Knowing more about the discipline of mathematical neuroscience

[Nano-Passion]

I've been looking for curriculum (e.g. classes needed) for mathematical/theoretical neuroscience but with no success. Math, physics, and neuroscience are some of my prime interests, but I have no idea on how to go about thinking if I should pursue theoretical neuroscience instead of theoretical physics. Of course, I was hoping that looking at the curricula of theoretical neuroscience would shed some light but that has turned fruitless. In addition, theoretical neuroscience is not mentioned in bureau of labor statistics [or anywhere online to my knowledge]; which would have helped me to learn more of their work environment and average weekly work time among other things.

Can anyone start shedding some light? I've always been keenly interested in neuroscience but need a good push in the right direction. My attempt of learning more of this discipline has been rather pitiful.

 

[Nano-Passion]

Bump.. someone please help. This field has been very vague to me. Its probably a very new sub-sub discipline..

 

[apeiron]

Bump.. someone please help. This field has been very vague to me. Its probably a very new sub-sub discipline..

Are you more interested in neurons or brains. A first big decision perhaps.

Physics is not especially useful as an entry qualification - biology or medicine would be more traditional paths. But a facility with mathematical modelling would of course be good. You just need to work out what kind of modelling approaches will buy you a future career.

So you could come from a computer science modelling angle, or a dynamical one, for example. Or try to combine the best of both, as is currently the state of the art.

If you are worried about working hours, neuroscience tends to follow the medical model - ridiculously long. And most true neuroscience involves being good in the lab more than being good with spinning theories.

If you don't actually like lab work/real biology, then getting into computer science, neural networks and artificial intelligence may be more like what you imagine as "theoretical neuroscience" as a career.

 

[atyy]

Who have you read that you consider a mathematical neuroscientist? What journals do they publish in? Why don't you see what programmes are available at the institutions of the authors in those journals?

As an example, I read an interesting article by Kouh and Poggio in http://www.mitpressjournals.org/loi/neco. I googled Kouh and found that he did that as a physics graduate student at MIT. So you could contact MIT physics and ask whether it is possible to do mathematical neuroscience as a sub-discipline of physics there. It looks like they have at least one http://web.mit.edu/physics/people/faculty/seung_sebastian.html who does a lot of neurobiology. Interestingly, Kouh's co-author, Poggio is not listed in MIT physics, so it seems the department can be quite flexible.

 

[Nano-Passion]

Are you more interested in neurons or brains. A first big decision perhaps.

How do I know if I'm more interested in neurons than brains? To me the brain is a collection of neurons and are the same thing. I'm not terribly interested in learning things along the approach of behavioral psychology and social psychology; I'm slightly more interested in knowing things from a fundamental perspective.

Physics is not especially useful as an entry qualification - biology or medicine would be more traditional paths. But a facility with mathematical modelling would of course be good. You just need to work out what kind of modelling approaches will buy you a future career.

It is very hard to think about making this transition, I've completely indulged myself with the thought of physics and mathematics that its almost a part of my identity. Perhaps I should take physics to around quantum field theory to see how physics feels to me while simultaneously taking biology classes?

So you could come from a computer science modelling angle, or a dynamical one, for example. Or try to combine the best of both, as is currently the state of the art.

Mathematical/dynamical angles attract me more.

If you are worried about working hours, neuroscience tends to follow the medical model - ridiculously long. And most true neuroscience involves being good in the lab more than being good with spinning theories.

What does it mean to be good in the lab as opposed to being with theorizing? And around how many hours are we talking about? At some point I accepted that as a physicist there will probably be around 60 hour work weeks [that is probably a minimum]. I mean, long work hours don't scare me as long as I love what I do and there is intellectual stimulation; but on the other hand I love many things in life and I'm kind of a romantic. Aside from it being something that has always appealed to me, part of the reason I started thinking about neuroscience is because I was under the disbelief that they work less hours than physicist. I was attracted to something that would give me more time for other life aspects.

I think part of the reason that I wanted to enter Neuroscience is because I've always had an appreciation for our immensely complex machinery; and I find beauty in that. But it might be misplaced, and I'm trying really hard to figure if I would like this type of thing or not.. Personally, I love the big questions; things such as consciousness intrigue me. But that train of thought sounds highly fanboy-ish and uncorrelated to what everyday neuroscientists work on..

