Dynamical Neuroscience: Wiki Article Entry - Input Needed

[Pythagorean]

I've just made a wiki article entry, and would be interested on input from professionals.

http://en.wikipedia.org/wiki/Dynamical_Neuroscience

thanks!

 

[sshzp4]

I am not going to critique anything specific but make this note: The moment you say 'dynamical' you mean a flow/difference mathematical mapping representation of a system. All comments about AI and the ANN neuron are absolutely irrelevant to 'dynamical neuroscience'. You don't study only 'learning and memory' type problems in 'dynamical neuroscience', you study the biological physics, chemical kinetics, electrochemistry, transport phenomena and emergent behavior of the systems as well.

So the article seems more suited to 'some differences between ANN and dynamical neuroscience'. I am going to recommend the article to be merged with some other article on dynamical systems and completely rewritten. Its got way too many facts muddled up and tries to make facts of personal conjectures.

Edit: The article is poorly written, ideas get thrown around everywhere. No structure and no clarity. Consider heavy revisions, and focus on improving single sections.

 

[jackmell]

I am not going to critique anything specific but make this note: The moment you say 'dynamical' you mean a flow/difference mathematical mapping representation of a system. All comments about AI and the ANN neuron are absolutely irrelevant to 'dynamical neuroscience'. You don't study only 'learning and memory' type problems in 'dynamical neuroscience', you study the biological physics, chemical kinetics, electrochemistry, transport phenomena and emergent behavior of the systems as well.

I disagree with that. The moment I hear "dynamical" I think evolution equations and when it's coupled with neuroscience, I think "massively fed-back non-linear evolution equations". I think both AI and neural networks are extremely relevant to the idea of approaching the brain from the perspective of it's dynamic properties. Neural networks are non-linear dynamical systems and artificial intelligence, I am utterly convinced can emerge from such systems. Personally, my view is that problems in "dynamical neuroscience" are mathematical problems: how do we understand the non-linear dynamical properties of very complicated coupled systems of non-linear equations that we believe model the dynamics of neural assemblies.

I am happy to see more effort to approach the workings of the brain in terms of it's purely intrinsic dynamic properties and am optimistic that will lead us to a more complete understanding of mind, consciousness, and self-awareness.

 

[sshzp4]

Jack -- "I am happy to see more effort to approach the workings of the brain in terms of it's purely intrinsic dynamic properties and am optimistic that will lead us to a more complete understanding of mind, consciousness, and self-awareness."

You put too much confidence in NLD and ANeurons, my friend :)

Well my comment should be examined under the light of the wiki-author putting too much emphasis on a comparison between ANN based AI and dynamical neuroscience. It seems like a slap on the face of scientists who, say, model the neurochemistry dynamics and should be viewed as being dynamical neuroscientists as well. Without the experimentalists and without the biochemists working in the field, you wouldn't have physics to model and would be left with blind conjectures. So in a nutshell, my statement is "don't draw boundaries based on personal experience/opinions in the description of a field".

My observation of irrelevance comes from constructed implications in the article such as "Even in this day and age of lightning communication, Dynamical Neuroscience didn't even receive it's own wiki article until 2010". For a good reason, obviously. Since the field is nascent and borrows formalism better addressed under ANN mathematics, or dynamics and wikipedia is not the forum to engage in opinionated descriptions.

(You might like Seung and Lee's work at MIT on NMF algorithms. They show the statistical perspective of how signals can be processed through 'articulate' decomposition for learning to take place <emph> without <\emph> using NN's. Minsky is the reason I gave up on NNs ever being able to describe 'emergent learned behavior'. The concepts of consciousness and self-awareness are completely over rated and are of purely human interest, not engineering. The point here is: yes, the neural net model is cool; but only because it is easy to understand. They have been working on this since the 60's and have mostly failed to come up with anything other than math demos.)

So Jack, my global point is the wiki-author could be allowing personal biases to decide what a field is about or not. Is that right?

 

[Pythagorean]

sshzp, I welcome your citicism, but perhaps you could be a bit more constructive.

The moment you say 'dynamical' you mean a flow/difference mathematical mapping representation of a system.

I believe I represented it this way throughout the article. Perhaps my mention of ANN was distracting and I should remove it. But you did see the reference to Izhikivech's Dynamical Systems in Neuroscience, no? This is an important point about thresholds vs. resonating.

So the article seems more suited to 'some differences between ANN and dynamical neuroscience'.

I think I only bring that up in the beginning, but if you would like to point to the specific cases that bother you,

I am going to recommend the article to be merged with some other article on dynamical systems and completely rewritten. Its got way too many facts muddled up and tries to make facts of personal conjectures.

Well this is a vague criticism. Not very helpful, really.

Edit: The article is poorly written, ideas get thrown around everywhere. No structure and no clarity. Consider heavy revisions, and focus on improving single sections. (Written by a biologist? :^D)

Very vague, still. And don't you think it would be insulting to biologists for you to use them as an insult? I'm a physics graduate student. My only experience is with Morris Lecar networks. It's a work in progress. (I'm going to add a separate section on attractor networks).

My observation of irrelevance comes from constructed implications in the article such as "Even in this day and age of lightning communication, Dynamical Neuroscience didn't even receive it's own wiki article until 2010". For a good reason, obviously. Since the field is nascent

Which was the point...

