Title: Informatics and Modeling Platform for Stable Isotope-Resolve Metabolomics



Abstract: Recent advances in stable isotope-resolved metabolomics (SIRM) are enabling orders-of-magnitude increase in the number of observable metabolic traits (a metabolic phenotype) for a given organism or community of organisms.  Analytical experiments that take only a few minutes to perform can detect stable isotope-labeled variants of thousands of metabolites.  Thus, unique metabolic phenotypes may be observable for almost all significant biological states, biological processes, and perturbations.  Currently, the major bottleneck is the lack of data analysis that can properly organize and interpret this mountain of phenotypic data as highly insightful biochemical and biological information for a wide range of biological research applications.  To address this limitation, we are developing bioinformatic, biostatistical, and systems biochemical tools, implemented in an integrated data analysis platform, that will directly model metabolic networks as complex inverse problems that are optimized and verified by experimental metabolomics data.  This integrated data analysis platform will enable a broad application of SIRM from the discovery of specific metabolic phenotypes representing biological states of interest to a mechanism-based understanding of a wide range of biological processes with particular metabolic phenotypes.

Title:  Some progresses on two-dimensional Riemann problems in gas dynamics

Abstract:  Two dimensional Riemann problems for compressible fluid flows assume the simplest piecewise sectorial initial state but provide the most fundamental wave configurations, including the reflection of oblique shocks and vortex-shock interaction etc. In this talk I will show many fascinating pictures, based on 2D Riemann solutions, to disclose the mysteries of compressible fluid world both through analytical tools (in the form of mathematical theorems) and computational techniques (in the form of simulations). The analysis is based on the characteristic decomposition theory we developed recently, while the simulations are obtained using the generalized Riemann problem (GRP) scheme that is equipped with a highly accurate solver in the construction of numerical fluxes by a way of tracking singularities analytically and keeping entropy exactly computed. 

Title:  Universal wave patterns

Abstract:  A feature of solutions of a (generally nonlinear) field

theory can be called "universal" if it is independent of side conditions like initial data. I will explain this phenomenon in some detail and then illustrate it in the context of the sine-Gordon equation, a fundamental relativistic nonlinear wave equation. In particular I will describe some recent results (joint work with R. Buckingham) concerning a universal wave pattern that appears for all initial data that crosses the separatrix in the phase portrait of the simple pendulum.  The pattern is fantastically complex and beautiful to look at but not hard to describe in terms of elementary solutions of the sine-Gordon equation and the collection of rational solutions of the famous inhomogeneous Painlev\'e-II equation.

Title:  Automating and Stabilizing the Discrete Empirical Interpolation Method for Nonlinear Model Reduction

Abstract:  The Discrete Empirical Interpolation Method (DEIM) is a technique for model reduction of nonlinear dynamical systems.  It is based upon a modification to proper orthogonal decomposition which is designed to reduce the computational complexity for evaluating reduced order nonlinear terms.  The DEIM approach is based upon an interpolatory projection and only requires evaluation of a few selected components of the original nonlinear term.  Thus, implementation of the reduced order nonlinear term requires a new code to be derived from the original code for evaluating the nonlinearity.  I will describe a methodology for automatically deriving a code for the reduced order nonlinearity directly from the original nonlinear code.  Although DEIM has been effective on some very difficult problems, it can under certain conditions introduce instabilities in the reduced model.  I will present a problem that has proved helpful in developing a method for stabilizing DEIM reduced models.