If you don't actually like lab work/real biology, then getting into computer science, neural networks and artificial intelligence may be more like what you imagine as "theoretical neuroscience" as a career.

I like the idea of neural networks and artificial intelligence. But then again I don't know too much about myself in this area, the only computer science classes that I took was Fortran in college and a bit of [rather basic] True BASIC in high school.

 

[Nano-Passion]

This is for apeiron and atyy, perhaps this would help pinpoint where my interest lies.

Things that I would find interesting to research on are some of the relatively intangible questions of today. Things such as what is curiosity? How do we learn? What is consciousness? How do we make sense of the world around us [such as object recognition]?

From that synopsis of my interest, would you conclude that my interest is rather misplaced and fan-boy like?

Who have you read that you consider a mathematical neuroscientist? What journals do they publish in? Why don't you see what programmes are available at the institutions of the authors in those journals?

I didn't think about learning more about it from there. Thanks.

As an example, I read an interesting article by Kouh and Poggio in http://www.mitpressjournals.org/loi/neco. I googled Kouh and found that he did that as a physics graduate student at MIT.

One problem is that I don't really understand what they are talking about. The most that I would get out of such an article would be the mathematical modeling of neural activity.

So you could contact MIT physics and ask whether it is possible to do mathematical neuroscience as a sub-discipline of physics there. It looks like they have at least one http://web.mit.edu/physics/people/faculty/seung_sebastian.html who does a lot of neurobiology. Interestingly, Kouh's co-author, Poggio is not listed in MIT physics, so it seems the department can be quite flexible.

Thanks for the links! What poggio works on is very interesting to me actually. I don't think I should contact MIT physics at the moment because my education at this point is quite premature and abysmal. I've failed to mention that at the moment the caliber of my education stands at Calculus I, Physics I, and Intro to Psychology.

 

[atyy]

Things that I would find interesting to research on are some of the relatively intangible questions of today. Things such as what is curiosity? How do we learn? What is consciousness? How do we make sense of the world around us [such as object recognition]?

From that synopsis of my interest, would you conclude that my interest is rather misplaced and fan-boy like?

Yeah, definitely misplaced. Those are not intangibles, they have been solved http://www.youtube.com/watch?v=6FNE4MnQ3QU&feature=youtu.be

(I haven't heard that lecture, but Grossberg is famous.)

Here's more stuff that may be helpful as google search seeds (I think these are all free).
http://www.ncbi.nlm.nih.gov/pubmed/20573887
http://www.ncbi.nlm.nih.gov/pubmed/20456940
http://othermind.net/papers/computation/internalmodel.pdf

 

[apeiron]

(I haven't heard that lecture, but Grossberg is famous.)

It's amazing what's online these days!

If you like Grossberg, here is a great interview about his career (and the perils of being too far ahead of your time).

Nano might like to read it too for its description of what the actual life of a most brilliant scientist is like (and why the best end up bitter and twisted ).

http://pcl.tuke.sk/kopco/w/chpt8.pdf

 

[Nano-Passion]

Yeah, definitely misplaced. Those are not intangibles, they have been solved http://www.youtube.com/watch?v=6FNE4MnQ3QU&feature=youtu.be

(I haven't heard that lecture, but Grossberg is famous.)

Here's more stuff that may be helpful as google search seeds (I think these are all free).
http://www.ncbi.nlm.nih.gov/pubmed/20573887
http://www.ncbi.nlm.nih.gov/pubmed/20456940
http://othermind.net/papers/computation/internalmodel.pdf

Thank you so much for sharing these links and Grossberg's interview; I haven't got the chance to read them but the last article "Robots With Internal Models a Route to Machine Consciousness?" by Owen Holland and Rod Goodman seems very interesting. I've always been interested in the idea of engineering a brain because it seems to really challenge our knowledge of the brain [and it has been].

Also it is hard for me to accept that the problem of consciousness has been completely solved at a fundamental level. Are you sure? Perhaps it is "solved" but at a fundamental level.. hmm I would wonder.