It seems like a slap on the face of scientists who, say, model the neurochemistry dynamics and should be viewed as being dynamical neuroscientists as well.

This is a good point. You might have read it before I added that part.
I figure since you're spending so much time defending your position, you way as well give more specific, constructive criticism :P

thank you!

 

[jackmell]

Well I don't want to go off-topic. Allow me however to reply to sshzp's comments:

I admire Pythagorean's efforts to make an effort at emphasizing the dynamics of the brain and did not feel it was poorly written. I do indeed have enormous confidence in non-linear dynamics and believe strongly it is the ultimate key in understanding how the brain works. However I am quite critical of the past 50 years of AI and agree they have failed miserably because their work has been based on models that are linear: transistors that are either "on" or "off", and the linear program. I do not believe the current implementation of neural networks will ever emerge artificial intelligence because they too are based on the current computer technology that is inherently linear and have always proposed that we will have to wait for a critical point in technology when someone creates a new qualitatively different device that is intrinsically non-linear. When these devices are then coupled in very complex ways to mimic the cortex, I have great faith this will lead to emergent properties that will be akin to real artificial intelligence.

 

[Pythagorean]

You don't study only 'learning and memory' type problems in 'dynamical neuroscience'

I really didn't mean to imply that, but if that's how you interpreted it then I need to rewrite the intro, because obviously it's made a terrible first impression on you.

My personal experience every time I tell people I work in Computational Neuroscience is they think I'm designing ANN, so I wanted to clear that misconception up.

you study the biological physics, chemical kinetics, electrochemistry, transport phenomena and emergent behavior of the systems as well.

I agree. I need to find a way to work this stuff in. I do have a section "beyond the neuron" to illustrate the point, but perhaps I need to make it clearer.

I do indeed have enormous confidence in non-linear dynamics and believe strongly it is the ultimate key in understanding how the brain works.

I think this is too strong of a statement. It's not the ultimate key, but it is definitely a fruitful pursuit.

 

[jackmell]

Allow me please to contribute something concrete:

W. Freeman's article, "How the brain makes chaos to make sense of the world" attempts to model the olfactory bulb by a system of non-linear delay differential equations:

http://sulcus.berkeley.edu/FreemanWWW/manuscripts/IC8/87.html

Also, Terrence Senjowski suggested strange attractors may have some part in memory formation in the brain. As you know strange attractors are a hallmark of non-linear dynamics. Terrence is co-author of "The Computational Brain". I do not have the reference where he makes this suggestion however.

One final note: I'm sure you're aware of the "Blue Brain" project where an IBM group is attempting to model the cortex. My understanding is that their work is centered on the (non-linear) Hodgkin-Huxley equations and have plans as I understand it, to begin incorporating "history" in the form of likewise non-linear integro-differential equations. We are aware that neurons exhibit such a "history" phenomenon: their present behaviour is dependent on their past behavior.

 

[sshzp4]

@Pythagorean
"I figure since you're spending so much time defending your position, you way as well give more specific, constructive criticism :P "

I will leave that task for your advisors :). I love to bark at all things (I get paid to do that), but am in general too lazy to start the process of a detailed review (unless I get paid to do that).

Since you are still a student, your effort is great for a school project. But as the reviewer of a professional technical review article, the article is shoddy. If I stumbled across that article while just surfing the web, I would have added a significant section with choice abuses. Reviewing and being reviewed are both hard processes, but I am sure you will find out. (So best get obdurated to that feeling from receiving vague comments that leave it up to you to find out the implications :D)

@Jack -- I do hope you are correct. But I will still quote you on the following "I do not believe the current implementation of neural networks will ever emerge artificial intelligence but have always proposed that we will have to wait for a critical point in technology when someone creates a new qualitatively different device that is intrinsically non-linear", and describe that as a mere conjecture or prediction, not the current state of truth. We have been trying ever since the perceptrons were conceived to create Bayesian NNs to process statistical data. That's still a hypothesis. My point is, right now statistics and trained classification seem better approaches to modeling intelligent behavior. However, this view can be debated based on the background of the observer. Most CS people will claim statistics is better but EE folks will call NNs a happier approach.

And Jack, remember NNs are conceptually more closer to statistics and classification, and are usually used as blackbox algorithms. NLD using perceptrons might lead to non-deterministic behavior (the feared counterpart of deterministic chaos), which can only be analyzed statistically. Anyway, quite irrelevant for the geometer's topic, but good to think about.

Sid

 

[Pythagorean]

I will leave that task for your advisorss [...] since you are still a student, your effort is great for a school project.

It's not a school project, nor do my advisors know about it.

But as the reviewer of a professional technical review article, the article is shoddy. If I stumbled across that article while just surfing the web, I would have added a significant section with choice abuses. Reviewing and being reviewed are both hard processes, but I am sure you will find out. (So best get obdurated to that feeling from receiving vague comments that leave it up to you to find out the implications :D)

Point taken. It has changed a bit since I posted this.

And to be honest, you've actually given me a lot more than vague comments. You've giving me an idea of how certain types of people interpret my article, and that comes with identifying your own biases and unspoken assumptions. I actually have some work to do thanks to you and other, more gentle critics.

but I should sleep on it.

