Convex recovery of a structured signal from independent random linear measurements

This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.Comment: 18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contribution

Optimal quantum detectors for unambiguous detection of mixed states

We consider the problem of designing an optimal quantum detector that distinguishes unambiguously between a collection of mixed quantum states. Using arguments of duality in vector space optimization, we derive necessary and sufficient conditions for an optimal measurement that maximizes the probability of correct detection. We show that the previous optimal measurements that were derived for certain special cases satisfy these optimality conditions. We then consider state sets with strong symmetry properties, and show that the optimal measurement operators for distinguishing between these states share the same symmetries, and can be computed very efficiently by solving a reduced size semidefinite program.Comment: Submitted to Phys. Rev.

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Mechanisms of Endothelial Dysfunction in Resistance Arteries from Patients with End-Stage Renal Disease

The study focuses on the mechanisms of endothelial dysfunction in the uremic milieu. Subcutaneous resistance arteries from 35 end-stage renal disease (ESRD) patients and 28 matched controls were studied ex-vivo. Basal and receptor-dependent effects of endothelium-derived factors, expression of endothelial NO synthase (eNOS), prerequisites for myoendothelial gap junctions (MEGJ), and associations between endothelium-dependent responses and plasma levels of endothelial dysfunction markers were assessed. The contribution of endothelium-derived hyperpolarizing factor (EDHF) to endothelium-dependent relaxation was impaired in uremic arteries after stimulation with bradykinin, but not acetylcholine, reflecting the agonist-specific differences. Diminished vasodilator influences of the endothelium on basal tone and enhanced plasma levels of asymmetrical dimethyl L-arginine (ADMA) suggest impairment in NO-mediated regulation of uremic arteries. eNOS expression and contribution of MEGJs to EDHF type responses were unaltered. Plasma levels of ADMA were negatively associated with endothelium-dependent responses in uremic arteries. Preserved responses of smooth muscle to pinacidil and NO-donor indicate alterations within the endothelium and tolerance of vasodilator mechanisms to the uremic retention products at the level of smooth muscle. We conclude that both EDHF and NO pathways that control resistance artery tone are impaired in the uremic milieu. For the first time, we validate the alterations in EDHF type responses linked to kinin receptors in ESRD patients. The association between plasma ADMA concentrations and endothelial function in uremic resistance vasculature may have diagnostic and future therapeutic implications

National records of 3000 European bee and hoverfly species: A contribution to pollinator conservation

Pollinators play a crucial role in ecosystems globally, ensuring the seed production of most flowering plants. They are threatened by global changes and knowledge of their distribution at the national and continental levels is needed to implement efficient conservation actions, but this knowledge is still fragmented and/or difficult to access. As a step forward, we provide an updated list of around 3000 European bee and hoverfly species, reflecting their current distributional status at the national level (in the form of present, absent, regionally extinct, possibly extinct or non-native). This work was attainable by incorporating both published and unpublished data, as well as knowledge from a large set of taxonomists and ecologists in both groups. After providing the first National species lists for bees and hoverflies for many countries, we examine the current distributional patterns of these species and designate the countries with highest levels of species richness. We also show that many species are recorded in a single European country, highlighting the importance of articulating European and national conservation strategies. Finally, we discuss how the data provided here can be combined with future trait and Red List data to implement research that will further advance pollinator conservation

Predicting bee community responses to land-use changes: Effects of geographic and taxonomic biases

Land-use change and intensification threaten bee populations worldwide, imperilling pollination services. Global models are needed to better characterise, project, and mitigate bees' responses to these human impacts. The available data are, however, geographically and taxonomically unrepresentative; most data are from North America and Western Europe, overrepresenting bumblebees and raising concerns that model results may not be generalizable to other regions and taxa. To assess whether the geographic and taxonomic biases of data could undermine effectiveness of models for conservation policy, we have collated from the published literature a global dataset of bee diversity at sites facing land-use change and intensification, and assess whether bee responses to these pressures vary across 11 regions (Western, Northern, Eastern and Southern Europe; North, Central and South America; Australia and New Zealand; South East Asia; Middle and Southern Africa) and between bumblebees and other bees. Our analyses highlight strong regionally-based responses of total abundance, species richness and Simpson's diversity to land use, caused by variation in the sensitivity of species and potentially in the nature of threats. These results suggest that global extrapolation of models based on geographically and taxonomically restricted data may underestimate the true uncertainty, increasing the risk of ecological surprises

Plastic Growth response of European beech provenances to dry site conditions

Due to projected global warming, there is a great concern about the ability of European beech to adapt to future climate conditions. Provenance trials provide an excellent basis to assess the potential of various provenances to adjust to given climate conditions. In this study we compared the performance of four European beech (Fagus sylvatica L.) provenances growing in a provenance trial at the Fruška Gora Mountain, Serbia. Three of the investigated provenances (Höllerbach and Hasbruch from Germany and Vrani Kamen from Croatia) originate from moist sites, with annual precipitation sums being twice as high as at the provenance trial in Serbia. The performance of these provenances are compared to the growth of the local provenance Fruška Gora which is well adapted to dry site conditions. We analysed tree-ring width, mean vessel area, vessel density and water-conductive area for the period from 2006 to 2012. In spite of differences in climate conditions at their place of origin all beech provenances showed a similar pattern in radial increment. Also the wood- anatomical variables showed similar inter-annual patterns for all provenances and no significant differences between the provenances. This indicates that beech provenances from moist environments can adjust to the relatively dry temperate climate in Serbia