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.

Análisis comparativo de tres técnicas de derivación de células madre

Las células madre embrionarias (Embryonic Stem Cells; ESC) son células pluripotentes que presentan la capacidad de dividirse indefinidamente a la vez que mantienen la habilidad para diferenciarse a cualquier tipo celular. Aunque de manera rutinaria se derivan a partir de la masa celular interna de embriones en estadio de blastocisto, también pueden derivarse a partir de embriones en estadios precompactacionales y de embriones reconstruidos por procesos de transferencia nuclear. Debido a que durante el desarrollo embrionario temprano, momento en el que se derivan las ESC, tienen lugar profundos cambios de metilación en el genoma, tanto la derivación como el cultivo se consagran como técnicas que pueden alterar los patrones de metilación en genes regulados por impronta genómica. Con el objetivo de analizar la estabilidad epigenética de embriones preimplantacionales y ESC murinas, en este trabajo se ha optimizado un protocolo de anàlisis de los niveles de metilación mediante pirosecuenciación. Para ello se han seleccionado tres genes regulados por impronta genómica (H19/Igf2, Snrpn and Peg3), dos genes relacionados con el mantenimiento de pluripotencia en ESC (Oct4, Nanog y Sox2) y dos genes marcadores de diferenciación temprana (Cdx2 y Gata6). Nuestros resultados muestran que algunos grupos de embriones preimplantacionales presentan una hipo e hipermetilación en las regiones diferencialmente metiladas (Differentially Methylated Regions, DMRs) de los genes Snrpn y Peg3. Además, la línea de ESC analizada presentó anomalías en los tres genes regulados por impronta genómica. No obstante, el hecho de que esta línea fuera inestable a nivel cariotípico no permite establecer una relación entre el cultivo in vitro o la técnica de derivación y la inestabilidad epigenética demostrada. Por todo esto, parece pertinente analizar tanto la integridad epigenética como la estabilidad cromosómica de ESC antes de proceder a realizar ensayos clínicos en humanos.

Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.

On stability of solutions to systems of convex inequalities

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

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

A non-possibility theorem for joint-stability in interindustry models

Joint-stability in interindustry models relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots and offer an analytical demonstration that shows the impossibility of consistency between demand-driven and supply-driven models.

The effects of uncertainty about countries' compliance with the Stability and Growth Pact

The Stability and Growth Pact (SGP) was established to govern discretionary fiscal policy in the European Monetary Union. This article studies the effects created when there is uncertainty about the members’ commitment to respecting the established deficit limits in the SGP. We will show that, even if countries respect the SGP deficit ceiling, the presence of uncertainty about their compliance will bring about higher volatility in key economic variables, which could, in turn, affect unemployment and growth negatively. This finding shows that it is important to reduce uncertainty about the members’ commitment towards the SGP. Keywords: fiscal policy rules, monetary union, Stability and Growth Pact, uncertainty, commitment. JEL No.: E63, F55, H62, H87

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes.Against this background the relevance of perturbations and subcompositions can beclearly seen. Moreover we can identify a number of hypotheses of interest involvingthe specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Improving Clustering Algorithms for Image Segmentation using Contour and Region Information

In image segmentation, clustering algorithms are very popular because they are intuitive and, some of them, easy to implement. For instance, the k-means is one of the most used in the literature, and many authors successfully compare their new proposal with the results achieved by the k-means. However, it is well known that clustering image segmentation has many problems. For instance, the number of regions of the image has to be known a priori, as well as different initial seed placement (initial clusters) could produce different segmentation results. Most of these algorithms could be slightly improved by considering the coordinates of the image as features in the clustering process (to take spatial region information into account). In this paper we propose a significant improvement of clustering algorithms for image segmentation. The method is qualitatively and quantitative evaluated over a set of synthetic and real images, and compared with classical clustering approaches. Results demonstrate the validity of this new approach

Necessary and sufficient conditions for robust stability using modal intervals

In this paper, robustness of parametric systems is analyzed using a new approach to interval mathematics called Modal Interval Analysis. Modal Intervals are an interval extension that, instead of classic intervals, recovers some of the properties required by a numerical system. Modal Interval Analysis not only simplifies the computation of interval functions but allows semantic interpretation of their results. Necessary, sufficient and, in some cases, necessary and sufficient conditions for robust performance are presented

Stability of cascade networks via fluid models

Vegeu el resum a l'inici del document de l'arxiu adjunt