Formalized linear algebra over Elementary Divisor Rings in Coq

This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support essential operations of linear algebra, the classification theorem of finitely presented modules over such rings and the uniqueness of the Smith normal form up to multiplication by units. We present formally verified algorithms computing this normal form on a variety of coefficient structures including Euclidean domains and constructive principal ideal domains. We also study different ways to extend B\'ezout domains in order to be able to compute the Smith normal form of matrices. The extensions we consider are: adequacy (i.e. the existence of a gdco operation), Krull dimension $\leq 1$ and well-founded strict divisibility

Matrices à blocs et en forme canonique

International audienceNous présentons une formalisation réalisée avec Coq visant essentiellement à prouver l'existence des formes matricielles canoniques de Frobenius et de Jordan, ainsi que leurs propriétés. Nous définissons formellement des notions importantes, comme les matrices diagonales par blocs ou les matrices compagnes, et prouvons des résultats intermédiaires originaux, comme le théorème fondamental de similitude sur un corps, ou encore l'unicité de la forme normale de Smith. Outre la formalisation de la théorie de la réduction des endormorphismes des espaces vectoriels de dimension finie, ce travail ouvre la voie à la certification d'algorithmes efficaces de calcul du polynôme caractéristique ou de la forme de Frobenius

Subcutaneous phaeohyphomycosis due to Phialemoniopsis ocularis successfully treated by voriconazole

International audienceWe report a case of subcutaneous infection in a 67 year-old Cambodian man who presented with a 5-month history of swelling of the right foot. Histopathology was compatible with phaeohyphomycosis and the hyphomycete Phialemoniopsis ocularis was identified by the means of morphological and molecular techniques. The patient responded well to a 6-month oral treatment with voriconazole alone

Formalizing the Ring of Witt Vectors

The ring of Witt vectors $\mathbb{W} R$ over a base ring $R$ is an important tool in algebraic number theory and lies at the foundations of modern $p$-adic Hodge theory. $\mathbb{W} R$ has the interesting property that it constructs a ring of characteristic $0$ out of a ring of characteristic $p > 1$, and it can be used more specifically to construct from a finite field containing $\mathbb{Z}/p\mathbb{Z}$ the corresponding unramified field extension of the $p$-adic numbers $\mathbb{Q}_p$ (which is unique up to isomorphism). We formalize the notion of a Witt vector in the Lean proof assistant, along with the corresponding ring operations and other algebraic structure. We prove in Lean that, for prime $p$, the ring of Witt vectors over $\mathbb{Z}/p\mathbb{Z}$ is isomorphic to the ring of $p$-adic integers $\mathbb{Z}_p$. In the process we develop idioms to cleanly handle calculations of identities between operations on the ring of Witt vectors. These calculations are intractable with a naive approach, and require a proof technique that is usually skimmed over in the informal literature. Our proofs resemble the informal arguments while being fully rigorous

Antimicrobial resistance among migrants in Europe: a systematic review and meta-analysis

BACKGROUND: Rates of antimicrobial resistance (AMR) are rising globally and there is concern that increased migration is contributing to the burden of antibiotic resistance in Europe. However, the effect of migration on the burden of AMR in Europe has not yet been comprehensively examined. Therefore, we did a systematic review and meta-analysis to identify and synthesise data for AMR carriage or infection in migrants to Europe to examine differences in patterns of AMR across migrant groups and in different settings. METHODS: For this systematic review and meta-analysis, we searched MEDLINE, Embase, PubMed, and Scopus with no language restrictions from Jan 1, 2000, to Jan 18, 2017, for primary data from observational studies reporting antibacterial resistance in common bacterial pathogens among migrants to 21 European Union-15 and European Economic Area countries. To be eligible for inclusion, studies had to report data on carriage or infection with laboratory-confirmed antibiotic-resistant organisms in migrant populations. We extracted data from eligible studies and assessed quality using piloted, standardised forms. We did not examine drug resistance in tuberculosis and excluded articles solely reporting on this parameter. We also excluded articles in which migrant status was determined by ethnicity, country of birth of participants' parents, or was not defined, and articles in which data were not disaggregated by migrant status. Outcomes were carriage of or infection with antibiotic-resistant organisms. We used random-effects models to calculate the pooled prevalence of each outcome. The study protocol is registered with PROSPERO, number CRD42016043681. FINDINGS: We identified 2274 articles, of which 23 observational studies reporting on antibiotic resistance in 2319 migrants were included. The pooled prevalence of any AMR carriage or AMR infection in migrants was 25·4% (95% CI 19·1-31·8; I2 =98%), including meticillin-resistant Staphylococcus aureus (7·8%, 4·8-10·7; I2 =92%) and antibiotic-resistant Gram-negative bacteria (27·2%, 17·6-36·8; I2 =94%). The pooled prevalence of any AMR carriage or infection was higher in refugees and asylum seekers (33·0%, 18·3-47·6; I2 =98%) than in other migrant groups (6·6%, 1·8-11·3; I2 =92%). The pooled prevalence of antibiotic-resistant organisms was slightly higher in high-migrant community settings (33·1%, 11·1-55·1; I2 =96%) than in migrants in hospitals (24·3%, 16·1-32·6; I2 =98%). We did not find evidence of high rates of transmission of AMR from migrant to host populations. INTERPRETATION: Migrants are exposed to conditions favouring the emergence of drug resistance during transit and in host countries in Europe. Increased antibiotic resistance among refugees and asylum seekers and in high-migrant community settings (such as refugee camps and detention facilities) highlights the need for improved living conditions, access to health care, and initiatives to facilitate detection of and appropriate high-quality treatment for antibiotic-resistant infections during transit and in host countries. Protocols for the prevention and control of infection and for antibiotic surveillance need to be integrated in all aspects of health care, which should be accessible for all migrant groups, and should target determinants of AMR before, during, and after migration. FUNDING: UK National Institute for Health Research Imperial Biomedical Research Centre, Imperial College Healthcare Charity, the Wellcome Trust, and UK National Institute for Health Research Health Protection Research Unit in Healthcare-associated Infections and Antimictobial Resistance at Imperial College London

