Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Level-wise node size distribution of randomly generated regular trees

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

RADIC: un middleware de tolerancia a fallos que preserva el rendimiento

La tolerancia a fallos es una línea de investigación que ha adquirido una importancia relevante con el aumento de la capacidad de cómputo de los súper-computadores actuales. Esto es debido a que con el aumento del poder de procesamiento viene un aumento en la cantidad de componentes que trae consigo una mayor cantidad de fallos. Las estrategias de tolerancia a fallos actuales en su mayoría son centralizadas y estas no escalan cuando se utiliza una gran cantidad de procesos, dado que se requiere sincronización entre todos ellos para realizar las tareas de tolerancia a fallos. Además la necesidad de mantener las prestaciones en programas paralelos es crucial, tanto en presencia como en ausencia de fallos. Teniendo en cuenta lo citado, este trabajo se ha centrado en una arquitectura tolerante a fallos descentralizada (RADIC – Redundant Array of Distributed and Independant Controllers) que busca mantener las prestaciones iniciales y garantizar la menor sobrecarga posible para reconfigurar el sistema en caso de fallos. La implementación de esta arquitectura se ha llevado a cabo en la librería de paso de mensajes denominada Open MPI, la misma es actualmente una de las más utilizadas en el mundo científico para la ejecución de programas paralelos que utilizan una plataforma de paso de mensajes. Las pruebas iniciales demuestran que el sistema introduce mínima sobrecarga para llevar a cabo las tareas correspondientes a la tolerancia a fallos. MPI es un estándar por defecto fail-stop, y en determinadas implementaciones que añaden cierto nivel de tolerancia, las estrategias más utilizadas son coordinadas. En RADIC cuando ocurre un fallo el proceso se recupera en otro nodo volviendo a un estado anterior que ha sido almacenado previamente mediante la utilización de checkpoints no coordinados y la relectura de mensajes desde el log de eventos. Durante la recuperación, las comunicaciones con el proceso en cuestión deben ser retrasadas y redirigidas hacia la nueva ubicación del proceso. Restaurar procesos en un lugar donde ya existen procesos sobrecarga la ejecución disminuyendo las prestaciones, por lo cual en este trabajo se propone la utilización de nodos spare para la recuperar en ellos a los procesos que fallan, evitando de esta forma la sobrecarga en nodos que ya tienen trabajo. En este trabajo se muestra un diseño propuesto para gestionar de un modo automático y descentralizado la recuperación en nodos spare en un entorno Open MPI y se presenta un análisis del impacto en las prestaciones que tiene este diseño. Resultados iniciales muestran una degradación significativa cuando a lo largo de la ejecución ocurren varios fallos y no se utilizan spares y sin embargo utilizándolos se restablece la configuración inicial y se mantienen las prestaciones.

Desenvolupament d'un node sensor sense fils autoalimentat. Mòdul piezo-magnètic

En aquest projecte es pretén implementar un dispositiu capaç de ser auto-suficient i no dependre de cap tipus de pila, bateria o fil elèctric que l’abasteixi d’energia elèctrica. El dispositiu recol·lectarà la energia magnètica generada per la corrent elèctrica a un fil i la transformarà en energia elèctrica, que serà emmagatzemada per el seu posterior ús. A demès, aquest projecte s’ha desenvolupat en col·laboració amb un segon projecte, dintre del qual s’implementarà una xarxa de sensors, mitjançant el protocol MIWI. Aquest projecte es divideix en tres grans blocs. El primer bloc del projecte serà una introducció teòrica de tots els coneixements relacionats amb el concepte d’energy harvesting i els mecanismes físic implicats. Al segon bloc podrem veure com s’han realitzat els càlculs, simulacions i posada en marxa, dels diferents elements que formaran el dispositiu recol·lector d’energia. Per últim en el tercer bloc veurem el prototip ja implementat. Es valoraran els resultats obtinguts, i es veuran els temps que necessitarà per alimentar al microcontrolador.

Super M, un videojoc per practicar les matemàtiques

Desenvolupament d'un videojoc per a Android i un videojoc per a navegador; tots dos relacionats amb la pràctica de les matemàtiques.

Anomalous Proper-Motions in the Cygnus Super Bubble Region

In an analysis of proper motions of O and B stars contained the Input Catalogue for Hipparcos, we have found a clear deviation from the expected pattern of systematic motions which can be readily identified with the associations Cygnus OB1 and Cygnus OB9, located near de the edge of the Cygnus Superbubble. Teha anomalous motions are directed outwards from the center of the Superbubble, which is coincident with tha association Cygnus OB2. This seems to support the hypothesis of a strong stellar and supernova activity in Cygnus 0B2 giving rise to the Superbubble and, by means of gravitational instabilities in its boundaries, to Cygnus 0B1 and Cygnus OB9. New uvby-beta aperture photometry of selected O and B stars in the area of Cygnus OB1 and Cygnus OB9 is also presented and analyzed in this paper.

Super-resolution of remotely sensed images with variable-pixel linear reconstruction

This paper describes the development and applications of a super-resolution method, known as Super-Resolution Variable-Pixel Linear Reconstruction. The algorithm works combining different lower resolution images in order to obtain, as a result, a higher resolution image. We show that it can make significant spatial resolution improvements to satellite images of the Earth¿s surface allowing recognition of objects with size approaching the limiting spatial resolution of the lower resolution images. The algorithm is based on the Variable-Pixel Linear Reconstruction algorithm developed by Fruchter and Hook, a well-known method in astronomy but never used for Earth remote sensing purposes. The algorithm preserves photometry, can weight input images according to the statistical significance of each pixel, and removes the effect of geometric distortion on both image shape and photometry. In this paper, we describe its development for remote sensing purposes, show the usefulness of the algorithm working with images as different to the astronomical images as the remote sensing ones, and show applications to: 1) a set of simulated multispectral images obtained from a real Quickbird image; and 2) a set of multispectral real Landsat Enhanced Thematic Mapper Plus (ETM+) images. These examples show that the algorithm provides a substantial improvement in limiting spatial resolution for both simulated and real data sets without significantly altering the multispectral content of the input low-resolution images, without amplifying the noise, and with very few artifacts.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Modulation of plant HMG-CoA reductase by protein phosphatase 2A: Positive and negative control at a key node of metabolism

The enzyme HMG-CoA reductase (HMGR) has a key regulatory role in the mevalonate pathway for isoprenoid biosynthesis, critical not only for normal plant development, but also for the adaptation to demanding environmental conditions. Consistent with this notion, plant HMGR is modulated by many diverse endogenous signals and external stimuli. Protein phosphatase 2A (PP2A) is involved in auxin, abscisic acid, ethylene and brassinosteroid signaling and now emerges as a positive and negative multilevel regulator of plant HMGR, both during normal growth and in response to a variety of stress conditions. The interaction with HMGR is mediated by B" regulatory subunits of PP2A, which are also calcium binding proteins. The new discoveries uncover the potential of PP2A to integrate developmental and calcium-mediated environmental signals in the control of plant HMGR.