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

On symmetric square values of quadratic polynomials

We prove that there does not exist a non-square quadratic polynomial with integer coefficients and an axis of symmetry which takes square values for N consecutive integers for N=7 or N >= 9. At the opposite, if N <= 6 or N=8 there are infinitely many

Towards Odor-Sensitive Mobile Robots

J. Monroy, J. Gonzalez-Jimenez, "Towards Odor-Sensitive Mobile Robots", Electronic Nose Technologies and Advances in Machine Olfaction, IGI Global, pp. 244--263, 2018, doi:10.4018/978-1-5225-3862-2.ch012 Versión preprint, con permiso del editorOut of all the components of a mobile robot, its sensorial system is undoubtedly among the most critical ones when operating in real environments. Until now, these sensorial systems mostly relied on range sensors (laser scanner, sonar, active triangulation) and cameras. While electronic noses have barely been employed, they can provide a complementary sensory information, vital for some applications, as with humans. This chapter analyzes the motivation of providing a robot with gas-sensing capabilities and also reviews some of the hurdles that are preventing smell from achieving the importance of other sensing modalities in robotics. The achievements made so far are reviewed to illustrate the current status on the three main fields within robotics olfaction: the classification of volatile substances, the spatial estimation of the gas dispersion from sparse measurements, and the localization of the gas source within a known environment

Convex Global 3D Registration with Lagrangian Duality

The registration of 3D models by a Euclidean transformation is a fundamental task at the core of many application in computer vision. This problem is non-convex due to the presence of rotational constraints, making traditional local optimization methods prone to getting stuck in local minima. This paper addresses finding the globally optimal transformation in various 3D registration problems by a unified formulation that integrates common geometric registration modalities (namely point-to-point, point-to-line and point-to-plane). This formulation renders the optimization problem independent of both the number and nature of the correspondences. The main novelty of our proposal is the introduction of a strengthened Lagrangian dual relaxation for this problem, which surpasses previous similar approaches [32] in effectiveness. In fact, even though with no theoretical guarantees, exhaustive empirical evaluation in both synthetic and real experiments always resulted on a tight relaxation that allowed to recover a guaranteed globally optimal solution by exploiting duality theory. Thus, our approach allows for effectively solving the 3D registration with global optimality guarantees while running at a fraction of the time for the state-of-the-art alternative [34], based on a more computationally intensive Branch and Bound method.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Initialization of 3D Pose Graph Optimization using Lagrangian duality

Pose Graph Optimization (PGO) is the de facto choice to solve the trajectory of an agent in Simultaneous Localization and Mapping (SLAM). The Maximum Likelihood Estimation (MLE) for PGO is a non-convex problem for which no known technique is able to guarantee a globally optimal solution under general conditions. In recent years, Lagrangian duality has proved suitable to provide good, frequently tight relaxations of the hard PGO problem through convex Semidefinite Programming (SDP). In this work, we build from the state-of-the-art Lagrangian relaxation [1] and contribute a complete recovery procedure that, given the (tractable) optimal solution of the relaxation, provides either the optimal MLE solution if the relaxation is tight, or a remarkably good feasible guess if the relaxation is non-tight, which occurs in specially challenging PGO problems (very noisy observations, low graph connectivity, etc.). In the latter case, when used for initialization of local iterative methods, our approach outperforms other state-ofthe- art approaches converging to better solutions. We support our claims with extensive experiments.University of Malaga travel grant, the Spanish grant program FPU14/06098 and the project PROMOVE (DPI2014-55826-R), funded by the Spanish Government and the "European Regional Development Fund". Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech