SIAM Life Sciences Meeting

I’m currently in San Diego for the SIAM Life Sciences conference.  I gave a talk reviewing my work on binocular rivalry.  My slides are here.

Artiefest

Our lab is hosting a symposium at NIH in honor of our chief Arthur Sherman. The meeting will be June 7 and 8 and is open to everyone. The talks will cover a wide range of topics. Information is here.

Criticality

I attended a conference on Criticality in Neural Systems at NIH this week.  I thought I would write a pedagogical post on the history of critical phenomena and phase transitions since it is a long and somewhat convoluted line of thought to link criticality as it was originally defined in physics to neuroscience.  Some of this is a recapitulation of a previous post.

Criticality is about phase transitions, which is a change in the state of matter, such as between gas and liquid. The classic paradigm of phase transitions and critical phenomena is the Ising model of magnetization. In this model, a bunch of spins that can be either up or down (north or south) sit on lattice points. The lattice is said to be magnetized if all the spins are aligned and unmagnetized or disordered if they are randomly oriented. This is a simplification of a magnet where each atom has a magnetic moment which is aligned with a spin degree of freedom of the atom. Bulk magnetism arises when the spins are all aligned.  The lowest energy state of the Ising model is for all the spins to be aligned and hence magnetized. If the only thing that spins had to deal with was the interaction energy then we would be done.  What makes the Ising model interesting and for that matter all of statistical mechanics is that the spins are also coupled to a heat bath. This means that the spins are subjected to random noise and the size of this noise is given by the temperature. The noise wants to randomize the spins. The presence of randomness is why there is the word “statistical” in statistical mechanics. What this means is that we can never say for certain what the configuration of a system is but only assign probabilities and compute moments of the probability distribution. Statistical mechanics really should have been called probabilistic mechanics.

Aspen summer program

The Aspen Center is a famous place where physicists congregate during the summer.  This summer they will be hosting a program on the physics of behavior (see the invitation letter from the organizers below).  This will combine neuroscience and animal behavior and should be very interesting.  I plan to be attending.  I encourage everyone to apply.

The Aspen Center for Physics will be hosting a 3-week long workshop on Physics of Behavior between May 27 and June 16, 2012, with an application deadline of January 31, 2012. The idea of the workshop stems from the understanding that the role of physics in biology is broad, as physical constraints define the strategies and the biological machinery that living systems use to shape their behavior in the dynamic, noisy, and resource-limited physical world. To date, such holistic, physics-driven picture of behavior has been achieved, arguably, only for bacterial chemotaxis. Can a similar understanding emerge for other, more complex living systems?To begin answering this, we would like to use the Aspen Center workshop to bring together a diverse group of scientists, from field biologists to theoretical physicists, broadly interested in animal behavior. We would like to broaden the horizons of physicists by inviting experts who quantify behavior of a wide range of model organisms, from molecular circuits to mammals. We would like to explore behavior as possibly optimal responses given the physical and the statistical structure of environment. Our topics will include, in particular, navigation and foraging, active sensing, locomotion and rhythmic behavior, and learning, memory, and adaptive behaviors.

As workshop organizers, we encourage you to apply.  We would also like you to encourage other people who are active in this field to apply.  We do need to be clear, however, that we cannot guarantee admission to the workshop.  Admission to the workshop is granted not by the workshop organizers, but by the Admissions Committee of the Center (with some input from the workshop organizers).  The Admissions Committee will endeavor to accommodate as many applicants to the Workshop as possible, but because of the constraints imposed by the rest of the AspenCenter for Physics program, they may not be able to admit everyone who applies.

We encourage you to visit the web site of the workshop here , and of the Center, http://www.aspenphys.org/, for more information and for application instructions. For those of you unfamiliar with the Center, it is located in lively and beautiful Aspen, CO. It’s a great place to work, to enjoy the mountains, and to bring  family. The Center partially subsidizes lodging for admitted participants. The Center requires that theorists commit for a minimum stay of two weeks, and a three week stay is preferred. Shorter durations are possible for experimentalists.

