Upcoming MAMS Colloquium Series
Fall 2024
11/22/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. David White (Denison University)
Title: Time series analysis, protests, and the opioid epidemic
Abstract: An overview of time series data (that is, data sampled at different points in time) and common statistical models for such data, including ARIMA models that factor in what the past knows about the present, and spectral models based on Fourier analysis. I’ll illustrate these models with vignettes from my research, on problems related to policing, protests, and opioid overdose in Ohio. I will explain what our research says about the impact of police use of force (e.g., rubber bullets and tear gas) on protest dynamics and violence. I will also explain how these techniques can create an “early warning system” using data on drug seizures by law enforcement to predict for spikes in the monthly death rate. The goal of this research is to save lives by alerting people when dangerous fentanyl analogues are detected in the Ohio drug supply, so that action can be taken to prevent overdoses. I’ll also tell a bit of my story, about how despite being trained in category theory and homotopy theory, I expanded my research to include these applied statistics topics. Lastly, I will also provide a road-map to a corpus of freely available datasets where even simplistic analyses would be valuable, publishable, and might save lives. I hope to inspire the listener to get involved with the efforts of the harm reduction community to reduce overdose deaths. This talk assumes only a basic knowledge of statistics, and students are welcome.
11/15/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Annalisa Quaini (University of Houston)
Title: Bridging Large Eddy Simulation and Reduced Order Modeling of convection-dominated flows through spatial filtering
Abstract: Reduced order Models (ROMs) are inexpensive surrogates for expensive models. The surrogate is constructed by extracting the dominant system dynamics from selected high-resolution simulations. Leveraging the so-called offline/online paradigm, the expense incurred in the construction process is amortized over many surrogate solutions. The presence of flow phenomena over large spatial and temporal ranges in convection-dominated flows poses significant challenges to traditional ROMs: a large number of modes may be required to accurately describe the fluid dynamics, which limits the computational efficiency. On the other hand, if one chooses to reduce the number of modes to improve efficiency, a severe loss of information compromises the solution accuracy.
We propose to recover stability for classical ROMs through closures and stabilizations that are inspired by Large Eddy Simulation (LES). A key ingredient for the construction of these ROMs, which we call LES-ROMs, is spatial filtering, i.e., the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. We will show that LES-ROMs are extremely easy to implement, very efficient, and, when carefully tuned, accurate in capturing the average physical quantities of interest in challenging convection-dominated flows.
11/8/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Todd Quinto (Tufts University)
Title: What can be imaged by novel ellipsoidal and hyperbolic Radon transforms
Abstract: This talk with include deep functional analysis and cool pictures to describe the properties of new integral transforms (Radon transforms) that integrate over ellipsoids and hyperboloids and generalizations. We discuss implications for thermoacoustic tomography (TAT).
We will start by explaining some basic microlocal analytic principles and how they apply to standard backprojection type reconstruction methods for our transforms. Then, we will apply it to the general transform and a transform in thermoacoustic tomography (TAT).
In TAT, one is interested in finding cancers, which respond differently to heating than normal tissue. We will describe the model and apply our theory to describe which features will be visible using this data and which will not be visible. We will predict artifacts, which are added streaks or other “features” that appear in the reconstruction but are not in the object. In addition, we present reconstructions of image phantoms in two dimensions that illustrate our microlocal theory. [Journal of Functional Analysis 285(2023) 110056]
10/25/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Artem Zvavitch (Kent State University)
Title: Sumset estimates in convex geometry
Abstract: In this talk, we will discuss several inequalities in convex geometry inspired by sumset estimates in additive combinatorics and inequalities in information theory. We will explore the connections between these inequalities and various inequalities related to mixed volumes and Loomis-Whitney type estimates for the volumes of orthogonal projections. Additionally, we will present several open questions and demonstrate the relationship of these questions to “simple” inequalities concerning determinants.
10/11/2024, Friday. 3:15-4:15 pm in Wickenden 321
Speaker: Dr. Grzegorz Rempala (Ohio State University)
Title: SIR Dynamics on Networks: Law of Large Numbers, Correlation Equation, and Exact Closure Conditions
Abstract: In this talk, I will present some recent results on a widely used closure method for modeling contagion dynamics on random networks, specifically within the configuration model framework. This method approximates the dynamics of node triples by using only pairwise interactions and is often justified heuristically. Using the martingale theory, I will rigorously derive the necessary and sufficient conditions under which the closure is asymptotically exact. The results provide a robust criterion for determining when closure methods can effectively capture contagion dynamics on large-scale networks. This work is in collaboration with Eben Kenah (OSU) and Istvan Kiss (Northeastern University).
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.