Normal forms, stability and splitting of invariant manifolds II. Finitely differentiable Hamiltonians

This paper is a sequel to ``Normal forms, stability and splitting of invariant manifolds I. Gevrey Hamiltonians", in which we gave a new construction of resonant normal forms with an exponentially small remainder for near-integrable Gevrey Hamiltonians at a quasi-periodic frequency, using a method of periodic approximations. In this second part we focus on finitely differentiable Hamiltonians, and we derive normal forms with a polynomially small remainder. As applications, we obtain a polynomially large upper bound on the stability time for the evolution of the action variables and a polynomially small upper bound on the splitting of invariant manifolds for hyperbolic tori.

Genotype 3 is associated with accelerated fibrosis progression in chronic hepatitis C.

BACKGROUND/AIMS: While several risk factors for the histological progression of chronic hepatitis C have been identified, the contribution of HCV genotypes to liver fibrosis evolution remains controversial. The aim of this study was to assess independent predictors for fibrosis progression. METHODS: We identified 1189 patients from the Swiss Hepatitis C Cohort database with at least one biopsy prior to antiviral treatment and assessable date of infection. Stage-constant fibrosis progression rate was assessed using the ratio of fibrosis Metavir score to duration of infection. Stage-specific fibrosis progression rates were obtained using a Markov model. Risk factors were assessed by univariate and multivariate regression models. RESULTS: Independent risk factors for accelerated stage-constant fibrosis progression (>0.083 fibrosis units/year) included male sex (OR=1.60, [95% CI 1.21-2.12], P<0.001), age at infection (OR=1.08, [1.06-1.09], P<0.001), histological activity (OR=2.03, [1.54-2.68], P<0.001) and genotype 3 (OR=1.89, [1.37-2.61], P<0.001). Slower progression rates were observed in patients infected by blood transfusion (P=0.02) and invasive procedures or needle stick (P=0.03), compared to those infected by intravenous drug use. Maximum likelihood estimates (95% CI) of stage-specific progression rates (fibrosis units/year) for genotype 3 versus the other genotypes were: F0-->F1: 0.126 (0.106-0.145) versus 0.091 (0.083-0.100), F1-->F2: 0.099 (0.080-0.117) versus 0.065 (0.058-0.073), F2-->F3: 0.077 (0.058-0.096) versus 0.068 (0.057-0.080) and F3-->F4: 0.171 (0.106-0.236) versus 0.112 (0.083-0.142, overall P<0.001). CONCLUSIONS: This study shows a significant association of genotype 3 with accelerated fibrosis using both stage-constant and stage-specific estimates of fibrosis progression rates. This observation may have important consequences for the management of patients infected with this genotype.

Does Warfare Matter? Severity, Duration, and Outcomes of Civil Wars

Importa si una guerra civil es combat com un conflicte irregular, convencional o simètric no convencional? En altres paraules, tenen les “tecnologies de la rebel·lió” un impacte sobre la gravetat d’una guerra, la seva durada o el seu resultat? Aquest treball mostra que els conflictes irregulars duren més que els altres tipus de conflicte, mentre els convencionals tendeixen a ser més greus en termes de letalitat al camp de batalla. D’altra banda, els conflictes irregulars tendeixen a ser guanyats pels governs, mentre els altres són més propensos a acabar en empat. Substancialment, aquests resultats ens ajuden a donar sentit a l’evolució de les guerres civils, les quals tendeixen a ser més curtes, més intenses i més difícils per als governs. Teòricament, aquests resultats donen suport a la importància de la tecnologia de rebel·lió a l’estudiar la gravetat, la durada i els resultats de les guerres civils; a més, contribueixen a una millor comprensió de la contribució històrica de la guerra irregular a la construcció de l’Estat i al canvi social.

Development of a multistrain bacterial bioreporter platform for the monitoring of hydrocarbon contaminants in marine environments.