 

[sshzp4]

@ Jack -- Conjectures and hypothesis against a concrete theory constructed on experimental fact? You should use the term 'speculated' instead of 'suggested'. Wells speculated man could land on moon, gave him the privilege of being described as the progenitor of the idea for a long time. But 'gravity shutters' didn't work.

Speculation is merely the cautious way to claim that they said it first; if proven wrong they say it was 'mere speculation', otherwise its always an I told you so. Its a very dangerous form of academic fudgery.

EOT

Sid

Edit: Oh, I see the point of your last post. You were helping the geometer with references. I assumed it was an extension of your earlier comment. Anyway, never mind.

 

[jackmell]

I think it would be a good idea to have a neurophysiologist comment about the article (seriously). I'd be curious to know what they think about the article. I am a big believer in constructive criticism. No way you could swing that Sid right? Just asking that's all. And you're right, I've expressed my personal opinions about how the brain should be approached. I apologize for going off-topic and should have concentrated on the writing instead. Sides, I have an etouffee to make now.

 

[sshzp4]

@ Jack: Oh I could try swinging that! :) When you have been criticized enough (for everything from a misplaced punctuation mark to the presence of a hyphen in a misleading place) all criticisms are just indicators of the presence of issues that lead thoughts astray off the topic at hand. The more vague a critique is or the more destructive it is, the more the indication that you haven't been able to get the idea across. So the nature of a critique usually gives you an idea of where the issues with your authorship lie (Assuming of course that the reviewer grasps the language of the discourse and there is no conflict of interest).

 

[apeiron]

1) the page is all about neurons not brains, so should be called dynamic neuron science at most. Dynamical approaches to brains would cite the likes of Walter Freeman, Scott Kelso, Karl Friston, Stephen Grossberg, Paul Nunez, etc, etc.

2) the page is based on a fundamental misconception. Yes neurons/brains have a dynamic basis (like all biology), but what is important about them of course is the way they capture information. Talking about a purely "dynamic" approach is just wrong from the start (unless you have the explicit limited research ambition of studying the physiologic-dynamic aspects of their functioning).

Neural nets are a computational attempt to model what is going on (an informational basis to the information processing!). So there is room for a dynamical approach to information processing. Some people talk about hybrid disciplines like infodynamics.

But anyway, the page does not spell out where it sits on a spectrum of approaches (not that it is about "brain dynamics" as opposed to neuron physiology in the first place).

 

[Pythagorean]

1) the page is all about neurons not brains, so should be called dynamic neuron science at most. Dynamical approaches to brains would cite the likes of Walter Freeman, Scott Kelso, Karl Friston, Stephen Grossberg, Paul Nunez, etc, etc.

As discussed with ssh, this is not the case, but it may be the result of bad communication. I may have changed the page to reflect this before you read it, but also note that I'm still in the process of adding sections beyond neurons. This is not, by any means, a complete page. I intend to add a holistic section.

Btw, the whole nervous system is of interest, not just the CNS.

2) the page is based on a fundamental misconception. Yes neurons/brains have a dynamic basis (like all biology), but what is important about them of course is the way they capture information. Talking about a purely "dynamic" approach is just wrong from the start (unless you have the explicit limited research ambition of studying the physiologic-dynamic aspects of their functioning).

This is the same case with neurobiology, neurophilosophy, and neurophysics, all of which are their own disciplines and have their own wiki articles. No one discipline accounts for all the aspects of the subject it studies. There are, however, many scientists, who are only trained in their field of analysis.

Neural nets are a computational attempt to model what is going on (an informational basis to the information processing!). So there is room for a dynamical approach to information processing. Some people talk about hybrid disciplines like infodynamics.

agreed...

 

[Pythagorean]

OK, major revisions, refined citations, added content. Please continue to point out overly speculative claims and suggest new sections or contet:

http://en.wikipedia.org/wiki/Dynamical_Neuroscience

Section to add, yet:
Applications (both medical and theoretical)
Chaos and nature
more cognitive content

Possibly this:
http://www.scholarpedia.org/article/Dynamic_causal_modeling

 

[apeiron]

It is looking better. But to focus things, what are you seeing as distinctive about "dynamical neuroscience" here?

To me, the central idea you want to articulate seems to be that neuroscientific approaches to explaining mind or cognitive function (the higher level stuff) has been based on a "too simple" model of the components. So a more accurate dynamical description of these components may serve as a better foundation for high level explanations.

If this is the case (I may just misread your intent) then it would be helpful to make a connection to the arguments that standard ANN modelling is too simplistic. And second, examples of modelling that makes use of more dynamical componentry.

The lurking thought when people stress dynamics is that there must be something big we have been missing by taking familiar linear, computational, atomistic approaches to modelling the neuron, and the brain. So if we go back to basics, we may finally unlock the secrets via some new dynamical principle.

I think this is true. But I don't personally think the secret exists "down in the neurons". I don't even think it exists in the collective behaviour of neurons or even, separately, at some whole brain level (as some like Nunez and Freeman sort of argued).

Instead, I believe these dynamical principles (actually they would be info-dynamical) would exist over all scales of neural organisation. They would be very general. Which is why I personally follow a systems science/theoretical biology/semiotics approach to modelling.

But anyway, the point I am trying to make is that you probably have a specific hypothesis about the reason for framing the research issues in the particular way you have. That is, we need to study neuron-level dynamics, component level dynamics, because somehow the secret we are missing can be found at this scale of mechanism. The existence of the page would make more sense if you spelt out this theoretical context.

