A minimalistic approach for fast computation of geodesic distances on triangular meshes

The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm based on front propagation to compute approximate geodesic distances on meshes. Our method is practical and simple to implement and does not require any heavy pre-processing. The convergence of our algorithm depends on the number of discrete level sets around the source points from which distance information propagates. To appropriately implement our method on GPUs taking into account memory coalescence problems, we take advantage of a graph representation based on a breadth-first search traversal that works harmoniously with our parallel front propagation approach. We report experiments that show how our method scales with the size of the problem. We compare the mean error and processing time obtained by our method with such measures computed using other methods. Our method produces results in competitive times with almost the same accuracy, especially for large meshes. We also demonstrate its use for solving two classical geometry processing problems: the regular sampling problem and the Voronoi tessellation on meshes.Comment: Preprint submitted to Computers & Graphic

Nonextensive Quantum H-Theorem

A proof of the quantum $H$-theorem taking into account nonextensive effects on the quantum entropy $S^Q_q$ is shown. The positiveness of the time variation of $S^Q_q$ combined with a duality transformation implies that the nonextensive parameter $q$ lies in the interval [0,2]. It is also shown that the equilibrium states are described by quantum $q$-power law extensions of the Fermi-Dirac and Bose-Einstein distributions. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the quantum distributions contained in the quantum statistics theory.Comment: 5 pages, LaTe

Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

Status of MIND

The Magnetised Iron Neutrino Detector (MIND) has been identied as the ideal candidate for the de-tection of the golden \wrong sign muon " channel at a Neutrino Factory. However, previous analyses of the channel relied on a parameterisation of the detector performance which assumed pefect muon pattern recog-nition. For the rst time, a study of the muon reconstruction eciency involvoing full pattern recognition has been carried out. Using a simple pattern recognition algorithm it is shown that past results assuming perfect muon identication can already be reproduced after one simple cut

'Noise trader risk' and Bayesian market making in FX derivatives: rolling loaded dice?

ABSTRACT This paper develops and simulates a model of a Bayesian market maker who transacts with noise and position traders in derivative markets. The impact of noise trading is examined relative to price determination in FX futures, noise transmission from futures to options, and risk-management behaviour linking the two markets. The model simulations show noise trading in futures results in wider bid–ask spreads, increased price volatility, and greater variation in hedging costs. Above all, the Bayesian market maker manages price-risk by trend chasing not for speculative purposes, but to avoid being caught on the wrong side of the market. The pecuniary effects from this risk-management strategy suggest that noise trading tends to constrain the market maker’s capacity to arbitrage; particularly when the underlying price is mean averting as opposed to a Martingale and trading sessions exhibit significant price volatility. Copyright r 2008 John Wiley & Sons, Ltd. Copyright r 2008 John Wiley & Sons, Ltd.Noise trading; market making; FX derivatives; Bayesian agent; noise transmission

Hunting for the New Symmetries in Calabi-Yau Jungles

It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CY_d (d \geq 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with changing of some restrictions on the generalized Cartan matrices associated with the Dynkin diagrams that characterize affine Kac-Moody algebras. We propose that these new Berger graphs can be directly connected with the generalizations of Lie and Kac-Moody algebras.Comment: 29 pages, 15 figure

A Layman's guide to SUSY GUTs

The determination of the most straightforward evidence for the existence of the Superworld requires a guide for non-experts (especially experimental physicists) for them to make their own judgement on the value of such predictions. For this purpose we review the most basic results of Super-Grand unification in a simple and clear way. We focus the attention on two specific models and their predictions. These two models represent an example of a direct comparison between a traditional unified-theory and a string-inspired approach to the solution of the many open problems of the Standard Model. We emphasize that viable models must satisfy {\em all} available experimental constraints and be as simple as theoretically possible. The two well defined supergravity models, $SU(5)$ and $SU(5)\times U(1)$, can be described in terms of only a few parameters (five and three respectively) instead of the more than twenty needed in the MSSM model, \ie, the Minimal Supersymmetric extension of the Standard Model. A case of special interest is the strict no-scale $SU(5)\times U(1)$ supergravity where all predictions depend on only one parameter (plus the top-quark mass). A general consequence of these analyses is that supersymmetric particles can be at the verge of discovery, lurking around the corner at present and near future facilities. This review should help anyone distinguish between well motivated predictions and predictions based on arbitrary choices of parameters in undefined models.Comment: 25 pages, Latex, 11 figures (not included), CERN-TH.7077/93, CTP-TAMU-65/93. A complete ps file (1.31MB) with embedded figures is available by request from [email protected]