This is random, but as I was just relaxing by the water today [one of my favorite activity], a high interest resurfaced in me; and that is the the study of our sensory input and how we perceive the world around us.. things such as our retinal organ and how it constitutes reality around us.

It's amazing what's online these days!

If you like Grossberg, here is a great interview about his career (and the perils of being too far ahead of your time).

Nano might like to read it too for its description of what the actual life of a most brilliant scientist is like (and why the best end up bitter and twisted ).

http://pcl.tuke.sk/kopco/w/chpt8.pdf

Thanks for sharing the link of his interview.. it was amazing! Not only was it very interesting but it also really influenced me as a consequence! I've always been too afraid to step out of the study of physics and mathematics even though I knew I also loved neuroscience and biology.. but Grossberg showed me not to be afraid and to study what you want; its part of the fun!

"Stephen Grossberg [1] is a cognitive scientist, neuroscientist, biomedical engineer, mathematician, and neuromorphic technologist." ~ Wikipedia

I wonder how he got so many degrees.. but I suppose it was different back then and everything now seems to be highly specialized. I presume that is why I've always been afraid to step out of the boundary of math and physics.

 

[Nano-Passion]

Yeah, definitely misplaced. Those are not intangibles, they have been solved http://www.youtube.com/watch?v=6FNE4MnQ3QU&feature=youtu.be

Okay well what are the big unsolved questions of today in neuro-biology, neuroscience, etc.?

 

[atyy]

Okay well what are the big unsolved questions of today in neuro-biology, neuroscience, etc.?

Hmmm, did you see my indicating not to take me too seriously?

Anyway, the "big questions" question is too broad for me to answer. I'd be happy to suggest more google search seeds, but I think it's best to make your own big question.

 

[Nano-Passion]

Hmmm, did you see my indicating not to take me too seriously?

Anyway, the "big questions" question is too broad for me to answer. I'd be happy to suggest more google search seeds, but I think it's best to make your own big question.

Hahah.. whoops. I perceived it to be more of a taunt as in "hahh we solved them already! Your too late to work on these interesting questions. "

I found some very interesting questions:
http://en.wikiversity.org/wiki/Unsolved_problems_in_neuroscience

I like the ones that has to do with learning, memory, perceptions, and decisions. Does it sound like mathematical neuroscience would suit me?

 

[Pythagorean]

I like the ones that has to do with learning, memory, perceptions, and decisions. Does it sound like mathematical neuroscience would suit me?

Those topics are being approached from many angles, some utilizing mathematics, some not. I don't think anybody can judge whether it is a fit for you; you really have to keep investigating these things and see how you react long-term; whether your interest wanes or not.

I've always been one to jump from interest to interest, so I've been very cautious; but so far my flame has kept burning towards a mathematical neuroscience career.

 

[Nano-Passion]

Those topics are being approached from many angles, some utilizing mathematics, some not. I don't think anybody can judge whether it is a fit for you; you really have to keep investigating these things and see how you react long-term; whether your interest wanes or not.

I've always been one to jump from interest to interest, so I've been very cautious; but so far my flame has kept burning towards a mathematical neuroscience career.

What can I investigate to know if this is a fit for me or not? I need someone to put me in the right direction. Perhaps taking more biology-related classes will help?

I'm interested, from what interest to what interest have you been jumping too? And why is it that your flame burns more toward a mathematical neuroscience career?

 

[Pythagorean]

You're already investigating, but is'a really young and diverse field so it will take some time to absorb and differentiate all the different views and language. Just keep at it.

I think some popular pedagogical approaches out there are:

Dynamical Systems in Neuroscience (Izhikevich)
Mathematical Foundations of Neuroscience (Ermentrout and Terman)
Theoretical Neuroscience (Dayan and Abbot)
Handbook of Brain Theory and Neural Networks (Arbib)
From Molecules to Networks (John & John)

I myself have not read much of these thoroughly, and some I've only heard of. I took a class with Molecules to Networks and I did spend the most time on Izhikevich's geometrical approach. But mostly, I have a geometer adviser that is interested in biological systems applications. So I have spent time actually employing the models

Mathematical Neuroscience in general is broader than my expertise (I have heard Izhikevich's book called idiosynchratic more than once).As for classes, assuming you don't have a theoretical/computaitonal program, then you are in a similar position as me:

I have an undergrad in Physics

Graduate Classes I've taken:
Neurobiology
Molecular Neuroscience
Neurochemistry

(not near as quantitative as any of my math/physics classes ever were though):

Nonlinear Dynamics and Chaos by Strogatz
Differential Equations, Calculus.

