Tuesdays at 4:10 in Carver 268 unless otherwise noted. |
| For more information, contact Tathagata Basak Hien Nguyen |
Spring 2012
Thursday, February 23 at 4:10 in 298 Carver- Jessica Conway (University of British Columbia) HIV treatments for infection prevention: Stochastic Model Predictions
Host: Zhijun Wu (Math Bio job candidate) Abstract Poster
Monday, February 27 at 4:10 in 282 Carver - Marissa Eisenberg (MBI/Ohio State) Exploring cholera transmission dynamics using identifiability and parameter estimation
Host: Alex Roitershtein (Math Bio job candidate) Abstract Poster
Friday, March 2 at 3:10 in 298 Carver - Alan Veliz-Cuba (University of Nebraska) An algebraic approach to reverse engineering discrete and continuous models of biological systems
Host: Steve Willson (Math Bio job candidate) Abstract Poster
March 6 - Michelle Cirillo (University of Delaware) Powerful and productive mathematics discourse
Host: Heather Bolles/CEUME Abstract Poster
March 20 - Jon Peterson (Purdue) Host; Alex Roitershtein
March 27 - David Radford (University of Illinois at Chicago) host: Richard Ng
April 3 - Lu Wang (Johns Hopkins) Host: Hien Nguyen
April 10 - Holly Swisher (Oregon State University) Host: Ling Long
April 17 - Mahamadi Warma (University of Puerto Rico-Rio Piedras) Dirichlet and Neumann boundary conditions for the p-laplace operator: What is in between?
Host: Paul Sacks Abstract Poster
April 24 - Lexing Ying (University of Texas - Austin) Host: Hailiang Liu
September 27 (Thursday) - Fan Chung Graham () Host: Leslie Hogben
Abstracts
Michelle Cirillo (University of Delaware) Powerful and productive mathematics discourse
This talk provides an overview of research on mathematics classroom discourse. More specifi cally, the presenter will share highlights from research related to typical classroom interaction patterns in contrast to mathematics discourse that is more powerful and productive. Data from an Introduction to Proof course as well as video that highlights the discourse of what “doing mathematics” looks like amongst mathematicians will be presented to consider how purposeful attention to discourse can impact student learning. The infl uence of mathematics tasks and context will also be discussed. The talk will conclude with a look towards how mathematics classroom discourse can be more powerful and productive when purposeful attention is paid to its facilitation.
Mahamadi Warma (University of Puerto Rico-Rio Piedras) Dirichlet and Neumann boundary conditions for the p-laplace operator: What is in between?
Alan Veliz-Cuba (University of Nebraska) An algebraic approach to reverse engineering discrete and continuous models of biological systems
Discrete models have been used successfully in modeling biological systems such as gene regulatory networks. When certain regulation mechanisms are unknown it is important to be able to identify the best model with the available data. In this context, reverse engineering of discrete dynamical systems from partial information is an important problem. We will present a framework and algorithm to reverse-engineer the possible wiring diagrams of a discrete model from data. The algorithm consists on using an ideal of polynomials to encode all possible wiring diagrams, and choose those that are minimal using the primary decomposition. We will also show that these results can be applied to reverse-engineer continuous models.
Marissa Eisenberg (MBI/Ohio State) Exploring cholera transmission dynamics using identifiability and parameter estimation
Waterborne diseases cause over 3.5 million deaths annually, with cholera alone responsible for 3-5 million cases/year and over 100,000 deaths/year. Many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. One question of interest is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine these issues by exploring the identifiability and parameter estimation of a differential equation model of waterborne disease transmission dynamics. We use a novel differential algebra approach together with several numerical approaches to examine the theoretical and practical identifiability of a waterborne disease model and establish if it is possible to determine the transmission rates from outbreak case data (i.e. whether the transmission rates are identifiable). Our results show that both direct and environmental transmission routes are identifiable, though they become practically unidentifiable with fast water dynamics. Adding measurements of pathogen shedding or water concentration can improve identifiability and allow more accurate estimation of waterborne transmission parameters, as well as the basic reproduction number. Parameter estimation for a recent outbreak in Angola suggests that both transmission routes are needed to explain the observed cholera dynamics. I will also discuss some ongoing applications to the current cholera outbreak in Haiti.
