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.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

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.

On the homotopy theory of spectral categories

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

News Shocks and Business Cycles: Bridging the Gap from Different Methodologies

An important disconnect in the news driven view of the business cycle formalized by Beaudry and Portier (2004), is the lack of agreement between different—VAR and DSGE—methodologies over the empirical plausibility of this view. We argue that this disconnect can be largely resolved once we augment a standard DSGE model with a financial channel that provides amplification to news shocks. Both methodologies suggest news shocks to the future growth prospects of the economy to be significant drivers of U.S. business cycles in the post-Greenspan era (1990-2011), explaining as much as 50% of the forecast error variance in hours worked in cyclical frequencies

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.