The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for

Charmed meson decay constants in three-flavor lattice QCD

We present the first lattice QCD calculation with realistic sea quark content of the D^+ meson decay constant f_{D^+}. We use the MILC Collaboration's publicly available ensembles of lattice gauge fields, which have a quark sea with two flavors (up and down) much lighter than a third (strange). We obtain f_{D^+} = 201 +/- 3 +/- 17 MeV, where the errors are statistical and a combination of systematic errors. We also obtain f_{D_s} = 249 +/- 3 +/- 16 MeV for the D_s meson.Comment: note added on recent CLEO measurement; PRL versio

Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

Filtration rates of the non-native Chinese mystery snail (Bellamya chinensis) and potential impacts on microbial communities

Invasive species in the phylum Mollusca, including gastropods and bivalves, have caused substantial impacts in freshwater ecosystems. The Chinese mystery snail, Bellamya chinensis, is a large viviparid snail native to Southeastern Asia and widely introduced throughout United States and parts of Canada and Europe. B. chinensis is a facultative filter-feeding detritivore that can both graze epiphytic diatoms using its radula and filter-feed its breathing water. Despite mounting concern associated with the expanding range and increasing abundance of B. chinensis in many parts of its invaded range, the potential ecological impacts of this non-native species remain largely unknown. Here, we used a series of laboratory experiments to assess filtration rates of B. chinensis and quantify its effects on microbial communities. According to both microcosm (24-hour, 4-L suspension) and mesocosm (5-day, 90-L suspension) experimental trials, B. chinensis exhibited an average filtration rate of 106-113 mL snail-1h-1(1.45 mL mg DW-1h-1) and an individual maximum of 471 mL snail-1h-1(6.15 mL mg DW-1h-1). These values are comparable to reported filtration rates for high-profile invasive, freshwater bivalves. Relationships between snail size and filtration rate relationship suggests that B. chinensis display an ontogenetic shift in feeding behavior from primarily radular grazing to increased filter-feeding at threshold size of approximately 44 mm shell height. Our experiments also revealed that high snail densities can result in small, significant shifts in bacterial community composition. These results suggest that B. chinensis may influence microbial communities either directly by using bacteria as a food source or indirectly by producing sufficiently large quantities of fecal and pseudo-fecal material to affect bacterial activity and growth. The overall ecological effects and importance of B. chinensis filtration behavior remain unclear, but our experimental results suggest that these impacts may be large and should be further investigated to better understand its potential role in coupling benthic and pelagic food webs in lake ecosystems.Las especies invasoras del phyllum Mollusca, incluyendo los gasterópodos y bivalvos, han causado impactos importantes en los ecosistemas dulceacuícolas. Bellamya chinensis, es un vivíparo de gran tamaño, nativo del sureste de Asia y ampliamente introducido a lo largo de los Estados Unidos y parte de Canadá y Europa. B. chinensis es una especie detritivora- filtradora facultativa, que puede tanto ramonear diatomeas epifitas usando su rádula como filtrar el agua que respiran. A pesar de la creciente preocupación asociada al incremento en la abundancia y rango de distribución de B. chinensis en las regiones ya colonizadas, el potencial impacto ecológico de esta especie introducida permanece ampliamente desconocido. En este estudio, usamos series de experimentos de laboratorio para evaluar las tasas de filtración de B. chinensis y cuantificar su efecto en las comunidades microbianas. De acuerdo con los experimentos realizados tanto en los microcosmos (24-hour, 4-L suspensión) como en los mesocosmos (5-day, 90-L suspensión), B. chinensis mostró una tasa promedio de filtración de 106-113 mL caracol-1h-1(1.45 mL mg peso seco-1h-1) y un máximo por individuo de 471 mL caracol-1h-1(6.15 mL mg peso seco-1h-1). Estos valores son comparables a otros reportados para especies de bivalvos dulceacuícolas altamente invasivas. La relación entre el tamaño de los caracoles y las tasas de filtración sugieren que B. chinensis muestra un cambio ontogénico en la manera de alimentarse, de ramoneo a una mayor alimentación por filtración, a partir de un umbral de tamaño de la concha de aproximadamente 44 mm de altura. Nuestros experimentos también revelan que altas densidades de caracoles generan pequeños cambios pero significativos en las comunidades microbianas. Estos resultados sugieren que B. chinensis afectaría las comunidades microbianas de forma directa usando las bacterias como fuente de alimentación o indirectamente al producir una cantidad de materia fecal o seudo-fecal, suficiente para afectar la actividad y crecimiento bacteriano. El impacto ecológico global y el comportamiento como filtrador de B. chinensis aún no son claros, pero nuestros resultados experimentales sugieren que estos impactos pueden ser importantes y se deben investigar mejor para entender más su papel potencial en el acoplamiento de las redes tróficas bentónicas y pelágicas en los sistemas lacustres

