UTD Computational Science Seminar (Fall 2014 and Spring 2015)

Spring 2015: All seminars are held on TUESDAY from 12 noon to 1pm in FO 2.702.



Schedule

Date Speaker Affiliation Title Abstract
Apr 28
Matthew Titsworth
UTD
Computational (Multiplicity-Free Semi-Simple K-linear Rigid Monoidal) Category Theory
Fusion and modular categories are ubiquitous in the study of 2+1 and 3+1 dimensional topological phases. They also have an arithmetic description as solutions to systems of so called "pentagon equations" and "hexagon equations." In this talk we will detail an approach for classifying fusion and modular categories of small rank by finding exact solutions to pentagon/hexagon equations and computing invariants to determine equivalence classes. To illustrate the power of this approach we will construct a novel D(S_3) category obtained through these methods.
Apr 21
Scott Cooper,
Kelly Kutach,
Patrick Seaman
Pioneer Natural Resources,
Texas Instruments,
Ole' Media
SIAM Student Chapter
Industry Panel
Flyer [pdf]
Apr 7
Sonny Skaaning
Math, UTD
Base Stock List Price Policy in Continuous Time
Abstract [pdf]
Mar 24
Artur Safin
Math, UTD
Analytic Estimation of Gamma Ray Attenuation in a Cased-Hole Environment
Gamma logging tools provide means of classifying lithology in a borehole, and in particular help distinguish between shale and non-shale formations. One particular limitation of this technique is the lack of flexibility in regards to variations in casing thickness and density. To address this issue, we derive and evaluate an analytic method for estimating the attenuation of gamma ray spectra through cylindrical casing by combining Lambert's law with the Klein-Nishina scattering formula.
Mar 10
Yifei Lou
Math, UTD
A Non-convex Approach for Signal and Image Processing
A fundamental problem in compressed sensing (CS) is to reconstruct a sparse signal under a few linear measurements far less than the physical dimension of the signal. Currently, CS favors incoherent systems, in which any two measurements are as little correlated as possible. In reality, however, many problems are coherent, in which case conventional methods, such as L1 minimization, do not work well. In this talk, a novel non-convex sparsity promoting functional is introduced: the difference of L1 and L2 norms (L1-L2). Efficient minimization algorithms are constructed and analyzed based on the difference of convex function methodology. The resulting DC algorithms (DCA) can be viewed as convergent and stable iterations on top of L1 minimization, hence improving L1 consistently.

Through experiments, we discover that both L1 and L1-L2 obtain better recovery results from more coherent matrices, which appears unknown in theoretical analysis of exact sparse recovery. In addition, numerical studies motivate us to consider a weighted difference model L1-aL2 (a>1) to deal with ill-conditioned matrices when L1-L2 fails to obtain a good solution. An extension of this weighted difference model to image processing will be also discussed, which turns out to be a weighted difference of anisotropic and isotropic total variation (TV), based on the well-known TV model and natural image statistics. Numerical experiments on image denoising, image deblurring, and magnetic resonance imaging (MRI) reconstruction demonstrate that our method improves on the classical TV model consistently, and is on par with representative start-of-the-art methods.
Mar 3
Xun Jia
UTSW
GPU-based high performance computing in medical physics for radiation oncology
Radiation therapy is a form of cancer treatment that utilizes ionizing radiation to kill cancer cells. With the recent advancements in imaging and treatment technologies, high-performance computing plays an increasingly role for the success of modern radiotherapy. In particular, GPU-based computation readily available on the desktop is highly desirable. Not only does its high processing power conquer the computational barriers associated with those novel techniques, the low cost and ease of maintenance also make it suitable for the translations of those techniques to routine clinical practice. This talk will first give an introduction to medical physics in radiation oncology. It will then present a few research topics currently conducted at our group, including 3D/4D cone beam CT reconstruction, treatment plan optimization, and Monte Carlo simulation for radiation transport.
Feb 10
Yannan Shen
Math, UTD
On models of short pulse type in continuous media
We develop a mathematical model for ultra-short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. The fundamental equation in the model is the short-pulse equation (SPE) which will be derived in frequency band gaps. We use a multi-scale ansatz to relate the SPE to the nonlinear Schroedinger equation, thereby characterizing the change of width of the pulse from the ultra short regime to the classical slow varying envelope approximation. We will discuss families of solutions of the SPE in characteristic coordinates, as well as discussing the global wellposedness of generalizations of the model that describe uni- and bi-directional nonlinear waves.
Feb 3
Jameson Graber
International Center for Decision and Risk Analysis, UTD
Mean field games: an introduction
Mean field game theory has been making many advances in the past decade. Its many applications are found in economics and finance, networks and cybersecurity, and even biology. In this presentation we introduce the fundamentals of the theory, starting with an explanation of the two conceptual components--game theory and mean field theory--and then putting them together. We will see how this leads to interesting mathematical models composed of nonlinear partial differential equations, and we will discuss some of the technical tools used to analyze them. Finally, we will present some of latest results on mean field games and make some remarks on open problems.
Jan 27
Sue Minkoff
Math, UTD
SIAM Student Chapter Event
How to write a CV/Resume and Cover Letter
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Dec 5
Andrea Barreiro
Mathematics, SMU
Dynamics and complexity of neural spike correlations
Correlations among neural spike times are found widely in the brain; they can be used to modulate or limit information in population coding, and open the possibility for cooperative coding of sensory inputs across neural populations. Correlations also introduce a daunting complexity; when every neuron is potentially correlated with every other, the amount of information needed to represent spiking activity grows exponentially with the number of cells.

