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.

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.

Strategic mass killings

Since World War II there have been about fifty episodes of large-scale mass killings of civilians and massive forced displacements. They were usually meticulously planned and independent of military goals. We provide a model where conflict onset, conflict intensity and the decision to commit mass killings are all endogenous, with two main goals: (1) to identify the key variables and situations that make mass killings more likely to occur; and (2) to distinguish conditions under which mass killings and military conflict intensity reinforce each other from situations where they are substitute modes of strategic violence. We predict that mass killings are most likely in societies with large natural resources, significant proportionality constraints for rent sharing, low productivity and low state capacity. Further, massacres are more likely in a civil than in an interstate war, as in the latter group sizes matter less for future rents. In non polarized societies there are asymmetric equilibria with only the larger group wanting to engage in massacres. In such settings the smaller group compensates for this by fighting harder in the first place. In this case we can talk of mass killings and fighting efforts to be substitutes. In contrast, in polarized societies either both or none of the groups can be ready to do mass killings in case of victory. Under the "shadow of mass killings" groups fight harder. Hence, in this case massacres and fighting are complements. We also present novel empirical results on the role of natural resources in mass killings and on what kinds of ethnic groups are most likely to be victimized in massacres and forced resettlements, using group level panel data.

Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

Variétés CR polarisées et G-polarisées, partie I

Polarized and G-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation &em&F&/em& (given by the action of a Lie group G in the G-polarized case) and a transverse CR distribution. Polarized means that (E,J) is roughly speaking invariant by&em&F&/em&. Both structures are therefore linked up. The interplay between them gives to polarized CR-manifolds a very rich geometry. In this paper, we study the properties of polarized and G-polarized manifolds, putting special emphasis on their deformations.

Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values

New Radicals and new applications of Dynamic Nuclear Polarization of biological systems

Dynamic Nuclear Polarization (DNP) is an emerging technique that could revolutionize the NMR study of small molecules at very low concentrations by the increase in sensitivity that results from transfer of polarization between electronic and nuclear spins. Although the underlying physics has been known for a long time, in the last few years there has been a lot of excitement on the chemistry and biology NMR community caused by the demonstration that the highly polarized nuclei that are prepared in solid state at very low temperatures (1-2 K) could be rapidly transferred to liquid samples at room temperature and studied in solution by conventional NMR techniques. In favorable cases several order of magnitude increases in sensitivity have been achieved. The technique is now mature enough that a commercial instrument is available. The efficiency of DNP depends on two crucial aspects: i) the efficiency of the nuclear polarization process and ii) the efficiency of the transfer from the initial solid state to the fluid state in which NMR is measured. The preferred areas of application (iii) will be dictated by situations in which the low concentration of the sample or its intrinsic low receptivity are the limiting factors .

Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica

En el marc del projecte "Modelització de les propietats òptiques de partícules metàl•liques en matriu dielèctrica" s'han desenvolupat un conjunt d'eines numèriques que permeten avançar en l'ús de l'espectroscòpia òptica per a l'obtenció d'informació morfològica de materials compostos consistents en partícules metàl•liques en matriu dielèctrica. S'han implementat esquemes numèrics per a calcular les propietats òptiques de materials compostos on les partícules poden presentar una distribució de mides i formes i diferent graus d'ordenament espacial. Les simulacions s'han realitzat a dos nivells: i) amb l’aproximació quasi-estàtica, que permet descriure el comportament d'aquests materials en termes de constants òptiques efectives i ii) amb càlculs electrodinàmics exactes, que han servit per avaluar la validesa de l’aproximació anterior i que han permès d'estudiar la interacció de partícules amb feixos de llum focalitzats o amb polarització no homogènia. A través de l’anàlisi d'aquestes simulacions, s'han desenvolupat models senzills que permeten parametritzar la influència de diferents quantitats físiques en el comportament òptic del material. Aquests models s'han implementat en un programari de càlcul que permeten trobar el valor òptim dels paràmetres físics d'interès mitjançant l'ajust d'espectres òptics. Els models s'han avaluat amb l'anàlisi de dades experimentals subministrades per altres laboratoris.

