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.

Decision analysis for the genotype designation in low-template-DNA profiles

What genotype should the scientist specify for conducting a database search to try to find the source of a low-template-DNA (lt-DNA) trace? When the scientist answers this question, he or she makes a decision. Here, we approach this decision problem from a normative point of view by defining a decision-theoretic framework for answering this question for one locus. This framework combines the probability distribution describing the uncertainty over the trace's donor's possible genotypes with a loss function describing the scientist's preferences concerning false exclusions and false inclusions that may result from the database search. According to this approach, the scientist should choose the genotype designation that minimizes the expected loss. To illustrate the results produced by this approach, we apply it to two hypothetical cases: (1) the case of observing one peak for allele xi on a single electropherogram, and (2) the case of observing one peak for allele xi on one replicate, and a pair of peaks for alleles xi and xj, i ≠ j, on a second replicate. Given that the probabilities of allele drop-out are defined as functions of the observed peak heights, the threshold values marking the turning points when the scientist should switch from one designation to another are derived in terms of the observed peak heights. For each case, sensitivity analyses show the impact of the model's parameters on these threshold values. The results support the conclusion that the procedure should not focus on a single threshold value for making this decision for all alleles, all loci and in all laboratories.

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

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

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.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

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.

Accuracy of sentinel lymph node dissection for melanoma staging in the presence of a collision tumour with a lymphoproliferative disease.

Sentinel lymph node dissection (SLND) identifies melanoma patients with metastatic disease who would benefit from radical lymph node dissection (RLND). Rarely, patients with melanoma have an underlying lymphoproliferative disease, and melanoma metastases might develop as collision tumours in the sentinel lymph node (SLN). The aim of this study was to measure the incidence and examine the effect of collision tumours on the accuracy of SLND and on the validity of staging in this setting. Between 1998 and 2012, 750 consecutive SLNDs were performed in melanoma patients using the triple technique (lymphoscintigraphy, gamma probe and blue dye). The validity of SLND in collision tumours was analysed. False negativity was reflected by the disease-free survival. The literature was reviewed on collision tumours in melanoma. Collision tumours of melanoma and chronic lymphocytic leukaemia (CLL) were found in two SLN and in one RLND (0.4%). Subsequent RLNDs of SLND-positive cases were negative for melanoma. The patient with negative SLND developed relapse after 28 months with an inguinal lymph node metastasis of melanoma; RLND showed collision tumours. The literature review identified 12 cases of collision tumours. CLL was associated with increased melanoma incidence and reduced overall survival. This is, to our knowledge, the first assessment of the clinical value of SLND when collision tumours of melanoma and CLL are found. In this small series of three patients with both malignancies present in the same lymph node basin, lymphocytic infiltration of the CLL did not alter radioisotope uptake into the SLN. No false-negative result was observed. Our data suggest the validity of SLND in collision tumours, but given the rarity of the problem, further studies are necessary to confirm this reliability.

Repeated Interaction and the Revelation of the Monitor's Type: A Principal-Monitor-Agent Problem

This paper studies a dynamic principal-monitor-agent relation where a strategic principal delegates the task of monitoring the effort of a strategic agent to a third party. The latter we call the monitor, whose type is initially unknown. Through repeated interaction the agent might learn his type. We show that this process damages the principal's payoffs. Compensation is assumed exogenous, limiting to a great extent the provision of incentives. We go around this difficulty by introducing costly replacement strategies, i.e. the principal replaces the monitor, thus disrupting the agent's learning. We found that even when replacement costs are null, if the revealed monitor is strictly preferred by both parties, there is a loss in efficiency due to the impossibility of bene…tting from it. Nonetheless, these strategies can partially recover the principal's losses. Additionally, we establish upper and lower bounds on the payoffs that the principal and the agent can achieve. Finally we characterize the equilibrium strategies under public and private monitoring (with communication) for different cost and impatience levels.

