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International audience; The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living beings? Is the so-called “naturalness” of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems? Rosen appears to answer “yes” and to ground this transfer of the concept of “natural equivalence” in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of “category” in his more recent objections to the computational models that have pervaded almost every domain of biology since the 1990s.; L'objectif de cet article est de rendre compte de la justification épistémologique de la proposition faite, dès 1958, par le biomathématicien Robert Rosen d'introduire le concept mathématique de " catégorie " et celui - corrélatif - d'" équivalence naturelle " dans la modélisation mathématique appliquée au vivant. Nos questions sont les suivantes : en quoi la notion mathématique de catégorie permet-elle, selon Rosen, de donner accès à des formalismes plus " naturels " pour la modélisation du vivant ? La naturalité de certaines équivalences (que la notion mathématique de catégorie sert justement à généraliser et à mettre en évidence) est-elle analogue à la naturalité des systèmes vivants ? Rosen semble faire fond sur cette dernière hypothèse, féconde, mais pourtant discutable. Cet article propose ensuite de mesurer l'évolution du discours de Rosen à ce sujet, en particulier dans ses conséquences apparemment décisives pour la critique des modèles computationnels du vivant, modèles aujourd'hui en pleine expansion.

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.

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

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

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

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.

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

The numerical simulation of air flow in a building or a house is certainly a very challenging field of engineering applications. The objectives differ from one application to the other, ranging from the optimization of air conditioning systems in buildings to the study of the propagation of harmful products via the air conditioning system. In this paper, we address the problem of coupling the Navier-Stokes equations for incompressible fluids and a temperature equation. To solve this problem in 3d, we use an anisotropic mesh adaptation strategy. The meshes are generated by a local remeshing techniques based on an anisotropic version of Delaunay kernel. The method is fairly general and applies to other cases as well. We illustrate this problem with an example showing the heating of the last floor of a furnished house.

Admettant l'hypoth\`ese de Schinzel et la finitude des groupes de Tate-Shafarevich des courbes elliptiques sur les corps de nombres, toute intersection lisse de deux quadriques dans l'espace projectif de dimension n satisfait au principe de Hasse si n>4. Le m\^eme r\'esultat vaut pour n=4, c'est-\`a-dire pour les surfaces de del Pezzo de degr\'e 4, lorsque le groupe de Brauer est r\'eduit aux constantes et que la surface est suffisamment g\'en\'erale. ----- Assuming Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups of elliptic curves over number fields, smooth intersections of two quadrics in n-dimensional projective space satisfy the Hasse principle if n>4. The same result holds for n=4, i.e., for del Pezzo surfaces of degree 4, provided the Brauer group is reduced to constants and the surface is sufficiently general., Comment: 6 pages, in French, with abridged English version; old paper (2005), posted for archival purposes

International audience; In this paper, we use reducibility of an univariate polynomial in order to compute efficiently the ideal of relations between its roots.; Dans cet article, nous exploitons la réductibilité d'un polynôme d'une variable pour calculer efficacement l'idéal des relations algébriques entre ses racines.

In this paper, we study the cohomological dimen- sion of groups GS := Gal(KS/K), where KS is the maximal pro-p-extension of a number field K, unramified outside a finite set S of places of K. This dimension is well-understood only when S contains all places above p; in the case where only some of the places above p are contained in S, one can still obtain some results if KS/K contains at least one Zp-extension K1/K. Indeed, in that case, the study of the Zp((Gal(K1/K)))-module Gal(KS/K1) ab allows one to give sucient

