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In this paper, we introduce a new partial consistency for constraint networks which is called Structural Consistency of level w and is denoted w-SC consistency. This consistency is based on a new approach. While conventional consistencies generally rely on local properties extended to the entire network, this new partial consistency considers global consistency on subproblems. These subproblems are defined by partial constraint graphs whose tree-width is bounded by a constant w. We introduce a filtering algorithm which achieves w-SC consistency. We also analyze w-SC filtering w.r.t. other classical local consistencies to prove that this consistency is generally incomparable although this consistency can be regarded as a special case of inverse consistency. Finally, we present experimental results to assess the usefulness of this approach. We show that w-SC is a significantly more powerful level of filtering and more effective w.r.t. the runtime than SAC and that w-SC is a complementary approach to AC or SAC. So we can offer a combination of filterings, whose power is greater than w-SC or SAC.

International audience; In my paper at Inventiones 2009, we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle Ψ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf cohomology of both Harris-Taylor perverse sheaves and those of Ψ. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.; Dans [2], on détermine les groupes de cohomologie des espaces de Lubin-Tate par voie globale en calculant les fibres des faisceaux de cohomologie du faisceau pervers des cyclesévanescentscyclesévanescents Ψ d'une variété de Shimura de type Kottwitz-Harris-Taylor. L'ingrédient le plus complexe consistè a contrôler lesfì eches de deux suites spectrales calculant l'une les faisceaux de cohomologie des faisceaux pervers d'Harris-Taylor, et l'autre ceux de Ψ. Dans cet article, nous contournons ces difficultés en utilisant la théorie classique des représentations du groupe mirabolique ainsi qu'un argument géométrique simple. Abstract (Mirabolic group, ramified Newton stratification and cohomology of Lubin-Tate spaces) In [2], we determine the cohomology of Lubin-Tate spaces globally using the comparison theorem of Berkovich by computing the fibers at supersingular points of the perverse sheaf of vanishing cycle Ψ of some Shimura variety of Kottwitz-Harris-Taylor type. The most difficult argument deals with the control of maps of the spectral sequences computing the sheaf coho-mology of both Harris-Taylor perverse sheaves and those of Ψ. In this paper, we bypass these difficulties using the classical theory of representations of the mirabolic group and a simple geometric argument.

51 pages, in French, v2: extended introduction, journal version; International audience; The aim of this paper is to prove a generalization of the famous Theorem A of Quillen for strict $\infty$-categories. This result is central to the homotopy theory of strict $\infty$-categories developed by the authors. The proof presented here is of a simplicial nature and uses Steiner's theory of augmented directed complexes. In a subsequent paper, we will prove the same result by purely $\infty$-categorical methods.

In this paper, we develop new estimation results for functional regressions where both the regressor Z ( t ) and the response Y ( t ) are functions of Hilbert spaces, indexed by the time or a spatial location. The model can be thought as a generalization of the multivariate regression where the regression coefficient is now an unknown operator Π . We propose to estimate the operator Π by Tikhonov regularization, which amounts to apply a penalty on the L 2 norm of Π . We derive the rate of convergence of the mean-square error, the asymptotic distribution of the estimator, and develop tests on Π . As trajectories are often not fully observed, we consider the scenario where the data become more and more frequent (infill asymptotics). We also address the case where Z is endogenous and instrumental variables are used to estimate Π . An application to the electricity consumption completes the paper.

In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets $$V^1, V^2, \ldots , V^m$$ , each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset $$V^i$$ . To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by , and the restriction of this problem where every vector has at most c zeros by . was only known to be -hard, even for . We show that, assuming the unique games conjecture, it is -hard to -approximate for any fixed and . This result is tight as any solution is a -approximation. We also prove without assuming UGC that is -hard even for . Finally, we show that is polynomial-time solvable for fixed (which cannot be extended to ).

This paper is an introduction to the theory of 1d stochastic Burgers equation under periodic boundary conditions and with a stochastic force, sufficiently smooth in the space variable. We prove the classical results on the existence and uniqueness of solutions, study their regularity and discuss their properties when the time goes to infinity or the viscosity goes to zero. The latter limit describes the turbulence in the Burgers equation, named by U. Frish "the burgulence". Our paper may be used as an elementary introduction to the modern methods of stochastic PDE., Comment: in French

According to the real $\tau$-conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size of such an expression. It is known that this conjecture implies a superpolynomial lower bound on the arithmetic circuit complexity of the permanent. In this paper, we use the Wronksian determinant to give an upper bound on the number of real roots of sums of products of sparse polynomials of a special form. We focus on the case where the number of distinct sparse polynomials is small, but each polynomial may be repeated several times. We also give a deterministic polynomial identity testing algorithm for the same class of polynomials. Our proof techniques are quite versatile; they can in particular be applied to some sparse geometric problems that do not originate from arithmetic circuit complexity. The paper should therefore be of interest to researchers from these two communities (complexity theory and sparse polynomial systems).

Dans un r\'ecent article, Lagarias et Soundararajan \'etudient les solutions friables \`a l'\'equation a+b=c. Sous l'hypoth\`ese de Riemann g\'en\'eralis\'ees aux fonctions L de Dirichlet, ils obtiennent une estimation pour le nombre de solutions pond\'er\'ees par un poids lisse et une minoration pour le nombre de solutions non pond\'er\'ees. Le but de cet article est de pr\'esenter des arguments qui permettent d'une part de pr\'eciser les termes d'erreur et d'\'etendre les domaines de validit\'e de ces estimations afin de faire le lien avec un travail de la Bret\`eche et Granville, d'autre part d'obtenir le comportement asymptotique exact du nombre de solutions non pond\'er\'ees. In a recent paper, Lagarias and Soundararajan study the y-smooth solutions to the equation a+b=c. Under the Generalised Riemann Hypothesis, they obtain an estimate for the number of those solutions weighted by a compactly supported smooth function, as well as a lower bound for the number of bounded unweighted solutions. In this paper, we aim to prove a more precise estimate for the number of weighted solutions that is valid when y is relatively large with respect to x, so as to connect our estimate with the one obtained by La Bret\`eche and Granville in a recent work. We also prove the conjectured upper bound for the number of bounded unweighted solutions, thus obtaining its exact asymptotic behaviour., Comment: 20 pages

This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are “cut" by the boundary. In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function. This implicit representation of the immersed boundary enables us to discretize efficiently the fluxes in the cut-cells by imposing the strict conservation of total kinetic energy at the discrete level. The accuracy and robustness of our method are assessed on benchmark flows.