 

[Pythagorean]

When I introduced myself to the neuroscience/brain/mind community here on physicsforums, I was really interested in the higher-order problems like consciousness and cognition, so you may be mixing those connotations in with my writing, knowing that I'm the author (of course, it's possible that I'm also "leaking philosophy" in my writing).

Dynamical neuroscience doesn't serve to be holistic. There are, of course, holistic dynamical approaches.

In some respects, the field is a lot like a blacksmith. The blacksmith makes lots of different things out of metal, mostly because he's good at working with metal. The things he makes may applied all kinds of different way, from helping, to killing, to hanging on your wall as art. He's not very concerned with how people apply it. As the market grows and diversifies, the blacksmiths may specialize (like focusing on a market that uses particular metals and cuts that are safe for children in nursery construction). So then the blacksmith begins to learn more about child care and nurseries since the market is there, and he can provide a higher quality product, tailored for a specific demographic.

a dynamical scientist works with dynamical systems, because they know about the machinery of dynamical systems (specifically, they're versed in nonlinear dynamics, which requires a good mathematical background). Many dynamical scientists are like your unfocused blacksmith, they are only interested in dynamical systems in general, they don't cater to one particular group. But neuroscience, obviously, has exploded with interest and technology in the last couple decades and so there is now a demographic for dynamical scientists, so it has become more efficient to specialize in neuroscience, and learn the subject along with it.

Dynamic neueroscience has a very large medical and physiological component too that make no guesses about the consciousness or other cognitive aspects. At a certain point, your questions will push you over the line to dynamical psychology (yeah, it's out there), which is not the topic I'm covering. Cognitive neuroscience is the acceptable in-between.

addendum:

and ANN's are still acceptable dynamical systems if their global constraints are such. It's just that each individual neuron is not dynamical. The interaction dynamics can be very dynamical, depending on the model.

addendum2:

examples of modelling that makes use of more dynamical componentry.

That's what the morris-lecar (which I summarized with equtions) and hodgkin-huxley models are, they focus more on the dynamics of singular neurons. They are based on resonance, not the digital all-or-none firing, but they still exhibit excitability (similar to all-or-none firing, but not quite the same) and can still be coupled together in a meaningful network.

 

[apeiron]

Your focus still seems to be just on the cellular level, so it is not "neuroscience". That is one big source of confusion here. And there is already a wiki on biological neurons that you link to which is about a dynamical sub-discipline.
http://en.wikipedia.org/wiki/Biological_neuron_model


And to call it dynamical, I would expect a justification. Is is dynamical that ignores the emergence of computational features (which it sounds as though you are saying)? Is it dynamical as the way to explain emergent computational features (which is what people would expect)?

 

[Pythagorean]

Your focus still seems to be just on the cellular level, so it is not "neuroscience". That is one big source of confusion here. And there is already a wiki on biological neurons that you link to which is about a dynamical sub-discipline.
http://en.wikipedia.org/wiki/Biological_neuron_model

This is a matter of personal availability, not focus. See "attractor networks" in my article and "cognitive neuroscience" with "hopfield networks". This is where I need input from people (that's why I noted that i need more for the cognitive neuroscience section) but remember that it has to have a dynamical basis (it has to have a nonlinear mathematical formulation that exhibits rich dynamics) and it has to be based on empirical observation (to be science, of course).

Remember that I take a reductionist approach (and also remember that I do not think our approaches are mutually exclusive, and in fact think they're beneficial in terms of synergy) so I'm already spent on what I can offer the page. I've had to do a lot of research to expand it as much as I have, and it will take more research to expand it more, but this is why I'm asking for input, because I'm not completely sure where to look.

Note also, that I'm still reviewing old discussions from you. I just came across Scott Kelso, which I'm going to look into to add.

And to call it dynamical, I would expect a justification. Is is dynamical that ignores the emergence of computational features (which it sounds as though you are saying)? Is it dynamical as the way to explain emergent computational features (which is what people would expect)?

I'm not sure those are directly relevant. Dynamical refers to the mathematics. This is mathematical biology, but more specified. Dynamics is a subject of math, neuroscience as a subject of biology. Of course, nowadays, (neuroscience is interdisciplinary).

It doesn't directly make a judgments about computationalism, emergence, etc. It does the actual analysis on the models and looks for realistic regimes that explain observed behavior. The problem is that the nature of the equations is not simple, there are thousands of regimes to look in (depending on how many dimensions and parameters your model has).

 

[Pythagorean]

also note the textbook:
http://books.google.com/books?id=kV...&resnum=4&ved=0CCQQ6AEwAw#v=onepage&q&f=false

 

[apeiron]

I'm not sure those are directly relevant. Dynamical refers to the mathematics. This is mathematical biology, but more specified. Dynamics is a subject of math, neuroscience as a subject of biology. Of course, nowadays, (neuroscience is interdisciplinary).

OK, I understand. But my point is that it is a fundamental mistake (arguably) to believe that it is possible to create a "proper" dynamical description, and from that derive the computational (or rather informational) aspects of the system in question.

This is a huge issue, widely discussed, most especially in mathematical biology (Rosen, Patttee, Salthe, Brier, etc). And also in developmental systems theory (Oyama, etc) - http://en.wikipedia.org/wiki/Developmental_systems_theory

So to put up a page that is "just dynamics" needs justification to make sense. Otherwise it sounds like you are taking a regressive step.

