Department of Mathematics, Colorado State University
Mathematical Modeling for Virus: HIV-1 and 2019-nCoV
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
Department of Mathematical Sciences, Carnegie Mellon University
Long time behaviors of a nonlinear stochastic heat equation in d ≥ 3
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
Biostatistics and Informatics, Colorado School of Public Health,
University of Colorado Denver
Studying Complex Diseases Using Integrative -Omics and Network Approaches
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.
Max-Planck Institute for Complex Systems, Dresden, Germany
Infinite densities, and the Moses/Noah/Joseph effects in anomalous diffusion
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.
Department of Mathemtics, University of North Carolina at Chapel Hill
Cluster formation and self-assembly in stratified fluids: a novel mechanism for particulate aggregation
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.