Last week I gave a talk on obesity at Georgia State University in Atlanta, GA. Tomorrow, I will be giving a talk on the kinetic theory of coupled oscillators at George Mason University in Fairfax, VA. Both of these talks are variations of ones I have given before so instead of uploading my slides, I’ll just point to links to previous talks, papers, and posts on the topics. For obesity, see here and for kinetic theory, see here, here and here.
Archive for the ‘Talks’ Category
I’m in beautiful Marseille again for a workshop on spike-timing dependent plasticity (STDP). My slides are here. The paper in which this talk is based can be obtained here. This paper greatly shaped how I think about neuroscience. I’ll give a summary of the paper and STDP for the uninitiated later.
Erratum: In my talk I said that I had reduced the models to disjunctive normal form. Actually, I had it backwards. I reduced it to conjunctive normal form. I’ll attribute this mixup to jet lag and lack of sleep.
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.
Here are some links to previous posts that pertain to the comments above.
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.
I gave a talk on obesity yesterday at Montclair State University. The talk was mostly the same as the plenary talk I gave at the SIAM Annual and Life Sciences meeting in 2010, which I summarized here. Science and math writer Barry Cipra also wrote a piece about the talk in SIAM News. I find it amusing that he called me a mathematical obesity expert. I presented the “push hypothesis” for the obesity epidemic in more detail here.
I’m on my way back from the 2011 Joint Mathematics Meeting. I gave a talk yesterday on finite size effects in neural networks. I gave a pedagogical talk on the strategy that Michael Buice and I have employed to analyze finite size networks in networks of coupled spiking neurons. My slides are here. We’ve adapted the formalism we used to analyze the finite size effects of the Kuramoto system (see here for summary) to a system of synaptically coupled phase oscillators.
I was in New York yesterday and gave a talk at NYU in a joint Center for Neural Science and Courant Institute seminar. My slides are here. The talk is an updated version of the talk I gave before and summarized here. The new parts include recent work on applying the model to Autism (see here) and some new work on resolving why mutual inhibition models of binocular rivalry do not reproduce Levelt’s fourth proposition, which states that as the contrast is decreased to both eyes, the dominance time of the percepts increases. I will summarize the results of that work in detail when we finish the paper.
My blog post on the summary of my SIAM talk on obesity was picked up by Reddit.com. There is also a story by mathematics writer Barry Cipra in SIAM news (not yet available online). I thought I would explicitly clarify the “push” hypothesis here and reiterate that this is my opinion and not NIH policy. What we had done previously was to derive a model of human metabolism that gives a prediction of how much you would weigh given how much you eat. The model is fully dynamic and can capture how much you gain or lose weight depending on changes in diet or physical activity. The parameters in the model have been calibrated with physiological measurements and validated in several independent studies of people undergoing weight change due to diet changes.
We then applied this model to the US population. We used data from the National Health and Nutrition Examination Survey, which has kept track of the body weights of a representative sample of the US population for the past several decades and food availability data from the USDA. Since the 1970’s, the average US body weight has increased linearly. The US food availability per person has also increased linearly. However, when we used the food availability data in the model, it predicted that the weight gain would grow linearly at a faster rate. The USDA has used surveys and other investigative techniques to try to account for how much food is wasted. If we calibrate the wastage to 1970 then we predict that the difference between the amount consumed and the amount available progressively increased from 1970 to 2005. We interpreted this gap to be a progressive increase of food waste. An alternative hypothesis would be that everyone burned more energy than the model predicted.
This also makes a prediction for the cause of the obesity epidemic although we didn’t make this the main point of the paper. In order to gain weight, you have to eat more calories than you burn. There are three possibilities for how this could happen: 1) We could decrease energy expenditure by reducing physical activity and thus increase weight even if we ate the same amount of food as before, 2) There could be a pull effect where we became hungrier and start to eat more food, and 3) There could be a push effect where we eat more food than we would have previously because of increased availability. Now the data rules out hypothesis 1) since we assumed that physical activity stayed constant and still showed an increasing gap between energy intake and energy expenditure. If anything, we may be exercising more than expected. Hypothesis 2) would predict that the gap between intake and expenditure should fall and waste should decrease as we utilize more of the available food. This then leaves us with hypothesis 3) where we are being supplied more food than we need to maintain our body weight and while we are eating some of this excess food, we are wasting more and more of it as well.
The final question, which is outside my realm of expertise, is why food supply increased. The simple answer is that food policy changed dramatically in the 1970’s. Earl Butz was appointed to be the US Secretary of Agriculture in 1971. At that time food prices were quite high so he decided to change farm policy and vastly increase the production of corn and soybeans. As a result, the supply of food increased dramatically and the price of food began to drop. The story of Butz and the consequences of his policy shift is documented in the film King Corn.
I visited the University of Pittsburgh today to give a colloquium. I was supposed to have come in February but my plane was cancelled because of a snow storm. This was not the really big snow storm that closed Washington, DC and Baltimore for a week but a smaller one that hit New England and not the DC area. My flight was on Southwest and I presume that they have such a tightly correlated flight system, where planes circulate around the country in a “just in time” fashion, that a disturbance in one part of the country affects the rest of the country. So while other airlines just had cancellations in New England, Southwest flights were cancelled for the day all across the US. It seems that there is a trade off between business efficiency and robustness. I drove this time. My talk was on the finite size effects in the Kuramoto model, which I’ve given several times already. However, I have revised the slides on pedagogical grounds and they can be found here.
