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Monday, September 8, 2014 - 14:00 ,
Location: Skiles 005 ,
Dr. Marta Canadell ,
Georgia Tech Mathematics ,
Organizer: Martin Short

We explain a method for the computation of normally hyperbolic invariant manifolds (NHIM) in discrete dynamical systems.The method is based in finding a parameterization for the manifold formulating a functional equation. We solve the invariance equation using a Newton-like method taking advantage of the dynamics and the geometry of the invariant manifold and its invariant bundles. The method allows us to compute a NHIM and its internal dynamics, which is a-priori unknown.We implement this method to continue the invariant manifold with respect to parameters, and to explore different mechanisms of breakdown. This is a joint work with Alex Haro.

Monday, April 28, 2014 - 14:00 ,
Location: Skiles 005 ,
Deanna Needell ,
Claremont McKenna College ,
Organizer: Martin Short

In this talk we will discuss results for robust signal reconstruction
from random observations via synthesis and analysis methods in
compressive signal processing (CSP). CSP is a new and exciting field
which arose as an efficient alternative to traditional signal
acquisition techniques. Using a (usually random) projection, signals
are measured directly in compressed form, and methods are then needed
to recover the signal from those measurements. Synthesis methods
attempt to identify the low-dimensional representation of the signal
directly, whereas analysis type methods reconstruct in signal space.
We also discuss special cases including provable near-optimal
reconstruction guarantees for total-variation
minimization and new techniques in super-resolution.

Monday, April 14, 2014 - 14:00 ,
Location: Skiles 005 ,
Professor Ke Chen ,
The University of Liverpool, UK ,
Organizer: Haomin Zhou

Mathematical imaging is not only a multidisciplinary research area but also a major cross-disciplinesubject within mathematical sciences as image analysis techniques involve analysis, optimization, differential geometry and nonlinear partial differential equations, computational algorithms and numerical analysis.In this talk I first review various models and techniques in the variational frameworkthat are used for restoration of images. Then I discuss more recent work on i) choice of optimal coupling parameters for the TV model,ii) the blind deconvolution and iii) high order regularization models.This talk covers joint work with various collaborators in imaging including J. P. Zhang, T.F. Chan, R. H. Chan, B. Yu, L. Sun, F. L. Yang (China), C. Brito (Mexico), N. Chumchob (Thailand), M. Hintermuller (Germany), Y. Q. Dong (Denmark), X. C. Tai (Norway) etc.

Monday, April 7, 2014 - 14:00 ,
Location: Skiles 005 ,
Ming-Jun Lai ,
University of Georgia ,
Organizer: Martin Short

I mainly discuss the following problem: given a set of scattered locations and nonnegative values, how can one construct a smooth interpolatory or fitting surface of the given data? This problem arises from the visualization of scattered data and the design of surfaces with shape control. I shall start explaining scattered data interpolation/fitting based on bivariate spline functions over triangulation without nonnegativity constraint. Then I will explain the difficulty of the problem of finding nonnegativity perserving interpolation and fitting surfaces and recast the problem into a minimization problem with the constraint. I shall use the Uzawa algorithm to solve the constrained minimization problem. The convergence of the algorithm in the bivariate spline setting will be shown. Several numerical examples will be demonstrated and finally a real life example for fitting oxygen anomalies over the Gulf of Mexico will be explained.

Monday, March 31, 2014 - 14:00 ,
Location: Skiles 005 ,
Benjamin Seibold ,
Temple University ,
Organizer: Martin Short

Initially homogeneous vehicular traffic flow can become inhomogeneous
even in the absence of obstacles. Such ``phantom traffic jams'' can be
explained as instabilities of a wide class of ``second-order''
macroscopic traffic models. In this unstable regime, small
perturbations amplify and grow into nonlinear traveling waves. These
traffic waves, called ``jamitons'', are observed in reality and have
been reproduced experimentally. We show that jamitons are analogs of
detonation waves in reacting gas dynamics, thus creating an
interesting link between traffic flow, combustion, water roll waves,
and black holes. This analogy enables us to employ the Zel'dovich-von
Neumann-Doering theory to predict the shape and travel velocity of the
jamitons. We furthermore demonstrate that the existence of jamiton
solutions can serve as an explanation for multi-valued parts that
fundamental diagrams of traffic flow are observed to exhibit.

