Computational Neuroscience.

madness

Yes, I agree it's false. I think it comes from a mistaken view that everything in physics is simple and linear and can be solved exactly. In other words, it come from a lack of understanding of what mathematical modelling is actually useful for.

Without concrete quantitative predictions, there's not much to verify or falsify in an experiment. Sometimes I feel like biology papers are just stabbing around in the dark with no real hypothesis to test (or at least no hypothesis that is strictly defined before you get the results of the experiment). I definitely believe mathematical models are an important part of understanding the brain.

Pythagorean

Sorry, I meant jack's statement was false.

Pythagorean

Additionally, there's other problems with this kind of statement:

"You share 98% DNA with monkeys"
"You share 50% DNA with your siblings"

no catastrophe theory needed to explain the problem with intuition here... the problem is that the statements are ambiguous. The are both true in their original context. A biologist does not need to know much mathematics (let alone catastrophe theory) to demonstrate to a student that there's two different ways to count groups of things.

Pythagorean

OP, I think madness answered your question best:

Computational Neuroscience is a really new field and it's multidisciplinary as well as interdisciplinary. Consider the University of Waterloo in Canada. Their Computational Neuroscience institute is supported by several classic departments. It is directed by a computer science PhD and has research contributions from faculty/students in physics, mathematics, electrical engineering, and neurobiology.

All that it takes to be computational neuroscience right now is that you apply computational approaches to neuroscience problems. One approach is the deterministic nonlinear approach. It will depend on your university, though, so you should actually look at what kind of research people are doing, maybe even try looking at their papers or their websites. "Computational Neuroscience" is a huge, complex field, with lots of interacting disciplines but also little pockets of interest.

mazinse

You cant make assumptions that biologists dont like math. When you have multidisciplinary fields like biochem, biophysics and bioengineer.

atyy

I do think that nonlinear differential equations are the only way to understand the brain. However, it must also be understood that formalisms that seem not related to nonlinear differential equations are intimately related. For example, the Volterra approximation is used when the dynamical system "resets" to the same state in the absence of a stimulus, ie. when the stimulus can be considered a "disturbance" about a fixed point. Similarly, although at the microscopic level, there may be a fundamental distinction between fixed points and limit cycles, if the experimentalist only measures a coarse-grained variable in which he is unable to distinguish the separate states in a limit cycle, the resulting coarse grained variable may be described by a probabilistic dynamical system. The basic message is that because the deterministic nonlinear dynamics of the brain are very high dimensional, if one is working in a regime in which an effective theory with fewer degrees of freedom provides sufficient accuracy for one's purposes, then one should use the effective theory. This in general requires guesswork and luck. Mostly luck - the systematic hardwork prepares you to take advantage of luck when it comes your way.

jackmell

That I believe is misleading. When I say 98%, I mean 98% of the proteins coded by ape DNA can be found in humans. However (close to) 100% of the proteins coded by my brother's DNA can be found in me.

Now, I'm not sure that's the way to interpret that. If not, I'd appreciate someone saying so. But I believe that's what it means when we say 98% of the DNA found in apes can be found in humans. But I haven't researched it yet so you guys can jump on Jack if that's not right.

Ok, maybe don't need to know much about Catastrophe Theory. Couldn't hurt. Sides, I think you're missing my point entirely: the vast difference between humans and apes appear to be due to just a small number of genes. There was a paper recently that suggested three major changes in humans (musscle in jaw bone, a different brain protein, don't remember the other) had a tremendous affect in shaping human evolution 2 million years ago.

Keep in mind, I do not believe the answer to this question has been firmly established. I'm only proposing a possible answer based on dynamics:

Why or more precisely, how can a small change create a very large difference? One possibility is that perhaps the genetic dynamics trajected through a critical point. It could have just as eassily been 99.9% similarity and still effected a very big change because of the qualitative change that often occurs when passing through a critical point. My proposal is that maybe humans emerged from the ape lineage through a critical-point transition in genetic dynamics. But just saying that is not easily understood. But if you know non-linear dynamics, it then becomes much easier to understand. Likewise, the entire principle of "Punctuated Equilibrium" is beautifully explanable by critical-point non-linear dynamics.

jackmell

You know I'm not a smart-ellic. But if I was I could, but woundn't, set up a poll: How many biologist in here like DEs?

Pythagorean

I get your point; I just wanted you to concede that it doesn't require catastrophe theory to understand, but furthermore, I want you to acknowledge that it might give geometers a bad name in the eyes of biologists when they hear that talk. Especially since, you know, the biologists are the ones that figured out gene expression...

In fact, the amount of genetics we share with all vertebrae (let alone other hominids) is an amazing example of diversity that can occur with small gene sets. One interesting example is the hox genes, which decide vertebrae flavor. In snakes, during development, their genetic dynamics get "stuck" in a "thorax loop"

http://www.ncbi.nlm.nih.gov/pubmed/1...?dopt=Citation

We have the evo-devo story:



for fun (it's a fish! no a reptile! no it's a panda bear! no a human!):
http://www.youtube.com/watch?list=SP...tailpage#t=10s

Pythagorean

I completely agree that many of the formalisms in dynamical systems (especially those that don't obey the principle of superposition) highlight an important cognitive flaw in thinking about problems (the tendency to dichotomize things into linear trends).

When I can, I see the whole world in terms of nonlinear dynamics: from my social relationships to the physics of the atmosphere when I'm sailing, to my biophysical signatures when I'm being mindful. Superposition is the special case. I just wanted to remove the elitist tone is all.

atyy

Good thought!