Algebraic properties of isochronous centers of polynomial quadratic-like Hamiltonian systems

Projecte de recerca elaborat a partir d’una estada a la School of Mathematics and Statistics de la University of Plymouth, United Kingdom, entre abril juliol del 2007.Aquesta investigació és encara oberta i la memòria que presento constitueix un informe de la recerca que estem duent a terme actualment. En aquesta nota estudiem els centres isòcrons dels sistemes Hamiltonians analítics, parant especial atenció en el cas polinomial. Ens centrem en els anomenats quadratic-like Hamiltonian systems. Diverses propietats dels centres isòcrons d'aquest tipus de sistemes van ser donades a [A. Cima, F. Mañosas and J. Villadelprat, Isochronicity for several classes of Hamiltonian systems, J. Di®erential Equations 157 (1999) 373{413]. Aquell article estava centrat principalment en el cas en que A; B i C fossin funcions analítiques. El nostre objectiu amb l'estudi que estem duent a terme és investigar el cas en el que aquestes funcions són polinomis. En aquesta nota formulem una conjectura concreta sobre les propietats algebraiques que venen forçades per la isocronia del centre i provem alguns resultats parcials.

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

Geography of resonances and Arnold diffusion in a priori unstable Hamiltonian systems

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

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

New roles for community pharmacists in modern health care systems: a challenge for pharmacy education and research.

The academic activities led by the Unit of Community Pharmacy can be classified as translational. Our group is interested in person-centered pharmaceutical services aimed at a more responsible use of drugs (effectiveness, safety, efficiency) in collaboration with physicians and other health care professionals in a primary care setting. The following domains of education and research are high priorities for our group: medication therapy management, medication adherence, integrated care, individualization of therapies, care management for the elderly and e-health.

Grothendieck topologies from unique factorisation systems

This article presents a way to associate a Grothendieck site structure to a category endowed with a unique factorisation system of its arrows. In particular this recovers the Zariski and Etale topologies and others related to Voevodsky's cd-structures. As unique factorisation systems are also frequent outside algebraic geometry, the same construction applies to some new contexts, where it is related with known structures dened otherwise. The paper details algebraic geometrical situations and sketches only the other contexts.

The evolution of inbred social systems in spiders and other organisms: from short-term gains to long-term evolutionary dead-ends?

The question of why some social systems have evolved close inbreeding is particularly intriguing given expected short- and long-term negative effects of this breeding system. Using social spiders as a case study, we quantitatively show that the potential costs of avoiding inbreeding through dispersal and solitary living could have outweighed the costs of inbreeding depression in the origin of inbred spider sociality. We further review the evidence that despite being favored in the short term, inbred spider sociality may constitute in the long run an evolutionary dead end. We also review other cases, such as the naked mole rats and some bark and ambrosia beetles, mites, psocids, thrips, parasitic ants, and termites, in which inbreeding and sociality are associated and the evidence for and against this breeding system being, in general, an evolutionary dead end.

Colloidal systems for the delivery of cyclosporin A to the anterior segment of the eye.

Due to the eye's specific anatomical and physiological conformation, the treatment of eye diseases is a real challenge for pharmaceutical therapy. The presence of efficient protective barriers (i.e., the conjunctival and corneal membranes) and protective mechanisms (i.e., blinking and nasolachrymal drainage) makes this organ particularly impervious to local drug therapy. To overcome these issues, numerous strategies have been envisioned using pharmaceutical technology. Many formulations currently on the market or still under development are emulsions or colloidal systems intended to enhance precorneal residence time and corneal penetration, causing a consequent increase in drug bioavailability after instillation. After a review of some recent developments in the field of cyclosporin A formulations for the eye, a novel micellar formulation of cyclosporine A based on a diblock methoxy-poly(ethylene glycol)-hexysubstituted poly(lactides) (MPEG-hexPLA) is described.

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.

SYSGENET: a meeting report from a new European network for systems genetics.

