A Reciprocity Theorem for Monomer-Dimer Coverings

The problem of counting monomer-dimer coverings of a lattice is a longstanding problem in statistical mechanics. It has only been exactly solved for the special case of dimer coverings in two dimensions. In earlier work, Stanley proved a reciprocity principle governing the number $N(m,n)$ of dimer coverings of an $m$ by $n$ rectangular grid (also known as perfect matchings), where $m$ is fixed and $n$ is allowed to vary. As reinterpreted by Propp, Stanley's result concerns the unique way of extending $N(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $N(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. In particular, Stanley shows that $N(m,n)$ is always an integer satisfying the relation $N(m,-2-n) = \epsilon_{m,n}N(m,n)$ where $\epsilon_{m,n} = 1$ unless $m\equiv$ 2(mod 4) and $n$ is odd, in which case $\epsilon_{m,n} = -1$. Furthermore, Propp's method is applicable to higher-dimensional cases. This paper discusses similar investigations of the numbers $M(m,n)$, of monomer-dimer coverings, or equivalently (not necessarily perfect) matchings of an $m$ by $n$ rectangular grid. We show that for each fixed $m$ there is a unique way of extending $M(m,n)$ to $n < 0$ so that the resulting bi-infinite sequence, $M(m,n)$ for $n \in {Z}$, satisfies a linear recurrence relation with constant coefficients. We show that $M(m,n)$, a priori a rational number, is always an integer, using a generalization of the combinatorial model offered by Propp. Lastly, we give a new statement of reciprocity in terms of multivariate generating functions from which Stanley's result follows.Comment: 13 pages, 12 figures, to appear in the proceedings of the Discrete Models for Complex Systems (DMCS) 2003 conference. (v2 - some minor changes

Association between Work-Related Hyperthermia Emergency Department Visits and Ambient Heat in Five Southeastern States, 2010-2012--A Case-Crossover Study

The objective of this study is to assess ambient temperatures\u27 and extreme heat events\u27 contribution to work-related emergency department (ED) visits for hyperthermia in the southeastern United States to inform prevention. Through a collaborative network and established data framework, work-related ED hyperthermia visits in five participating southeastern U.S. states were analyzed using a time stratified case-crossover design. For exposure metrics, day- and location-specific measures of ambient temperatures and county-specific identification of extreme heat events were used. From 2010 to 2012, 5,017 work-related hyperthermia ED visits were seen; 2,298 (~46%) of these visits occurred on days when the daily maximum heat index was at temperatures the Occupational Safety and Health Administration designates as having lower or moderate heat risk. A 14% increase in risk of ED visit was seen for a 1°F increase in average daily mean temperature, modeled as linear predictor across all temperatures. A 54% increase in risk was seen for work-related hyperthermia ED visits during extreme heat events (two or more consecutive days of unusually high temperatures) when controlling for average daily mean temperature. Despite ambient heat being a well-known risk to workers\u27 health, this study\u27s findings indicate ambient heat contributed to work-related ED hyperthermia visits in these five states. Used alone, existing OSHA heat-risk levels for ambient temperatures did not appear to successfully communicate workers\u27 risk for hyperthermia in this study. Findings should inform future heat-alert communications and policies, heat prevention efforts, and heat-illness prevention research for workers in the southeastern United States

Wigner solids of wide quantum wells near Landau filling ν=1\nu=1

Microwave spectroscopy within the Landau filling ($\nu$) range of the integer quantum Hall effect (IQHE) has revealed pinning mode resonances signifying Wigner solids (WSs) composed of quasi-particles or -holes. We study pinning modes of WSs in wide quantum wells (WQWs) for $0.8\le\nu\le1.2$, varying the density, $n$, and tilting the sample by angle $\theta$ in the magnetic field. Three distinct WS phases are accessed. One phase, S1, is phenomenologically the same as the WS observed in the IQHEs of narrow QWs. The second phase, S2, exists at $\nu$ further from $\nu=1$ than S1, and requires a sufficiently large $n$ or $\theta$, implying S2 is stabilized by the Zeeman energy. The melting temperatures of S1 and S2, estimated from the disappearance of the pinning mode, show different behavior vs $\nu$. At the largest $n$ or $\theta$, S2 disappears and the third phase, S1A, replaces S1, also exhibiting a pinning mode. This occurs as the WQW $\nu=1$ IQHE becomes a two-component, Halperin-Laughlin \pone state. We interpret S1A as a WS of the excitations of \pone, which has not been previously observed

An unbiased approach elucidates variation in (S)-(+)-linalool, a context-specific mediator of a tri-trophic interaction in wild tobacco

Plant volatile organic compounds (VOCs) mediate many interactions, and the function of common VOCs is especially likely to depend on ecological context. We used a genetic mapping population of wild tobacco, Nicotiana attenuata, originating from a cross of 2 natural accessions from Arizona and Utah, separated by the Grand Canyon, to dissect genetic variation controlling VOCs. Herbivory-induced leaf terpenoid emissions varied substantially, while green leaf volatile emissions were similar. In a field experiment, only emissions of linalool, a common VOC, correlated significantly with predation of the herbivore Manduca sexta by native predators. Using quantitative trait locus mapping and genome mining,we identified an (S)-(+)-linalool synthase (NaLIS). Genome resequencing, gene cloning, and activity assays revealed that the presence/absence of a 766-bp sequence in NaLIS underlies the variation of linalool emissions in 26 natural accessions. We manipulated linalool emissions and composition by ectopically expressing linalool synthases for both enantiomers, (S)-(+)- and (R)-(−)-linalool, reported to oppositely affect M. sexta oviposition, in the Arizona and Utah accessions.We used these lines to test ovipositingmoths in increasingly complex environments. The enantiomers had opposite effects on oviposition preference, but themagnitude of the effect depended strongly both on plant genetic background, and complexity of the bioassay environment. Our study reveals that the emission of linalool, a common VOC, differs by orders-of-magnitude among geographically interspersed conspecific plants due to allelic variation in a linalool synthase, and that the response of a specialist herbivore to linalool depends on enantiomer, plant genotype, and environmental complexity

