Title: On Nonlinear Schrödinger Type Equations: Wave Modulation and Mathematical Analysis Abstract: The nonlinear Schrödinger (NLS) equation describes the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear […]
Title: The fractional p-Laplacian operator. Motivation for its definition and related boundary value problems Abstract: Last decades, nonlocal operators, as the fractional Laplacian, have gained to much attention due to […]
Abstract: Two-point boundary-value problems (BVPs) appear frequently in applied mathematics. When looking for solutions of boundary-value problems for some partial differential equations (PDEs) in mathematical physics, two-point BVPs come up as a result of applying the method of separation of variables, for instance. In the case of linear PDEs, the resulting two-point BVPs fall into […]
Abstract: The 2022 Los Angeles City Council scandal intensified public demand for governance reform, leading to the creation of the Los Angeles Charter Reform Commission. The commission is now considering proposals from civic and academic groups. Major recommendations include: eliminating the automatic election of candidates who win a primary majority, expanding the size of the […]
Abstract: The shape of the fluctuations as heat approaches equilibrium in an insulated body are governed by the first Neumann eigenfunction of the Laplacian. Rauch's hot spots conjecture states that the extrema of the first nontrivial Neumann Laplacian eigenfunction for a Lipschitz domain lies on the boundary. While this conjecture is false in general, its […]
Abstract: It is common to use adjuvants in immunotherapeutic regimens to strengthen the immune response. However, multiple dosages are required making it inconvenient for the patient. Hydrogels have been proposed […]
Abstract: Earlier work has shown that similarity-based predictive models can improve upon predictive performance, as compared to using the entire training data to help build models, particular regarding model discrimination […]
Abstract: Modern machine learning is ultimately a simple process: We iteratively update the weights of machine learning models to minimize a problem-specific loss. When it works well, we deploy the model in human-facing domains like healthcare, finance, or the justice system. But even though we know how models are trained, we don't understand why they […]
Abstract: Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This talk focuses on a variant of AA in which multiple Picard […]
Abstract: Transparency is vital for efficiency in social systems, yet individuals with critical information often strategically postpone disclosure, even when required, to benefit themselves. To study this behavior, we introduce […]
Abstract: The problem of classification in machine learning has often been approached in terms of function approximation. In this talk, we propose an alternative approach for classification in arbitrary compact […]
Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents […]
