Robust Prediction Variance Estimation for Gaussian Process Regression Under Covariance Smoothness Misspecification

Colloquiums, News

Abstract: Best Linear Unbiased Prediction (BLUP) has been a dominant approach in Generalized Linear Mixed Models, spatial models, and Gaussian Process Regression (GPR). In addition to their optimal properties, BLUP procedures quantify prediction uncertainty. However, the general implementation of BLUP goes as follows: (i) assume the probability distribution and covariance function are known and that…

NLS with higher order dispersion

Colloquiums, News

Abstract: We study a higher order dispersion nonlinear Schr6dinger (NLS) equation with the k-Laplacian (-Δ)k, and the potential term expressed as a power nonlinearity (for any positive power). When k = 1 we recover the NLS with the standard Laplacian and when k = 2 we get the bi-harmonic NLS. We investigate well-posedness of solutions…

New Constructions of Multidimensional Periodic Array Families for Video Watermarking

Colloquiums, News

Abstract: Families of periodic arrays are useful in a variety of applications, including multiple target recognition, optical communications, and digital watermarking. In video watermarking, these arrays can be employed as watermarks to ensure copyright protection and to verify the authenticity of the original video. In video watermarking, watermarks based on periodic arrays can be embedded…

Computer Science and Computational Thinking Education

Colloquiums, News

Abstract: Modem education requires our students to develop 21st-century problem-solving skills. This presentation offers an in-depth look at the integration of Computer Science and Computational Thinking at the primary and secondary education levels. Through a practical approach, we will discuss how gamification—highlighting the highly successful model of the Bebras Challenge—can motivate students and facilitate the…

From Classical SDEs to Conditional McKean-Vlasov Systems: Theory and Open Problems

Colloquiums, Colloquiums Spring 2026, News

Abstract: This talk presents a structured overview of stochastic differential equations (SDEs), beginning with classical Itô diffusions and progressively incorporating jumps, regime switching, and interacting particle systems. We then introduce McKean—Vlasov equations, where the dynamics depend on the law of the solution itself, highlighting their nonlinear and mean-field nature. Particular emphasis is placed on conditional…

Metapopulation model framework for Puerto Rico applied to COVID-19.

Colloquiums, Colloquiums Spring 2025, News

Abstract: The COVID-19 pandemic has highlighted significant challenges for public health systems worldwide, demonstrating not only the lethality of infectious diseases but also the critical role of public behavior that influence case numbers and mortality rates, particularly in geographically isolated regions like Puerto Rico. This study presents a metapopulation model framework to analyze the transmission…

Incorporating seasonality in functional magnetic resonance imaging to assess reliability

Colloquiums, Colloquiums Spring 2025, News

Abstract: Functional magnetic resonance imaging (fMRI) is a noninvasive tool for studying regions related to some particular stimulus. To find these regions, the stimulus is typically applied in the form of event-related or block-design. Due to this, fMRI experiments have a natural seasonal pattern. In this work, we used different seasonal time series models in…

A Riemann-Hilbert approach to the Fractional NSL equation on a half-line.

Colloquiums, Colloquiums Spring 2025, News

Abstract: The fractional Schrodinger equation generalizes the standard Schrodinger equation by incorporating fractional derivatives, extending traditional quantum mechanics through fractional calculus. This approach provides a more flexible framework for modeling quantum systems with anomalous diffusion or complex geometries. Research in this field is dynamic, with ongoing exploration of both theoretical foundations and experimental implications, offering…