We hope you will choose to apply. Please don’t hesitate to contact us if you have questions.

Sincerely,

The Organizers
Ila Fiete, UT Austin
Ilya Nemenman, Emory U
Leslie Osborne, U Chicago
William Ryu, U Toronto
Greg Stephens, Princeton U

Talk in Marseille

I just returned from an excellent meeting in Marseille. I was quite impressed by the quality of talks, both in content and exposition. My talk may have been the least effective in that it provoked no questions. Although I don’t think it was a bad talk per se, I did fail to connect with the audience. I kind of made the classic mistake of not knowing my audience. My talk was about how to extend a previous formalism that much of the audience was unfamiliar with. Hence, they had no idea why it was interesting or useful. The workshop was on mean field methods in neuroscience and my talk was on how to make finite size corrections to classical mean field results. The problem is that many of the participants of the workshop don’t use or know these methods. The field has basically moved on.

In the classical view, the mean field limit is one where the discreteness of the system has been averaged away and thus there are no fluctuations or correlations. I have been struggling over the past decade trying to figure out how to estimate finite system size corrections to mean field. This led to my work on the Kuramoto model with Eric Hildebrand and particularly Michael Buice. Michael and I have now extended the method to synaptically coupled neuron models. However, to this audience, mean field pertains more to what is known as the “balanced state”. This is the idea put forth by Carl van Vreeswijk and Haim Sompolinsky to explain why the brain seems so noisy. In classical mean field theory, the interactions are scaled by the number of neurons N so in the limit of N going to infinity the effect of any single neuron on the population is zero. Thus, there are no fluctuations or correlations. However in the balanced state the interactions are scaled by the square root of the number of neurons so in the mean field limit the fluctuations do not disappear. The brilliant stroke of insight by Carl and Haim was that a self consistent solution to such a situation is where the excitatory and inhibitory neurons balance exactly so the net mean activity in the network is zero but the fluctuations are not. In some sense, this is the inverse of the classical notion. Maybe it should have been called “variance field theory”. The nice thing about the balanced state is that it is a stable fixed point and no further tuning of parameters is required. Of course the scaling choice is still a form of tuning but it is not detailed tuning.

Hence, to the younger generation of theorists in the audience, mean field theory already has fluctuations. Finite size corrections don’t seem that important. It may actually indicate the success of the field because in the past most computational neuroscientists were trained in either physics or mathematics and mean field theory would have the meaning it has in statistical mechanics. The current generation has been completely trained in computational neuroscience with it’s own canon of common knowledge. I should say that my talk wasn’t a complete failure. It did seem to stir up interest in learning the field theory methods we have developed as people did recognize it provides a very useful tool to solve the problems they are interested in.

Addendum 2011-11-11

Here are some links to previous posts that pertain to the comments above.

http://sciencehouse.wordpress.com/2009/06/03/talk-at-njit/

http://sciencehouse.wordpress.com/2009/03/22/path-integral-methods-for-stochastic-equations/

http://sciencehouse.wordpress.com/2009/01/17/kinetic-theory-of-coupled-oscillators/

http://sciencehouse.wordpress.com/2010/09/30/path-integral-methods-for-sdes/

http://sciencehouse.wordpress.com/2010/02/03/paper-now-in-print/

http://sciencehouse.wordpress.com/2009/02/27/systematic-fluctuation-expansion-for-neural-networks/

Snowbird summary

The Snowbird meeting finishes today.  I think it has been highly successful with over 800 participants.  Last night, I was on the “forward looking panel” moderated by Alan Champneys and one of the questions asked was what defines nonlinear dynamics and this meeting.  I gave a rather flip answer about how we are now in the age of machine learning and statistics and this meeting is everything in applied math that is not that.  Of course that is not true given that data assimilation was a major part of this meeting and Sara Solla gave a brilliant talk on applying the generalized linear model to neural data to estimate functional connectivity in the underlying cortical circuit.