In this talk I discuss recent work towards understanding how the structure and transfer of correlated activity is affected by both intrinsic neuron dynamics and network architecture. I first present an interesting and non-intuitive result about how the phase space structure of neural models - specifically the bifurcation that mediates their transition from rest to firing - affects their ability to transmit common signals. Second, I analyze the ability of pairwise maximum entropy models - a technique borrowed from statistical mechanics for representing spiking activity in a simpler way - to perform on a broad class of feedforward circuits. This study provides an explanation for the surprising finding that responses in primate retinal ganglion cells are well-described by this model, even in cases where the circuit architecture seems likely to create a richer set of outputs (Shlens et al., J Neurosci, 2006; 2009; Schneidman et al., Nature, 2006), and identifies pathways by which specific circuit mechanisms influence the complexity of correlation structure.
Nov 14
Adrianna Gillman
CAAM, Rice
Fast direct solution techniques for elliptic partial differential equations
In many areas of science and engineering, the cost of solving a linear boundary value problem determines what can and ca nnot be modeled computationally. In some cases, it is possible to recast the problem as an integral equation which somet imes leads to a reduction in the dimensionality of the problem. Alternatively, the differential equation can be discretized directly with a finite element or finite difference method. Either way, one is left with having to solve a large linear system. The computational cost of directly inverting the linear system via Gaussian elimination grows as O(N^3) where N is the size of the system. Due to recent developments (multigrid, FMM, FFT, etc.), there are fast methods for most of these linear systems of equations. By fast, we mean that the computational cost of solving the problem grows as O(N log^k N) where k is a small integer, normally k = 0, 1, or 2. Many fast schemes are based on iterative techniques that build a sequence of approximate solutions that converges to the exact solution and often require the use of a problem specific preconditioner. In this talk, we will present methods that directly invert the system by exploiting structure in the matrix with a cost that grows linearly with the problem size. Such fast direct methods are more robust, versatile and stable than iterative schemes. They are also much faster for problems with multiple right-hand sides.
Nov 7
Russell Hewett
Total E&P Research and Technology USA
A polarized-trace solver for the Helmholtz equation
Full-waveform inversion is a method for recovering Earth's physical parameters by matching seismic observations with geophysical simulations. To avoid issues due to nonconvexity in full-waveform inversion, the problem is treated in the frequency domain. Frequency domain imaging requires scalable solvers for the Helmholtz equation to make feasible imaging in high resolution and in 3D, however, this remains an open problem. We present recent developments on a domain-decomposed preconditioner for the acoustic Helmholtz equation, based on the notion of polarization, that demonstrates substantial scalability and performance improvements over the state-of-the-art. I will also introduce PySIT, an open source seismic inversion toolbox written in Python, which is designed for rapid prototyping and reproducible research.
Oct 31
William Frensley
Electrical Engineering, UTD
The Many Levels of Semiconductor Device Physics
I will present a very quick tour of the logical chain that is presumed to exist between fundamental physics and active device technology, showing how the mathematical structures change with physical length scale, and illustrating the behavior at each level with simple numerical solutions and simulations. The macroscopic description consists of a set of partial differential equations. The point to be made is that the the conventional procedure (taking those equations to define a problem in modern analysis and constructing numerical solutions as dictated by asymptotic error analysis) produces a confidence in the results which is entirely unwarranted. Discrete numerical models, constructed by the simplest possible procedures directly from the physical system, come much closer to the true behavior of the device, because the discretization "errors" tend to correct the deficiencies in the macroscopic equations.
Oct 24
Yanping Chen
Mathematical Sciences, UTD
The Boltzmann collision operator for a cylindrically symmetric velocity distribution function in a plasma
We develop a model for collision processes in industrially relevant plasmas. To reduce the computational cost of solving the Maxwell-Boltzmann equations, we assume that the velocity distribution function is cylindrically symmetric in velocity space and only axially dependent in physical space. Then the Boltzmann collision operator is also cylindrically symmetric. If the external force is only axially dependent, the Maxwell-Boltzmann system reduces to a system of equations in two velocity and one spatial dimensions.
Oct 17
Brian Brennan
Mathematics, Baylor U.
Numerical Analysis of a Multi-Physics Model for Trace Gas Sensors
Abstract
Oct 10
Dan Reynolds
Mathematics, SMU
Scalable Algorithms for Multi-physics Simulations: Modeling Cosmological Reionization
Since the scientific revolution, the desire to create realistic models for physical systems has provided a continual stream for mathematical research. With the advent of computing these models have only increased in both accuracy and complexity, enabling detailed study of intricate physical processes. At the same time, however, as these models grow more detailed they increasingly exhaust the limits of classical numerical methods, posing new challenges in computational mathematics research.

