Generic Nekhoroshev theory without small divisors

In this article, we present a new approach of Nekhoroshev theory for a generic unperturbed Hamiltonian which completely avoids small divisors problems. The proof is an extension of a method introduced by P. Lochak which combines averaging along periodic orbits with simultaneous Diophantine approximation and uses geometric arguments designed by the second author to handle generic integrable Hamiltonians. This method allows to deal with generic non-analytic Hamiltonians and to obtain new results of generic stability around linearly stable tori.

Theory of mind tasks and executive functions: A systematic review of group studies in neurology.

A growing number of studies have been addressing the relationship between theory of mind (TOM) and executive functions (EF) in patients with acquired neurological pathology. In order to provide a global overview on the main findings, we conducted a systematic review on group studies where we aimed to (1) evaluate the patterns of impaired and preserved abilities of both TOM and EF in groups of patients with acquired neurological pathology and (2) investigate the existence of particular relations between different EF domains and TOM tasks. The search was conducted in Pubmed/Medline. A total of 24 articles met the inclusion criteria. We considered for analysis classical clinically accepted TOM tasks (first- and second-order false belief stories, the Faux Pas test, Happe's stories, the Mind in the Eyes task, and Cartoon's tasks) and EF domains (updating, shifting, inhibition, and access). The review suggests that (1) EF and TOM appear tightly associated. However, the few dissociations observed suggest they cannot be reduced to a single function; (2) no executive subprocess could be specifically associated with TOM performances; (3) the first-order false belief task and the Happe's story task seem to be less sensitive to neurological pathologies and less associated to EF. Even though the analysis of the reviewed studies demonstrates a close relationship between TOM and EF in patients with acquired neurological pathology, the nature of this relationship must be further investigated. Studies investigating ecological consequences of TOM and EF deficits, and intervention researches may bring further contributions to this question.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Mechanisms of leukocyte lipid body formation and function in inflammation

An area of increasingly interest for the understanding of cell signaling are the spatio-temporal aspects of the different enzymes involved in lipid mediator generation (eicosanoid-forming enzymes, phospholipases and their regulatory kinases and phosphatases) and pools of lipid precursors. The compartmentalization of signaling components within discrete and dynamic sites in the cell is critical for specificity and efficiency of enzymatic reactions of phosphorilation, enzyme activation and function. We hypothesized that lipid bodies - inducible non-membrane bound cytoplasmic lipid domains - function as specialized intracellular sites of compartmentalization of signaling with major roles in lipid mediator formation within leukocytes engaged in inflammatory process. Over the past years substantial progresses have been made demonstrating that all enzymes involved in eicosanoid synthesis localize at lipid bodies and lipid bodies are distinct sites for eicosanoid generation. Here we will review our current knowledge on the mechanisms of formation and functions of lipid bodies pertinent to inflammation.

A discrete forest in a continuous landscape : investigating interactions between natural resource management and sustainable development