Phase transition in the globalization of trade

Globalization processes interweave economic structures at a worldwide scale, trade playing a central role as one of the elemental channels of interaction among countries. Despite the significance of such phenomena, measuring economic globalization still remains an open problem. More quantitative treatments could improve the understanding of globalization at the same time that help a formal basis for comparative economic history. In this letter, we investigate the time evolution of the statistical properties of bilateral trade imbalances between countries in the trade system. We measure their cumulative probability distribution at different moments in time to discover a sudden transition circa 1960 from a regime where the distribution was always represented by a steady characteristic function to a new state where the distribution dilates as time goes on. This suggests that the rule that was governing the statistical behavior of bilateral trade imbalances until the 60's abruptly changed to a new form persistent in the last decades. In the new regime, the figures for the different years collapse into a universal master curve when rescaled by the corresponding global gross domestic product value. This coupling points to an increased interdependence of world economies and its onset corresponds in time with the starting of the last globalization wave.Comment: Final versio

The Indian Ocean humpback dolphin <i>Sousa plumbea</i> (G.Cuvier, 1829). A status report for the Arabian region. Scientific Committee document SC/54/SM6, International Whaling Commission, 26 April-10 May 2002, Shimonoseki, Japan

Available data on the genus Sousa are reviewed for the Arabian region. Nominal usage of Sousa plumbea (G. Cuvier 1828) is retained as a pragmatic measure, based on geographic and morphologic affiliation. Distribution is described for the region to include much of the Arabian (Persian) Gulf, Arabian Sea, Gulf of Aden and Red Sea, but notably excludes the Gulf of Oman. This discontinuous distribution suggests the possible presence of discreet populations within the region. Most available information on Sousa plumbea in the region originates from the Sultanate of Oman, where this species is among the most commonly recorded cetacean. However, there is no absolute measure of abundance here or elsewhere in the region and the status of the species is unknown. Beach cast individuals represent nearly two-thirds of all records (n=269) of this species in Oman. Live sightings indicate unusually large group sizes (up to 100 individuals) in the Arabian Sea and Arabian Gulf. Occasional association with Tursiops sp. and Delphinus sp. is documented. Mating behaviour and the presence of calves are recorded in the months of April and May and calves are additionally reported in October and December. Little is known about the ecology of this species in the region.Threats to Indian Ocean humpback dolphins in the Arabian region include incidental capture in fishing nets, general coastal and offshore development (e.g. land reclamation, dredging, port and harbor construction), pollution, boat traffic, oil and gas exploration (including seismic surveying), military exercises and toxins associated with red tide events. Evidence for historic and current directed catches of Sousa plumbea is presented.Intraspecific variation in cranial measurements is presented for cranially adult skulls originating from the Arabian Sea coast of Oman and initial comparison with limited data from the Saudi Arabian Gulf coast are drawn. Cranial abnormalities in skull specimens from Oman are discussed. Curated specimens from the Arabian region are listed

Locally Optimally Emitting Clouds and the Origin of Quasar Emission Lines

The similarity of quasar line spectra has been taken as an indication that the emission line clouds have preferred parameters, suggesting that the environment is subject to a fine tuning process. We show here that the observed spectrum is a natural consequence of powerful selection effects. We computed a large grid of photoionization models covering the widest possible range of cloud gas density and distance from the central continuum source. For each line only a narrow range of density and distance from the continuum source results in maximum reprocessing efficiency, corresponding to ``locally optimally-emitting clouds'' (LOC). These parameters depend on the ionization and excitation potentials of the line, and its thermalization density. The mean QSO line spectrum can be reproduced by simply adding together the full family of clouds, with an appropriate covering fraction distribution. The observed quasar spectrum is a natural consequence of the ability of various clouds to reprocess the underlying continuum, and can arise in a chaotic environment with no preferred pressure, gas density, or ionization parameter.Comment: 9 pages including 1 ps figure. LaTeX format using aaspp4.st

Microarray analyses demonstrate the involvement of type i interferons in psoriasiform pathology development in D6-deficient mice

The inflammatory response is normally limited by mechanisms regulating its resolution. In the absence of resolution, inflammatory pathologies can emerge, resulting in substantial morbidity and mortality. We have been studying the D6 chemokine scavenging receptor, which played an indispensable role in the resolution phase of inflammatory responses and does so by facilitating removal of inflammatory CC chemokines. In D6-deficient mice, otherwise innocuous cutaneous inflammatory stimuli induce a grossly exaggerated inflammatory response that bears many similarities to human psoriasis. In the present study, we have used transcriptomic approaches to define the molecular make up of this response. The data presented highlight potential roles for a number of cytokines in initiating and maintaining the psoriasis-like pathology. Most compellingly, we provide data indicating a key role for the type I interferon pathway in the emergence of this pathology. Neutralizing antibodies to type I interferons are able to ameliorate the psoriasis-like pathology, confirming a role in its development. Comparison of transcriptional data generated from this mouse model with equivalent data obtained from human psoriasis further demonstrates the strong similarities between the experimental and clinical systems. As such, the transcriptional data obtained in this preclinical model provide insights into the cytokine network active in exaggerated inflammatory responses and offer an excellent tool to evaluate the efficacy of compounds designed to therapeutically interfere with inflammatory processes