On the complexity of the Whitehead minimization problem

The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.

Addressing the net balances problem as a prerequisite for EU budget reform: a proposal

Conflict among member states regarding the distribution of net financial burdens has been allowed to contaminate the entire design of the EU budget with very negative consequences in terms of equity, efficiency and transparency. To get around this problem and pave the way for a substantive budget reform, we propose to decouple distributional negotiations from the rest of the budget process by linking member state net balances in a rigid manner to relative prosperity. This would be achieved through the introduction of a system of compensating horizontal transfers that would take to its logical conclusion the Commission's proposal for a generalized compensation mechanism. We discuss the impact of the proposed scheme on member states? incentives and illustrate its financial implications using revenue and expenditure projections for 2013 that are based on the current Financial Perspectives and Own Resources Decision.

Orbit decidability and the conjugacy problem for some extensions of groups

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The generic Hanna Neumann conjecture and post correspondence problem

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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.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

Symmetry for a Dirichlet-Neumann problem arising in water waves

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The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

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.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

A Political Agency Model of Coattail Voting

In this paper, I provide a formal justi…cation for a well-established coattail effect, when a popular candidate at one branch of government attracts votes to candidates from the same political party for other branches of government. A political agency frame- work with moral hazard is applied to analyze coattails in simultaneous presidential and congressional elections. I show that coattail voting is a natural outcome of the optimal reelection scheme adopted by a representative voter to motivate politicians' efforts in a retrospective voting environment. I assume that an office-motivated politician (executive or congressman) prefers her counterpart to be affiliated with the same political party. This correlation of incentives leads the voter to adopt a joint performance evaluation rule, which is conditioned on the politicians belonging to the same party or different parties. The two-sided coattail effects then arise. On the one hand, the executive's suc- cess/failure props up/drags down her partisan ally in congressional election, which implies presidential coattails. On the other hand, the executive's reelection itself is affected by the congressman's performance, which results in reverse coattails. JEL classi…fication: D72, D86. Keywords: Coattail voting; Presidential coattails; Reverse coattails; Simultaneous elections; Political Agency; Retrospective voting.