Summary Forests are key ecosystems of the earth and associated with a large range of functions. Many of these functions are beneficial to humans and are referred to as ecosystem services. Sustainable development requires that all relevant ecosystem services are quantified, managed and monitored equally. Natural resource management therefore targets the services associated with ecosystems. The main hypothesis of this thesis is that the spatial and temporal domains of relevant services do not correspond to a discrete forest ecosystem. As a consequence, the services are not quantified, managed and monitored in an equal and sustainable manner. The thesis aims were therefore to test this hypothesis, establish an improved conceptual approach and provide spatial applications for the relevant land cover and structure variables. The study was carried out in western Switzerland and based primarily on data from a countrywide landscape inventory. This inventory is part of the third Swiss national forest inventory and assesses continuous landscape variables based on a regular sampling of true colour aerial imagery. In addition, land cover variables were derived from Landsat 5 TM passive sensor data and land structure variables from active sensor data from a small footprint laserscanning system. The results confirmed the main hypothesis, as relevant services did not scale well with the forest ecosystem. Instead, a new conceptual approach for sustainable management of natural resources was described. This concept quantifies the services as a continuous function of the landscape, rather than a discrete function of the forest ecosystem. The explanatory landscape variables are therefore called continuous fields and the forest becomes a dependent and function-driven management unit. Continuous field mapping methods were established for land cover and structure variables. In conclusion, the discrete forest ecosystem is an adequate planning and management unit. However, monitoring the state of and trends in sustainability of services requires them to be quantified as a continuous function of the landscape. Sustainable natural resource management iteratively combines the ecosystem and gradient approaches. Résumé Les forêts sont des écosystèmes-clés de la terre et on leur attribue un grand nombre de fonctions. Beaucoup de ces fonctions sont bénéfiques pour l'homme et sont nommées services écosystémiques. Le développement durable exige que ces services écosystémiques soient tous quantifiés, gérés et surveillés de façon égale. La gestion des ressources naturelles a donc pour cible les services attribués aux écosystèmes. L'hypothèse principale de cette thèse est que les domaines spatiaux et temporels des services attribués à la forêt ne correspondent pas à un écosystème discret. Par conséquent, les services ne sont pas quantifiés, aménagés et surveillés d'une manière équivalente et durable. Les buts de la thèse étaient de tester cette hypothèse, d'établir une nouvelle approche conceptuelle de la gestion des ressources naturelles et de préparer des applications spatiales pour les variables paysagères et structurelles appropriées. L'étude a été menée en Suisse occidentale principalement sur la base d'un inventaire de paysage à l'échelon national. Cet inventaire fait partie du troisième inventaire forestier national suisse et mesure de façon continue des variables paysagères sur la base d'un échantillonnage régulier sur des photos aériennes couleur. En outre, des variables de couverture ? terrestre ont été dérivées des données d'un senseur passif Landsat 5 TM, ainsi que des variables structurelles, dérivées du laserscanning, un senseur actif. Les résultats confirment l'hypothèse principale, car l'échelle des services ne correspond pas à celle de l'écosystème forestier. Au lieu de cela, une nouvelle approche a été élaborée pour la gestion durable des ressources naturelles. Ce concept représente les services comme une fonction continue du paysage, plutôt qu'une fonction discrète de l'écosystème forestier. En conséquence, les variables explicatives de paysage sont dénommées continuous fields et la forêt devient une entité dépendante, définie par la fonction principale du paysage. Des méthodes correspondantes pour la couverture terrestre et la structure ont été élaborées. En conclusion, l'écosystème forestier discret est une unité adéquate pour la planification et la gestion. En revanche, la surveillance de la durabilité de l'état et de son évolution exige que les services soient quantifiés comme fonction continue du paysage. La gestion durable des ressources naturelles joint donc l'approche écosystémique avec celle du gradient de manière itérative.

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria delsConjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics espotencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funciódensitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps queles distribucions de probabilitat quàntiques

KAM theory for conformally symplectic systems

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the system is close to integrable, but we use an a-posteriori format. Our unknowns are a parameterization of the solution and a parameter. We show that if there is a sufficiently approximate solution of the invariance equation, which also satisfies some explicit non–degeneracy conditions, then there is a true solution nearby. We present results both in Sobolev norms and in analytic norms. The a–posteriori format has several consequences: A) smooth dependence on the parameters, including the singular limit of zero dissipation; B) estimates on the measure of parameters covered by quasi–periodic solutions; C) convergence of perturbative expansions in analytic systems; D) bootstrap of regularity (i.e., that all tori which are smooth enough are analytic if the map is analytic); E) a numerically efficient criterion for the break–down of the quasi–periodic solutions. The proof is based on an iterative quadratically convergent method and on suitable estimates on the (analytical and Sobolev) norms of the approximate solution. The iterative step takes advantage of some geometric identities, which give a very useful coordinate system in the neighborhood of invariant (or approximately invariant) tori. This system of coordinates has several other uses: A) it shows that for dissipative conformally symplectic systems the quasi–periodic solutions are attractors, B) it leads to efficient algorithms, which have been implemented elsewhere. Details of the proof are given mainly for maps, but we also explain the slight modifications needed for flows and we devote the appendix to present explicit algorithms for flows.

