### Norbert Wiener Center Archives for Academic Year 2017

#### Organizational Meeting

When: Tue, August 30, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: () -

#### Equiangular tight frames generated by nonabelian groups

When: Tue, September 6, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Joey Iverson (UMD) -

#### Behavior of Gabor frame operators on Wiener amalgam spaces

When: Tue, September 13, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Anirudha Poria () -
Abstract: It is well known that the Gabor expansions converge to identity operator in weak* sense on the Wiener amalgam spaces as sampling density tends to infinity. In this talk, I will discuss the convergence of Gabor expansions to identity operator in the operator norm as well as weak* sense on Wiener amalgam spaces as the sampling density tends to infinity. Also discuss the validity of the Janssen's representation and the Wexler-Raz biorthogonality condition for Gabor frame operator on Wiener amalgam spaces.

#### TBA

When: Tue, September 20, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: TBA () -

#### Complex Symmetric Composition Operators on the Hardy Space

When: Tue, September 27, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Sivaram Narayan (Central Michigan University) -
Abstract: We say that a bounded operator T on a complex Hilbert space H is complex symmetric if there exists a conjugation (i.e., a conjugate linear, isometric involution) J such that T=JT^*J. In this talk, we will first discuss a few general results about complex symmetric operators on a Hilbert space. We will then focus for most of the talk on the complex symmetry of composition operators C_\varphi f = f \circ \varphi induced on the Hardy space H^2 by analytic self-maps \varphi of the open unit disk D. We show that there are complex symmetric composition operators on H^2 induced by \varphi that are linear-fractional but not automorphisms. In doing so, we answer a recent question of Noor, and partially answer the original problem posed by Garcia and Hammond.

#### The Analysis of Periodic Point Processes

When: Tue, October 4, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Stephen Casey (American University) -
Abstract: Our talk addresses the problems of extracting information from periodic point processes. These problems arise in numerous situations, from radar pulse repetition interval analysis to bit synchronization in communication systems. We divide our analysis into two cases: periodic processes created by a single source, and those processes created by several sources. We wish to extract the fundamental period of the generators, and, in the second case, to
deinterleave the processes.

We first present very efficient algorithm for extracting the fundamental period from a set of sparse and noisy observations of a single source periodic process. The procedure is computationally straightforward, quickly convergent, and stable with respect to noise. Its use is justified by a theorem which shows that for a set of randomly chosen positive integers, the probability that they do not all share a common prime factor approaches one quickly as the cardinality of the set increases. The proof of this theorem rests on a probabilistic interpretation of the Riemann zeta function. We then build upon this procedure to deinterleave
and then analyze data from multiple periodic processes. This relies on the probabilistic interpretation of the Riemann zeta function, the equidistribution theorem of Weyl, and techniques from spectrum analysis. We present simulations of the procedures, which were developed jointly by the speaker and Kevin Duke of American University.

We close by using our a probabilistic interpretation of the Riemann zeta function to to develop numerical approximations of the sums $\sum_{n=1}^\infty \frac{1}{n^{2k+1}}$, for k in the natural numbers.

#### Connectivity and Irreducibility of Finite Unit-Norm Tight Frame Varieties

When: Tue, October 11, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Nate Strawn (Georgetown University) -
Abstract: We demonstrate the connectivity of algebraic varieties of finite unit norm tight frames (FUNTFs). Our central technique involves explicit continuous lifts of paths from the polytope of eigensteps (or, Gelfand-Tsetlin patterns) to spaces of FUNTFs. After demonstrating this connectivity result, we refine our analysis to show that the set of nonsingular points on these spaces is also connected. Using tools from real algebraic geometry, this refined connectivity result shows that FUNTFs varieties are irreducible in the algebro-geometric sense. This last result allows us to show that generic FUNTFs are full spark, and hence the full spark FUNTFs are dense in the space of FUNTFs. This resolves an important theoretical question regarding the application of FUNTFs in the field of Compressed Sensing. We conclude with open questions and future directions. This is joint work with Dustin Mixon and Jameson Cahill.

