Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.Comment: 4 pages, 2 figure

Properties of a square root transformation regression model

We consider the problem of modelling the conditional distribution of a response given a vector of covariates x when the response is a compositional data vector u. That is, u is defined on the unit simplex [...] This definition of the unit simplex differs subtly from that of Aitchison (1982), as we relax the con- dition that the components of u must be strictly positive. Under this scenario, use of the ratio (or logratio) to compare different compositions is not ideal since it is undefined in some instances, and subcompositional analysis is also not appropriate due to the possibility of division by zero. It has long been recognised that the square root transformation [...] transforms compositional data (including zeros) onto the surface of the (p-1)-dimensional hyperspher

Faunal assemblages and multi–scale habitat patterns in headwater tributaries of the South Fork Trinity River – an unregulated river embedded within a multiple–use landscape

Las cabeceras pueden representar el 80% de los kilómetros de recorrido en una cuenca fluvial y poseen unas propiedades físicas y biológicas únicas, cuya importancia hasta hace poco no se habían reconocido para el sostenimiento de un funcionamiento sano de las redes de cuencas y sus servicios ecológicos. Tomamos muestras de 60 cabeceras de los afluentes del río South Fork Trinity, una cuenca de 2.430 km2, boscosa en su mayor parte y de múltiples usos, situada en el noroeste de California. Nuestros objetivos eran: (1) diferenciar tipos de cabeceras únicos utilizando 69 variables abióticas y vegetales, medidas a tres escalas espaciales, y luego reducirlos a subconjuntos informativos; (2) determinar si distintos biotas ocupaban los distintos tipos de afluentes; (3) determinar las características medioambientales asociadas con la presencia y abundancia de dichas comunidades bióticas; y (4) utilizando una modelización de nichos, determinar los umbrales de los atributos claves para ilustrar cómo estos biotas podrían emplearse para la medición de la integridad del sistema y los servicios ecológicos. Varios taxones fueron suficientemente abundantes y extendidos para utilizarlos como bioindicadores; la presencia y abundancia de la trucha arco iris (Oncorhynchus mykiss), la riqueza en especies de la herpetofauna (reptiles y anfibios) y el cangrejo señal (Pacifastacus leniusculus) representaban diferentes posiciones tróficas, el valor como recursos comerciales (la trucha arco iris), la sensibilidad al estrés ambiental (anfibios), e indicadores de la biodiversidad (riqueza de especies de la herpetofauna). La riqueza de especies de la herpetofauna no difirió, pero la abundancia de la trucha arco iris, del cangrejo señal, la riqueza de anfibios, difirieron significativamente entre los tipos de afluentes. Los modelos de los nichos indicaron que los patrones de distribución y abundancia, tanto en los ambientes acuáticos como en los ribereños, estaban asociados con atributos físicos y estructurales a multiples escalas espaciales, tanto dentro como alrededor de los tramos acuáticos. Los bioindicadores respondieron a series únicas de atributos, reflejando la elevada heterogeneidad ambiental en las cabeceras de los afluentes en toda esta gran cuenca. Dichos atributos de los nichos representaban una amplia gama de ambientes de cabeceras fluviales, indicando respuestas a una serie de condiciones naturales y antropogénicas. Se demostró el valor de utilizar una serie de bioindicadores para elucidar las condiciones de las cabeceras y para examinar las numerosas perturbaciones que pueden influir sobre la integridad ecológica. Palabras clave: Cabeceras de afluentes, Bioindicadores, Multiescala, Integridad ecológica.Las cabeceras pueden representar el 80% de los kilómetros de recorrido en una cuenca fluvial y poseen unas propiedades físicas y biológicas únicas, cuya importancia hasta hace poco no se habían reconocido para el sostenimiento de un funcionamiento sano de las redes de cuencas y sus servicios ecológicos. Tomamos muestras de 60 cabeceras de los afluentes del río South Fork Trinity, una cuenca de 2.430 km2, boscosa en su mayor parte y de múltiples usos, situada en el noroeste de California. Nuestros objetivos eran: (1) diferenciar tipos de cabeceras únicos utilizando 69 variables abióticas y vegetales, medidas a tres escalas espaciales, y luego reducirlos a subconjuntos informativos; (2) determinar si distintos biotas ocupaban los distintos tipos de afluentes; (3) determinar las características medioambientales asociadas con la presencia y abundancia de dichas comunidades bióticas; y (4) utilizando una modelización de nichos, determinar los umbrales de los atributos claves para ilustrar cómo estos biotas podrían emplearse para la medición de la integridad del sistema y los servicios ecológicos. Varios taxones fueron suficientemente abundantes y extendidos para utilizarlos como bioindicadores; la presencia y abundancia de la trucha arco iris (Oncorhynchus mykiss), la riqueza en especies de la herpetofauna (reptiles y anfibios) y el cangrejo señal (Pacifastacus leniusculus) representaban diferentes posiciones tróficas, el valor como recursos comerciales (la trucha arco iris), la sensibilidad al estrés ambiental (anfibios), e indicadores de la biodiversidad (riqueza de especies de la herpetofauna). La riqueza de especies de la herpetofauna no difirió, pero la abundancia de la trucha arco iris, del cangrejo señal, la riqueza de anfibios, difirieron significativamente entre los tipos de afluentes. Los modelos de los nichos indicaron que los patrones de distribución y abundancia, tanto en los ambientes acuáticos como en los ribereños, estaban asociados con atributos físicos y estructurales a multiples escalas espaciales, tanto dentro como alrededor de los tramos acuáticos. Los bioindicadores respondieron a series únicas de atributos, reflejando la elevada heterogeneidad ambiental en las cabeceras de los afluentes en toda esta gran cuenca. Dichos atributos de los nichos representaban una amplia gama de ambientes de cabeceras fluviales, indicando respuestas a una serie de condiciones naturales y antropogénicas. Se demostró el valor de utilizar una serie de bioindicadores para elucidar las condiciones de las cabeceras y para examinar las numerosas perturbaciones que pueden influir sobre la integridad ecológica. Palabras clave: Cabeceras de afluentes, Bioindicadores, Multiescala, Integridad ecológica.Headwaters can represent 80% of stream kilometers in a watershed, and they also have unique physical and biological properties that have only recently been recognized for their importance in sustaining healthy functioning stream networks and their ecological services. We sampled 60 headwater tributaries in the South Fork Trinity River, a 2,430 km2, mostly forested, multiple–use watershed in northwestern California. Our objectives were: (1) to differentiate unique headwater types using 69 abiotic and vegetation variables measured at three spatial scales, and then to reduce these to informative subsets; (2) determine if distinct biota occupied the different tributary types; (3) determine the environmental attributes associated with the presence and abundance of these biotic assemblages; and (4) using niche modeling, determine key attribute thresholds to illustrate how these biota could be employed as metrics of system integrity and ecologi¬cal services. Several taxa were sufficiently abundant and widespread to use as bio–indicators: the presence and abundance of steelhead trout (Oncorhynchus mykiss), herpetofauna (reptile and amphibian) species richness, and signal crayfish (Pacifastacus leniusculus) represented different trophic positions, value as commercial resources (steelhead), sensitivity to environmental stress (amphibians), and indicators of biodiversity (herpetofauna species richness). Herpetofauna species richness did not differ, but abundances of steelhead trout, signal crayfish, and amphibian richness all differed significantly among tributary types. Niche models indicated that distribution and abun¬dance patterns in both riparian and aquatic environments were associated with physical and structural attributes at multiple spatial scales, both within and around reaches. The bio–indicators responded to unique sets of attributes, reflecting the high environmental heterogeneity in headwater tributaries across this large watershed. These niche attributes represented a wide range of headwater environments, indicating responses to a number of natural and anthropogenic conditions, and demonstrated the value of using a suite of bio–indicators to elucidate watershed conditions, and to examine numerous disturbances that may influence ecological integrity. Key words: Headwater tributaries, Bio–indicators, Multi–scale, Ecological integrity