Adaptively weighted maximum likelihood estimation of discrete distributions

SummaryDiscrete data arise in various research fields, typically when the observations are count data.I propose a robust and efficient parametric procedure for estimation of discrete distributions. The estimation is done in two phases. First, a very robust, but possibly inefficient, estimate of the model parameters is computed and used to indentify outliers. Then the outliers are either removed from the sample or given low weights, and a weighted maximum likelihood estimate (WML) is computed.The weights are determined via an adaptive process such that if the data follow the model, then asymptotically no observation is downweighted.I prove that the final estimator inherits the breakdown point of the initial one, and that its influence function at the model is the same as the influence function of the maximum likelihood estimator, which strongly suggests that it is asymptotically fully efficient.The initial estimator is a minimum disparity estimator (MDE). MDEs can be shown to have full asymptotic efficiency, and some MDEs have very high breakdown points and very low bias under contamination. Several initial estimators are considered, and the performances of the WMLs based on each of them are studied.It results that in a great variety of situations the WML substantially improves the initial estimator, both in terms of finite sample mean square error and in terms of bias under contamination. Besides, the performances of the WML are rather stable under a change of the MDE even if the MDEs have very different behaviors.Two examples of application of the WML to real data are considered. In both of them, the necessity for a robust estimator is clear: the maximum likelihood estimator is badly corrupted by the presence of a few outliers.This procedure is particularly natural in the discrete distribution setting, but could be extended to the continuous case, for which a possible procedure is sketched.RésuméLes données discrètes sont présentes dans différents domaines de recherche, en particulier lorsque les observations sont des comptages.Je propose une méthode paramétrique robuste et efficace pour l'estimation de distributions discrètes. L'estimation est faite en deux phases. Tout d'abord, un estimateur très robuste des paramètres du modèle est calculé, et utilisé pour la détection des données aberrantes (outliers). Cet estimateur n'est pas nécessairement efficace. Ensuite, soit les outliers sont retirés de l'échantillon, soit des faibles poids leur sont attribués, et un estimateur du maximum de vraisemblance pondéré (WML) est calculé.Les poids sont déterminés via un processus adaptif, tel qu'asymptotiquement, si les données suivent le modèle, aucune observation n'est dépondérée.Je prouve que le point de rupture de l'estimateur final est au moins aussi élevé que celui de l'estimateur initial, et que sa fonction d'influence au modèle est la même que celle du maximum de vraisemblance, ce qui suggère que cet estimateur est pleinement efficace asymptotiquement.L'estimateur initial est un estimateur de disparité minimale (MDE). Les MDE sont asymptotiquement pleinement efficaces, et certains d'entre eux ont un point de rupture très élevé et un très faible biais sous contamination. J'étudie les performances du WML basé sur différents MDEs.Le résultat est que dans une grande variété de situations le WML améliore largement les performances de l'estimateur initial, autant en terme du carré moyen de l'erreur que du biais sous contamination. De plus, les performances du WML restent assez stables lorsqu'on change l'estimateur initial, même si les différents MDEs ont des comportements très différents.Je considère deux exemples d'application du WML à des données réelles, où la nécessité d'un estimateur robuste est manifeste : l'estimateur du maximum de vraisemblance est fortement corrompu par la présence de quelques outliers.La méthode proposée est particulièrement naturelle dans le cadre des distributions discrètes, mais pourrait être étendue au cas continu.