Jessica Conway (University of British Columbia) HIV treatments for infection prevention: Stochastic Model Predictions
Drug treatments for HIV very effectively control infection. They can also be used to prevent the initiation of HIV infection, either in advance of risky exposure (termed pre-exposure prophylaxis, PrEP), or very shortly after accidental exposure to the virus (termed post-exposure prophylaxis, PEP). To investigate this use of HIV treatments, we developed a multi-type, continuous-time branching process model of the early stages of HIV infection within- host. We numerically extract probability distributions and extinction probabilities for viral-load from equations for the probability generating function, derived from the related Chapman-Kolmogorov equation. Using our model we can make predictions regarding the efficacy of PrEP and PEP depending on factors such as drug type, post-exposure initiation time, and duration of treatment.
Zhisheng Shuai (University of Victoria) Dynamical systems on networks and their applications to ecology and epidemiology
Coupled systems on networks can be used to describe many large-scale dynamical systems arising from different fields of science and engineering. Examples include biological and artificial neural networks, nonlinear oscillators on lattices, complex ecosystems and the transmission models of infectious diseases in heterogeneous populations. A new systematic approach, based on Kirchhoff's Matrix Tree Theorem from graph theory, is developed to guide the constructions of Lyapunov functions for coupled systems on networks. This graph-theoretic approach is applied to investigate global stability problems for several coupled systems in engineering, mathematical ecology, and mathematical epidemiology. The approach allows improvement of existing results in the literature and, particularly, resolution of a 30-year open problem in mathematical epidemiology.
During the second half of this talk, the graph-theoretic approach is further applied to a cholera model with differential infectivity. Cholera is a bacterial disease that can be transmitted to humans directly by person-to-person contact or indirectly via the environment (mainly contaminated water). A compartmental model for cholera dynamics is formulated that includes these two transmission pathways with nonlinear incidence, as well as stages of infection and infectivity states of the pathogen. Lyapunov functions and the graph-theoretic approach are used in the model analysis to show that a basic reproduction number gives a sharp threshold determining whether cholera dies out or becomes endemic.
Yulia Hristova (UM/IMA) Some inverse problems in computerized tomography
Computerized tomography (CT) is the name of a class of non-invasive imaging techniques in which the interior structure of an object is computed from external measurements. In order to recover an image of the interior one typically needs to solve an inverse problem.
While a number of CT methods are well studied and widely used (e.g. X-ray CT, MRI), new technologies are being developed with the aim to overcome the limitations of the existing ones.
In this talk I will give a brief overview of some of the mathematical ideas
behind tomography and I will discuss several novel imaging techniques and
the associated mathematics. Applications of these to medical imaging and
national security will be presented.
James Rossmanith (UW-Madison) Computationial methods for fluid and kinetic models of collisionless plasma
Plasma is a state of matter in which electrons have dissociated from their nuclei, thus resulting in an ionized gas. Such ionized gases appear in variety of applications including in astrophysics, space physics, as well as in laboratory settings such as in magnetically confined fusion. Modeling and understanding the basic phenomenon in plasma has long been a topic in scientific computing, yet many problems remain far too numerically intensive for modern computers. The main difficulty is that plasma phenomena span a wide range of spatial and temporal scales, requiring modeling tools from both fluid and kinetic theory.
