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.

On stability of solutions to systems of convex inequalities

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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

Spatio-temporal variations in reproductive patterns and population structure of Pasiphaea multidentata (Decapoda: Caridea) in the Blanes canyon and adjacent margin, North-western Mediterranean Sea

The bathyal faunal communities of the NW Mediterranean slopes have been studied consistently in the last two decades, with a special focus on population structure, trophic dynamics and benthopelagic coupling of commercial deep-sea decapod crustaceans and fishes (reviewed in Sardà et al. 2004) and associated species (Cartes and Sardà, 1993; Company and Sardà, 1997, 2000; Cartes et al., 2001; Company et al., 2001, 2003, 2004). One of the major topographic features in the North-western Mediterranean slope is the presence of submarine canyons. Canyons play a major role in funnelling energy and organic matter from the shelf to bathyal and abyssal depths (Puig et al., 2000), but the implications of this enhanced organic supply in the deep-sea benthic communities is still mostly unknown. Trophic supply can follow two major pathways – vertical deposition in the water column (Billett et al., 1983; Baldwin et al., 1998; Lampitt et al., 2001) or down-slope advection on the margins (Puig et al., 2001; Bethoux et al., 2002; Canals et al., 2006) – and can be a limiting factor in the deep-sea, being especially important in the oligotrophic Mediterranean Sea (Sardà et al., 2004). Differences in the quantity, quality and timing of organic matter input to the deep seafloor have been used to explain patterns of biomass and abundance in benthic communities (Levin et al., 1994; Gooday & Turley, 1990; Billett et al., 2001; Galéron et al., 2001; Puig et al., 2001; Gage, 2003) as well as other biological process and in particular the existence of seasonal reproduction (Tyler et al., 1994; Company et al., 2004 (MEPS). Reproduction is a highly energetic process tightly linked to food availability and quality.

Gérard Grisey : la cuantificación temporal deducida de los procesos perceptivos

En el presente trabajo, tratamos diferentes perspectivas sobre la poética, estrategias compositivas y repercusión perceptiva del tiempo en la música de Gérard Grisey. En el primer capítulo, abordamos la concepción del tiempo como unidad y proporcionalidad duracional y su relación con otros parámetros musicales. A continuación, presentamos tres enfoques sobre el tiempo que emergen de la poética de Grisey y del análisis de sus obras: la ruptura con la proporcionalidad duracional y la relación entre tiempo y sonido, el concepto de cambio de escala temporal y la analogía entre tiempo y cosmos. En el segundo capítulo, proponemos tres categorías temporales basadas principalmente en el concepto de previsibilidad: tiempo no lineal, tiempo lineal y tiempo procesual. En el tercer y último capítulo, exponemos los fundamentos de la Teoría de la Información, su relación con el discurso de Grisey y su método de aplicación.

Degeneració Lobular Fronto-Temporal. Fenotips Clínics i Evolució

Estudi retrospectiu de recollida de dades clíniques i de neuroimatge de pacients diagnosticats, em La clínica diària, de Degeneració Lobular Fronto-Temporal (DLFT) entre gener de 1996 i Marc de 2008. Es descriuen dades demogràfiques i clíniques i es classifiquen en fenotips al diagnòstic inicial segons variants de: DFT-vc (Demència fronto-temporal variant de conducta), APNF (Afàsia Progressiva no fluent) DS (Demència Semàntica) SCB (Síndrome Còrtico-Basal) y PSP (Paràlisis Supranuclear Progressiva). Es descriuen els canvis clínics durant el seguiment i s’analitzen els patrons radiològics en les neuroimatges disponibles. S’inclouen també dades d’ApoE i l’estudi anatomopatològic realitzat a 17 d’ells.

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

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

A la llum de les matrius: projecte d'exposició temporal

El treball presenta el projecte d'una exposició temporal al Museu d'Art sobre el fons de xilografies procedents de la Impremta Carreras

Stability of cascade networks via fluid models

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New delay-dependent stability criteria for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations

The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range dependent, and distributeddelay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs) and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method

EU's democracy promotion policy in the Mediterranean: Squaring the stability – democracy circle?

Why does the EU have an ambiguous and inconsistent democracy promotion (DP) policy towards the Mediterranean countries? This paper argues that the EU´s DP is determined by a crucial conflict of interests conceptualised as a stability – democracy dilemma. The EU has been attempting to promote democracy, but without risking the current stability and in connivance with incumbent autocratic regimes. In view of this dilemma, the four main characteristics of the EU´s DP promotion are explored, namely: gradualism, a strong notion of partnership-building, a narrow definition of civil society, and a strong belief in economic liberalisation. A fifth feature, relation of the EU with moderate Islamists, is analysed in the paper as it represents the most striking illustration of its contradictions. The paper concludes by arguing that the definition of a clear DP by the EU that considered engagement with moderate Islamists would represent a major step towards squaring its stability – democracy circle.

Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians

In this paper, we give a new construction of resonant normal forms with a small remainder for near-integrable Hamiltonians at a quasi-periodic frequency. The construction is based on the special case of a periodic frequency, a Diophantine result concerning the approximation of a vector by independent periodic vectors and a technique of composition of periodic averaging. It enables us to deal with non-analytic Hamiltonians, and in this first part we will focus on Gevrey Hamiltonians and derive normal forms with an exponentially small remainder. This extends a result which was known for analytic Hamiltonians, and only in the periodic case for Gevrey Hamiltonians. As applications, we obtain an exponentially large upper bound on the stability time for the evolution of the action variables and an exponentially small upper bound on the splitting of invariant manifolds for hyperbolic tori, generalizing corresponding results for analytic Hamiltonians.