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COEFFICIENTS OF SYLVESTER'S DENUMERANT
No full textFor a given sequence α = [α 1 , α 2 , . . . , α N +1 ] of N + 1 positive integers, we consider the combinatorial function E(α)(t) that counts the non-negative integer solutions of the equation α 1 x 1 + α 2 x 2 + · · · + α N x N + α N +1 x N +1 = t, where the right-hand side t is a varying non-negative integer. It is well-known that E(α)(t) is a quasi-polynomial function in the variable t of degree N . In combinatorial number theory this function is known as Sylvester's denumerant. Our main result is a new algorithm that, for every fixed number k, computes in polyno-mial time the highest k + 1 coefficients of the quasi-polynomial E(α)(t) as step polynomials of t (a simpler and more explicit representation). Our algorithm is a consequence of a nice poset structure on the poles of the associated rational generating function for E(α)(t) and the geometric reinterpretation of some rational generating functions in terms of lattice points in polyhedral cones. Our algorithm also uses Barvinok's fundamental fast decomposition of a polyhedral cone into unimodular cones. This paper also presents a simple algorithm to predict the first non-constant coefficient and concludes with a report of several compu-tational experiments using an implementation of our algorithm in LattE integrale. We compare it with various Maple programs for partial or full computation of the denumerant
Sedimentation waves on the Martian North Polar Cap: Analogy with megadunes in Antarctica
No full textInternational audienceComplex interactions between katabatic winds and the cryosphere may lead to the formation of sedimentation waves at the surface of ice sheets. These have been first described and named snow megadunes in Antarctica. Here we use topographic data, optical images, subsurface radar soundings and spectroscopic data acquired by Mars orbiters, to show that the surface of the Martian North Polar Cap displays two superimposed sets of sedimentation waves with differing wavelengths. These sedimentation waves have similarities with Antarctic snow megadunes regarding their surface morphology, texture, grain size asymmetry, and internal stratigraphic architecture. Both sets of Martian sedimentation waves present young ice and occasional sastrugi fields, indicative of net accumulation, on their shallow-dipping upwind sides, their tops and the intervening troughs. Old layers of dusty ice, indicative of net ablation, are exhumed on the steep-dipping downwind sides of the larger waves. Smooth surfaces of coarse-grained ice, indicative of reduced accumulation associated with sublimation metamorphism, cover the steep-dipping downwind sides of the smaller waves. These surface characteristics and the internal stratigraphy revealed by radar soundings are consistent with the interpretation that both sets of Martian sedimentation waves grow and migrate upwind in response to the development of periodic accumulation/ablation patterns controlled by katabatic winds. The recognition of these sedimentation waves provides the basis for the development of a common model of ice/wind interaction at the surface of Martian and terrestrial glaciers. Martian smaller waves, characterized by reduced net accumulation on their downwind sides, are analogous to Antarctic snow megadunes that have been described so far. A terrestrial equivalent remains to be discovered for the larger Martian waves, characterized by net ablation on their downwind sides. © 2014 Elsevier B.V
Quantifying trust dynamics in signed graphs, the S-Cores approach
No full textInternational audienceLately, there has been an increased interest in signed net-works with applications in trust, security, or social comput-ing. This paper focuses on the issue of defining models and metrics for reciprocity in signed graphs. In unsigned di-rected networks, reciprocity quantifies the predisposition of network members in creating mutual connections. On the other hand, this concept has not yet been investigated in the case of signed graphs. We capitalize on the graph degener-acy concept to identify subgraphs of the signed network in which reciprocity is more likely to occur. This enables us to assess reciprocity at a global level, rather than at an exclu-sively local one as in existing approaches. The large scale experiments we perform on real world data sets of trust net-works lead to both interesting and intuitive results. We be-lieve these reciprocity measures can be used in various social applications such as trust management, community detection and evaluation of individual nodes. The global reciprocity we define in this paper is closely correlated to the clustering structure of the graph, more than the local reciprocity as it is indicated by the experimental evaluation we conducted
Ensemble meteorological reconstruction using circulation analogues of 1781–1785
No full textInternational audienceThis paper uses a method of atmospheric flow analogues to reconstruct an ensemble of atmospheric vari-ables (namely sea-level pressure, surface temperature and wind speed) between 1781 and 1785. The properties of this ensemble are investigated and tested against observations of temperature. The goal of the paper is to assess whether the atmospheric circulation during the Laki volcanic erup-tion (in 1783) and the subsequent winter were similar to the conditions that prevailed in the winter 2009/2010 and dur-ing spring 2010. We find that the 3 months following the Laki eruption in June 1783 barely had analogues in 2010. The cold winter of 1783/1784 yielded circulation analogues in 2009/2010. The reconstructed surface temperature over land bears significant correlations with local observations, al-though the amplitude of the reconstruction is weaker
Giant field enhancement in electromagnetic Helmholtz nanoantenna
No full textInternational audienceInspired by the acoustic Helmholtz resonator, we propose a slit-box electromagnetic nanoantenna able to concentrate the energy of an incident beam into surfaces a thousand times smaller than with a classical lens. This design produces a giant electric field enhancement throughout the slit. The intensity enhancement reaches 10 4 in the visible up to 10 8 in the THz range even with focused beams thanks to an omnidirectional reception. These properties could target applications requiring extreme light concentration, such as SEIRA, non-linear optics and biophotonics
A convergent route to functional protected amines, diamines, and β-amino acids
No full textInternational audiencePhthalimide protected amines react with NBS under peroxide initiation to give geminal phthalimido-bromo derivatives, which are readily converted into the corresponding xanthates. These xanthates in turn undergo radical additions to numerous olefins, providing a convergent and modular access to densely functionalized protected amines and diamines
Quantitative retardance imaging using quadri-wave lateral shearing interferometry (QWLSI)
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Viscosity Solutions of Fully Nonlinear Elliptic Path Dependent PDEs
No full textThis paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type assumptions on the nonlinearity and an additional assumption formulated on some partial differential equation defined locally by freezing the path