The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

Simulador de conducció enfocat a la investigació

El desenvolupament de sistemes d’assistència a la conducció (ADAS) és, avui dia, una de les àrees de recerca de més interès pel Centre de Visió per Computador. A partir de la informació adquirida per sensors instal·lats en un vehicle, els ADAS assisteixen al conductor per tal d’evitar situacions de perill. La validació d’aquests sistemes però, requereix de l’obtenció "manual" de les dades que defineixen l’entorn de conducció de forma precisa: una tasca costosa i subjecta a l’error humà. Per tal de resoldre aquest problema, en aquest projecte s’ha implementat IOCS, un simulador de conducció creat a partir d’un de robots, capaç de crear entorns realistes de conducció i d’obtenir, simultàniament, les dades sobre l’entorn inferides per un ADAS i les que el descriuen objectivament. Aquesta funcionalitat facilita extremadament el procés de validació actual dels sistemes d’assistència a la conducció.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

"Vegeu el resum a l'inici del document del fitxer adjunt."

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Predictive and distributed routing balancing (PR-DRB): high speed interconnection networks

Current parallel applications running on clusters require the use of an interconnection network to perform communications among all computing nodes available. Imbalance of communications can produce network congestion, reducing throughput and increasing latency, degrading the overall system performance. On the other hand, parallel applications running on these networks posses representative stages which allow their characterization, as well as repetitive behavior that can be identified on the basis of this characterization. This work presents the Predictive and Distributed Routing Balancing (PR-DRB), a new method developed to gradually control network congestion, based on paths expansion, traffic distribution and effective traffic load, in order to maintain low latency values. PR-DRB monitors messages latencies on intermediate routers, makes decisions about alternative paths and record communication pattern information encountered during congestion situation. Based on the concept of applications repetitiveness, best solution recorded are reapplied when saved communication pattern re-appears. Traffic congestion experiments were conducted in order to evaluate the performance of the method, and improvements were observed.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Ampliació i millora d'un vehicle teledirigit

En el projecte Ampliació i millora d’un vehicle teledirigit s’ha dut a terme l’ampliació d’un prototip de vehicle ràdio controlat fent servir dues plaques Arduino Duemilanove. Una es situa en el comandament i l’altra en el vehicle i controlen el comportament dels dos dispositius. Es transmet la informació necessària entre elles a través de dos mòduls XBee que posteriorment se’ls hi incorpora. Les plaques fetes servir en el prototip inicial eren unes SARD-13192 de Freescale i el primer que es fa en aquest sentit és una revisió del codi font utilitzat i l’adaptació a les plaques Arduino. Un acceleròmetre ADXL335 que s’incorpora a una de les plaques permet que el prototip es pugui controlar segons la posició del comandament. A més, un cop finalitzat el nou prototip és capaç de desplaçar-se endavant i endarrere, girar aturat i en moviment, i a diferents velocitats que es representen en tot moment en uns LEDs. També guarda l’últim circuit efectuat que es pot reproduir a voluntat de l’usuari, i emmagatzema les dades del recorregut de tota una sessió per exportar a l’ordinador. Per últim s’han dut a terme les proves necessàries per constatar que totes les millores s’han implementat amb èxit.

Implementació de les físiques d'un vehicle en un videojoc 3D

En la carrera del mundo de los videojuegos por alcanzar insospechables cotas de realismo con las que seguir sorprendiendo y enganchando al público, los motores de física se han convertido en la herramienta de presente y futuro. Atraídos por el auge de esta nueva tecnología, hemos lidiado con los motores referencia hoy día en el mercado, seleccionando luego uno de ellos e implementando un humilde videojuego de carreras como muestra de su potencial y de los conocimientos adquiridos.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. When comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.