Again, to repeat, it has been argued as a no-go theorem that "just dynamics" can't give us a full story in neuroscience. Robert Rosen and Howard Pattee are the best sources here.

If you just want to highlight a class of nonlinear mathematical modelling, then that's great. I'm merely saying that from my perspective, it sounds really odd not to acknowledge the wider context of debate.

The cutting edge of modelling would be about how dynamical processes (which are well-modelled in terms of attractors, metastability, etc) are harnessed by informational ones (which is where semiosis, symbol-grounding, the epistemic cut, etc, come in).

 

[Pythagorean]

OK, I understand. But my point is that it is a fundamental mistake (arguably) to believe that it is possible to create a "proper" dynamical description, and from that derive the computational (or rather informational) aspects of the system in question.

I don't believe that. I believe in an interdisciplinary approach. What you call a "systems approach" (btw, 'systems neuroscience' academically is a synthesis class, it's a lot like a 'final lesson', you integrate all the subdisciplines for research, you collaborate across the fields, so most actively researching neuroscientist are "systems" neuroscientists by default.

For instance, follow the Dynamical Neuroscience conferences which I cite:
http://neuro.dgimeetings.com/Home.aspx
to see the broad spectrum of contributing fields.

Anyway, with respect the viewpoint you keep projecting on me, I believe that all fields follow from each other in a... well, a dynamical way. It's not like all of psychology is going to be discovered from neurons or all off neurons will be understood solely from psychology; it's that development of both fields will provide insights to each other.

Dynamical sciences been successful in employing "reductionist" (that's a relative term) modeling to describe emergent cognitive proerties (again, see attractor networks in the article).

And as I've also demonstrated in the article (Gluck, in the cognitive neuroscience section) it works in reverse too, but that's not a dynamical example that I know of. I still mentioned hopfield networks though.

And in the intro:

"Information theory draws on thermodynamics in the development of infodynamics which can involve nonlinear systems, especially with regards to the brain."

So please point to specifically where you're confused.

 

[apeiron]

You think you know what you are talking about? Fine.

 

[Pythagorean]

Yes, I do know what I'm talking about here: my perspective. Which you are misrepresenting, and which is more aligned with your perspective than you realize.

The wiki is based on scientific contributions, which will take time to research and digest before all major perspectives are represented.

 

[Pythagorean]

Here's the agenda for the 18th Dynamical Neuroscience Conference that might help clarify some of the topic of dynamical neurosicence:

http://neuro.dgimeetings.com/Home.aspx

 

[JFGariepy]

Yes, I do know what I'm talking about here: my perspective. Which you are misrepresenting, and which is more aligned with your perspective than you realize.

The wiki is based on scientific contributions, which will take time to research and digest before all major perspectives are represented.

These statements are so contrary to the Wikipedia spirit that only this quotation is enough to justify a request for deletion of the article. Wikipedia is not a place where perspectives meet like in a debate, it is not a public place to express your views. I proposed the merge to Computational Neuroscience and the deletion of most of the content. Even the textbook you provide uses "dynamical systems in neuroscience" rather than "dynamical neuroscience". There is no justification in the litterature referenced to create a separate page for dynamical systems, which have been used throughout the history of what has been called computational neuroscience. The whole discussion here proves that you are trying to introduce your personal views in Wikipedia, which in itself is unnacceptable on top of all the fundamental debate behind it. Most people using non-linear equations in computational neuroscience do not define themselves as "dynamical neuroscientists".

I think it would be a good idea to have a neurophysiologist comment about the article (seriously).

Now you have it :)


You can participate to the merger proposal vote here : http://en.wikipedia.org/wiki/Talk:Computational_neuroscience#Merger_proposal

 

[jackmell]

Now you have it :)


You can participate to the merger proposal vote here : http://en.wikipedia.org/wiki/Talk:Computational_neuroscience#Merger_proposal

Thank you.

I have much faith in mankind one day solving the problem of mind, consciousness, and artificial intelligence and believe non-linear dynamics will play an important role.

 

[Pythagorean]

OK, I've done some research, I found the proper name for my field: Neurodynamics.

Here's a bit about it's history:
http://resources.metapress.com/pdf-preview.axd?code=g384811610556546&size=largest

Here's what people are saying about it now (well, 9 years ago anyway):

Current Opinion in Neurobiology, August 2001, Volume 11, Issue 4. Neurodynamics: nonlinear dynamics and neurobiology: Henry D. I. Abarbanel, a and Michael I. Rabinovich

"The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems."

-----

These statements are so contrary to the Wikipedia spirit that only this quotation is enough to justify a request for deletion of the article. Wikipedia is not a place where perspectives meet like in a debate, it is not a public place to express your views. I proposed the merge to Computational Neuroscience and the deletion of most of the content. Even the textbook you provide uses "dynamical systems in neuroscience" rather than "dynamical neuroscience". There is no justification in the litterature referenced to create a separate page for dynamical systems, which have been used throughout the history of what has been called computational neuroscience. The whole discussion here proves that you are trying to introduce your personal views in Wikipedia, which in itself is unnacceptable on top of all the fundamental debate behind it. Most people using non-linear equations in computational neuroscience do not define themselves as "dynamical neuroscientists".

