Modular Curves Of Genus 2

We prove that there is only a finite number of genus 2 curves C defined over Q such that there exists a nonconstant morphism pi:X_1(N) --->C defined over Q and the jacobian of C, J(C), is a Q-factor of the new part of the jacobian of X_1(N), J_1(N)^{new}. Moreover, we prove that there are only 149 genus two curves of this kind with the additional requeriment that their jacobians are Q-simple. We determine the corresponding newforms and present equations for all these curves

Covering techniques and rational points on some genus 5 curves

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.Comment: Contemporary Mathematics AMS, to appea

Real-Time odor classification through sequential bayesian filtering

The classification of volatiles substances with an e-nose is still a challenging problem, particularly when working under real-time, out-of-the-lab environmental conditions where the chaotic and highly dynamic characteristics of the gas transportation induce an almost permanent transient state in the e-nose readings. In this work, a sequential Bayesian filtering approach is proposed to efficiently integrate information from previous e-nose observations while updating the belief about the gas class on a real-time basis. We validate our proposal with two real olfaction datasets composed of dynamic time-series experiments (gas transitions are Considered, but no mixture of gases), showing an improvement in the classification rate when compared to a stand-alone probabilistic classifier.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Robust Stereo Visual Odometry through a Probabilistic Combination of Points and Line Segments

Most approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. In order to effectively combine both types of features, their associated errors are weighted according to their covariance matrices, computed from the propagation of Gaussian distribution errors in the sensor measurements. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Project "PROMOVE: Advances in mobile robotics for promoting independent life of elders", funded by the Spanish Government and the "European Regional Development Fund ERDF" under contract DPI2014-55826-R

Geometric-based Line Segment Tracking for HDR Stereo Sequences

In this work, we propose a purely geometrical approach for the robust matching of line segments for challenging stereo streams with severe illumination changes or High Dynamic Range (HDR) environments. To that purpose, we exploit the univocal nature of the matching problem, i.e. every observation must be corresponded with a single feature or not corresponded at all. We state the problem as a sparse, convex, `1-minimization of the matching vector regularized by the geometric constraints. This formulation allows for the robust tracking of line segments along sequences where traditional appearance-based matching techniques tend to fail due to dynamic changes in illumination conditions. Moreover, the proposed matching algorithm also results in a considerable speed-up of previous state of the art techniques making it suitable for real-time applications such as Visual Odometry (VO). This, of course, comes at expense of a slightly lower number of matches in comparison with appearance based methods, and also limits its application to continuous video sequences, as it is rather constrained to small pose increments between consecutive frames.We validate the claimed advantages by first evaluating the matching performance in challenging video sequences, and then testing the method in a benchmarked point and line based VO algorithm.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech.This work has been supported by the Spanish Government (project DPI2017-84827-R and grant BES-2015-071606) and by the Andalucian Government (project TEP2012-530)

Stereo visual odometry by combining points and lines

Poster presented at ICVSS2016: international Computer Vision Summer SchoolMost approaches to stereo visual odometry reconstruct the motion based on the tracking of point features along a sequence of images. However, in low-textured scenes it is often difficult to encounter a large set of point features, or it may happen that they are not well distributed over the image, so that the behavior of these algorithms deteriorates. This paper proposes a probabilistic approach to stereo visual odometry based on the combination of both point and line segment that works robustly in a wide variety of scenarios. The camera motion is recovered through non-linear minimization of the projection errors of both point and line segment features. The method, of course, is computationally more expensive that using only one type of feature, but still can run in real-time on a standard computer and provides interesting advantages, including a straightforward integration into any probabilistic framework commonly employed in mobile robotics.Universidad de Málag

Análisis espacial de la composición florística de huertos familiares en Malinalco, Tenancingo y Villa Guerrero, Estado de México