I am only able to integrate my biology and physics because of the broader internet community, and the books I mentioned above which gives me access to what other universities are doing.

 

[Nano-Passion]

You're already investigating, but is'a really young and diverse field so it will take some time to absorb and differentiate all the different views and language. Just keep at it.

I think some popular pedagogical approaches out there are:

Dynamical Systems in Neuroscience (Izhikevich)
Mathematical Foundations of Neuroscience (Ermentrout and Terman)
Theoretical Neuroscience (Dayan and Abbot)
Handbook of Brain Theory and Neural Networks (Arbib)
From Molecules to Networks (John & John)

I myself have not read much of these thoroughly, and some I've only heard of. I took a class with Molecules to Networks and I did spend the most time on Izhikevich's geometrical approach. But mostly, I have a geometer adviser that is interested in biological systems applications. So I have spent time actually employing the models

Mathematical Neuroscience in general is broader than my expertise (I have heard Izhikevich's book called idiosynchratic more than once).


As for classes, assuming you don't have a theoretical/computaitonal program, then you are in a similar position as me:

I have an undergrad in Physics

Graduate Classes I've taken:
Neurobiology
Molecular Neuroscience
Neurochemistry

(not near as quantitative as any of my math/physics classes ever were though):

Nonlinear Dynamics and Chaos by Strogatz
Differential Equations, Calculus.

I am only able to integrate my biology and physics because of the broader internet community, and the books I mentioned above which gives me access to what other universities are doing.

I've seen some of those books recommended before, unfortunately they are well above my level of study. I guess my best option is to take classes and see how I feel about them. Looking up articles and the such doesn't seem to be helping too much at the moment, it isn't a good indicator of whether you will like the field or not in my opinion. Because if that was the case, then I would like every field due to my diverse interests.

 

[Pythagorean]

Then I think just a basic cell biology and neurobiology class, a classical mechanics class, and the supporting math:

differential equations, calculus, probability and statistics.

These are the building blocks that will help you understand those books.

 

[Nano-Passion]

Then I think just a basic cell biology and neurobiology class, a classical mechanics class, and the supporting math:

differential equations, calculus, probability and statistics.

These are the building blocks that will help you understand those books.

At the moment I've taken

Physics I
Calculus I
Intro to Psychology

Next semester will be [in terms of math & physics]
Physics II
Calculus II

At the moment I'm not planning to take biology and chemistry classes because I'm at a community college and the non-major credits won't transfer once I go into Rutgers Brunswick [pretty sure I want to go there at the moment and confident I'll be accepted]. What would your advice be on this? Take the classes anyways or just wait till I transfer to a university?

And what are the prerequisites of neurobiology?

 

[Pythagorean]

I think you'll be able to handle basic neurobiology just fine. You may have to play a little catch up, but I don't expect it to be too serious. All the neuroscience courses I've taken had prerequisites, but my physics degree was enough to convince the neuribio teacher to let me in and the neurobio class along with the physics degree got me into the rest of the classes.

So far, you seem to be on the same track as I was. I did not take any fundamental biology and only basic chemistry classes. I do, however, study a lot of biology on my own. I'm fascinated by it at many levels (abiogenesis, evo/devo, unicellular to multicellular transition, neurogenetics).

 

[madness]

Most computational/mathematical neuroscience PhDs specifically ask for people with backgrounds in physics, mathematics and computer science. Having said this, I don't think that the level of maths required to do computational neuroscience is especially high. You will find linear algebra, differential equations and probability very useful. Techniques from dynamical systems and statistical physics are sometimes used but you don't necessarily need a background in those subjects.

