On the heterochromatic number of hypergraphs associated to geometric graphs and to matroids

The heterochromatic number hc(H) of a non-empty hypergraph H is the smallest integer k such that for every colouring of the vertices of H with exactly k colours, there is a hyperedge of H all of whose vertices have different colours. We denote by nu(H) the number of vertices of H and by tau(H) the size of the smallest set containing at least two vertices of each hyperedge of H. For a complete geometric graph G with n > 2 vertices let H = H(G) be the hypergraph whose vertices are the edges of G and whose hyperedges are the edge sets of plane spanning trees of G. We prove that if G has at most one interior vertex, then hc(H) = nu(H) - tau(H) + 2. We also show that hc(H) = nu(H) - tau(H) + 2 whenever H is a hypergraph with vertex set and hyperedge set given by the ground set and the bases of a matroid, respectively

Valor del suelo y vivienda, contención al crecimiento urbano y densificación en Bogotá 1969-2012

In 1979, Bogotá implemented an urban growth boundary with an increase in height limits in central areas. These policies were aimed to protect the surrounding rural areas and consolidate a dense and multi-use city center. Internationally, these policies are criticized arguing that they increase the prices of urban land, which is opposed by the argument that this increase is compensated by raising height limits to avoid higher housing prices. The present study analyzed the height limits and the increase in the price of homes and land, gathering historical prices from different sources and crossing these data with the height regulations of each era. The results show that the increases in the height limits and their use by real estate investment were differentiated and contrary to the intentions of zoning plans, greater in the areas of high social stratum, moderate in the middle stratum, and smaller and even negative for the low stratum. The land in the high stratum sector increased more than seventeen times in value while housing prices remained stable; the valuation was much lower in the lower stratum and housing is now more expensiveEn 1979 Bogotá implementó un perímetro de crecimiento con un aumento de los límites de altura en el centro. Estas políticas buscaban proteger la ruralidad circundante y consolidar un centro denso y de uso múltiple. Estas políticas son criticadas internacionalmente con el argumento de que aumentan el precio del suelo, sin embargo, esto puede ser compensado con el aumento en los límites de altura para no afectar los precios de la vivienda. El presente estudio analizó los límites de altura y el incremento del precio del suelo, recopilando precios históricos de diferentes fuentes y cruzando estos datos con las normativas de alturas de cada época. Los resultados muestran que los aumentos del límite de alturas y su aprovechamiento, por medio de la inversión inmobiliaria, fueron diferenciados y contrarios a las intenciones de los planes de ordenamiento, siendo estos aumentos mayores en las zonas de estrato social alto, moderados en estrato medio, y menores e incluso negativos para el estrato bajo. El suelo en el sector de estrato alto tuvo una valorización de más de diecisiete veces, mientras que los precios de la vivienda permanecieron estables; la valorización fue mucho menor en el estrato bajo y la vivienda es ahora más costosa

Genetic and demographic recovery of an isolated population of brown bear Ursus arctos L., 1758

The brown bear Ursus arctos L., 1758 population of the Cantabrian Mountains (northwestern Spain) became isolated from other bear populations in Europe about 500 years ago and has declined due to hunting and habitat degradation. At the beginning of the 20th century, the Cantabrian population split into eastern and western subpopulations, and genetic exchange between them ceased. In the early 1990s, total population size was estimated to be < 100 bears. Subsequently, reduction in human-caused mortality has brought about an increase in numbers, mainly in the western subpopulation, likely promoting male-mediated migration and gene flow from the western nucleus to the eastern. To evaluate the possible genetic recovery of the small and genetically depauperate eastern subpopulation, in 2013 and 2014 we genotyped hair and faeces samples (116 from the eastern subpopulation and 36 from the western) for 18 microsatellite markers. Data from the annual count of females with cubs of the year (COY) during the past twenty-six years was used to analyze demographic changes. The number of females with COY fell to a minimum of seven in the western and three in eastern subpopulations in the biennium 1993¿1994 and reached a respective maximum of 54 and 10 individuals in 2013¿2014. We also observed increased bear dispersal and gene flow, mainly from the western to the eastern subpopulation. Of the 26 unique genotypes detected in the eastern subpopulation, 14 (54%) presented an admixture composition, and seven (27%) were determined to be migrants from the western subpopulation. Hence, the two separated and clearly structured subpopulations identified in the past currently show some degree of genetic admixture. This research shows the partial demographic recovery and a change in genetic composition due to migration process in a population of bears that has been isolated for several centuriesPeer Reviewe

Summability of the perturbative expansion for a zero-dimensional disordered spin model

We show analytically that the perturbative expansion for the free energy of the zero dimensional (quenched) disordered Ising model is Borel-summable in a certain range of parameters, provided that the summation is carried out in two steps: first, in the strength of the original coupling of the Ising model and subsequently in the variance of the quenched disorder. This result is illustrated by some high-precision calculations of the free energy obtained by a straightforward numerical implementation of our sequential summation method.Comment: LaTeX, 12 pages and 4 figure

Critical properties of Ising model on Sierpinski fractals. A finite size scaling analysis approach

