# Spring 2016 Colloquia

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## STOR Colloquium: Noah Forman, University of Oxford

Exchangeability and continuum random trees A sequence of random variables is exchangeable if its distribution is invariant under finite permutations of indices. De Finetti showed that such sequences may be viewed as a mixtures of i.i.d. (independent, identically distributed) sequences. The Chinese restaurant process (CRP) is a simple model related to many exchangeable objects, which has recently gained prominence in connection with the clustering problem in machine learning. Continuum random trees (CRTs), on the other hand, are related to various…

Find out more »## STOR Colloquium: Sanchayan Sen, Eindhoven University of Technology

Asymptotics of high dimensional random structures: Probabilistic combinatorial optimization, stochastic geometry and random matrices One key focus of probability theory over the last few years has been on understanding asymptotics in the context of high dimensional structures. The aim of this talk is to give an overview of three major themes that have arisen in my work. More precisely: a) Probabilistic combinatorial optimization: One major conjecture in probabilistic combinatorics, formulated by statistical physicists using non-rigorous arguments and enormous simulations in…

Find out more »## STOR Colloquium: Nicolas Fraiman, Harvard University

Effects of limited choice and cooperation in network formation, epidemics and evolution. How does having structural or dynamical constraints affect the outcomes of stochastic models? In this talk I will discuss changes obtained from the addition of limited choice, cooperation or competition into processes that describe the evolution of networks and populations. I will analyze three models motivated by applications in communication networks, spread of epidemics, and evolutionary biology. The focus is on asymptotic behavior and phase transitions. Based on…

Find out more »## STOR Colloquium: Sayan Banerjee, University of Warwick

Couplings and geometry A coupling of (the laws of) two Markov processes specifies a particular construction of copies of the two processes simultaneously on the same space. They have a long history and find numerous applications in probability and analysis, ranging from yielding bounds on the mixing times of Markov chains to studying harmonic maps. It is natural to ask whether we can construct a coupling where the coupled processes actually meet (successful coupling). If such a coupling exists, how…

Find out more »## STOR Colloquium: Yu-Ting Chen, Harvard University

Stochastic interacting systems on graphs For more realistic modeling, there have been significant interests for the use of general graphs for interacting particle systems arising from biological or social contexts. However, the generality of spatial structure can lead to fundamental issues. They include the missing link to the stochastic PDE method that can give very detailed and clean information of interacting particle systems after rescaling, and the question of which graph parameters are essential to describe certain probability laws of…

Find out more »## STOR Colloquium: Subhro Ghosh, Princeton University

Rigidity phenomena in random point sets In several naturally occurring (infinite) random point processes, we establish that the number of the points inside a bounded domain can be determined, almost surely, by the point configuration outside the domain. This includes key examples coming from random matrices and random polynomials. We further explore other random processes where such ''rigidity'' extends to a number of moments of the mass distribution. The talk will focus on particle systems with such curious "rigidity" phenomena,…

Find out more »## STOR Colloquium: Maria Mayorga, North Carolina State University

A Nested-Compliance Table Policy for Emergency Medical Service Systems under Relocation The goal of Emergency Medical Service (EMS) systems is to provide rapid response to emergency calls in order to save lives. This paper proposes a relocation strategy to improve the performance of EMS systems. In practice, EMS systems often use a compliance table to relocate ambulances. A compliance table specifies ambulance base stations as a function of the state of the system. We consider a nested-compliance table, which restricts…

Find out more »## STOR Colloquium: Lexin Li, University of California at Berkeley

Tensor Regression and Applications in Neuroimaging Analysis Classical regression methods treat covariates (response or predictor) as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional array (tensor). Traditional statistical and computational methods are proving insufficient for analysis of such data due to their ultrahigh dimensionality as well as complex structure. In this talk, we propose a new family of tensor regression models that reduce the…

Find out more »## STOR Colloquium: David Dunson, Duke University

Probabilistic modeling of big table and networks In many applications, data consist of high-dimensional complex and highly-structured discrete data. Our focus here is on high-dimensional unordered categorical data, which arise in epidemiology, social surveys and brain connectomics. In the first part of the talk, I will focus on data that can be structured as a multiway contingency table but that otherwise have no obvious structure a priori. For such problems, we rely on probabilistic tensor factorizations, introducing new classes of…

Find out more »## STOR Colloquium: Alfredo Garcia, ARO and University of Florida

Alfredo Garcia, Army Research Office (ARO) and University of Florida Iterative Mechanisms for Electricity Markets Abstract: We consider the problem of designing the rules by which dispatch and payment to electricity market participants are gradually adjusted while taking into account network and reliability constraints so as to ensure the market clears with an efficient outcome. Small adjustments (which require minimal information from market participants at each iteration) facilitate the identification of incentives for ensuring truthful reporting of private…

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