Talk_id  Date  Speaker  Title 
14373

Friday 8/24 4:10 PM

Hyenkyun Woo, Korea University of Technology & Education

Bregmandivergence for Legendre exponential families and data analysis
 Hyenkyun Woo, Korea University of Technology & Education
 Bregmandivergence for Legendre exponential families and data analysis
 08/24/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
Bregmandivergence is a wellknown generalized distance framework in various applications, such as machine learning and image processing. In this talk, by using dual structure of the Bregmandivergence associated with the subclass of convex function of Legendre function, we analyze the structure of the Legendre exponential families whose cumulant function corresponds to the conjugate convex function of Legendre type. Actually, Legendre exponential families are the extended version of the regular exponential families to include nonregular exponential families, such as the inverse Gaussian distribution. The main advantage of the proposed Bregmandivergencebased approach is that it offers systematic successive approximation tools to handle closed domain issues arising in nonregular exponential families and the statistical distribution having discrete random variables, such as Bernoulli distribution and Poisson distribution. In addition, we also introduce the generalized centerbased clustering algorithm based on the Tweedie distribution.

14375

Friday 8/31 4:10 PM

Gerard Awanou, University of Illinois, Chicago

Discrete Aleksandrov solutions of the MongeAmpere equation
 Gerard Awanou, University of Illinois, Chicago
 Discrete Aleksandrov solutions of the MongeAmpere equation
 08/31/2018
 4:10 PM  5:00 PM
 1502 Engineering Building
A discrete analogue of the Dirichlet problem of the Aleksandrov theory of the MongeAmere equation is derived in this paper. The discrete solution is not required to be convex, but only discrete convex in the sense of Oberman. We prove that the uniform limit on compact subsets of discrete convex functions which are uniformly bounded and which interpolate the Dirichlet boundary data is a continuous convex function which satisfies the boundary condition strongly. The domain of the solution needs not be uniformly convex. We obtain the first proof of convergence of a wide stencil finite difference scheme to the Aleksandrov solution of the elliptic MongeAmpere equation when the right hand side is a sum of Dirac masses. The discrete scheme we analyze for the Dirichlet problem, when coupled with a discretization of the second boundary condition, as proposed by Benamou and Froese, can be used to get a good initial guess for geometric methods solving optimal transport between two measures.

14378

Friday 9/7 4:10 PM

Tom Needham, Ohio State University

GromovMonge Quasimetrics and Distance Distributions
 Tom Needham, Ohio State University
 GromovMonge Quasimetrics and Distance Distributions
 09/07/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
In applications in computer graphics and computational anatomy, one seeks measurepreserving maps between shapes which preserve geometry as much as possible. Inspired by this, we define a distance between arbitrary compact metric measure spaces by blending the Monge formulation of optimal transport with the GromovHausdorff construction. We show that the resulting distance is an extended quasimetric on the space of compact mmspaces, which has convenient lower bounds defined in terms of distance distributions. We provide rigorous results on the effectiveness of these lower bounds when restricted to simple classes of mmspaces such as metric graphs or plane curves.This is joint work with Facundo Mémoli.

14376

Friday 9/14 4:10 PM

Dongwook Lee, University of California, Santa Cruz

New Polynomialfree, Variable Highorder Methods using Gaussian Process Modeling for CFD
 Dongwook Lee, University of California, Santa Cruz
 New Polynomialfree, Variable Highorder Methods using Gaussian Process Modeling for CFD
 09/14/2018
 4:10 PM  5:00 PM
 1502 Engineering Building
In this talk, an entirely new class of highorder numerical algorithms for computational fluid dynamics is introduced. The new method is based on the Gaussian Processes (GP) modeling that generalizes the Gaussian probability distribution. The new approach is to adopt the idea of the GP prediction technique which utilizes the covariance kernel functions and use it to interpolate and/or reconstruct highorder approximations for computational fluid dynamics simulations. The new GP highorder method is proposed as a new numerical highorder formulation in finite difference and finite volume frameworks, alternative to the conventional polynomialbased approaches.