You took that post out of context. I differentiated between the article and my post. In my POST I was talking about my perspective. The WIKI article is supposed to be about the collective perspective of the members of the field (which I'm still struggling to perfect through my research, admittedly).

 

[JFGariepy]

OK, I've done some research, I found the proper name for my field: Neurodynamics.

Here's a bit about it's history:
http://resources.metapress.com/pdf-preview.axd?code=g384811610556546&size=largest

Here's what people are saying about it now (well, 9 years ago anyway):

Current Opinion in Neurobiology, August 2001, Volume 11, Issue 4. Neurodynamics: nonlinear dynamics and neurobiology: Henry D. I. Abarbanel, a and Michael I. Rabinovich



-----



You took that post out of context. I differentiated between the article and my post. In my POST I was talking about my perspective. The WIKI article is supposed to be about the collective perspective of the members of the field (which I'm still struggling to perfect through my research, admittedly).

Well at least you see that the questions I raised concerning the name of your field and its exact definition was justified and it wasn't bad faith on my part. It's very important to watch for these things on Wikipedia if we don't want the encyclopedia to become a live discussion forum where people define things the way they want. Good luck with your future contributions.

 

[Pythagorean]

Here's a paper highlghting the specific advantages of a dynamical view:

http://sulcus.berkeley.edu/FreemanWWW/manuscripts/IC13/90.html

 

[jackmell]

Here's a paper highlghting the specific advantages of a dynamical view:

http://sulcus.berkeley.edu/FreemanWWW/manuscripts/IC13/90.html

That was 20 years ago and the other, nine. Can you cite a more recent opinion of neuroscientist on the matter of using non-linear dynamics, chaos theory, strange attractors, emergence, and self-organization as tools for understanding brain function?

Have you seen the brain series on Charlie Rose? I just caught a part of episode 10 yesterday. I'd be interested in what those guys think about neurodynamics. Maybe even you can contact Charlie and ask him if he could create an episode about neurodyanmics. Get Freeman in there maybe. Here's the link:

http://www.charlierose.com/view/collection/10702

 

[apeiron]

That was 20 years ago and the other, nine. Can you cite a more recent opinion of neuroscientist on the matter of using non-linear dynamics, chaos theory, strange attractors, emergence, and self-organization as tools for understanding brain function?

Freeman actually impressed me the most out of all the "dynamicists" who sprang up in the 80s/90s. But equally, he showed that attractors and other "straight non-linear models" lacked real bite. They are good for making analogies, but not then for producing actual predictive models.

So just as we would say the brain is not a Turing computer, we can also say it is not a straight dynamical system either.

 

[Pythagorean]

jackmell:

strictly neuron behavior
Here's some more recent papers that make use of nonlinear dynamics to understand neuron behavior itself (generally, drawing no conclusions about cognitive aspects). These have been productive in medical and general physiological understanding.

from the nonlinear dynamics journal:
http://www.springerlink.com/content/n2567128x6372603/

Izhikevich gives his opinions in the text, "Dynamical Systems in Neuroscience" written in 2007:
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=11063

http://www2.gsu.edu/~matals/ashilnikov_cv.pdf - Shilinikov's CV (scroll down to publications. You see a lot of direct medical applications for nonlinear dynamics)On the more cognitive side:

http://www.mitpressjournals.org/doi/abs/10.1162/jocn.1995.7.4.512
(A Dynamic Systems Approach to the Development of Cognition and Action)

Lewis, Marc D. (2005) Bridging emotion theory and neurobiology through dynamic systems modeling. BEHAVIORAL AND BRAIN SCIENCES; 28, 169–245

 

[jackmell]

Freeman actually impressed me the most out of all the "dynamicists" who sprang up in the 80s/90s. But equally, he showed that attractors and other "straight non-linear models" lacked real bite. They are good for making analogies, but not then for producing actual predictive models.

Apeiron, can you provide the reference where he "showed" this please? I do not recall him taking this position in the paper I studied some time ago, "How the brain makes chaos to make sense of the world."

Even so, I'm skeptical of his appraisal and remain unperturbed in my belief that mind can emerge from equation.

Pythagorean, thank you for posting those references.

 

[apeiron]

Apeiron, can you provide the reference where he "showed" this please? I do not recall him taking this position in the paper I studied some time ago, "How the brain makes chaos to make sense of the world."

Even so, I'm skeptical of his appraisal and remain unperturbed in my belief that mind can emerge from equation.

Pythagorean, thank you for posting those references.

I meant he showed me (by his failure). I talked to Freeman and others like Friston and Kelso a lot at the time. They had a well motivated approach. But it did not pan out in my opinion. It did not achieve lift off as hoped.

But "son of dynamical systems" still could. That's why I would keep track of guys like Friston who are trying to get some blend of dynamic and computational principles, as in the bayesian brain model.

 

[Pythagorean]

This is anecdotal, but from my experience, one of the great things about defining a system with a set of nonlinear differential equations, is that (because of the nature of nonlinearity) you no longer need to use algorithms to describe different behavior.

That is, you don't need to make a bunch of if statements when you're organizing the behavioral structure of a system. Instead, bifurcations already exist in the equation themselves. All relevant behaviors are contained in the system of equations and it's a matter of what parameter space you're in, so all you have to do is adjust the proper parameter values and the appropriate behavior is described by the equation.

