Microscopic origin of universality in Casimir forces

The microscopic mechanisms for universality of Casimir forces between macroscopic conductors are displayed in a model of classical charged fluids. The model consists of two slabs in empty space at distance $d$ containing classical charged particles in thermal equilibrium (plasma, electrolyte). A direct computation of the average force per unit surface yields, at large distance, the usual form of the Casimir force in the classical limit (up to a factor 2 due to the fact that the model does not incorporate the magnetic part of the force). Universality originates from perfect screening sum rules obeyed by the microscopic charge correlations in conductors. If one of the slabs is replaced by a macroscopic dielectric medium, the result of Lifshitz theory for the force is retrieved. The techniques used are Mayer expansions and integral equations for charged fluids.Comment: 31 pages, 0 figures, submitted to Journal of Statistical Physic

Random Matrix Theory and Chiral Symmetry in QCD

Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of chiral random matrix theory to the QCD partition function. We show that constraints imposed by chiral symmetry and its spontaneous breaking determine the structure of low-energy effective partition functions for the Dirac spectrum. We thus derive exact results for the low-lying eigenvalues of the QCD Dirac operator. We argue that the statistical properties of these eigenvalues are universal and can be described by a random matrix theory with the global symmetries of the QCD partition function. The total number of such eigenvalues increases with the square root of the Euclidean four-volume. The spectral density for larger eigenvalues (but still well below a typical hadronic mass scale) also follows from the same low-energy effective partition function. The validity of the random matrix approach has been confirmed by many lattice QCD simulations in a wide parameter range. Stimulated by the success of the chiral random matrix theory in the description of universal properties of the Dirac eigenvalues, the random matrix model is extended to nonzero temperature and chemical potential. In this way we obtain qualitative results for the QCD phase diagram and the spectrum of the QCD Dirac operator. We discuss the nature of the quenched approximation and analyze quenched Dirac spectra at nonzero baryon density in terms of an effective partition function. Relations with other fields are also discussed.Comment: invited review article for Ann. Rev. Nucl. Part. Sci., 61 pages, 11 figures, uses ar.sty (included); references added and typos correcte

Knowledge, attitudes and practice about zika

No Brasil um surto causado pelo vírus zika foi relatado em 2015 e estima-se a ocorrência de 1,5 milhões de casos entre 2015 e 2016. Este trabalho pretende descrever conhecimentos, atitudes e práticas sobre zika em gestantes e puérperas de uma maternidade de alto risco no estado do Rio de Janeiro. Objetiva traçar o perfil das mulheres, analisar as características socio-demográficas, clínico-epidemiológicas, investigar conhecimentos, atitudes e práticas sobre zika destas mulheres e construir um escore de avaliação do conhecimento sobre a doença. Trata-se de um estudo seccional realizado por meio de questionário estruturado elaborado com base no modelo da OMS. A criação do escore (EFWC) permitiu a qualificação do grau de conhecimento sobre zika. A maior parte das gestantes e puérperas julgou insuficiente a informação que possui sobre zika (71%) em relação a sinais e sintomas (68,3%), causa (67,5%), prevenção (61,8%) e consequências (57%). A partir do cálculo do escore, observou-se que 1,6% das mulheres não tinham conhecimento algum sobre zika; 58,5% das mulheres tem conhecimento ruim ou inferior sobre zika. Não foi observada correlação entre renda, escolaridade ou idade da população deste estudo ao conhecimento sobre zika medido pelo escore. In Brazil an outbreak caused by the zika virus was reported in 2015 and an estimated 1.5 million cases were reported in 2015 and 2016. This paper aims to describe knowledge, attitudes and practices about zika in pregnant and postpartum women of a high risk maternity hospital in the state of Rio de Janeiro. It aims to trace the profile of women, analyze the demographic, clinical and epidemiological characteristics, investigate knowledge, attitudes and practices about zika of these women and build a knowledge assessment score on the disease. This is a sectional study carried out using a structured questionnaire based on the WHO model. The score (EFWC) was elaborated to assess the degree of knowledge about zika. Most of pregnant and postpartum women considered the information they had about zika insufficient (71%) regarding signs and symptoms (68.3%), cause (67.5%), prevention (61.8%), consequences (57%). The score revealed that 1.6% of the women had no knowledge about zika; 58.5% of women had poor or inferior knowledge about zika. No correlation was found between income, schooling or age of the study population and knowledge about zika measured by the score.publishersversionpublishe

A Selberg integral for the Lie algebra A_n

A new q-binomial theorem for Macdonald polynomials is employed to prove an A_n analogue of the celebrated Selberg integral. This confirms the g=A_n case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra g.Comment: 32 page

Wnt5a induces ROR1 to complex with HS1 to enhance migration of chronic lymphocytic leukemia cells.

