An extension of a theorem of Schoenberg to products of spheres

We present a characterization for the continuous, isotropic and positive definite kernels on a product of spheres along the lines of a classical result of I. J. Schoenberg on positive definiteness on a single sphere. We also discuss a few issues regarding the characterization, including topics for future investigation

Fractionnement et caractérisation des lixiviats de centres d'enfouissement technique de déchets ménagers: intérêt de la chromatographie liquide haute performance sur le gel d'exclusion stérique

L'ultrafiltration et la chromatographie d'exclusion stérique haute performance sont utilisées pour la séparation et la caractérisation des composés organiques présents dans les lixiviats de centres d'enfouissement technique de déchets ménagers. Le fractionnement de la matière organique est obtenu sur des colonnes type TSK PW, en élution eau pH 4 et eau-méthanol. La spectroscopie en UV-visible et en fluorescence, un détecteur évaporatif à diffusion de lumière sont utilisés pour la caractérisation des fractions. Cette méthode rapide de séparation associée à une multidétection permet une mise en évidence, dans les fractions issues de l'ultrafiltration, de composés organiques caractéristiques. Dans la fraction de poids moléculaires inférieurs à 1000 Daltons, trois familles sont détectées. Les substances humiques et les protéines sont les principaux groupes présents dans la fraction de poids moléculaires supérieurs à 10000 Daltons.Landfill leachates represent a source of organic pollution characterized by an important organic load, with high chemical oxygen demand in recent sanitary landfills and some organic compounds refractory to biodegradation. Several researchers have examined the organic matter in these landfill leachates. In addition to measuring parameters such as chemical and biological oxygen demands (COD and BOD) and UV-absorbance, different analytical techniques were applied: gas chromatography with flame ionization or mass detection; high performance liquid chromatography; infrared spectroscopy; nuclear magnetic resonance spectrometry; and elementary analysis. Raw leachates or samples after fractionation on Sephadex gel were characterized by ultrafiltration or adsorption on XAD resins.Conclusions from these earlier studies were as follows:  - physico-chemical properties of leachates revealed not only a high organic pollution but also diversity and variability according to the age of the sanitary landfill and the climatic conditions; - gel permeation chromatography and ultrafiltration revealed two main fractions in the leachates: one with molecular weights below 1000 Daltons (Da), and another with molecular weights above 5000-10000 Da; - infrared spectroscopy and nuclear magnetic resonance spectrometry showed functional groups present in the humic and fulvic acid fractions of natural organic matter; - a varying number of peaks detected by gas chromatography with flame ionization or mass detection proved the complexity of the matrix. Few compounds were identified and quantified, with the exception of fatty acids. Moreover this technique was only applicable to molecules with low molecular weight.The purpose of the present work was to develop a new method of fractionation of organic matter in landfill leachates and to study their characterization and treatment biodegradation. Ultrafiltration, as a prefractionation step, divided the leachate into four fractions according to their molecular weight: above 10000 Da, from 10000 - 3000 Da, from 3000 - 1000 Da, and below 1000 Da. The second fractionation step was carried out using gel permeation chromatography. This technique has been was applied by earlier researchers for the characterization of landfill leachates, but at low pressure on Sephadex gels. In our study, we developed a high performance size-exclusion chromatography method using a polymer based TSK PW column, a hydrophilic cross-linked polyether. Three TSK G3000 PW columns and one G5000 PW column were tested with water at pH 4 with acetic acid and with a water/methanol mixture as mobile phases. This rapid method of separation, with short retention times, was coupled with on-line multidetection: UV-visible (254 nm - aromatic compounds), fluorescence spectroscopy (275/325 nm, protein-type molecules; 320/430 nm, humic-type molecules) and evaporative light scattering detection, ELSD. The ELSD allowed detection of all mineral and organic compounds that did not evaporate at the working temperature (45°C).The effect of the sodium chloride concentration on retention times was tested with eluants and columns. Secondary effects, often observed with size-exclusion chromatography, occurred with the gel chosen. The elution of sodium chloride solutions at different concentrations showed that the TSK PW gel bears electronegative charges, and that the density of these charges differs from one column to another. For the leachate we observed this influence: chromatograms obtained on two TSK G3000 columns were different for fractions with molecular weights below 1000 Da.The comparison of chromatograms obtained with the four detection methods provided information about the identity of the types of compounds present. For fractions with molecular weights below 1000 Da, separation was performed using a TSK G3000 PW column, with an eluant pH of 4 and a water-methanol mixture; three main families were detected. For fractions with molecular weights above 10000 Da, chromatographic separation was improved by elution with water/methanol (70/30) with TSK G5000 and G3000 columns in series; two main groups were identified, humic substances and protein-type compounds. The constituents of the two intermediate fractions with molecular weights between 10000 and 1000 Da were essentially humic substances, identified after separation on a TSK G3000 PW column with water-methanol (70/30) as the eluant

Statistical pairwise interaction model of stock market

Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns. Spin glass models have been applied and gave some valuable results but at the price of restrictive assumptions on the market dynamics or others are agent-based models with rules designed in order to recover some empirical behaviours. Here we show that the pairwise model is actually a statistically consistent model with observed first and second moments of the stocks orientation without making such restrictive assumptions. This is done with an approach based only on empirical data of price returns. Our data analysis of six major indices suggests that the actual interaction structure may be thought as an Ising model on a complex network with interaction strengths scaling as the inverse of the system size. This has potentially important implications since many properties of such a model are already known and some techniques of the spin glass theory can be straightforwardly applied. Typical behaviours, as multiple equilibria or metastable states, different characteristic time scales, spatial patterns, order-disorder, could find an explanation in this picture.Comment: 11 pages, 8 figure

