WSU Vancouver Mathematics and Statistics Seminar (Spring 2026)

Abstract

In this talk, I will give an introduction to simplicial homology and some examples where it is used in data analysis, followed by persistent homology and some more examples. Then I will talk about computing these objects over \(\mathbb{Z}_2\) using a standard algorithm and explain some optimizations for said algorithm.

Abstract

In this talk, we will explore the journey behind my graduate research at Washington State University. We will begin with a discussion of my work with the Washington State Data Exchange for Public Safety (WADEPS), in which I provide accessible video tutorials on meaningful analysis of police use of force. Motivated by my work with WADEPS, we will discuss my research with the WSU Criminology department using machine learning and topology to predict perceptions of police use of force and identify factors that impact use of force outcomes. Along with the analysis of police use of force and perceptions data, we will briefly discuss the extension of this research in which I use topology to provide a stable measure of time-series similarity for police calls data. Following my work constructing stable topological time-series measures, I will lastly discuss my latest research which uses topology to construct a stable measure of exponential divergence in dynamical systems. We will end with a discussion of open research questions I plan to investigate in the future.

Abstract

Mixed integer programs (MIPs) are optimization problems involving both continuous and integer decision variables and are typically NP-hard to solve. Recent applications of machine learning to MIPs have shown success primarily through learning heuristics for variable branching or cut selection within branch-and-bound frameworks. While effective in practice, such approaches remain heuristic in nature and are still subject to worst-case exponential behavior.

In this work, we introduce an optimal cut framework for mixed integer optimization, in which learned cuts guarantee that the solution of a MIP is also a solution to its continuous relaxation augmented with the cut. We characterize the existence of such cuts using first-order optimality conditions and establish conditions under which they are learnable from data while explicitly accounting for approximation error. Building on this framework, we propose a sequential linear programming algorithm that leverages optimal cuts to improve integer decisions and runs in polynomial time under stated problem assumptions. Our results provide an alternative to branching-based methods and offer theoretical guarantees for learning-assisted mixed integer optimization.

Abstract

This presentation introduces Eye2Heart, a mathematical model that couples cardiovascular and ocular hemodynamics through a system of nonlinear differential equations. Developed and verified using clinical and experimental data, the model captures key physiological interactions between the heart and the eye. Simulations reveal that elevated intraocular pressure restricts ocular perfusion, while reduced left ventricular compliance decreases cardiac output and retinal blood flow. When both occur together, venous circulation is further impaired, providing mechanistic insights into conditions such as normal-tension glaucoma. By linking the dynamics of the eye and heart, Eye2Heart advances the emerging field of oculomics and supports the development of physiologically grounded tools for precision medicine.

This is joint work with Lorenzo Sala (Université Paris-Saclay); Mohamed Zaid (Foresite Healthcare LLC); Faith Hughes (University of Maine); Marcela Szopos (Université Paris Cité); Virginia Huxley (University of Missouri); Alon Harris (Icahn School of Medicine at Mount Sinai); Giovanna Guidoboni (University of Maine)

Abstract

Spike sorting is the computational process of extracting the firing times of single neurons from recordings of local electrical fields. This is an important but hard problem in neuroscience, made complicated by the nonstationarity of the recordings and the dense overlap in electrical fields between nearby neurons. To address the spike-sorting problem, we have been openly developing the Kilosort framework. Here we describe the various algorithmic steps introduced in different versions of Kilosort. We also report the development of Kilosort4, a version with substantially improved performance due to clustering algorithms inspired by graph-based approaches. See Nature paper for details.