Counting non-isomorphic maximal independent sets of the n-cycle graph

The number of maximal independent sets of the n-cycle graph C_n is known to be the nth term of the Perrin sequence. The action of the automorphism group of C_n on the family of these maximal independent sets partitions this family into disjoint orbits, which represent the non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets. We provide exact formulas for the total number of orbits and the number of orbits having a given number of isomorphic representatives. We also provide exact formulas for the total number of unlabeled (i.e., defined up to a rotation) maximal independent sets and the number of unlabeled maximal independent sets having a given number of isomorphic representatives. It turns out that these formulas involve both Perrin and Padovan sequences.Comment: Revised versio

La rigidité générique des graphes biparti-complets dans Rd

Dans un article déjà commenté dans Topologie structurale, E.D. Bolkeret B. Roth ((Bolker 1980), (Whiteley 1979)) amorçaient une classification générique des graphes biparti-complets dans R2 et dans R3. Leur raisonnement était basé sur le calcul de la dimension de l’espace des autocontraintes (stress) pour une réalisation d’un graphe biparti-complet dans un espace donné. La classification qu’ils établissaient se limitait à R2 et A R3. Le texte qui suit se veut une généralisation de leurs résultats à des espaces de dimension supérieure. Nous pourrons établir la classification générique des structures construites sur des graphes biparti-complets en regard de leur comportement rigide dans un espace ambiant fixé de dimension supérieure ou égale à 2.In an article reviewed earlier in Structural Topology, E.D. Bolker and B. Roth ((Bolker 1980), (Whiteley 1979)) put together a generic classification of complete bipartite graphs in R2 and R’. Their reasoning was based on calculating the dimension of the space of stresses for a realization of a complete bipartite graph in a given space. The classification which they established applies only to R2 and R3. The text which follows is a generalization of their results to spaces of higher dimension. We can establish the generic classification of structures built over complete bipartite graphs with regard to their rigid behavior in a fixed ambient space of dimension greater than or equal to 2.Peer Reviewe

Multiplexed holographic transmission gratings recorded in holographic polymer-dispersed liquid crystals: static and dynamic studies

The optimization of the experimental parameters of two multiplexed holographic transmission gratings recorded in holographic polymer-dispersed liquid crystals is investigated. Two methods are used to record the holograms: simultaneous and sequential multiplexing. These two processes are optimized to produce two multiplexed Bragg gratings that have the same and the highest possible diffraction efficiencies in the first order. The two methods show similar results when suitable recording parameters are used. The parameters of the recorded gratings (mainly the refractive-index modulation) are retrieved by use of an extension of the rigorous coupled-wave theory to multiplexed gratings. Finally, the response of the holograms to an electric field is studied. We demonstrate few coupling effects between the behavior of both gratings, and we expect a possibility of switching from one grating to the other

Diagnostic changes as a reason for the increase in papillary thyroid cancer incidence in Geneva, Switzerland

Objective: Several studies have reported upward incidence trends of papillary thyroid cancer. It is unclear whether these trends reflect a real risk increase, by some attributed to iodine supplementation, or an artificial one, due to increased diagnostic activity or changed histological criteria. This study examines if these artificial factors explain the increased papillary thyroid cancer incidence in the Swiss canton of Geneva. Methods: All thyroid carcinomas (n = 436) recorded between 1970 and 1998 at the Geneva Cancer Registry were considered. European age-adjusted incidence trends were estimated using linear regression analysis. For papillary cancers we evaluated diagnostic modalities and way of presentation (in particular microcarcinoma < 1 cm or silent carcinoma). In addition, we reviewed the histological slides of follicular carcinomas. Results: Papillary thyroid cancer incidence increased significantly from 0.7 to 1.8/100,000 for men and from 3.1 to 4.3/100,000 for women between 1970-74 and 1995-98. The proportion of microcarcinomas and silent carcinomas increased from 17% to 24% between 1970-79 and 1990-98. At histological review, follicular cancers were more often reclassified as papillary cancer for cases diagnosed between 1970 and 1979 than for cases diagnosed between 1990 and 1998 (45% vs 25%, p = n.s.). Conclusions: The increasing papillary thyroid cancer incidence seems mainly due to changes in histological diagnostic criteria and, to a lesser extent, to increased diagnostic activity. If confirmed, the results of this study indicate that fears of increasing incidence rates of papillary thyroid cancer should not prevent implementation of adequate programs of iodine supplementation in the many areas where iodine deficiency still prevail

The warm interstellar medium around the Cygnus Loop

Observations of the oxygen lines [OII]3729 and [OIII]5007 in the medium immediately beyond the Cygnus Loop supernova remnant were carried out with the scanning Fabry-P\'erot spectrophotometer ESOP. Both lines were detected in three different directions - east, northeast and southwest - and up to a distance of 15 pc from the shock front. The ionized medium is in the immediate vicinity of the remnant, as evinced by the smooth brightening of both lines as the adiabatic shock transition (defined by the X-ray perimeter) is crossed. These lines are usually brighter around the Cygnus Loop than in the general background in directions where the galactic latitude is above 5 degrees. There is also marginal (but significant) evidence that the degree of ionization is somewhat larger around the Cygnus Loop. We conclude that the energy necessary to ionize this large bubble of gas could have been supplied by an O8 or O9 type progenitor or the particles heated by the expanding shock front. The second possibility, though highly atractive, would have to be assessed by extensive modelling.Comment: 18 pages, 8 figures, ApJ 512 in pres

Determination of an optimal response cut-off able to predict progression-free survival in patients with well-differentiated advanced pancreatic neuroendocrine tumours treated with sunitinib: an alternative to the current RECIST-defined response.

