Norbert Wiener Center Archives for Academic Year 2018


Organizational Meeting

When: Tue, September 4, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: () -


Harmonic analysis in combinatorics: a case study

When: Tue, September 11, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Dong Dong (UMD) -
Abstract:
The Roth theorem, which concerns the existence of three-term arithmetic progressions in certain sets, is a central topic in combinatorics. It also attracts researchers from different fields such as number theory, ergodic theory, analysis, and even computer science. In this talk, we will look at the Roth theorem from the harmonic analysis point of view. Surprisingly, harmonic analysis connects multilinear operators to very deep algebraic geometry. Although a few branches of mathematics are involved, this talk will be accessible to second-year graduate students and above.


Constrictions of bent functions using a family of permutations and Reed-Muller type codes

When: Tue, September 18, 2018 - 2:00pm
Where: EGR 2116
Speaker: Costas Karanikas (Aristotle University of Thessaloniki) - http://users.auth.gr/karanika/
Abstract: From a pair of permutations of the first n integers we get a family of permutations on 2^n objects. This family provides new bent functions ie Boolean sequences of length 2^(2n) whose Walsh transfom get values in {2^n,- 2^n}. The left half of a bent function determines a near-bent i.e., Boolean sequences of length 2^n (n odd) with Walsh spectrum in {0,2^n,-2^n} . We relate the support of near-bents with Reed - Muller type codes and using this we construct bents of higher degree using RM type codes and bents of lower type. We also discuss several ways for constructing bent functions and modify well-known constructions as for example Dillon H class and Maiorana- McFarland method .

A sharp Schrodinger maximal estimate in R^2

When: Tue, September 25, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Xiumin Du (UMD)
Abstract: We consider Carleson’s pointwise convergence problem of Schrodinger solutions. It is shown that the solution to the free Schrodinger equation converges to its initial data almost everywhere, provided that the initial data is in the Sobolev space H^s(R^n) with s > n/2(n+1) (joint with Larry Guth and Xiaochun Li in the case n = 2, and joint with Ruixiang Zhang in the case n >= 3). This is sharp up to the endpoint, due to a counterexample by Bourgain. This pointwise convergence problem can be approached by estimates of Schrodinger maximal function, which have some similar flavors as the Fourier restriction/extension estimates. In this talk, we'll focus on the case $n=2$ and see how polynomial partitioning method and decoupling theorem play a role in such estimates.

Mathematical approaches to understand and alter swallowing and gait functions in humans

When: Tue, October 23, 2018 - 2:00pm
Where: Kirwan Hall 1308
Speaker: Ervin Sejdic (PITT) -
Abstract: A human body comprises of several physiological systems that carry out specific functions necessary for
daily living. Traumatic injuries, diseases and aging negatively impact human functions, which can cause a
decreased quality of life and many other socio-economical and medical issues. Accurate models of
human functions are needed to propose interventions and treatments that can restore deteriorated
human functions. Therefore, our research aims to develop novel mathematical approaches that can
accurately assess changes in swallowing and gait functions by focusing on dynamical interactions
between musculoskeletal and other physiological systems. In this talk, I will present some of our recent
contributions dealing with both mathematical and clinical aspects of our work. Lastly, I will also present
our future research goals and our strategy to achieve these goals.

BIOGRAPHY
Dr. Ervin Sejdić received B.E.Sc. and Ph.D. degrees in electrical engineering from the University of
Western Ontario, London, Ontario, Canada in 2002 and 2008, respectively. From 2008 to 2010, he was a
postdoctoral fellow at the University of Toronto with a cross-appointment at Bloorview Kids Rehab,
Canada’s largest children’s rehabilitation teaching hospital. From 2010 until 2011, he was a research
fellow at Harvard Medical School with a cross-appointment at Beth Israel Deaconess Medical Center.
From his earliest exposure to research, he has been eager to contribute to the advancement of scientific
knowledge through carefully executed experiments and ground-breaking published work. This has
resulted in co-authoring over 130 journal publications. In February 2016, President Obama named Dr.
Sejdić as a recipient of the Presidential Early Career Award for Scientists and Engineers, “…the highest
honor bestowed by the United States Government on science and engineering professionals in the early
stages of their independent research careers.” In 2017, Dr. Sejdić was awarded the National Science
Foundation CAREER Award. In 2018, he was awarded the Chancellor’s Distinguished Research Award at
the University of Pittsburgh. Dr. Sejdić’s passion for discovery and innovation drives his constant
endeavors to connect advances in engineering to society’s most challenging problems. Hence, his
research interests include biomedical signal processing, gait analysis, swallowing difficulties, advanced
information systems in medicine, rehabilitation engineering, assistive technologies and anticipatory
medical devices.

Oscillations of Fourier series, Quantitative Sturm-Liouville Theory and Applications

When: Tue, November 6, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Stefan Steinerberger (Yale) - https://users.math.yale.edu/users/steinerberger/
Abstract: The function f(x) = a*sin(12*x) + b*sin(28x) has always between 24 and
56 roots (unless a=b=0). This follows from a classical theorem of Sturm (1836) that
has been forgotten and was recently rediscovered by Berard & Helffer. I will tell the
(quite fascinating) story behind it, give a simple proof and discuss quantitative
refinements, newly emerging connections to elliptic PDEs and the beginning of a
Sturm-Liouville theorem in higher dimensions.

Frames and some algebraic forays

When: Tue, November 13, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Prof. John Benedetto (UMD) -


Training 10k-layer CNNs with mean field theory and dynamical isometry[joint w/ RIT on Deep Learning]

When: Fri, November 16, 2018 - 12:00pm
Where: EGR 0108
Speaker: Lechao Xiao (Google Brain) - https://ai.google/research/people/105681
Abstract: In recent years, state-of-the-art methods in computer vision have utilized increasingly deep convolutional neural network architectures (CNNs), with some of the most successful models employing hundreds or even thousands of layers. A variety of pathologies such as vanishing/exploding gradients make training such deep networks challenging. While residual connections and batch normalization do enable training at these depths, it has remained unclear whether such specialized architecture designs are truly necessary to train deep CNNs. In this talk, we demonstrate that it is possible to train vanilla CNNs with ten thousand layers or more simply by using an appropriate initialization scheme. We derive this initialization scheme theoretically by developing a mean field theory for signal propagation and by characterizing the conditions for dynamical isometry, the equilibration of singular values of the input-output Jacobian matrix. These conditions require that the convolution operator be an orthogonal transformation in the sense that it is norm-preserving. We present an algorithm for generating such random initial orthogonal convolution kernels and demonstrate empirically that they enable efficient training of extremely deep architectures.

TBA

When: Tue, November 20, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Sui Tang (JHU) - http://www.math.jhu.edu/~stang/


TBA

When: Tue, November 27, 2018 - 2:00pm
Where: Kirwan Hall 3206
Speaker: Ahmad Mousavi (UMBC) -