International Institutions as Solutions to Underlying Games of Cooperation

This Working Paper was presented at the international workshop "Game Theory in International Relations at 50", organized and coordinated by Professor Jacint Jordana and Dr. Yannis Karagiannis at the Institut Barcelona d'Estudis Internacionals on May 22, 2009. The day-long Workshop was inspired by the desire to honour the ground-breaking work of Professor Thomas Schelling in 1959-1960, and to understand where the discipline International Relations lies today vis-à-vis game theory.

Gamma Knife radiosurgery after previous microvascular decompression decreases the chances of pain free in classical trigeminal neuralgia

Purpose: To evaluate the safety-efficacy of Gamma Knife surgery (GKS) as a second treatment for classical trigeminal neuralgia (CTN), and the influence of prior microvascular decompression (MVD). Methods: Between July 1992 and November 2010, 737 patients have been operated with GKRS for ITN and prospectively evaluated in Timone University Hospital in Marseille, France. Among these, 54 patients had a previous history of MVD. Radiosurgery using a Gamma Knife (model B or C or Perfexion) was performed on the basis of on both MR and CT targeting. A single 4 mm isocenter was positioned in the cisternal portion of the trigeminal nerve at a median distance of 7.6 mm (range 3.9-11.9) anteriorly to the emergence of the nerve (retrogasserian target). A median maximum dose of 85 Gy (range 70-90) was delivered. Here, the 45 patients with previous MVD and a follow-up longer than one year are evaluated (the patients with megadolichobasilar artery compression and multiple sclerosis were excluded). Results: The median age in this series was 56.75 years (range 28.09-82.39). The median follow-up period was 39.48 months (range 14.10-144.65). All the patients had a past history of surgery, with at least one previous failed MVD, but also radiofrequency lesion (RFL) in 16 patients (35.6%), balloon microcompression in 7 (15.6%) and glycerol rhizotomy in 1 (2.2%). Thirty-five patients (77.8%) were initially pain free after GKS within a median time of 14 days (range 0, 180). Patients from this group had less probability of being pain free compared to our global population of essential trigeminal neuralgia without previous MVD history (p=0.010, hazard ratio of 0.64). Their probability of remaining pain free at 3, 5, 7 and 10 years was 66.5%, 59.1%, 59.1% and 44.3%, respectively. Twelve patients (34.3%) initially pain free experienced a recurrence with a median delay of 31.21 months (range 3.40-89.93). The hypoesthesia actuarial rate at 1 year was 9.1% and remained stable till 12 years with a median delay of onset of 8 months (range 8-8). Conclusions: Retrogasserian GKS proofed to be safe and effective on the long-term basis even after failed previous MVD. Even if the initial result of pain free was only 77.8%, the toxicity was low with only 9.1% hypoesthesia. No patient reported a bothersome hypoesthesia. The probability of maintaining pain relief in the long-term was of 44.3% at 10 years.

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.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

A one-dimensional Keller-Segel equation with a drift issued from the boundary

We investigate in this note the dynamics of a one-dimensional Keller-Segel type model on the half-line. On the contrary to the classical configuration, the chemical production term is located on the boundary. We prove, under suitable assumptions, the following dichotomy which is reminiscent of the two-dimensional Keller-Segel system. Solutions are global if the mass is below the critical mass, they blow-up in finite time above the critical mass, and they converge to some equilibrium at the critical mass. Entropy techniques are presented which aim at providing quantitative convergence results for the subcritical case. This note is completed with a brief introduction to a more realistic model (still one-dimensional).

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

On stability of solutions to systems of convex inequalities

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

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Prostaglandin A1 Inhibits Replication of Classical Swine Fever Virus

Prostaglandins (Pgs) have been shown to inhibit the replication of several DNA and RNA viruses. Here we report the effect of prostaglandin (PgA1) on the multiplication of a positive strand RNA virus, Classical Swine Fever Virus (CSFV) in PK15 cells. PgA1 was found to inhibit the multiplication of CSFV. At a concentration of 5 µg/ml, which was nontoxic to the cells, PgA1 inhibitis virus production in 99%. In PgA1 treated cells the size and number of characteristic Classical Swine Fever focus decreased in amount.

La gestion des services environnementaux: entre règles et régulation négociée. Six études de cas de services forestiers pour la production d'eau potable dans trois pays

