Jurnal Edukasi
Not a member yet
4879 research outputs found
Sort by
A Point Counting Algorithm for Cyclic Covers of the Projective Line
No full textInternational audienceWe present a Kedlaya-style point counting algorithm for cyclic covers over a finite field with not dividing , and and not necessarily coprime. This algorithm generalizes the Gaudry-Gürel algorithm for superelliptic curves to a more general class of curves, and has essentially the same complexity. Our practical improvements include a simplified algorithm exploiting the automorphism of , refined bounds on the -adic precision, and an alternative pseudo-basis for the Monsky-Washnitzer cohomology which leads to an integral matrix when . Each of these improvements can also be applied to the original Gaudry-Gürel algorithm. We include some experimental results, applying our algorithm to compute Weil polynomials of some large genus cyclic covers
Second order mean field games with degenerate diffusion and local coupling
No full textInternational audienceWe analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as minimizers of two optimal control problems. We also show that such solutions are stable with respect to the data, so that in particular the degenerate case can be approximated by a uniformly parabolic (viscous) perturbation
Dispositif et méthode de caractérisation polarimétrique déportée par fibre optique
No full textDemande de brevet France n° 145 2244 déposée le 18 mars 2014, demande extension PCT EP2015/053437 18 février 201
Principal component analysis of electron beams generated in K-shell aluminum X-pinch plasma produced by a compact LC-generator
No full textInternational audiencePrincipal component analysis (PCA) method is applied and compared with the line ratios of H-like and He-like transitions, in order to investigate the effects of electron beam on the K-shell Aluminum synthetic spectra. It is also used as a diagnostics to estimate the plasma parameters of K-shell Al X-pinch plasma spectrum. This spectrum is produced by the explosion of two 25-μm Al wires on a compact LC (40 kV, 200 kA) generator. The database for the principal component extraction is created over a previously developed, non-LTE, collisional radiative K-shell Aluminum model. As a result, PCA shows an agreement with the line ratios which are sensitive to plasma electron temperatures, densities and beam fractions. Principal component analysis also illustrates that the addition to the non-LTE model of a fraction f of electrons in an energetic beam, generates the clusters in a three dimensional vector space which are translations of each other and follows reverse v-shaped cascade trajectories, except for the f = 0.0 case. Modeling of a typical shot by PCA gives the plasma electron temperature of Te = 100 eV, density of Ne = 1 × 1020 cm−3 and hot electron fraction of f = 0.2 (with a beam energy centered at 10 keV)
Coherent vorticity in turbulent channel flow: a wavelet viewpoint
No full textInternational audienceno abstrac
Microscale insight into the influence of humidity on the mechanical behavior of mudstones
No full textInternational audienc
Méthodes tropicales pour la localisation de valeurs propres et application à leur calcul numérique
No full textIn this thesis we use tropical mathematics to locate and numerically compute eigenvalues of matrices and matrix polynomials. The first part of the work focuses on eigenvalues of matrices, while the second part focuses on matrix polynomials and adds a numerical experimental side along the theoretical one.By “locating” an eigenvalue we mean being able to identify some bounds within which it must lie. This can be useful in situations where one only needs approximate eigenvalues; moreover, they make good starting values for iterative eigenvalue-finding algorithms. Rather than full location, our result for matrices is in the form of majorization bounds to control the absolute value of the eigenvalues. These bounds are to some extent a generalization to matrices of a result proved by Ostrowski for polynomials: he showed (albeit with different terminology) that the product of the k largest absolute values of the roots of a polynomial can be bounded from above and below by the product of its k largest tropical (max-times) roots, up to multiplicative factors which are independent of the coefficients of the polynomial. We prove an analogous result for matrices: the product of the k largest absolute values of eigenvalues is bounded, up to a multiplicative factor, by the product of the k largest tropical eigenvalues. It should be noted that tropical eigenvalues can be computed by using the solution to a parametric optimal assignment problem, in a way that is robust with respect to small perturbations in the data. Another