Torsion semi-stable representations can be constructed and studied using Breuil modules. In this paper, we define the notion of pylonet and prove that some categories of Breuil modules naturally define pylonets. As a consequence, we are able to define full subcategories of Breuil's categories with very nice properties (in particular, they are abelian). In a second part of this work, we try to make very explicit some abstract constructions coming from the general theory of pylonets (developped earlier in the paper). These explicitations should be very useful to make computations with torsion semi-stable Galois representations., Comment: 37 pages

In this paper, the duality in differential form is developed between a 3D primal surface and its dual manifold formed by the surface's tangent planes, that is, each tangent plane of the primal surface is represented as a four-dimensional vector that constitutes a point on the dual manifold. The iterated dual theorem shows that each tangent plane of the dual manifold corresponds to a point on the original 3D surface, that is, the "dual" of the "dual" goes back to the "primal." This theorem can be directly used to reconstruct 3D surface from image edges by estimating the dual manifold from these edges. In this paper, we further develop the work in our original conference papers resulting in the robust differential dual operator. We argue that the operator makes good use of the information available in the image data by using both points of intensity discontinuity and their edge directions; we provide a simple physical interpretation of what the abstract algorithm is actually estimating and why it makes sense in terms of estimation accuracy; our algorithm operates on all edges in the images, including silhouette edges, self occlusion edges, and texture edges, without distinguishing their types (thus, resulting in improved accuracy and handling locally concave surface estimation if texture edges are present); the algorithm automatically handles various degeneracies; and the algorithm incorporates new methodologies for implementing the required operations such as appropriately relating edges in pairs of images, evaluating and using the algorithm's sensitivity to noise to determine the accuracy of an estimated 3D point. Experiments with both synthetic and real images demonstrate that the operator is accurate, robust to degeneracies and noise, and general for reconstructing free-form objects from occluding edges and texture edges detected in calibrated images or video sequences.

cote interne IRCAM: Susini08a; None / None; National audience; Loudness change has been studied for tones with linearly varying levels revealing an asymmetry depending on the direction of change (increasing vs. decreasing) and the range of levels (high vs. low). Different assumptions were proposed to explain this asymmetry in favour of linearly increasing sounds. Teghtsoonian et al. (2005) and, more recently, Susini et al. (2006) explain that loudness of an increasing sound is influenced by the end level. Neuhoff (1999) describes this result by a survival advantage for detecting an approaching sound source. Whatever the assumption is, the results show that loudness judgments for abstract sounds (1000-Hz tones) synthetic vowel sounds were judged as significantly higher for increasing ramps. Those results are compared here with continuous and global ratings obtained on everyday life sounds such as accelerating and decelerating car sounds with a same duration (43 s), but with different temporal functions and range of levels. Overall, loudness judgments are significantly higher for accelerating car sounds than decelerating ones, but are judged on average similar considering continuous judgments. In addition, an increase in the speed (acceleration) is evaluated primarily in terms of its level at the end. These results confirms the previous studies mentioned.

Version incluant des corrections mineures à la version publiée. Ajout d'une note à la fin.; International audience; This paper is a continuation of the papers "Moduli spaces of decomposable morphims of sheaves and quotients by non-reductive groups" and "Espace abstraits de morphismes et mutations". I show here that the method used in the first paper to construct moduli spaces of morphisms and the one used in the second paper to extend the results of the first are particular cases of a more general method of construction of algebraic quotients. It is based on the notion of quasi-isomorphism. Let G, G' algebraic groups acting on algebraic varieties X, X' respectively. A quasi-morphism is a map $X/G\longrightarrow X'/G'$ that can be everywhere locally lifted to morphisms from open subsets of X to X' (plus some additional technical conditions...). A quasi-isomorphism is a quasi-morphism which is bijective and whose inverse is also a quasi-morphism. If there is a quasi-isomorphism between X and X'it is possible to deduce the existence of algebraic quotients of open subsets of X from the existence of quotients of the corresponding open subsets of X'. The method used to construct moduli spaces of morphisms is extended in this paper to complexes of decomposables sheaves.

International audience; The author gives a wide generalization of the so-called Spiegelungssatz of Leopoldt and extends most classical and unclassical results on Kummer duality. This long paper of one hundred pages, which includes a general approach to the mirror equalities and inequalities in a semisimple context, a technical description of the main situations and a careful discussion of the special case p = 2, actually appears to be the reference on this subject. The first emblematic Spiegelungssätze are the old theorem of A. Scholz [J. Reine Angew. Math. 166 (1932), 201–203; Zbl 004.05104] on the 3-rank of ideal classes of quadratic fields and the classical result of H.-W. Leopoldt on cyclotomic fields [J. Reine Angew. Math. 199 (1958), 165– 174; MR0096633 (20 #3116)]. Further extensions were given by S.-N. Kuroda [J. Number Theory 2 (1970), 282–297; MR0311624 (47 #186)] for generalized class groups, B. Oriat [in Journées Arithmétiques de Luminy (Luminy, 1978), 169–175, Ast ́erisque, 61, Soc. Math. France, Paris, 1979; see MR0556662 (80j:10003)], Oriat and P. Satgé [J. Reine Angew. Math. 307/308 (1979), 134–159; MR0534216 (80f:12007)] in a non-semisimple situation, the reviewer [in Séminaire de Théorie des Nombres, Paris 1986–87, 183–220, Progr. Math., 75, Birkhäuser Boston, Boston, MA, 1988; MR0990512 (90g:11146)] in cyclotomic towers, and many others. In the paper under review the main result is a nice theorem of reflexion for generalized class groups C(S,T) (Theorem 5.18) which, in the simplest case where S ∪ T contains both the p-adic places and the infinite ones, gives the following striking identity on the p-ranks of the χ-components of the generalized class groups: rgχ∗ (C(S,T) ) − rgχ(C( T∗, S∗) ) = ρχ(T , S ). Here χ → χ∗ is the classical mirror involution between the p-adic characters of the Galois group and ρχ(T , S ) is a quite elementary algebraic expression which only depends on the Galois properties of the finite sets of places S and T (T∗ and S∗ depending easily of T, S and infinite places) . By specializing S and T , this formula and those obtained without the restriction on the places above p ∞, from which most classical results easily follow, first give rise to various generalizations of many isolated results (especially in the intricate case p = 2) and also to interesting rank formulas for various arithmetic invariants including tame and higher kernels of K-theory for number fields (from a review by Jean-François Jaulent) . NOTE: These questions are developped in our book "Class Field Theory" (Chap. II, § 5), Springer Monographs in Mathematics, Springer second corrected printing 2005............. The whole paper is available (in PDF format) on:---- http://www.numdam.org/item?id=JTNB_1998__10_2_399_0 ........................................................................................................................................................................................................................ FOR A COMPLETE VIEW OF MY PUBLICATIONS, PLEASE LOOK AT MY HOME PAGE: http://monsite.orange.fr/maths.g.mn.gras/

The determination of roots of a function is a problem that manifests itself in almost every branch of acoustics. The usual way to determine them involves using Newton-Raphson iteration to refine their positions from approximate initial values which often leads to problems. This paper deals with an entirely different method based on winding number integral. This method has already been used but not when the function has branch points. In this paper, we give the strategy to use in order to deal with branch points arising from square root functions

Motivated by the fact that circular or spherical data are often much concentrated around a location $\pmb\theta$, we consider inference about $\pmb\theta$ under "high concentration" asymptotic scenarios for which the probability of any fixed spherical cap centered at $\pmb\theta$ converges to one as the sample size $n$ diverges to infinity. Rather than restricting to Fisher-von Mises-Langevin distributions, we consider a much broader, semiparametric, class of rotationally symmetric distributions indexed by the location parameter $\pmb\theta$, a scalar concentration parameter $\kappa$ and a functional nuisance $f$. We determine the class of distributions for which high concentration is obtained as $\kappa$ diverges to infinity. For such distributions, we then consider inference (point estimation, confidence zone estimation, hypothesis testing) on $\pmb\theta$ in asymptotic scenarios where $\kappa_n$ diverges to infinity at an arbitrary rate with the sample size $n$. Our asymptotic investigation reveals that, interestingly, optimal inference procedures on $\pmb\theta$ show consistency rates that depend on $f$. Using asymptotics "\`a la Le Cam", we show that the spherical mean is, at any $f$, a parametrically super-efficient estimator of $\pmb\theta$ and that the Watson and Wald tests for $\mathcal{H}_0:{\pmb\theta}={\pmb\theta}_0$ enjoy similar, non-standard, optimality properties. We illustrate our results through simulations and treat a real data example. On a technical point of view, our asymptotic derivations require challenging expansions of rotationally symmetric functionals for large arguments of $f$., Comment: 51 pages, 5 figures

Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or when $X$ is normal. We also prove the existence of a group scheme, that we will call the quasi-finite fundamental group scheme of $X$ at $x$, which classifies all the quasi-finite torsors over $X$, pointed over $x$. We define Galois torsors, which play in this context a role similar to the one of Galois covers in the theory of \'etale fundamental group., Comment: in French. Final version (finally!)

Pre-print of a publication in "Annales math\'ematiques du Qu{\'e}bec". Let $k$ be a totally real number field and let $k_\infty$ be its cyclotomic $\mathbb{Z}_p$-extension for $p$ totally split in $k$. This text completes our article entitled: "Approche $p$-adique de la conjecture de Greenberg pour les corps totalement r\'eels" (Annales Math\'ematiques Blaise Pascal 2017), by means of heuristics on the $p$-adic behavior of the norms, in $k_n/k$, of the ideals in $k_\infty$ ; indeed, this conjecture (on the nullity of the invariants $\lambda$ et $\mu$ of Iwasawa) depends of images in the torsion group ${\mathcal T}_k$ of the Galois group of the maximal abelian $p$-ramified pro-$p$-extension of $k$, thus of Artin symbols in a finite extension $F/k$ obtained by Galois descent of ${\mathcal T}_k$. An assumption of distribution of these norms implies $\lambda=\mu=0$. Several statistics and numerical examples in the quadratic case confirm the probable exactness of such properties which constitute the fundamental obstruction for a proof of Greenberg's conjecture in the sole context of Iwasawa's theory., Comment: in French, Completes with numerical computations and heuristics our previous paper arXiv:1611.09592 on Greenberg's conjecture. Annales math{\'e}matiques du Quebec, A para{\^i}tre