In this work I will present an overview of my work on developing high-order discontinuous Galerkin schemes for a variety of models of collisionless plasma. I will begin with fluid models of plasma, and describe numerical discretizations of the ideal magnetohydrodynamic, 5-momemt Euler-Maxwell, and 10-moment Euler-Maxwell systems. In particular, I will discuss the delicate issue of entropy stability and how this influences the finite dimensional approximation spaces in discontinuous Galerkin finite element schemes.
Next I will move to kinetic models of plasma; and in particular, numerical methods for the Vlasov-Poisson system. Important aspects of this work include positivity preservation and high-order accuracy in time.
I will conclude with a brief description of future work, including efforts to develop multiscale numerical discretizations.
Songting Luo (Michigan State) Computational wave propagation at large scales and nano scales
In this talk, I will report two projects related to wave propagation. One is the high frequency wave propagation at large scales, e.g., seismic wave propagation. A new efficient and accurate numerical method based on Geometrical Optics and Huygens Principle will be presented to construct the wave fields, which is verified by numerical examples. Another one is concerned with the scattering problems with the size of the scatter at nano scale. Both the wavefield and the quantum mechanics of the scatter must be considered simultaneously to study the nano optical responses. A linear system to study the nano optical response by combining the semi-classical theory and Time-Dependent Density Functional Theory will be derived and solved with a multiscale scheme. Model calculations will be presented.
Li Tian (Penn State) Adaptive finite element method for Peridynamic models
Peridynamics is a continuum mechanics based on integral equations for nonlocal material modeling. It extends the classical continuum mechanics by allowing long-range forces, therefore can be used to describe deformations with discontinuities like fractures and cracks.
Peridynamics is also an effective alternative of molecular dynamics, with lower computational cost. One of the speaker's current research areas is the adaptive finite element method(FEM) for such nonlocal problems, since large error may arise around discontinuities during numerical approximations.
In this presentation, the speaker will first give a brief introduction to the peridynamic theory, as well as the finite element discretization and error analysis for peridynamic constrained-value problem. Then the speaker will present the a posteriori error analysis for the nonlocal diffusion problem, which is the scalar version of the general peridynamic model. Based on the nonlocal a posteriori error analysis, a convergent adaptive FEM is derived for the model problem, which means we do get reduced numerical error by using adaptive refinement. Various numerical experiment will be presented to support the theoretical conclusions.
Irvin Hentzel (ISU) How to win at Farkle
FARKLE is a dice game which has been around since World War II and is currently played on Face Book. The players throw dice, and earn points when certain patterns appear like three of a kind, or three pairs. The player continues throwing and saving out valued combinations. If he managed to use all six dice, he gets another turn. If he makes a throw that has no value at all, he loses all the points accumulated so far during the turn. To play successfully, one must make decisions based on the expected value of the possible actions. I have computed the expected values and use these to explain a good strategy for play. Since there are many versions of FARKLE, the program can be easily modified for various changes in the point scoring values. But some of the more exotic rules like instant win for throwing 6 ones is not covered.
I am indebted to Mark Hunacek for his class notes for 104 which give the Face Book rules as well as probabilities for throwing a valueless hand. He is also a great person to talk about FARKLE with.