thing worth mentioning is that the multiplicative factor in the bound is of combinatorial nature and it is reminiscent of a work by Friedland, who essentially proved a specialization of our result to the particular case k = 1 (i.e. for the largest eigenvalue only). We can interpret the absolute value as an archimedean valuation; in this light, there is a correspondence between the present result and previous work by Akian, Bapat and Gaubert, who dealt with the same problem for matrices over fields with non- archimedean valuation (specifically Puiseux series, with the leading exponent as valuation) and showed in that case more stringent bounds, with no multiplicative factor, and with generic equality rather than upper and lower bounds.The second part of the thesis revolves around the computation of eigenvalues of matrix polynomials. For linear matrix polynomials, stable algorithms such as the QZ method have been known for a long time. Eigenproblems for matrix polynomials of higher degree are usually reduced to the linear case, using a linearization such as the companion linearization. This however can worsen the condition number and backward error of the computed eigenvalue with respect to perturbations in the coefficients of the original polynomial (even if they remain stable in the coefficients of the linearized). To mitigate this inconvenience it is common to perform a scaling of the matrix polynomial before linearizing. Various scaling methods have been proposed. In our work, we introduce a two-sided diagonal scaling strategy based on the tropical eigenvalues of the matrix polynomial obtained by taking entrywise valuation of the original one (and we will consider both the archimedean and non-archimedean case). We study the effect of this scaling on the conditioning and backward error, with both analytic formulas and numerical examples, showing that it can increase the accuracy of the computed eigenvalues by several orders of magnitude.Dans cette thèse nous utilisons des outils d'algèbre tropicale pour localiser et calculer de façon numérique les valeurs propres de matrices et de polynômes matriciels. La première partie porte sur les valeurs propres de matrices, la deuxième se concentre sur les polynômes matriciels tout en rajoutant à l'étude théorique un coté numérique.``Localiser'' une valeur propre veut dire pouvoir identifier des bornes entre lesquelles elle se trouve. Cela peut être utile dans des situations où l'on n'a besoin que de valeurs propres approximées; ces approximations permettent aussi d'obtenir de bons points d'initialisation d'algorithmes itératifs de calcul des valeurs propres. Notre résultat pour les matrices prend la forme d'inégalités de type majorisation qui contrôlent le module des valeurs propres. Ces bornes peuvent être vues comme une généralisation au cas matriciel d'un résultat prouvé par Ostrowski pour les polynômes : il a montré (en utilisant une terminologie différente) que le produit des k plus grands modules des racines d'un polynôme sont bornées inférieurement et supérieurement par le produit de ses k plus grandes valeurs propres tropicales, à un facteur multiplicatif près qui est indépendent des coefficients du polynôme. Nous prouvons un résultat analogue pour le cas d'une matrice : le produit des k plus grands modules des valeurs propres est borné, à un facteur multiplicatif près, par le produit des k plus grandes valeurs propres tropicales. On notera que les valeurs propres tropicales peuvent être calculées au moyen de la solution d'un problème d'affectation optimale paramètrique, et ceci de façon stable par rapport à des perturbations des données. On notera aussi que le facteur multiplicatif est de nature combinatoire, et qu'il est inspiré d'un résultat de Friedland, lequel a démontré notre inégalité dans le cas particulier k=1. On peut interpréter le module comme une valuation archimédienne; ainsi, il y a une correspondance entre le résultat présenté ici et un travail précédent d'Akian, Bapat et Gaubert, qui ont traité le même problème pour des matrices à coefficients dans un corps avec une valuation non-archimédienne (notamment le corps des séries de Puiseux, équipé de la valuation donnée par l'exposant dominant) et qui ont montré des bornes supérieures plus sérées pour ce cas, sans facteur multiplicatif, et avec égalité générique à la place de bornes supérieures et inférieures.La deuxième partie de la thèse traite du calcul des valeurs propres de polynômes matriciels. Pour des polynôme matriciels linéaires, des algorithmes stables tels que la méthode QZ sont connus dépuis longtemps. L'approche pour les polynômes de degré supérieur consiste souvent à se ramener au cas linéaire, à l'aide de linéarisations telles que la linéarisation compagnon. Cela peut