Let $F$ be a family of graphs. Then for every graph $G$ the maximum number of disjoint subgraphs of $G$, each isomorphic to a member of $F$, is at most the minimum size of a set of vertices that intersects every subgraph of $G$ isomorphic to a member of $F$. We say that $F$ packs if equality holds for every graph $G$. Only very few families pack. As the next best weakening we say that $F$ has the Erdős-Posa property if there exists a function $f$ such that for every graph $G$ and integer $k>0$ the graph $G$ has either $k$ disjoint subgraphs each isomorphic to a member of $F$ or a set of at most $f(k)$ vertices that intersects every subgraph of $G$ isomorphic to a member of $F$. The name is motivated by a [classical 1965 result of Erdős and Posa](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93P%C3%B3sa_theorem) stating that for every graph $G$ and integer $k>0$ the graph $G$ has either $k$ disjoint cycles or a set of $O(k\log k)$ vertices that intersects every cycle. Thus the family of all cycles has the Erdős-Posa property with $f(k)=O(k\log k)$. In contrast, the family of odd cycles fails to have the Erdős-Posa property. For every integer $\ell$, a sufficiently large Escher Wall is a non-bipartite graph that has an embedding in the projective plane such that every face is even and every homotopically non-trivial closed curve intersects the graph at least $\ell$ times. In particular, it contains no set of strictly less than $\ell$ vertices such that each odd cycle contains at least one them, yet it has no two disjoint odd cycles. By now there is a large body of literature proving that various families $F$ have the Erdős-Posa property. A very general theorem of Robertson and Seymour says that for every planar graph $H$ the family $F(H)$ of all graphs with a minor isomorphic to $H$ has the Erdős-Posa property. (When $H$ is non-planar, $F(H)$ does not have the Erdős-Posa property.) The present paper proves that for every planar graph $H$ the family $F(H)$ has the Erdős-Posa property with $f(k)=O(k\log k)$, which is asymptotically best possible for every graph $H$ with at least one cycle.

The study of Property (B) starts as a special case of Lehmer's conjecture. An algebraic field is said to satisfy Property (B) if there exists a positive constant bounding by below the height of every point of infinite order. In this paper we prove that, under certain uniformity conditions, the compositum of a familly of fields satisfies Property (B)., 26 pages, in French. Many typos mistakes deleted, the section 5 of the V1 has been deleted

The paper studies compactness properties of the affine Sobolev inequality of Lutwak et al. (J Differ Geom 62:17–38, 2002) and Zhang (J Differ Geom 53:183–202, 1999) in the case $$p=2$$ , and existence and regularity of related minimizers, in particular, solutions to the nonlocal Dirichlet problems $$\begin{aligned} -\sum _{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial ^2u}{\partial x_i\partial x_j}=f \text{ in } \Omega \subset {\mathbb {R}}^N, \end{aligned}$$ and $$\begin{aligned} -\sum _{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial ^2u}{\partial x_i\partial x_j}=u^{q-1},\quad u>0, \text{ in } \Omega \subset {\mathbb {R}}^N, \end{aligned}$$ where $$A_{ij}[u]=\int _\Omega \frac{\partial u}{\partial x_i}\frac{\partial u}{\partial x_j}{\mathrm {d}}{x}$$ and $$q\in (2,\frac{2N}{N-2})$$ .

In this paper we prove a convexity property of the relative entropy along entropic interpolations (solutions of the Schrödinger problem), and a regularity property of the entropic cost along the heat flow. Then we derive a dimensional EVI inequality and a contraction property for the entropic cost along the heat flow. As a consequence, we recover the equivalent results in the Wasserstein space, proved by Erbar, Kuwada and Sturm Résumé Dans cet article nous démontrons une propriété de convexité de l'entropie relative le long des interpolations entropiques (solutions duprobì eme de Schrödinger), et une propriété de régularité du coût entropique le long du flot de la chaleur. Ensuite, nous en déduisons une inégalité EVI dimensionnelle et une propriété de contraction pour le coût entropique le long du flot de la chaleur. En conséquence, nous retrouvons les résultatsrésultatséquivalents dans l'espace de Wasserstein, démontrés par Erbar, Kuwada et Sturm.

Let $P^+(n)$ denote the largest prime factor of the integer $n$ and $P_y^+(n)$ denote the largest prime factor $p$ of $n$ which satisfies $p\leqslant y$. In this paper, firstly we show that the triple consecutive integers with the two patterns $P^+(n-1)>P^+(n)P^+(n+1)$ have a positive proportion respectively. More generally, with the same methods we can prove that for any $J\in \mathbb{Z}, J\geqslant3$, the $J-$tuple consecutive integers with the two patterns $P^+(n+j_0)= \min\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ and $P^+(n+j_0)= \max\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ also have a positive proportion respectively. Secondly for $y=x^{\theta}$ with $0, Comment: in French

In earlier work we studied features of non-holomorphic modular functions associated with Feynman graphs for a conformal scalar field theory on a two-dimensional torus with zero external momenta at all vertices. Such functions, which we will refer to as modular graph functions, arise, for example, in the low energy expansion of genus-one Type II superstring amplitudes. We here introduce a class of single-valued elliptic multiple polylogarithms, which are defined as elliptic functions associated with Feynman graphs with vanishing external momenta at all but two vertices. These functions depend on a coordinate, $\zeta$, on the elliptic curve and reduce to modular graph functions when $\zeta$ is set equal to $1$. We demonstrate that these single-valued elliptic multiple polylogarithms are linear combinations of multiple polylogarithms, and that modular graph functions are sums of single-valued elliptic multiple polylogarithms evaluated at the identity of the elliptic curve, in both cases with rational coefficients. This insight suggests the many interrelations between modular graph functions (a few of which were established in earlier papers) may be obtained as a consequence of identities involving multiple polylogarithms, and explains an earlier observation that the coefficients of the Laurent polynomial at the cusp are given by rational numbers times single-valued multiple zeta values., Comment: 42 pages, significant clarifications added in section 5, minor typos corrected, and references added in version 2

Dans cet article, nous nous intéressons aux dimensions de certaines variétés qui ont été introduites récemment par Kisin pour démontrer la modularité de certaines représentations galoisiennes. Nous étudions plus spécialement un cas particulier pour lequel nous donnons une estimation de la dimension en question, puis, en nous basant sur ce résultat, nous énonçons une conjecture dans le cas général. In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the dimension we are interested in. Then, based on this result, we state a conjecture for the general case.

