A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

A chromosomal insertion toolbox for promoter probing, mutant complementation and pathogenicity studies in Ralstonia solanacearum

We describe here the construction of a delivery system for stable and directed insertion of gene constructs in a permissive chromosomal site of the bacterial wilt pathogen Ralstonia solanacearum. The system consists of a collection of suicide vectors the Ralstonia chromosome (pRC) series that carry an integration element flanked by transcription terminators and two sequences of homology to the chromosome of strain GMI1000, where the integration element is inserted through a double recombination event. Unique restriction enzyme sites and a GATEWAY cassette enable cloning of any promoter::gene combination in the integration element. Variants endowed with different selectable antibiotic resistance genes and promoter::gene combinations are described. We show that the system can be readily used in GMI1000 and adapted to other R. solanacearum strains using an accessory plasmid. We prove that the pRC system can be employed to complement a deletion mutation with a single copy of the native gene, and to measure transcription of selected promoters in monocopy both in vitro and in planta. Finally, the system has been used to purify and study secretion type III effectors. These novel genetic tools will be particularly useful for the construction of recombinant bacteria that maintain inserted genes or reporter fusions in competitive situations (i.e., during plant infection).

Interactive Calculus in a Virtual Learning Environment

The teaching of higher level mathematics for technical students in a virtual learningenvironment poses some difficulties, but also opportunities, now specific to that virtuality.On the other hand, resources and ways to do now manly available in VLEs might soon extend to all kinds of environments.In this short presentation we will discuss anexperience carried at Universitat Oberta deCatalunya (UOC) involving (an on line university), first, the translation of LaTeX written existent materials to a web based format(specifically, a combination of XHTML andMathML), and then the integration of a symbolic calculator software (WIRIS) running as a Java applet embedded in the materials, intending to achieve an evolution from memorising concepts and repetitive algorithms to understanding and experiment concepts and the use of those algorithms.

Traducción técnica del capítulo III del libro Advanced Data Warehouse design: from conventional to spatial and temporal applications

The proposal to work on this final project came after several discussions held with Dr. Elzbieta Malinowski Gadja, who in 2008 published the book entitled Advanced Data Warehouse Design: From Conventional to Spatial and Temporal Applications (Data-Centric Systems and Applications). The project was carried out under the technical supervision of Dr. Malinowski and the direct beneficiary was the University of Costa Rica (UCR) where Dr. Malinowski is a professor at the Department of Computer Science and Informatics. The purpose of this project was twofold: First, to translate chapter III of said book with the intention of generating educational material for the use of the UCR and, second, to venture in the field of technical translation related to data warehouse. For the first component, the goal was to generate a final product that would eventually serve as an educational tool for the post-graduate courses of the UCR. For the second component, this project allowed me to acquire new skills and put into practice techniques that have helped me not only to perfom better in my current job as an Assistant Translator of the Inter-American BAnk (IDB), but also to use them in similar projects. The process was lenggthy and required torough research and constant communication with the author. The investigation focused on the search of terms and definitions to prepare the glossary, which was the basis to start the translation project. The translation process itself was carried out by phases, so that comments and corrections by the author could be taken into account in subsequent stages. Later, based on the glossary and the translated text, illustrations had been created in the Visio software were translated. In addition to the technical revision by the author, professor Carme Mangiron was in charge of revising the non-technical text. The result was a high-quality document that is currently used as reference and study material by the Department of Computer Science and Informatics of Costa Rica.

