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Monday, October 16, 2017 - 14:00 ,
Location: Skiles 005 ,
Dr. Barak Sober ,
Tel Aviv University ,
barakino@gmail.com ,
Organizer: Doron Lubinsky

We approximate a function defined over a $d$-dimensional manifold $M
⊂R^n$ utilizing only noisy function values at noisy locations on the manifold. To produce
the approximation we do not require any knowledge regarding the manifold
other than its dimension $d$. The approximation scheme is based upon the
Manifold Moving Least-Squares (MMLS) and is therefore resistant to noise in
the domain $M$ as well. Furthermore, the approximant is shown to be smooth
and of approximation order of $O(h^{m+1})$ for non-noisy data, where $h$ is
the mesh size w.r.t $M,$ and $m$ is the degree of the local polynomial
approximation. In addition, the proposed algorithm is linear in time with
respect to the ambient space dimension $n$, making it useful for cases
where d is much less than n. This assumption, that the high dimensional data is situated
on (or near) a significantly lower dimensional manifold, is prevalent in
many high dimensional problems. Thus, we put our algorithm to numerical
tests against state-of-the-art algorithms for regression over manifolds and
show its dominance and potential.

Monday, October 2, 2017 - 13:55 ,
Location: Skiles 005 ,
Weilin Li ,
University of Maryland, College Park ,
wl298@math.umd.edu ,
Organizer: Wenjing Liao

We formulate
super-resolution as an inverse problem in the space of measures, and
introduce a discrete and a continuous model. For the discrete model, the
problem is to accurately recover a sparse high dimensional vector from
its noisy low frequency Fourier coefficients. We determine a sharp bound
on the min-max recovery error, and this is an immediate consequence of a
sharp bound on the smallest singular value of restricted Fourier
matrices. For the continuous model, we study the total variation
minimization method. We borrow ideas from Beurling in order to determine
general conditions for the recovery of singular measures, even those
that do not satisfy a minimum separation condition. This presentation
includes joint work with John Benedetto and Wenjing Liao.

Monday, September 25, 2017 - 13:55 ,
Location: Skiles 005 ,
Professor Alessandro Veneziani ,
Emory Department of Mathematics and Computer Science ,
Organizer: Martin Short

When we get to the point of including the huge and relevant experience of
finite element fluid modeling collected in over 25 years of experience in the treatment of
cardiovascular diseases, the risk of getting “lost in translation” is real. The most important issues
are the reliability that we need to guarantee to provide a trustworthy decision support to clinicians;
the efficiency we need to guarantee to fit into the demand coming from a large volume of patients
in Computer Aided Clinical Trials as well as short timelines required by special
circumstances (emergency) in Surgical Planning.
In this talk, we will report on some recent activities taken at Emory to
make this transition possible. Reliability requirements call for an appropriate integration of
measurements and numerical models, as well as for uncertainty quantification. In particular, image and data
processing are critical to feeding mathematical models. However, there are several challenges still
open, e.g. in simulating blood flow in patient-specific arteries after stent deployment; or in
assessing the correct boundary data set to be prescribed in complex vascular districts. The gap between
theory, in this case, is apparent and good simulation and assimilation practices in finite elements
for clinical hemodynamics need to be drawn. The talk will cover these topics.
For computational efficiency, we will cover some numerical techniques currently in use for coronary
blood flow, like the Hierarchical Model Reduction or efficient methods for
coping with turbulence in aortic flows. As Clinical Trials are currently one of the most important sources of
information for medical research and practice, we envision that the suitable achievement of reliability and
efficiency requirements will make Computer Aided Clinical Trials (specifically with a strong
Finite-Elements-in-Fluids component) an important source of information with a significant impact on the
quality of healthcare. This is a joint work with the scholars and students of the Emory Center for
Mathematics and Computing in Medicine (E(CM)2), the Emory Biomech Core Lab (Don Giddens and Habib Samady), the Beta-Lab at the University of Pavia (F. Auricchio ). This work is supported by the US National
Science Foundation, Projects DMS 1419060, 1412963 1620406, Fondazione Cariplo, Abbott
Vascular Inc., and the XSEDE Consortium.

Monday, September 18, 2017 - 13:55 ,
Location: Skiles 005 ,
Prof. Nathan Kutz ,
University of Washington, Applied Mathematics ,
Organizer: Martin Short

The emergence of data methods for the sciences in the last decade has
been enabled by the plummeting costs of sensors, computational power,
and data storage. Such vast quantities of data afford us new
opportunities for data-driven discovery, which has been referred to as
the 4th paradigm of scientific discovery. We demonstrate that we can use
emerging, large-scale time-series data from modern sensors to directly
construct, in an adaptive manner, governing equations, even nonlinear
dynamics, that best model the system measured using modern regression
techniques. Recent innovations also allow for handling multi-scale
physics phenomenon and control protocols in an adaptive and robust way.
The overall architecture is equation-free in that the dynamics and
control protocols are discovered directly from data acquired from
sensors. The theory developed is demonstrated on a number of canonical
example problems from physics, biology and engineering.

Friday, August 25, 2017 - 13:55 ,
Location: Skiles 005 ,
Prof. Song Li ,
Zhejiang University ,
Organizer: Haomin Zhou

In this talk, i shall provide some optimal PIR bounds, which confirmed a conjecture on optimal RIP bound. Furtheremore, i shall also investigate some results on signals recovery with redundant dictionaries, which are also related to statistics and sparse representation.