Archived
August 30 - Steve Butler (ISU) Generalizations of Apollonian circle packings Abstract Poster
September 6 - Adrian Jenkins (ISU) Normal forms for analytic functions in complex and p-adic dynamics Abstract Poster
September 13- Anita Layton (Duke) A mathematical model of the myogenic response of the rat afferent arteriole Host: Jue Yan Abstract Poster
September 20 - Leslie Hogben and others (ISU) These are your NFS Mathematics Institutes - Use them! Abstract Poster
September 27- Nic Lanchier (Arizona State) Two-strategy games on the lattice Host: Zhijun Wu Abstract Poster
October 4- Yuan Lou (Ohio State) Evolution of dispersal Host: Zhijun Wu Abstract Poster
October 11 - Benton Duncan (NDSU) Operator algebras and topological dynamics Host: J. Peters Abstract Poster
October 18 - Bin Zhang (Sichuan U) Cone multiple zeta values, Shintani multiple zeta values and their double subdivision Host: R. Ng Abstract Poster
October 25 - Jianqiang Zhao (Eckerd College) Non-standard relations of multiple polylog values at roots of unity Host: Ling Long Abstract Poster
November 15 - Chihoon Lee (Colorado State) Some stability properties of a reflected fractional Brownian motion on the positive orthant Host: Ananda Weerasinghe Abstract Poster
January 31 - Irvin Hentzel (ISU) How to win at Farkle Abstract Poster
February 7 - Li Tian (Penn State) Adaptive finite element method for Peridynamic models Host: Hailiang Liu Abstract Poster (Comp Math job candidate)
Friday, February 10 in Carver 294 at 2:10 p.m. - Songting Luo (Michigan State) Computational wave propagation at large scales and nano scales Host: Fritz Keinert Abstract Poster (Comp Math job candidate)
February 14 - James Rossmanith (UW-Madison) Computationial methods for fluid and kinetic models of collisionless plasma
Host: Jue Yan Abstract Poster (Comp Math job candidate)
Thursday, February 16 at 3:10 in 401 Carver- Yulia Hristova (UM/IMA) Some inverse problems in computerized tomography
Host: Glenn Luecke Abstract Poster (Comp Math job candidate)
Monday, February 20 at 4:10 in 282 Carver - Zhisheng Shuai (University of Victoria) Dynamical systems on networks and their applications to ecology and epidemiology
Host: Mike Smiley (Math Bio job candidate) Abstract Poster
Steve Butler (ISU) Generalizations of Apollonian circle packings
Three mutually tangent circles in the plane bound two curvilinear triangles, or holes. In each of the triangles we can insert a new circle which is tangent to all sides of the hole, and in the process create new holes. Repeating this insertion of a circle into each hole will produce the Apollonian gasket, one of the most famous examples of a circle packing. However, there is more than one way to fill a hole, and different methods lead to different types of packings. We will discuss some of these different variations, and in
particular show how to find the smallest field associated with a given packing.
Adrian Jenkins (ISU) Normal forms for analytic functions in complex and p-adic dynamics
In studying dynamical systems, it is often useful to reduce functions to a simpler form via conjugation. In complex analysis, this problem is well over 100 years old. By comparison, its p-adic analogue is relatively new. We will look at some results in both the complex and p-adic category, drawing comparisons where appropriate. We will look at both one variable functions, and well as some several-variable analogues. New results and open problems will be discussed.
Anita Layton (Duke) A mathematical model of the myogenic response of the rat afferent
arteriole
We have formulated a mathematical model of the rat afferent arteriole (AA). Our model consists of a series of arteriolar smooth muscle cells, each of which represents ion transport, cell membrane potential, cellular contraction, gap junction coupling, and wall mechanics. Blood flow through the AA lumen is described by Poiseuille flow. Model results suggest that interacting calcium and potassium fluxes, mediated by voltage-gated and voltage-calcium-gated channels, respectively, give rise to periodic oscillations in cytoplasmic calcium concentration, myosin light chain phosphorylation, and crossbridge formation with attending muscle stress mediating vasomotion. The AA model's representation of the myogenic response is based on the hypothesis that the voltage dependence of calcium channel openings responds to transmural pressure so that vessel diameter decreases with increasing pressure. With this configuration, the results of the AA model simulations agree well with findings in the experimental literature, notably those of Steinhausen et al. (J Physiol 505:493, 1997), which indicated that propagated vasoconstrictive response induced by local electrical stimulation decayed more rapidly in the upstream than in the downstream flow direction. The model can be incorporated into models of integrated renal hemodynamic regulation. This research was supported in part by NIH grants DK-42091 and DK-89066, and by NSF grant DMS-0715021
Leslie Hogben and others (ISU) These are your NFS Mathematics Institutes - Use them!
