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.

A Simple Characterization of Dynamic Completeness in Continuous Time

This paper investigates dynamic completeness of financial markets in which the underlying risk process is a multi-dimensional Brownian motion and the risky securities dividends geometric Brownian motions. A sufficient condition, that the instantaneous dispersion matrix of the relative dividends is non-degenerate, was established recently in the literature for single-commodity, pure-exchange economies with many heterogenous agents, under the assumption that the intermediate flows of all dividends, utilities, and endowments are analytic functions. For the current setting, a different mathematical argument in which analyticity is not needed shows that a slightly weaker condition suffices for general pricing kernels. That is, dynamic completeness obtains irrespectively of preferences, endowments, and other structural elements (such as whether or not the budget constraints include only pure exchange, whether or not the time horizon is finite with lump-sum dividends available on the terminal date, etc.)

Comparative Statics of Asset Prices: the effect of other assets' risk

Currently, financial economics is unable to predict changes in asset prices with respect to changes in the underlying risk factors, even when an asset's dividend is independent of a given factor. This paper takes steps towards addressing this issue by highlighting a crucial component of wealth effects on asset prices hitherto ignored by the literature. Changes in wealth do not only alter an agents risk aversion, but also her perceived 'riskiness' of a security. The latter enhances significantly the extent to which market- clearing leads to endogenously-generated correlation across asset prices, over and above that induced by correlation between payoffs, giving the appearance of 'contagion.'

Testing low-altitude infrared digital photography from a mini-UAV to retrieve information for biological conservation

Satellite remote sensing imagery is used for forestry, conservation and environmental applications, but insufficient spatial resolution, and, in particular, unavailability of images at the precise timing required for a given application, often prevent achieving a fully operational stage. Airborne remote sensing has the advantage of custom-tuned sensors, resolution and timing, but its price prevents using it as a routine technique for the mentioned fields. Some Unmanned Aerial Vehicles might provide a “third way” solution as low-cost techniques for acquiring remotely sensed information, under close control of the end-user, albeit at the expense of lower quality instrumentation and instability. This report evaluates a light remote sensing system based on a remotely-controlled mini-UAV (ATMOS-3) equipped with a color infra-red camera (VEGCAM-1) designed and operated by CATUAV. We conducted a testing mission over a Mediterranean landscape dominated by an evergreen woodland of Aleppo pine (Pinus halepensis) and (Holm) oak (Quercus ilex) in the Montseny National Park (Catalonia, NE Spain). We took advantage of state-of-the-art ortho-rectified digital aerial imagery (acquired by the Institut Cartogràfic de Catalunya over the area during the previous year) and used it as quality reference. In particular, we paid attention to: 1) Operationality of flight and image acquisition according to a previously defined plan; 2) Radiometric and geometric quality of the images; and 3) Operational use of the images in the context of applications. We conclude that the system has achieved an operational stage regarding flight activities, although with meteorological limits set by wind speed and turbulence. Appropriate landing areas can be sometimes limiting also, but the system is able to land on small and relatively rough terrains such as patches of grassland or short matorral, and we have operated the UAV as far as 7 km from the control unit. Radiometric quality is sufficient for interactive analysis, but probably insufficient for automated processing. A forthcoming camera is supposed to greatly improve radiometric quality and consistency. Conventional GPS positioning through time synchronization provides coarse orientation of the images, with no roll information.

La variació de la mida i forma del crani al llarg de l'evoluació dels homínids: aplicació a les restes de Dmanisi (Geòrgia)

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. El treball que es presenta és un estudi sobre la mida i la forma del crani en diferents espècies d'homínids. El treball es va realitzar a la Facultat de Biologia de la Universitat de Barcelona, a la Unitat d Antropologia. L'estudi de la mida es va realitzar a partir de mesures craniomètriques utilitzades en antropologia física clàssica. L'estudi de la forma es va realitzar aplicant una tècnica novedosa en aquest camp, la morfometria geomètrica. Es van estudiar 52 cranis de 12 espècies diferents d'homínids des dels més antics, els Australopithecus, fins formes modernes d'Homo sapiens. L'estudi de les diferents espècies d'homínids va servir de base per intentar classificar uns individus trobats a Europa, al jaciment de Dmanisi. Aquests individus es troben immersos en una gran debat en quant a la seva assignació taxonòmica ja que són les restes més antigues trobades al continent europeu (1,8 milions d'anys). Els resultats de l'estudi indiquen que els individus de Dmanisi es troben entre les formes africanes i asiàtiques, podriem parlar doncs d'una espècie de transició.