Petroleum hydrocarbons are common contaminants in marine and freshwater aquatic habitats, often occurring as a result of oil spillage. Rapid and reliable on-site tools for measuring the bioavailable hydrocarbon fractions, i.e., those that are most likely to cause toxic effects or are available for biodegradation, would assist in assessing potential ecological damage and following the progress of cleanup operations. Here we examined the suitability of a set of different rapid bioassays (2-3 h) using bacteria expressing the LuxAB luciferase to measure the presence of short-chain linear alkanes, monoaromatic and polyaromatic compounds, biphenyls, and DNA-damaging agents in seawater after a laboratory-scale oil spill. Five independent spills of 20 mL of NSO-1 crude oil with 2 L of seawater (North Sea or Mediterranean Sea) were carried out in 5 L glass flasks for periods of up to 10 days. Bioassays readily detected ephemeral concentrations of short-chain alkanes and BTEX (i.e., benzene, toluene, ethylbenzene, and xylenes) in the seawater within minutes to hours after the spill, increasing to a maximum of up to 80 muM within 6-24 h, after which they decreased to low or undetectable levels. The strong decrease in short-chain alkanes and BTEX may have been due to their volatilization or biodegradation, which was supported by changes in the microbial community composition. Two- and three-ring PAHs appeared in the seawater phase after 24 h with a concentration up to 1 muM naphthalene equivalents and remained above 0.5 muM for the duration of the experiment. DNA-damage-sensitive bioreporters did not produce any signal with the oil-spilled aqueous-phase samples, whereas bioassays for (hydroxy)biphenyls showed occasional responses. Chemical analysis for alkanes and PAHs in contaminated seawater samples supported the bioassay data, but did not show the typical ephemeral peaks observed with the bioassays. We conclude that bacterium-based bioassays can be a suitable alternative for rapid on-site quantitative measurement of hydrocarbons in seawater.

Use of drugs with more than a twenty-four-hour duration of action

AIM: To assess compliance with a drug regimen of two doses a day compared with one a day. PATIENTS AND METHODS: A prospective crossover study was set up in a general practice environment to compare compliance on a drug regimen of once a day versus twice a day. Data were collected by electronic monitoring in 113 patients with hypertension or angina pectoris. All patients were prescribed slow-release nifedipine twice a day during the first month and then crossed to a single daily dose of amlodipine for another month. RESULTS: Compliance, defined as the proportion of days on which the correct dose was taken, improved in 30% of patients (95% confidence interval 19-41%; P < 0.001) when the patients were switched from twice a day to once a day, but at the same time there was a 15% increase (95% confidence interval 5-25%; P < 0.02) in the number of patients with one or more no-dose days. Approximately 8% of patients displayed low compliance, irrespective of the dose regimen. Actual dose intervals were used to estimate the extent and timing of periods with unsatisfactory drug activity for various hypothetical drug durations of action. CONCLUSIONS: The apparent advantage of a single daily dose in terms of compliance appears to be clinically meaningful only when the duration of activity extends beyond the dose interval in all patients.

Duration of untreated psychosis: a proposition regarding treatment definition.

Aim: Duration of untreated psychosis (DUP) refers to the time elapsing between psychosis onset and treatment initiation. Despite a certain degree of consensus regarding the definition of psychosis onset, the definition of treatment commencement varies greatly between studies and DUP may be underestimated due to lack of agreement. In the present study, three sets of criteria to define the end of the untreated period were applied in a first-episode psychosis cohort to assess the impact of the choice of definition on DUP estimation. Methods: The DUP of 117 patients admitted in the Treatment and Early Intervention in Psychosis Program Psychosis in Lausanne was measured using the following sets of criteria to define treatment onset: (i) initiation of antipsychotic medication; (ii) entry into a specialized programme; and (iii) entry into a specialized programme and adequate medication with a good compliance. Results: DUP varied greatly according to definitions, the most restrictive criteria leading to the longest DUP (median DUP1 = 2.2 months, DUP2 = 7.4 months and DUP3 = 13.6 months). A percentage of 19.7 of the patients who did not meet these restrictive criteria had poorer premorbid functioning and were more likely to use cannabis. Longer DUP3 was associated with poorer premorbid functioning and with younger age at onset of psychosis. Conclusion: These results underline the need for a unique and standardized definition of the end of DUP. We suggest that the most restrictive definition of treatment should be used when using the DUP concept in future research.

