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 […]
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 […]
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 […]
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 […]
Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time […]
Abstract: A proper coloring of a graph is an assignment of colors from \( \{1, 2, \ldots, k\} \) to each node of a graph such that no two nodes […]
