Decomposition theorem and Riesz basis for axisymmetric potenials in the right hal-plane

The Weinstein equation with complex coefficients is the equation governing generalized axisymmetric potentials (GASP) which can be written as $L_m[u]=\Delta u+\left(m/x\right)\partial_x u =0$, where $m\in\mathbb{C}$. We generalize results known for $m\in\mathbb{R}$ to $m\in\mathbb{C}$. We give explicit expressions of fundamental solutions for Weinstein operators and their estimates near singularities, then we prove a Green's formula for GASP in the right half-plane $\mathbb{H}^+$ for Re $m<1$. We establish a new decomposition theorem for the GASP in any annular domains for $m\in\mathbb{C}$, which is in fact a generalization of the B\^ocher's decomposition theorem. In particular, using bipolar coordinates, we prove for annuli that a family of solutions for GASP equation in terms of associated Legendre functions of first and second kind is complete. For $m\in\mathbb{C}$, we show that this family is even a Riesz basis in some non-concentric circular annulus

Parallel hierarchical sampling:a general-purpose class of multiple-chains MCMC algorithms

This paper introduces the Parallel Hierarchical Sampler (PHS), a class of Markov chain Monte Carlo algorithms using several interacting chains having the same target distribution but different mixing properties. Unlike any single-chain MCMC algorithm, upon reaching stationarity one of the PHS chains, which we call the “mother” chain, attains exact Monte Carlo sampling of the target distribution of interest. We empirically show that this translates in a dramatic improvement in the sampler’s performance with respect to single-chain MCMC algorithms. Convergence of the PHS joint transition kernel is proved and its relationships with single-chain samplers, Parallel Tempering (PT) and variable augmentation algorithms are discussed. We then provide two illustrative examples comparing the accuracy of PHS with

Culture, Body and photography: an approach to the work of Antonio Briceño

El trabajo propone una reflexión en torno al uso de la fotografía en la producción de imaginarios sociales. Partiendo de tres ejes conceptuales: cuerpo, fotografía y de cultura, buscamos analizar cómo en la fotografía latinoamericana contemporánea se produce una nueva significación en la representación de los Pueblos Originarios de América Latina. A tal fin analizamos dos obras de Antonio Briceño.This work proposes a reflection around the photography and its incidence on the social imaginary productions. Beginning whit three conceptual axis: body, photography and culture, the author seeks to analyze how a new signification on the representation of the originals culture of Latin American is produced by the contemporary Latin American photography. So it is analyzed different works from Antonio Briceño.Fil: Rigat, Leticia. Universidad Nacional de Rosario. Facultad de Ciencias Políticas y Relaciones Internacionales. Instituto de Investigaciones. Centro de Estudios e Investigaciones en Comunicación y Cultura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A Conservative Approach to Leveraging External Evidence for Effective Clinical Trial Design

Prior probabilities of clinical hypotheses are not systematically used for clinical trial design yet, due to a concern that poor priors may lead to poor decisions. To address this concern, a conservative approach to Bayesian trial design is illustrated here, requiring that the operational characteristics of the primary trial outcome are stronger than the prior. This approach is complementary to current Bayesian design methods, in that it insures against prior-data conflict by defining a sample size commensurate to a discrete design prior. This approach is ethical, in that it requires designs appropriate to achieving pre-specified levels of clinical equipoise imbalance. Practical examples are discussed, illustrating design of trials with binary or time to event endpoints. Moderate increases in phase II study sample size are shown to deliver strong levels of overall evidence for go/no-go clinical development decisions. Levels of negative evidence provided by group sequential confirmatory designs are found negligible, highlighting the importance of complementing efficacy boundaries with non-binding futility criteria.Comment: 13 pages, 3 color figures, 4 table

Paraphrase scope and typology. A data‑driven approach from Computational Linguistics

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Boundary value problems and Heisenberg uniqueness pairs

We describe a general method for constructing Heisenberg uniqueness pairs $(\Gamma,\Lambda)$ in the euclidean space $\mathbb{R}^{n}$ based on the study of boundary value problems for partial differential equations. As a result, we show, for instance, that any pair made of the boundary $\Gamma$ of a bounded convex set $\Omega$ and a sphere $\Lambda$ is an Heisenberg uniqueness pair if and only if the square of the radius of $\Lambda$ is not an eigenvalue of the Laplacian on $\Omega$. The main ingredients for the proofs are the Paley-Wiener theorem, the uniqueness of a solution to a homogeneous Dirichlet or initial boundary value problem, the continuity of single layer potentials, and some complex analysis in $\mathbb{C}^{n}$. Denjoy's theorem on topological conjugacy of circle diffeomorphisms with irrational rotation numbers is also useful

Tree edit distance as a baseline approach for paraphrase representation

Finding an adequate paraphrase representation formalism is a challenging issue in Natural Language Processing. In this paper, we analyse the performance of Tree Edit Distance as a paraphrase representation baseline. Our experiments using Edit Distance Textual Entailment Suite show that, as Tree Edit Distance consists of a purely syntactic approach, paraphrase alternations not based on structural reorganizations do not find an adequate representation. They also show that there is much scope for better modelling of the way trees are aligned

Terrorismo parental: cuando los padres atentan contra sus hijos

La experiencia clínica en el ámbito de la asistencia en salud mental infantil suele mostrar como el sufrimiento emocional de los niños está indisociablemente vinculado a ciertas dificultades relacionales con sus figuras de apego. Pero, en no pocas ocasiones, quizás imbuidos por un modelo implícito de enfermedad mental de corte biomédico, o impelidos por las circunstancias familiares y/o administrativas, los profesionales acaban tratando únicamente al niño.Se deja entonces, de lado la situación familiar, que es la que genera y nutre las manifestaciones sintomáticas que motivan la consulta