Norbert Wiener Center Archives for Fall 2020 to Spring 2021
Organizational Meeting
When: Tue, September 10, 2019 - 2:00pmWhere: Kirwan Hall 1313
Speaker: () -
Jubilee of Fourier Analysis and Applications (Conference in Honor of John Benedetto's 80th Birthday)
When: Thu, September 19, 2019 - 9:00amWhere: Kirwan Hall 3206
Speaker: () - https://www.norbertwiener.umd.edu/jubilee/schedule.html
Jubilee of Fourier Analysis and Applications (Conference in Honor of John Benedetto's 80th Birthday)
When: Fri, September 20, 2019 - 9:00amWhere: Kirwan Hall 3206
Speaker: () - https://www.norbertwiener.umd.edu/jubilee/schedule.html
Jubilee of Fourier Analysis and Applications (Conference in Honor of John Benedetto's 80th Birthday)
When: Sat, September 21, 2019 - 9:00amWhere: Kirwan Hall 3206
Speaker: () - https://www.norbertwiener.umd.edu/jubilee/schedule.html
The Inverse Eigenvalue Problem
When: Tue, October 1, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Tanay Wakhare (UMD) -
Abstract: The Inverse Eigenvalue Problem asks what eigenvalues a matrix with a fixed pattern of nonzero entries can have. For instance, a symmetric tridiagonal matrix must have distinct eigenvalues. We survey known results, current progress, and conjectures about this problem and its generalizations.
Vertex Nomination, Consistent Estimation, and Adversarial Modification
When: Tue, October 8, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Vince Lyzinski (UMD) - https://www.math.umd.edu/~vlyzinsk/
Abstract: Given a pair of graphs G1 and G2 and a vertex set of interest in G1, the vertex nomination problem seeks to find the corresponding vertices of interest in G2 (if they exist) and produce a rank list of the vertices in G2, with the corresponding vertices of interest in G2 concentrating, ideally, at the top of the rank list. We study the effect of an adversarial contamination model on the performance of a spectral graph embedding-based vertex nomination scheme. In both real and simulated examples, we demonstrate that this vertex nomination scheme performs effectively in the uncontaminated setting; adversarial network contamination adversely impacts the performance of our VN scheme; and network regularization successfully mitigates the impact of the contamination. In addition to furthering the theoretic basis of consistency in vertex nomination, the adversarial noise model is grounded in theoretical developments that allow us to frame the role of an adversary in terms of maximal vertex nomination consistency classes.
Sampling and Frame Expansions for Ultra-Wideband and Adaptive-Band Signals
When: Tue, October 15, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Stephen Casey (AU ) -
Abstract: Our talk develops a new approach to signal sampling, designed to deal with
ultra-wide band (UWB) and adaptive frequency band (AFB) communication systems.
These systems require either very high sampling or rapidly changing sampling rates.
From a signal processing perspective, we have approached this problem
by implementing an appropriate signal decomposition in the analog portion
that provides parallel outputs for integrated digital conversion and processing.
This naturally leads to an architecture with windowed time segmentation and
parallel analog basis expansion. The method first windows
the signal and then decomposes the signal into a basis via a continuous-time
inner product operation, computing the basis coefficients in parallel. The
windowing families are key, and we develop families that have variable partitioning
length, variable roll-off and variable smoothness. We then show how these windowing
families preserve orthogonality of any orthonormal systems between adjacent blocks,
and use these to create bases in which do signal expansions in lapped transforms.
We compute error bounds, demonstrating how to decrease error systematically by
constructing more sophisticated basis systems. We also develop the method with
a modified Gegenbauer system designed specifically for UWB signals.
The overarching goal of the theory developed in this talk is to develop a
computable atomic decomposition of time-frequency space. The idea is to come up
with a way of non-uniformly tiling time and frequency so that if the signal has
a burst of high-frequency information, we tile quickly and efficiently in time
and broadly in frequency, whereas if the signal has a relatively low-frequency
segment, we can tile broadly in time and efficiently in frequency. Computability
is key; systems are designed so that they can be implemented in circuitry.