We've already gained a lot of ground (in terms of elegance and simplicity) by avoiding algorithms (which, to me, are patchwork... you can describe nearly anything with a long list of conditional algorithms, but it's not as intuitive or easy to manage as a system of two or three differential equations that can be written in two or three lines).

 

[Pythagorean]

oh, by the way, here's the weblog of Markus Dahlem, who uses the nonlinear approach to understanding migraine's in terms of volume transmission:
http://mdlabblog.blogspot.com/

Volume transmission is an extracellular interaction between neurons that don't utilize synapses. Some examples would be electromagnetic field effects between neurons and neurotransmitter concentrations.

 

[Pythagorean]

An article of Izhikevich (I have his book, Dynamical Systems in Neuroscience)

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1333071

a Quote from the conclusion:

As the reader can see in Fig. 2, many models of spiking neurons
have been proposed. Which one to choose? The answer depends
on the type of the problem. If the goal is to study how the
neuronal behavior depends on measurable physiological parameters,
such as the maximal conductances, steady–state (in)activation
functions and time constants, then the Hodgkin–Huxleytype
model is the best. Of course, you could simulate only tens
of coupled spiking neurons in real time.
In contrast, if you want to simulate thousands of spiking neurons
in real time with 1 ms resolution, then there are plenty of
models to choose from. The most efficient is the I&F model.
However, the model cannot exhibit even the most fundamental
properties of cortical spiking neurons, and for this reason it
should be avoided by all means. The only advantage of the I&F
model is that it is linear, and hence amenable to mathematical
analysis. If no attempts to derive analytical results are made,
then there is no excuse for using this model in simulations.
The quadratic I&F model is practically as efficient as the
linear one, and it exhibits many important properties of real neurons,
such as spikes with latencies, and bistability of resting and
tonic spiking modes. However, it is 1-D, and hence, it cannot
burst and cannot exhibit spike frequency adaptation. Thus, it can
be used in simulations of cortical neural networks only when biological
plausibility is not a great concern.

 

[Pythagorean]

Network Modeling of Epileptic Seizure Genesis in Hippocampus
Somayeh Raiesdana, S. Mohammad R. Hashemi Golpayegani, Member, IEEE, and S. Mohammad P. Firoozabadi

Proceedings of the 4th International SaD1.24
IEEE EMBS Conference on Neural Engineering
Antalya, Turkey, April 29 - May 2, 2009

Based on the use
of mathematical nonlinear models of neuronal networks, it is
possible to formulate hypotheses concerning the
mechanisms by which a given neuronal network can switch
between qualitatively different types of oscillations. This
switching behavior is a dynamical paradigm in epileptic
seizure when e.g. an EEG characterized by alpha rhythmic
activity suddenly changes into a spike- burst pattern. This
transition, however, depends on input conditions and on
modulating parameters where often even a subtle change in
one or more parameters can cause a dramatic change in the
behavior of neural circuits. This sensitivity to initial
condition or to a small perturbation is the major hallmark of
nonlinearity and chaos. Nowadays, modeling neuronal
ensemble is one of the most rapidly developing fields of
application of nonlinear dynamics and the success of such
models depends on the universality of the underlying
dynamical principles.
Epilepsy is a brain disorder characterized by periodic and
unpredictable seizures mediated by the recurrent
synchronous firing of large groups of neurons in the cortex
and seizure represents transitions of an epileptic brain from
its normal less ordered (chaotic) interictal state to an abnormal
(more ordered) ictal state

 

[Pythagorean]

"Lectures in Supercomputational Neuroscience Dynamics in Complex Brain Networks"

From Series: "Understanding Complex Systems"

Complex Systems are systems that comprise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations
of which are the spontaneous formation of distinctive temporal, spatial or functional
structures. Models of such systems can be successfully mapped onto quite diverse
“real-life” situations like the climate, the coherent emission of light from lasers,
chemical reaction-diffusion systems, biological cellular networks, the dynamics of
stock markets and of the internet, earthquake statistics and prediction, freeway traf-
fic, the human brain, or the formation of opinions in social systems, to name just
some of the popular applications.
Although their scope and methodologies overlap somewhat, one can distinguish
the following main concepts and tools: self-organization, nonlinear dynamics, synergetics, turbulence, dynamical systems, catastrophes, instabilities, stochastic processes, chaos, graphs and networks, cellular automata, adaptive systems, genetic algorithms and computational intelligence.

http://www.springerlink.com/content/t7u1m22m0116/front-matter.pdf

 

[Pythagorean]

"Computational Neurogenetic Modeling"

CNGM is concerned with the study and development of dynamic neuronal models for modeling brain functions with respect to genes and dynamic interactions between genes.

http://books.google.com/books/about/Computational_neurogenetic_modeling.html?id=GFdzpAasI4oC

 

[Pythagorean]

Subdiffusion and Superdiffusion in the biological sciences:

http://www.cell.com/biophysj/abstract/S0006-3495(09)00983-7
http://en.wikipedia.org/wiki/Anomalous_diffusion
http://www.cell.com/biophysj/abstract/S0006-3495(11)00877-0

Sub/superdiffusive systems are fractal objects, their derivatives being non-integer. This also means they don't depend just on nearest neighbors, but all other members of the ensemble!

