Numerical and Symbolical Methods for the GCD of Several Polynomials

The computation of the Greatest Common Divisor (GCD) of a set of polynomials is an important issue in computational mathematics and it is linked to Control Theory very strong. In this paper we present different matrix-based methods, which are developed for the efficient computation of the GCD of several polynomials. Some of these methods are naturally developed for dealing with numerical inaccuracies in the input data and produce meaningful approximate results. Therefore, we describe and compare numerically and symbolically methods such as the ERES, the Matrix Pencil and other resultant type methods, with respect to their complexity and effectiveness. The combination of numerical and symbolic operations suggests a new approach in software mathematical computations denoted as hybrid computations. This combination offers great advantages, especially when we are interested in finding approximate solutions. Finally the notion of approximate GCD is discussed and a useful criterion estimating the strength of a given approximate GCD is also developed

Karyotype, Sex Determination, and Meiotic Chromosome Behavior in Two Pholcid (Araneomorphae, Pholcidae) Spiders: Implications for Karyotype Evolution

There are 1,111 species of pholcid spiders, of which less than 2% have published karyotypes. Our aim in this study was to determine the karyotypes and sex determination mechanisms of two species of pholcids: Physocyclus mexicanus (Banks, 1898) and Holocnemus pluchei (Scopoli, 1763), and to observe sex chromosome behavior during meiosis. We constructed karyotypes for P. mexicanus and H. pluchei using information from both living and fixed cells. We found that P. mexicanus has a chromosome number of 2n = 15 in males and 2n = 16 in females with X0-XX sex determination, like other members of the genus Physocyclus. H. pluchei has a chromosome number of 2n = 28 in males and 2n = 28 in females with XY-XX sex determination, which is substantially different from its closest relatives. These data contribute to our knowledge of the evolution of this large and geographically ubiquitous family, and are the first evidence of XY-XX sex determination in pholcids

Spinal cord grey matter segmentation challenge

An important image processing step in spinal cord magnetic resonance imaging is the ability to reliably and accurately segment grey and white matter for tissue specific analysis. There are several semi- or fully-automated segmentation methods for cervical cord cross-sectional area measurement with an excellent performance close or equal to the manual segmentation. However, grey matter segmentation is still challenging due to small cross-sectional size and shape, and active research is being conducted by several groups around the world in this field. Therefore a grey matter spinal cord segmentation challenge was organised to test different capabilities of various methods using the same multi-centre and multi-vendor dataset acquired with distinct 3D gradient-echo sequences. This challenge aimed to characterize the state-of-the-art in the field as well as identifying new opportunities for future improvements. Six different spinal cord grey matter segmentation methods developed independently by various research groups across the world and their performance were compared to manual segmentation outcomes, the present gold-standard. All algorithms provided good overall results for detecting the grey matter butterfly, albeit with variable performance in certain quality-of-segmentation metrics. The data have been made publicly available and the challenge web site remains open to new submissions. No modifications were introduced to any of the presented methods as a result of this challenge for the purposes of this publication

Measurement of the branching fraction and CP content for the decay B(0) -> D(*+)D(*-)

This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APS.We report a measurement of the branching fraction of the decay B0→D*+D*- and of the CP-odd component of its final state using the BABAR detector. With data corresponding to an integrated luminosity of 20.4  fb-1 collected at the Υ(4S) resonance during 1999–2000, we have reconstructed 38 candidate signal events in the mode B0→D*+D*- with an estimated background of 6.2±0.5 events. From these events, we determine the branching fraction to be B(B0→D*+D*-)=[8.3±1.6(stat)±1.2(syst)]×10-4. The measured CP-odd fraction of the final state is 0.22±0.18(stat)±0.03(syst).This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A.P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation

Measurement of CP-violation asymmetries in D0 to Ks pi+ pi-

We report a measurement of time-integrated CP-violation asymmetries in the resonant substructure of the three-body decay D0 to Ks pi+ pi- using CDF II data corresponding to 6.0 invfb of integrated luminosity from Tevatron ppbar collisions at sqrt(s) = 1.96 TeV. The charm mesons used in this analysis come from D*+(2010) to D0 pi+ and D*-(2010) to D0bar pi-, where the production flavor of the charm meson is determined by the charge of the accompanying pion. We apply a Dalitz-amplitude analysis for the description of the dynamic decay structure and use two complementary approaches, namely a full Dalitz-plot fit employing the isobar model for the contributing resonances and a model-independent bin-by-bin comparison of the D0 and D0bar Dalitz plots. We find no CP-violation effects and measure an asymmetry of ACP = (-0.05 +- 0.57 (stat) +- 0.54 (syst))% for the overall integrated CP-violation asymmetry, consistent with the standard model prediction.Comment: 15 page

Search for rare quark-annihilation decays, B --> Ds(*) Phi

We report on searches for B- --> Ds- Phi and B- --> Ds*- Phi. In the context of the Standard Model, these decays are expected to be highly suppressed since they proceed through annihilation of the b and u-bar quarks in the B- meson. Our results are based on 234 million Upsilon(4S) --> B Bbar decays collected with the BABAR detector at SLAC. We find no evidence for these decays, and we set Bayesian 90% confidence level upper limits on the branching fractions BF(B- --> Ds- Phi) Ds*- Phi)<1.2x10^(-5). These results are consistent with Standard Model expectations.Comment: 8 pages, 3 postscript figues, submitted to Phys. Rev. D (Rapid Communications

Ordered Mesostructured CdS Nanowire Arrays with Rectifying Properties

Highly ordered mesoporous CdS nanowire arrays were synthesized by using mesoporous silica as hard template and cadmium xanthate (CdR2) as a single precursor. Upon etching silica, mesoporous CdS nanowire arrays were produced with a yield as high as 93 wt%. The nanowire arrays were characterized by XRD, N2adsorption, TEM, and SEM. The results show that the CdS products replicated from the mesoporous silica SBA-15 hard template possess highly ordered hexagonal mesostructure and fiber-like morphology, analogous to the mother template. The current–voltage characteristics of CdS nanoarrays are strongly nonlinear and asymmetrical, showing rectifying diode-like behavior