Developing statistical methods and scalable computational tools to uncover structure

Modern scientific research generates increasingly complex, high-dimensional datasets that demand innovative statistical methods and efficient computational tools. This presentation showcases our research group’s efforts to develop statistical methods and scalable computational tools that help researchers uncover meaningful patterns, explore hidden data structures, and extract scientific insight. By integrating statistics, machine learning (ML), artificial intelligence (AI),…

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

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

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

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

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

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…

Flyer Girls Club 2026

GIRLS MATH CLUB de Puero Rico (GMCPR)

GIRLS MATH CLUB DE PUERTO RICO Club de Matemáticas para Niñas de nivel Intermedio en escuelas públicas y privadas Las fechas de las reuniones del club son : Jueves, 26 de febrero, 4:00 pm – 6:30 pm Jueves, 26 de marzo, 4:00 pm – 6:30 pm Jueves, 30 de abril,4:00 pm – 6:30 pm