néanmoins dégrader le conditionnement et l'erreur inverse des valeurs propres calculées, par rapport aux coefficients du polynôme originel (même s'ils restent stables par rapport au linéarisé). Pour faire face à cet inconvénient il est commun de procéder à un changement d'échelle avant de linéariser le polynôme. Plusieurs techniques de changement d'échelle ont été proposées. Dans notre travail, nous introduisons un changement d'échelle par multiplication diagonale à gauche et à droite basée sur les valeurs propres tropicales du polynôme matriciel obtenu en prenant la valuation (archimédienne ou non, selon le cas) de chaque coefficient du polynôme originel. Nous étudions l'effet de ce scaling sur le conditionnement et sur l'erreur inverse, en obtenant des formules analytiques ainsi qu'en donnant des exemples numériques, et nous montrons que la précision des valeurs propres calculées peut être améliorée de plusieurs ordres de grandeur
Design and Analysis of an Improved BitMessage Anti-spam Mechanism
No full textThe BitMessage protocol offers privacy to its anonymous users. It is a completely decentralized messaging system, enabling users to exchange messages preventing accidental eavesdropping -- a nice features in the Post-Snowden Internet Era. Not only messages are sent to every node on the network (making it impossible to understand the intended recipient), but their content is encrypted with the intended recipient public key (so that s/he only can decipher it). As these two properties combined might facilitate spamming, a proof-of-work (PoW) mechanism has been designed to mitigate this threat:only messages exhibiting properties of the PoW are forwarded on the network: since PoW is based on computationally heavy cryptographic functions, this slows down the rate at which spammers can introduce unsolicited messages in the network on the one hand, but also makes it harder to send legitimate messages for regular users on the other hand.In this paper, we (i) carry on an analysis of the current PoW mechanism, (ii) propose a very simple, yet very effective, generalization of theformula that decouples spammers vs legitimate users penalty showing that (iii) at the optimum, our proposal halves the harm spammers can do, avoiding by definition any impact for legitimate users
On the radiative forcing of volcanic plumes: modelling the impact of Mount Etna in the Mediterranean
No full textInternational audienceThe impact of small to moderate volcanic eruptions on the regional to global radiative forcing and climate is still largely unknown and thought to be presently underestimated. In this work, daily average shortwave radiative forcing efficiencies at the surface (RFE Surf d), at top of the atmosphere (RFE TOA d) and their ratio (f), for upper tropospheric volcanic plumes with different optical characterization, are derived using the radiative transfer model UVSPEC and the LibRadtran suite. The optical parameters of the simulated aerosol layer, i.e., the Ångströem coefficient (α), the single scattering albedo (SSA) and the asymmetry factor (g), have been varied to mimic volcanic ash (bigger and more absorbing particles), sulphate aerosols (smaller and more reflective particles) and intermediate/mixed conditions. The characterization of the plume and its vertical distribution have been setup to simulate Mount Etna, basing on previous studies. The radiative forcing and in particular the f ratio is strongly affected by the SSA and g, and to a smaller extent by α, especially for sulphates-dominated plumes. The impact of the altitude and thickness of the plume on the radiative forcing, for a fixed optical characterization of the aerosol layer, has been found negligible (less than 1% for RFE Surf d , RFE TOA d and f). The simultaneous presence of boundary layer/lower tropospheric marine or dust aerosols, like expected in the Mediterranean area, modulates only slightly (up to 12 and 14% for RFE Surf d and RFE TOA d , and 3 to 4% of the f ratio) the radiative effects of the upper tropospheric volcanic layer
Single Shot Radiography Using an All-optical Compton Backscattering Source
No full textInternational audienceThe development of compact laser-based synchrotron sources is a field of active research. Here we present recent results on an all-optical Compton backscattering source using laser-accelerated electrons and a plasma mirror, as introduced in [K. Ta Phuoc et al., Nature Photonics 6 (5) (2012) 308-311].Scattering of quasi-monoenergetic electrons of up to 200 MeV energy with their proper drive-beam leads to emission of femtosecond X-ray pulses, whose energies exceed 100 keV. We demonstrate that the photon yield from the source is sufficient to illuminate a centimeter-size sample placed 90 centimeters behind the source