15445

Friday 10/19 4:10 PM

Paul Bendich, Duke University and Geometric Data Analytics

Topology and Geometry for Tracking and Sensor Fusion
 Paul Bendich, Duke University and Geometric Data Analytics
 Topology and Geometry for Tracking and Sensor Fusion
 10/19/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
Many systems employ sensors to interpret the environment. The targettracking task is to gather sensor data from the environment and then to partition these data into tracks that are produced by the same target. The goal of sensor fusion is to gather data from a heterogeneous collection of sensors (e.g, audio and video) and fuse them together in a way that enriches the performance of the sensor network at some task of interest.
This talk summarizes two recent efforts that incorporate mildly sophisticated mathematics into the general sensor arena.
First, a key problem in tracking is to 'connect the dots:' more precisely, to take a piece of sensor data at a given time and associate it with a previouslyexisting track (or to declare that this is a new object). We use topological data analysis (TDA) to form dataassociation likelihood scores, and integrate these scores into a wellrespected algorithm called Multiple Hypothesis Tracking. Tests on simulated data show that the TDA adds significant value over baseline, especially in the context of noisy sensor data.
Second, we propose a very general and entirely unsupervised sensor fusion pipeline that uses recent techniques from diffusion geometry and wavelet theory to fuse time series of arbitrary dimension arising from disparate sensor modalities. The goal of the pipeline is to differentiate classes of timeordered behavior sequences, and we demonstrate its performance on a wellstudied digit sequence database.
This talk represents joint work with many people. including Chris Tralie, Nathan Borggren, Sang Chin, Jesse Clarke, Jonathan deSena, John Harer, Jay Hineman, Elizabeth Munch, Andrew Newman, Alex Pieloch, David Porter, David Rouse, Nate Strawn, Adam Watkins, Michael Williams, and Peter Zulch.

16449

Friday 10/26 4:10 PM

Akil Narayan, University of Utah

Sampling techniques for building computational emulators and highdimensional approximation
 Akil Narayan, University of Utah
 Sampling techniques for building computational emulators and highdimensional approximation
 10/26/2018
 4:10 PM  5:00 PM
 1502 Engineering Building
We present an overview of techniques for building mathematical emulators of parametrized scientific models. We will primarily discuss forward emulation, where one seeks to predict the output of a model given a parametric input. We will emphasize methods that boast stability, accuracy, and computational efficiency. The focus will be on emulators built from nonadapted polynomials, and time permitting we will also explore adapted approximations and reduced order modeling. The talk will highlight some recent notable advances made in the field of building emulators from sample data, and will identify frontiers where mathematical or computational advances are needed.

15448

Friday 11/9 4:10 PM

Wenrui Hao, Pennsylvania State University

Computational modeling for cardiovascular risk evaluation
 Wenrui Hao, Pennsylvania State University
 Computational modeling for cardiovascular risk evaluation
 11/09/2018
 4:10 PM  5:00 PM
 1502 Engineering Building
Atherosclerosis, the leading cause of death in the United State, is a disease in which a plaque builds up inside the arteries. The LDL and HDL concentrations in the blood are commonly used to predict the risk factor for plaque growth. In this talk, I will describe a recent mathematical model that predicts the plaque formation by using the combined levels of (LDL, HDL) in the blood. The model is given by a system of partial differential equations within the plaque with a free boundary. This model is used to explore some drugs of regression of a plaque in mice, and suggest that such drugs as used for mice may also slow plaque growth in humans. Some mathematical questions, inspired by this model, will also be discussed. I will also mention briefly some related projects about abdominal aortic aneurysm (AAA) and red blood cell aggregation, which would have some potential blood biomarkers for diagnosis of AAA.

15446

Friday 11/16 4:10 PM

Jun Song, University of Illinois at UrbanaChampaign

Spectral and Statistical Analyses of Nucleosome Positioning: New Answers to Old Questions
 Jun Song, University of Illinois at UrbanaChampaign
 Spectral and Statistical Analyses of Nucleosome Positioning: New Answers to Old Questions
 11/16/2018
 4:10 PM  5:00 PM
 C304 Wells Hall
Nucleosomes form the fundamental building blocks of eukaryotic
chromatin, and previous attempts to understand the principles
governing their genomewide distribution have spurred much interest
and debate in biology. In particular, the precise role of DNA sequence
in shaping local chromatin structure has been controversial.
In this talk, I will described categorical spectral analysis methods
and statistical physics approaches for rigorously quantifying the
contribution of hithertodebated sequence features to three
distinct aspects of genomewide nucleosome landscape: occupancy,
translational positioning, and rotational positioning.
