absolutely crucial to progress in the last 10-15 years in cognitive and systems neuroscience.

The second example that springs to mind also pertains to dopamine; in this case, the utility of the computational approach was in understanding the pattern of effects produced by release of dopamine, rather than in characterizing the pattern of dopamine release itself. At the cellular level Jeremy Seaman's work is a great example of this approach; he has used Fisher discriminant analysis and other multivariate techniques to better characterize multi-unit activity recorded in prefrontal cortex, under various dopamine conditions. Ultimately his work has been the primary computational approach contributing to what is now the modal understanding of dopamine's effect in the prefrontal cortex, which is to enhance signal to noise ratio.

A third example has to do with the application of graph theory to neural networks, and in particular our understanding of small-world connected graphs. The implication of this work for neuroscience was not lost on the mathematicians that originally pursued this line of work, but its actual utility for neuroscience has been most famously demonstrated by Olaf Sporns in understanding what is coming to be called the "connectome" - that is, the graph of structurally- and functionally-connected neural systems. Although this is still an active line of research, small-world connectivity appears to be a ubiquitous feature of cortex.

I would be remiss not to mention the work of a large group of researchers trained in the "parallel distributed processing" or connectionism tradition, including Matt Botvinick, Jon Cohen, Michael Frank, Ken Norman, Yuko Munakata, Randy O'Reilly. There are too many excellent examples from their work to name, but all of these researchers have used behavioral and neural data to build neural network models of cortical and subcortical processing, at varying levels of biological detail; validated these models in terms of their fit to existing behavioral and neural data; and used these models to derive predictions that have subsequently been tested using a variety of approaches. The following is a woefully incomplete, but at least representative, list of the progress made by these researchers: the discovery of parallels between the dimensionality-reduction or "abstraction" techniques that can be useful in reinforcement learning to cortical processing (in the case of Matt Botvinick); the discovery of parallels between the exploration/exploitation dilemma in reinforcement learning and the function of the locus coereleus/norepinephrine system (in the case of Jon Cohen); the understanding of fine-grained functional consequences of differences in dopamine receptor subtypes, as well as prefrontal/striatal interactions (in the case of Michael Frank), the discovery of the large-scale consequences of cellular-level long-term depression and potentiation phenomena for hemodynamic patterns in memory tasks (in the case of Ken Norman), the discovery of the role of prefrontal inhibitory neurotransmission in tasks requiring "selection" of information under competition (in the case of Yuko Munakata), and the discovery of the computational underpinnings of the tri-partite division of labor between hippocampus, posterior cortex, and prefrontal cortex (in the case of Randy O'Reilly). Jay McClelland, David Rumelhart, David Seidenberg, Geoff Hinton, and many others laid the groundwork for much of this progress, although their contact with detailed neural phenomena was more limited than that made by their trainees (and their trainees' trainees), above.

I would conclude by seconding Chuck's suggestion to do a PubMed search. Your question is too broad for a comprehensive answer conveyed in anything shorter than a book!

> **Comments:**
> **username_2**: Schultz is an excellent example! (I'm sure many of the others are, too, but I haven't heard of any but the superhuman names like Cohen (met him very very briefly about 10-11 years ago), and the PDP power hitters (McClelland, Rumelhart, Hinton)).  I was trying to find those with mathematical might while preserving experimental bent, as even Ermentrout is getting a bit theoretical for some experimentalists' tastes.  
> **username_0**: Thanks for the great answer, and to the other answerers!  This is plenty to get me going.  

---

### Answer by username_2 on 2012-07-05. Score: 11

There are many neuroscientists who use the techniques of advanced mathematics and statistics to analyze actual neural data for patterns.

[George Gerstein](https://web.archive.org/web/20180626182016/http://mulab.physiol.upenn.edu:80/), who is now retired, has been a pioneer in applying "particle" methods in analyzing neuronal interactions. The originator of the [Gravity transform](https://web.archive.org/web/20180409183300/http://mulab.physiol.upenn.edu:80/gravity.html), he used this tool to untangle some of the stochastic processes that were underlying the firing patterns. He also brought into widespread use tools like the [joint peristimulus time histogram](https://web.archive.org/web/20180520215041/http://mulab.physiol.upenn.edu:80/jpst.html), which allow an "at a glance" view of co-firings.

[Emery Brown](https://sleep.hms.harvard.edu/) is both an anesthesiologist and academic statistician who has done a lot of modeling with actual hippocampal place cell data in a Bayesian framework, as well as modeling firing patterns with point processes. He, along with some other groups, have successfully used tools like Granger Causality to reveal connectivity among cells and subcircuits.

[G. Bard Ermentrout](http://www.pitt.edu/%7Ephase/) is a bit more theoretical, as he is a mathematician, but has done a lot with determining the phase space relationships and coupling in neuronal firing patterns, and has often tested his models with [neural data](https://pubmed.ncbi.nlm.nih.gov/17928562/). He has "written the book" on the [subject](https://rads.stackoverflow.com/amzn/click/com/038787707X).

There are hundreds more examples, but these are the first three that sprang to mind. Neuroscientists are eager and willing to collaborate with mathematicians, statisticians, and others of the theoretical ilk (as you're seeing), so doing a quick Pubmed search on areas that are of particular interest to you is probably the best way to seek out these subfields.


---

### Answer by username_3 on 2012-07-05. Score: 8

The use of neural-networks in the cognitive sciences has been around [since Turing](https://cogsci.stackexchange.com/q/1263/29). However, many of the networks common in connectionism suffer from a lack of biological plausibility. Of these abstract ones, even the ones that try to capture some properties of biological neural networks only do some metaphorically. See for instance the [limitations of cascade correlation as a metaphor for neurogenesis](https://cogsci.stackexchange.com/q/214/29). However, these abstract networks are still used because they provide a great bridge between theory in neuroscience and psychology. The networks are abstract and powerful enough to deal with questions in psychology (say learning or developmental-psychology) but still try to ground themselves in some way (at least by analogy) in biological network. I will give two examples from this abstract working down towards biology point of view.

Most of the early approaches to neural nets, represented activation as real-valued outputs that were multiplied by the weights of interneuron connections. This approach is being replaced by more reasonable [spiking neuron models](http://en.wikipedia.org/wiki/Spiking_neural_network) that incorporate a more realistic coding medium (rate of action potentials) while still maintaining a relatively abstract level that is usable in psychology and machine learning applications. However, these models still tend to be too abstract to realistically model specific organisms.

Chris Eliasmith and his students have pushed a little further in the gap between abstract psychology-useful models and concrete biologically-useful models by proposing the [neural engineering framework](http://ctnsrv.uwaterloo.ca/cnrglab/node/215). This computational model allows users to run a [range of simulations](http://ctnsrv.uwaterloo.ca/cnrglab/node/219) from close-to-biology studies like translational vestibular ocular reflex in monkeys and recognition of song by zebra finch to psychology-studies like parametric working memory and other kinds of cognitive models.

Thus these approaches allow you to understand certain properties of biological neural networks by looking at the essential features of abstract models

Of course, you can push things closer to biology, and @ChuckSherrington's answer gives some great examples of this.


---