Monday, April 24, 2017 - 14:05 ,
Location: Skiles 005 ,
Prof. George Mohler ,
IUPUI Computer Science ,
Organizer: Martin Short

In this talk we focus on classification problems where noisy sensor
measurements collected over a time window must be classified into one or
more categories. For example, mobile phone health and insurance apps
take as input time series from the accelerometer, gyroscope and GPS
radio of the phone and output predictions as to whether the user is
still, walking, running, biking, driving etc. Standard approaches to
this problem consist of first engineering features from statistics of
the data (or a transform) over a window and then training a
discriminative classifier. For two applications we show how these
features can instead be learned in an end-to-end modeling framework with
the advantages of increased accuracy and decreased modeling and
training time. The first application is reconstructing unobserved neural connections from Calcium fluorescence time series and we introduce a novel convolutional neural network architecture
with an inverse covariance layer to solve the problem. The second
application is driving detection on mobile phones with applications to
car telematics and insurance.

Monday, April 17, 2017 - 14:00 ,
Location: Skiles 005 ,
Dr. Andre Souza ,
Georgia Tech ,
andre.souza@math.gatech.edu ,
Organizer: Molei Tao

In this talk we discuss how to find probabilities of extreme events in stochastic differential equations. One approach to calculation would be to perform a large number of simulations and gather statistics, but an efficient alternative is to minimize Freidlin-Wentzell action. As a consequence of the analysis one also determines the most likely trajectory that gave rise to the extreme event. We apply this approach to stochastic systems whose deterministic behavior exhibit chaos (Lorenz and Kuramoto-Sivashinsky equations), comment on the observed behavior, and discuss.

Monday, April 10, 2017 - 14:00 ,
Location: Skiles 005 ,
Elisabetta Matsumoto ,
GT Physics ,
Organizer: Sung Ha Kang

The properties of euclidean space seem natural and obvious to us, to thepoint that it took mathematicians over two thousand years to see analternative to Euclid’s parallel postulate. The eventual discovery ofhyperbolic geometry in the 19th century shook our assumptions, revealingjust how strongly our native experience of the world blinded us fromconsistent alternatives, even in a field that many see as purelytheoretical. Non-euclidean spaces are still seen as unintuitive and exotic,but with direct immersive experiences we can get a better intuitive feel forthem. The latest wave of virtual reality hardware, in particular the HTCVive, tracks both the orientation and the position of the headset within aroom-sized volume, allowing for such an experience. We use this nacenttechnology to explore the three-dimensional geometries of theThurston/Perelman geometrization theorem. This talk focuses on oursimulations of H³ and H²×E.

Monday, April 3, 2017 - 14:00 ,
Location: Skiles 005 ,
Prof. Michael Muskulus ,
NTNU: Norwegian University of Science and Technology ,
michael.muskulus@ntnu.no ,
Organizer: Joseph Walsh

This talk addresses an important problem in arctic engineering due to interesting dynamic phenomena in a forced linear system. The nonautonomous system considered is representative of a whole class of engineering problems that are not approachable by standard techniques from dynamical system theory.The background are ice-induced vibrations of structures (e.g. wind turbines or measurement masts) in regions with active sea ice. Ice is a complex material and the mechanism for ice-induced vibrations is not fully clear at present. In particular, the conditions under which the observed, qualitatively different vibration regimes are active cannot be predicted accurately so far. A recent mathematical model developed by Delft University of Technology assumes that a number of parallel ice strips are pushing with a constant velocity against a flexible structure. The structure is modelled as a single degree of freedom harmonic oscillator. The contact force acts on the structure, but at the same time slows down the advancement of the ice, thereby introducing a dynamic nonlinearity in the otherwise linear system. When the local contact force becomes large enough, the ice crushes and the corresponding strip is reset to a random offset in front of the structure.This is the first mathematical model that exhibits all three different dynamic regimes that are observed in reality: for slow ice velocities the structure undergoes quasi-static sawtooth responses where all ice strips fail at the same time (a kind of synchronization phenomenon), for large ice velocities the structure response appears random, and for intermediate ice velocities the system exhibits vibrations at the structure eigenfrequency, commonly called frequency lock-in behavior. The latter type of vibrations causes a lot of damage to the structure and poses a safety and economic risk, so its occurrence needs to be predicted accurately.As I will show in this talk, the descriptive terms for the three vibration regimes are slightly misleading, as the mechanisms behind the observed behaviors are somewhat different than intuition suggests. I will present first results in analyzing the system and offer some explanations of the observed behaviors, as well as some simple criteria for the switch between the different vibration regimes.

Monday, March 13, 2017 - 14:00 ,
Location: Skiles 005 ,
Prof. Yao Li ,
University of Massachusetts Amherst ,
yaoli@math.umass.edu ,
Organizer: Molei Tao

In
this talk I will present my recent result about the ergodic properties
of nonequilibrium steady-state (NESS) for a stochastic energy exchange
model. The energy exchange model is numerically reduced from a
billiards-like deterministic particle system that models the microscopic
heat conduction in a 1D chain. By using a technique called the induced
chain method, I proved the existence, uniqueness, polynomial speed of
convergence to the NESS, and polynomial speed of mixing for the
stochastic energy exchange model. All of these are consistent with the
numerical simulation results of the original deterministic
billiards-like system.