Monomial patterns in the sequence Akb

AbstractWe consider the pattern of zero and nonzero elements in the sequence Akb, where A is an n × n nonnegative matrix and b is an n × 1 nonnegative column vector. We establish a tight bound of k < n for the first occurrence of a given monomial pattern, and we give a graph theoretic characterization of triples (A, b, i) such that there exists a k, k ⩾ n, for which Akb is an i-monomial. The appearance of monomial patterns with a single nonzero entry is linked to controllability of discrete n-dimensional linear dynamic systems with positivity constraints on the state and control

A New GTSeq Resource to Facilitate Multijurisdictional Research and Management of Walleye Sander Vitreus

Conservation and management professionals often work across jurisdictional boundaries to identify broad ecological patterns. These collaborations help to protect populations whose distributions span political borders. One common limitation to multijurisdictional collaboration is consistency in data recording and reporting. This limitation can impact genetic research, which relies on data about specific markers in an organism\u27s genome. Incomplete overlap of markers between separate studies can prevent direct comparisons of results. Standardized marker panels can reduce the impact of this issue and provide a common starting place for new research. Genotyping-in-thousands (GTSeq) is one approach used to create standardized marker panels for nonmodel organisms. Here, we describe the development, optimization, and early assessments of a new GTSeq panel for use with walleye (Sander vitreus) from the Great Lakes region of North America. High genome-coverage sequencing conducted using RAD capture provided genotypes for thousands of single nucleotide polymorphisms (SNPs). From these markers, SNP and microhaplotype markers were chosen, which were informative for genetic stock identification (GSI) and kinship analysis. The final GTSeq panel contained 500 markers, including 197 microhaplotypes and 303 SNPs. Leave-one-out GSI simulations indicated that GSI accuracy should be greater than 80% in most jurisdictions. The false-positive rates of parent-offspring and full-sibling kinship identification were found to be low. Finally, genotypes could be consistently scored among separate sequencing runs \u3e94% of the time. Results indicate that the GTSeq panel that we developed should perform well for multijurisdictional walleye research throughout the Great Lakes region

Simulating the formation and evolution of galaxies: Multi-phase description of the interstellar medium, star formation, and energy feedback

We present a multi-phase representation of the ISM in NB-TSPH simulations of galaxy formation and evolution with particular attention to the case of early-type galaxies. Cold gas clouds are described by the so-called sticky particles algorithm. They can freely move throughout the hot ISM medium; stars form within these clouds and the mass exchange among the three baryonic phases (hot gas, cold clouds, stars) is governed by radiative and Compton cooling and energy feedback by supernova (SN) explosions, stellar winds, and UV radiation. We also consider thermal conduction, cloud-cloud collisions, and chemical enrichment. Our model agrees with and improves upon previous studies on the same subject. The results for the star formation rate are very promising and agree with recent observational data on early-type galaxies. These models lend further support to the revised monolithic scheme of galaxy formation, which has recently been also strengthened by high redshift data leading to the so-called downsizing and top-down scenarios.Comment: 17 pages, 17 figure

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that stellar birth is primarily controlled by the interplay between gravity and magnetostatic support, modulated by ambipolar diffusion. Recently, however, both observational and numerical work has begun to suggest that support by supersonic turbulence rather than magnetic fields controls star formation. In this review we outline a new theory of star formation relying on the control by turbulence. We demonstrate that although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic scale star formation. (ABSTRACT ABBREVIATED)Comment: Invited review for "Reviews of Modern Physics", 87 pages including 28 figures, in pres

Molecular line mapping of the giant molecular cloud associated with RCW 106 - III. Multi-molecular line mapping

We present multi-molecular line maps obtained with the Mopra Telescope towards the southern giant molecular cloud (GMC) complex G333, associated with the HII region RCW 106. We have characterised the GMC by decomposing the 3D data cubes with GAUSSCLUMPS, and investigated spatial correlations among different molecules with principal component analysis (PCA). We find no correlation between clump size and line width, but a strong correlation between emission luminosity and line width. PCA classifies molecules into high and low density tracers, and reveals that HCO+ and N2H+ are anti-correlated.Comment: 24 pages, 21 figures accepted by MNRA

Identification of 12 new susceptibility loci for different histotypes of epithelial ovarian cancer.

To identify common alleles associated with different histotypes of epithelial ovarian cancer (EOC), we pooled data from multiple genome-wide genotyping projects totaling 25,509 EOC cases and 40,941 controls. We identified nine new susceptibility loci for different EOC histotypes: six for serous EOC histotypes (3q28, 4q32.3, 8q21.11, 10q24.33, 18q11.2 and 22q12.1), two for mucinous EOC (3q22.3 and 9q31.1) and one for endometrioid EOC (5q12.3). We then performed meta-analysis on the results for high-grade serous ovarian cancer with the results from analysis of 31,448 BRCA1 and BRCA2 mutation carriers, including 3,887 mutation carriers with EOC. This identified three additional susceptibility loci at 2q13, 8q24.1 and 12q24.31. Integrated analyses of genes and regulatory biofeatures at each locus predicted candidate susceptibility genes, including OBFC1, a new candidate susceptibility gene for low-grade and borderline serous EOC

Algebra and Trigonometry Refresher for Calculus Students

XX, 192 tr.; 27 cm

The William Lowell Putnam mathematical competition: problems and solutions 1965-1984

The Putnam Competition has been providing a challenge to gifted college mathematics students since 1928. This book, the second of the Putnam Competition volumes, contains problems with their solutions for the years 1965-1984. Additional solutions are presented for many of the problems. Included is an essay on recollections of the first Putnam Exam by Herbert Robbins, as well as appendices listing the winning teams and students from 1965 through 1984. This volume offers the problem solver an enticing sample of challenging problems and their solutions