Applied Math Seminar

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 as a vehicle to administer adjuvant and antigen in a sustained slow release thus reducing the need for re-administration. In this instance, we use experimental […]

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 for binary responses. My collaborators and I have some updated results to share, regarding similarity-based modeling for joint consideration of model calibration and discrimination, as […]

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 […]