Given some time to reflect on that question, I think the common theme of Snowbird is the concept of taking a complicated system and reducing it to something simpler that can be analyzed.   What we do is to create nontrivial models that can be accessed mathematically. This is distinctly different from other branches of applied math like optimization and numerical methods.  However, one difference between previous meetings and now is that before the main tools to analyze these reduced systems were methods of dynamical systems such as geometric singular perturbation theory (e.g. see here) and bifurcation theory.  Today, a much wider range of methods are being utilized.

Another question posed was whether there was too much biology  at this meeting.   I said yes because I thought there were too many parallel sessions.  Although, I said it partially with tongue in cheek, I think there are both good and bad things about biology being overly represented.   It is good that biology is doing well and attracting lots of people but it would be a bad thing if the meeting becomes so large that it devolves into multiple concurrent meetings where people only go to the talks that are directly related to what they already know. In a meeting with fewer parallel sessions one has more chance to learn something new and see something unexpected.  I really have no idea what should be done about this if anything at all.

Finally, a question about how data will be relevant to our field was posed from the audience. My answer was that the big trend right now was in massive data mining but I thought that it had overpromised and would eventually fail to deliver.  Eventually, dynamical systems methods will be required to help reduce and analyze the data.  However, I do want to add that data will play a bigger and bigger role in dynamical systems research.  In the past, we mostly strived to just qualitatively match experiments but now the data has improved to the point that we can try to quantitatively match it.   This will require using statistics.  Readers of this blog will know that I have been an advocate of using Bayesian methods.  I really believe that the marriage of dynamical systems and statistics will have great impact. Statistics is about fitting models to data but the models used are rather simple and generally not  motivated by mechanisms.  Our field is about producing models based on the underlying mechanisms.  It will be a perfect fit.

Snowbird meeting

I’m currently at the biannual SIAM Dynamical Systems Meeting in Snowbird Utah.  If a massive avalanche were to roll down the mountain and bury the hotel at the bottom, much of applied dynamical systems research in the world would cease to exist.  The meeting has been growing steadily for the past thirty years and has now maxed out the capacity of Snowbird.   The meeting will either eventually have to move to a new venue or restrict the number of speakers. My inclination is to move but I don’t think that is the most popular sentiment.  Thus far, I have found the invited talks to be very interesting.  Climate change seems to be the big theme this year.  Chris Jones and Raymond Pierrehumbert  both gave talks on that topic.  I chaired the session by noted endocrinologist and neuroscientist Stafford Lightman who gave a very well received talk on the dynamics of hormone secretion. Chiara Daraio gave a very impressive talk on manipulating sound propagation with chains of ball bearings.  She’s basically creating the equivalent of nonlinear optics and electronics in acoustics.  My talk this afternoon is on finite size effects in spiking neural networks.  It is similar but not identical to the one I gave in New Orleans in January (see here).  The slides are here.

The Philosopher’s Zone

Last Thursday I had to drive from Baltimore to State College, PA for the 16th Congress of the US National Congress on Theoretical and Applied Mechanics to give a talk in one of the sessions.  I gave a condensed version of the kinetic theory of coupled oscillators talk I gave in Warwick last month.  The theme of the session was on recent advances in nonlinear dynamics so the topics were quite diverse.  I’m not sure my talk resonated with the audience.  The only question I received was how was this related to the NIH!

During the six hours of driving I did going back and forth, I listened to podcasts of the Australian radio show The Philosopher’s Zone.  This is a wonderful program hosted by Alan Saunders, who has a PhD in philosophy and is also a food expert.  Every show consists of Saunders talking to a guest, who is usually a philosopher but not always, about either a book she has recently written or some other philosophical topic.  The topics can range from the philosophy of Buffy the Vampire Slayer to Stoicism and everything in between.  Saunders has a knack for making complex philosophical ideas accessible and interesting.  In addition to The Philosopher’s Zone, I still regularly listen to Quirks and Quarks, The Science Show, Radio Lab, and The Naked Scientists.  I’ll also sneak in All in the Mind from time to time.