Very expected from a dynamical systems perspective!

http://arxiv.org/ftp/math-ph/papers/0311/0311047.pdf

I wonder if these could be used to model modulation in neural networks:

http://arxiv.org/abs/0805.3769v1

 

[Nano-Passion]

You probably know this but your wiki article is no longer there. Why?

 

[Pythagorean]

You probably know this but your wiki article is no longer there. Why?

reading the posts in this thread by JFGariepy might help understand that. I think though, that I started too early. The dynamical systems approach to neuroscience is still developing and it makes it difficult to comment on. It is the physicist's approach to computational neuroscience, so it could be integrated into the computational neuroscience page.

Instead I decided to contribute at a lower level, so I made this page:

http://en.wikipedia.org/wiki/Morris–Lecar_model

This is a popular model in computational neuroscience, based on the physics of real neurons; the Hodgkin Huxley model is the original, but this model reduces the dimensions in half for faster computation at the cost of simplifying assumptions.

 

[Nano-Passion]

reading the posts in this thread by JFGariepy might help understand that. I think though, that I started too early. The dynamical systems approach to neuroscience is still developing and it makes it difficult to comment on. It is the physicist's approach to computational neuroscience, so it could be integrated into the computational neuroscience page.

Instead I decided to contribute at a lower level, so I made this page:

http://en.wikipedia.org/wiki/Morris–Lecar_model

This is a popular model in computational neuroscience, based on the physics of real neurons; the Hodgkin Huxley model is the original, but this model reduces the dimensions in half for faster computation at the cost of simplifying assumptions.

Oh.. so then what would be the difference between theoretical and dynamical neuroscience?

 

[Pythagorean]

Oh.. so then what would be the difference between theoretical and dynamical neuroscience?

Theoretical neuroscience is an umbrella term encompassing many current approaches. Dynamical approach to neuroscience is a particular theoretical approach that utilizes time-smooth continuous equations to describe neural events as the neural systems evolve through state-space. They are structurally deterministic, but noise terms and random processes can be integrated into them. There's also symbolic dynamics which utilize the Markov partition.

A large part of dynamical systems approach is studying quantities geometrically (i.e you draw the average trajectories of your system and you begin to see structures that have functional meaning in the state-space of the system). You generally measure quantities of the system like: the lyapunov constant, the natural measure, the basin of attraciton, etc.

 

[atyy]

Hmmm, but is there such a thing as non-dynamical neuroscience?

I can imagine that some of the "optimization" approaches are considered non-dynamical by some. But that would be like saying statistical mechanics which maximizes free energy is non-dynamical, and place Boltzmann's work on kinetic theory out of the realm of statistical mechanics, which is strictly correct, but surely not your intention. Also many dynamical systems can be described as optimal (but not uniquely) through the use of Lagrangians (maybe take a look at Enzo Tonti's work for how far this can go).

Even if you consider anatomy as non-dynamical, I'm sure most anatomists do their work because they know how it fits in with physiology. Similarly, most physiologists know how important network topology (ie. anatomy) is for interpreting physiology. It's the same at a lower level in chemistry, where no one would interpret the diagram A+B→C as non-dynamical because the rate constants were not explicitly included.

Incidentally, I have read books where it is said that control or systems theory goes beyond dynamics, in the strictly true sense that most dynamics deals with autonomous equations. But I'm sure you'd disagree with that!

 

[apeiron]

Incidentally, I have read books where it is said that control or systems theory goes beyond dynamics, in the strictly true sense that most dynamics deals with autonomous equations. But I'm sure you'd disagree with that!

There is definitely a live issue here. It seems obvious both that everything is grounded in biological dynamics, yet also that dynamics is only half the story. Therefore some kind of hybrid is the "higher view".

The same issue arise in biology, with the fundamental division between genes and organisms, or replication and metabolism. And there have been continuing efforts to marry the two sides, as in systems biology, relational biology, evo-devo, biosemiotics, etc.

 

[Pythagorean]

dynamics in this sense refers to the dynamical systems theory (DST) approach, which entails nonlinear equations that generally have no analytical solution.

Much quantitative scientific work relies on the expectation of equilibrium which allows for linear equations. Thus, you can take the system apart into its components, solve each one, and put them back together, because they obey the superposition principle.

Nonlinear systems are more general (if you make particular terms first order or particular constants zero, you can reduce the equations to linear). They do not obey superposition principle (so you will often hear the sum of the parts is not equal to the whole).

So naturally, dynamical systems are closer to the reality, since they make less simplifying assumptions (particularly the assumption of equilibrium and superposition) but previously to the computer age scientists would have had to derive, literally, thousands of equations... the "accounting" errors associated with this kind of work with paper and pen wouldn't even make it worth it. And these solution would not be analytical, they would be numerical.

Poincare discovered a way to geometrically assert things about the system (it's stable points, where it attracts solutions in state space, where it repels solutions, etc) without explicitly finding solutions. So this is what was done before computers with systems that had low enough dimension that you could visualize it geometrically.

So dynamical systems theorists are often sometimes called "geometers" because a major emphasis is visualizing the system in state space. The actual "dynamical" word only serves the purpose of a coup against the equilibrium assumption.

But yeah, there is no panacea. No one approach will tell the whole story of anything, ever. So there's no reason to jump in the DST bucket and ignore the rest of the world.