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.
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.
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.
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.
4176 Campus Drive - William E. Kirwan Hall
College Park, MD 20742-4015
P: 301.405.5047 | F: 301.314.0827