Conservation genetics and population monitoring of the Alpine Salamander (Salamandra Atra) :

SUMMARYIn the context of the biodiversity crisis, amphibians are experiencing the most severe worldwide decline of all vertebrates and are in urgent need of better management. Efficient conservation strategies rely on sound knowledge of the species biology and of the genetic and demographic processes that might impair their welfare. Nonetheless, these processes are poorly understood in amphibians. Delineating population boundaries remains consequently problematic for these species, while it is of critical importance to define adequate management units for conservation. In this study, our attention focused on the alpine salamander (Salamandra atra), a species that deserves much interest in terms of both conservation biology and evolution. This endemic alpine species shows peculiar life-history traits (viviparity, reduced activity period, slow maturation) and has a slow population turnover, which might be problematic for its persistence in a changing environment. Due to its elusive behaviour (individuals spend most of their time underground and are unavailable for sampling), dynamic processes of gene and individuals were poorly understood for that species. Consequently, its conservation status could hardly be reliably assessed. Similarly the fire salamander (Salamandra salamandra) also poses special challenges for conservation, as no clear demarcation of geographical populations exists and dispersal patterns are poorly known. Through a phylogeographic analysis, we first studied the evolutionary history of the alpine salamander to better document the distribution of the genetic diversity along its geographical range. This study highlighted the presence of multiple divergent lineages in Italy together with a clear genetic divergence between populations from Northern and Dinaric Alps. These signs of cryptic genetic differentiation, which are not accounted for by the current taxonomy of the species, should not be neglected for further definition of conservation units. In addition, our data supported glacial survival of the species in northern peripheral glacial réfugia and nunataks, a pattern rarely documented for long-lived species. Then, we evaluated the level of gene flow between populations at the local scale and tested for asymmetries in male versus female dispersal using both field-based (mark-recapture) and genetic approaches. This study revealed high level of gene flow between populations, which stems mainly from male dispersal. This corroborated the idea that salamanders are much better dispersers than hitherto thought and provided a well- supported example of male-biased dispersal in amphibians. In a third step, based on a mark- recapture survey, we addressed the problem of sampling unavailability in alpine salamanders and evaluated its impact on two monitoring methods. We showed that about three quarters of individuals were unavailable for sampling during sampling sessions, a proportion that can vary with climatic conditions. If not taken into account, these complexities would result in false assumptions on population trends and misdirect conservation efforts. Finally, regarding the daunting task of delineating management units, our attention was drawn on the fire salamander. We conducted a local population genetic study that revealed high levels of gene flow among sampling sites. Management units for this species should consequently be large. Interestingly, despite the presence of several landscape features often reported to act as barriers, genetic breaks occurred at unexpected places. This suggests that landscape features may rather have idiosyncratic effects on population structure. In conclusion, this work brought new insights on both genetic and demographic processes occurring in salamanders. The results suggest that some biological paradigms should be taken with caution when particular species are in focus. Species- specific studies remain thus fundamental for a better understanding of species evolution and conservation, particularly in the context of current global changes.RESUMEDans le contexte de la crise de la biodiversité actuelle, les amphibiens subissent le déclin le plus important de tous les vertébrés et ont urgemment besoin d'une meilleure protection. L'établissement de stratégies de conservation efficaces repose sur des connaissances solides de la biologie des espèces et des processus génétiques et démographiques pouvant menacer leur survie. Ces processus sont néanmoins encore peu étudiés chez les amphibiens.Dans cette étude, notre attention s'est portée sur la salamandre noire (Salamandra atra), une espèce endémique des Alpes dont les traits d'histoire de vie atypiques (viviparité, phase d'activité réduite, lent turnover des populations) pourraient la rendre très vulnérable face aux changements environnementaux. Par ailleurs, en raison de son comportement cryptique (les individus passent la plupart de leur temps sous terre) la dynamique des gènes et des individus est mal comprise chez cette espèce. Il est donc difficile d'évaluer son statut de conservation de manière fiable. La salamandre tachetée {Salamandra salamandra), pour qui il n'existe aucune démarcation géographique apparente des populations, pose également des problèmes en termes de gestion. Dans un premier temps, nous avons étudié l'histoire évolutive de la salamandre noire afin de mieux décrire la distribution de sa diversité génétique au sein de son aire géographique. Cela a permis de mettre en évidence la présence de multiples lignées en Italie, ainsi qu'une nette divergence entre les populations du nord des Alpes et des Alpes dinariques. Ces résultats seront à prendre en compte lorsqu'il s'agira de définir des unités de conservation pour cette espèce. D'autre part, nos données soutiennent l'hypothèse d'une survie glaciaire dans des refuges nordiques périglaciaires ou dans des nunataks, fait rarement documenté pour une espèce longévive. Nous avons ensuite évalué la différentiation génétique des populations à l'échelle locale, ce qui a révélé d'important flux de gènes, ainsi qu'une asymétrie de dispersion en faveur des mâles. Ces résultats corroborent l'idée que les amphibiens dispersent mieux que ce que l'on pensait, et fournissent un exemple robuste de dispersion biaisée en faveur des mâles chez les amphibiens. Nous avons ensuite abordé le problème de Γ inaccessibilité des individus à la capture. Nous avons montré qu'environ trois quarts des individus sont inaccessibles lors des échantillonnages, une proportion qui peut varier en fonction des conditions climatiques. Ignoré, ce processus pourrait entraîner une mauvaise interprétation des fluctuations de populations ainsi qu'une mauvaise allocation des efforts de conservation. Concernant la définition d'unités de gestion pour la salamandre tachetée, nous avons pu mettre en évidence un flux de gènes important entre les sites échantillonnés. Les unités de gestion pour cette espèce devraient donc être étendues. Etonnamment, malgré la présence de nombreuses barrières potentielles au flux de gènes, les démarcations génétiques sont apparues à des endroits inattendus. En conclusion, ce travail a apporté une meilleure compréhension des processus génétiques et démographiques en action chez les salamandres. Les résultats suggèrent que certains paradigmes biologiques devraient être considérés avec précaution quand il s'agit de les appliquer à des espèces particulières. Les études spécifiques demeurent donc fondamentales pour une meilleure compréhension de l'évolution des espèces et leur conservation, tout particulièrement dans le contexte des changements globaux actuels.

