Large Deviations for Random Power Moment Problem

We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with this point satisfies a large deviation principle. Moderate deviation are also studied completing earlier results on asymptotic normality given by \citeauthorChKS93 [Ann. Probab. 21 (1993) 1295-1309]. Surprisingly, our large deviations results allow us to compute explicitly the (n+1)th moment range size of the set of all probability measures having the same n first moments. The main tool to obtain these results is the representation of M_n on canonical moments [see the book of \citeauthorDS97].Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/00911790400000055

Generalized Dirichlet distributions on the ball and moments

The geometry of unit $N$-dimensional $\ell_{p}$ balls has been intensively investigated in the past decades. A particular topic of interest has been the study of the asymptotics of their projections. Apart from their intrinsic interest, such questions have applications in several probabilistic and geometric contexts (Barthe et al. 2005). In this paper, our aim is to revisit some known results of this flavour with a new point of view. Roughly speaking, we will endow the ball with some kind of Dirichlet distribution that generalizes the uniform one and will follow the method developed in Skibinsky (1967), Chang et al. (1993) in the context of the randomized moment space. The main idea is to build a suitable coordinate change involving independent random variables. Moreover, we will shed light on a nice connection between the randomized balls and the randomized moment space.Comment: Last section modified. Article accepted by ALE

A toolbox on the distribution of the maximum of Gaussian process

In this paper we are interested in the distribution of the maximum, or the maximum of the absolute value, of certain Gaussian processes for which the result is exactly known

Large Deviations for Random Matricial Moment Problems

We consider the moment space $\mathcal{M}_n^{K}$ corresponding to $p \times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or K=\D). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \rightarrow \infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\times p$ matrices. Then we lift a random element of $\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP on Carth\'eodory and Schur random functions. These last functions are well connected to the above random measure. In all these problems, we take advantage of the so-called canonical moments technique by introducing new (matricial) random variables that are independent and have explicit distributions.Comment: 34 page

A PBIL for load balancing in network coding based multicasting

One of the most important issues in multicast is how to achieve a balanced traffic load within a communications network. This paper formulates a load balancing optimization problem in the context of multicast with network coding and proposes a modified population based incremental learning (PBIL) algorithm for tackling it. A novel probability vector update scheme is developed to enhance the global exploration of the stochastic search by introducing extra flexibility when guiding the search towards promising areas in the search space. Experimental results demonstrate that the proposed PBIL outperforms a number of the state-of-the-art evolutionary algorithms in terms of the quality of the best solution obtained

3D-footprint: a database for the structural analysis of protein–DNA complexes

3D-footprint is a living database, updated and curated on a weekly basis, which provides estimates of binding specificity for all protein–DNA complexes available at the Protein Data Bank. The web interface allows the user to: (i) browse DNA-binding proteins by keyword; (ii) find proteins that recognize a similar DNA motif and (iii) BLAST similar DNA-binding proteins, highlighting interface residues in the resulting alignments. Each complex in the database is dissected to draw interface graphs and footprint logos, and two complementary algorithms are employed to characterize binding specificity. Moreover, oligonucleotide sequences extracted from literature abstracts are reported in order to show the range of variant sites bound by each protein and other related proteins. Benchmark experiments, including comparisons with expert-curated databases RegulonDB and TRANSFAC, support the quality of structure-based estimates of specificity. The relevant content of the database is available for download as flat files and it is also possible to use the 3D-footprint pipeline to analyze protein coordinates input by the user. 3D-footprint is available at http://floresta.eead.csic.es/3dfootprint with demo buttons and a comprehensive tutorial that illustrates the main uses of this resource

Niveles de estrés y formas de afrontamiento en estudiantes de Medicina en comparación con estudiantes de otras escuelas

Objective: To assess the levels of stress and the coping strategies in students of the faculties of Medicine, Law and Psychology at a private university in Lima. Materials and Methods: Cross-sectional analytic and comparative study involving three university careers. For data collection, the SISCO inventory for academic stress and the questionnaire of stress coping (CAE) were used. For inferential analysis, Spearman’s rank correlation coefficient, Kruskall Wallis and Dunn Test (multiple comparison post hoc) were used. Results: The average age was 19.5 ± 2.5 years. Of them, 33.9% were students from the Medical faculty and 92.4% were worried or nervous (stress manifestations). The students from the Medical faculty had the highest level of stress (median, 46.7) compared to the students from the Psychology faculty (median, 39.1) and the students from the Law faculty (median, 40.2) (p < 0.05). The most common coping strategies were focusing on the problem, positive re-evaluation, and social support. The least used strategy was religion. Conclusion: The Medical faculty students show the highest level of stress. Coping strategies in the three groups are focusing on the problem, positive re-evaluation, and social supportObjetivo: Evaluar los niveles de estrés y formas de afrontarlo en alumnos de las facultades de Medicina, Derecho y Psicología de una universidad privada de Lima. Material y métodos: Estudio transversal analítico que involucró a estudiantes de tres carreras universitarias. Se utilizó el inventario SISCO de estrés académico y el cuestionario de afrontamiento del estrés (CAE). Se realizó la comparación de las medianas entre los puntajes obtenidos de ambos cuestionarios. Para el análisis inferencial se utilizaron las pruebas estadísticas de Kruskall Wallis, el test de Dunn (comparaciones múltiples post hoc) y el coeficiente de correlación por rangos de Spearman. Resultados: La edad media fue 19.5 ± 2.5 años, el 33.9% realizaba la carrera de Medicina y el 92.4% del total presentó preocupación o nerviosismo como manifestaciones de estrés. Los estudiantes de Medicina presentaron mayores niveles de estrés (mediana = 46.7) en comparación con los estudiantes de Psicología (mediana = 39.1) y Derecho (mediana = 40.2) (p < 0.05). Las formas de afrontamiento más frecuentes fueron la focalización en la solución del problema, la reevaluación positiva y la búsqueda de apoyo social. La forma de afrontamiento menos frecuente fue la religión. Conclusión: Los estudiantes de Medicina presentan mayores niveles de estrés. Las formas de afrontamiento más comunes son las denominadas activas: focalización en la solución del problema, reevaluación positiva y búsqueda de apoyo social.Revisión por pare

Canonical moments and random spectral measures

We study some connections between the random moment problem and the random matrix theory. A uniform draw in a space of moments can be lifted into the spectral probability measure of the pair (A,e) where A is a random matrix from a classical ensemble and e is a fixed unit vector. This random measure is a weighted sampling among the eigenvalues of A. We also study the large deviations properties of this random measure when the dimension of the matrix grows. The rate function for these large deviations involves the reversed Kullback information.Comment: 32 pages. Revised version accepted for publication in Journal of Theoretical Probabilit