Performance Comparisons of Greedy Algorithms in Compressed Sensing

Compressed sensing has motivated the development of numerous sparse approximation algorithms designed to return a solution to an underdetermined system of linear equations where the solution has the fewest number of nonzeros possible, referred to as the sparsest solution. In the compressed sensing setting, greedy sparse approximation algorithms have been observed to be both able to recovery the sparsest solution for similar problem sizes as other algorithms and to be computationally efficient; however, little theory is known for their average case behavior. We conduct a large scale empirical investigation into the behavior of three of the state of the art greedy algorithms: NIHT, HTP, and CSMPSP. The investigation considers a variety of random classes of linear systems. The regions of the problem size in which each algorithm is able to reliably recovery the sparsest solution is accurately determined, and throughout this region additional performance characteristics are presented. Contrasting the recovery regions and average computational time for each algorithm we present algorithm selection maps which indicate, for each problem size, which algorithm is able to reliably recovery the sparsest vector in the least amount of time. Though no one algorithm is observed to be uniformly superior, NIHT is observed to have an advantageous balance of large recovery region, absolute recovery time, and robustness of these properties to additive noise and for a variety of problem classes. The algorithm selection maps presented here are the first of their kind for compressed sensing

Experimental Combat-Stress Model in Rats: Histological Examination of Effects of Amelogenesis-A Possible Measure of Diminished Vagal Tone Episodes

Developmental defects of enamel-stress histomarker rings (accentuated striae) may be a potential measure of diminished vagal tone in research on extreme stress such as exposure to combat. To develop an animal model of this measure, we examined the enamel of rat incisors which erupt continuously. We examined incisors from 15 stressed-colony rats and 7 control-rats for these histomarkers using the Visible Burrow System (VBS). VBS was developed to study combat stress in rats. No stress rings were found in any of the rat incisors examined. In contrast to humans, rats have likely evolved to prioritize incisor strength during combat stress. Studies of amelogenesis during combat stress in other rodents with continuously growing incisors are warranted. Laboratory animals such as rabbits or marmosets may be especially suitable, since they less frequently use their incisors for self defense

CGIHT: Conjugate Gradient Iterative Hard Thresholding\ud for Compressed Sensing and Matrix Completion

We introduce the Conjugate Gradient Iterative Hard Thresholding (CGIHT) family of algorithms for the efficient solution of constrained underdetermined linear systems of equations arising in compressed sensing, row sparse approximation, and matrix completion. CGIHT is designed to balance the low per iteration complexity of simple hard thresholding algorithms with the fast asymptotic convergence rate of employing the conjugate gradient method. We establish provable recovery guarantees and stability to noise for variants of CGIHT with sufficient conditions in terms of the restricted isometry constants of the sensing operators. Extensive empirical performance comparisons establish significant computational advantages for CGIHT both in terms of the size of problems which can be accurately approximated and in terms of overall computation time

Conjugate Gradient Iterative Hard Thresholding:\ud Observed Noise Stability for Compressed Sensing

Conjugate Gradient Iterative Hard Thresholding (CGIHT) for compressed sensing combines the low per iteration complexity of fast greedy sparse approximation algorithms with the improved convergence rates of more complicated, projection based algorithms. This article shows that CGIHT is robust to\ud additive noise and is typically the fastest greedy algorithm in the presence of noise

Anticipations, Recessions and Policy: An Intertemporal Disequilibrium Model

This paper presents an intertemporal disequilibrium model with rational expectations, i.e. a model in which agents anticipate the future rationally, but in which prices and wages may not adjust fast enough to maintain continuous market clearing. Therefore, optimizing firms and households base their intertemporal plans on anticipations of both future quantity constraints and future prices. Such a model shows clearly that the effect of a policy depends not only on its current values but its anticipated path, After a presentation of the model and its basic dynamics, we therefore consider the effects of various paths of fiscal policy on the economy