We study the geometry and the cohomology of the tamely ramified cover of Drinfeld’s p-adic symmetric space over a p-adic field K. For this tame level, we prove, in a purely local way, most of a conjecture of Harris on the form of the $$\ell $$ -adic cohomologies, as well as the torsion freeness of the integral cohomology. In this paper, we also compute the $$\ell $$ -adic cohomology of Coxeter Deligne–Lusztig variety associated to $$\mathrm{GL}_d,$$ and some results of independent interest on the coefficient systems over the Bruhat–Tits building associated to $$\mathrm{GL}_d(K)$$ have been established.

This paper deals with a natural stochastic optimization procedure derived from the so-called Heavy-ball method differential equation, which was introduced by Polyak in the 1960s with his seminal contribution [Pol64]. The Heavy-ball method is a second-order dynamics that was investigated to minimize convex functions f . The family of second-order methods recently received a large amount of attention, until the famous contribution of Nesterov [Nes83], leading to the explosion of large-scale optimization problems. This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout the iterations of the algorithm. We first describe some almost sure convergence results in the case of general non-convex coercive functions f . We then examine the situation of convex and strongly convex potentials and derive some non-asymptotic results about the stochastic heavy-ball method. We end our study with limit theorems on several rescaled algorithms., 39 pages, 3 pages

In this paper, we study an inverse scattering problem on Liouville surfaces having two asymptotically hyperbolic ends. The main property of Liouville surfaces consists in the complete separability of the Hamilton-Jacobi equations for the geodesic flow. An important related consequence is the fact that the stationary wave equation can be separated into a system of a radial and angular ODEs. The full scattering matrix at fixed energy associated to a scalar wave equation on asymptotically hyperbolic Liouville surfaces can be thus simplified by considering its restrictions onto the generalized harmonics corresponding to the angular separated ODE. The resulting partial scattering matrices consists in a countable set of $2 \times 2$ matrices whose coefficients are the so called transmission and reflection coefficients. It is shown that the reflection coefficients are nothing but generalized Weyl-Titchmarsh functions for the radial ODE in which the generalized angular momentum is seen as the spectral parameter. Using the Complex Angular Momentum method and recent results on 1D inverse problem from generalized Weyl-Titchmarsh functions, we show that the knowledge of the reflection operators at a fixed non zero energy is enough to determine uniquely the metric of the asymptotically hyperbolic Liouville surface under consideration., 39 pp

Nous pr\'esentons dans cet article une approche constructive, dans le style de Bishop, de la th\'eorie des diviseurs et des anneaux de Krull. Nous accordons une place centrale aux "anneaux \`a diviseurs," appel\'es PvMD dans la litt\'erature anglaise. Les r\'esultats classiques sont obtenus comme r\'esultats d'algorithmes explicites sans faire appel aux hypoth\`eses de factorisation compl\`ete. We give give an elementary and constructive version of the theory of "Pr\"ufer v-Multiplication Domains" (which we call "anneaux \`a diviseurs" in the paper) and Krull Domains. The main results of these theories are revisited from a constructive point of view, following the Bishop style, and without assuming properties of complete factorizations., Comment: in French, Quelques typos dans la bibliographie ont \'et\'e corrig\'es par rapport \`a la version publi\'ee et la version 1 sur ArXiv

Let $X$ be an algebraic scheme over an algebraically closed field and $\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \'etale cohomology groups $\mathrm{H}^i(X,\mathbb{Z}/\ell\mathbb{Z})$ are finite-dimensional. Using an $\ell$-adic variant of M. Artin's good neighborhoods and elementary results on the cohomology of pro-$\ell$ groups, we express the cohomology of $X$ as a well controlled colimit of that of toposes constructed on $BG$ where the $G$ are computable finite $\ell$-groups. From this, we deduce that the Betti numbers modulo $\ell$ of $X$ are algorithmically computable (in the sense of Church-Turing). The proof of this fact, along with certain related results, occupies the first part of this paper. This relies on the tools collected in the second part, which deals with computational algebraic geometry. Finally, in the third part, we present a "universal" formalism for computation on the elements of a field., Comment: In French. v2 has been considerably reworked and expanded. v3 incorporates slight corrections and simplifications and a few additions (notably: computability of the morphism from hyper\v{c}ech cohomology, graded algebra structure, and a worked out example); submitted for publication

An integer is said to be $y$-friable if its greatest prime factor is less than $y$. In this paper, we obtain estimates for exponential sums over $y$-friable numbers up to $x$ which are non-trivial when $y \geq \exp\{c \sqrt{\log x} \log \log x\}$. As a consequence, we obtain an asymptotic formula for the number of $y$-friable solutions to the equation $a+b=c$ which is valid unconditionnally under the same assumption. We use a contour integration argument based on the saddle point method, as developped in the context of friable numbers by Hildebrand & Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers., 31 pages, in French

Let B ( ϑ ) B (\vartheta ) denote the first normalised Bernoulli function, and consider the series f ( ϑ ) := ∑ n ⩾ 1 B ( n ϑ ) / n f(\vartheta ):=\sum _{n\geqslant 1}B(n\vartheta )/n . In a previous paper, we determined the set E ∗ E^* of those real numbers ϑ \vartheta at which f ( ϑ ) f(\vartheta ) converges. Let B 2 ( ϑ ) B_2(\vartheta ) designate the second Bernoulli function and let ⟨ t ⟩ \langle t\rangle denote the fractional part of the real number t t . Put F ( ϑ ) := ∑ n ⩾ 1 B 2 ( n ϑ ) / 2 n 2 = π 2 / 72 + ∫ 0 ϑ f ( t ) d t . F(\vartheta ):=\sum _{n\geqslant 1}{B_2(n\vartheta )/ 2n^2}=\pi ^2/72+\int _0^\vartheta f(t)\mathrm {d} t. It has been shown by Báez-Duarte, Balazard, Landreau and Saias (2005) that F ( ϑ ) F(\vartheta ) and ∫ 0 ∞ ⟨ t ⟩ ⟨ ϑ t ⟩ d t / t 2 \int _0^\infty \langle t\rangle \langle \vartheta t\rangle \mathrm {d} t/t^2 have the same differentiability points. Moreover, using delicate functional equations, Balazard and Martin recently proved that the corresponding set is precisely E := E ∗ ∖ Q E:=E^*\smallsetminus \mathbb {Q} and that F ′ ( ϑ ) = f ( ϑ ) F’(\vartheta )=f(\vartheta ) whenever ϑ ∈ E \vartheta \in E . We provide a short, direct proof of this last result, based on standard results from Diophantine approximation theory and uniform distribution theory.