The duration of prograde garnet crystallization in the UHP eclogites at Lago di Cignana, Italy

The distinct core-to-rim zonation of different REEs in garnet in metamorphic rocks, specifically Sm relative to Lu, suggests that Sm-Nd and Lu-Hf isochron ages will record different times along a prograde garnet growth history. Therefore, REE zonations in garnet must be measured in order to correctly interpret the isochron ages in terms of the garnet growth interval, which could span several m.y. New REE profiles, garnet crystal size distributions, and garnet growth modeling, combined with previously published Sm-Nd and Lu-Hf geochronology on a UHP eclogite of the Zermatt-Saas Fee (ZSF) ophiolite, Lago di Cignana (Italy), demonstrate that prograde garnet growth of this sample occurred over a similar to 30 to 40 m.y. interval. Relative to peak metamorphism at 38 to 40 Ma, garnet growth is estimated to have begun at similar to 11 to 14 kbar pressure at similar to 70 to 80 Ma. Although such a protracted garnet growth interval is surprising, this is supported by plate tectonic reconstructions which suggest that subduction of the Liguro-Piemont ocean occurred through slow and oblique convergence. These results demonstrate that REE zonations in garnet, coupled to crystal size distributions, provide a powerful means for understanding prograde metamorphic paths when combined with Sm-Nd and Lu-Hf geochronology. (C) 2009 Elsevier B.V. All rights reserved.

Bayesian nash equilibrium in ''linear'' cournot models with private information about costs

Calculating explicit closed form solutions of Cournot models where firms have private information about their costs is, in general, very cumbersome. Most authors consider therefore linear demands and constant marginal costs. However, within this framework, the nonnegativity constraint on prices (and quantities) has been ignored or not properly dealt with and the correct calculation of all Bayesian Nash equilibria is more complicated than expected. Moreover, multiple symmetric and interior Bayesianf equilibria may exist for an open set of parameters. The reason for this is that linear demand is not really linear, since there is a kink at zero price: the general ''linear'' inverse demand function is P (Q) = max{a - bQ, 0} rather than P (Q) = a - bQ.

Genetic structure of a linear population of Beta vulgaris ssp maritima (sea beet) revealed by isozyme and RFLP analysis

Knowledge of the genetic structure of plant populations is necessary for the understanding of the dynamics of major ecological processes. It also has applications in conservation biology and risk assessment for genetically modified crops. This paper reports the genetic structure of a linear population of sea beet, Beta vulgaris ssp. maritima (the wild relative of sugar beet), on Furzey Island, Poole Harbour. The relative spatial positions of the plants were accurately mapped and the plants were scored for variation at isozyme and RFLP loci. Structure was analysed by repeated subdivision of the population to find the average size of a randomly mating group. Estimates of F-ST between randomly mating units were then made, and gave patterns consistent with the structure of the population being determined largely by founder effects. The implications of these results for the monitoring of transgene spread in wild sea beet populations are discussed.

Performance of classic electrocardiographic criteria for left ventricular hypertrophy in an African population.

ECG criteria for left ventricular hypertrophy (LVH) have been almost exclusively elaborated and calibrated in white populations. Because several interethnic differences in ECG characteristics have been found, the applicability of these criteria to African individuals remains to be demonstrated. We therefore investigated the performance of classic ECG criteria for LVH detection in an African population. Digitized 12-lead ECG tracings were obtained from 334 African individuals randomly selected from the general population of the Republic of Seychelles (Indian Ocean). Left ventricular mass was calculated with M-mode echocardiography and indexed to body height. LVH was defined by taking the 95th percentile of body height-indexed LVM values in a reference subgroup. In the entire study sample, 16 men and 15 women (prevalence 9.3%) were finally declared to have LVH, of whom 9 were of the reference subgroup. Sensitivity, specificity, accuracy, and positive and negative predictive values for LVH were calculated for 9 classic ECG criteria, and receiver operating characteristic curves were computed. We also generated a new composite time-voltage criterion with stepwise multiple linear regression: weighted time-voltage criterion=(0.2366R(aVL)+0.0551R(V5)+0.0785S(V3)+ 0.2993T(V1))xQRS duration. The Sokolow-Lyon criterion reached the highest sensitivity (61%) and the R(aVL) voltage criterion reached the highest specificity (97%) when evaluated at their traditional partition value. However, at a fixed specificity of 95%, the sensitivity of these 10 criteria ranged from 16% to 32%. Best accuracy was obtained with the R(aVL) voltage criterion and the new composite time-voltage criterion (89% for both). Positive and negative predictive values varied considerably depending on the concomitant presence of 3 clinical risk factors for LVH (hypertension, age >/=50 years, overweight). Median positive and negative predictive values of the 10 ECG criteria were 15% and 95%, respectively, for subjects with none or 1 of these risk factors compared with 63% and 76% for subjects with all of them. In conclusion, the performance of classic ECG criteria for LVH detection was largely disparate and appeared to be lower in this population of East African origin than in white subjects. A newly generated composite time-voltage criterion might provide improved performance. The predictive value of ECG criteria for LVH was considerably enhanced with the integration of information on concomitant clinical risk factors for LVH.