 

[Nano-Passion]

I think you'll be able to handle basic neurobiology just fine. You may have to play a little catch up, but I don't expect it to be too serious. All the neuroscience courses I've taken had prerequisites, but my physics degree was enough to convince the neuribio teacher to let me in and the neurobio class along with the physics degree got me into the rest of the classes.

So far, you seem to be on the same track as I was. I did not take any fundamental biology and only basic chemistry classes. I do, however, study a lot of biology on my own. I'm fascinated by it at many levels (abiogenesis, evo/devo, unicellular to multicellular transition, neurogenetics).

Hmm, so it seems that biology isn't as cumulative as mathematics or physics?

And actually all the things you listed were very fascinating and it actually suits my interest really closely; and I've thought about those things for a while. They are things I would want to study, that is, with the exception of evolution/devolution with respect to complex organisms [deer, etc.] of this time because it seems very very chaotic.

Most computational/mathematical neuroscience PhDs specifically ask for people with backgrounds in physics, mathematics and computer science. Having said this, I don't think that the level of maths required to do computational neuroscience is especially high. You will find linear algebra, differential equations and probability very useful. Techniques from dynamical systems and statistical physics are sometimes used but you don't necessarily need a background in those subjects.

How much background in computer science is generally recommended for computational neuroscience? I took Fortran and for one reason or another I wasn't completely thrilled about the class, even though I've always been interested in the idea of AI and the idea of DNA being a code of life.. bleh but I guess that wouldn't transition to a computer science class.

 

[madness]

I have absolutely no background in computer science and I haven't had any problems. If you want to start simulating neural systems then you will need to know how to use some package like Matlab or a programming language. The elements of computer science that cross over with computational neuroscience are fields like cognitive science, artificial intelligence and machine learning. I have very little knowledge of these fields at the moment but perhaps I'll need to pick some of them up depending on the direction my research takes.

Computational neuroscience is very inter-disciplinary. If you have a background in at least one or two of the subjects involved then you can most likely find some area of computational neuroscience that would suit you.

 

[Nano-Passion]

I have absolutely no background in computer science and I haven't had any problems. If you want to start simulating neural systems then you will need to know how to use some package like Matlab or a programming language. The elements of computer science that cross over with computational neuroscience are fields like cognitive science, artificial intelligence and machine learning. I have very little knowledge of these fields at the moment but perhaps I'll need to pick some of them up depending on the direction my research takes.

Computational neuroscience is very inter-disciplinary. If you have a background in at least one or two of the subjects involved then you can most likely find some area of computational neuroscience that would suit you.

Huh? I'm baffled. What is your major and how far are you in your studies? It confounds me to think that you don't need much background in computer science for computational neuroscience.. my common sense hints me of the complete polar opposite!

 

[madness]

Yeah I can see why you would be baffled really. My background is an undergraduate in maths and physics and my current level is studying for a PhD in computational neuroscience. Perhaps I'm biased but I would say that computer science is not important for computational neuroscience. All of the computational skills I use now were taught to me in my undergraduate degree in physics (e.g. Matlab).

Having said this, my programme is pretty flexible and I intend to pursue interests in the biophysical/mathematical modelling of cells and networks. There are people in my programme with computer science backgrounds and they will most likely be working on the interface between artificial intelligence, machine learning and neuroscience. This ties into what I said in my last post - computational neuroscience is very inter-disciplinary and for each background you can find a different niche.

 

[Pythagorean]

yeah, whoops, I didn't explicitly mention computer science skills, either. I also learned to program through scientific programming with MatLab, but also went through a phase of being really interested and learning Python on my own and taking a java class.

Good programming practices will just make your life much much easier, and allow you to focus more on your scientific questions than technical questions.

You can actually have quite large, complex data sets (especially if you go the differential equations / nonlinearity, chaos, complexity route). If you don't know how to efficiently use your computers memory/processpr, calculations could take weeks, rather than days (or even hours).

 

[Nano-Passion]

Yeah I can see why you would be baffled really. My background is an undergraduate in maths and physics and my current level is studying for a PhD in computational neuroscience. Perhaps I'm biased but I would say that computer science is not important for computational neuroscience. All of the computational skills I use now were taught to me in my undergraduate degree in physics (e.g. Matlab).

