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.

Why the EU does not Have an Independent Competition Agency: French Interests and Transaction Costs in Early European Integration

A major achievement of new institutionalism in economics and political science is the formalisation of the idea that certain policies are more efficient when administered by a politically independent organisation. Based on this insight, several policy actors and scholars criticise the European Community for relying too much on a multi-task, collegial, and politicised organisation, the European Commission. This raises important questions, some constitutional (who should be able to change the corresponding procedural rules?) and some political-economic (is Europe truly committed to free and competitive markets?). Though acknowledging the relevance of legal and normative arguments, this paper contributes to the debate with a positive political-scientific perspective. Based on the view that institutional equilibria raise the question of equilibrium institutions, it shows that collegiality was (a) an equilibrium institution during the Paris negotiations of 1950-51; and (b) an institutional equilibrium for the following 50 years. The conclusion points to some recent changes in the way that European competition policy is implemented, and discusses how these affect the “constitutional” principle of collegial European governance.

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.

The Good, the Bad and the Populist: A Model of Political Agency with Emotional Voters

This paper attempts to extend existing models of political agency to an environment in which voting may be divided between informed and instrumental, informed and ‘expressive’ (Brennan and Lomasky (1993)) and uninformed due to ‘rational irrationality’ (Caplan (2007)). It constructs a model where politicians may be good, bad or populist. Populists are more willing than good politicians to pander to voters who may choose inferior policies in a large-group electoral setting because their vote is insignificant compared with those that voters would choose were their vote decisive in determining the electoral outcome. Bad politicians would ideally like to extract tax revenue for their own ends. Initially we assume the existence of only good and populist politicians. The paper investigates the incentives for good politicians to pool with or separate from populists and focuses on three key issues – (1) how far the majority of voter’s preferences are from those held by the better informed incumbent politician (2) the extent to which the population exhibits rational irrationality and expressiveness (jointly labelled as emotional) and (3) the cost involved in persuading uninformed voters to change their views in terms of composing messages and spreading them. This paper goes on to consider how the inclusion of bad politicians may affect the behaviour of good politicians and suggests that a small amount of potential corruption may be socially useful. It is also argued that where bad politicians have an incentive to mimic the behaviour of good and populist politicians, the latter types of politician may have an incentive to separate from bad politicians by investing in costly public education signals. The paper also discusses the implications of the model for whether fiscal restraints should be soft or hard.

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."

Agency cost of government ownership: a study of voluntary audit comitte formation in China

In this paper, we investigate the agency costs of government ownership and their impact on corporate governance and firm value. China is used as a laboratory because of the prevalent state shareholdings in exchange-listed firms. In this context, we specifically consider the trade-offs involved in the voluntary formation of an audit committee when the controlling shareholder is the state. The decision to improve corporate governance (in this case, introduce an audit committee) is shown to be value relevant and a function of existing agency relationships and non-trivial implementation costs. Our findings are robust to the level of pyramid groups, the ownership-control wedge, and financial leverage. The research adds to the debate regarding the effect of government shareholdings on corporate culture and performance - a topic that hastaken on renewed importance in recent times.

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.