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Colloquium: FALL 2011

Time & location: All talks are on Thursday in Gibson 414 at 3:00pm unless otherwise noted. Refreshments in Gibson 426 after the talk.

Comments indicating vacations, special lectures, or change in location or time are made in green.

Organizer: Mahir Can


September 6

"Categorization is Cognition: On the Structure of Distributed Measurements"

David BalduzziMax Planck Institute for Biological Cybernetics                                                                Universitaet Tuebingen, Germany

Location:  Goldring-Woldenberg Hall, Room 3111

                  (the new Business school building on the third floor)

Abstract:

This talk presents an information-geometric approach to analyzing how neurons "see the world". Neurons are modeled as probabilistic input/output devices that categorize ("measure") inputs according to the outputs they assign to them. I consider two main questions. First: How sharply do neurons categorize their inputs? This is quantified via effective information. Second: How are categorizations by neuronal assemblies composed out of sub-categorizations? The indecomposability of categorizations is quantified via integrated information, which has an interesting geometric interpretation.

Finally, time permitting, I will sketch two very different applications of these ideas. First, it turns out that effective information relates to measures of capacity (arising in statistical learning theory) that bound the expected future performance of classifiers. Second, experimental results using transcranial magnetic stimulation suggest that integrated information is higher during wakefulness than during sleep or under anesthesia. Combining these results with a simple thought experiment, I will argue that integrated information is necessary for cognitive function.

 


September 8

Topic

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Abstract: TBA



September 15

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Abstract: TBA

September 22

Topic

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Abstract: TBA

September 29

A New Model for Self-Organized Dynamics

Eitan TadmorUniversity of Maryland

Abstract:

Self-organized dynamics is driven by "rules of engagement", which describe how each agent interacts with its "neighbors". They consist of long-term attraction, mid-range alignment and short-range repulsion. Many self-propelled models are driven by the balance between these three forces, which yield emerging structures of interest. Examples in social contexts include the consensus of voters, traffic flows, or evolution of languages, and examples of biological processes include the formation of flocks of birds or school of fish, tumor growth etc.

 

We will survey a few recent examples of such models driven by self-alignment. In particular, we introduce a new particle-based model which, we argue, addresses several drawbacks of existing models for self-organized dynamics. The model is independent of the number of agents: only their geometry in phase space is involved. We will explain the emerging behavior of flocking in the proposed model, when the pairwise long-range interactions between its agents decays sufficiently slow. The methodology presented here is based on the new notion of active sets, which carries over from particle to kinetic and hydrodynamic descriptions, and we discuss the unconditional flocking at the level of hydrodynamic description.

October 6

Topic

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Abstract: TBA

October 13

Fall Break

October 20

COLLOQUIUM

Jian-Guo LiuDuke University

Abstract:  Dynamics of Orientation Alignment and Phase Transition

Phase transition of directional field appears in some physical and biological systems such as ferromagnetism near Currie temperature, flocking dynamics near critical mass of self propelled particles. Dynamics of orientational alignment associated with the phase transition can be effectively described by a mean field kinetic equation. The natural free energy of the kinetic equation is non-convex with a minimum level set consisting of a sphere at super-critical case, a typic spontaneous symmetry breaking behavior in physics. In this talk, I will present some analytical results on this dynamics equation of orientational alignment and exponential convergence rate to the equilibria for both supper and sub critical cases, as well at algebraic convergence rate the critical case.

A new entropy and spontaneous symmetry breaking analysis played an important role in our analysis. This is a joint work with Pierre Degond and Amic Frouvelle.

October 27

Topic

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Abstract: TBA

November 3

Topic

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Abstract: TBA

November 10

Eulerian numbers, chromatic quasisymmetric functions and Hessenberg varieties

Michelle WachsUniversity of Miami

Abstract:

We consider three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a  q-analog of a generalization of the Eulerian numbers, the one in symmetric function theory deals with a  refinement of Stanley's chromatic symmetric functions, and the one in algebraic geometry deals with a representation of the symmetric group on the cohomology of the regular semisimple Hessenberg variety of type A.  Our purpose is to explore some connections between these topics and consequences of these connections.  This talk is based on joint work with John Shareshian.

 

November 17

Information Extraction from Data Using Nonconvex Optimization

Rick ChartrandLos Alamos national laboratory

Abstract:

In this talk we'll take a look at two classes of interesting results that can be obtained by exploiting the sparsity of real-world images and other signals. The first is the ability to reconstruct signals from many fewer data than previously thought possible, using efficient algorithms. This new and popular field is known as compressive sensing, because the results show that it is possible to directly measure a compressed version of a signal, without knowledge of the signal itself. The many potential applications include reducing exposure time in medical imaging, reducing the data storage/transmission/processing burden on deployed sensor systems, and national security applications.

We'll see how substituting a nonconvex objective function into the convex optimization problem typically used in this field has the effect of reducing still further the number of measurements needed to reconstruct signal.  A very surprising result is that simple algorithms, designed only for finding one of the many local minima of the optimization problem, typically find the global minimum.

The second type of result comes from applying the optimization technology developed in compressive sensing to matrix optimization problems. In particular, we can decompose a matrix of high-dimensional data into two parts: a low-dimensional model of the data that is robust to large perturbations, and a set of perturbations from the model, which often contains interesting features of the data. As an example, we'll see that when applied to video, the result is to extract all moving objects, leaving behind the stationary background.

November 24

THANKSGIVING HOLIDAY BREAK

December 1

The Dynamics of Assembly in Biological Networks

Eric DeedsUniversity of kansas

Abstract:

Large multicomponent protein complexes, such as the ribosome and proteasome, are crucial for cellular function.  Our work focuses on building computational models of the assembly of these structures.  Rings represent an important class of structural motifs; they can display remarkable thermodynamic stability that causes the overall assembly reaction to approach completion.  Our model of ring assembly indicates that the dynamics of this process can display complex behaviors.  We have found that rings can optimize assembly according to a wide range of criteria by exhibiting at least one protein interaction that is significantly weaker than the others in the ring.  Analysis of the experimentally available structures of heteromeric 3-membered rings indicates that most have evolved such a weak bond, as we would predict.  We have also examined the process of complex formation in the context of large protein-protein interaction and signaling networks.  These networks are combinatorially complex, in the sense that they can generate astronomical numbers of possible molecular species.  We employed a recently developed rule- and agent-based modeling technique to simulate the dynamics of two large networks.  Our results indicate that the combinatorial complexity of this network engenders "drift" in the space of molecular possibilities.   To produce large complexes that assemble reliably into well-defined, stable structures, cells have had to evolve mechanisms that constrain and eliminate this drift.

Location: Stanley Thomas 302

Time: 3:30 PM


December 8

A Montage of Statistical Analyses in Olympic Skating and Diving

Jay EmersonYale University

Abstract:

This talk engages several apparently separate yet actually related problems in Olympic diving and figure skating.  It is intended for all audiences.  I will invite the audience to participate in parts of the analysis, and will conclude with a discussion of challenges we face in teaching statistics.

Spring 2012



Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu