Implementing the De-thinning Method for High Energy Cosmic Rays Extensive Air Shower Simulations

To simulate the interaction of cosmic rays with the Earth atmosphere requires highly complex computational resources and several statistical techniques have been developed to simplify those calculations. It is common to implement the thinning algorithms to reduce the number of secondary particles by assigning weights to representative particles in the evolution of the cascade. However, since this is a compression method with information loss, it is required to recover the original flux of secondary particles without introduce artificial biases. In this work we present the preliminary results of our version of the de-thinning algorithm for the reconstruction of thinned simulations of extensive air showers initiated by cosmic rays and photons in the energy range $10^{15} < E/\mathrm{eV} < 10^{17}$.Comment: 5 pages, 2 figures, 1 table, Proceedings X SILAFAE Medellin-2014. To appear in Nuclear Physics B - Proceedings Supplement

Generating sequences and Poincar\'e series for a finite set of plane divisorial valuations

Let $V$ be a finite set of divisorial valuations centered at a 2-dimensional regular local ring $R$. In this paper we study its structure by means of the semigroup of values, $S_V$, and the multi-index graded algebra defined by $V$, \gr_V R. We prove that $S_V$ is finitely generated and we compute its minimal set of generators following the study of reduced curve singularities. Moreover, we prove a unique decomposition theorem for the elements of the semigroup. The comparison between valuations in $V$, the approximation of a reduced plane curve singularity $C$ by families of sets $V^{(k)}$ of divisorial valuations, and the relationship between the value semigroup of $C$ and the semigroups of the sets $V^{(k)}$, allow us to obtain the (finite) minimal generating sequences for $C$ as well as for $V$. We also analyze the structure of the homogeneous components of \gr_V R. The study of their dimensions allows us to relate the Poincar\'e series for $V$ and for a general curve $C$ of $V$. Since the last series coincides with the Alexander polynomial of the singularity, we can deduce a formula of A'Campo type for the Poincar\'e series of $V$. Moreover, the Poincar\'e series of $C$ could be seen as the limit of the series of $V^{(k)}$, $k\ge 0$

Coulomb integrals and conformal blocks in the AdS3-WZNW model

We study spectral flow preserving four-point correlation functions in the AdS3-WZNW model using the Coulomb gas method on the sphere. We present a multiple integral realization of the conformal blocks and explicitly compute amplitudes involving operators with quantized values of the sum of their spins, i.e., requiring an integer number of screening charges of the first kind. The result is given as a sum over the independent configurations of screening contours yielding a monodromy invariant expansion in powers of the worldsheet moduli. We then examine the factorization limit and show that the leading terms in the sum can be identified, in the semiclassical limit, with products of spectral flow conserving three-point functions. These terms can be rewritten as the m-basis version of the integral expression obtained by J. Teschner from a postulate for the operator product expansion of normalizable states in the H3+-WZNW model. Finally, we determine the equivalence between the factorizations of a particular set of four-point functions into products of two three-point functions either preserving or violating spectral flow number conservation. Based on this analysis we argue that the expression for the amplitude as an integral over the spin of the intermediate operators holds beyond the semiclassical regime, thus corroborating that spectral flow conserving correlators in the AdS3-WZNW model are related by analytic continuation to correlation functions in the H3+-WZNW model.Comment: 28 pages; references modified, published versio

Developing indicators to measure Technology Institutes` performance

Technology institutes (TIs) are non-profit innovation and technology organisations aimed to encourage competitiveness of firms. They are a key organisation in the Spanish National Innovation System because of their size and closeness to the productive sector. Despite this, there is a lack of studies trying to measure their performance and its determinants. This work sheds some light on this. We study the influence of operative, financial, organisational, relational and general variables on three measures of results: selffinance, impact and added value. Our conclusions show the relevance of this approach and are confirmed by grouping TIs according to their service supply characteristics.Publicad