The problem of the competitiveness of nuclear energy: a biophysical explanation

In this study I try to explain the systemic problem of the low economic competitiveness of nuclear energy for the production of electricity by carrying out a biophysical analysis of its production process. Given the fact that neither econometric approaches nor onedimensional methods of energy analyses are effective, I introduce the concept of biophysical explanation as a quantitative analysis capable of handling the inherent ambiguity associated with the concept of energy. In particular, the quantities of energy, considered as relevant for the assessment, can only be measured and aggregated after having agreed on a pre-analytical definition of a grammar characterizing a given set of finite transformations. Using this grammar it becomes possible to provide a biophysical explanation for the low economic competitiveness of nuclear energy in the production of electricity. When comparing the various unit operations of the process of production of electricity with nuclear energy to the analogous unit operations of the process of production of fossil energy, we see that the various phases of the process are the same. The only difference is related to characteristics of the process associated with the generation of heat which are completely different in the two systems. Since the cost of production of fossil energy provides the base line of economic competitiveness of electricity, the (lack of) economic competitiveness of the production of electricity from nuclear energy can be studied, by comparing the biophysical costs associated with the different unit operations taking place in nuclear and fossil power plants when generating process heat or net electricity. In particular, the analysis focuses on fossil-fuel requirements and labor requirements for those phases that both nuclear plants and fossil energy plants have in common: (i) mining; (ii) refining/enriching; (iii) generating heat/electricity; (iv) handling the pollution/radioactive wastes. By adopting this approach, it becomes possible to explain the systemic low economic competitiveness of nuclear energy in the production of electricity, because of: (i) its dependence on oil, limiting its possible role as a carbon-free alternative; (ii) the choices made in relation to its fuel cycle, especially whether it includes reprocessing operations or not; (iii) the unavoidable uncertainty in the definition of the characteristics of its process; (iv) its large inertia (lack of flexibility) due to issues of time scale; and (v) its low power level.