905 research outputs found

    On Foundation of the Generalized Nambu Mechanics

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    We outline the basic principles of canonical formalism for the Nambu mechanics---a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of Nambu bracket which generalizes the Poisson bracket to the multiple operation of higher order n3n \geq 3 on classical observables and is described by Hambu-Hamilton equations of motion given by n1n-1 Hamiltonians. We introduce the fundamental identity for the Nambu bracket which replaces Jacobi identity as a consistency condition for the dynamics. We show that Nambu structure of given order defines a family of subordinated structures of lower order, including the Poisson structure, satisfying certain matching conditions. We introduce analogs of action from and principle of the least action for the Nambu mechanics and show how dynamics of loops (n2n-2-dimensional objects) naturally appears in this formalism. We discuss several approaches to the quantization problem and present explicit representation of Nambu-Heisenberg commutation relation for n=3n=3 case. We emphasize the role higher order algebraic operations and mathematical structures related with them play in passing from Hamilton's to Nambu's dynamical picture.Comment: 27 page

    On Mean Pose and Variability of 3D Deformable Models

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    International audienceWe present a novel methodology for the analysis of complex object shapes in motion observed by multiple video cameras. In particular, we propose to learn local surface rigidity probabilities (i.e., deformations), and to estimate a mean pose over a temporal sequence. Local deformations can be used for rigidity-based dynamic surface segmentation, while a mean pose can be used as a sequence keyframe or a cluster prototype and has therefore numerous applications, such as motion synthesis or sequential alignment for compression or morphing. We take advantage of recent advances in surface tracking techniques to formulate a generative model of 3D temporal sequences using a probabilistic framework, which conditions shape fitting over all frames to a simple set of intrinsic surface rigidity properties. Surface tracking and rigidity variable estimation can then be formulated as an Expectation-Maximization inference problem and solved by alternatively minimizing two nested fixed point iterations. We show that this framework provides a new fundamental building block for various applications of shape analysis, and achieves comparable tracking performance to state of the art surface tracking techniques on real datasets, even compared to approaches using strong kinematic priors such as rigid skeletons

    Polymeric Separation Media: Binding of a§ unsaturated Carbonyl Compounds to Insoluble Resins through Michael Additions or Chelation of Derivatives

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    This is the publisher's version, also available electronically from "http://www.degruyter.com"

    Inertie des stratégies de protection de l’innovation

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    Cet article vise à intégrer une dimension temporelle dans l’analyse des choix de protection de l’innovation. La littérature existante porte principalement sur le choix de la méthode par l’entreprise : méthodes formelles (principalement le brevet) et méthodes informelles (secret, rapidité de mise sur le marché et complexité du design). Plusieurs travaux ont mis en évidence les facteurs de choix des stratégies de protection et plus précisément l’importance de la taille de l’entreprise, du recours à des coopérations, des dépenses liées à la R&D, de la taille du marché et du secteur d’appartenance. Nous avons donc prolongé cet apport en mobilisant des notions existantes telles que le chemin de dépendance et les phénomènes d’escalade qui soulignent que les organisations font fréquemment preuve d\u27une faible réactivité aux transformations de leur environnement. Elles paraissent notamment avoir du mal à réduire des investissements dont les performances sont décevantes. Et plus généralement, l\u27engagement dans un choix semble se renforcer jusqu\u27à parfois devenir irréversible. Il en découle nos deux questions de recherche : dans quelle mesure le choix d’une stratégie de protection de l’innovation favorise-t-il ultérieurement le choix d’une stratégie identique et quels sont les facteurs influençant le changement de stratégie de protection de l’innovation ?  Pour y répondre, nous avons recours à l\u27analyse des données issues des enquêtes CIS 4 et CIS2006. Grâce à l\u27utilisation de modèles logistique et probit, nous suivons l\u27évolution des choix d\u27entreprises sur deux périodes. Que les entreprises utilisent les méthodes informelles, une combinaison de méthodes (brevet et méthodes informelles) ou même n\u27utilisent aucune méthode, nous trouvons que le choix considéré est très nettement dépendant du fait qu\u27un choix identique ait été effectué dans la période précédente. L\u27utilisation du brevet seul ne semble en revanche pas sujet au même état de dépendance, ce qui fait apparaître cette stratégie de protection comme davantage transitoire ou instable. En plus de l\u27inertie constatée dans les choix, les résultats montrent clairement une nette différence entre brevet et méthodes informelles. Alors que le choix d\u27utiliser le brevet est peu sensible aux modifications d\u27autres variables, l\u27utilisation des méthodes informelles se montre quant à elle beaucoup plus changeante, rejoignant l\u27idée d\u27une certaine souplesse dans son utilisation

    Extreme value distributions and Renormalization Group

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    In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\'echet families. The problem is approached using the language of Renormalization Group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of the differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections.Comment: 16 pages, 5 figures. Final versio

    Using Extreme Value Theory for Determining the Probability of Carrington-Like Solar Flares

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    Space weather events can negatively affect satellites, the electricity grid, satellite navigation systems and human health. As a consequence, extreme space weather has been added to the UK and other national risk registers. By their very nature, extreme space weather events occur rarely and, therefore, statistical methods are required to determine the probability of their occurrence. Space weather events can be characterised by a number of natural phenomena such as X-ray (solar) flares, solar energetic particle (SEP) fluxes, coronal mass ejections and various geophysical indices (Dst, Kp, F10.7). In this paper extreme value theory (EVT) is used to investigate the probability of extreme solar flares. Previous work has assumed that the distribution of solar flares follows a power law. However such an approach can lead to a poor estimation of the return times of such events due to uncertainties in the tails of the probability distribution function. Using EVT and GOES X-ray flux data it is shown that the expected 150-year return level is approximately an X60 flare whilst a Carrington-like flare is a one in a 100-year event. It is also shown that the EVT results are consistent with flare data from the Kepler space telescope mission.Comment: 13 pages, 4 figures; updated content following reviewer feedbac

    A direct route to cyclic organic nanostructures via ring-expansion metathesis polymerization of a dendronized macromonomer

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    Cyclic organic nanostructures were prepared via ring-expansion metathesis polymerization of a dendronized norbornene macromonomer. The strategy provides a direct, efficient route to nanoscale rings in a single operation. AFM imaging confirmed toroidal features having diameters of ca. 35−40 nm

    Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

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    Some results on the ordered statistics of eigenvalues for one-dimensional random Schr\"odinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown that the slowly decaying averaged return probability of the Sinai problem, \mean{P(x,t|x,0)}\sim \ln^{-2}t, is converted into a power law decay, \mean{P(x,t|x,0)}\sim t^{-\sqrt{2\rho/g}}, where gg is the strength of the random force field and ρ\rho the density of absorbers.Comment: 10 pages ; LaTeX ; 4 pdf figures ; Proceedings of the meeting "Fundations and Applications of non-equilibrium statistical mechanics", Nordita, Stockholm, october 2011 ; v2: appendix added ; v3: figure 2.left adde

    Deformations of the Tracy-Widom distribution

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    In random matrix theory (RMT), the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists in removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristc of extreme values of an uncorrelated sequence, is obtained.Comment: 9 pages, 1 figur
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