We study the forward problem of the magnetic Schr\"odinger operator with potentials that have a strong singularity at the origin. We obtain new resolvent estimates and give some applications on the spectral measure and on the solutions of the associated evolution problem.

Juan Antonio Barceló Luis Vega Miren Zubeldia

A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of their contractions) are shown to have a bicrossproduct structure. This is done for both the algebra and, in a low-dimensional example, for the (dual) group aspects of the deformation.

J. A. de Azcarraga M. del Olmo J. C. Perez Bueno M. Santander

The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for how to calculate the index. In this paper we give an affirmative answer to this conjecture for the exceptional Riemannian symmetric spaces and for the classical symmetric spaces Sp(r,R)/U(r). Our methodology is new and based on the idea of using slice representations for studying totally geodesic submanifolds.

Jürgen Berndt Carlos Olmos Juan Sebastián Rodríguez

In this letter, we analyze the problem of detecting spectrum holes in cognitive radio systems. We consider that a group of unlicensed users can sense the radio signal energy, perform some simple processing and transmit the result to a central entity, where the decision about the presence or not of licensed users is made. We show that the proposed cooperative schemes present good performances even without any knowledge about the measurements statistics in the unlicensed users and with only partial knowledge of them in the central entity.

Juan Augusto Maya Leonardo Rey Vega Cecilia G. Galarza

In this work we demonstrate the usage of the VegasFlow library on multidevice situations: multi-GPU in one single node and multi-node in a cluster. VegasFlow is a new software for fast evaluation of highly parallelizable integrals based on Monte Carlo integration. It is inspired by the Vegas algorithm, very often used as the driver of cross section integrations and based on Google's powerful TensorFlow library. In this proceedings we consider a typical multi-GPU configuration to benchmark how different batch sizes can increase (or decrease) the performance on a Leading Order example integration.

Juan M. Cruz-Martinez Stefano Carrazza

The generalized uncertainty principle (GUP) modifies the uncertainty relation between momentum and position giving room for a minimal length, as predicted by candidates theories of quantum gravity. Inspired by GUP, Planck's distribution is derived by considering a new quantization of the electromagnetic field. We elaborate on the thermodynamics of the black body radiation obtaining Wien's law and the Stefan-Boltzmann law. We show that such thermodynamics laws are modified at Planck-scale.

Pasquale Bosso Juan Manuel López Vega

Recent advances in observational techniques and theoretical modelling of galaxy kinematics allow us to use more than just optical morphology to discern the structure and dynamics of galaxies. Here, we show for three barred galaxies (UGC 10205, NGC 6221 and NGC4340) that both kinematics and photometry are necessary to fully understand the properties of these galaxies. Kinematic and spectrophotometric data enable us to detect structures such as bars and gas shocks that are not directly visible in the images; conversely, imaging can be crucial for understanding the kinematic and dynamical behavior of a galaxy.

Juan Carlos Vega Beltran Peter Erwin John Beckman Alessandro Pizzella Enrico Maria Corsini Francesco Bertola Werner W. Zeilinger

The study of canvas fabrics in works of art is a crucial tool for authentication, attribution and conservation. Traditional methods are based on thread density map matching, which cannot be applied when canvases do not come from contiguous positions on a roll. This paper presents a novel approach based on deep learning to assess the similarity of textiles. We introduce an automatic tool that evaluates the similarity between canvases without relying on thread density maps. A Siamese deep learning model is designed and trained to compare pairs of images by exploiting the feature representations learned from the scans. In addition, a similarity estimation method is proposed, aggregating predictions from multiple pairs of cloth samples to provide a robust similarity score. Our approach is applied to canvases from the Museo Nacional del Prado, corroborating the hypothesis that plain weave canvases, widely used in painting, can be effectively compared even when their thread densities are similar. The results demonstrate the feasibility and accuracy of the proposed method, opening new avenues for the analysis of masterpieces.

Juan José Murillo-Fuentes Pablo M. Olmos Laura Alba-Carcelén

In this paper we present a new algorithm, denoted as TEP, to decode low-density parity-check (LDPC) codes over the Binary Erasure Channel (BEC). The TEP decoder is derived applying the expectation propagation (EP) algorithm with a tree- structured approximation. Expectation Propagation (EP) is a generalization to Belief Propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal constraints in some check nodes of the LDPC code's Tanner graph. The algorithm has the same computational complexity than BP, but it can decode a higher fraction of errors when applied over the BEC. In this paper, we focus on the asymptotic performance of the TEP decoder, as the block size tends to infinity. We describe the TEP decoder by a set of differential equations that represents the residual graph evolution during the decoding process. The solution of these equations yields the capacity of this decoder for a given LDPC ensemble over the BEC. We show that the achieved capacity with the TEP is higher than the BP capacity, at the same computational complexity.

Pablo M. Olmos Juan José Murillo-Fuentes Fernando Pérez-Cruz

We present the tree-structure expectation propagation (Tree-EP) algorithm to decode low-density parity-check (LDPC) codes over discrete memoryless channels (DMCs). EP generalizes belief propagation (BP) in two ways. First, it can be used with any exponential family distribution over the cliques in the graph. Second, it can impose additional constraints on the marginal distributions. We use this second property to impose pair-wise marginal constraints over pairs of variables connected to a check node of the LDPC code's Tanner graph. Thanks to these additional constraints, the Tree-EP marginal estimates for each variable in the graph are more accurate than those provided by BP. We also reformulate the Tree-EP algorithm for the binary erasure channel (BEC) as a peeling-type algorithm (TEP) and we show that the algorithm has the same computational complexity as BP and it decodes a higher fraction of errors. We describe the TEP decoding process by a set of differential equations that represents the expected residual graph evolution as a function of the code parameters. The solution of these equations is used to predict the TEP decoder performance in both the asymptotic regime and the finite-length regime over the BEC. While the asymptotic threshold of the TEP decoder is the same as the BP decoder for regular and optimized codes, we propose a scaling law (SL) for finite-length LDPC codes, which accurately approximates the TEP improved performance and facilitates its optimization.

Pablo M. Olmos Juan José Murillo-Fuentes Fernando Pérez-Cruz