Talk at Jackfest

I’m currently in Banff, Alberta for a Festschrift for Jack Cowan (webpage here). Jack is one of the founders of theoretical neuroscience and has infused many important ideas into the field. The Wilson-Cowan equations that he and Hugh Wilson developed in the early seventies form a foundation for both modeling neural systems and machine learning. My talk will summarize my work on deriving “generalized Wilson-Cowan equations” that include both neural activity and correlations. The slides can be found here. References and a summary of the work can be found here. All videos of the talks can be found here.


Addendum: 17:44. Some typos in the talk were fixed.

Addendum: 18:25. I just realized I said something silly in my talk.  The Legendre transform is an involution because the transform of the transform is the inverse. I said something completely inane instead.

Talk at GRC

I’m currently in Mt. Snow, Vermont to give a talk at the Gordon Research Conference on Computer Aided Drug Design. Yes, I know nothing about drug design. I am here because the organizer, Anthony Nicholls, asked me to give a pedagogical talk on Bayesian Inference. My slides are here. I only arrived yesterday but the few talks I’ve seen have been quite interesting. One interesting aspect of this conference is that many of the participants are from industry. The evening sessions are meant to be of more general interest. Last night were two talks about how to make science more reproducible. As I’ve posted before, many published results are simply wrong. The very enterprising Elizabeth Iorns has started something called the Reproducibility Initiative. I am not completely clear about how it works but it is part of another entity she started called Science Exchange, which helps to facilitate collaborations with a fee-for-service model. The Reproducibility Initiative piggy backs on Science Exchange by providing a service (for a fee) to validate any particular result. Papers that pass approval get a stamp of approval. It is expected that pharma would be interested in using this service so they can inexpensively check if possible drug targets actually hold up. Many drugs fail at phase three of clinical trials because they’ve been shown to be ineffective and this may be due to the target being wrong to start with.

On a final note, I flew to Albany and drove here. Unlike in the past when I would have printed out a map, I simply assumed that I could use Google Maps on my smart phone to get here. However, Google Maps doesn’t really know where Mt. Snow is. It tried to take me up a dirt road to the back of the ski resort. Also, just after I turned up the road, the phone signal disappeared so I was blind and had no paper backup. I was suspicious that this was the right way to go so I turned back to the main highway in hopes of finding a signal or a gas station to ask for directions. A few miles down Route 9, I finally did get a signal and also found a sign that led me the way. Google Maps still tried to take me the wrong way. I should have followed what I always tell my daughter – Always have a backup plan.


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.

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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,, 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.


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.