Seminars & Colloquia
Samuel S. Wu
University of Florida
Thursday,October 20, 2016
Title: Privacy-preserving Data Collection Techniques for Clinical Trials
Abstract: A major obstacle that hinders medical and social research is the lack of reliable data due to people's reluctance to reveal condential information to strangers. Fortunately, most statistical inference always targets a well dened population rather than a particular individual subject and, in many current applications, data can be collected using a web-based system or other mobile devices. These two characteristics enable us to develop new data collection methods with strong privacy protection. These new technologies hold the promise of removing trust obstacle, promoting objective data collection, allowing rapid data dissemination, and helping unrestricted sharing of big data.
The new methods ensure that the raw data stay with research participants and only masked data are collected, which can be distributed and shared freely. The new method guarantees that the masked data will still be analyzable by standard statistical methods. A critical feature of the method is that the keys to generate the masking matrices are held separately,which ensures that nobody sees the actual data. Also, because of the specially designed transformations, statistical inference on parameters of interest can be conducted with the same results as if the original data were used, hence the new method hides sensitive data with no efficiency loss and improves over Warner's randomized response technique. In addition, we will present some variations of the method and their properties regarding data quality assurance, data security, and missing data imputation.
St. Lawrence University
Thursday, October 13, 2106
Title: Are ascidians taking over the world: the biology and distribution of an invasive species
Abstract: Recent marine invasive species have included colonial ascidians, a group of invertebrates (Phylum Chordata) that reproduce sexually and asexually, have fast growth, and maintain freedom from predation in newly settled habitats. The ascidian species Didemnum vexillum, native to Japan, is found worldwide in temperate marine environments. In 2005, a survey of Narragansett Bay indicated that this species preferred manmade habitat in higher salinity environment. A follow-up survey was conducted 10 years later to determine the extent of D. vexillum presence and to determine the mechanism of its spread locally, using microsatellite data. I will share preliminary observations from the 2015 survey and discuss research on the impacts of this invasive species on native mussels
Friday, September 30, 2016
Title: Does body composition vary between individuals of different gender/ethnicity?
Abstract: Obesity is becoming a worldwide epidemic. It is well known that many disease risks, such as insulin resistance and heart disease, are directly linked to obesity. Further, some studies suggest that certain ethnic groups, as well as gender groups, are more prone to develop these diseases than others. The four ethnic groups specific to our study are: Aboriginal, Chinese, European, and South Asian populations.We parameterize an existing mathematical model of body composition change according to ethnicity and gender and determine that differences in body composition exist between the various ethnic/gender groups. Here, we pay special attention to visceral adipose tissue (VAT), the type of fat accumulation that has been linked to insulin resistance within various ethnic groups. We interpret our results in a biological sense, in the hopes that they can be used clinically to help individuals attain a healthy body weight.
Tuesday, March 1, 2016
Title:Mathematical and Computational Modeling of a Swimming Lamprey with Sensory Feedbac
Abstract: The swimming of a simple vertebrate, the lamprey, can shed light on how a flexible body can couple with a fluid environment to swim rapidly and efficiently. Animals use stretch-receptor information to sense how their bodies are bending (proprioception), and then adjust the neural signals to their muscles to improve performance. I will present recent progress in the development of a computational model of a lamprey swimming in a viscous, incompressible fluid where a simple central pattern generator model, based on phase oscillators, is coupled to the evolving body dynamics of the swimmer through curvature feedback. The system is numerically simulated using the immersed boundary method. I will examine how the emergent swimming behavior and cost of transport depends upon these functional forms of proprioceptive feedback chosen in the model, as well as discuss future directions.
Arizona State University
Friday, Febrary 19,2016
Title:Cell Migration in Wound Healing: Modeling and Analysis
Abstract: Collective cell migration plays a substantial role in maintaining the cohesion of cell layers in the context of wound healing, embryonic development, and the progression of cancer. Disruption of cell migration can cause diseases such as necrotizing enterocolitis, an intestinal inflammatory disease that is a major cause of death in premature infants. We extend a mathematical model of cell layer migration during experimental necrotizing enterocolitis based on an assumption of elastic deformation of the cell layer that leads to a generalized Stefan problem. Analysis and numerical results indicate that a large class of constitutive equations for the dependence of cell proliferation on stretch leads to traveling wave solutions with constant wave speed. In the case where there is no cell proliferation, we prove the existence and uniqueness of similarity under scaling solutions using Wazewski’s Principle.
University of Califoria, Santa Barbara
Friday, February 05, 2016
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
Tuesday, February 02,2016
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.
University of Alberta
Thursday, January 28, 2106
Title: Mathematical Modelling of Biological Systems: Microtubule Pattern Formation and Drug metabolism in the liver
Abstact: 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.
Daniel B. Larremore
Santa Fe Institute
Thursday, November 12,2015
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.
Professor of Mathematics
at University of Central Florida
Thursday, November 5, 2015
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
SC 356 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.