In this talk, I will discuss recent research into numerical methods for large scale multi-physics simulations. Within this broad field, our work focuses on scalable algorithms for implicit-time simulations of coupled systems of partial differential equations. We primarily consider systems of nonlinear PDEs, that model physical processes that evolve on significantly different time scales. In this talk we will examine these issues in the context of astrophysical simulations for cosmological reionization within the early universe, although these mathematical issues and methods equally apply to a broad range of computational problems in science and engineering.
Oct 3
Panel Discussion
Mathematical Sciences, UTD
Interactive Engagement in Mathematics Courses
Interactive Engagement is a pedagogical method that promotes conceptual understanding of students using classroom activities that yield immediate feedback through discussion with peers and instructors. A recent NSF-sponsored study has demonstrated the effectiveness of interactive engagement in calculus courses. In this special seminar, a panel of graduate students and faculty will share their experiences employing interactive engagement and related active learning methods in Lectures and Recitation Sections here at UTD.

Graduate student Teaching Assistants and all those teaching freshman and sophomore Mathematics courses are strongly encouraged to attend and participate in the discussion.
Sep 26
Marcio Borges
National Laboratory for Scientific Computing,
Brazil
Markov chain Monte Carlo methods (MCMC) applied to porous media flows
Abstract
Sep 12
Jordan Kaderli
Mathematical Sciences, UTD
Investigation of Microseismic Source Location via Full Waveform Inversion
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Sep 5
Panel of Graduate Students
Mathematical Sciences, UTD
What I did this summer
In the first Computational Science Seminar of the year, several mathematics and statistics graduate students will share their experiences doing an internship or attending a conference or workshop this summer. Students will talk about the application process, what they did, and what they learned from their experience. You are encouraged to ask questions and also to share your own experiences.