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

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.

Untangling the Genetic Basis of Fibrolytic Specialization by Lachnospiraceae and Ruminococcaceae in Diverse Gut Communities

The Lachnospiraceae and Ruminococcaceae are two of the most abundant families from the order Clostridiales found in the mammalian gut environment, and have been associated with the maintenance of gut health. While they are both diverse groups, they share a common role as active plant degraders. By comparing the genomes of the Lachnospiraceae and Ruminococcaceae with the Clostridiaceae, a more commonly free-living group, we identify key carbohydrate-active enzymes, sugar transport mechanisms, and metabolic pathways that distinguish these two commensal groups as specialists for the degradation of complex plant material

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

Manipulating the Gut Microbiome for Human Health

Mounting evidence suggests that particular aspects of human health and disease may be attributable to the trillions of microbes that inhabit our gastrointestinal tract, collectively referred to as the gut microbiota. As part of the mini-symposium entitled Manipulating the Gut Microbiome for Human Health, Drs. McCormick and Blanchard introduce the symposium, which will offer session lectures and a follow-up interactive, discussion-based workshop on topics related to attempts to manipulate the gut microbiota to improve health

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

An In Vitro Model of the Horse Gut Microbiome Enables Identification of Lactate-Utilizing Bacteria That Differentially Respond to Starch Induction

Laminitis is a chronic, crippling disease triggered by the sudden influx of dietary starch. Starch reaches the hindgut resulting in enrichment of lactic acid bacteria, lactate accumulation, and acidification of the gut contents. Bacterial products enter the bloodstream and precipitate systemic inflammation. Hindgut lactate levels are normally low because specific bacterial groups convert lactate to short chain fatty acids. Why this mechanism fails when lactate levels rapidly rise, and why some hindgut communities can recover is unknown. Fecal samples from three adult horses eating identical diets provided bacterial communities for this in vitro study. Triplicate microcosms of fecal slurries were enriched with lactate and/or starch. Metabolic products (short chain fatty acids, headspace gases, and hydrogen sulfide) were measured and microbial community compositions determined using Illumina 16S rRNA sequencing over 12-hour intervals. We report that patterns of change in short chain fatty acid levels and pH in our in vitro system are similar to those seen in in vivo laminitis induction models. Community differences between microcosms with disparate abilities to clear excess lactate suggest profiles conferring resistance of starch-induction conditions. Where lactate levels recover following starch induction conditions, propionate and acetate levels rise correspondingly and taxa related to Megasphaera elsdenii reach levels exceeding 70% relative abundance. In lactate and control cultures, taxa related to Veillonella montpellierensis are enriched as lactate levels fall. Understanding the microbial dynamics underlying lactic acidosis and laminitis will lead to better informed models of health and the development of a probiotic treatment to prevent acidosis