###
*Almost* *k-wise* *vs*. *k-wise* *independent* . . .

, 2013

"... A family of permutations in Sn is k-wise independent if a uniform permutation chosen from the family maps any sequence of k distinct elements to any sequence of k distinct elements with equal probability. Efficient constructions of k-wise independent permutations are known for k = 2 and k = 3 base ..."

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A family of

*permutations*in Sn is*k-wise**independent*if a*uniform**permutation*chosen from the family maps any sequence of*k*distinct elements to any sequence of*k*distinct elements with equal probability. Efficient constructions of*k-wise**independent**permutations*are known for*k*=*2*and*k*= 3###
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

### Akademisk avhandling för teknisk doktorsexamen vid

, 1994

"... mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group ..."

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of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a

*permutational*representation of the corresponding*group*.*Group*elements correspond###
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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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### Exact Random Generation of Symmetric and Quasi-symmetric Alternating-sign Matrices

, 2008

"... We show how to adapt the Monotone Coupling from the Past exact sampling algorithm to sample from some symmetric subsets of nite distributive lattices. The method is applied to generate uniform random elements of all symmetry classes of alternating-sign matrices. 1 ..."

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We show how to adapt the Monotone Coupling from the Past exact sampling algorithm to sample from some symmetric subsets of nite distributive lattices. The method is applied to generate

*uniform*random elements of all symmetry classes of alternating-sign matrices. 1### ABSTRACT Title of dissertation: Weakly Compressible Navier-Stokes Approximation of Gas Dynamics

"... This dissertation addresses mathematical issues regarding weakly compressible approximations of gas dynamics that arise both in fluid dynamical and in kinetic settings. These approximations are derived in regimes in which (1) transport coeffi-cients (viscosity and thermal conductivity) are small and ..."

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and (

*2*) the gas is near an abso-lute equilibrium — a spatially*uniform*, stationary state. When we consider regimes in which both the transport scales and Re vanish, we derive the weakly compressible Stokes approximation — a linear system. When we consider regimes in which the transport scales vanish### permission. Structured Codes in Information Theory: MIMO and Network Applications

"... All rights reserved. ..."