Effects of cobalt-chromium everolimus eluting stents or bare metal stent on fatal and non-fatal cardiovascular events: patient level meta-analysis

Objectives: To examine the safety and effectiveness of cobalt-chromium everolimus eluting stents compared with bare metal stents. Design: Individual patient data meta-analysis of randomised controlled trials. Cox proportional regression models stratified by trial, containing random effects, were used to assess the impact of stent type on outcomes. Hazard ratios with 95% confidence interval for outcomes were reported. Data sources and study selection: Medline, Embase, the Cochrane Central Register of Controlled Trials. Randomised controlled trials that compared cobalt-chromium everolimus eluting stents with bare metal stents were selected. The principal investigators whose trials met the inclusion criteria provided data for individual patients. Primary outcomes: The primary outcome was cardiac mortality. Secondary endpoints were myocardial infarction, definite stent thrombosis, definite or probable stent thrombosis, target vessel revascularisation, and all cause death. Results: The search yielded five randomised controlled trials, comprising 4896 participants. Compared with patients receiving bare metal stents, participants receiving cobalt-chromium everolimus eluting stents had a significant reduction of cardiac mortality (hazard ratio 0.67, 95% confidence interval 0.49 to 0.91; P=0.01), myocardial infarction (0.71, 0.55 to 0.92; P=0.01), definite stent thrombosis (0.41, 0.22 to 0.76; P=0.005), definite or probable stent thrombosis (0.48, 0.31 to 0.73; P<0.001), and target vessel revascularisation (0.29, 0.20 to 0.41; P<0.001) at a median follow-up of 720 days. There was no significant difference in all cause death between groups (0.83, 0.65 to 1.06; P=0.14). Findings remained unchanged at multivariable regression after adjustment for the acuity of clinical syndrome (for instance, acute coronary syndrome v stable coronary artery disease), diabetes mellitus, female sex, use of glycoprotein IIb/IIIa inhibitors, and up to one year v longer duration treatment with dual antiplatelets. Conclusions: This meta-analysis offers evidence that compared with bare metal stents the use of cobalt-chromium everolimus eluting stents improves global cardiovascular outcomes including cardiac survival, myocardial infarction, and overall stent thrombosis.

Effects of cobalt-chromium everolimus eluting stents or bare metal stent on fatal and non-fatal cardiovascular events: patient level meta-analysis

Objectives: To examine the safety and effectiveness of cobalt-chromium everolimus eluting stents compared with bare metal stents. Design: Individual patient data meta-analysis of randomised controlled trials. Cox proportional regression models stratified by trial, containing random effects, were used to assess the impact of stent type on outcomes. Hazard ratios with 95% confidence interval for outcomes were reported. Data sources and study selection: Medline, Embase, the Cochrane Central Register of Controlled Trials. Randomised controlled trials that compared cobalt-chromium everolimus eluting stents with bare metal stents were selected. The principal investigators whose trials met the inclusion criteria provided data for individual patients. Primary outcomes: The primary outcome was cardiac mortality. Secondary endpoints were myocardial infarction, definite stent thrombosis, definite or probable stent thrombosis, target vessel revascularisation, and all cause death. Results: The search yielded five randomised controlled trials, comprising 4896 participants. Compared with patients receiving bare metal stents, participants receiving cobalt-chromium everolimus eluting stents had a significant reduction of cardiac mortality (hazard ratio 0.67, 95% confidence interval 0.49 to 0.91; P=0.01), myocardial infarction (0.71, 0.55 to 0.92; P=0.01), definite stent thrombosis (0.41, 0.22 to 0.76; P=0.005), definite or probable stent thrombosis (0.48, 0.31 to 0.73; P<0.001), and target vessel revascularisation (0.29, 0.20 to 0.41; P<0.001) at a median follow-up of 720 days. There was no significant difference in all cause death between groups (0.83, 0.65 to 1.06; P=0.14). Findings remained unchanged at multivariable regression after adjustment for the acuity of clinical syndrome (for instance, acute coronary syndrome v stable coronary artery disease), diabetes mellitus, female sex, use of glycoprotein IIb/IIIa inhibitors, and up to one year v longer duration treatment with dual antiplatelets. Conclusions: This meta-analysis offers evidence that compared with bare metal stents the use of cobalt-chromium everolimus eluting stents improves global cardiovascular outcomes including cardiac survival, myocardial infarction, and overall stent thrombosis.