Prognostic importance of anaemia in patients with acute pulmonary embolism.

Although associated with adverse outcomes in other cardiopulmonary diseases, limited evidence exists on the prognostic value of anaemia in patients with acute pulmonary embolism (PE). We sought to examine the associations between anaemia and mortality and length of hospital stay in patients with PE. We evaluated 14,276 patients with a primary diagnosis of PE from 186 hospitals in Pennsylvania, USA. We used random-intercept logistic regression to assess the association between anaemia at the time of presentation and 30-day mortality and discrete-time logistic hazard models to assess the association between anaemia and time to hospital discharge, adjusting for patient (age, gender, race, insurance type, clinical and laboratory variables) and hospital (region, size, teaching status) factors. Anaemia was present in 38.7% of patients at admission. Patients with anaemia had a higher 30-day mortality (13.7% vs. 6.3%; p <0.001) and a longer length of stay (geometric mean, 6.9 vs. 6.6 days; p <0.001) compared to patients without anaemia. In multivariable analyses, anaemia remained associated with an increased odds of death (OR 1.82, 95% CI: 1.60-2.06) and a decreased odds of discharge (OR 0.85, 95% CI: 0.82-0.89). Anaemia is very common in patients presenting with PE and is independently associated with an increased short-term mortality and length of stay.

Some personal views on the control of schistosomiasis mansoni

Our views are based, on a recent study of a district of Uniao dos Palmares (Alagoas). Although being a very compact community (32 city blocks holding two thousand families), transmission is very uneven, the geometric mean egg counts in the various blocks ranging between extremes of 96 and 1920. (Results do not correlate with the availability of domestic water supply). We thus are led to conclude that: (a) transmission is primarily peridomestic, resulting from pollution of open ditches and other collections of water; (b) control of transmission can be done on a selective basis, requiring quite medest investments. Given the inefficacy of population-based chemotherapy, when used alone, the author insists that this alternative cannot any longer be overlooked. He also regrets the emphasis placed upon vaccine development; allegations that this would, at any rate, prevent severe morbidity can be dismissed, since-whatever the cause-morbidity due to schistosomiasis has been rapidly declining in Northeast Brazil.

Seroepidemioplogy of schistosomiasis mansoni

In population surveys in wich the Schistosoma mansoni intensity of infection is low, or in localities where the schistosomiasis control program had success the parasitologic methods lack in sensitivity. Despite of some limitations the immunological methods are useful to provide valuable information in such field conditions. Thus, the prevalaence of schistosomiasis in untreated population can be determined by the detection of IgG or IgM antibodies, as well as the incidence by the IgA antibodies , employing mainly immunofluorescence (IF) and immunoenzymatic (ELISA), and in some extent hemagglutination (HA) or even skin test. The true prevalence and incidence of schistosomiasis can be estimated using a probabilistic model equation, since knowing before-hand the sensitivity and specificity of emploved test. The sensitivity and the specificity of serologic test become higher in low aged group, under 14. The geometric mean IF titers also gives a positive correlation with the intensity of infection. Presently there are need of serologic tests wich are economic and pratical in soroepidemiologic inquires, requiring no specialized personnel to collect population blood or serum and also easily interpret the test results. The reagents for such tests are desired to be stable and reproducible. Moreover, it is expected that the tests can distinguish an ative infection.

Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

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.

Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

New developments and applications in modelling occupational exposure to airborne contaminants

Résumé: L'évaluation de l'exposition aux nuisances professionnelles représente une étape importante dans l'analyse de poste de travail. Les mesures directes sont rarement utilisées sur les lieux même du travail et l'exposition est souvent estimée sur base de jugements d'experts. Il y a donc un besoin important de développer des outils simples et transparents, qui puissent aider les spécialistes en hygiène industrielle dans leur prise de décision quant aux niveaux d'exposition. L'objectif de cette recherche est de développer et d'améliorer les outils de modélisation destinés à prévoir l'exposition. Dans un premier temps, une enquête a été entreprise en Suisse parmi les hygiénistes du travail afin d'identifier les besoins (types des résultats, de modèles et de paramètres observables potentiels). Il a été constaté que les modèles d'exposition ne sont guère employés dans la pratique en Suisse, l'exposition étant principalement estimée sur la base de l'expérience de l'expert. De plus, l'émissions de polluants ainsi que leur dispersion autour de la source ont été considérés comme des paramètres fondamentaux. Pour tester la flexibilité et la précision des modèles d'exposition classiques, des expériences de modélisations ont été effectuées dans des situations concrètes. En particulier, des modèles prédictifs ont été utilisés pour évaluer l'exposition professionnelle au monoxyde de carbone et la comparer aux niveaux d'exposition répertoriés dans la littérature pour des situations similaires. De même, l'exposition aux sprays imperméabilisants a été appréciée dans le contexte d'une étude épidémiologique sur une cohorte suisse. Dans ce cas, certains expériences ont été entreprises pour caractériser le taux de d'émission des sprays imperméabilisants. Ensuite un modèle classique à deux-zone a été employé pour évaluer la dispersion d'aérosol dans le champ proche et lointain pendant l'activité de sprayage. D'autres expériences ont également été effectuées pour acquérir une meilleure compréhension des processus d'émission et de dispersion d'un traceur, en se concentrant sur la caractérisation de l'exposition du champ proche. Un design expérimental a été développé pour effectuer des mesures simultanées dans plusieurs points d'une cabine d'exposition, par des instruments à lecture directe. Il a été constaté que d'un point de vue statistique, la théorie basée sur les compartiments est sensée, bien que l'attribution à un compartiment donné ne pourrait pas se faire sur la base des simples considérations géométriques. Dans une étape suivante, des données expérimentales ont été collectées sur la base des observations faites dans environ 100 lieux de travail différents: des informations sur les déterminants observés ont été associées aux mesures d'exposition des informations sur les déterminants observés ont été associé. Ces différentes données ont été employées pour améliorer le modèle d'exposition à deux zones. Un outil a donc été développé pour inclure des déterminants spécifiques dans le choix du compartiment, renforçant ainsi la fiabilité des prévisions. Toutes ces investigations ont servi à améliorer notre compréhension des outils des modélisations ainsi que leurs limitations. L'intégration de déterminants mieux adaptés aux besoins des experts devrait les inciter à employer cet outil dans leur pratique. D'ailleurs, en augmentant la qualité des outils des modélisations, cette recherche permettra non seulement d'encourager leur utilisation systématique, mais elle pourra également améliorer l'évaluation de l'exposition basée sur les jugements d'experts et, par conséquent, la protection de la santé des travailleurs. Abstract Occupational exposure assessment is an important stage in the management of chemical exposures. Few direct measurements are carried out in workplaces, and exposures are often estimated based on expert judgements. There is therefore a major requirement for simple transparent tools to help occupational health specialists to define exposure levels. The aim of the present research is to develop and improve modelling tools in order to predict exposure levels. In a first step a survey was made among professionals to define their expectations about modelling tools (what types of results, models and potential observable parameters). It was found that models are rarely used in Switzerland and that exposures are mainly estimated from past experiences of the expert. Moreover chemical emissions and their dispersion near the source have also been considered as key parameters. Experimental and modelling studies were also performed in some specific cases in order to test the flexibility and drawbacks of existing tools. In particular, models were applied to assess professional exposure to CO for different situations and compared with the exposure levels found in the literature for similar situations. Further, exposure to waterproofing sprays was studied as part of an epidemiological study on a Swiss cohort. In this case, some laboratory investigation have been undertaken to characterize the waterproofing overspray emission rate. A classical two-zone model was used to assess the aerosol dispersion in the near and far field during spraying. Experiments were also carried out to better understand the processes of emission and dispersion for tracer compounds, focusing on the characterization of near field exposure. An experimental set-up has been developed to perform simultaneous measurements through direct reading instruments in several points. It was mainly found that from a statistical point of view, the compartmental theory makes sense but the attribution to a given compartment could ñó~be done by simple geometric consideration. In a further step the experimental data were completed by observations made in about 100 different workplaces, including exposure measurements and observation of predefined determinants. The various data obtained have been used to improve an existing twocompartment exposure model. A tool was developed to include specific determinants in the choice of the compartment, thus largely improving the reliability of the predictions. All these investigations helped improving our understanding of modelling tools and identify their limitations. The integration of more accessible determinants, which are in accordance with experts needs, may indeed enhance model application for field practice. Moreover, while increasing the quality of modelling tool, this research will not only encourage their systematic use, but might also improve the conditions in which the expert judgments take place, and therefore the workers `health protection.