Linear response functions for a vibrational configuration interaction state

Linear response functions are implemented for a vibrational configuration interaction state allowing accurate analytical calculations of pure vibrational contributions to dynamical polarizabilities. Sample calculations are presented for the pure vibrational contributions to the polarizabilities of water and formaldehyde. We discuss the convergence of the results with respect to various details of the vibrational wave function description as well as the potential and property surfaces. We also analyze the frequency dependence of the linear response function and the effect of accounting phenomenologically for the finite lifetime of the excited vibrational states. Finally, we compare the analytical response approach to a sum-over-states approach

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

N-dimensional dynamical systems exploiting instabilities in full

We report experimental and numerical results showing how certain N-dimensional dynamical systems are able to exhibit complex time evolutions based on the nonlinear combination of N-1 oscillation modes. The experiments have been done with a family of thermo-optical systems of effective dynamical dimension varying from 1 to 6. The corresponding mathematical model is an N-dimensional vector field based on a scalar-valued nonlinear function of a single variable that is a linear combination of all the dynamic variables. We show how the complex evolutions appear associated with the occurrence of successive Hopf bifurcations in a saddle-node pair of fixed points up to exhaust their instability capabilities in N dimensions. For this reason the observed phenomenon is denoted as the full instability behavior of the dynamical system. The process through which the attractor responsible for the observed time evolution is formed may be rather complex and difficult to characterize. Nevertheless, the well-organized structure of the time signals suggests some generic mechanism of nonlinear mode mixing that we associate with the cluster of invariant sets emerging from the pair of fixed points and with the influence of the neighboring saddle sets on the flow nearby the attractor. The generation of invariant tori is likely during the full instability development and the global process may be considered as a generalized Landau scenario for the emergence of irregular and complex behavior through the nonlinear superposition of oscillatory motions

Proximal tibia volumetric bone mineral density is correlated to the magnitude of local acceleration in male long distance runners.

Introduction: The beneficial effect of physical exercise on bone mineral density (BMD) is at least partly explained by the forces exerted directly on the bones. Male runners present generally higher BMD than sedentary individuals. We postulated that the proximal tibia BMD is related to the running distance as well as to the magnitude of the shocks (while running) in male runners. Methods: A prospective study (three yearly measurements) included 81 healthy male subjects: 16 sedentary lean subjects and three groups of runners (5-30 km/week, n=19; 30-50 km/week, n=29; 50-100 km/week, n=17). Several measurements were performed at the proximal tibia level: volumetric BMD (vBMD), cortical index (CI) i.e. an index of cortical bone thickness and peak accelerations (an index of shocks during heel strike) while running (measured by a 3-D accelerometer). A general linear model assessed the prediction of vBMD or CI by a) simple effects (running distance, peak accelerations, time) and b) interactions (for instance if vBMD prediction by peak acceleration depends on running distance). Results: CI and vBMD a) increase with running distance to reach a plateau over 30 km/wk, b) are positively associated with peak accelerations over 30 km/week. Discussion: Running may be associated with high peak accelerations in order to have beneficial effects on BMD. More important strains are needed to be associated with the same increase in BMD during running sessions of short duration than those of long duration. Conclusion: CI and vBMD are associated with the magnitude of the shocks during heel strike in runners. Key words: Bone mineral density, strains, physical exercise, running distance.