Last Monday I gave a plenary talk at the joint Life Sciences and Annual SIAM meeting. My slides can be downloaded from a previous post. The talk summarized the work I’ve been doing on obesity and human body weight change for the past six years. The main idea is that at the most basic level, the body can be modeled as a fuel tank. You put food into the tank by eating and you use up energy to maintain bodily functions and do physical work. The difference between food intake rate and energy expenditure rate is the rate of change of your body weight. In calculating body weight you need to convert energy (e.g. Calories consumed) into mass (e.g. kilograms). However, the difficulty in doing this is that your body is not homogeneous. You are comprised of water, bones, minerals, fat, protein and carbohydrates in the form of glycogen. Each of these quantities has its own energy density (e.g. Calories/kg). So in order to figure out how much you’ll weigh you need to figure out how the body partitions energy into these different components.
Here are the slides for my SIAM talk on generalizing the Wilson-Cowan equations to include correlations. This talk was mostly on the paper with Michael Buice and Jack Cowan that I summarized here. However, I also contrasted our work with the recent work of Paul Bressloff who uses a system size expansion of the Markov process that Michael and Jack proposed as a microscopic model for Wilson-Cowan in their 2007 paper. The difference between the two approaches stems from the interpretation of what the Wilson-Cowan equation describes. In our interpretation, the Wilson-Cowan equation describes the firing rate or stochastic intensity of a Poisson process. A Poisson distribution is notable because all cumulants are equal to the mean. Our expansion is in terms of factorial cumulants (we called them normal ordered cumulants in the paper because we didn’t know there was a name for them), which are deviations from Poisson statistics. Bressloff, on the other hand, considers the Wilson -Cowan equation to be the average population firing rate of a large population of neurons. In the infinite size limit, there are no fluctuations. His expansion is in terms of regular cumulants and the inverse system size is the small parameter. In our formulation, the expansion parameter is related to the distance to a critical point where the expansion would break down. In essence, we use a Bogoliubov hierarchy of time scales expansion where the higher order factorial cumulants decay to steady state much faster than the lower order ones.
I am currently in Pittsburgh for the SIAM joint Life Sciences and Annual meetings. SIAM is the Society for Industrial and Applied Mathematics and has nothing to do with the country currently named Thailand. I just gave my invited joint plenary talk. My slides are here. The talk was on my recent work on human body weight change and obesity. I have posted on this topic recently here and here. I would write a summary of the talk but I’m feeling a bit under the weather right now and will leave it for another time.
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.
I visited the Gatsby Computational Neuroscience Unit in London on Friday. I talked about how the dynamics of many observed neural responses to visual stimuli can be explained by varying just two parameters in a “micro-cortical circuit” at the sub-millimetre level. The circuit consists of recurrent excitation, lateral inhibition and fatigue mechanisms like synaptic depression. Recurrently connected pools of neurons inhibit other pools and the competition between pools with fatigue leads to all the varied observed responses we see. I also covered my recent paper on autism where we describe how perturbing the synaptic balance in the micro-cortical circuit can then lead to alterations in performance of simple saccade tasks that seem to match clinical observations. My slides for the talk are here.
I’m currently in England at the Dendrites, Neurones, and Networks workshop. The talks have really impressed me. The field of computational neuroscience has really reached a critical mass where truly excellent work is being done in multiple directions. I gave a talk on finite system size effects in neural networks. I mostly covered the work on the Kuramoto model with a little bit on synaptically coupled phase neurons at the end. My slides are here.
I just gave a seminar in the math department at the University of Iowa today. I gave a talk that was similar to the one I gave at the Mathematical Biosciences Institute on Bayesian Inference for dynamical systems. My slides are here. I was lucky I made it to give this talk. My flight from Chicago O’Hare to Cedar Rapids, Iowa was cancelled yesterday and I was rebooked on another flight tonight, which wouldn’t have been of much use for my talk this afternoon. There was one fight left last evening to Cedar Rapids but bad weather cancelled several flights yesterday so there were many stranded travelers. I was number 38 on the standby list and thought I had no chance to make it out that night. However, on a whim I decided to wait it out and I started to move up the list because other people had evidently given up as well. To my great surprise and relief I was the last person to get on the plane. There was a brief scare when they asked me to get off because we exceeded the weight limitation but then they changed their mind and let us all fly. (Someone else had kindly volunteered to take my place). I learned two lessons. One is to keep close watch of your flight at all times so you can get on the standby list as soon as possible and two is that even number 38 on a plane that only seats 50 can still make it.
I’m currently at the University of Toronto to give two talks in a series that is jointly hosted by the Physics department and the Fields Institute. The Fields Institute is like the Canadian version of the Mathematical Sciences Research Institute in the US and is named in honour of Canadian mathematician J.C. Fields, who started the Fields Medal (considered to be the most prestigious prize for mathematics). The abstracts for my talks are here.
The talk today was a variation on my kinetic theory of coupled oscillators talk. The slides are here. I tried to be more pedagogical in this version and because it was to be only 45 minutes long, I also shortened it quite a bit. However, in many ways I felt that this talk was much less successful than the previous versions. In simplifying the story, I left out much of the history behind the topic and thus the results probably seemed somewhat disembodied. I didn’t really get across why a kinetic theory of coupled oscillators is interesting and useful. Here is the post giving more of the backstory on the topic, which has a link to an older version of the talk as well. Tomorrow, I’ll talk about my obesity work.