Ab initio absorption spectrum of NiO combining molecular dynamics with the embedded cluster approach in a discrete reaction field

We developed a procedure that combines three complementary computational methodologies to improve the theoretical description of the electronic structure of nickel oxide. The starting point is a Car-Parrinello molecular dynamics simulation to incorporate vibrorotational degrees of freedom into the material model. By means ofcomplete active space self-consistent field second-order perturbation theory (CASPT2) calculations on embedded clusters extracted from the resulting trajectory, we describe localized spectroscopic phenomena on NiO with an efficient treatment of electron correlation. The inclusion of thermal motion into the theoretical description allowsus to study electronic transitions that, otherwise, would be dipole forbidden in the ideal structure and results in a natural reproduction of the band broadening. Moreover, we improved the embedded cluster model by incorporating self-consistently at the complete active space self-consistent field (CASSCF) level a discrete (or direct) reaction field (DRF) in the cluster surroundings. The DRF approach offers an efficient treatment ofelectric response effects of the crystalline embedding to the electronic transitions localized in the cluster. We offer accurate theoretical estimates of the absorption spectrum and the density of states around the Fermi level of NiO, and a comprehensive explanation of the source of the broadening and the relaxation of the charge transferstates due to the adaptation of the environment

Electron localization function at the correlated level

The electron localization function (ELF) has been proven so far a valuable tool to determine the location of electron pairs. Because of that, the ELF has been widely used to understand the nature of the chemical bonding and to discuss the mechanism of chemical reactions. Up to now, most applications of the ELF have been performed with monodeterminantal methods and only few attempts to calculate this function for correlated wave functions have been carried out. Here, a formulation of ELF valid for mono- and multiconfigurational wave functions is given and compared with previous recently reported approaches. The method described does not require the use of the homogeneous electron gas to define the ELF, at variance with the ELF definition given by Becke. The effect of the electron correlation in the ELF, introduced by means of configuration interaction with singles and doubles calculations, is discussed in the light of the results derived from a set of atomic and molecular systems

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Capacity-approaching rate function for layered multiantenna architectures

The simultaneous use of multiple transmit and receive antennas can unleash very large capacity increases in rich multipath environments. Although such capacities can be approached by layered multi-antenna architectures with per-antenna rate control, the need for short-term feedback arises as a potential impediment, in particular as the number of antennas—and thus the number of rates to be controlled—increases. What we show, however, is that the need for short-term feedback in fact vanishes as the number of antennas and/or the diversity order increases. Specifically, the rate supported by each transmit antenna becomes deterministic and a sole function of the signal-to-noise, the ratio of transmit and receive antennas, and the decoding order, all of which are either fixed or slowly varying. More generally, we illustrate -through this specific derivation— the relevance of some established random CDMA results to the single-user multi-antenna problem.

Salience theory of choice under risk

We present a theory of choice among lotteries in which the decision maker's attention is drawn to (precisely defined) salient payoffs. This leads the decision maker to a context-dependent representation of lotteries in which true probabilities are replaced by decision weights distorted in favor of salient payoffs. By endogenizing decision weights as a function of payoffs, our model provides a novel and unified account of many empirical phenomena, including frequent risk-seeking behavior, invariance failures such as the Allais paradox, and preference reversals. It also yields new predictions, including some that distinguish it from Prospect Theory, which we test.

Monetary policy rules and macroeconomic stability: Evidence and some theory

We estimate a forward-looking monetary policy reaction function for thepostwar United States economy, before and after Volcker's appointmentas Fed Chairman in 1979. Our results point to substantial differencesin the estimated rule across periods. In particular, interest ratepolicy in the Volcker-Greenspan period appears to have been much moresensitive to changes in expected inflation than in the pre-Volckerperiod. We then compare some of the implications of the estimated rulesfor the equilibrium properties of inflation and output, using a simplemacroeconomic model, and show that the Volcker-Greenspan rule is stabilizing.

A comment on the Nash program and the theory of implementation

The mechanisms in the Nash program for cooperative games are madecompatible with the framework of the theory of implementation. This is donethrough a reinterpretation of the characteristic function that avoids feasibilityproblems, thereby allowing an analysis that focuses exclusively on the payoff space. In this framework, we show that the core is the only majorcooperative solution that is Maskin monotonic. Thus, implementation of mostcooperative solutions must rely on refinements of the Nash equilibrium concept(like most papers in the Nash program do). Finally, the mechanisms in theNash program are adapted into the model.