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.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On stability of solutions to systems of convex inequalities

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

Potential isomorphism of elementary substructures of a strictly stable homogeneous model

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

The generator problem for Z-stable C*-algebras

The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry

A compositional approach to stable isotope data analysis

Isotopic data are currently becoming an important source of information regardingsources, evolution and mixing processes of water in hydrogeologic systems. However, itis not clear how to treat with statistics the geochemical data and the isotopic datatogether. We propose to introduce the isotopic information as new parts, and applycompositional data analysis with the resulting increased composition. Results areequivalent to downscale the classical isotopic delta variables, because they are alreadyrelative (as needed in the compositional framework) and isotopic variations are almostalways very small. This methodology is illustrated and tested with the study of theLlobregat River Basin (Barcelona, NE Spain), where it is shown that, though verysmall, isotopic variations comp lement geochemical principal components, and help inthe better identification of pollution sources

Natural abundance of stable isotopes (15N and 13C) and isotopic fractionation of sea bream muscle as markers of food and culture conditions and its relationship with metabolic and proteomic analyses

Els isòtops estables com a traçadors de la cadena alimentària, s'han utilitzat per caracteritzar la relació entre els consumidors i els seus aliments, ja que el fraccionament isotòpic implica una discriminació en contra de certs isòtops. Però les anàlisis d'isòtops estables (SIA), també es poden dur a terme en peixos cultivats amb dietes artificials, com la orada (Sparus aurata), la especie más cultivada en el Mediterráneo. Canvis en l'abundància natural d'isòtops estables (13C i 15N) en els teixits i les seves reserves poden reflectir els canvis en l'ús i reciclatge dels nutrients ja que els enzims catabòlics implicats en els processos de descarboxilació i desaminació mostren una preferència pels isòtops més lleugers. Per tant, aquestes anàlisis ens poden proporcionar informació útil sobre l'estat nutricional i metabòlic dels peixos. L'objectiu d'aquest projecte va ser determinar la capacitat dels isòtops estables per ser utilitzats com a marcadors potencials de la capacitat de creixement i condicions de cria de l'orada. En aquest sentit, les anàlisis d'isòtops estables s'han combinat amb altres metabòlics (activitats citocrom-c-oxidasa, COX, i citrat sintasa, CS) i els paràmetres de creixement (ARN/ADN). El conjunt de resultats obtinguts en els diferents estudis realitzats en aquest projecte demostra que el SIA, en combinació amb altres paràmetres metabòlics, pot servir com una eina eficaç per discriminar els peixos amb millor potencial de creixement, així com a marcador sensible de l'estat nutricional i d'engreix. D'altra banda, la combinació de l'anàlisi d'isòtops estables amb les eines emergents, com ara tècniques de proteòmica (2D-PAGE), ens proporciona nous coneixements sobre els canvis metabòlics que ocorren en els músculs dels peixos durant l‟increment del creixement muscular induït per l'exercici.

Applications of stochastic analysis in finance and statistical inference

First: A continuous-time version of Kyle's model (Kyle 1985), known as the Back's model (Back 1992), of asset pricing with asymmetric information, is studied. A larger class of price processes and of noise traders' processes are studied. The price process, as in Kyle's model, is allowed to depend on the path of the market order. The process of the noise traders' is an inhomogeneous Lévy process. Solutions are found by the Hamilton-Jacobi-Bellman equations. With the insider being risk-neutral, the price pressure is constant, and there is no equilibirium in the presence of jumps. If the insider is risk-averse, there is no equilibirium in the presence of either jumps or drifts. Also, it is analised when the release time is unknown. A general relation is established between the problem of finding an equilibrium and of enlargement of filtrations. Random announcement time is random is also considered. In such a case the market is not fully efficient and there exists equilibrium if the sensitivity of prices with respect to the global demand is time decreasing according with the distribution of the random time. Second: Power variations. it is considered, the asymptotic behavior of the power variation of processes of the form _integral_0^t u(s-)dS(s), where S_ is an alpha-stable process with index of stability 0&alpha&2 and the integral is an Itô integral. Stable convergence of corresponding fluctuations is established. These results provide statistical tools to infer the process u from discrete observations. Third: A bond market is studied where short rates r(t) evolve as an integral of g(t-s)sigma(s) with respect to W(ds), where g and sigma are deterministic and W is the stochastic Wiener measure. Processes of this type are particular cases of ambit processes. These processes are in general not of the semimartingale kind.

Contribution to Asterisk Open Source Project

With this final master thesis we are going to contribute to the Asterisk open source project. Asterisk is an open source project that started with the main objective of develop an IP telephony platform, completely based on Software (so not hardware dependent) and under an open license like GPL. This project was started on 1999 by the software engineer Mark Spencer at Digium. The main motivation of that open source project was that the telecommunications sector is lack of open solutions, and most of the available solutions are based on proprietary standards, which are close and not compatible between them. Behind the Asterisk project there is a company, Digum, which is the project leading since the project was originated in its laboratories. This company has some of its employees fully dedicated to contribute to the Asterisk project, and also provide the whole infrastructure required by the open source project. But the business of Digium isn't based on licensing of products due to the open source nature of Asterisk, but it's based on offering services around Asteriskand designing and selling some hardware components to be used with Asterisk. The Asterisk project has grown up a lot since its birth, offering in its latest versions advanced functionalities for managing calls and compatibility with some hardware that previously was exclusive of proprietary solutions. Due to that, Asterisk is becoming a serious alternative to all these proprietaries solutions because it has reached a level of maturity that makes it very stable. In addition, as it is open source, it can be fully customized to a givenrequirement, which could be impossible with the proprietaries solutions. Due to the bigness that is reaching the project, every day there are more companies which develop value added software for telephony platforms, that are seriously evaluating the option of make their software fully compatible withAsterisk platforms. All these factors make Asterisk being a consolidated project but in constant evolution, trying to offer all those functionalities offered by proprietaries solutions. This final master thesis will be divided mainly in two blocks totally complementaries. In the first block we will analyze Asterisk as an open source project and Asterisk as a telephony platform (PBX). As a result of this analysis we will generate a document, written in English because it is Asterisk project's official language, which could be used by future contributors as an starting point on joining Asterisk. On the second block we will proceed with a development contribution to the Asterisk project. We will have several options in the form that we do the contribution, such as solving bugs, developing new functionalities or start an Asterisk satellite project. The type of contribution will depend on the needs of the project on that moment.

