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Math & Stats Department Colloquium
Friday, January 31, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Xinwei Deng (Virginia Tech)

Title: New Songs for Old Stories: Interface between Experimental Design and Machine Learning

Abstract: Experimental design and machine learning techniques have been widely used in engineering and data science applications. However, these two major areas have not been well integrated, especially on using experimental design thinking to enhance machine learning and using machine learning ideas to improve data collection. In this talk, we will present several recent research on the interface between experimental design and machine learning to facilitate data collection, modeling, and decision-making in the era of data science and AI. Specifically, two research works will be presented. The first part will introduce an active learning approach, called QS-learning, to enable effective modeling and efficient optimization for a new type of data with quantitative-sequence (QS) factors. The QS factor involves a sequence of multiple components associated with their quantities, widely used in health care, logistics, and many other disciplines. The second part will present a variational mutual information (MI) estimator for data and model parameters, leading to a simple and powerful contrastive MI estimator for Bayesian optimal experimental design. The performance of the proposed methods is evaluated by both numerical examples and real applications.

This colloquium will be held concurrently with CANSSI ONTARIO STATISTICS SEMINAR ().

PDEs & Applications Seminar

Friday, January 31, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Hengrong Du (University of California, Irvine)

Title: Hydrodynamics of Nematic Liquid Crystals and Nematic Electrolytes

Abstract: In this talk, we will discuss recent developments in the analysis of hydrodynamic models for nematic liquid crystals and nematic electrolytes. We will focus on the Ericksen–Leslie (EL) system, a strongly coupled PDE model combining the incompressible Navier–Stokes equations for fluid flow with gradient-flow-like equations for the nematic order parameter field. A key result includes a concentrated-compactness framework for the simplified EL system in 2D, with applications to stochastic models. Additionally, we will explore new insights into the nematic electrolytes model, highlighting analytical techniques and challenges in studying the coupling between fluid motion, nematic alignment, and electrostatic effects.

Zoom Link:

Meeting ID: 978 9733 0214

Passcode: upon request
 

PDEs & Applications Seminar

Friday, January 24, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Anirban Dutta (Queen's University)

Title: An introductory overview on singular integration

Abstract: In this talk, we will explore the concept of singular integration and its connection with maximal L^p regularity (according to me). We will outline the proof of the L^p mapping property, which will serve to demonstrate that if an operator possesses maximal L^p regularity for some p in (1, ∞), then it must also exhibit the L^p mapping property for all p in (1, ∞).

Math & Stats Department Colloquium
Friday, January 24, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Félix Parraud (Queen's University)

Title: A history of the notion of strong convergence in random matrix theory, or why we care about the norm of random matrices

Abstract: Proving results of strong convergence in Random Matrix Theory is roughly equivalent to studying the largest eigenvalue of a broad class of random matrices. In the last twenty years, those types of results have had a strong impact in various areas of mathematics, such as operator algebra, graph theory, representation theory, or quantum information theory. In this talk, I will start by defining basic objects, such as what a random matrix is, or the notion of strong convergence. I will then give you a history of the different results on the topic, their consequences in different fields, as well as some basic methods of proof.

Math & Stats Department Colloquium
Friday, January 17, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Jean-Christophe Nave (McGill University)

Title: Simulating problems with a wide range of scales without paying (much) for it

Abstract: In this talk I will present a new strategy to solve evolution PDEs which solutions develop a wide range of scales. Typical approaches to capture fine scales include mesh refinement (h-adaptivity) and polynomial adaptivity. I will show that by geometrizing the problem, one may leverage the semigroup structure of the solution operator. As a result, one may discretize this operator as a composition of submaps over finite time intervals. This leads to a new type of space-time adaptivity: compositional adaptivity. This approach possesses exceptional resolution properties while remaining computationally efficient. I will illustrate this technique with problems from fluid dynamics.

Math & Stats Department Colloquium
Friday, January 10, 2025

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Sinan Gezici (Bilkent University)

Title: Optimal Decision Rules for Hypothesis Testing Problems under General Criterion Involving Error Probabilities

Abstract: In this talk, we consider M-ary hypothesis-testing problems and characterize optimal decision rules under general criterion involving pairwise error probabilities, where likelihood ratios are employed as sufficient statistics. It is proved that an optimal decision rule can be obtained as a randomization between at most two deterministic decision rules in certain cases while a randomization among at most M(M-1)+1 deterministic decision rules can be required in other cases for optimality. We focus on some special cases of this generic approach such as prospect theory based hypothesis testing, where behavioral decision-makers distort probabilities and costs. We investigate the optimality of the likelihood ratio test (LRT) for prospect theory based binary hypothesis testing, and show that randomization of LRTs can be required for optimality. We provide various detection examples to illustrate the results.

Math & Stats Department Colloquium
Friday, November 29th, 2024

Time: 2:30 p.m.  Place: Jeffery Hall, Room 234

Speaker: Sina Sanjari (Royal Military College of Canada)

Title: Optimality of Symmetric Policies under Decentralized Information and Controlled Measure

Abstract: We consider multi-agent stochastic systems comprising a finite number of decision-makers and their mean-field limits. We focus on stochastic exchangeable systems with centralized, mean-field sharing, and fully decentralized information structures. For finite population systems, we show that an optimal policy exists that is exchangeable (permutation invariant). We then show that a sequence of exchangeable optimal policies for a finite population setting converges to an optimal policy for the infinite population problem, which is conditionally symmetric (identical), independent, and decentralized. This symmetry in optimal decision-making proves the optimality of a representative single-agent problem with controlled probability measures. Finally, we discuss connections to the measure-valued Markov decision processes and a dynamic programming approach.