BACKGROUND: Sunitinib prolongs progression-free survival (PFS) in patients with advanced pancreatic neuroendocrine tumours (pNET). Response Evaluation Criteria in Solid Tumors (RECIST)-defined partial responses (PR; classically defined as ⩾30% size decrease from baseline) are infrequent. METHODS: Individual data of pNET patients from the phase II [NCT00056693] and pivotal phase III [NCT00428597] trials of sunitinib were analysed in this investigator-initiated, post hoc study. The primary objective was to determine the optimal RECIST (v.1.0) response cut-off value to identify patients who were progression-free at 11 months (median PFS in phase III trial); and the most informative time-point (highest area under the curve (AUC) by receiver operating characteristic (ROC) analysis and logistic regression) for prediction of benefit (PFS) from sunitinib. RESULTS: Data for 237 patients (85 placebo; 152 sunitinib (n=66.50 mg \u274-weeks on/2-weeks off\u27 schedule; n=86 \u2737.5 mg continuous daily dosing (CDD)\u27)) and 788 scans were analysed. The median PFS for sunitinib and placebo were 9.3 months (95% CI 7.6-12.2) and 5.4 months (95% CI 3.5-6.01), respectively (hazard ratio (HR) 0.43 (95% CI 0.29-0.62); P CONCLUSIONS: A 10% reduction within marker lesions identifies pNET patients benefiting from sunitinib treatment with implications for maintenance of dose intensity and future trial design

SSU1 Checkup, a Rapid Tool for Detecting Chromosomal Rearrangements Related to the SSU1 Promoter in Saccharomyces cerevisiae: An Ecological and Technological Study on Wine Yeast

Chromosomal rearrangements (CR) such as translocations, duplications and inversions play a decisive role in the adaptation of microorganisms to specific environments. In enological Saccharomyces cerevisiae strains, CR involving the promoter region of the gene SSU1 lead to a higher sulfite tolerance by enhancing the SO2 efflux. To date, three different SSU1 associated CR events have been described, including translocations XV-t-XVI and VIII-t-XVI and inversion inv-XVI. In the present study, we developed a multiplex PCR method (SSU1 checkup) that allows a rapid characterization of these three chromosomal configurations in a single experiment. Nearly 600 S. cerevisiae strains collected from fermented grape juice were genotyped by microsatellite markers. We demonstrated that alleles of the SSU1 promoter are differently distributed according to the wine environment (cellar versus vineyard) and the nature of the grape juice. Moreover, rearranged SSU1 promoters are significantly enriched among commercial starters. In addition, the analysis of nearly isogenic strains collected in wine related environments demonstrated that the inheritance of these CR shapes the genetic diversity of clonal populations. Finally, the link between the nature of SSU1 promoter and the tolerance to sulfite was statistically validated in natural grape juice containing various SO2 concentrations. The SSU1 checkup is therefore a convenient new tool for addressing population genetics questions and for selecting yeast strains by using molecular markers.Fil: Marullo, Philippe. Universite de Bordeaux; FranciaFil: Claisse, Olivier. Universite de Bordeaux; FranciaFil: Raymond Eder, María Laura. Universidad Católica de Córdoba. Instituto de Investigaciones en Recursos Naturales y Sustentabilidad José Sanchez Labrador S. J. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Recursos Naturales y Sustentabilidad José Sanchez Labrador S. J.; ArgentinaFil: Börlin, Marine. Universite de Bordeaux; FranciaFil: Feghali, Nadine. Lebanese University; LíbanoFil: Bernard, Margaux. Universite de Bordeaux; FranciaFil: Legras, Jean Luc. Université Montpellier II; FranciaFil: Albertin, Warren. Universite de Bordeaux; FranciaFil: Rosa, Alberto Luis. Universidad Católica de Córdoba. Instituto de Investigaciones en Recursos Naturales y Sustentabilidad José Sanchez Labrador S. J. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Recursos Naturales y Sustentabilidad José Sanchez Labrador S. J.; ArgentinaFil: Masneuf Pomarede, Isabelle. Universite de Bordeaux; Franci

Mercury's Moment of Inertia from Spin and Gravity Data

Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 plus or minus 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 plus or minus 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 plus or minus 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 plus or minus 0.025