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Monday, November 21, 2016 - 14:05 ,
Location: Skiles 005 ,
Dr. Christina Frederick ,
Georgia Tech Mathematics ,
Organizer: Martin Short

We present a multiscale approach for identifying features in ocean beds
by solving inverse problems in high frequency seafloor acoustics. The
setting is based on Sound Navigation And Ranging (SONAR) imaging used in
scientific, commercial, and military applications. The forward model
incorporates multiscale simulations, by coupling Helmholtz equations and
geometrical optics for a wide range of spatial scales in the seafloor
geometry. This allows for detailed recovery of seafloor parameters
including material type. Simulated backscattered data is generated using
numerical microlocal analysis techniques. In order to lower the
computational cost of the large-scale simulations in the inversion
process, we take advantage of a \r{pre-computed} library of
representative acoustic responses from various seafloor
parameterizations.

Monday, November 14, 2016 - 14:05 ,
Location: Skiles 005 ,
Dr. Maryam Yashtini ,
Georgia Tech Mathematics ,
Organizer: Martin Short

Many real-world problems reduce to optimization problems that are solved
by iterative methods. In this talk, I focus on recently developed
efficient algorithms for solving large-scale optimization problems that
arises in medical imaging and image
processing. In the first part of my talk, I will introduce the Bregman
Operator Splitting with Variable Stepsize (BOSVS) algorithm for solving
nonsmooth inverse problems. The proposed algorithm is designed to handle
applications where the matrix in the fidelity
term is large, dense, and ill-conditioned. Numerical results are provided
using test problems from parallel magnetic resonance imaging. In the
second part, I will focus on the Euler's Elastica-based model which is
non-smooth and non-convex, and involves high-order
derivatives. I introduce two efficient alternating minimization methods
based on operator splitting and alternating direction method of
multipliers, where subproblems can be solved efficiently by Fourier
transforms and shrinkage operators. I present the analytical
properties of each algorithm, as well as several numerical experiments
on image inpainting problems, including comparison with some existing
state-of-art methods to show the efficiency and the effectiveness of the
proposed methods.

Monday, November 7, 2016 - 14:05 ,
Location: Skiles 005 ,
JD Walsh ,
GA Tech Mathematics, doctoral candidate ,
Organizer: Martin Short

The boundary method is a new algorithm for solving semi-discrete
transport problems involving a variety of ground cost functions. By
reformulating a transport problem as an optimal coupling problem, one
can construct a partition of its continuous space whose boundaries allow
accurate determination of the transport map and its associated
Wasserstein distance. The boundary method approximates region boundaries
using the general auction algorithm, controlling problem size with a
multigrid discard approach. This talk describes numerical and
mathematical results obtained when the ground cost is a convex
combination of lp norms, and shares preliminary work involving other
ground cost functions.

Tuesday, November 1, 2016 - 14:05 ,
Location: Skiles 006 ,
Dr. Mehdi Vahab ,
Florida State University Math ,
Organizer: Martin Short

An adaptive hybrid level set moment-of-fluid method is developed to study
the material solidification of static and dynamic multiphase systems. The
main focus is on the solidification of water droplets, which may undergo
normal or supercooled freezing. We model the different regimes of freezing
such as supercooling, nucleation, recalescence, isothermal freezing and
solid cooling accordingly to capture physical dynamics during impact and
solidification of water droplets onto solid surfaces. The numerical
simulations are validated by comparison to analytical results and
experimental observations. The present simulations demonstrate the ability
of the method to capture sharp solidification front, handle contact line
dynamics, and the simultaneous impact, merging and freezing of a drop.
Parameter studies have been conducted, which show the influence of the
Stefan number on the regularity of the shape of frozen droplets. Also, it
is shown that impacting droplets with different sizes create ice shapes
which are uniform near the impact point and become dissimilar away from it.
In addition, surface wettability determines whether droplets freeze upon
impact or bounce away.

Monday, October 24, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Lars Ruthotto ,
Emory University Math/CS ,
Organizer: Martin Short

Image registration is an essential task in almost all areas involving
imaging techniques. The goal of image registration is to find
geometrical correspondences between two or more images. Image
registration is commonly phrased as a variational problem that is known
to be ill-posed and thus regularization is commonly used to ensure
existence of solutions and/or introduce prior knowledge about the
application in mind. Many relevant applications, e.g., in biomedical
imaging, require that plausible transformations are diffeomorphic, i.e.,
smooth mappings with a smooth inverse.
This talk will present and compare two modeling strategies and numerical
approaches to diffeomorphic image registration. First, we will discuss
regularization approaches based on nonlinear elasticity. Second, we will
phrase image registration as an optimal control problem involving
hyperbolic PDEs which is similar to the popular framework of Large
Deformation Diffeomorphic Metric Mapping (LDDMM). Finally, we will
consider computational aspects and present numerical results for
real-life medical imaging problems.