Cette thèse est construite en quatre parties : trois annexes qui présentent six études de cas (env. 800 pages), précédées par une analyse transversale, plus synthétique (env. 150 pages), dont traite ce résumé. Chaque annexe contient une synthèse détaillée des études de cas. Cette thèse aborde la « gestion des ressources naturelles » en affirmant d'emblée que l'appellation est inappropriée, car ce ne sont pas les ressources qui sont gérées, mais leurs usages. Il s'agit donc d'identifier et d'analyser ce qui influence les comportements humains en lien avec la ressource. Cette affirmation fonde la perspective des sciences sociales sur la gestion des ressources naturelles, dans laquelle s'inscrit cette thèse. L'approche néo-institutionnaliste considère que les usages sont influencés par des institutions, qui sont elles-mêmes influencées par les usagers. Ces institutions sont des constructions humaines qui composent le contexte institutionnel dans lequel les acteurs décident de leurs usages (abattre un arbre, prélever de l'eau, etc.). Les usages des ressources ne sont donc jamais libres et il s'agit de comprendre comment ces règles du jeu influencent les pratiques. Elles sont nombreuses, interdépendantes et forment la trame sur laquelle se décident les usages. Pour saisir cette complexité, l'auteur applique le cadre d'analyse des régimes institutionnels des ressources (RIR) qui se limite à l'analyse de deux types de droits d'usages : ceux issues des règles de la propriété (titres de propriété, servitudes, etc.) et ceux issus des politiques publiques (lois, ordonnances, etc.). Le RIR permet d'identifier un « régime institutionnel », spécifique à la ressource étudiée, dont les évolutions peuvent être comparées dans le temps ou entre plusieurs lieux. Dans cette recherche, ce cadre d'analyse a été appliqué au même objet - la gestion forestière dans les zones de captage d'eau souterraine destinée au réseau public - dans trois pays : en France, en Suisse et en Indonésie. Trois années de recherche de terrain ont permis à l'auteur de s'intéresser non seulement aux règles prédéterminées (la réglementation), mais aussi aux règles effectivement activées sur le terrain (la régulation) par les acteurs rencontrés. Les études de cas montrent que les règles prévues sont inégalement activées et que les acteurs privilégient parfois la négociation directe pour résoudre leurs rivalités d'usages, à la place d'invoquer leurs droits acquis. Ce constat conduit l'auteur à proposer un élargissement de la focale du RIR, qui constitue le coeur de sa thèse. On ne s'intéresse plus seulement à ce qui « est » régulé, mais aussi à ce qui ne l'« est pas » et qui échappe à l'application classique du RIR. Ce renversement de perspective est crucial pour comprendre les usages concrets des ressources dans les régimes peu intégrés, où les pratiques s'expliquent davantage par la marge de manoeuvre laissée aux acteurs que par les règles prédéterminées. Cette relecture, testée avec succès dans cette thèse, permet d'intégrer la marge de manoeuvre à l'analyse au moyen du RIR. Elle se concrétise par l'identification des lacunes et incohérences dans les régimes institutionnels étudiés. Le champ d'application du RIR s'en trouve élargi et sa vulgarisation pour des non-spécialistes est facilitée, notamment pour les environnementalistes. La complémentarité entre les approches s'en trouve renforcée. Les résultats montrent deux choses : premièrement les acteurs disposent toujours d'une marge de manoeuvre pour négocier des régulations ponctuelles, qui sont autant d'alternatives à l'application des règles prévues. Deuxièmement, la conclusion d'accords issus de la négociation bi-/multilatérale dépend directement de la marge de manoeuvre laissée par le contexte institutionnel. Ceci explique pourquoi la négociation entre les propriétaires forestiers et les exploitants de captages s'imposent en Indonésie, est envisageable en France, mais n'aboutit pas en Suisse. Les nombreuses tentatives infructueuses de mise en oeuvre de solutions négociées, notamment sous forme de paiements pour services environnementaux (PSE), trouvent ici une explication. - This thesis (written in French) is built in four parts: three annexes that present six case studies (approx. 800 pages), preceded by a transverse, more conceptual analysis (approx. 150 pages), which this summary is about. Each annexe contains a detailed summary of the case studies. 'Natural resource management' is an inappropriate designation because it is not the resources that are managed but the uses made of them, therefore this thesis addresses the identification and analysis of the influences on human behaviour in relation to the resource. This statement roots the social sciences perspective on the management of natural resources, in which this thesis fits. A neoinstitutionalist approach considers that the uses are influenced by institutions, which are themselves influenced by users. These institutions are human constructions that form the institutional context in which the actors decide on the use of resources (felling a tree, collecting water, etc.). Thus, the uses of resources are never independent from institutional influences and it becomes necessary to understand how these rules of the game affect practices. They are numerous, interrelated and form the basis for the uses of resources. To understand this complexity, the author applies the institutional regime resource framework (IRR) which limits the analysis to two types of use rights: those resulting from the property rights (deeds, easements, etc.) and those from public policies (laws, ordinances, etc.). The IRR identifies an 'institutional regime', specific to the resource, from which developments can be compared over time or between several places. In this research, this analytical framework has been applied to the same topic - forest management in the recharging areas of groundwater piped for public supply - in three countries: France, Switzerland and Indonesia. Three years of field research allow the author to look not only at predetermined rules (rules), but also at regulations that are actually activated on the ground (rules-in-use). The case studies show that the predetermined rules are unevenly applied and that sometimes actors favour direct negotiation to resolve their rivalry of uses, instead of invoking their vested rights. From this observation the author proposes an enlargement of the IRR's scope, forming the core of his thesis. The interest covers not only what 'is' regulated, but what 'is not' and so is beyond the classical application of the IRR. This shift in perspective is crucial to understand the concrete uses of resources in poorly integrated regimes, where practices are explained by the margin of manoeuvre left to the actors rather than predetermined rules. This reinterpretation, tested successfully in this research, allows the margin of manoeuvre to be integrated in the analysis using the IRR and is made concrete by the identification of gaps and inconsistencies in the investigated institutional context. The new interpretation of the IRR in this thesis complements and enhances its classical application. In particular, its use and understanding by non-specialists, especially environmentalists, is facilitated. The results show two things: first the actors always have leeway to negotiate ad hoc regulations, which are alternatives to the application of the predefined rules. Second, the conclusion of bi/multilateral negotiated agreements depends directly on the leeway left by the institutional context. This explains why the negotiation between forest owners and operators of water catchments is needed in Indonesia, is possible in France, but does not succeed in Switzerland. This offers an explanation for many unsuccessful attempts to implement negotiated solutions, notably payments for environmental services (PES).