Euclid’s lemma can be derived from the algebraic gcd property, but it is not at all apparent that Euclid himself does this. We would be quite surprised if he didn’t use this property because he points it out early on and because we expect him to make use of the Euclidean algorithm in some significant way. In this paper, we explore the question of just how the algebraic gcd property enters into Euclid’s proof, if indeed it does. Central to Euclid’s development is the idea of four numbers being proportional: a is to b as c is to d. Euclid gives two different definitions of proportionality, one in Book VII for numbers (“Pythagorean proportionality”) and one in Book V for general magnitudes (“Eudoxean proportionality”). We will discover that it is essential to keep in mind the difference between these two definitions and that many authorities, possibly including Euclid himself, have fallen into the trap of believing that Eudoxean proportionality for numbers is easily seen to be the same as Pythagorean proportionality. Finally, we will suggest a way to make Euclid’s proof good after 2300 years.

In this paper, we generalize Mauduit and Rivat's theorem on the Rudin-Shapiro sequence. Weakening the hypothesis needed in their theorem, we prove a prime number theorem for a large class of functions defined on the digits. Our result covers the case of generalized Rudin-Shapiro sequences as well as bloc-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai., Comment: in French

Let $\cal{F}$ be a regular codimension 1 holomorphic foliation on a compact K\" ahler manifold. One assumes in addition that $\cal{F}$ possesses a transverse invariant positive current. The aim of this paper is to establish the following alternative: - There exists an invariant hypersurface. - The foliation admits a transverse invariant hermitian metric with constant curvature, in French

[Departement_IRSTEA]Eaux [TR1_IRSTEA]ARCEAU [Departement_IRSTEA]Eaux [TR1_IRSTEA]ARCEAU; Cette communication présente une comparaison de trois types de méthodes de prédétermination des pluies extrêmes : 1) l’approche purement locale qui consiste à ajuster une distribution (lois généralisée des valeurs extrêmes GEV, de Pareto généralisée GP, ou par type de temps MEWP) sur un échantillon de pluies journalières relevées à un site cible, 2) les approches locales régionales qui consistent à enrichir l’échantillon d’observations du site cible par des données observées dans une région homogène et 3) les approches purement régionales que l’on peut utiliser en site non jaugé. Pour les deux dernières la distribution des pluies se déduit soit d’une analyse fréquentielle (AF) basée sur la théorie des valeurs extrêmes, soit de simulations du modèle SHYREG de génération stochastique de pluie. La comparaison s’appuie sur un jeu de 1568 stations pluviométriques issues de Météo‑France et d’EDF dans la moitié Sud de la France. Le protocole de comparaison a été défini à partir des différents échantillons de calage/validation. Les critères de comparaison permettent de juger du biais et de la variabilité des quantiles et intervalles de confiance. Les principaux résultats soulignent : 1) localement, l’ajustement d’une loi GP sur les dépassements de seuil présente de meilleures performances qu’une loi GEV sur les maxima annuel. 2) la loi exponentielle est inadaptée en particulier en région méditerranéenne. 3) de faibles performances des approches locales comparées aux approches locales‑régionales et purement régionales, exceptée pour l’AF par type de temps MEWP comparable à l’approche locale‑régionale hors région méditerranéenne avec plus de 10 ans pour le calage. 4) des performances comparables pour les approches locales régionales des méthodes d’AF et celle basée sur les simulations du modèle stochastique de pluie SHYREG. 5) une dégradation assez faible des critères lorsque l’on passe d’un ajustement de loi en version locale‑régionale à purement régionale. / This paper focuses on a comparison of 3 families of extreme rainfall frequency analysis methods: 1) purely local approaches which consist in fitting a probability distribution function (pdf) to a sample of observed daily rainfall, 2) local‑regional approaches where the sample of annual maxima daily rainfall at the target site is enlarged by rainfall observations in a surrounding homogeneous neighbourhood and 3) purely regional approaches for estimating the extreme rainfall pdf at an ungaged site. For 2) and 3) the extreme rainfall pdf can be estimated either by frequency analysis based on the extreme value theory or from the simulations of the French stochastical rainfall model named SHYREG. The comparison relies on a dataset of 1568 daily rainfall gages belonging to the French Weather Service (Météo‑France) or the French Electricity Company (EDF) in the southern half of France. A comparison methodology and several comparison criteria have been defined to evaluate the bias and variances of the quantiles and the confidence intervals. The main results are: 1) At the local scale, the General Pareto Distribution fitted on a peak over threshold sample performs better that the Generalized Extreme Value pdf fitted on max annual sample, 2) the exponential pdf is clearly unsuitable in Mediterranean area, 3 the local approaches perform poorly compared to the local‑regional and purely regional frequency analyses except for the MEWP weather pattern frequency analysis which is comparable to the local regional frequency analysis for non‑Mediterranean climate and when the calibration sample size exceeds 10 years, 4) the local regional frequency analysis and the SHYREG method performances are comparable, and 5) there is only a weak decrease in performances when using a purely regional frequency analysis instead of a local‑regional frequency analysis.

