Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

Expression and function of proton-sensing G-protein-coupled receptors in inflammatory pain

<p>Abstract</p> <p>Background</p> <p>Chronic inflammatory pain, when not effectively treated, is a costly health problem and has a harmful effect on all aspects of health-related quality of life. Despite the availability of pharmacologic treatments, chronic inflammatory pain remains inadequately treated. Understanding the nociceptive signaling pathways of such pain is therefore important in developing long-acting treatments with limited side effects. High local proton concentrations (tissue acidosis) causing direct excitation or modulation of nociceptive sensory neurons by proton-sensing receptors are responsible for pain in some inflammatory pain conditions. We previously found that all four proton-sensing G-protein-coupled receptors (GPCRs) are expressed in pain-relevant loci (dorsal root ganglia, DRG), which suggests their possible involvement in nociception, but their functions in pain remain unclear.</p> <p>Results</p> <p>In this study, we first demonstrated differential change in expression of proton-sensing GPCRs in peripheral inflammation induced by the inflammatory agents capsaicin, carrageenan, and complete Freund's adjuvant (CFA). In particular, the expression of TDAG8, one proton-sensing GPCR, was increased 24 hours after CFA injection because of increased number of DRG neurons expressing TDAG8. The number of DRG neurons expressing both TDAG8 and transient receptor potential vanilloid 1 (TRPV1) was increased as well. Further studies revealed that TDAG8 activation sensitized the TRPV1 response to capsaicin, suggesting that TDAG8 could be involved in CFA-induced chronic inflammatory pain through regulation of TRPV1 function.</p> <p>Conclusion</p> <p>Each subtype of the OGR1 family was expressed differently, which may reflect differences between models in duration and magnitude of hyperalgesia. Given that TDAG8 and TRPV1 expression increased after CFA-induced inflammation and that TDAG8 activation can lead to TRPV1 sensitization, it suggests that high concentrations of protons after inflammation may not only directly activate proton-sensing ion channels (such as TRPV1) to cause pain but also act on proton-sensing GPCRs to regulate the development of hyperalgesia.</p

Recovery from Mercury Contamination in the Second Songhua River, China

Mercury pollution in the Second Songhua River (SSR) was serious in the last century due to effluent from a chemical corporation. Effects of riverine self-purification on mercury removal were studied by comparing monitoring data of mercury concentrations varieties in water, sediment, and fish in the past, about 30 years. The present work suggested that a river of such a size like the SSR possessed the potential ability to recover from mercury pollution under the condition that mercury sources were cut off, though it needs a very long time, which might be several decades or even a century of years. During the 30 years with no effluent containing mercury input, total mercury (T-Hg) of water and sediment in some typical segments, mostly near the past effluent outlet, had decreased radically but still higher than the background values, though the decrease amplitudes were over 90% compared with that in 1975. T-Hg had decreased by more than 90% in most fishes, but some were still not suitable for consumption. Methylmercury concentrations (MeHg) of water, sediment, and fish were higher or close to the background levels in 2004. In the coming decades, the purification processes in the SSR would be steady and slow for a long period

Capability of common SNPs to tag rare variants

Genome-wide association studies are based on the linkage disequilibrium pattern between common tagging single-nucleotide polymorphisms (SNPs) (i.e., SNPs having only common alleles) and true causal variants, and association studies with rare SNP alleles aim to detect rare causal variants. To better understand and explain the findings from both types of studies and to provide clues to improve the power of an association study with only common SNPs genotyped, we study the correlation between common SNPs and the presence of rare alleles within a region in the genome and look at the capability of common SNPs in strong linkage disequilibrium with each other to capture single rare alleles. Our results indicate that common SNPs can, to some extent, tag the presence of rare alleles and that including SNPs in strong linkage disequilibrium with each other among the tagging SNPs helps to detect rare alleles

Understanding the dynamics of Toll-like Receptor 5 response to flagellin and its regulation by estradiol

© 2017 The Author(s). Toll-like receptors (TLRs) are major players of the innate immune system. Once activated, they trigger a signalling cascade that leads to NF-ΰ B translocation from the cytoplasm to the nucleus. Single cell analysis shows that NF-ΰ B signalling dynamics are a critical determinant of transcriptional regulation. Moreover, the outcome of innate immune response is also affected by the cross-talk between TLRs and estrogen signalling. Here, we characterized the dynamics of TLR5 signalling, responsible for the recognition of flagellated bacteria, and those changes induced by estradiol in its signalling at the single cell level. TLR5 activation in MCF7 cells induced a single and sustained NF-k B translocation into the nucleus that resulted in high NF-k B transcription activity. The overall magnitude of NF-k B transcription activity was not influenced by the duration of the stimulus. No significant changes are observed in the dynamics of NF-k B translocation to the nucleus when MCF7 cells are incubated with estradiol. However, estradiol significantly decreased NF-k B transcriptional activity while increasing TLR5-mediated AP-1 transcription. The effect of estradiol on transcriptional activity was dependent on the estrogen receptor activated. This fine tuning seems to occur mainly in the nucleus at the transcription level rather than affecting the translocation of the NF-k B transcription factor

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

Functional diversity of marine ecosystems after the Late Permian mass extinction event

Article can be accessed from http://www.nature.com/ngeo/journal/v7/n3/full/ngeo2079.htmlThe Late Permian mass extinction event was the most severe such crisis of the past 500 million years and occurred during an episode of global warming. It is assumed to have had significant ecological impact, but its effects on marine ecosystem functioning are unknown and the patterns of marine recovery are debated. We analysed the fossil occurrences of all known Permian-Triassic benthic marine genera and assigned each to a functional group based on their inferred life habit. We show that despite the selective extinction of 62-74% of marine genera there was no significant loss of functional diversity at the global scale, and only one novel mode of life originated in the extinction aftermath. Early Triassic marine ecosystems were not as ecologically depauperate as widely assumed, which explains the absence of a Cambrian-style Triassic radiation in higher taxa. Functional diversity was, however, significantly reduced in particular regions and habitats, such as tropical reefs, and at these scales recovery varied spatially and temporally, probably driven by migration of surviving groups. Marine ecosystems did not return to their pre-extinction state, however, and radiation of previously subordinate groups such as motile, epifaunal grazers led to greater functional evenness by the Middle Triassic