Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Problèmes d'échantillonnage lors d'une enquête sur la plombémie d'enfants citadin [Sampling problems in a survey of blood lead levels in city children].

A study on lead pollution was carried out on a sample of ca. 300 city children. This paper presents the errors producing bias in the sample. It is emphasized that, in Switzerland, the difference between the Swiss and the migrant population (the latter being mainly Italian and Spanish) must be taken into account.

Análisis de rendimiento de aplicaciones paralelas de memoria compartida: problema N-body

Este trabajo analiza el rendimiento de cuatro nodos de cómputo multiprocesador de memoria compartida para resolver el problema N-body. Se paraleliza el algoritmo serie, y se codifica usando el lenguaje C extendido con OpenMP. El resultado son dos variantes que obedecen a dos criterios de optimización diferentes: minimizar los requisitos de memoria y minimizar el volumen de cómputo. Posteriormente, se realiza un proceso de análisis de las prestaciones del programa sobre los nodos de cómputo. Se modela el rendimiento de las variantes secuenciales y paralelas de la aplicación, y de los nodos de cómputo; se instrumentan y ejecutan los programas para obtener resultados en forma de varias métricas; finalmente se muestran e interpretan los resultados, proporcionando claves que explican ineficiencias y cuellos de botella en el rendimiento y posibles líneas de mejora. La experiencia de este estudio concreto ha permitido esbozar una incipiente metodología de análisis de rendimiento, identificación de problemas y sintonización de algoritmos a nodos de cómputo multiprocesador de memoria compartida.

Quantifying rates of landscape evolution and tectonic processes by thermochronology and numerical modeling of crustal heat transport using PECUBE

PECUBE is a three-dimensional thermal-kinematic code capable of solving the heat production-diffusion-advection equation under a temporally varying surface boundary condition. It was initially developed to assess the effects of time-varying surface topography (relief) on low-temperature thermochronological datasets. Thermochronometric ages are predicted by tracking the time-temperature histories of rock-particles ending up at the surface and by combining these with various age-prediction models. In the decade since its inception, the PECUBE code has been under continuous development as its use became wider and addressed different tectonic-geomorphic problems. This paper describes several major recent improvements in the code, including its integration with an inverse-modeling package based on the Neighborhood Algorithm, the incorporation of fault-controlled kinematics, several different ways to address topographic and drainage change through time, the ability to predict subsurface (tunnel or borehole) data, prediction of detrital thermochronology data and a method to compare these with observations, and the coupling with landscape-evolution (or surface-process) models. Each new development is described together with one or several applications, so that the reader and potential user can clearly assess and make use of the capabilities of PECUBE. We end with describing some developments that are currently underway or should take place in the foreseeable future. (C) 2012 Elsevier B.V. All rights reserved.

The Commons and anti-commons problems in the tourism economy

Countries specialised in tourism tend to face two problems with contradictory effects: the commons and the anti-commons, which lead to tourism over- and under-production, respectively. This paper develops a two-period model to analyse the joint effects of both problems on a small and remote tourism economy. Congestion and the complementariness between foreign transport and local tourism services are key features in this type of markets. As a result, direct selling and the presence of foreign tour-operators emerge as possible market arrangements with different implications in terms of welfare and public intervention. Four main results are obtained. First, in the direct selling situation the optimal policy depends on the relative importance of the problems. Second, the existence of tour-operators always leads to tourism over-production. Third, the presence of a single tour-operator does not solve the congestion problem. Lastly, the switch from several tour-operators to a single one is welfare reducing.

Some variational problems from image processing

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

The analysis of approximate quickselect and related problems

Approximate Quickselect, a simple modification of the well known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Approximate Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm. The key element appearing in the analysis of Approximate Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us. In particular, we have been able to carry out a precise analysis of the expected number of moves of the ith element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results. Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.

The efficacy of melatonin for sleep problems in children with autism, fragile X syndrome, or autism and fragile X syndrome.

STUDY OBJECTIVE: To determine the efficacy of melatonin on sleep problems in children with autistic spectrum disorder (ASD) and fragile X syndrome (FXS). METHODS: A 4-week, randomized, double blind, placebo-controlled, crossover design was conducted following a 1-week baseline period. Either melatonin, 3 mg, or placebo was given to participants for 2 weeks and then alternated for another 2 weeks. Sleep variables, including sleep duration, sleep-onset time, sleep-onset latency time, and the number of night awakenings, were recorded using an Actiwatch and from sleep diaries completed by parents. All participants had been thoroughly assessed for ASD and also had DNA testing for the diagnosis of FXS. RESULTS: Data were successfully obtained from the 12 of 18 subjects who completed the study (11 males, age range 2 to 15.25 years, mean 5.47, SD 3.6). Five participants met diagnostic criteria for ASD, 3 for FXS alone, 3 for FXS and ASD, and 1 for fragile X premutation. Eight out of 12 had melatonin first. The conclusions from a nonparametric repeated-measures technique indicate that mean night sleep duration was longer on melatonin than placebo by 21 minutes (p = .02), mean sleep-onset latency was shorter by 28 minutes (p = .0001), and mean sleep-onset time was earlier by 42 minutes (p = .02). CONCLUSION: The results of this study support the efficacy and tolerability of melatonin treatment for sleep problems in children with ASD and FXS.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

GPs' role in the detection of psychological problems of young people: a population-based study.

BACKGROUND: Among young people, about one in three females and one in five males report experiencing emotional distress but 65-95% of them do not receive help from health professionals. AIM: To assess the differences among young people who seek help and those who do not seek help for their psychological problems, considering the frequency of consultations to their GP and their social resources. DESIGN OF STUDY: School survey. SETTING: Post-mandatory school. METHOD: Among a Swiss national representative sample of 7429 students and apprentices (45.6% females) aged 16-20 years, 1931 young people reported needing help for a problem of depression/sadness (26%) and were included in the study. They were divided into those who sought help (n = 256) and those who did not (n = 1675), and differences between them were assessed. RESULTS: Only 13% of young people needing help for psychological problems consulted for that reason and this rate was positively associated with the frequency of consultations to the GP. However, 80% of young people who did not consult for psychological problems visited their GP at least once during the previous year. Being older or a student, having a higher depression score, or a history of suicide attempt were linked with a higher rate of help seeking. Moreover, confiding in adults positively influenced the rate of help seeking. CONCLUSION: The large majority of young people reporting psychological problems do not seek help, although they regularly consult their GP. While young people have difficulties in tackling issues about mental health, GPs could improve the situation by systematically inquiring about this issue.

Propagation connectivity of random hypergraphs

We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is inspired by a simple linear time algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for the propagation connectivity threshold, and point out some algorithmic implications.

On problems of calculating energy expenditure and substrate utilization from respiratory exchange data.

Indirect calorimetry based on respiratory exchange measurement has been successfully used from the beginning of the century to obtain an estimate of heat production (energy expenditure) in human subjects and animals. The errors inherent to this classical technique can stem from various sources: 1) model of calculation and assumptions, 2) calorimetric factors used, 3) technical factors and 4) human factors. The physiological and biochemical factors influencing the interpretation of calorimetric data include a change in the size of the bicarbonate and urea pools and the accumulation or loss (via breath, urine or sweat) of intermediary metabolites (gluconeogenesis, ketogenesis). More recently, respiratory gas exchange data have been used to estimate substrate utilization rates in various physiological and metabolic situations (fasting, post-prandial state, etc.). It should be recalled that indirect calorimetry provides an index of overall substrate disappearance rates. This is incorrectly assumed to be equivalent to substrate "oxidation" rates. Unfortunately, there is no adequate golden standard to validate whole body substrate "oxidation" rates, and this contrasts to the "validation" of heat production by indirect calorimetry, through use of direct calorimetry under strict thermal equilibrium conditions. Tracer techniques using stable (or radioactive) isotopes, represent an independent way of assessing substrate utilization rates. When carbohydrate metabolism is measured with both techniques, indirect calorimetry generally provides consistent glucose "oxidation" rates as compared to isotopic tracers, but only when certain metabolic processes (such as gluconeogenesis and lipogenesis) are minimal or / and when the respiratory quotients are not at the extreme of the physiological range. However, it is believed that the tracer techniques underestimate true glucose "oxidation" rates due to the failure to account for glycogenolysis in the tissue storing glucose, since this escapes the systemic circulation. A major advantage of isotopic techniques is that they are able to estimate (given certain assumptions) various metabolic processes (such as gluconeogenesis) in a noninvasive way. Furthermore when, in addition to the 3 macronutrients, a fourth substrate is administered (such as ethanol), isotopic quantification of substrate "oxidation" allows one to eliminate the inherent assumptions made by indirect calorimetry. In conclusion, isotopic tracers techniques and indirect calorimetry should be considered as complementary techniques, in particular since the tracer techniques require the measurement of carbon dioxide production obtained by indirect calorimetry. However, it should be kept in mind that the assessment of substrate oxidation by indirect calorimetry may involve large errors in particular over a short period of time. By indirect calorimetry, energy expenditure (heat production) is calculated with substantially less error than substrate oxidation rates.