Spectral Theory of Sparse Non-Hermitian Random Matrices

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples -- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erd\H{o}s-R\'{e}nyi graphs, and adjacency matrices of weighted oriented Erd\H{o}s-R\'{e}nyi graphs -- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors.Comment: 60 pages, 10 figure

Glucocorticoids promote Von Hippel Lindau degradation and Hif-1α stabilization

Glucocorticoid (GC) and hypoxic transcriptional responses play a central role in tissue homeostasis and regulate the cellular response to stress and inflammation, highlighting the potential for cross-talk between these two signaling pathways. We present results from an unbiased in vivo chemical screen in zebrafish that identifies GCs as activators of hypoxia-inducible factors (HIFs) in the liver. GCs activated consensus hypoxia response element (HRE) reporters in a glucocorticoid receptor (GR)-dependent manner. Importantly, GCs activated HIF transcriptional responses in a zebrafish mutant line harboring a point mutation in the GR DNA-binding domain, suggesting a nontranscriptional route for GR to activate HIF signaling. We noted that GCs increase the transcription of several key regulators of glucose metabolism that contain HREs, suggesting a role for GC/HIF cross-talk in regulating glucose homeostasis. Importantly, we show that GCs stabilize HIF protein in intact human liver tissue and isolated hepatocytes. We find that GCs limit the expression of Von Hippel Lindau protein (pVHL), a negative regulator of HIF, and that treatment with the c-src inhibitor PP2 rescued this effect, suggesting a role for GCs in promoting c-src–mediated proteosomal degradation of pVHL. Our data support a model for GCs to stabilize HIF through activation of c-src and subsequent destabilization of pVHL

Challenging claims in the study of migratory birds and climate change

Recent shifts in phenology in response to climate change are well established but often poorly understood. Many animals integrate climate change across a spatially and temporally dispersed annual life cycle, and effects are modulated by ecological interactions, evolutionary change and endogenous control mechanisms. Here we assess and discuss key statements emerging from the rapidly developing study of changing spring phenology in migratory birds. These well-studied organisms have been instrumental for understanding climate-change effects, but research is developing rapidly and there is a need to attack the big issues rather than risking affirmative science. Although we agree poorly on the support for most claims, agreement regarding the knowledge basis enables consensus regarding broad patterns and likely causes. Empirical data needed for disentangling mechanisms are still scarce, and consequences at a population level and on community composition remain unclear. With increasing knowledge, the overall support (‘consensus view’) for a claim increased and between-researcher variability in support (‘expert opinions') decreased, indicating the importance of assessing and communicating the knowledge basis. A proper integration across biological disciplines seems essential for the field's transition from affirming patterns to understanding mechanisms and making robust predictions regarding future consequences of shifting phenologies

Mg and its alloys for biomedical applications: Exploring corrosion and its interplay with mechanical failure

The future of biomaterial design will rely on temporary implant materials that degrade while tissues grow, releasing no toxic species during degradation and no residue after full regeneration of the targeted anatomic site. In this aspect, Mg and its alloys are receiving increasing attention because they allow both mechanical strength and biodegradability. Yet their use as biomedical implants is limited due to their poor corrosion resistance and the consequential mechanical integrity problems leading to corrosion assisted cracking. This review provides the reader with an overview of current biomaterials, their stringent mechanical and chemical requirements and the potential of Mg alloys to fulfil them. We provide insight into corrosion mechanisms of Mg and its alloys, the fundamentals and established models behind stress corrosion cracking and corrosion fatigue. We explain Mgs unique negative differential effect and approaches to describe it. Finally, we go into depth on corrosion improvements, reviewing literature on high purity Mg, on the effect of alloying elements and their tolerance levels, as well as research on surface treatments that allow to tune degradation kinetics. Bridging fundamentals aspects with current research activities in the field, this review intends to give a substantial overview for all interested readers; potential and current researchers and practitioners of the future not yet familiar with this promising material. © 2017 by the authors. Licensee MDPI, Basel, Switzerland

Proportions of the aesthetic African-Caribbean face : idealized ratios, comparison with the golden proportion and perceptions of attractiveness

Abstract Background In the absence of clear guidelines for facial aesthetic surgery, most surgeons rely on expert intuitive judgement when planning aesthetic and reconstructive surgery. One of the most famous theories regarding “ideal” facial proportions is that of the golden proportion. However, there are conflicting opinions as to whether it can be used to assess facial attractiveness. The aim of this investigation was to assess facial ratios of professional black models and to compare the ratios with the golden proportion. Methods Forty photographs of male and female professional black models were collected. Observers were asked to assign a score from 1 to 10 (1 = not very attractive, 10 = very attractive). A total of 287 responses were analysed for grading behaviour according to various demographic factors by two groups of observers. The best graded photographs were compared with the least well-graded photographs to identify any differences in their facial ratios. The models’ facial ratios were calculated and compared with the golden proportion. Results Differences in grading behaviour were observed amongst the two assessment groups. Only one out of the 12 facial ratios was not significantly different from the golden proportion. Conclusions Only one facial ratio was observed to be similar to the golden proportion in professional model facial photographs. No correlation was found between facial ratios in professional black models with the golden proportion. It is proposed that an individualistic treatment for each ratio is a rather better method to guide future practice