Monday, March 24, 2014 - 14:00 ,
Location: Skiles 005 ,
Seth Marvel ,
University of Michigan ,
Organizer: Martin Short

In this talk, I will present work on two very different
problems, with the only common theme being a substantial departure from
standard approaches. In the first part, I will discuss how the spread of
many common contagions may be more accurately modeled with nonlocal
approaches than with the current standard of local approaches, and I will
provide a minimal mathematical foundation showing how this can be done. In
the second part, I will present a new computational method for ranking
items given only a set of pairwise preferences between them. (This is
known as the minimum feedback arc set problem in computer science.) For a
broad range of cases, this method appears to beat the current "world
record" in both run time and quality of solution.

Monday, March 10, 2014 - 14:00 ,
Location: Skiles 005 ,
Ray Treinen ,
Texas State, San Marcos ,
Organizer: John McCuan

The symmetric configurations for the equilibrium shape of a fluid interfaceare given by the geometric differential equation mean curvature isproportional to height. The equations are explored numerically tohighlight the differences in classically treated capillary tubes andsessile drops, and what has recently emerged as annular capillary surfaces. Asymptotic results are presented.

Monday, March 3, 2014 - 14:00 ,
Location: Skiles 005 ,
Seong Jun Kim ,
GT Math ,
Organizer: Sung Ha Kang

In this talk, the two approaches for computing the long time behavior of highly oscillatory dynamical systems will be introduced. Firstly, a generalization of the backward-forward HMM (BF HMM) will be discussed. It is intended to deal with the multiple time scale (>2) behavior of certain nonlinear systems where the non-linearity is introduced as a perturbation to a primarily linear problem. Focusing on the Fermi-Pasta-Ulam problem, I propose a three-scale version of the BF HMM. Secondly, I will consider a multiscale method using a signal processingidea. The dynamics on the slow time scale can be approximated by an averaged system gained by fltering out the fast oscillations. An Adaptive Local Iterative Filtering (ALIF) algorithm is used to do such averaging with respect to fast oscillations.

Monday, February 24, 2014 - 14:00 ,
Location: Skiles 005 ,
Le Song ,
Georgia Tech CSE ,
Organizer: Martin Short

Dynamical processes, such
as
information diffusion in social networks, gene regulation in
biological systems and
functional collaborations between brain regions, generate a
large
volume of high dimensional “asynchronous” and
“interdependent”
time-stamped event data. This type of timing information is rather
different from traditional iid.
data and discrete-time temporal data, which calls for new
models and
scalable algorithms for learning, analyzing and utilizing
them. In
this talk, I will present methods based on multivariate point
processes, high dimensional sparse recovery, and randomized
algorithms for addressing a sequence of problems arising from
this
context. As a concrete example, I will also present
experimental
results on learning and optimizing information cascades in web
logs,
including estimating hidden diffusion
networks
and influence maximization with the learned networks.
With both careful model and algorithm design, the framework is
able
to handle millions of events and millions of networked
entities.

Monday, February 17, 2014 - 14:00 ,
Location: Skiles 005 ,
Junshan Lin ,
Auburn University ,
Organizer: Haomin Zhou

Resonances are important in the study of transient phenomenaassociated with the wave equation, especially in understanding the largetime behavior of the solution to the wave equation when radiation lossesare small. In this talk, I will present recent studies on the scatteringresonances for photonic structures and Schrodinger operators. I will beginwith a study on the finite symmetric photoinc structure to illustrate theconvergence behavior of resonances. Then a general perturbation approachwill be introduced for the analysis of near bound-state resonances for bothcases. In particular, it is shown that, for a finite one dimensionalphotonic crystal with a defect, the near bound-state resonances converge tothe point spectrum of the infinite structure with an exponential rate whenthe number of periods increases. An analogous exponential decay rate alsoholds for the Schrodinger operator with a potential function that is alow-energy well surrounded by a thick barrier. The analysis also leads to asimple and accurate numerical approach to approximate the near bound-stateresonances. This is a joint work with Prof. Fadil Santosa in University ofMinnesota.