How Can Math Enhance Your Understanding of Neuroscience?

[PieceOfPi]

Hi all,

Back when I was in high school, I was in this group where we competed with other school on a Jeopardy-style quiz competition where all the questions are related to basic neuroscience. Ever since then, I was fascinated by neuroscience.

Right now, I'm a sophomore at a university and currently a math major. My school doesn't have neuroscience department, and I'm not a biology major either because I didn't have a very good introduction in biology back when I was in high school (and thus, I'm still scared of biology). However, I still want to give neuroscience a try (as I'm starting to get fascinated again), and I was wondering if there is any way to make some connection between neuroscience from now so that I might be able to do something related to neuroscience in grad school or etc (If it's necessary, I'm willing to give one more try on biology, as I've heard biology in college is bit different from high school). Right now, I'm considering of taking a course in biopsychology in next quarter.

Feel free to leave any comment or question.

Thanks

 

[atyy]

arXiv isn't as widely used in neuroscience as in physics, so I've linked directly to the authors' websites from which you can access their papers.

Biess, Liebermann and Flash, A computational model for redundant human three-dimensional pointing movements: integration of independent spatial and temporal motor plans simplifies movement dynamics, J Neurosci 27:13045-64, 2007. (It should be free from http://www.pubmed.org or the Journal's page, because of the recent NIH public access policy.)

Brunel and Hakim, Fast global oscillations in networks of integrate-and-fire neurons with low firing rates http://arxiv.org/abs/cond-mat/9904278

Xiao-Jing Wang, http://wanglab.med.yale.edu/

Larry Abbott, http://neurotheory.columbia.edu/~larry/

Bard Ermentrout, http://www.pitt.edu/~phase/

Nancy Kopell, http://math.bu.edu/people/nk/

John Beggs, http://biocomplexity.indiana.edu/research/info/beggs.php

 

[Cincinnatus]

Of those people that he listed there. I believe Nancy Kopell, Bard Ermentrout and Tamar Flash all have math backgrounds. The rest have physics or computational neuroscience backgrounds. I myself majored in mathematics as an undergraduate. Though I also took a lot of neuroscience classes. I'm now a graduate student in computational neuroscience.

A while back, I posted a list of the most influential computational/theoretical neuroscience papers in the biology section of this forum. You might want to look there. Here's the link: https://www.physicsforums.com/showthread.php?t=248832

Atyy's list of people is somewhat biased in a particular direction of research though. Almost everyone he mentioned is working on the dynamical systems / biophysics side of things. There's a whole other set of people who are doing neuroscience that is a bit closer to computer science than to physics. Of course, we can't just divide computational neuroscientists into those "like physicists" and those "like computer scientists"... So let's say these are fuzzy sets and divide them anyway .

 

[atyy]

A while back, I posted a list of the most influential computational/theoretical neuroscience papers in the biology section of this forum. You might want to look there. Here's the link: https://www.physicsforums.com/showthread.php?t=248832

Wow, what a great list!

Of course, we can't just divide computational neuroscientists into those "like physicists" and those "like computer scientists"... So let's say these are fuzzy sets and divide them anyway .

OK, can you provide an example for clueless experimentalists like me? Say the guys who authored "Theoretical Neuroscience" (I wonder if they deliberately avoided calling it "Computational Neuroscience"?), Abbott clearly is "like physicists", is Dayan "like computer scientists"?

 

[PieceOfPi]

Thanks! It's interesting to know there are quite a few of mathematicians/physicians who are involved in neuroscience.

BTW, if I want to consider neuroscience, what classes should I take? Should I take introductory biology? organic chemistry? psychology? computer science?

 

[Cincinnatus]

Say the guys who authored "Theoretical Neuroscience" (I wonder if they deliberately avoided calling it "Computational Neuroscience"?), Abbott clearly is "like physicists", is Dayan "like computer scientists"?

I guess that's fair to say Peter Dayan is more "like a computer scientist"... at least more than Larry Abbott... I'm actually not so comfortable categorizing specific people in this way. Theoretical neuroscience is very interdisciplinary. Almost everyone I know is interested in projects on both sides of this artificial "physics-like" / "cosci-like" divide.

This is a good place to quote David Marr. Paraphasing, Marr wrote that to understand any neural system we need to understand it at 3 levels.

1). The computational level
2). The algorithmic level
3). The implementation level

To understand a system at the computational level you need to know what it is that the system needs to do. For example, the visual system needs to recognize objects in the world. We can recognize a chair as being the same chair despite a completely different image falling on our retina when the chair is rotated or the light level is changed etc. The computational "problem" that our object recognition system must solve is "how to represent object invariances in the visual world?"

To understand a system at the algorithmic level you need to know what algorithm the system is implementing. Keeping with the object recognition example, we do not yet know how the visual system accomplishes this. We have several candidate theories from computational neuroscience as well as computer vision...

To understand a system at the implementation level we need to know how the actual biological parts of the brain in question implement the algorithm. In the case of object recognition, we know various structures in the ventral visual pathway are involved. We also know quite a bit about the response properties of cells in some of these areas... Though so far, no one has been able to put it all together into a complete (accepted) theory.

The artificial division of the field into "physics-like" and "cosci-like" that I referred to earlier might correspond roughly to people who are most interested in the implementation level as the former and people more interested in the computational and algorithmic levels in the latter group.