Mathematical Sciences

School of Natural Sciences & Mathematics

Computational Science Seminar S15

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
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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 state-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
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