The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

The Ethical Orientation of U.S. Small Business Decision Makers: A Preliminary Study

Recent news reports of escalating ethics violations in the workplace has produced growing concern. This study surveyed small business decision makers concerning their ethical orientation. These results were then compared to general responses as reflected in the norms for validating the three instruments. Small business decision makers perceived themselves as less likely to engage in exploitative power behavior and perceived their organizations as fostering a more collective and procedurally oriented climate that might be interpreted as attempting to institutionalize morality. Additionally, small business decision makers had lower idealism and relativism scores, suggesting that they were more likely to use power to adjust personal injustices or to protect oneself from potential exploitation. Further implication of this preliminary study are discussed

A random-effects hurdle model for predicting bycatch of endangered marine species

Understanding and reducing the incidence of accidental bycatch, particularly for vulnerable species such as sharks, is a major challenge for contemporary fisheries management worldwide. Bycatch data, most often collected by at-sea observers during fishing trips, are clustered by trip and/or vessel and typically involve a large number of zero counts and very few positive counts. Though hurdle models are very popular for count data with excess zeros, models for clustered forms have received far less attention. Here we present a novel random-effects hurdle model for bycatch data that makes available accurate estimates of bycatch probabilities as well as other clusterspecific targets. These are essential for informing conservation and management decisions as well as for identifying bycatch hotspots, often considered the first step in attempting to protect endangered marine species. We validate our methodology through simulation and use it to analyze bycatch data on critically endangered hammerhead sharks from the U.S. National Marine Fisheries Service Pelagic Observer Program

Improving well-being and outcomes for looked after children in Wales: a context sensitive review of interventions

Improving outcomes for looked after children and young people has been a longstanding concern in Wales. This article reports the findings of a scoping study which sought to identify interventions aimed at improving outcomes for looked after children that are effective or promising. The study was commissioned by an independent funding body to inform a £5 million investment programme for Wales. It comprised a rapid review of literature, informed through consultation with an expert advisory panel and groups of young people who had been in care. The article outlines the rapid review method, provides details of shortlisted interventions and describes the interventions subsequently approved for investment. It concludes that although there are many promising interventions which address the factors associated with poor outcomes for looked after children, the evidence base is weak. It is argued that decision-making on interventions should be informed by appraisal of the empirical evidence available, but should also be guided by professional judgement that considers the needs, priorities and preferences of service users, carers, practitioners and policy-makers

Homological Error Correction: Classical and Quantum Codes

We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for non-orientable surfaces it is impossible to construct homological codes based on qudits of dimension $D>2$, while for orientable surfaces with boundaries it is possible to construct them for arbitrary dimension $D$. We give a method to obtain planar homological codes based on the construction of quantum codes on compact surfaces without boundaries. We show how the original Shor's 9-qubit code can be visualized as a homological quantum code. We study the problem of constructing quantum codes with optimal encoding rate. In the particular case of toric codes we construct an optimal family and give an explicit proof of its optimality. For homological quantum codes on surfaces of arbitrary genus we also construct a family of codes asymptotically attaining the maximum possible encoding rate. We provide the tools of homology group theory for graphs embedded on surfaces in a self-contained manner.Comment: Revtex4 fil