Plenary speakers
Title: Mathematical Design of a Bioartificial Pancreas
Abstract: With the recent developments of new technologies in biomedical engineering and medicine, the need for new mathematical and numerical methods to aid these developments has never been greater. In particular, the design of an implantable bioartificial pancreas for the treatment of Type 1 diabetes, hinges on the development of mathematical and computational techniques for solving nonlinear moving boundary problems. In this talk we present a complex, multi-scale model, and a recent well-posedness result in the area of fluid-poroelastic structure interaction, which have helped the design of a first implantable bioartificial pancreas without the need for immunosuppressant therapy. This is a joint work with bioengineer Shuvo Roy (UCSF), and mathematicians Yifan Wang (UCI), Lorena Bociu (NCSU), Boris Muha (University of Zagreb), and Justin Webster (University of Maryland, Baltimore County).
Title: Static condensation, hybridization and the devising of the HDG methods
Abstract: The hybridizable discontinuous Galerkin (HDG) methods were introduced in the framework of second-order diffusion problems by hybridization and static condensation. We show that the exact solution can be characterized as the solution of local Dirichlet problems (hybridization) which can then be patched together by the transmission conditions (static condensation). Our goal is to show that the HDG methods are nothing but a discrete version of this characterization. To do so, we show that this is also the case for the well known continuous Galerkin and the mixed methods. We end by sketching how to define HDG methods for general PDEs.
Title: His or Her Mathematical Models --- Understanding Sex Differences in Physiology
Abstract: Imagine someone having a heart attack. Do you visualize the dramatic Hollywood portrayal of a heart attack, in which a man collapses, grabbing his chest in agony? Even though heart disease is the leading killer of women worldwide, the misconception that heart disease is a men’s disease has persisted. A dangerous misconceptions and risks women ignoring their own symptoms. Gender biases and false impressions are by no means limited to heart attack symptoms. Such prejudices exist throughout our healthcare system, from scientific research to disease diagnosis and treatment strategies. A goal of our research program is to address this gender equity, by identifying and disseminating insights into sex differences in health and disease, using computational modeling tools.
Title: Statistical and Machine Learning Foundation for Large and Complex Spatio-Temporal Data
Abstract: The rapid development of information technology makes it possible to collect massive amounts of data in multiple modalities, posing severe challenges to data scientists for multi-tasking the tremendous amount of data in real-time. Due to complex structure as well as the huge dimension of spatio-temporal data, the conventional statistical modeling is computationally inefficient and inadequate for the classification of spatial objects. These problems are arising in the technology-based modern world, such as computer vision and medical imaging. Thus they need to be solved from a broader perspective of data science. We present some recent developments from the standpoint of statistically principled high dimensional machine learning techniques, such as high dimensional discriminant analysis and deep networks.