### Authors:

, 1997

"... 1 Dedicated to Ludwig Elsner on the occasion of his sixtieth birthday We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these s ..."

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1 Dedicated to Ludwig Elsner on the occasion of his sixtieth birthday We describe canonical forms for elements of a classical Lie group of matrices under similarity transformations in the group. Matrices in the associated Lie algebra and Jordan algebra of matrices inherit related forms under these similarity transforma-tions. In general, one cannot achieve diagonal or Schur form, but the form that can be achieved displays the eigenvalues of the matrix. We also discuss matrices in in-tersections of these classes and their Schur-like forms. Such multistructered matrices arise in applications from quantum physics and quantum chemistry. 1

### Disthbution IJnli~nited CONTRACT TITLE: THEORETICAL STUDIES OF HIGH-POWER ULTRAVIOLET AND INFRARED MATERIALS

, 1978

"... ~f d1400 Wilson Boulevard nc assi ie ..."

### Université de Cergy-Pontoise

, 804

"... Abstract. We classify nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in H 1 loc (R3; R 3) satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg-Landau system are given by an explicit solution equivariant under the ..."

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Abstract. We classify nonconstant entire local minimizers of the standard Ginzburg-Landau functional for maps in H 1 loc (R3; R 3) satisfying a natural energy bound. Up to translations and rotations, such solutions of the Ginzburg-Landau

*system*are given by an explicit solution equivariant under### 0 QUANTITATIVE UNIFORM IN TIME CHAOS PROPAGATION FOR BOLTZMANN COLLISION PROCESSES

, 2010

"... ar ..."

###
*14* *th* ICCRTS “*C* *2* and Agility” Shannon Entropy as a Metric of Situational Awareness in *C* *2* Structures Topic *5* – Experimentation and Analysis

"... The present work is intended to investigate the possibility of using the concept of entropy to create metrics of situational awareness in command and control systems. The organizations are represented in its structural and functional forms, using MOISE+ model. Two metrics of situational awareness ar ..."

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of entropy and the entropy after the use of the

*information*obtained from the sensors is used to measure the*information*gain provided by a*C**2**system*. The difference between the*information*gains of two air forces in conflict is conceived as a simple metric of*information*superiority. A simulation study### 1Generalized Signal Alignment: On the Achievable DoF for Multi-User MIMO Two-Way Relay Channels

"... Abstract—This paper studies the achievable degrees of freedom (DoF) for multi-user multiple-input multiple-output (MIMO) two-way relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent message ..."

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messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary

*information*exchange pattern, the consid-ered channel model is a unified one. It includes several existing channel models as special cases:K-user MIMO Y channel, multi-pair MIMO two-way relay channel, generalized### RICE UNIVERSITY Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing

, 2011

"... The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."

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The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sam-pling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement

### DOI: 10.1007/s00526-003-0210-4

, 2003

"... Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of sol ..."

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Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map

*system*is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity### 1On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD

, 2013

"... This article gives theoretical insights into the performance of K-SVD, a dictionary learning algorithm that has gained significant popularity in practical applications. The particular question studied here is when a dictionary Φ ∈ Rd×K can be recovered as local minimum of the minimisation criterion ..."

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it is further demonstrated that given a finite number of training samples N, such that N / logN = O(K3d), except with probability O(N−Kd) there is a local minimum of the K-SVD criterion within distance O(KN−

*1/4*) to the generating dictionary. Index Terms dictionary learning, sparse coding, K-SVD, finite sample