The CSP formalism has shown, for many years, its interest for the representation of numerous kinds of problems, and also often provide effective resolution methods in practice. This formalism has also provided a useful framework for the knowledge representation as well as to implement efficient methods for reasoning about knowledge. The data of a CSP are usually expressed in terms of a constraint network. This network is a (constraints) graph when the arity of the constraints is equal to two (binary constraints), or a (constraint) hypergraph in the case of constraints of arbitrary arity, which is generally the case for problems of real life. The study of the structural properties of these networks has made it possible to highlight certain properties, which led to the definition of new tractable classes, but in most cases, they have been defined for the restricted case of binary constraints. So, several representations by graphs have been proposed for the study of constraint hypergraphs to extend the known results to the binary case. Another approach, finer, is interested in the study of the microstructure of CSP, which is defined by graphs. This helped, offering a new theoretical framework to propose other tractable classes. In this paper, we propose to extend the notion of microstructure to any type of CSP. For this, we propose three kinds of graphs that can take into account the constraints of arbitrary arity. We show how these new theoretical tools can already provide a framework for developing new tractable classes for CSPs. We think that these new representations should be of interest for the community, firstly for the generalization of existing results, but also to obtain original results.

In this short paper, we will provide a characterisation of interpretable groups in a beautiful pair (K, E) of algebraically closed fields : every interpretable group is, up to isogeny, the extension of the subgroup of E-rational points of an algebraic group by an interpretable group which is the quotient of an algebraic group by the E-rational points of an algebraic subgroup.---Dans une belle paire (K;E) de corps alg\'ebriquement clos, un groupe d\'efinissable se projette, \`a isog\'enie pr\`es, sur les points E-rationnels d'un groupe alg\'ebrique ayant pour noyau un groupe alg\'ebrique. Un groupe interpr\'etable est, \`a isog\'enie pr\`es, l'extension des points E-rationnels d'un groupe alg\'ebrique par un groupe interpr\'etable, qui est lui le quotient d'un groupe alg\'ebrique par les points E-rationnels d'un sous-groupe alg\'ebrique., Comment: in French

Binary programs with a quadratic objective function are NP-hard in general, even if the linear optimization problem over the same feasible set is tractable. In this paper, we address such problems by computing quadratic global underestimators of the objective function that are separable but not necessarily convex. Exploiting the binary constraint on the variables, a minimizer of the separable underestimator over the feasible set can be computed by solving an appropriate linear minimization problem over the same feasible set. Embedding the resulting lower bounds into a branch-and-bound framework, we obtain an exact algorithm for the original quadratic binary program. The main practical challenge is the fast computation of an appropriate underestimator, which in our approach reduces to solving a series of semidefinite programs. We exploit the special structure of the resulting problems to obtain a tailored coordinate-descent method for their solution. Our extensive experimental results on various quadratic combinatorial optimization problems show that our approach outperforms both CPLEX and the related QCR method as well as the SDP-based software BiqCrunch on instances of the quadratic shortest path problem and the quadratic assignment problem.

An integer n is said to be y-friable if its largest prime factor $P^+(n)$ is less than y. In this paper, it is shown that the y-friable integers less than x have a weak exponent of distribution at least $3/5-\varepsilon$ when $(\log x)^c\leq y\leq x^{1/c}$ for some $c=c(\varepsilon)\geq 1$, that is, they are well distributed in the residue classes of a fixed integer $a$, on average over moduli $\leq x^{3/5-\varepsilon}$ for each fixed $a\neq 0$ and $\varepsilon>0$. We present an application to the estimation of the sum $\sum_{2\leq n\leq x, P^+(n)\leq y}\tau(n-1)$ when $(\log x)^c\leq y$. This follows and improves on previous work of Fouvry and Tenenbaum. Our proof combines the dispersion method of Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec, and recent work of Harper on friable integers in arithmetic progressions., Comment: 27 pages, in French, English abstract

Polarized and $G$-polarized CR manifolds are smooth manifolds endowed with a double structure: a real foliation $\Cal F$ (given by the action of a Lie group $G$ in the $G$-polarized case) and a transverse CR distribution $(E,J)$. Polarized means that $(E,J)$ is roughly speaking invariant by $\Cal F$. 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., Comment: In French. Improved statements. Main Theorems 10.1 and 13.1 are now proved without any metric condition. Also, some remarks added, typos removed and some references added

We give a proof and extension of two formulas of Frobenius and Stickelberger of Differential Calculus that they used in a fundamental paper concerning elliptic functions theory. Our main ingredient is the introduction of a bilinear form which is a vast generalization of Leibniz formula. This bilinear form is also connected to the Lagrange product formula. As a corollary, we give a different proof of a theorem of P.J. Olver., 26 pages, in French

International audience; We give a more building-oriented and somewhat simpler proof of the `saturation' theorem of Kapovich and Millson for any complex semisimple group. The main difference with their approach lies in the combinatorial part of the proof. We state a theorem of folding/unfolding triangles in the affine building, only in combinatorial terms. For the analytical part, we gather materials that appear in distinct papers of Kapovich, Leeb and Millson to complete the proof

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible system of p^n-th roots of a fixed uniformizer pi of K. As a result, we obtain a new classification of p-adic representations of G_K = Gal(Kbar/K) by some (phi, \tau)-modules. We then make a link between the theory of (phi,tau)-modules discussed above and the so-called theory of (phi,N_nabla)$-modules developped by Kisin. As a corollary, we answer a question of Tong Liu: we prove that, if K is a finite extension of Q_p, every representation of G_K of E(u)-finite height is potentially semi-stable., Comment: 51 pages serious problem in Section 3 fixed; 2010-65

International audience; In this paper we are looking for quantitative estimates for the convergene to equilibrium of non reversible Markov processes, especialy in short times. The models studied are simple enough to get an explicit expression of the L2 distance betweeen the semigroup and the invariant measure throught time and to compare it with the corresponding reversible cases.

In this short paper we try to describe the fundamental contribution of Quillenin the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.

Inventories of extreme floods ar ungauged sites and regional flood frequency analyses: methodological reflexions. This paper presents additional developments about a flood frequency approach proposed by Gaume [2010], that aimed to incorporate available information on extreme floods at ungauged sites in a regional flood frequency analysis. Extreme floods, indeed, may represent a very large additional record length if compared with gauged series, and therefore may highly improve the accuracy of flood quantiles estimates. However, the proposed approach requires to calibrate an index flood relationship (here an exponent of catchment surface), which represents a complement of parametrisation of the regional statistical model. The performances and robustness of this approach are tested here and compared to the conventional regionalisation approach of Hosking [ 1997]. The comparison is based both on simulations and on a case study. The inference procedure used is based on a GEV distribution associated with a specific likelihood formulation and a Bayesian MCMC approach for parameters estimation. The parameters of the index flood relationship and the GEV distribution are all calibrated in the same time using the MCMC algorithm, and therefore the uncertainty associated with the index flood relationship calibration is taken into account. The inference results obtained without incorporation of extreme events are first compared, with focus on the effects of the index flood relationship estimation and on the presence of heterogeneities around this relationship. This first comparison is based on simulations and illustrates some limitations of both of the methods : sensitivity to the length of local series in the case of the Hosking approach, presence of bias for small catchment surfaces and relative sensitivity to heterogeneities in the case of the proposed approach. As far as the available information is limited to gauged series and if heterogeneity remains limited, the two approaches finally show similar performances. The two approaches are then applied to a case study : the Ardèche region in south east of France (168 gauged records at 5 sites and 19 ungauged extremes). This application confirms the very positive effect of the information on extreme floods, that clearly enables to outperform the results based only on gauged series., Cet article présente des développements et une évaluation de l’approche d’analyse régionale des débits proposée par Gaume [ 2010], consistant à incorporer dans l’analyse régionale les informations relatives aux crues extrêmes observées sur des bassins non jaugés. L’information sur les crues extrêmes s’apparente en effet à une longue durée d’enregistrements supplémentaires qui est susceptible d’améliorer grandement l’estimation des quantiles de crue. Toutefois, cette approche nécessite de calibrer une relation d’index de crue (ici un exposant de la surface du bassin versant), ce qui représente un complément de paramétrisation du modèle régional utilisé. Une évaluation des performances et de la robustesse de la méthode sont proposées ici par comparaison à une approche régionale plus classique proposée par Hosking [ 1997]. La procédure d’inférence utilisée s’appuie sur une distribution GEV, associée à une formulation spécifique de la vraisemblance et une approche Bayésienne MCMC pour l’estimation des paramètres. Les paramètres de la relation d’index de crue et de la distribution GEV sont évalués ici conjointement au sein de l’algorithme MCMC, ce qui permet de tenir compte de l’incertitude associée à l’ajustement de la relation d’index de crue. Dans un premier temps, les performances des deux méthodes sont comparées à partir de simulations, sans utiliser d’informations sur les crues extrêmes. La sensibilité aux hétérogénéités autour de la relation d’index de crue est notamment examinée. Dans un deuxième temps, les deux approches sont appliquées à une étude de cas : la région de l’Ardèche (168 années stations sur 5 site et 19 crues extrêmes sur sites non jaugés)., N’guyen Chi Cong, Payrastre Olivier Renaud, Gaume Eric. Inventaires de crues extrêmes sur des sites non jaugés et analyse statistique régionale des débits: réflexions méthodologiques et évaluation des performances. In: Evénements extrêmes fluviaux et maritimes. Leurs variabilités spatiales et chronologiques dans l'ouest de l’Europe. 34èmes journées de l’hydraulique Paris, 1 et 2 février 2012. 2012.

International audience; A society facing a choice problem has also to choose the voting rule itself from a set of different possible voting rules. A voting rule is self-selective if it chooses itself when it is also used in choosing the voting rule. A set of voting rules is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this paper a society which makes a choice from a set of three alternatives {a,b,c} and a set of the three well-known scoring voting rules {Borda, Plurality, Antiplurality}. We will derive an a priori probability for the stability of this triplet of voting rules, under the Impartial Anonymous Culture assumption (IAC). In order to solve this problem, we need to specify Ehrhart polynomials, which count the number of integer points inside a (convex) polytope. We discuss briefly a recent algorithmic solution to this method before applying it. We also discuss the impact of different behavioral assumptions for the voters (consequentialist or nonconsequentialist) on the probability of stability for the triplet {Borda, Plurality, Antiplurality}.

For large-scale woodwind instrument makers, producing instruments with exactly the same playing characteristics is a constant aim. This paper explores manufacturing consistency by comparing five Howarth S10 student model oboes. Psychophysical testing involving nine musicians is carried out to investigate perceived differences in the playing properties of the two Howarth oboes believed to be most dissimilar. Further testing, involving one musician and combinations of the five oboes, provides information regarding the relative playabilities of the instruments at specific pitches. Meanwhile, input impedance measurements are made on the five oboes for fingerings throughout the playing range and their bore profiles are measured. The main findings are (i) the two instruments used in the preliminary psychophysical testing are perceived as identical by most of the musicians, although differences are identified by two players when playing the note F6 and by one player when playing in the lowest register, (ii) a variation in the playability of F6 across the five oboes is due to differences in the elevation of the C key, and (iii) variations in the playing properties in the lowest register are related to input impedance differences which, in turn, appear to be at least partly due to bore profile differences.

LGEP 2011 ID = 879; International audience; The aim of the method detailed in this paper is to get an equivalent thermal model of a stator slot, in order to simplify the calculation of desired temperatures in an electrical machine winding. This study is divided in two steps: First, the equivalent thermal conductivity is deduced from a homogenization of the winding, and next, a discretization is achieved using the finite integration technique considering transient analysis. In order to evaluate the method, results from the equivalent model are compared with finite element simulations considering two slot geometries.