Is bundling anticompetitive?

I analyze the implications of bundling on price competition in a market for complementary products. Using a model of imperfect competition with product differentiation, I identify the incentives to bundle for two types of demand functions and study how they change with the size of the bundle. With an inelastic demand, bundling creates an advantage over uncoordinated rivals who cannot improve by bundling. I show that this no longer holds with an elastic demand. The incentives to bundle are stronger and the market outcome is symmetric bundling, the most competitive one. Profits are lowest and consumer surplus is maximized.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Programa vellesa, activitat física i dependència (Vafid): justificació i bases per a la sistematització

El present estudi es centra en els programes d’activitat física adreçats a persones grans en situació de dependència, que es esenvolupen en grup i que utilitzen el moviment actiu com a principal eina de treball. Es tracta d’una recerca que, per una banda, estudia i analitza les bases teòriques que avalen la importància i la necessitat de l’aplicació d’aquest tipus de programes. Per l’altra, justifica i defineix, amb detall, les línies directrius que han de guiar el seu desenvolupament i la seva aplicació en l’àmbit d’institucions d’atenció a les persones grans (residències, centres de dia i centres sòciosanitaris). El marc conceptual (capítol II) es construeix a partir d’una àmplia recerca bibliogràfica sobre les quatre dimensions d’anàlisi clau (l’envelliment, la dependència, l’atenció a les persones grans i l’activitat física) que fonamenta i justifica la proposta de programa que es fa en la segona part (capítol III). En aquesta es defineixen els referents, les finalitats, els objectius, els recursos que es poden utilitzar, les indicacions bàsiques per a organitzar el treball, els aspectes metodològics essencials per a l’aplicació del programa i les condicions necessàries per a poder-lo implementar. El resultat de tot el procés de recerca i estudi permet dir que, a nivell teòric, l’activitat física és una eina útil, eficaç i amb moltes possibilitats cara a l’atenció a les persones grans en situació de dependència. Que els esmentats programes han de ser fruit d’un procés de planificació, han de considerar les diferents dimensions de l’ésser en interacció constant, han de ser aplicats donant més importància al procés que al producte i que els recursos disponibles s’han d’utilitzar d’acord amb aquests plantejaments. En les línies de futur per a aquesta recerca, es planteja la seva continuació a partir de l’aplicació del programa VAFiD en diferents grups i la seva avaluació (seguint el model d’avaluació responent de Robert Stake) per determinar-ne la coherència i la qualitat.

Enrutament i control de flux en xarxes híbrides satèl·lit-terrestre

Les xarxes híbrides satèl·lit-terrestre ofereixen connectivitat a zones remotes i aïllades i permeten resoldre nombrosos problemes de comunicacions. No obstant, presenten diversos reptes, ja que realitzen la comunicació per un canal mòbil terrestre i un canal satèl·lit contigu. Un d'aquests reptes és trobar mecanismes per realitzar eficientment l'enrutament i el control de flux, de manera conjunta. L'objectiu d'aquest projecte és simular i estudiar algorismes existents que resolguin aquests problemes, així com proposar-ne de nous, mitjançant diverses tècniques d'optimització convexa. A partir de les simulacions realitzades en aquest estudi, s'han analitzat àmpliament els diversos problemes d'enrutament i control de flux, i s'han avaluat els resultats obtinguts i les prestacions dels algorismes emprats. En concret, s'han implementat de manera satisfactòria algorismes basats en el mètode de descomposició dual, el mètode de subgradient, el mètode de Newton i el mètode de la barrera logarítmica, entre d'altres, per tal de resoldre els problemes d'enrutament i control de flux plantejats.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

The Accessibility City. When Transport Infrastructure Matters in Urban Spatial Structure

Suburbanization is changing the urban spatial structure and less monocentric metropolitan regions are becoming the new urban reality. Focused only on centers, most works have studied these spatial changes neglecting the role of transport infrastructure and its related location model, the “accessibility city”, in which employment and population concentrate in low-density settlements and close to transport infrastructure. For the case of Barcelona, we consider this location model and study the population spatial structure between 1991 and 2006. The results reveal a mix between polycentricity and the accessibility city, with movements away from the main centers, but close to the transport infrastructure.