Análisis morfométrico de la extremidad anterior en Carnivora

Durante los cuatro años de disfrute de la beca (2006 – 2009) se ha consolidado una base de datos de medidas osteológicas del esqueleto apendicular de numerosas especies del O. Carnivora. Concretamente, se han medido 364 individuos de 126 especies. Los ejemplares pertenecían a las colecciones del Phyletisches Museum (Jena, Alemania), el Museum für Naturkunde (Berlín, Alemania), el Museu de Ciències Naturals de la Ciutadella (Barcelona, España), el Múseum National d'Histoire Naturelle (París, Francia), y el Museo Nacional de Ciencias Naturales (Madrid, España). Asimismo, con estos datos se han estado preparando tres artículos sobre la morfología de ciertos elementos del esqueleto apendicular en carnívoros, dos de los cuales se encuentran actualmente en estado de revisión para su publicación científica. Dos de ellos, "Scapula, habitat and locomotion in Carnivora" y "Size and shape in the carnivore scapula", relacionan la morfología escapular con factores como el tamaño del animal, el tipo de locomoción que presenta y el hábitat en el que se encuentra; el primero mediante metodología multivariante (análisis funcional) y el segundo bajo las nuevas técnicas de morfometría geométrica. El tercer artículo, "Scaling and mechanics in the carnivore calcaneus: A comparison of natural and artificial selection", evalúa el efecto de diferentes tipos de selección, natural frente a artificial, sobre la morfología del calcáneo y su influencia en la biomecánica de este hueso. Finalmente, también se ha desarrollado un estudio experimental sobre la búsqueda de estabilidad durante la locomoción arbórea, cuyos resultados han dado lugar al artículo "The search for stability on narrow supports: An experimental study in cats and dogs", que también se halla bajo revisión actualmente.

Epidemiological Characteristics of Schistosoma mansoni Infection in Rural and Urban Endemic Areas of Minas Gerais, Brazil

To compare the epidemiological profile and socioeconomic factors associated to the infection by Schistosoma mansoni in a rural and an urban endemic area a cross-sectional study was performed in Água Branca de Minas (rural area) and Bela Fama (urban area), both situated in the State of Minas Gerais, Brazil. Two hundred and eighty eight individuals were surveyed in the rural area and 787 in the urban area. Water contact and socioeconomic questionnaires were used to identify risk factors for the infection. The prevalences of 38.8% and 9.7% and the geometric mean of eggs per gram of faeces of 117.8 and 62.3 were found in the rural and urban areas, respectively. By multivariate statistical analysis age groups over nine years old and previous specific treatment were associated with the infection in rural area. In urban area age over nine years old, low quality housing, weekly fishing and swimming were associated after adjustment by logistic regression

Schistosomiasis control based on repeated chemotherapy in a rural village of the sugar-cane zone in Northeast Brazil

A schedule of repeated chemotherapy with oxamniquine, consisting of biannual treatment of school-aged (7-13 years) children and annual treatment of all other age groups, was used in a representative rural village from a highly endemic area of schistosomiasis in Pernambuco. Significant reductions in infection were obtained only after two cycles of treatment, as the overall prevalence decreased from 72.6% to 41.7% and the geometric mean egg counts per gram of faeces among positives fell from 188.4 to 76. In a school-aged cohort (n=29) three treatments at six-month intervals were necessary to significantly reduce the proportion of positives (from 75.9% to 51.7%). In a cohort of children under 7 years of age (n=20) the proportion of positives actually increased (from 30% to 45%) despite two annual treatments. Water contact was intense and host snail density was relatively high. As there is no short-term perspective of improved sanitation, auxiliary measures such as focal mollusciciding are needed for an adequate control of schistosomiasis in this and alike areas.