Correlations and Renormalization in Lattice Gases

A complete formulation is given of an exact kinetic theory for lattice gases. This kinetic theory makes possible the calculation of corrections to the usual Boltzmann / Chapman-Enskog analysis of lattice gases due to the buildup of correlations. It is shown that renormalized transport coefficients can be calculated perturbatively by summing terms in an infinite series. A diagrammatic notation for the terms in this series is given, in analogy with the diagrammatic expansions of continuum kinetic theory and quantum field theory. A closed-form expression for the coefficients associated with the vertices of these diagrams is given. This method is applied to several standard lattice gases, and the results are shown to correctly predict experimentally observed deviations from the Boltzmann analysis.Comment: 94 pages, pure LaTeX including all figure

On parity functions in conformal field theories

We examine general aspects of parity functions arising in rational conformal field theories, as a result of Galois theoretic properties of modular transformations. We focus more specifically on parity functions associated with affine Lie algebras, for which we give two efficient formulas. We investigate the consequences of these for the modular invariance problem.Comment: 18 pages, no figure, LaTeX2

Phosphotyrosine Signaling Analysis in Human Tumors Is Confounded by Systemic Ischemia-Driven Artifacts and Intra-Specimen Heterogeneity

Tumor protein phosphorylation analysis may provide insight into intracellular signaling networks underlying tumor behavior, revealing diagnostic, prognostic or therapeutic information. Human tumors collected by The Cancer Genome Atlas program potentially offer the opportunity to characterize activated networks driving tumor progression, in parallel with the genetic and transcriptional landscape already documented for these tumors. However, a critical question is whether cellular signaling networks can be reliably analyzed in surgical specimens, where freezing delays and spatial sampling disparities may potentially obscure physiologic signaling. To quantify the extent of these effects, we analyzed the stability of phosphotyrosine (pTyr) sites in ovarian and colon tumors collected under conditions of controlled ischemia and in the context of defined intratumoral sampling. Cold-ischemia produced a rapid, unpredictable, and widespread impact on tumor pTyr networks within 5 minutes of resection, altering up to 50% of pTyr sites by more than 2-fold. Effects on adhesion and migration, inflammatory response, proliferation, and stress response pathways were recapitulated in both ovarian and colon tumors. In addition, sampling of spatially distinct colon tumor biopsies revealed pTyr differences as dramatic as those associated with ischemic times, despite uniform protein expression profiles. Moreover, intratumoral spatial heterogeneity and pTyr dynamic response to ischemia varied dramatically between tumors collected from different patients. Overall, these findings reveal unforeseen phosphorylation complexity, thereby increasing the difficulty of extracting physiologically relevant pTyr signaling networks from archived tissue specimens. In light of this data, prospective tumor pTyr analysis will require appropriate sampling and collection protocols to preserve in vivo signaling features.National Institutes of Health (U.S.) (Grant U24 CA159988

6D supergravity without tensor multiplets

We systematically investigate the finite set of possible gauge groups and matter content for N = 1 supergravity theories in six dimensions with no tensor multiplets, focusing on nonabelian gauge groups which are a product of SU(N) factors. We identify a number of models which obey all known low-energy consistency conditions, but which have no known string theory realization. Many of these models contain novel matter representations, suggesting possible new string theory constructions. Many of the most exotic matter structures arise in models which precisely saturate the gravitational anomaly bound on the number of hypermultiplets. Such models have a rigid symmetry structure, in the sense that there are no moduli which leave the full gauge group unbroken.Comment: 31 pages, latex; v2, v3: minor corrections, references adde

An Analysis of Private School Closings

We add to the small literature on private school supply by exploring exits of K-12 private schools. We find that the closure of private schools is not an infrequent event, and use national survey data from the National Center for Education Statistics to study closures of private schools. We assume that the probability of an exit is a function of excess supply of private schools over the demand, as well as the school's characteristics such as age, size, and religious affiliation. Our empirical results generally support the implications of the model. Working Paper 07-0

Communication Research

Contains reports on seven research projects.Rockefeller FoundationCarnegie Foundatio