Assembling genes from predicted exons in linear time with dynamic programming

In a number of programs for gene structure prediction in higher eukaryotic genomic sequences, exon prediction is decoupled from gene assembly: a large pool of candidate exons is predicted and scored from features located in the query DNA sequence, and candidate genes are assembled from such a pool as sequences of nonoverlapping frame-compatible exons. Genes are scored as a function of the scores of the assembled exons, and the highest scoring candidate gene is assumed to be the most likely gene encoded by the query DNA sequence. Considering additive gene scoring functions, currently available algorithms to determine such a highest scoring candidate gene run in time proportional to the square of the number of predicted exons. Here, we present an algorithm whose running time grows only linearly with the size of the set of predicted exons. Polynomial algorithms rely on the fact that, while scanning the set of predicted exons, the highest scoring gene ending in a given exon can be obtained by appending the exon to the highest scoring among the highest scoring genes ending at each compatible preceding exon. The algorithm here relies on the simple fact that such highest scoring gene can be stored and updated. This requires scanning the set of predicted exons simultaneously by increasing acceptor and donor position. On the other hand, the algorithm described here does not assume an underlying gene structure model. Indeed, the definition of valid gene structures is externally defined in the so-called Gene Model. The Gene Model specifies simply which gene features are allowed immediately upstream which other gene features in valid gene structures. This allows for great flexibility in formulating the gene identification problem. In particular it allows for multiple-gene two-strand predictions and for considering gene features other than coding exons (such as promoter elements) in valid gene structures.

Upgrading or polarization? occupational change in Britain, Germany, Spain and Switzerland, 1990-2008

This paper analyzes the pattern of occupational change in four Western European countries over the last two decades: what kind of jobs have been expanding -- high-paid jobs, low-paid jobs or both? By addressing this issue, we also examine what theoretical account is consistent with the observed pattern of change: skill-biased technical change, skill supply evolution or wage-setting institutions? Our empirical findings show a picture of massive occupational upgrading that closely matches educational expansion. In all four countries, by far the strongest employment growth occurred at the top of the occupational hierarchy, among managers and professionals. Yet in parallel, in Britain and Switzerland, as well as in Germany and Spain after 1996 and 2002 respectively, relative employment declined more strongly in the middling occupations (among clerks and production workers) than at the bottom (among interpersonal service workers). This slightly polarized pattern of occupational upgrading is consistent with the "routinization" hypothesis that technology is a better substitute for average-paid jobs in production and the office that for low-paid jobs in interpersonal services. However, we find large cross-country differences in the employment evolution at the bottom of the occupational hierarchy, among low-paid services workers: sizeable growth in Britain and Spain, but stagnation in Germany and Switzerland. This results points towards the possibility that wage-setting institutions filter the pattern of occupational change.

Electoral Platforms, Implemented Policies, and Abstention

Recent studies of American politics evidence that political polarization of both the electorate and the political elite have moved 'almost in tandem for the past half century' (McCarty et al., 2003, p.2), and that party polarization has steadily increased since the 1970s. On the other hand, the empirical literature on party platforms and implemented policies has consistently found an imperfect but nonnegligible correlation between electoral platforms and governmental policies: while platforms tend to be polarized, policies are moderate or centrist. However, existing theoretical models of political competition are not manifestly compatible with these observations. In this paper, we distinguish between electoral platforms and implemented policies by incorporating a non-trivial policy-setting process. It follows that voters may care not only about the implemented policy but also about the platform they support with their vote. We find that while parties tend to polarize their positions, the risk of alienating their constituency prevents them from radicalizing. The analysis evidences that the distribution of the electorate, and not only the (expected) location of a pivotal voter, matters in determining policies. Our results are consistent with the observation of polarized platforms and moderate policies, and the alienation and indifference components of abstention.

Network revenue management with product-specific no-shows

Revenue management practices often include overbooking capacity to account for customerswho make reservations but do not show up. In this paper, we consider the network revenuemanagement problem with no-shows and overbooking, where the show-up probabilities are specificto each product. No-show rates differ significantly by product (for instance, each itinerary andfare combination for an airline) as sale restrictions and the demand characteristics vary byproduct. However, models that consider no-show rates by each individual product are difficultto handle as the state-space in dynamic programming formulations (or the variable space inapproximations) increases significantly. In this paper, we propose a randomized linear program tojointly make the capacity control and overbooking decisions with product-specific no-shows. Weestablish that our formulation gives an upper bound on the optimal expected total profit andour upper bound is tighter than a deterministic linear programming upper bound that appearsin the existing literature. Furthermore, we show that our upper bound is asymptotically tightin a regime where the leg capacities and the expected demand is scaled linearly with the samerate. We also describe how the randomized linear program can be used to obtain a bid price controlpolicy. Computational experiments indicate that our approach is quite fast, able to scale to industrialproblems and can provide significant improvements over standard benchmarks.

Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.