Fingerprinting By Design: Authentication and Security
When: Tue, November 12, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Brian Sadler (Army Research Laboratory) -
Abstract: Fingerprints are commonly understood as traits that uniquely identify an individual, an object, or a message, and can be exploited to detect and prevent impersonation, fraud, or unlawful duplication. In this talk we consider the intentional introduction of fingerprints to provide security in wireless communications. This addresses the fingerprint design, and its embedding into a communications waveform, so that it has several desired properties including stealth, security, and predictable performance. The framework draws on communications, signal processing, cryptographic hashing, and information theory, enabling control of performance trade-offs by design. Privacy and security analysis quantify the limited ability of an eavesdropper to detect and estimate the fingerprint or to impersonate a legitimate user. Fingerprints provide a message, and a secret codebook design is described that enables secure side-channel communications through fingerprint coding.
Shannon Sampling via Poisson, Cauchy, Jacobi and Selberg
When: Tue, November 19, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Stephen Casey (American University) -
Abstract: Our talk develops connections between some of the most powerful formulae in analysis
– the Poisson summation formula, Cauchy’s integral and residue formulae, Jacobi interpola-
tion, and the Selberg trace formula – to the Shannon sampling formula. These connections
allow us to extend sampling in new directions, e.g., to unions of non-commensurate lattices,
to the Riemann Sphere and to the Poincare disk. We close by discussing how to develop
sampling for arbitrary Riemann surfaces using Ahlfors covering theory.
Tightness of Exponential Bases and Discrete Geometry in Abelian Groups
When: Tue, November 26, 2019 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Sam Ferguson (Metron, Inc.) -
Abstract: Fuglede's conjecture, posed in 1974, arose from the work of von Neumann on momentum operators in quantum mechanics. For subsets E of Euclidean space with positive, finite measure, it says E tiles space by translations alone iff the square-integrable functions on E have an orthogonal basis of complex exponentials.
In 2004, Tao disproved the assertion by finding a counterexample to the analogous conjecture in a finite-dimensional vector space over a field with a prime number of elements. Which vector spaces of the type used by Tao lead to counterexamples, and which do not? In the first part of this talk, we give new counterexamples and proofs which yield an almost complete answer.
While Fuglede's conjecture fails, perhaps E having a Riesz basis of complex exponentials is the more natural property? Alas, it is not even known if the unit disk has such a basis. In the second part of this talk, to better understand this question, we examine tightness of exponential bases on subsets of finite abelian groups. Under certain hypotheses, we successfully estimate quantitative measures of optimal tightness in terms of discrete geometry information.
Organizatorial Meeting
When: Tue, February 4, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: (UMD) -
Shannon Sampling via Poisson, Cauchy, Jacobi and Levin
When: Tue, February 11, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Dr. Stephen Casey (American University) -
Active Learning for Convolutional Neural Nets on Image Classification Tasks
When: Tue, February 18, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Zeyad Emam (UMD) -
Multi-tiling and exponential Riesz bases in finite abelian groups
When: Tue, March 3, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Sam Ferguson (Metron) -
Dynamic Network-level Analysis of Neural Data Underlying Auditory Processing: Case Studies Beyond the Linear, Static, and Gaussian Domains
When: Tue, March 10, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Betash Babadi (UMD) -
N/A
When: Tue, March 10, 2020 - 2:00pmWhere: Kirwan Hall 3206
Speaker: Betash Babadi (UMD) -
Persistent Homology Ideas for Multiscale Geometric Data Laplacian Computation
When: Tue, April 21, 2020 - 2:00pmWhere: Zoom
Speaker: Michael Rawson (UMD) -
Geometry of the Bures-Wasserstein Distance
When: Tue, May 19, 2020 - 2:00pmWhere: Zoom
Speaker: Chris Dock (UMD) -