Talk:Neuropercolation

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Comments:

General remark: the connection between determinism and randomness, and discrete and continuum model should be much more clearly explained. Specific examples will be mentioned in this review. If the basic models is "neural mass", i.e. is a continuum model, how does it related to a grid model?

>> Thank you: I add the corresponing text and references to clarify these points.

The sentence "Neuropercolarion extends..." is somewhat misleading! Ising model, a fundamental model of phase transition is discrete. There is no reason to compare directly neuropercolation to models based on differential equations.

>> I removed the mentioned reference to differential equations, to avoid any potential misleading format. I do agree that the present article should focus on teh CA approach used in neuropercolation. Perhaps in a separate entry or part of anotehr entry the issue of ODE vs CA formalism can be addressed.

To the subsection "Properties of Neuropercolation Models":

+ Interaction with noise:

"Whenever he is looking at any piece of neural tissue, the investigator becomes immediately confronted with the choice between two conflicting issues: the question of how intricate wiring of the neuropil is strictly predetermined by some genetically prescribed blueprint, and how much freedom is left to chance within some framework of statistical probabilities or some secondary mechanism of trial and error, or selecting connections according to necessities or the individual history of the animal. Even on brief reflection one has to arrive at the conclusion that the case may not rest on either extreme..." (Szent‡gothai, J., 1978a, Specificity versus (quasi-) randomness in cortical connectivity, inArchitectonics of the Cerebral Cortex Connectivity, (Brazier, M.A.B., and Petsche, H., Eds.), New York, Raven Press, pp.77-97.), see also Szent‡gothai, J., 1990, "Specificity versus (quasi-) randomness" revisited, Acta Morphologica Hungarica, 38:159-167.

>> Thank you for the reference, I include it to the entry.

A possible resolution of the determinism-randomness dilemma was based on the principle described as "randomness in the small and structure in the large" (Anninos et al. 1970, Harth et al. 1970). Anninos PA, Beek B. Csermely TJ, Harth E and Pertile G., 1970, Dynamics of neural structures, J.Theor. Biol., 26: 121-148. Harth, E.M., Csermely, T.J., Beek, B. and Lindsay, R.P., 1970, Brain functions and neural dynamics, J.Theor.Biol. 26:93-100.

>> Yes, I add some elaboration on the emergence phenomenon from micro, through meso, to macro structures in the article.

+ long axon effects: some works of CDGilbert should be cited, say: Das, A and Gilbert,CD: Long-range horizontal connections and their role in cortical reorganization revealed by optical recording of cat primary visual cortex. Nature, 375, pp. 780-784 (1995).

About the role of inhibition. The fundamental citation is: Freund TF, Buzsáki G (1996) Interneurons of the hippocampus. Hippocampus 6:347-470[ISI][M

>> Thank you, these references and some others are included.

(Hippocampal interneurons are almost exclusively inhibitory).

The technical results seem to be interesting and appropriate

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The results connecting neurally-inspired cellular automata to phase transitions are quite nice, as are the connections between the behavior of neural masses and Neuropercolation. This is clearly a very well-developed area of work and there are many results to cover. However, in covering all of these findings the article becomes longer than the typical encyclopedia article, which is meant to be concise. I have nothing bad to say about all of your excellent work; my only suggestion is that you try to focus on the essence of it and try to state that as briefly as possible.

>> Thank you. I try to make the description more concise as possible. I do realize that adding several examples expanded the description. I try to separate such elaborations, as separate 'boxes', which can be omitted when reading the main text. An alternative is to more them to appendix, but I think those are discouraged by the editorial rules. So I streamline as much as I can,. but that will not drastically reduce the volume. Presently I am still within the max limits, although I do realize that more compact format is preferable.

Toward the end of the article, you outline in broad strokes the interplay of development, neural activity, and learning in bringing the nervous system toward a critical point. I find this quite interesting. Could you elaborate on the possible benefits of operating near this point? What experimental evidence is there that the brain might operate near this point?

>> Presently we consider this as a hypothesis, and stated as such. Some experimental evidence by WJ Freeman, JAS Kelso, etc may provide support to such approach. I do add some text accordingly, as requested.

