Verifiable conditions of ℓ1\ell_1-recovery of sparse signals with sign restrictions

We propose necessary and sufficient conditions for a sensing matrix to be "s-semigood" -- to allow for exact $\ell_1$-recovery of sparse signals with at most $s$ nonzero entries under sign restrictions on part of the entries. We express the error bounds for imperfect $\ell_1$-recovery in terms of the characteristics underlying these conditions. Furthermore, we demonstrate that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse $\ell_1$-recovery and to efficiently computable upper bounds on those $s$ for which a given sensing matrix is $s$-semigood. We concentrate on the properties of proposed verifiable sufficient conditions of $s$-semigoodness and describe their limits of performance

Spin-lattice interactions of ions with unfilled F-shells measured by ESR in uniaxially stressed crystals

Spin-lattice interactions of ions with unfilled F-shells measured by electron spin resonance in uniaxially stressed crystal

Direct one-phonon spin-lattice relaxation times for Nd sup 3 plus and U sup 3 plus ions in CaF sub 2 in sites of tetragonal symmetry

Phonon spin-lattice relaxation times for uranium and neodymium ions in calcium fluorid

On the irreversibility of entanglement distillation

We investigate the irreversibility of entanglement distillation for a symmetric d-1 parameter family of mixed bipartite quantum states acting on Hilbert spaces of arbitrary dimension d x d. We prove that in this family the entanglement cost is generically strictly larger than the distillable entanglement, such that the set of states for which the distillation process is asymptotically reversible is of measure zero. This remains true even if the distillation process is catalytically assisted by pure state entanglement and every operation is allowed, which preserves the positivity of the partial transpose. It is shown, that reversibility occurs only in cases where the state is quasi-pure in the sense that all its pure state entanglement can be revealed by a simple operation on a single copy. The reversible cases are shown to be completely characterized by minimal uncertainty vectors for entropic uncertainty relations.Comment: 5 pages, revtex

Spin-lattice Interaction in Ruby Measured by ESR in Uniaxially Stressed Crystals

Spin-lattice Hamiltonian determined for chromium ions in ruby single crystal

Blind Deconvolution of Ultrasonic Signals Using High-Order Spectral Analysis and Wavelets

Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter using wavelet shrinkage is presented for the estimation of the reflectivity function. The final result shows an improved signal to noise ratio with better axial resolution.Comment: 8 pages, CIARP 2005, LNCS 377

Studies in Astronomical Time Series Analysis. VI. Bayesian Block Representations

This paper addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. We present a simple nonparametric modeling technique and an algorithm implementing it - an improved and generalized version of Bayesian Blocks (Scargle 1998) - that finds the optimal segmentation of the data in the observation interval. The structure of the algorithm allows it to be used in either a real-time trigger mode, or a retrospective mode. Maximum likelihood or marginal posterior functions to measure model fitness are presented for events, binned counts, and measurements at arbitrary times with known error distributions. Problems addressed include those connected with data gaps, variable exposure, extension to piecewise linear and piecewise exponential representations, multi-variate time series data, analysis of variance, data on the circle, other data modes, and dispersed data. Simulations provide evidence that the detection efficiency for weak signals is close to a theoretical asymptotic limit derived by (Arias-Castro, Donoho and Huo 2003). In the spirit of Reproducible Research (Donoho et al. 2008) all of the code and data necessary to reproduce all of the figures in this paper are included as auxiliary material.Comment: Added some missing script files and updated other ancillary data (code and data files). To be submitted to the Astophysical Journa

Estimating point-to-point and point-to-multipoint traffic matrices: An information-theoretic approach

© 2005 IEEE.Traffic matrices are required inputs for many IP network management tasks, such as capacity planning, traffic engineering, and network reliability analysis. However, it is difficult to measure these matrices directly in large operational IP networks, so there has been recent interest in inferring traffic matrices from link measurements and other more easily measured data. Typically, this inference problem is ill-posed, as it involves significantly more unknowns than data. Experience in many scientific and engineering fields has shown that it is essential to approach such ill-posed problems via "regularization". This paper presents a new approach to traffic matrix estimation using a regularization based on "entropy penalization". Our solution chooses the traffic matrix consistent with the measured data that is information-theoretically closest to a model in which source/destination pairs are stochastically independent. It applies to both point-to-point and point-to-multipoint traffic matrix estimation. We use fast algorithms based on modern convex optimization theory to solve for our traffic matrices. We evaluate our algorithm with real backbone traffic and routing data, and demonstrate that it is fast, accurate, robust, and flexible.Yin Zhang, Member, Matthew Roughan, Carsten Lund, and David L. Donoh

On Verifiable Sufficient Conditions for Sparse Signal Recovery via ℓ1\ell_1 Minimization

We propose novel necessary and sufficient conditions for a sensing matrix to be "$s$-good" - to allow for exact $\ell_1$-recovery of sparse signals with $s$ nonzero entries when no measurement noise is present. Then we express the error bounds for imperfect $\ell_1$-recovery (nonzero measurement noise, nearly $s$-sparse signal, near-optimal solution of the optimization problem yielding the $\ell_1$-recovery) in terms of the characteristics underlying these conditions. Further, we demonstrate (and this is the principal result of the paper) that these characteristics, although difficult to evaluate, lead to verifiable sufficient conditions for exact sparse $\ell_1$-recovery and to efficiently computable upper bounds on those $s$ for which a given sensing matrix is $s$-good. We establish also instructive links between our approach and the basic concepts of the Compressed Sensing theory, like Restricted Isometry or Restricted Eigenvalue properties