ROR1 (receptor tyrosine kinase-like orphan receptor 1) is a conserved, oncoembryonic surface antigen expressed in chronic lymphocytic leukemia (CLL). We found that ROR1 associates with hematopoietic-lineage-cell-specific protein 1 (HS1) in freshly isolated CLL cells or in CLL cells cultured with exogenous Wnt5a. Wnt5a also induced HS1 tyrosine phosphorylation, recruitment of ARHGEF1, activation of RhoA and enhanced chemokine-directed migration; such effects could be inhibited by cirmtuzumab, a humanized anti-ROR1 mAb. We generated truncated forms of ROR1 and found its extracellular cysteine-rich domain or kringle domain was necessary for Wnt5a-induced HS1 phosphorylation. Moreover, the cytoplamic, and more specifically the proline-rich domain (PRD), of ROR1 was required for it to associate with HS1 and allow for F-actin polymerization in response to Wnt5a. Accordingly, we introduced single amino acid substitutions of proline (P) to alanine (A) in the ROR1 PRD at positions 784, 808, 826, 841 or 850 in potential SH3-binding motifs. In contrast to wild-type ROR1, or other ROR1P→︀A mutants, ROR1P(841)A had impaired capacity to recruit HS1 and ARHGEF1 to ROR1 in response to Wnt5a. Moreover, Wnt5a could not induce cells expressing ROR1P(841)A to phosphorylate HS1 or activate ARHGEF1, and was unable to enhance CLL-cell motility. Collectively, these studies indicate HS1 plays an important role in ROR1-dependent Wnt5a-enhanced chemokine-directed leukemia-cell migration

On Poincare and logarithmic Sobolev inequalities for a class of singular Gibbs measures

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular pair interaction. The functional inequalities come from convexity. We prove and characterize optimality in the case of quadratic confinement via a factorization of the measure. This optimality phenomenon holds for all beta Hermite ensembles including the Gaussian unitary ensemble, a famous exactly solvable model of random matrix theory. We further explore exact solvability by reviewing the relation to Dyson-Ornstein-Uhlenbeck diffusion dynamics admitting the Hermite-Lassalle orthogonal polynomials as a complete set of eigenfunctions. We also discuss the consequence of the log-Sobolev inequality in terms of concentration of measure for Lipschitz functions such as maxima and linear statistics.Comment: Minor improvements. To appear in Geometric Aspects of Functional Analysis -- Israel Seminar (GAFA) 2017-2019", Lecture Notes in Mathematics 225

Intertwinings for general β Laguerre and Jacobi processes

We show that, for β≥1, the semigroups of β-Laguerre and β-Jacobi processes of different dimensions are intertwined in analogy to a similar result for β-Dyson Brownian motion recently obtained in Ramanan and Shkolnikov (Intertwinings of β-Dyson Brownian motions of different dimensions, 2016. arXiv:1608.01597). These intertwining relations generalize to arbitrary β≥1 the ones obtained for β=2 in Assiotis et al. (Interlacing diffusions, 2016. arXiv:1607.07182) between h-transformed Karlin–McGregor semigroups. Moreover, they form the key step toward constructing a multilevel process in a Gelfand–Tsetlin pattern leaving certain Gibbs measures invariant. Finally, as a by-product, we obtain a relation between general β-Jacobi ensembles of different dimensions

Large-scale synchrony of gap dynamics and the distribution of understory tree species in maple-beech forests

Large-scale synchronous variations in community dynamics are well documented for a vast array of organisms, but are considerably less understood for forest trees. Because of temporal variations in canopy gap dynamics, forest communities—even old-growth ones—are never at equilibrium at the stand scale. This paucity of equilibrium may also be true at the regional scale. Our objectives were to determine (1) if nonequilibrium dynamics caused by temporal variations in the formation of canopy gaps are regionally synchronized, and (2) if spatiotemporal variations in canopy gap formation aVect the relative abundance of tree species in the understory. We examined these questions by analyzing variations in the suppression and release history of Acer saccharum Marsh. and Fagus grandifolia Ehrh. from 481 growth series of understory saplings taken from 34 mature stands. We observed that (1) the proportion of stems in release as a function of time exhibited a U-shaped pattern over the last 35 years, with the lowest levels occurring during 1975–1985, and that (2) the response to this in terms of species composition was that A. saccharum became more abundant at sites that had the highest proportion of stems in release during 1975–1985. We concluded that the understory dynamics, typically thought of as a stand-scale process, may be regionally synchronized

The Wasteland of Random Supergravities

We show that in a general \cal{N} = 1 supergravity with N \gg 1 scalar fields, an exponentially small fraction of the de Sitter critical points are metastable vacua. Taking the superpotential and Kahler potential to be random functions, we construct a random matrix model for the Hessian matrix, which is well-approximated by the sum of a Wigner matrix and two Wishart matrices. We compute the eigenvalue spectrum analytically from the free convolution of the constituent spectra and find that in typical configurations, a significant fraction of the eigenvalues are negative. Building on the Tracy-Widom law governing fluctuations of extreme eigenvalues, we determine the probability P of a large fluctuation in which all the eigenvalues become positive. Strong eigenvalue repulsion makes this extremely unlikely: we find P \propto exp(-c N^p), with c, p being constants. For generic critical points we find p \approx 1.5, while for approximately-supersymmetric critical points, p \approx 1.3. Our results have significant implications for the counting of de Sitter vacua in string theory, but the number of vacua remains vast.Comment: 39 pages, 9 figures; v2: fixed typos, added refs and clarification