WSU Vancouver Mathematics and Statistics Seminar (Fall 2025)

Abstract (click to read)

Relocalization is the task of estimating a camera's six degrees of freedom (6-DoF) pose within a known map, a problem with key applications in robotics, AR, and autonomous systems. In this talk, I will present our work from the G-RIPS Sendai 2025 program in collaboration with Mitsubishi Electric, where we developed a novel RGB-D relocalization pipeline designed to be robust to illumination changes. Our approach combines global feature extraction using ResNet18 + NetVLAD on both RGB and depth modalities with a late-fusion strategy (Net-AF) and local matching via ASIFT and SuperPoint. Depth data is further projected into 3D point clouds for pose estimation using RANSAC and the Kabsch algorithm. We evaluated our pipeline on the Stanford 2D-3D-Semantics dataset, including illumination-augmented variants, and observed strong performance under well-lit conditions, while identifying key challenges under low-light conditions. I will discuss the lessons learned, the promise of multimodal fusion, and future directions such as dynamic fusion weighting and depth-aware feature learning.

Abstract (click to read)

One widely used measure of chaos in nonlinear dynamical systems is the Lyapunov exponent, which measures the rate of exponential divergence of neighboring trajectories in a system's phase space. This measure relies solely on Euclidean distance, which we experimentally show decrease its stability on known chaotic systems when subject to small amounts of added Gaussian noise. Many real-world systems are arguably likely to contain some inherent noise. To address this limitation, we introduce a novel measure of chaos in nonlinear dynamical systems using persistent homology, the Persistence exponent, and prove its theoretical stability. We also show its greater experimental stability in comparison with the Lyapunov exponent on a variety of differential systems with known dynamics; modeling fluid motion, taffy pulling, and autocatalytic chemical reactions. We finally show greater experimental stability of the Persistence exponent on time series data obtained from a real Belousov-Zhabotinsky chemical reaction.

Abstract (click to read)

One widely used measure of chaos in nonlinear dynamical systems is the Lyapunov exponent, which measures the rate of exponential divergence of neighboring trajectories in a system's phase space. This measure relies solely on Euclidean distance, which we experimentally show decrease its stability on known chaotic systems when subject to small amounts of added Gaussian noise. Many real-world systems are arguably likely to contain some inherent noise. To address this limitation, we introduce a novel measure of chaos in nonlinear dynamical systems using persistent homology, the Persistence exponent, and prove its theoretical stability. We also show its greater experimental stability in comparison with the Lyapunov exponent on a variety of differential systems with known dynamics; modeling fluid motion, taffy pulling, and autocatalytic chemical reactions. We finally show greater experimental stability of the Persistence exponent on time series data obtained from a real Belousov-Zhabotinsky chemical reaction.

Abstract (click to read)

In the planar case, Blank introduced words associated to immersed curves, providing a combinatorial tool to encode winding numbers and to derive minimal area null-homotopies. Chambers and Wang later proved that the minimal swept area of a null homotopy is bounded below by the total winding number area, with equality in the consistent winding case.

This talk extends the picture to immersed spheres in \(\mathbb{R}^3\). We introduce a cable system construction, the 3D analogue of Blank's words, which assigns to each region of the complement an integer index via oriented cable crossings. We prove that these cable indices agree with the Brouwer degree of the region. Using this, a lower bound for the swept 3-volume of any null homotopy is obtained, expressed as a weighted sum of region volumes with multiplicities. We also discuss progress toward the equality case, algorithmic constructions of sense-preserving null homotopies, and possible reductions to 1D via curves representing the cable system.

Abstract (click to read)

In the planar case, Blank introduced words associated to immersed curves, providing a combinatorial tool to encode winding numbers and to derive minimal area null-homotopies. Chambers and Wang later proved that the minimal swept area of a null homotopy is bounded below by the total winding number area, with equality in the consistent winding case.

This talk extends the picture to immersed spheres in \(\mathbb{R}^3\). We introduce a cable system construction, the 3D analogue of Blank's words, which assigns to each region of the complement an integer index via oriented cable crossings. We prove that these cable indices agree with the Brouwer degree of the region. Using this, a lower bound for the swept 3-volume of any null homotopy is obtained, expressed as a weighted sum of region volumes with multiplicities. We also discuss progress toward the equality case, algorithmic constructions of sense-preserving null homotopies, and possible reductions to 1D via curves representing the cable system.

Abstract (click to read)

This talk concerns the problem of reliably comparing cycle representatives from persistence modules drawn from separate data clouds given there exists a notion of cross-dissimilarity between the two sets. To do this, the talk features a primer on topological data analysis and the notion of distance between data clouds. It then will cover the tools required for a preliminary attempt at cycle comparison at the chain level using the Grassmannian distance. This method will then be outlined, and a minor result concerning its stability will be presented. Results from computer implementation will be presented along, and the talk will finish with potential refinements to the method that are being sought.

Abstract (click to read)

In this talk, we will formally derive general bounds on the quality of solution for mixed-integer programs and discuss their application and scalability on learning resource distribution problems for energy network resilience against high-impact low-probability events. This work is a part of a collaboration with Prof. Anamika Dubey and Shishir Lamichhane from WSU EECS. See related work in the manuscript on scalable stochastic OPF.

Abstract (click to read)

I present a winter beehive thermoregulation model that couples a heat PDE with spatially varying diffusivity and Robin (Newton-cooling) boundary conditions to a thermotactic Keller-Segel equation for bee density with no-flux walls. The coupling links clustering to metabolic heating via the source and yields a Boltzmann-type steady state. To simulate in Matlab, I volume-average the heat PDE (using the divergence theorem and the Robin law) to obtain a lumped ODE. Using Langstroth hive dimensions to set \(C_{\text{eff}}\) (volume/materials) and \(H_{\text{eff}}\) (surface area/insulation), and driving \(T_{\text{ext}}(t)\) with a 12-h sinusoid, I simulate temperature and honey usage. To quantify extra honey burned, peak/mean metabolic power, and time below \(T_{\text{opt}}\) under varying insulation and cold-snap magnitudes, yielding actionable thresholds for wraps and emergency feeding

Abstract (click to read)

Estimating neuronal network activity as point processes is challenging due to the singular nature of events and high signal dimensionality. This project analyzes spiking neural networks (SNNs) using counting process statistics, which are equivalent integral representations of point processes. The counting process offers several advantages over traditional point process methods. Using continuous cumulative counts provides smoother trajectories that reduce discrete event singularities and enable direct applications of standard statistical techniques.

A small SNN of Leaky Integrate-and-Fire (LIF) neurons is simulated, and spiking events are counted as a vector counting process \(N(t)\). The Poisson counting process serves as our null model with known dynamic statistics over time: both mean\((t)\) and variance\((t)\) are proportional to time (\(= r_i(t)\) for each independent source with rate \(r_i\)). By standardizing the data, mean dynamics and heteroscedasticity can be removed, allowing comparison to this baseline. We test two hypotheses about the underlying stochastic processes: \(H_1\): Neural spike trains follow a homogeneous Poisson process with constant rate; and \(H_2\): Neural spike trains follow an inhomogeneous Poisson process with time-varying rate.

To test the sensitivity of our framework, we introduce systematic perturbations to the baseline Poisson process by adding Gaussian noise to firing rates. These perturbations mimic biologically relevant scenarios such as attention modulation or external stimuli. Real neural systems exhibit non-Poisson behavior due to network interactions, synaptic correlations, and external modulations. Establishing statistical frameworks to detect and quantify deviations can help us better understand how neural systems process information and respond to environmental demands.