Enhanced Transferrin Receptor Expression by Proinflammatory Cytokines in Enterocytes as a Means for Local Delivery of Drugs to Inflamed Gut Mucosa

Therapeutic intervention in inflammatory bowel diseases (IBDs) is often associated with adverse effects related to drug distribution into non-diseased tissues, a situation which attracts a rational design of a targeted treatment confined to the inflamed mucosa. Upon activation of immune cells, transferrin receptor (TfR) expression increases at their surface. Because TfR is expressed in all cell types we hypothesized that its cell surface levels are regulated also in enterocytes. We, therefore, compared TfR expression in healthy and inflamed human colonic mucosa, as well as healthy and inflamed colonic mucosa of the DNBS-induced rat model. TfR expression was elevated in the colonic mucosa of IBD patients in both the basolateral and apical membranes of the enterocytes. Increased TfR expression was also observed in colonocytes of the induced colitis rats. To explore the underlying mechanism CaCo-2 cells were treated with various proinflammatory cytokines, which increased both TfR expression and transferrin cellular uptake in a mechanism that did not involve hyper proliferation. These findings were then exploited for the design of targetable carrier towards inflamed regions of the colon. Anti-TfR antibodies were conjugated to nano-liposomes. As expected, iron-starved Caco-2 cells internalized anti-TfR immunoliposomes better than controls. Ex vivo binding studies to inflamed mucosa showed that the anti-TfR immunoliposomes accumulated significantly better in the mucosa of DNBS-induced rats than the accumulation of non-specific immunoliposomes. It is concluded that targeting mucosal inflammation can be accomplished by nano-liposomes decorated with anti-TfR due to inflammation-dependent, apical, elevated expression of the receptor

The origin and speciation of orchids

SummaryOrchids constitute one of the most spectacular radiations of flowering plants. However, their origin, spread across the globe, and hotspots of speciation remain uncertain due to the lack of an up-to-date phylogeographic analysis.We present a new Orchidaceae phylogeny based on combined high-throughput and Sanger sequencing data, covering all five subfamilies, 17/22 tribes, 40/49 subtribes, 285/736 genera, and c. 7% (1921) of the 29 524 accepted species, and use it to infer geographic range evolution, diversity, and speciation patterns by adding curated geographical distributions from the World Checklist of Vascular Plants.The orchids' most recent common ancestor is inferred to have lived in Late Cretaceous Laurasia. The modern range of Apostasioideae, which comprises two genera with 16 species from India to northern Australia, is interpreted as relictual, similar to that of numerous other groups that went extinct at higher latitudes following the global climate cooling during the Oligocene. Despite their ancient origin, modern orchid species diversity mainly originated over the last 5 Ma, with the highest speciation rates in Panama and Costa Rica.These results alter our understanding of the geographic origin of orchids, previously proposed as Australian, and pinpoint Central America as a region of recent, explosive speciation

The Eighteenth Data Release of the Sloan Digital Sky Surveys: Targeting and First Spectra from SDSS-V

The eighteenth data release of the Sloan Digital Sky Surveys (SDSS) is the first one for SDSS-V, the fifth generation of the survey. SDSS-V comprises three primary scientific programs, or "Mappers": Milky Way Mapper (MWM), Black Hole Mapper (BHM), and Local Volume Mapper (LVM). This data release contains extensive targeting information for the two multi-object spectroscopy programs (MWM and BHM), including input catalogs and selection functions for their numerous scientific objectives. We describe the production of the targeting databases and their calibration- and scientifically-focused components. DR18 also includes ~25,000 new SDSS spectra and supplemental information for X-ray sources identified by eROSITA in its eFEDS field. We present updates to some of the SDSS software pipelines and preview changes anticipated for DR19. We also describe three value-added catalogs (VACs) based on SDSS-IV data that have been published since DR17, and one VAC based on the SDSS-V data in the eFEDS field.Comment: Accepted to ApJ

The eighteenth data release of the Sloan Digital Sky Surveys : targeting and first spectra from SDSS-V

The eighteenth data release of the Sloan Digital Sky Surveys (SDSS) is the first one for SDSS-V, the fifth generation of the survey. SDSS-V comprises three primary scientific programs, or "Mappers": Milky Way Mapper (MWM), Black Hole Mapper (BHM), and Local Volume Mapper (LVM). This data release contains extensive targeting information for the two multi-object spectroscopy programs (MWM and BHM), including input catalogs and selection functions for their numerous scientific objectives. We describe the production of the targeting databases and their calibration- and scientifically-focused components. DR18 also includes ~25,000 new SDSS spectra and supplemental information for X-ray sources identified by eROSITA in its eFEDS field. We present updates to some of the SDSS software pipelines and preview changes anticipated for DR19. We also describe three value-added catalogs (VACs) based on SDSS-IV data that have been published since DR17, and one VAC based on the SDSS-V data in the eFEDS field.Publisher PDFPeer reviewe