International audience; An integer n is called friable when its prime number factorization consists exclusively of (relatively) small factors. Let P(n) be the largest prime factor occurring in this factorization, and let S(x,y) denote the set {n? x,P(n)? y}. This work investigates the asymptotic behaviour of the summatory function Psi_f(x, y):=\sum_{n\in S(x,y)}f(n) when f is a multiplicative arithmetical function satisfying some simple and general conditions concerning its mean behaviour on primes and on powers of primes. One such condition is |\sum_{p? z}f(p)\log p-\kappa z|? Cz/R(z) (z>1), where C is a constant and \kappa>0; requirements on R are technical conditions too long to state here, but satisfied by any "reasonable" positive increasing function. By setting R(z)=(\log z)^\delta in the very general Théorème 2.1, the authors obtain a more general as well as more precise estimate on \Psi_f(x, y) (Corollaire 2.2) than that recently obtained by J. M. Song [Acta Arith. 102 (2002), no. 2, 105--129; MR1889623 (2003a:11123)]. Their next result (Corollaire 2.3) offers a general estimate in the case where f(p) is on average very close to a constant, and contains without loss of precision estimates of the literature for particular functions f, such as the so-called Piltz functions \tau_k, or the function µ^2 where µ is the Möbius function. Then, as a further application of their first result, they establish an Erdös-Wintner theorem on friable integers (Théorème 2.4). They finally mention an application to the case where f(n) is the characteristic function of the integers that can be represented as a sum of two squares of integers (Théorème 2.5); their estimate is uniformly valid for x ? 3, exp((\log x)^{2/5+\epsilon})? y? x. The paper begins with an historical introduction, and is followed by an extensive bibliography on the subject.

National audience; In order to solve efficiently large scale problems arising from the simulation of heterogeneous structures, described up to the microscale, a multiscale computational strategy strongly related to homogenization techniques has been proposed in Ladevèze and Dureisseix, Int. J. for Computational Civil and Structural Engineering 1:18-28, 2000. In this paper, specific tools required to address the case of composite materials are proposed: the use of a third scale and of the periodic media homogenization theory within the areas located far from the boundaries.

Article dans revue scientifique avec comité de lecture.; Nous présentons dans ce travail une méthode, issue de travaux de Bilu et de Bilu et Hanrot, qui permet, sous certaines conditions, de borner de façon bien plus précise que par la méthode de Baker les solutions d'équations diophantiennes superelliptiques. Cette méthode s'applique en particulier à l'équation de Catalan $|x^p -y^q| = 1$, où $q > p$ sont deux premiers, et nous permet de prouver que cette dernière n'a pas de solution non triviale quand $q$ ne divise pas $h^-(\Q(\zeta_p))$. || In this paper we present a method coming from work by Bilu and Bilu and Hanrot which, under certain assumptions, allows one to obtain bounds for the solutions of superelliptic equations that are much sharper than usual bound derived through the use of

International audience; In this paper, we introduce a new numerical scheme for the nonlinear Schrödinger equation and the Davey-Stewartson systems. This is a relaxation type scheme that avoids the resolution of nonlinear systems. We give convergence results for the semi-discret version, locally in time for all data and globally in time for small data.; Dans cette note, nous présentons un nouveau schéma numérique pour l'équation de Schrödinger non linéaire et les systèmes de Davey et Stewartson. C'est un schéma de type relaxation qui supprime la résolution de systèmes non linéaires. Nous donnons des résultats d'existence et de convergence pour une version semi-discrète, localement en temps pour toute donnée initiale et globalement en temps à données petites.

International audience; This paper is devoted to studying the global convergence of the Newton method generalized to systems of non differentiable equations issued from the contact mechanics. In the first part, sorne theoretical results are presented for a typical obstacle problem. In the second part, the behaviour of the Newton algorithm is analyzed by an heuristic approach. In this way, others non linearities, like friction or elastoplasticity, together with unilateral contact, can be taken up.; Cet article présente une étude de la convergence globale de la méthode de Newton généralisée aux systèmes d'équations non différentiables issues de la mécanique du contact. La première partie fournit quelques résultats théoriques pour un problème d'obstacle type. Dans la seconde partie, seule une approche heuristique permet d'appréhender le comportement de l'algorithme de Newton pour des problèmes comportant, outre le contact unilatéral, des non linéarités comme le frottement et l'élasto-plasticité.

International audience; This paper describes change of basis algorithms for symmetric polynomials. We consider below the three usual following bases : monomial forms, symmetric elementary and Newton polynomials. The originality consists in retaining only one representative of the orbit to make the computations. It is a crucial point if we realize that one orbit can contain commonly hundreds of terms. We implemented these algorithms in FRANZLISP with an interface MACSYMA.