Monday, October 17, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Yanzhao Cao ,
Auburn University Mathematics ,
Organizer: Martin Short

A nonlinear filtering problem can be classified as a stochastic Bayesian
optimization problem of identifying the state of a stochastic dynamical
system based on noisy observations of the system. Well known numerical
simulation methods include unscented Kalman filters and particle
filters. In this talk, we consider a class of efficient numerical
methods based on forward backward stochastic differential equations.
The backward SDEs for nonlinear filtering problems are similar to the
Fokker-Planck equations for SDEs. We will describe the process of
deriving such backward SDEs as well as high order numerical algorithms
to solve them, which in turn solve nonlinear filtering problems.

Monday, October 3, 2016 - 14:00 ,
Location: Skiles 005 ,
Prof. Qin Li ,
UW-Madison ,
qinli@math.wisc.edu ,
Organizer: Molei Tao

Many kinetic equations have the corresponding fluid limits. In the zero limit of the Knudsen number, one derives the Euler equation out of the Boltzmann equation and the heat equation out of the radiative transfer equation. While there are good numerical solvers for both kinetic and fluid equations, it is not quite well-understood when the two regimes co-exist. In this talk, we model the layer between the fluid and the kinetic using a half-space equation, study the well-posedness, design a numerical solver, and utilize it to couple the two sets of equations that govern separate domains. It is a joint work with Jianfeng Lu and Weiran Sun.

Monday, September 12, 2016 - 14:05 ,
Location: Skiles 005 ,
Prof. Jacob Eisenstein ,
GA Tech School of Interactive Computing ,
Organizer: Martin Short

Language change is a complex social phenomenon, revealing
pathways of communication and sociocultural influence. But while language
change has long been a topic of study in sociolinguistics, traditional
linguistic research methods rely on circumstantial evidence, estimating the
direction of change from differences between older and younger speakers. In
this research, we use a data set of several million Twitter users to track
language changes in progress. First, we show that language change can be
viewed as a form of social influence: we observe complex contagion for
``netspeak'' abbreviations (e.g., lol) and phonetic spellings, but not for
older dialect markers from spoken language. Next, we test whether specific
types of social network connections are more influential than others, using
a parametric Hawkes process model. We find that tie strength plays an
important role: densely embedded social ties are significantly better
conduits of linguistic influence. Geographic locality appears to play a
more limited role: we find relatively little evidence to support the
hypothesis that individuals are more influenced by geographically local
social ties, even in the usage of geographical dialect markers.

Monday, August 8, 2016 - 14:00 ,
Location: Skiles 006 ,
Prof. Yunho Kim ,
UNIST, Korea ,
Organizer: Sung Ha Kang

Inspired by the usefulness of difference of convex functions in some problems, e.g. sparse representations, we use such an idea of difference of convex functions to propose a method of finding an eigenfunction of a self-adjointoperator. In a matrix setting, this method always finds an eigenvector of a symmetric matrix corresponding to the smallest eigenvalue without solving Ax=b. In fact, such a matrix A is allowed to be singular, as well. We can apply the same setting to a generalized eigenvalue problem. We will discuss its convergence as well.

Wednesday, June 22, 2016 - 11:00 ,
Location: Skiles 006 ,
Dr. Ha Quang, Minh ,
Istituto Italiano di Tecnologia (Italy) ,
Organizer: Sung Ha Kang

Symmetric positive definite (SPD) matrices play important roles in numerous areas of mathematics, statistics, and their applications in machine learning, optimization, computer vision, and related fields. Among the most important topics in the study of SPD matrices are the distances between them that can properly capture the geometry of the set of SPD matrices. Two of the most widely used distances are the affine-invariant distance and the Log-Euclidean distance, which are geodesic distances corresponding to two different Riemannian metrics on this set. In this talk, we present our recently developed concept of Log-Hilbert-Schmidt (Log-HS) distance between positive definite Hilbert-Schmidt operators on a Hilbert space.This is the generalization of the Log-Euclidean distance between SPD matrices to the infinite-dimensional setting. In the case of reproducing kernel Hilbert space (RKHS) covariance operators, we obtain closed form formulas for the Log-HS distance, expressed via Gram matrices. As a practical example, we demonstrate an application of the Log-HS distance to the problem of image classification in computer vision.