Decentralization in Croatia: problems and possible solutions

El 2001 Croàcia va posar en marxa la iniciativa destinada a afluixar un alt grau de centralització mitjançant l'ampliació dels mandats de les unitats locals i el canvi de les fonts de finançament de les funcions públiques. No obstant això, els passos inicials en el procés de descentralització no ha estat seguida per altres mesures de descentralització fiscal, i en conseqüència, el seu nivell s'ha mantingut pràcticament sense canvis. El treball es proposa elaborar els principals problemes i obstacles en relació amb l'aplicació efectiva del procés de descentralització i donar tres grups de propostes per a la descentralització: (i) la divisió dels poders obligatoris entre les diferents unitats locals, (ii) el canvi en el finançament i (Iii) modificar la divisió territorial del país.

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

From bargaining solutions to claims rules: a proportional approach

Is it important to negotiate on proportions rather than on numbers? To answer this question, we analyze the behavior of well-known bargaining solutions and the claims rules they induce when they are applied to a "proportionally transformed" bargaining set SP -so-called bargaining-in-proportions set. The idea of applying bargaining solutions to claims problems was already developed in Dagan and Volij (1993). They apply the bargaining solutions over a bargaining set that is the one de ned by the claims and the endowment. A comparison among our results and theirs is provided. Keywords: Bargaining problem, Claims problem, Proportional, Constrained Equal Awards, Constrained Equal Losses, Nash bargaining solution. JEL classi fication: C71, D63, D71.

Estabilitat i diagènesis dels fitòlits de silici en els jaciments arqueològics

Estudi realitzat a partir d’una estada al Kimmel Center for Archaeological Research, Israel, entre 2010 i 2012. Els fitòlits són un dels components principals dels sediments arqueològics. Són relativament estables i menys propensos a la degradació biològica que altres restes vegetals, però també poden ser afectats per la diagènesis. Per entendre com la diagènesis afecta als fitòlits hem desenvolupat una aproximació experimental utilitzant solucions alcalines per determinar l’estabilitat individual de fitòlits fòssils i moderns. L’experimentació ha estat completada amb un estudi de camp a Izbet Sartah. Els resultats mostren com la diagènesis canvia la composició dels conjunts de fitòlits, i per tant afecta la interpretació arqueològica. Conseqüentment, hem desenvolupat un mètode per determinar l’estat de preservació dels fitòlits en els jaciments arqueològics. L’experimentació mostra com els fitòlits moderns són més solubles que els fitòlits fòssils. Tant els fitòlits fòssils com els moderns són menys estables si són cremats. No totes les morfologies es preserven igual, indicant així que hi ha unes morfologies més estables que unes altres. Els fitòlits amb decoracions delicades, especialment aquells formats a la inflorescència de gramínies, són més propensos a la dissolució que els de les fulles. L’avaluació de l’estat de preservació dels fitòlits en jaciments arqueològics es pot realitzar utilitzant un conjunt de tècniques com ara: l’Index de Variació de Fitòlits, el mètode de dissolució ràpida, la identificació de morfologies delicades i la utilització del FTIR. Proposem que la diagènesis dels fitòlits depèn directament de la quantitat inicial de fitòlits en els sediments, la velocitat de sedimentació, i la presència o absència de fitòlits i plantes modernes en l’àrea estudiada. Els resultats d’aquesta investigació han estat publicats en dos articles afegits al final de l’informe (Cabanes et al., 2011 i Cabanes et al., in press), presentats en congressos internacionals i utilitzats indirectament en altres investigacions.

Stable complexes involving acetylcholinesterase and amyloid-ß-peptide change the biochemical properties of the enzyme and increase the neurotoxicity of Alzheimer's fibrils

Brain acetylcholinesterase (AChE) forms stable complexes with amyloid-beta peptide (Abeta) during its assembly into filaments, in agreement with its colocalization with the Abeta deposits of Alzheimer's brain. The association of the enzyme with nascent Abeta aggregates occurs as early as after 30 min of incubation. Analysis of the catalytic activity of the AChE incorporated into these complexes shows an anomalous behavior reminiscent of the AChE associated with senile plaques, which includes a resistance to low pH, high substrate concentrations, and lower sensitivity to AChE inhibitors. Furthermore, the toxicity of the AChE-amyloid complexes is higher than that of the Abeta aggregates alone. Thus, in addition to its possible role as a heterogeneous nucleator during amyloid formation, AChE, by forming such stable complexes, may increase the neurotoxicity of Abeta fibrils and thus may determine the selective neuronal loss observed in Alzheimer's brain.