Abstract: I will demonstrate the institutes' webpages then we will have a speaker (5 min) for each of the following:
American Institute of Mathematics (AIM),
Institute for Advanced Study (IAS),
Institute for Computational and Experimental Mathematics (ICERM)
Institute for Mathematics and its Applications (IMA),
Institute for Pure and Applied Mathematics (IPAM),
Mathematical Biosciences Institute (MBI),
Mathematical Sciences Research Institute (MSRI),
Statistical and Applied Mathematical Sciences Institute (SAMSI)
Other mathematics institutes such as BIRS, Oberwolfach, DIMACS, etc. for which there is a volunteer will also be included.
Programs for faculty and graduate students offered by each institute will be described briefly by a faculty member with experience at that institute. Links to the pages of all the institutes can be found at http://mathinstitutes.org/.
Nic Lanchier (Arizona State) Two-strategy games on the lattice
In the seventies, biologists Maynard Smith and Price used concepts from game theory to describe animal conflicts. Their work is the origin of the popular framework known today as evolutionary game theory. Space is another component that has been identified as a key factor in how ecological communities are shaped. Spatial game models or games involving graphs - AMS classification 91A43 - are therefore of primary interest for biologists but also sociologists and economists. There is however a lack of analytical results in this field. The objective of this talk is to explore the framework analytically through a simple spatial game process based on the voter model. Our results indicate that the behavior of this process strongly differs from the one of its non-spatial mean-field approximation, which reveals the importance of space in game theoretic interactions.
Yuan Lou (Ohio State) Evolutionary of dispersal
A general question in the study of the evolution of dispersal is what kind of dispersal strategies can convey competitive advantages and thus will evolve. We mainly focus on a reaction-diffusion-advection model for two competing species, in which the species are assumed to have the same population dynamics but different dispersal strategies. We found a conditional dispersal strategy which results in the ideal free distribution of species, and we investigate whether such dispersal strategy is evolutionarily stable. Discrete and nonlocal dispersal models will also be discussed.
Benton Duncan (NDSU) Operator algebras and topological dynamics
Bin Zhang (Sichuan U) Cone multiple zeta values, Shintani multiple zeta values and their double subdivision
Jianqiang Zhao (Eckerd College) Non-standard relations of multiple polylog values at roots of unity
In this talk I'll survey recent results on the relations among the multiple polylog values at roots of unity. The primary tool is the motivic theory of these numbers established by Delign, Racinet and many others. Computations show that the standard relations coming from the regularized double shuffle relations, weight one relations, distribution relations don't provide all the possible relations. However, it is conjectured that mixed pentagon relations and octahedral relations should suffice. Some evidence of this will be given at the end of the talk.
Chihoon Lee (Colorado State) Some stability properties of a reflected fractional Brownian motion on the positive orthant
We consider a multidimensional reflected fractional Brownian motion process (rfBm) on the positive orthant with drift and Hurst parameter 1/2<H<1. Under a natural stability condition on the drift vector and reflection directions, we show uniform return time results to some compact sets hold. Also, under slightly stronger stability assumptions, we establish a geometric drift towards a compact set for the 1-skeleton rfBm chain. These results can be viewed as steps towards the further analysis of rfBm with the aim of establishing recurrent properties for reflected processes driven by non Markovian processes. Motivation for this study is that rfBm appears as a limiting workload process for fluid queueing network models fed by a large number of heavy tailed ON/OFF sources in heavy traffic.
Jonas Kibelbek (ISU)
Using power series expansions of differential forms on a curve, we can construct the formal group of the Jacobian of the curve, which encodes arithmetic information about the curve and is related to some space of weight 2 modular forms (often for a noncongruence subgroup of SL_2(Z)). We will carry out this construction explicitly for the Fermat curves and derive several congruences for binomial coefficients, including p-adic limits for Jacobi sums, generalizing a result of Katz.