#### Complex Variables Techniques in Scattering Theory

When: Tue, October 18, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Irina Mitrea (Temple University) -
Abstract: This talk serves as an illustration of the principle that combining techniques originating in Complex Variables, Geometric Measure Theory, and Harmonic Analysis creates a potent mix, leading to sharp versions of many significant results in Complex Analysis and opening the door for pursuing new directions all together. Specifically, I will concentrate on Scattering Theory for null-solutions of perturbed Dirac operators in exterior Ahlfors-David regular domains, treated via methods and tools of a Complex Variables flavor such as higher dimensional versions of the Cauchy's operator, Hardy spaces, Fatou theorems, unique continuation property, etc.

#### Enumeration and Generation of Binary and Quad-Phase Code PSL Equivalence Classes

When: Tue, October 25, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Greg Coxson (United States Naval Academy) -
Abstract: The problem of optimizing binary and quad-phase aperiodic autocorrelation sidelobe levels is notoriously difficult, and likely NP-hard. Some have likened these problems to that of seeking needles in a haystack. I have at times tried to find aspects of these problems that can be used to predict behavior for all code lengths N, but these efforts have always ended in frustration. However, recently, I posed a question about the binary case that not only yielded an enumeration result for all code lengths N, but even led to a similar result for the quad-phase case. A side benefit of the work is a pair of simple algorithms for visiting, one-by-one, single representatives of each PSL equivalence class for any code length N of interest. Such algorithms can be employed, ideally in combination with other methods, to expedite searches for low-sidelobe binary and quad-phase codes.

#### TBA

When: Tue, November 1, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Alex Cloninger (Yale) -

#### Discrete directional Gabor frames

When: Tue, November 15, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: James Murphy (Johns Hopkins University) -

#### Regularization of the Inverse Laplace Transform with Applications in NMR Relaxometry

When: Tue, December 6, 2016 - 2:00pm
Where: Kirwan Hall 1311
Speaker: Christiana Sabett (UMD) -

#### Organizational meeting

When: Mon, January 30, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: () -

#### Edge, Ridge and Blob Detection with Symmetric Molecules

When: Mon, February 6, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Rafael Reisenhofer (University of Bremen) -

#### FFT 2017

When: Thu, February 16, 2017 - 9:00am
Where: Kirwan Hall 3206
Speaker: FFT 2017 (FFT 2017) - http://www.norbertwiener.umd.edu/FFT/2017/schedule.html
Abstract: See the list of speakers and abstracts at http://www.norbertwiener.umd.edu/FFT/2017/schedule.html.
Main lectures:
1) Charles Chui (Stanford) Thursday, February 16, 2017, 4:15-5:00
2) Robert Kanigel (MIT) Thursday, February 16, 2017, 6:40-7:30
3) David Donoho (Stanford) Friday, February 17, 2017, 3:30-4:30

#### FFT 2017

When: Fri, February 17, 2017 - 9:00am
Where: Kirwan Hall 3206
Speaker: FFT 2017 () - http://www.norbertwiener.umd.edu/FFT/2017/schedule.html
Abstract: Abstract: See the list of speakers and abstracts at http://www.norbertwiener.umd.edu/FFT/2017/schedule.html.
David Donoho (Stanford) Friday, February 17, 2017, 3:30-4:30

#### Real roots of random polynomials

When: Mon, February 20, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Yen Do (UVA) -

#### Principal Component Filter Banks: Optimality Criteria for Multi-Dimensional Signal Encoding

When: Mon, February 27, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Michelle Quirk () -

#### High-precision quantum algorithms

When: Mon, March 6, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Andrew Childs (UMD) -

#### A recommender system to restore images with impulse noise

When: Mon, March 13, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Alfredo Nava-Tudela (UMD) -

#### Topological sensor data fusion

When: Mon, March 27, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Michael Robinson (American University) -

#### Variational inference with deep generative models

When: Mon, April 3, 2017 - 1:00pm
Where: Kirwan Hall 3206

#### Universal spatiotemporal sampling sets for discrete spatially invariant evolution processes

When: Mon, April 10, 2017 - 1:00pm
Where: Kirwan Hall 3206
Speaker: Sui Tang (JHU) -