Having said this, my programme is pretty flexible and I intend to pursue interests in the biophysical/mathematical modelling of cells and networks. There are people in my programme with computer science backgrounds and they will most likely be working on the interface between artificial intelligence, machine learning and neuroscience. This ties into what I said in my last post - computational neuroscience is very inter-disciplinary and for each background you can find a different niche.

Wow, so not much programming knowledge is needed for your study computational neuroscience? What knowledge then is needed? It is hard to imagine what one would do all day in that field?

yeah, whoops, I didn't explicitly mention computer science skills, either. I also learned to program through scientific programming with MatLab, but also went through a phase of being really interested and learning Python on my own and taking a java class.

Good programming practices will just make your life much much easier, and allow you to focus more on your scientific questions than technical questions.

You can actually have quite large, complex data sets (especially if you go the differential equations / nonlinearity, chaos, complexity route). If you don't know how to efficiently use your computers memory/processpr, calculations could take weeks, rather than days (or even hours).

So your biggest challenge is basically to apply your physics/mathematical knowledge to model a phenomena in programming language? Kind of like translating and then seeing if your translation holds true for the real world.

 

[Pythagorean]

the programming aspect is essentially two fold.

The first is producing your data with the scientific model (this involves deriving the model, writing the pseudocode/algorithm on paper, then finally coding it. It's generally procedural/functional coding, not object-oriented).

The second is turning your data (a bunch of numbers) into something visually intuitive. There's a lot of creative control involved in this part.

MATLAB and (and the numpy/scipy python packages) are designed for this kind of method, so they have many supporting functions that make it easy. Doing this kind of programming in Java or C is not as straightforward (passing arguments is more complicated).

 

[AlephZero]

So your biggest challenge is basically to apply your physics/mathematical knowledge to model a phenomena in programming language? Kind of like translating and then seeing if your translation holds true for the real world.

That's a pretty good description of any "real world" programming activity. Knowing some computer science can help, but often it doesn't help much.

Look at this this way: if you want to chop down a tree and build yourself a log cabin, is it more useful to have studied continuum mechanics of composite materials, or know how to use an axe and a saw?

 

[Nano-Passion]

That's a pretty good description of any "real world" programming activity. Knowing some computer science can help, but often it doesn't help much.

Look at this this way: if you want to chop down a tree and build yourself a log cabin, is it more useful to have studied continuum mechanics of composite materials, or know how to use an axe and a saw?

Ahah.. good analogy.

For AlephZero & Pythagorean:

It doesn't seem that I'm terribly interested in computational neuroscience. It sounds as if your prime task is to attempt to write a code that will sufficiently model the brain. But then again there seems to be no distinct line, like madness has stated, it is a very interdisciplinary field. So I'm pretty confused at the moment haha. What I do know is that I'm interested in the interface between machine learning, AI, and neuroscience and in the mathematical description/unification of the brain.

I also wouldn't mind studying other biophysical things bordering the transition of nonliving to living phenomena.

Taking a step back and looking at my interest.. it seems that throughout my life I've been curious of what is relatively fundamental. Else than physics, I'm keen on learning how such immensely complex life processes comes from inanimate objects.

 

[Pythagorean]

The computer's just a tool like a calculator. You should write the models on paper, derive them mathematically, then (naturally) you're not going to want to solve the mathematics for 10000 neurons by hand so you use a numerical ODE solver or you write a snippet to compute the probabilities. Then you have to represent the data somehow (you don't just publish a bunch of numbers in a paper, you publish graphical representation) so you might as well have your code do that for you too (you're more then welcome to open up excel and do it all manuallly with your data, but it's the long route).

So while computer science is not at all the emphasis, any modern scientists (whether data mining, classifying behavior, integrating statistics, or simulating time-evolved equations) has everything to gain from knowing how to do some basic programming.

There's possibly more general, theoretical mathematics you can do, but I'd think most of them still rely on mining numerical data sets in the end... you're pretty much always going to be slower than the guy who has the same scientific knoweldge as you, but more programming skills.

Else than physics, I'm keen on learning how such immensely complex life processes comes from inanimate objects.

ribozyme :)