Extreme value statistics of smooth random Gaussian fields

We consider the Gumbel or extreme value statistics describing the distribution function p_G(x_max) of the maximum values of a random field x within patches of fixed size. We present, for smooth Gaussian random fields in two and three dimensions, an analytical estimate of p_G which is expected to hold in a regime where local maxima of the field are moderately high and weakly clustered. When the patch size becomes sufficiently large, the negative of the logarithm of the cumulative extreme value distribution is simply equal to the average of the Euler Characteristic of the field in the excursion x > x_max inside the patches. The Gumbel statistics therefore represents an interesting alternative probe of the genus as a test of non Gaussianity, e.g. in cosmic microwave background temperature maps or in three-dimensional galaxy catalogs. It can be approximated, except in the remote positive tail, by a negative Weibull type form, converging slowly to the expected Gumbel type form for infinitely large patch size. Convergence is facilitated when large scale correlations are weaker. We compare the analytic predictions to numerical experiments for the case of a scale-free Gaussian field in two dimensions, achieving impressive agreement between approximate theory and measurements. We also discuss the generalization of our formalism to non-Gaussian fields.Comment: 10 pages, 2 figures, accepted for publication in MNRA

Plasticity of the Muscle Stem Cell Microenvironment

Satellite cells (SCs) are adult muscle stem cells capable of repairing damaged and creating new muscle tissue throughout life. Their functionality is tightly controlled by a microenvironment composed of a wide variety of factors, such as numerous secreted molecules and different cell types, including blood vessels, oxygen, hormones, motor neurons, immune cells, cytokines, fibroblasts, growth factors, myofibers, myofiber metabolism, the extracellular matrix and tissue stiffness. This complex niche controls SC biology-quiescence, activation, proliferation, differentiation or renewal and return to quiescence. In this review, we attempt to give a brief overview of the most important players in the niche and their mutual interaction with SCs. We address the importance of the niche to SC behavior under physiological and pathological conditions, and finally survey the significance of an artificial niche both for basic and translational research purposes

Three Poet Artists : Eldon Grier, P.K. Page, Joe Rosenblatt

Fiamengo discusses poetry's strong reliance on visual imagery. Includes poems by three artists. Biographical notes

Fitting high-dimensional Copulae to Data

This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions higher than two, and in comparison to other papers we consider not only simple Archimedean and Gaussian copulae but also Hierarchical Archimedean Copulae. Afterwards we provide an empirical part to support the theory