Upcoming MAMS Colloquium Series

Fall 2024

9/27/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Hyebin Song (The Pennsylvania State University)
Title: Weighted shape-constrained estimation with applications to Markov chain autocovariance function estimation
Abstract: In this talk, I will introduce a novel weighted l2 projection method for estimating covariance functions, with an emphasis on estimation of autocovariance sequences from reversible Markov chains. Shape-constrained estimation of a function with discrete support has been investigated and successfully applied to various application problems. Notably, Berg and Song (2023) connected this idea with uncertainty quantification in Markov chain Monte Carlo (MCMC) samples and proposed a shape-constrained estimator for autocovariance sequences. While the least-squares objective is commonly used in shape-constrained regression, it can be suboptimal due to correlation and unequal variances in the input function. To address this, we introduce a weighted least-squares method that defines a weighted norm on transformed data. Our approach involves transforming input data into the frequency domain and weighting the input sequence based on their asymptotic variances, exploiting the asymptotic independence of periodogram ordinates. I will discuss the computational aspects, theoretical properties, and the improved performance of this method compared to its non-weighted counterpart.

9/20/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Andrea Arnold (Worcester Polytechnic Institute)
Title: Data-Driven Modeling and Uncertainty Quantification of Microglia Phenotypes During Ischemic Stroke
Abstract: Neuroinflammation immediately follows the onset of ischemic stroke. During this process, microglial cells are activated in and recruited to the tissue surrounding the irreversibly injured infarct core, referred to as the penumbra. Microglial cells are activated into two distinct phenotypes; however, the dynamics between the detrimental M1 phenotype and beneficial M2 phenotype are not fully understood. This talk will address recent data-driven modeling approaches to better understand and predict microglial cell dynamics during middle cerebral artery (MCAO)-induced ischemic stroke using phenotype-specific cell count data obtained from experimental studies. Each modeling approach incorporates aspects of inverse problems and uncertainty quantification in making forecast predictions.

9/13/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Luis Rademacher (UC Davis)
Title: The k-set problem: General shapes and random point sets
Abstract: Given a finite set S of n points in R^d, a k-set is a subset of S of size k which can be strictly separated from the rest of S by a hyperplane. Similarly, one may consider k-facets, which are hyperplanes that pass through d points of S and have k points on one side. A notorious open problem is to determine the asymptotics of the maximum number of k-sets given n, k and d. The first part will be an introduction to basic facts and techniques about the k-set problem. The second part will be about two aspects of the problem: (1) A variation with hyperplanes replaced by algebraic surfaces. (2) For a probability distribution P on R^d, the expected number of k-facets of a sample of n random points from P. This is based on joint work with Brett Leroux.