Scarf's Theorem and Applications in Combinatorics

A theorem due to Scarf in 1967 is examined in detail. Several versions of this theorem exist, some which appear at first unrelated. Two versions can be shown to be equivalent to a result due to Sperner in 1928: for a proper labelling of the vertices in a simplicial subdivision of an n-simplex, there exists at least one elementary simplex which carries all labels {0,1,..., n}. A third version is more akin to Dantzig's simplex method and is also examined. In recent years many new applications in combinatorics have been found, and we present several of them. Two applications are in the area of fair division: cake cutting and rent partitioning. Two others are graph theoretic: showing the existence of a fractional stable matching in a hypergraph and the existence of a fractional kernel in a directed graph. For these last two, we also show the second implies the first

A Meta-Analysis of Genome-Wide Association Scans Identifies IL18RAP, PTPN2, TAGAP, and PUS10 As Shared Risk Loci for Crohn's Disease and Celiac Disease

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

First Astronomical Use of Multiplexed Transition Edge Bolometers

We present performance results based on the first astronomical use of multiplexed superconducting bolometers. The Fabry-Perot Interferometer Bolometer Research Experiment (FIBRE) is a broadband submillimeter spectrometer that achieved first light in June 2001 at the Caltech Submillimeter Observatory (CSO). FIBRE'S detectors are superconducting transition edge sensor (TES) bolometers read out by a SQUID multiplexer. The Fabry-Perot uses a low resolution grating to order sort the incoming light. A linear bolometer array consisting of 16 elements detects this dispersed light, capturing 5 orders simultaneously from one position on the sky. With tuning of the Fabry-Perot over one free spectral range, a spectrum covering Δλ/λ= 1/7 at a resolution of δλ/λ ≈ 1/1200 can be acquired. This spectral resolution is sufficient to resolve Doppler-broadened line emission from external galaxies. FIBRE operates in the 350 µm and 450 µm bands. These bands cover line emission from the important star formation tracers neutral carbon [Cl] and carbon monoxide (CO). We have verified that the multiplexed bolometers are photon noise limited even with the low power present in moderate resolution spectrometry

Scanning tunneling microscopy of deoxyribonucleic acid during replication

Scanning tunneling microscopy was used to produce topographic images of uncoated and unlabeled deoxyribonucleic acid (DNA) in air, on a graphite substrate. The images show for the first time a DNA molecule that had been isolated while it was replicating

Renal cell carcinoma: ESMO Clinical Practice Guidelines for diagnosis, treatment and follow-up

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Les phlébotomes (Diptera-Psychodidae) de l'île de Chypre.II - Presence de Leishmania (Leishmania) infantum Nicolle, 1908 (zymodeme MON 1) chez Phlebotomus (Larroussius) tobbi Adler et Theodor, 1930

Dans le foyer leishmanien cypriote, les auteurs ont disseque 2910 femelles de phlebotomes appartenant a 11 especes : Phlebotomus papatasi, P. sergenti, P. jacusieli, P. alexandri, P. tobbi, P. galilaeus, P. mascittii, P. economidesi, Sergentomyia fallax, S. minuta et S. azizi . Les deux larroussius (P. galilaeus et P. tobbi ) sont les especes les plus abondantes. Elles representent plus de 60 % des captures realisees avec des pieges CDC. Des promastigotes ont ete observees chez un seul specimen appartenant a l'espece P. tobbi . Elles ont ete mises en culture puis identifiees selon la methode isoenzymatique. La souche de Leishmania isolee appartient a l'espece Leishmania infantum , zymodeme MON 1. Le meme zymodeme a ete aussi isole et identifie chez quatre chiens de l'ile. En l'absence des vecteurs habituels de L. infantum dans l'est mediterraneen (P. neglectus ef P. syriacus) et en raison de sa repartition a Chypre, P. tobbi constitue vraisemblablement un bon vecteur local. Sa faible anthropophilie expliquerait peut-etre le tres faible nombre de cas humains. Le role de P. galilaeus dans la transmission de la leishmaniose a Chypre reste a preciser

Epidemiologic Relationship between Toscana Virus Infection and Leishmania infantum Due to Common Exposure to Phlebotomus perniciosus Sandfly Vector

Sand flies are recognised vectors of parasites in the genus Leishmania and a number of arthropod-borne viruses, in particular viruses within the genus Phlebovirus, family Bunyaviridae. In southern France, Toscana phlebovirus (TOSV) is recognized as a prominent cause of summer meningitis. Since Leishmania and TOSV have a common vector (Phlebotomus perniciosus), an epidemiologic link has been assumed for a long time. However, there is no scientific evidence of such a link between human leishmaniosis and phleboviral infections. To identify a possible link, we investigated the presence and distribution of antibodies against these two microorganisms (i) in individuals and (ii) at a spatial level in the city of Marseille (south-eastern France). Five hundred sera were selected randomly in the biobank of the Department of Parasitology of the Public Hospitals of Marseille. All sera were previously tested for IgG against Leishmania by Western Blotting, and TOSV IgG were detected by indirect immunofluorescence. The seropositivity rates were 21.4% for TOSV and 28% for Leishmania. Statistical analysis demonstrated that seropositivity for one pathogen was significantly associated with seropositivity to the other pathogen. This result provided the first robust evidence for the existence of an epidemiological relationship between Leishmania infantum and TOSV. Addresses of tested patients were geolocalized and integrated into Geographical Information System software, in order to test spatial relationship between the two pathogens. Spatial analysis did not allow to identify (i) specific patterns for the spatial distribution of positive serological results for TOSV or Leishmania, and (ii) a spatial relationship between Leishmania and TOSV positive serological results. This may reflect the fact that the sample studied was not powerful enough to demonstrate either a spatial clustering or co-location, i.e. that the actual risk exposure area is smaller than the mean of distance between patients in our study (245 m)