## Applied Math Seminar at Colorado State University## Thursday 3:00-4:00PM, Weber 223 |

Jan 30 Back to top

Title Mathematical Modeling for Virus: HIV-1 and 2019-nCoV

Abstract In this talk, we examine several aspects of mathematical modeling for 2019-nCoV and HIV-1, two types of viruses that have big impacts on human societies. 2019-nCoV, a coronavirus that originated from China and is now spreading worldwide, may cause acute pneumonia. While the classical SEIR model may still apply, this epidemic also offers new opportunities for Smart Data research. HIV-1 is a retrovirus that causes acquired immunodeficiency syndrome (AIDS), a condition in humans in which the immune system fails progressively. We shall discuss how geometry, dynamical systems, and partial differential equations can be utilized to model HIV-1 structure, assembly, and intracellular transport. This talk is based on the joint efforts with researchers at CSU and other institutions.

Oct 10 Back to top

Title Long time behaviors of a nonlinear stochastic heat equation in d ≥ 3

Abstract In this talk, we study the solution to a nonlinear stochastic heat equation in d ≥ 3. In a weak disorder regime, we prove (i) the solution converges to the stationary distribution in large time; (ii) the diffusive scale fluctuations are described by the Edwards-Wilkinson equation.

Mar 05 Back to top

Title Studying Complex Diseases Using Integrative -Omics and Network Approaches

Abstract New technologies now allow biomedical investigators to comprehensively study the molecular repertoire of a biological system or organism. The resulting high-dimensional datasets, also referred to as -omics profiles (e.g., transcriptomic, proteomic, metabolomic) can be used to identify molecular mechanisms associated with a disease. With collaborators studying chronic obstructive pulmonary disease (COPD), we have analyzed a variety of -omics data sets to gain insight into the development of COPD. In this talk, I will present our work for integrating -omics profiles to identify molecular networks associated with COPD, and for identifying COPD subtypes. Our methods are based on high dimensional data approaches including canonical correlation analysis and deep learning.

Mar 06 (2-3PM) Back to top

Title Infinite densities, and the Moses/Noah/Joseph effects in anomalous diffusion

Abstract When we obtain a "blind" ensemble of data sets, representing individual time series of experimental data, we don't usually know which type of stochastic process describes the dynamics that generated it. It is important to know if our data represents normal or anomalous diffusion, and if it is the latter - what are the basic properties in the underlying process, which are responsible for this phenomenon? Using a well known process, known as Levy walk, as an example, we show that the scaling of the mean-squared displacement of the process with time, can be decomposed into the sum of three other exponents, which tell us individually whether our process is anomalous due to non-stationary increments, power-law distributions, or intrinsic time-correlations (respectively known as "Moses", "Noah" and "Joseph" effects). The appearance of these effects, may indicate that an infinite-density lies at the root of all these processes.

Mar 12 Back to top

Title Cluster formation and self-assembly in stratified fluids: a novel mechanism for particulate aggregation

Abstract The experimental and mathematical study of the motion of bodies immersed in fluids with variable concentration fields (e.g. temperature or salinity) is a problem of great interest in many applications, including delivery of chemicals in laminar micro-channels, or in the distribution of matter in the ocean. In this lecture we present some recent experimental and mathematical advances we have made for several such problems. First, we review results on how the shape of a tube can be used to sculpt the profile of chemical delivery in pressure driven laminar shear flows. Then, we explore recent results for the behavior of matter trapped vertically in a variable density water column. For this second problem, we experimentally observe and mathematically model a new attractive mechanism we have found in our laboratory by which particles suspended within stratification may self-assemble and form large aggregates without need for short range binding effects (adhesion). This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and the geometry of the aggregate, which produces toroidal flows. We show that these flows yield attractive horizontal forces between particles. We experimentally observe that many particles demonstrate a collective motion revealing a system which self-assembles, appearing to solve jigsaw-like puzzles on its way to organizing into a large scale disc-like shape, with the effective force increasing as the collective disc radius grows. We overview our modeling and simulation campaign towards understanding this intriguing dynamics, which may play an important role in the formation of particle clusters in lakes and oceans.