TESIS DE MAESTRÍAEl objetivo de este trabajo se realizó mediante un análisis espacial de la composición florística y de la distribución biogeográfica de los huertos familiares en Malinalco, Tenancingo y Villa Guerrero, enriquecido con la perspectiva etnobotánica. Para tal fin se hizo uso del análisis espacial basado en fotointerpretación cartográfica a partir de imágenes de satélite, procesos en campo, un análisis comparativo, el cálculo de la composición florística y un análisis de factores que inciden en los procesos de cambio. El análisis espacial de la composición florística de huertos familiares que responde al problema de la diversidad biológica y cultural de México es resultado de la forma, ubicación y topografía de su territorio, así como de las relaciones entre los grupos humanos y los ecosistemas. De acuerdo con las condiciones geográficas, la mayor parte de la Región Sur del Estado de México, de donde los municipios de Malinalco, Tenancingo y Villa Guerrero se encuentran localizados, pertenece al ecosistema de bosque subtropical caducifolio, donde la interacción de los factores fisiográficos, biológicos y socioculturales favorece una amplia agrobiodiversidad en los distintos ambientes. Los huertos suelen ser espacios contiguos a las residencias de sus propietarios (Vogl et al., 2004) aunque algunas veces se encuentren a una cierta distancia de las mismas. Se trata de espacios complejos donde convergen numerosos elementos culturales, ecológicos, sociales y económicos (Gispert et al., 2004). La distribución espacial y estructura de los huertos no es uniforme en las viviendas de las comunidades de la región, tampoco es uniforme la composición florística, ni la superficie. Mediante la información obtenida, se diagnostico el cambio, la pérdida y/o beneficios de comunidades vegetales dentro de la zona y se obtuvo información actualizada sobre el estado vegetal correspondiente a parte de la zona sur del estado. Los datos satelitales nos proporcionaron una perspectiva más amplia de la situación actual de la zona y aportó un conocimiento más detallado para la implementación de estrategias, para mejorar estos agroecosistemas, como beneficio local, regional y global. El estudio encuentra sustento teórico en: Los Agroecosistemas (Altieri y Merrick, 1987; Gutiérrez, 2007, 2011 y 2012); los Sistemas Agroforestales Indígenas (Alcorn, 1990); Los Huertos de Traspatio (Méndez y Gliessman, 2002), la Organización y el Ordenamiento Espacial de los Individuos (Pielou, 1979). Las plantas alimentarias, ornamentales y medicinales, ocupan los tres primeros lugares de importancia en los agro ecosistemas con huertos familiares. Las investigaciones que se realizaron en los espacios geográficos que ocupan los huertos familiares, proporcionaron elementos valiosos de análisis para reconsiderar la importancia de las funciones y utilización de las partes de las plantas existentes.CONACY

3D Well-composed Polyhedral Complexes

A binary three-dimensional (3D) image $I$ is well-composed if the boundary surface of its continuous analog is a 2D manifold. Since 3D images are not often well-composed, there are several voxel-based methods ("repairing" algorithms) for turning them into well-composed ones but these methods either do not guarantee the topological equivalence between the original image and its corresponding well-composed one or involve sub-sampling the whole image. In this paper, we present a method to locally "repair" the cubical complex $Q(I)$ (embedded in $\mathbb{R}^3$) associated to $I$ to obtain a polyhedral complex $P(I)$ homotopy equivalent to $Q(I)$ such that the boundary of every connected component of $P(I)$ is a 2D manifold. The reparation is performed via a new codification system for $P(I)$ under the form of a 3D grayscale image that allows an efficient access to cells and their faces

Right triangles with algebraic sides and elliptic curves over number fields

Given any positive integer n, we prove the existence of infinitely many right triangles with area n and side lengths in certain number fields. This generalizes the famous congruent number problem. The proof allows the explicit construction of these triangles; for this purpose we find for any positive integer n an explicit cubic number field Q(\lambda) (depending on n) and an explicit point P_\lambda of infinite order in the Mordell-Weil group of the elliptic curve Y^2=X^3-n^2*X over Q(\lambda).Comment: To appear in Math. Slovac