Improved bounds for sparse recovery from adaptive measurements

It is shown here that adaptivity in sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. An adaptive sampling-and-refinement procedure called distilled sensing is discussed and analyzed, resulting in fundamental new asymptotic scaling relationships in terms of the minimum feature strength required for reliable signal detection or localization (support recovery). In particular, reliable detection and localization using non-adaptive samples is possible only if the feature strength grows logarithmically in the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the feature strength exceeds a constant, and localization is possible when the feature strength exceeds any (arbitrarily slowly) growing function of the problem dimension

Finding needles in noisy haystacks

The theory of compressed sensing shows that samples in the form of random projections are optimal for recovering sparse signals in high-dimensional spaces (i.e., finding needles in haystacks), provided the measurements are noiseless. However, noise is almost always present in applications, and compressed sensing suffers from it. The signal to noise ratio per dimension using random projections is very poor, since sensing energy is equally distributed over all dimensions. Consequently, the ability of compressed sensing to locate sparse components degrades significantly as noise increases. It is possible, in principle, to improve performance by "shaping" the projections to focus sensing energy in proper dimensions. The main question addressed here is, can projections be adaptively shaped to achieve this focusing effect? The answer is yes, and we demonstrate a simple, computationally efficient procedure that does so

Enhanced Bound State Formation in Two Dimensions via Stripe-Like Hopping Anisotropies

We have investigated two-electron bound state formation in a square two-dimensional t-J-U model with hopping anisotropies for zero electron density; these anisotropies are introduced to mimic the hopping energies similar to those expected in stripe-like arrangements of holes and spins found in various transition metal oxides. In this report we provide analytical solutions to this problem, and thus demonstrate that bound-state formation occurs at a critical exchange coupling, J_c, that decreases to zero in the limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be contrasted with J_c/t = 2 for either a one-dimensional chain, or a two-dimensional plane with isotropic hopping. Most importantly, this behaviour is found to be qualitatively similar to that of two electrons on the two-leg ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter result as guidance, we have evaluated the pair correlation function, thus determining that the bound state corresponds to one electron moving along one chain, with the second electron moving along the opposite chain, similar to two electrons confined to move along parallel, neighbouring, metallic stripes. We emphasize that the above results are not restricted to the zero density limit - we have completed an exact diagonalization study of two holes in a 12 X 2 two-leg ladder described by the t-J model and have found that the above-mentioned lowering of the binding energy with hopping anisotropy persists near half filling.Comment: 6 pages, 3 eps figure

Photoelasticity as a Research Technique for Analyzing Stresses in Dental Structures

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67063/2/10.1177_00220345550340060601.pd

Improved bounds for sparse recovery from adaptive measurements

It is shown here that adaptivity in sampling results in dramatic improvements in the recovery of sparse signals in white Gaussian noise. An adaptive sampling-and-refinement procedure called distilled sensing is discussed and analyzed, resulting in fundamental new asymptotic scaling relationships in terms of the minimum feature strength required for reliable signal detection or localization (support recovery). In particular, reliable detection and localization using non-adaptive samples is possible only if the feature strength grows logarithmically in the problem dimension. Here it is shown that using adaptive sampling, reliable detection is possible provided the feature strength exceeds a constant, and localization is possible when the feature strength exceeds any (arbitrarily slowly) growing function of the problem dimension

Obtención empírica del límite frecuencial entre las bandas de baja y altra frecuencia en análisis de variabilidad del ritmo cardíaco: aplicación en ratas y humanos

Se propone un nuevo método para la determinación empírica de los límites entre las bandas de baja frecuencia y alta frecuencia del espectro de potencia de las series RR en los estudios de variabilidad del ritmo cardíaco. El método se ha aplicado a series RR obtenidas en humanos y ratas Sprague-Dawley. Para humanos el límite coincide con la recomendación de 0,15 Hz mientras que para ratas Sprague-Dawley la metodología empleada sugiere un límite de 0,75 Hz.Postprint (published version

Electromagnetic Response of Layered Superconductors with Broken Lattice Inversion Symmetry

We investigate the macroscopic effects of charge density waves (CDW) and superconductivity in layered superconducting systems with broken lattice inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D) transition metal dichalcogenides (TMD). We work with the low temperature time dependent Ginzburg-Landau theory and study the coupling of lattice distortions and low energy CDW collective modes to the superconducting order parameter in the presence of electromagnetic fields. We show that superconductivity and piezoelectricity can coexist in these singular metals. Furthermore, our study indicates the nature of the quantum phase transition between a commensurate CDW phase and the stripe phase that has been observed as a function of applied pressure.Comment: 9 pages, 1 figure. Final version. Accepted in Phys.Rev.