Another suggestion on presentation- You mention that the Neuropercolation model offers an alternative to systems of differential equations. This is a good point to make, but I think it could be even more forceful if you described the possible benefits of using a Neuropercolation approach. Also, under what conditions would a differential equation model be more appropriate? Letting readers know why a Neuropercolation approach is useful will help them to think more clearly about it.

-John Beggs

>> I have decided removing the reference and comparison to differential equations, see also my comments to reviewer 1. I do believe that the link between percolation theory/CA and ODE/PDE is important. But the focus of teh present paper is different, so I omit these references for better focus and clarity.

- the author -

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The article is certainly interesting - I enjoyed reading it - but it is a bit disjointed in places. For instance, the 10 Building Blocks seem a bit out of place, and require more explanation so as to be accessible to a non-specialist (such as myself). I suppose eventually all the technical terms (e.g. divergent-convergent cortical projection) will have entries in Scholarpedia, but this may not happen for a while.

>> Author response: Yes, the original version contained some sections which were less relevant to neuropercolation, as also noted by other reviewers. Accordingly, the "Principles of Neurodynamics" is cut to 5, which are directly reflected in neuroperc models at present.

I also think there should be more explanation of magnetization, susceptibility, correlation length and power laws toward the end of the article. What is the physical significance of these parameters? At the very least the definitions should be given. Why does it matter that the scaling relationship is satisfied and that the exponents are well-defined?

Are you saying that you cannot have a phase transition without a scaling relationship? Why not? This was all very unclear to me. If there isn't space to explain it, either remove it or summarize it.

>> We have added the definition of susceptibility and refer to teh definition of correlation length. We also compressed the section on "Critical exponents and finite size scaling." At the end of thsi section we emphasize that the fact that the error of the identitity function is low, justifies the terminology 'weak Ising model", and the reference to critical behavior and phase transition in the case of neuropercolation. As rigorous proof of phase transition can not be given for such systems, the given numerical evidence is a suitable way to generalize the concept of criticality for neuropercolation.

Figure 4 is a bit unclear. The leftmost panel is mainly white, not black as stated (as noticed by another reviewer). Is there any way to exhibit these models evolving in time, or perhaps to provide a link to a page where this can be seen?

>> Yes, thank you for the comment. There has been a misprint which is corrected now.!

There seem to be at least three separate goals of the work (forgive me if I am being unkind):

1) To model the brain mathematically

2) To simulate behaviour observed in the brain with a simple mathematical model which need not have a biological basis [Perhaps also 2a) to simulate behaviour observed in other models of the brain with simpler models of the brain]

3) To prove interesting mathematical results, which need have nothing to do with the brain, but which were motivated by 1) and 2)

These are all, in my opinion, very worthwhile goals, but it is not clear which (subset) of them is being persued at different points in the article. I don't mean you should actually state the goal, but if something, e.g. the value of some parameter, has a biological significance, this should be mentioned.

>> At the present stage we are far from modeling the brain, we rather are limited to model part of the neural cortex, the neuropil. As we mentioned previously, we reduced the description of the 10 Principles of neurodynamics, and kept only the first 5, which describe lower-level behavior. This should clarify the 1./ item above.

As for 2 and 3: The motivation of neuropercolation as listed as: (i) introduce role of noise, (ii) long range axon effects, (iii) inhibitory effects. These properties have been incrementally introduced in neuropercolation models and studied, if possible, using rigorous mathematical tools, otherwise using computer simulations.

It is clear, that once the generalization is given and mathematically formulated, the mathematically object can be studied on its own, whithout neccessarily having biological significance. Such studies are very interesting and completely justified for their own right. Obviously, it is hoped that at least some of the mathematical resulst will have ultimately impact on the biological understanding. But it can take a long time, years, decades, or may be more. In the mean time, computational models are used to provide insight on teh behavior of biologically-relevant systems.

The last section is very interesting, and like the reviewer above, I think it should be expanded, with the experimental evidence included.

Wouldn't it be possible to say something about the continuous models in just one paragraph, with some advantages and disadvantages? There can be a separate page also, but I expect that many readers would like to know your opinion about the comparison, if only in outline.

>> In reference to coments by otehr reviewers as well, we removed the reference to continuous models, for the tiem being, as neuropercolation models address discrete structures.

Elaboration of teh link between discrete and continuous models will be elaborated separately and perhaps addressed in a separate aprticle in teh future.

- the author -

Amites Sarkar