Seminars & Colloquia
Title:Discovery of Dynamically-Coherent Structures as a Manifold Learning Problem
Abstract: In oceans and in the atmosphere, coherent structures are regions in which the advected material, such as spilled oil or pollen, does not get dispersed by the flow. When the model equations are not known or accessible and trajectories of the advected particles are complicated curves, it is often difficult to detect such regions from simulated data. There are several currently-used definitions of the coherent structures and, consequently, algorithms to detect them. In this talk, two ways of measuring “coherence” between trajectories will be presented. We represent available data by a high-dimensional geometric graph: trajectories are vertices and “coherence” is the length of edges. This setup allows us to formulate detection of the coherent structures as a manifold-learning problem. We solve it using the Diffusion Maps algorithm, which detects coarse regularities inside the graph and allows us to visualize coherent structures
Ihsan Topaloglu Indiana University Tuesday, February 02,2016 2:00pm SC362
Title:Regularization and Covergence of Nonlocal Interaction Energies and their Gradient Flows
Abstract: A variety of physical and biological processes – from self-assembly of nano particles to collective behavior of many-agent systems such as biological swarming – can be modeled by an aggregation equation where particles self-assemble to minimize a nonlocal interaction energy. In general, these energies are neither convex nor differentiable, placing them outside the scope of most existing results on energy minimization and gradient flows.
In this talk, I will present on my recent work with Katy Craig, in which we restore convexity and differentiability by regularization of interaction kernels and prove that the regularized energies Gamma-converge to the original energy. This allows us to recover not only the minimizers but also the gradient flow of these singular energies as limits of the well-understood convex case. Our study also provides a first step in understanding the connection between the gradient flows of non-convex interaction energies and the aggregation equation via a singular perturbation approach.
Diana White University of Alberta Thursday, January 28, 2106 2:30 PM Location: TBA
Title: Mathematical Modelling of Biological Systems: Microtubule Pattern Formation and Drug metabolism in the liver
Abbstact: Diana will present work on two separate projects. First, she will present a novel non-local transport partial differential equation model which describes how microtubules(MTs) organize as they interact with motor proteins. MTs, whose organization is crucial for normal cellular development, are rigid protein polymers that have been found to organize into various patterns in vitro and in vivo, through their interactions with motor proteins. Such in vitro patterns include vortices, asters, and bundles. Numerical simulations of our model reveal persistent MT patterns, comparable to those observed in an in vitro setting. Next, she will present a computational approach that she developed to describe blood and drug flow within a liver, as well as drug metabolism. Understanding how drugs and toxins are metabolized and eliminated from the liver is not only crucial for understanding normal liver function, but can also provide useful insight into drug discovery for cancers and other diseases.
Title:Networks and the evolution of malaria's virulence in humans and apes
Abstract: Despite extensive research and public health efforts, there remain hundreds of millions of malaria cases annually, causing over half a million deaths, mostly children. Key to malaria's ongoing transmission is the fact that humans develop only a weak immunity, stemming from the parasite’s evasion of the immune system by sequential expression of camouflage-like proteins on the surface of infected red blood cells. The genetic variation within the camouflage-encoding var genes is sufficiently high dimensional that immunity to a single camouflage variant doesn't hinder future infections. What’s more, each parasite genome contains ~60 different var genes, which rapidly recombine, precluding the use of traditional phylogenetic techniques. I will present a series of investigations to understand the key mechanisms and constraints underlying the ongoing evolution of var genes.
We first developed a framework capable of mapping rapidly recombining genes to networks in which evolutionary constraints are revealed in large-scale network structures. Applying this approach to multiple genomes, we identified the parts of the camouflage proteins that evolve differently than others. To improve the quality of network community detection, we developed a bipartite stochastic block model using maximum likelihood-based inference, and then applied it to an expanded data set including var genes from ape-infecting malaria parasites. This revealed the deep origins of the malaria parasite's current immune evasion strategy, which evolved tens of millions of years ago in an ancient ancestor of extant malaria species. This frames the current adaptive struggle in humans in a broader evolutionary context, with implications for parasite population genetics as malaria prevention efforts shift toward elimination. It also begs for the continued development of principled network-based mathematical models to answer open biological questions.Qiyu Sun Professor of Mathematics at University of Central Florida Thursday, November 5, 2015 4:00PM SC356
Title:Wiener's Lemma for matrices and its applications to sampling
Abstract: The classical Wiener's lemma states that a periodic function with an absolutely convergent Fourier series, which vanishes nowhere on the real line, has Fourier series of its reciprocal being absolutely convergent. In this talk, I will discuss Wiener's lemma to localized matrices, and its applications to sampling theory for spatially distributed system.
Professor and Chair
Thursday, October 22, 2015
Title:Moving Neighborhood Networks: The dynamic topology of communicating agent
Abstract: This talk will consider the dynamic "social" network that arises when mobile agents are able to communicate only locally. We consider a number of different models of such behavior and demonstrate the natural applicability in such settings as coordinated behaviors and epidemiology. By use a model of coupled chaotic oscillators as a "probe" to better understand the effect of the spatial dynamics as in impacts the underlying communication characteristics of the resultant social network.