Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g. based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the $\ell^1$-norm but also in the vector space $\ell^0$ (when considered as the strict inductive limit of the spaces $\R^n$ as $n$ tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with Tikhonov regularization with sparsity constraints

Neural network based correlation for estimating water permeability constant in RO desalination process under fouling

YesThe water permeability constant, (Kw) is one of many important parameters that affect optimal design and operation of RO processes. In model based studies, e.g.within the RO process model, estimation of Kw is therefore important. There are only two available literature correlations for calculating the dynamic Kw values. However, each of them are only applicable for a given membrane type, given feed salinity over a certain operating pressure range. In this work, we develop a time dependent neural network (NN) based correlation to predict Kw in RO desalination processes under fouling conditions. It is found that the NN based correlation can predict the Kw values very closely to those obtained by the existing correlations for the same membrane type, operating pressure range and feed salinity. However, the novel feature of this correlation is that it is able to predict Kw values for any of the two membrane types and for any operating pressure and any feed salinity within a wide range. In addition, for the first time the effect of feed salinity on Kw values at low pressure operation is reported. While developing the correlation, the effect of numbers of hidden layers and neurons in each layer and the transfer functions is also investigated

Benchmark datasets for 3D MALDI- and DESI-imaging mass spectrometry

BACKGROUND: Three-dimensional (3D) imaging mass spectrometry (MS) is an analytical chemistry technique for the 3D molecular analysis of a tissue specimen, entire organ, or microbial colonies on an agar plate. 3D-imaging MS has unique advantages over existing 3D imaging techniques, offers novel perspectives for understanding the spatial organization of biological processes, and has growing potential to be introduced into routine use in both biology and medicine. Owing to the sheer quantity of data generated, the visualization, analysis, and interpretation of 3D imaging MS data remain a significant challenge. Bioinformatics research in this field is hampered by the lack of publicly available benchmark datasets needed to evaluate and compare algorithms. FINDINGS: High-quality 3D imaging MS datasets from different biological systems at several labs were acquired, supplied with overview images and scripts demonstrating how to read them, and deposited into MetaboLights, an open repository for metabolomics data. 3D imaging MS data were collected from five samples using two types of 3D imaging MS. 3D matrix-assisted laser desorption/ionization imaging (MALDI) MS data were collected from murine pancreas, murine kidney, human oral squamous cell carcinoma, and interacting microbial colonies cultured in Petri dishes. 3D desorption electrospray ionization (DESI) imaging MS data were collected from a human colorectal adenocarcinoma. CONCLUSIONS: With the aim to stimulate computational research in the field of computational 3D imaging MS, selected high-quality 3D imaging MS datasets are provided that could be used by algorithm developers as benchmark datasets

How Habitat Change and Rainfall Affect Dung Beetle Diversity in Caatinga, a Brazilian Semi-Arid Ecosystem

The aim of the present study was to evaluate how dung beetle communities respond to both environment and rainfall in the Caatinga, a semi-arid ecosystem in northeastern Brazil. The communities were sampled monthly from May 2006 to April 2007 using pitfall traps baited with human feces in two environments denominated “land use area” and “undisturbed area.” Abundance and species richness were compared between the two environments and two seasons (dry and wet season) using a generalized linear model with a Poisson error distribution. Diversity was compared between the two environments (land use area and undisturbed area) and seasons (dry and wet) using the Two-Way ANOVA test. Non-metric multidimensional scaling was performed on the resemblance matrix of Bray-Curtis distances (with 1000 random restarts) to determine whether disturbance affected the abundance and species composition of the dung beetle communities. Spearman's correlation coefficient was used to determine whether rainfall was correlated with abundance and species richness. A total of 1097 specimens belonging to 13 species were collected. The most abundant and frequent species was Dichotomius geminatus Arrow (Coleoptera: Scarabaeidae). The environment exerted an influence over abundance. Abundance and diversity were affected by season, with an increase in abundance at the beginning of the wet season. The correlation coefficient values were high and significant for abundance and species richness, which were both correlated to rainfall. In conclusion, the restriction of species to some environments demonstrates the need to preserve these areas in order to avoid possible local extinction. Therefore, in extremely seasonable environments, such as the Caatinga, seasonal variation strongly affects dung beetle communities