The first scientific meeting of the newly established European SYSGENET network took place at the Helmholtz Centre for Infection Research (HZI) in Braunschweig, April 7-9, 2010. About 50 researchers working in the field of systems genetics using mouse genetic reference populations (GRP) participated in the meeting and exchanged their results, phenotyping approaches, and data analysis tools for studying systems genetics. In addition, the future of GRP resources and phenotyping in Europe was discussed.

Cost evaluation of cardiovascular magnetic resonance versus coronary angiography for the diagnostic work-up of coronary artery disease: Application of the European Cardiovascular Magnetic Resonance registry data to the German, United Kingdom, Swiss, and United States health care systems.

ABSTRACT: BACKGROUND: Cardiovascular magnetic resonance (CMR) has favorable characteristics for diagnostic evaluation and risk stratification of patients with known or suspected CAD. CMR utilization in CAD detection is growing fast. However, data on its cost-effectiveness are scarce. The goal of this study is to compare the costs of two strategies for detection of significant coronary artery stenoses in patients with suspected coronary artery disease (CAD): 1) Performing CMR first to assess myocardial ischemia and/or infarct scar before referring positive patients (defined as presence of ischemia and/or infarct scar to coronary angiography (CXA) versus 2) a hypothetical CXA performed in all patients as a single test to detect CAD. METHODS: A subgroup of the European CMR pilot registry was used including 2,717 consecutive patients who underwent stress-CMR. From these patients, 21% were positive for CAD (ischemia and/or infarct scar), 73% negative, and 6% uncertain and underwent additional testing. The diagnostic costs were evaluated using invoicing costs of each test performed. Costs analysis was performed from a health care payer perspective in German, United Kingdom, Swiss, and United States health care settings. RESULTS: In the public sectors of the German, United Kingdom, and Swiss health care systems, cost savings from the CMR-driven strategy were 50%, 25% and 23%, respectively, versus outpatient CXA. If CXA was carried out as an inpatient procedure, cost savings were 46%, 50% and 48%, respectively. In the United States context, cost savings were 51% when compared with inpatient CXA, but higher for CMR by 8% versus outpatient CXA. CONCLUSION: This analysis suggests that from an economic perspective, the use of CMR should be encouraged as a management option for patients with suspected CAD.

Monopolistic competition and different wage setting systems

In this paper we match the static disequilibrium unemployment model without frictions in the labor market and monopolistic competition with an infinite horizon model of growth. We compare the wages set at the firm, sector and national (centralized) levels, their unemployment rates and growth of the economic variables, for the Cobb-Douglas production function, in order to see under wich conditions the inverse U hypothesis between unemployment and centralization of wage bargain is confirmed. We also analyze, in the three wage setting systems, the effect of an increase in the monopoly power on employment and growth.

Migration of sharks into freshwater systems during the Miocene and implications for Alpine paleoelevation

Trace-element and isotopic compositions of fossilized shark teeth sampled from Miocene marine sediments of the north Alpine Molasse Basin, the Vienna Basin, and the Pannonian Basin generally show evidence of formation in a marine environment under conditions geochemically equivalent to the open ocean. In contrast, two of eight shark teeth from the Swiss Upper Marine Molasse locality of La Moliere have extremely low delta O-18 values (10.3% and 11.3%) and low Sr-87/Sr-86 ratios (0.707840 and 0.707812) compared to other teeth from this locality (21.1%,22.4%o and 0.708421-0.708630). The rare earth element (REE) abundances and patterns from La Moliere not only differ between dentine and enameloid of the same tooth, but also between different teeth, supporting variable conditions of diagenesis at this site. However, the REE patterns of enameloid from the ``exotic'' teeth analyzed for O and Sr isotopic compositions are similar to those of teeth that have O and Sr isotopic compositions typical of a marine setting at this site. Collectively, this suggests that the two ``exotic'' teeth were formed while the sharks frequented a freshwater environment with very low O-18-content and Sr isotopic composition controlled by Mesozoic calcareous rocks. This is consistent with a paleogeography of high-elevation (similar to 2300 m) Miocene Alps adjacent to a marginal sea.