Nous derivats del 1-1'-bisnaftalè en el camp de l'enantioreconeixement: enantiodiferenciació i síntesi enantioselectiva

La línia principal d’investigació del nostre grup de recerca es basa en la síntesi i estudi de nous agents de solvatació quirals (CSAs), és a dir, compostos enantiopurs que s’utilitzen per a determinar la puresa enantiomèrica mitjançant la Ressonància Magnètica Nuclear (RMN). Al present treball volem sintetitzar i estudiar estructuralment la dicetona racèmica 14 amb la qual, mitjançant reaccions de reducció, podem obtenir el diol 12, el nou CSA que volem sintetitzar. També forma part del present treball la resolució de la dicetona racèmica 14, és a dir, aconseguir la separació dels seus dos enantiòmers mitjançant la formació de derivats diastereoisomèrics de 14 amb un reactiu enantiopur.

La dolçaina : nous recursos interpretatius?

Aquest projecte és fruit de la meva necessitat de buscar amb el meu instrument, la dolçaina, recursos interpretatius presents en altres instruments de la música tradicional. Aquests recursos, per desconeguts, em resulten nous i poden suposar la porta d’entrada a la investigació i estudi d’altres tradicions musicals. Aquest estudi pot també contribuir a veure la nostra pròpia tradició i patrimoni musical d’una altra manera. Com a punt de partida es descriuen els recursos que s’utilitzen actualment en la interpretació de dolçaina. Posteriorment s’analitzen i descriuen diferents recursos a estudiar i aplicar. Tot i que el projecte està orientat a la pràctica, s’aporta abundant informació i reflexions al voltant de la dolçaina, la música tradicional i sobre aspectes comuns entre músiques de diferents indrets.

L’impacte de les institucions internacionals sobre la Unió Europea: presa de decisions, integració i europeïtzació

Projecte de recerca elaborat a partir d’una estada a la Center for European Integration de la Freie Universität Berlin, Alemania, entre 2007 i 2009. El tema central del projecte consisteix en la descripció matemàtica de processos espai-temporals mitjançant la teoria dels Continuous-Time Random Walks. L'aportació més significativa del nostre treball en aquest camp consisteix en considerar per primera vegada la interacció entre diversos processos actuant de manera acoblada, ja que fins ara els models existents es limitaven a l'estudi de processos individuals o independents. Aquesta idea fa possible, per exemple, plantejar un sistema de transport en l'espai i a la vegada un procés de reacció (una reacció química, per exemple), i estudiar estadísticament com cada un pot alterar el comportament de l'altre. Això suposa un salt qualitatiu important en la descripció de processos de reacció-dispersió, ja que els nostres models permeten incorporar patrons de dispersió i comportaments temporals (cicles de vida) força realistes en comparació amb els models convencionals. Per tal de completar aquest treball teòric ha estat necessari també desenvolupar algunes eines numèriques (models de xarxa) per facilitar la implementació dels models. En la vessant pràctica, hem aplicat aquestes idees al cas de la dinàmica entre virus i el sistema immunològic que té lloc quan es produeix una infecció a l'organisme. Diferents estudis experimentals portats a terme els últims anys mostren com la resposta immunològica dels organismes superiors presenta una dinàmica temporal força complexa (per exemple, en el cas de la resposta programada). Per aquest motiu, les nostres tècniques matemàtiques són d'especial utilitat per a l'anàlisi d'aquests sistemes. Finalment, altres possibles aplicacions dels models, com ara l'estudi d'invasions biològiques, també han estat considerades.