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 Events
Wed 16 Jan 2019, 3:45pm SPECIAL
ESB 4133 (PIMS lounge), Earth Sciences Building
PIMS Afternoon Tea
ESB 4133 (PIMS lounge), Earth Sciences Building
Wed 16 Jan 2019, 3:45pm-4:15pm

Details

The PIMS Tea continues every Wednesday throughout the term.
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Dr Eric Foxall
University of Alberta
Wed 16 Jan 2019, 4:00pm
MATH 104
Applied Math Seminar: Diffusion limit for the partner model at the critical value
MATH 104
Wed 16 Jan 2019, 4:00pm-5:00pm

Details

Abstract: The partner model is a stochastic SIS model of infection spread over a dynamic network of monogamous partnerships. In previous work, Edwards, Foxall and van den Driessche identify a threshold in parameter space for spread of the infection and show the time to extinction of the infection is of order log(N) below the threshold, where N is population size, and grows exponentially in N above the threshold. Later, Foxall shows the time to extinction at threshold is of order sqrt(N). Here we go further and derive a single-variable diffusion limit for the number of infectious individuals rescaled by sqrt(N) in both population and time, and show convergence in distribution of the rescaled extinction time. Since the model has effectively four variables and two relevant time scales, the proof features a succession of probability estimates to control trajectories, as well as an averaging result to contend with the fast partnership dynamics.

(This is joint work with Rick Durrett and Anirban Basak.)
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Dr Elina Robeva
Massachusetts Institute of Technology
Thu 17 Jan 2019, 12:30pm
Mathematics of Information and Applications Seminar
ESB 4133
Maximum likelihood estimation under total positivity
ESB 4133
Thu 17 Jan 2019, 12:30pm-1:30pm

Abstract

Nonparametric density estimation is a challenging statistical problem -- in general the maximum likelihood estimate (MLE) does not even exist! Introducing shape constraints allows a path forward. In this talk I will discuss non-parametric density estimation under total positivity (i.e. log-supermodularity). Though they possess very special structure, totally positive random variables are quite common in real world data and exhibit appealing mathematical properties. Given i.i.d. samples from a totally positive distribution, we prove that the MLE exists with probability one if there are at least 3 samples. We characterize the domain of the MLE, and give algorithms to compute it. If the observations are 2-dimensional or binary, we show that the logarithm of the MLE is a piecewise linear function and can be computed via a certain convex program. Finally, I will discuss statistical guarantees for the convergence of the MLE, and will conclude with a variety of further research directions.
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Dr Eric Foxall
University of Alberta
Thu 17 Jan 2019, 4:00pm
Department Colloquium
MATH 100
Individual-based modelling of interacting populations
MATH 100
Thu 17 Jan 2019, 4:00pm-5:00pm

Abstract

In this talk we explore a variety of individual-based stochastic models inspired from ecology, epidemiology, game theory and the social sciences. Our goal in each case is to understand the (global) population-level behaviour in terms of the (local) interaction rules. We pay special attention to large-population limit processes, both deterministic and stochastic, and to phase transitions that occur as model parameters are varied.

Note for Attendees

Pre-colloquium refreshments will be served in MATH 125 at 3:45 p.m.
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Dr Elina Robeva
Massachusetts Institute of Technology
Fri 18 Jan 2019, 3:00pm
Department Colloquium
ESB 2012
Orthogonal Tensor Decomposition
ESB 2012
Fri 18 Jan 2019, 3:00pm-4:00pm

Abstract

Tensor decomposition has many applications. However, it is often a hard problem. In this talk I will discuss a family of tensors, called orthogonally decomposable tensors, which retain some of the properties of matrices that general tensors don't. A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. Such tensors are interesting because their decomposition can be found efficiently. We study their spectral properties and give a formula for all of their eigenvectors. We also give equations defining all real symmetric orthogonally decomposable tensors. Analogously, we study nonsymmetric orthogonally decomposable tensors, describing their singular vector tuples and giving polynomial equations that define them. In an attempt to extend the definition to a larger set of tensors, we define tight-frame decomposable tensors and study their properties. Finally, I will conclude with some open questions and future research directions.

Note for Attendees

Refreshments will be served at 2:30 p.m. in ESB 4133 (PIMS Lounge).
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Zane Li
UCLA
Mon 21 Jan 2019, 3:00pm
Harmonic Analysis Seminar
MATH 126
A proof of l^2 decoupling for the parabola inspired from efficient congruencing
MATH 126
Mon 21 Jan 2019, 3:00pm-4:00pm

Abstract

 Vinogradov's Mean Value Theorem was proven separately by Wooley's efficient congruencing method and Bourgain-Demeter-Guth's decoupling method. While similarities between the methods have been observed no precise dictionary has been written. We give a proof of l^2 decoupling for the parabola inspired by efficient congruencing in two dimensions. We will mention where tools like ball inflation and l^2 L^2 decoupling come into play. Making this proof quantitative also allows us to match a bound obtained by Bourgain for the discrete Fourier restriction problem in two dimensions without resorting to using the divisor bound.
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USC
Mon 21 Jan 2019, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 21 Jan 2019, 4:00pm-5:00pm

Abstract

 
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