Episciences.org
Not a member yet
6707 research outputs found
Sort by
Les ateliers relais, sociologie d’un partenariat entre éducation populaire et Éducation nationale: Thèse en sociologie, sous la direction de Thierry Berthet, soutenue le 8 juillet 2021, Aix-Marseille Université (AMU)
No full textPour une publication sur ÉpisciencesRésumé de la thèse d'Alicia Jacquot, intitulée "Les ateliers relais, sociologie d’un partenariat entre éducation populaire et Éducation nationale", sous la direction de Thierry Berthet, soutenue le 8 juillet 2021 à Aix-Marseille Université
Concurrent normals of immersed manifolds
No full textIt is conjectured since long that for any convex body there exists a point in the interior of which belongs to atleast normals from different points on the boundary of . The conjectureis known to be true for . Motivated by a recent results of Y. Martinez-Maure, and an approach by A.Grebennikov and G. Panina, we prove the following: Let a compact smooth-dimensional manifold be immersed in . We assume thatat least one of the homology groups with vanishes. Then under mild conditions, almost every normal line to contains an intersection point of at least normals from differentpoints of , where is the sum of Betti numbers of
Students using programming for pure and applied mathematics investigations
No full textIn this paper, we recount our research on undergraduate mathematics students learning to use programming for mathematics investigation projects. More precisely, we focus on how a particular theoretical perspective (the Instrumental Approach) helps us better understand this student activity. Pulling data from students' and instructors' experiences in a sequence of courses (offered since 2001), our results expose, at the micro and macro levels, how the student activity is organized (through stable 'ways of doing'), and highlights the complexity of this activity (as an intertwined web of 'ways of doing' involving a combination of both mathematics and programming competencies). We end with concrete recommendations to instructors.Dans cet article, nous présentons notre recherche sur les étudiants de premier cycle en mathématiques apprenant à utiliser la programmation pour des projets d'investigation en mathématiques. Plus précisément, nous nous concentrons sur la façon dont une certaine perspective théorique (l'Approche instrumentale) nous aide à mieux comprendre cette activité de l’étudiant. S’appuyant sur des données des expériences d’étudiants et d’instructeurs dans une séquence de cours (offerts depuis 2001), nos résultats décrivent comment l'activité de l’étudiant est organisée (par le biais de «façons de faire» stables), et met en évidence la complexité de cette activité (comme un réseau entrelacé de « manières de faire » impliquant une combinaison de compétences en mathématiques et en programmation). Nous terminons par quelques recommandations concrètes pour les instructeurs
Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms
No full textGiven a boolean predicate on labeled networks (e.g., proper coloring,leader election, etc.), a self-stabilizing algorithm for is a distributedalgorithm that can start from any initial configuration of the network (i.e.,every node has an arbitrary value assigned to each of its variables), andeventually converge to a configuration satisfying . It is known thatleader election does not have a deterministic self-stabilizing algorithm usinga constant-size register at each node, i.e., for some networks, some of theirnodes must have registers whose sizes grow with the size of the networks.On the other hand, it is also known that leader election can be solved by adeterministic self-stabilizing algorithm using registers of bits per node in any -node bounded-degree network. We show that this latterspace complexity is optimal. Specifically, we prove that every deterministicself-stabilizing algorithm solving leader election must use \Omega(\log \logn)-bit per node registers in some -node networks. In addition, we show thatour lower bounds go beyond leader election, and apply to all problems thatcannot be solved by anonymous algorithms.Comment: Final journal version for DMTCS (Conference version at OPODIS 2021
The solutions of classical and nonlocal nonlinear Schr\"{o}dinger equations with nonzero backgrounds: Bilinearisation and reduction approach
No full textIn this paper we develop a bilinearisation-reduction approach to derivesolutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS)equations with nonzero backgrounds. We start from the second orderAblowitz-Kaup-Newell-Segur coupled equations as an unreduced system. With apair of solutions we bilinearize the unreduced system and obtainsolutions in terms of quasi double Wronskians. Then we implement reductions byintroducing constraints on the column vectors of the Wronskians and finallyobtain solutions to the reduced equations, including the classical NLS equationand the nonlocal NLS equations with reverse-space, reverse-time andreverse-space-time, respectively. With a set of plane wave solution as a background solution, we present explicit formulae for these columnvectors. As examples, we analyze and illustrate solutions to the focusing NLSequation and the reverse-space nonlocal NLS equation. In particular, we presentformulae for the rouge waves of arbitrary order for the focusing NLS equation.Comment: 44 pages, 11 figure
Completeness of Nominal PROPs
No full textWe introduce nominal string diagrams as string diagrams internal in thecategory of nominal sets. This leads us to define nominal PROPs and nominalmonoidal theories. We show that the categories of ordinary PROPs and nominalPROPs are equivalent. This equivalence is then extended to symmetric monoidaltheories and nominal monoidal theories, which allows us to transfercompleteness results between ordinary and nominal calculi for string diagrams.Comment: arXiv admin note: text overlap with arXiv:1904.0753
Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
No full textA Rota-Baxter Leibniz algebra is a Leibniz algebra equipped with a Rota-Baxter operator . We define representation and dualrepresentation of Rota-Baxter Leibniz algebras. Next, we define a cohomologytheory of Rota-Baxter Leibniz algebras. We also study the infinitesimal andformal deformation theory of Rota-Baxter Leibniz algebras and show that ourcohomology is deformation cohomology. Moreover, We define an abelian extensionof Rota-Baxter Leibniz algebras and show that equivalence classes of suchextensions are related to the cohomology groups.Comment: 25 Page
Sufficient Statistics and Split Idempotents in Discrete Probability Theory
No full textA sufficient statistic is a deterministic function that captures an essentialproperty of a probabilistic function (channel, kernel). Being a sufficientstatistic can be expressed nicely in terms of string diagrams, as Tobias Fritzshowed recently, in adjoint form. This reformulation highlights the role ofsplit idempotents, in the Fisher-Neyman factorisation theorem. Examples of asufficient statistic occur in the literature, but mostly in continuousprobability. This paper demonstrates that there are also several fundamentalexamples of a sufficient statistic in discrete probability. They emerge aftersome combinatorial groundwork that reveals the relevant dagger splitidempotents and shows that a sufficient statistic is a deterministic daggerepi
Call-By-Name Is Just Call-By-Value with Delimited Control
No full textDelimited control operator shift0 exhibits versatile capabilities: it canexpress layered monadic effects, or equivalently, algebraic effects. Little didwe know it can express lambda calculus too! We present , acall-by-value lambda calculus extended with shift0 and control delimiter with carefully crafted reduction theory, such that the lambda calculus withbeta and eta reductions can be isomorphically embedded into viaa right inverse of a continuation-passing style translation. While call-by-namereductions of lambda calculus can trivially simulate its call-by-value version,we show that addition of shift0 and is the golden mean of expressivepower that suffices to simulate beta and eta reductions while still admitting asimulation back. As a corollary, calculi , , and all correspond equationally
-quasicontinuous spaces
No full textIn this paper, as a common generalization of -continuous spaces and-quasicontinuous posets, we introduce the concepts of-quasicontinuous spaces and -convergence of nets forarbitrary topological spaces by the cuts. Some characterizations of-quasicontinuity of spaces are given. The main results are: (1) a spaceis -quasicontinuous if and only if its weakly irreducible topology ishypercontinuous under inclusion order; (2) A space is-quasicontinuous if and only if the -convergence in is topological