Biomedical Mathematics Seminar

Abstract: Accurately predicting mood fluctuations in mood disorders is critical for early intervention and personalized treatment. This study developed a neurophysiologically grounded mood prediction model by integrating behavioral modeling, electroencephalography, functional magnetic resonance imaging (fMRI), and physiological data from wearable devices in premenstrual syndrome (PMS). First, applying the active inference framework to a risk-taking behavioral …

Abstract: Evolutionary biology studies populations of reproducing individuals and how their composition changes over time.An important question is the fixation probability of a single mutant that attempts to invade a homogeneous population.Many real populations experience gradients of chemicals or nutrients that cause mutations to be beneficial in some spatial regions and harmful in others.We will …

Abstract: A central goal of scientific computing is to develop accurate and efficient solvers for scientific problems, and this goal is often pursued through sophisticated numerical methods. In modern machine learning, by contrast, the basic optimization procedure is often comparatively simple, typically gradient descent and its variants, while much of the complexity is shifted to …

Abstract: A central challenge of modern dynamical systems theory is to make nonlinear systems tractable without sacrificing fidelity. Koopman operator theory pursues this goal by lifting nonlinear dynamics into a linear, but infinite dimensional, operator acting on a function space. This operator-theoretic perspective underlies a broad class of modern data-driven methods, from dynamic mode decomposition …