Novel ATP-Independent RNA Annealing Activity of the Dengue Virus NS3 Helicase

The flavivirus nonstructural protein 3 (NS3) bears multiple enzymatic activities and represents an attractive target for antiviral intervention. NS3 contains the viral serine protease at the N-terminus and ATPase, RTPase, and helicase activities at the C-terminus. These activities are essential for viral replication; however, the biological role of RNA remodeling by NS3 helicase during the viral life cycle is still unclear. Secondary and tertiary RNA structures present in the viral genome are crucial for viral replication. Here, we used the NS3 protein from dengue virus to investigate functions of NS3 associated to changes in RNA structures. Using different NS3 variants, we characterized a domain spanning residues 171 to 618 that displays ATPase and RNA unwinding activities similar to those observed for the full-length protein. Interestingly, we found that, besides the RNA unwinding activity, dengue virus NS3 greatly accelerates annealing of complementary RNA strands with viral or non-viral sequences. This new activity was found to be ATP-independent. It was determined that a mutated NS3 lacking ATPase activity retained full-RNA annealing activity. Using an ATP regeneration system and different ATP concentrations, we observed that NS3 establishes an ATP-dependent steady state between RNA unwinding and annealing, allowing modulation of the two opposing activities of this enzyme through ATP concentration. In addition, we observed that NS3 enhanced RNA-RNA interactions between molecules representing the ends of the viral genome that are known to be necessary for viral RNA synthesis. We propose that, according to the ATP availability, NS3 could function regulating the folding or unfolding of viral RNA structures

Quantifying the Link between Anatomical Connectivity, Gray Matter Volume and Regional Cerebral Blood Flow: An Integrative MRI Study

Background In the graph theoretical analysis of anatomical brain connectivity, the white matter connections between regions of the brain are identified and serve as basis for the assessment of regional connectivity profiles, for example, to locate the hubs of the brain. But regions of the brain can be characterised further with respect to their gray matter volume or resting state perfusion. Local anatomical connectivity, gray matter volume and perfusion are traits of each brain region that are likely to be interdependent, however, particular patterns of systematic covariation have not yet been identified. Methodology/Principal Findings We quantified the covariation of these traits by conducting an integrative MRI study on 23 subjects, utilising a combination of Diffusion Tensor Imaging, Arterial Spin Labeling and anatomical imaging. Based on our hypothesis that local connectivity, gray matter volume and perfusion are linked, we correlated these measures and particularly isolated the covariation of connectivity and perfusion by statistically controlling for gray matter volume. We found significant levels of covariation on the group- and regionwise level, particularly in regions of the Default Brain Mode Network. Conclusions/Significance Connectivity and perfusion are systematically linked throughout a number of brain regions, thus we discuss these results as a starting point for further research on the role of homology in the formation of functional connectivity networks and on how structure/function relationships can manifest in the form of such trait interdependency

Chagas Disease Risk in Texas

Chagas disease is endemic in Texas and spread through triatomine insect vectors known as kissing bugs, assassin bugs, or cone–nosed bugs, which transmit the protozoan parasite, Trypanosoma cruzi. We examined the threat of Chagas disease due to the three most prevalent vector species and from human case occurrences and human population data at the county level. We modeled the distribution of each vector species using occurrence data from México and the United States and environmental variables. We then computed the ecological risk from the distribution models and combined it with disease incidence data to produce a composite risk map which was subsequently used to calculate the populations expected to be at risk for the disease. South Texas had the highest relative risk. We recommend mandatory reporting of Chagas disease in Texas, testing of blood donations in high risk counties, human and canine testing for Chagas disease antibodies in high risk counties, and that a joint initiative be developed between the United States and México to combat Chagas disease