Decay properties of restricted isometry constants

Abstract—Many sparse approximation algorithms accurately recover the sparsest solution to an underdetermined system of equations provided the matrix’s restricted isometry constants (RICs) satisfy certain bounds. There are no known large deterministic matrices that satisfy the desired RIC bounds; however, members of many random matrix ensembles typically satisfy RIC bounds. This experience with random matrices has colored the view of the RICs ’ behavior. By modifying matrices assumed to have bounded RICs, we construct matrices whose RICs behave in a markedly different fashion than the classical random matrices; RICs can satisfy desirable bounds and also take on values in a narrow range. Index Terms—Compressed sensing, restricted isometry constants, RIP, sparse approximation I

Long-term forest soil warming alters microbial communities in temperate forest soils

Soil microbes are major drivers of soil carbon cycling, yet we lack an understanding of how climate warming will affect microbial communities. Three ongoing field studies at the Harvard Forest Long-term Ecological Research (LTER) site (Petersham, MA) have warmed soils 5°C above ambient temperatures for 5, 8, and 20 years. We used this chronosequence to test the hypothesis that soil microbial communities have changed in response to chronic warming. Bacterial community composition was studied using Illumina sequencing of the 16S ribosomal RNA gene, and bacterial and fungal abundance were assessed using quantitative PCR. Only the 20-year warmed site exhibited significant change in bacterial community structure in the organic soil horizon, with no significant changes in the mineral soil. The dominant taxa, abundant at 0.1% or greater, represented 0.3% of the richness but nearly 50% of the observations (sequences). Individual members of the Actinobacteria, Alphaproteobacteria and Acidobacteria showed strong warming responses, with one Actinomycete decreasing from 4.5 to 1% relative abundance with warming. Ribosomal RNA copy number can obfuscate community profiles, but is also correlated with maximum growth rate or trophic strategy among bacteria. Ribosomal RNA copy number correction did not affect community profiles, but rRNA copy number was significantly decreased in warming plots compared to controls. Increased bacterial evenness, shifting beta diversity, decreased fungal abundance and increased abundance of bacteria with low rRNA operon copy number, including Alphaproteobacteria and Acidobacteria, together suggest that more or alternative niche space is being created over the course of long-term warming

Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality

We show that the generating functions of avalanche observables in SOC models exhibits a Lee-Yang phenomenon. This establishes a new link between the classical theory of critical phenomena and SOC. A scaling theory of the Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte

Pregnancy Induces Persistent Changes that Potentiate Apoptotic Signaling and Responses to DNA Damage

A full-term pregnancy reduces the lifetime risk of breast cancer by up to 50%. This effect is mediated, in part, by p53-dependent pathways. Gene expression profiling was used to investigate the mechanisms that alter apoptotic responses to DNA damage in the mammary gland. Radiation-induced responses in BALB/c-Trp53+/+ and BALB/c-Trp53-/- mice identified 121 genes that were altered by radiation and p53 status (p53-IR). To determine the effect of parity, mice were mated, force-weaned and mammary glands were allowed to involute for 21 days (parous) and compared with age-matched nulliparous mice. Gene expression profiles were determined in mammary tissues from nulliparous (N), parous (P), irradiated nulliparous (N-IR) and irradiated parous (P-IR) mice. The p53-IR gene signature did not differ among the N-IR and P-IR groups indicating that transcriptional activity of p53 was not altered by parity. However, expression profiles of apoptosis-related genes differed significantly in the parous group. The alterations in parous mammary tissues was accompanied by over-representation of biological processes that included “signal transduction” (e=1.69E-05). Within this set, Wnt signaling was especially pronounced (e Parity-regulated genes collaborate with p53-dependent targets, which act as a “switch”, to elicit apoptosis following ionizing radiation. The epigenetic states of the parity-regulated genes Tgfb2 and Wnt5a provide a mechanism for the persistent alterations in gene expression and apoptosis in parous mammary epithelial cells