The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a detailed numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the critical properties of the Ising model on some two dimensional deterministic fractal lattices with different Hausdorff dimensions. Those with finite ramification order do not display ordered phases at any finite temperature, whereas the lattices with infinite connectivity show genuine critical behavior. In particular we considered two Sierpinski carpets constructed using different generators and characterized by Hausdorff dimensions d_H=log 8/log 3 = 1.8927.. and d_H=log 12/log 4 = 1.7924.., respectively. The data show in a clear way the existence of an order-disorder transition at finite temperature in both Sierpinski carpets. By performing several Monte Carlo simulations at different temperatures and on lattices of increasing size in conjunction with a finite size scaling analysis, we were able to determine numerically the critical exponents in each case and to provide an estimate of their errors. Finally we considered the hyperscaling relation and found indications that it holds, if one assumes that the relevant dimension in this case is the Hausdorff dimension of the lattice.Comment: 21 pages, 7 figures; a new section has been added with results for a second fractal; there are other minor change

The end of the cold Loneliness: 3D comparison between Doto antarctica and a new sympatric species of Doto (Heterobranchia: Nudibranchia)

Although several studies are devoted to determining the diversity of Antarctic heterobranch sea slugs, new species are still being discovered. Among nudibranchs, Doto antarctica Eliot, 1907 is the single species of this genus described from Antarctica hitherto, the type locality being the Ross Sea. Doto antarctica was described mainly using external features. During our Antarctic research on marine benthic invertebrates, we found D. antarctica in the Weddell Sea and Bouvet Island, suggesting a circumpolar distribution. Species affiliation is herein supported by molecular analyses using cytochrome c oxidase subunit I, 16S rRNA, and histone H3 markers. We redescribe D. antarctica using histology, micro-computed tomography (micro-CT), and 3D-reconstruction of the internal organs. Moreover, we describe a new, sympatric species, namely D. carinova Moles, Avila & Wägele n. sp., and provide an anatomical comparison between the two Antarctic Doto species. Egg masses in both species are also described here for the first time. We demonstrate that micro-CT is a useful tool for non-destructive anatomical description of valuable specimens. Furthermore, our high resolution micro-CT data reveal that the central nervous system of both Doto species possesses numerous accessory giant cells, suggested to be neurons herein. In addition, the phylogenetic tree of all Doto species sequenced to date suggests a scenario for the evolution of the reproductive system in this genus: bursa copulatrix seems to have been reduced and the acquisition of a distal connection of the oviduct to the nidamental glands is a synapomorphy of the Antarctic Doto species. Overall, the combination of thorough morphological and anatomical description and molecular analyses provides a comprehensive means to characterize and delineate species, thus suggesting evolutionary scenarios

Inflation and nonequilibrium renormalization group

We study de spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques.Comment: 6 pages, 1 figure, submitted to J. Phys.

On the Phase Structure of the 3D Edwards Anderson Spin Glass

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses.Comment: 30 pages and 17 figures. Final version to be published in PR

Los montes submarinos en los márgenes continentales de Iberia

Seamounts are first-order morphological elements on continental margins and in oceanic domains, which have been extensively researched over recent decades in all branches of oceanography. These features favour the development of several geological processes, and their study gives us a better understanding of their geological and morphological domains. The seamounts around Iberia are numerous and provide excellent examples of the geodiversity of these morphological elements. Here we present a compilation of 15 seamounts around the Iberian Peninsula. These seamounts have different origins related to the geodynamic evolution (volcanism, extensional or compressive tectonics, and diapirism) of the domains where they are located. The current configuration of their relief has been influenced by Neogene-Quaternary tectonics. Their positioning controls the current morpho-sedimentary processes in the basins and on the margins, and highlights the fact that downslope processes on seamount flanks (mass flows, turbidite flows, and landslides) and processes parallel to seamounts (contouritic currents) correspond to the major geological features they are associated with them. Biogenic structures commonly develop on the tops of seamounts where occasionally isolated shelves form that have carbonate-dominated sedimentation.Los montes submarinos son rasgos morfológicos singulares, cuyo estudio tiene gran relevancia desde el punto de vista de las distintas ramas de la oceanografía. Su presencia favorece el desarrollo de diferentes procesos geológicos y proporciona un mejor conocimiento de los dominios geológicos y morfológicos en los que se encuentran. En el entorno de Iberia, los montes submarinos tienen una amplia representación y tipología. En este trabajo, se presenta una recopilación geológica de 15 montes submarinos (ocho en el Mar Mediterráneo y siete en el Océano Atlántico) de los márgenes continentales de Iberia y en el dominio Oceánico Atlántico, utilizándose levantamientos batimétricos y geofísicos. El origen de estos montes es muy diferente y está relacionado con la evolución geodinámica del dominio geológico en el que aparecen (volcanismo, tectónica extensional o compresional y diapirismo). La configuración actual del relieve ha sido controlada por la actividad tectónica en el Neógeno-Cuaternario. Su presencia controla el desarrollo de los procesos morfosedimentarios recientes de márgenes y cuencas. Los principales procesos sedimentarios asociados a estos montes se relacionan con procesos longitudinales (flujos en masa, flujos turbidíticos, deslizamientos) y transversales a dichos montes (corrientes de contorno). Además es frecuente en ellos el desarrollo de cuerpos biogénicos sobre sus cimas e incluso de plataformas con sedimentación carbonatada. Los montes submarinos de Iberia muestran una gran geodiversidad y constituyen un elemento morfológico de primer orden para comprender los procesos geológicos que tienen lugar en sus márgenes continentales y dominios oceánicos adyacentes.Versión del editor0,000