Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes

A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon–Bézout process.The authors thank to Drs. Mariano Gasca and Juan I. Ramos for pointing us some references and for their useful comments which have greatly improved the presentation. The authors also thank a reviewer for pointing out a mistake in the original Proof of Lemma 5. The research reported in this paper was partially supported by Project MTM2010-19969 from the Ministerio de Ciencia e Innovacion of Spain and Grant PAID-06-09-2734 from the Universidad Politecnica de Valencia. M. A. G. M. acknowledges support from the Spanish Ministry of Science and Education (MEC), Fulbright Commission, and FECYT.García March, MÁ.; Gimenez Palomares, F.; Villatoro, FR.; Pérez Quiles, MJ.; Fernández De Córdoba Castellá, PJ. (2011). Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes. Applied Mathematics and Computation. 217(18):7427-7431. https://doi.org/10.1016/j.amc.2011.02.034S742774312171

Microbiological Characterization of the Biofilms Colonizing Bioplastics in Natural Marine Conditions: A Comparison between PHBV and PLA

Biodegradable polymers offer a potential solution to marine pollution caused by plastic waste. The marine biofilms that formed on the surfaces of poly(lactide acid) (PLA) and poly(3- hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) were studied. Bioplastics were exposed for 6 months to marine conditions in the Mediterranean Sea, and the biofilms that formed on their surfaces were assessed. The presence of specific PLA and PHBV degraders was also studied. PHBV showed extensive areas with microbial accumulations and this led to higher microbial surface densities than PLA (4.75 vs. 5.16 log CFU/cm2 ). Both polymers’ surfaces showed a wide variety of microbial structures, including bacteria, fungi, unicellular algae and choanoflagellates. A high bacterial diversity was observed, with differences between the two polymers, particularly at the phylum level, with over 70% of bacteria affiliated to three phyla. Differences in metagenome functions were also detected, revealing a higher presence of proteins involved in PHBV biodegradation in PHBV biofilms. Four bacterial isolates belonging to the Proteobacteria class were identified as PHBV degraders, demonstrating the presence of species involved in the biodegradation of this polymer in seawater. No PLA degraders were detected, confirming its low biodegradability in marine environments. This was a pilot study to establish a baseline for further studies aimed at comprehending the marine biodegradation of biopolymers

Wide-Geographic and Long-Term Analysis of the Role of Pathogens in the Decline of Pinna nobilis to Critically Endangered Species

20 Pág.A mass mortality event (MME) affecting the fan mussel Pinna nobilis was first detected in Spain in autumn 2016 and spread north- and eastward through the Mediterranean Sea. Various pathogens have been blamed for contributing to the MME, with emphasis in Haplosporidium pinnae, Mycobacterium sp. and Vibrio spp. In this study, samples from 762 fan mussels (necropsies from 263 individuals, mantle biopsies from 499) of various health conditions, with wide geographic and age range, taken before and during the MME spread from various environments along Mediterranean Sea, were used to assess the role of pathogens in the MME. The number of samples processed by both histological and molecular methods was 83. The most important factor playing a main role on the onset of the mass mortality of P. nobilis throughout the Mediterranean Sea was the infection by H. pinnae. It was the only non-detected pathogen before the MME while, during MME spreading, its prevalence was higher in sick and dead individuals than in asymptomatic ones, in MME-affected areas than in non-affected sites, and it was not associated with host size, infecting both juveniles and adults. Conversely, infection with mycobacteria was independent from the period (before or during MME), from the affection of the area by MME and from the host health condition, and it was associated with host size. Gram (-) bacteria neither appeared associated with MME.This work was funded by: DG Pesca i Medi Mari (GOIB),EsMarEs (order IEO by MITECO, Spanish government), Life UFE IP-PAF INTEMARES (LIFE15 IPE ES 012) “Gestión integrada, innovadora y participativa de la Red Natura 2000 en el medio marino español,” the research project “Estado de conservación del bivalvo amenazado Pinna nobilis en el PNAC” (OAPN 024/2010), the project RECONNECT (MIS 5017160) of the Programme Interreg V-B “Balkan-Mediterranean 2014–2020.” MTES (French Government), DREAL (Direction Régionale Environnement Aménagement Logement) and Région Occitanie (France) for funding research and monitoring of Pinna.GC and PP were contracted under the INIA-CCAA cooperative research programme for postdoctoral incorporation from the Spanish National Institute for Agricultural and Food Research and Technology (INIA) (DOC INIA 8/2013 and 15/2015). MV-L was supported by a Juan de la Cierva-Incorporación postdoctoral contract (ICJI-2016-29329, MICIU Programme). ML-S and EÁ were supported by a Personal Técnico de Apoyo contract MINECO programme (PTA2015-11709-I and PTA2015-10829- I, respectively). CP and GS were supported by the project RECONNECT (MIS 5017160) financed by the Transnational Cooperation Programme Interreg V-B “Balkan-Mediterranean 2014–2020” and co-funded by the European Union and national funds of the participating countries. CP was supported by Sorbonne University.Peer reviewe

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements