Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

In vitro engineering of human stratified urothelium: analysis of its morphology and function.

PURPOSE: Gastric or intestinal patches, commonly used for reconstructive cystoplasty, may induce severe metabolic complications. The use of bladder tissues reconstructed in vitro could avoid these complications. We compared cellular differentiation and permeability characteristics of human native with in vitro cultured stratified urothelium. MATERIALS AND METHODS: Human stratified urothelium was induced in vitro. Morphology was studied with light and electron microscopy and expression of key cellular proteins was assessed using immunohistochemistry. Permeability coefficients were determined by measuring water, urea, ammonia and proton fluxes across the urothelium. RESULTS: As in native urothelium the stratified urothelial construct consisted of basal membrane and basal, intermediate and superficial cell layers. The apical membrane of superficial cells formed villi and glycocalices, and tight junctions and desmosomes were developed. Immunohistochemistry showed similarities and differences in the expression of cytokeratins, integrin and cellular adhesion proteins. In the cultured urothelium cytokeratin 20 and integrin subunits alpha6 and beta4 were absent, and symplekin was expressed diffusely in all layers. Uroplakins were clearly expressed in the superficial umbrella cells of the urothelial constructs, however, they were also present in intermediate and basal cells. Symplekin and uroplakins were expressed only in the superficial cells of native bladder tissue. The urothelial constructs showed excellent viability, and functionally their permeabilities for water, urea and ammonia were no different from those measured in native human urothelium. Proton permeability was even lower in the constructs compared to that of native urothelium. CONCLUSIONS: Although the in vitro cultured human stratified urothelium did not show complete terminal differentiation of its superficial cells, it retained the same barrier characteristics against the principal urine components. These results indicate that such in vitro cultured urothelium, after being grown on a compliant degradable support or in coculture with smooth muscle cells, is suitable for reconstructive cystoplasty.

Pollution and pollutant transport in the geosphere - An introduction to the symposium

Environmental research in earth sciences is focused on the geosphere, i.e. (1) waters and sediments of rivers, lakes and oceans, and (2) soils and underlying shallow rock formations,both water-unsaturated and -saturated. The subsurface is studied down to greater depths at sites where waste repositories or tunnels are planned and mining activities exist. In recent years, earth scientists have become more and more involved in pollution problems related to their classical field of interest, e.g. groundwater, ore deposits, or petroleum and non-metal natural deposits (gravel, clay, cement precursors). Major pollutants include chemical substances, radioactive isotopes and microorganisms. Mechanisms which govern the transport of pollutants are of physical, chemical (dissolution, precipitation, adsorption), or microbiological (transformation) nature. Land-use planning must reflect a sustainable development and sound scientific criteria. Today's environmental pollution requires working teams with an interdisciplinary background in earth sciences, hydrology, chemistry, biology, physics as well as engineering. This symposium brought together for the first time in Switzerland earth and soil scientists, physicists and chemists, to present and discuss environmental issues concerning the geosphere.

Translation of biomechanical concepts in bone tissue engineering: from animal study to revision knee arthroplasty.

Bone defects in revision knee arthroplasty are often located in load-bearing regions. The goal of this study was to determine whether a physiologic load could be used as an in situ osteogenic signal to the scaffolds filling the bone defects. In order to answer this question, we proposed a novel translation procedure having four steps: (1) determining the mechanical stimulus using finite element method, (2) designing an animal study to measure bone formation spatially and temporally using micro-CT imaging in the scaffold subjected to the estimated mechanical stimulus, (3) identifying bone formation parameters for the loaded and non-loaded cases appearing in a recently developed mathematical model for bone formation in the scaffold and (4) estimating the stiffness and the bone formation in the bone-scaffold construct. With this procedure, we estimated that after 3 years mechanical stimulation increases the bone volume fraction and the stiffness of scaffold by 1.5- and 2.7-fold, respectively, compared to a non-loaded situation.

Who Matters in Coordination Problems?

We consider a common investment project that is vulnerable to a self-ful lling coordination failure and hence is strategically risky. Based on their private information, agents - who have heterogeneous investment incentives - form expectations or 'sentiments' about the project's outcome. We find that the sum of these sentiments is constant across di erent strategy profiles and it is independent of the distribution of incentives. As a result, we can think of sentiment as a scarce resource divided up among the di erent payo types. Applying this nding, we show that agents who bene t little from the project's success have a large impact on the coordination process. The agents with small bene ts invest only if their sentiment towards the project is large per unit investment cost. As the average sentiment is constant, a subsidy decreasing the investment costs of these agents will \free up" a large amount of sentiment, provoking a large impact on the whole economy. Intuitively, these agents, insensitive to the project's outcome and hence to the actions of others, are in uential because they modify their equilibrium behavior only if the others change theirs substantially.

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.

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.