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Asymptotic formula for the multiplicative function
No full textFor a fixed integer , we define the multiplicative functionwhere is the divisorfunction and is the number of distinct prime divisors of . Themain purpose of this paper is the study of the mean value of the function by using elementary methods
The hidden symmetry of Kontsevich's graph flows on the spaces of Nambu-determinant Poisson brackets
No full textKontsevich's graph flows are -- universally for all finite-dimensional affinePoisson manifolds -- infinitesimal symmetries of the spaces of Poissonbrackets. We show that the previously known tetrahedral flow and the recentlyobtained pentagon-wheel flow preserve the class of Nambu-determinant Poissonbi-vectors on and on , including the general case . We detect that the Poisson bracket evolution is trivial in the second Poissoncohomology, , for theNambu-determinant bi-vectors on . For the globalCasimirs and inverse density on, we analyse the combinatorics of their evolution induced by theKontsevich graph flows, namely and with differential-polynomialright-hand sides. Besides the anticipated collapse of these formulas by usingthe Civita symbols (three for the tetrahedron and five for thepentagon-wheel graph cocycle ), as dictated by the behaviour of the inverse density underreparametrizations , we discoveranother, so far hidden discrete symmetry in the construction of these evolutionequations.Comment: Published version; 27+iii pages, 1 figure, 2 tables, 8 research problems; Keywords: Poisson geometry, Nambu-determinant Poisson bracket, Poisson cohomology, symmetry, Kontsevich's graph comple
Matrix continued fractions and Expansions of the Error Function
No full textIn this paper we recall some results and some criteria on the convergence ofmatrix continued fractions. The aim of this paper is to give some propertiesand results of continued fractions with matrix arguments. Then we givecontinued fraction expansions of the error function erf(A) where A is a matrix.At the end, some numerical examples illustrating the theoretical results arediscussed
Geometric Model Checking of Continuous Space
No full textTopological Spatial Model Checking is a recent paradigm where model checkingtechniques are developed for the topological interpretation of Modal Logic. TheSpatial Logic of Closure Spaces, SLCS, extends Modal Logic with reachabilityconnectives that, in turn, can be used for expressing interesting spatialproperties, such as "being near to" or "being surrounded by". SLCS constitutesthe kernel of a solid logical framework for reasoning about discrete space,such as graphs and digital images, interpreted as quasi discrete closurespaces. Following a recently developed geometric semantics of Modal Logic, wepropose an interpretation of SLCS in continuous space, admitting a geometricspatial model checking procedure, by resorting to models based on polyhedra.Such representations of space are increasingly relevant in many domains ofapplication, due to recent developments of 3D scanning and visualisationtechniques that exploit mesh processing. We introduce PolyLogicA, a geometricspatial model checker for SLCS formulas on polyhedra and demonstratefeasibility of our approach on two 3D polyhedral models of realistic size.Finally, we introduce a geometric definition of bisimilarity, proving that itcharacterises logical equivalence
An Ontology based Smart Management of Linguistic Knowledge
No full textoai:episciences.org:jdmdh:9998Natural language processing provides a very significant contribution to various application areas such as multilingual big data, information retrieval, data integration and multilingual web. However, handling linguistic knowledge to develop such lingware applications is a crucial issue, especially for linguistic novice users. To deal with this issue, a "smart" linguistic knowledge management may help the users to understand the meaning, scope and especially the use of related techniques and algorithms. In this paper, (1) we propose a semantic processing of linguistic knowledge based on a multilingual linguistic domain ontology, called LingOnto. Compared to related work, LingOnto does not only handles linguistic data, but also linguistic processing functionalities and linguistic processing features. Besides, it allows, via a reasoning engine, inferring new linguistic knowledge and assisting in the process of proposing lingware applications. This is particularly useful for novice users, but can also provide new perspectives for the expert ones. LingOnto covers the French, English and Arabic languages. (2) We propose also an assisted user friendly ontology visualization tool called LingGraph. It facilitates the interaction with LingOnto. It offers an easy to use interface for users not familiar with ontologies. It is based on a SPARQL pattern-based approach to allow a smart search interaction functionality to visualize only the ontological view corresponding to the user’s needs and preferences. In order to evaluate LingOnto, we apply it to a framework of identifying valid natural language processing pipelines. Finally, we give the results of the carried-out experiments
Further results on Hendry's Conjecture
No full textRecently, a conjecture due to Hendry was disproved which stated that everyHamiltonian chordal graph is cycle extendible. Here we further explore theconjecture, showing that it fails to hold even when a number of extraconditions are imposed. In particular, we show that Hendry's Conjecture failsfor strongly chordal graphs, graphs with high connectivity, and if we relax thedefinition of "cycle extendible" considerably. We also consider the originalconjecture from a subtree intersection model point of view, showing that aresult of Abuieda et al is nearly best possible.Comment: 9 pages, 2 figures. The results in this manuscript were originally presented at the Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM) in 2015. v2: Edited to acknowledge recent similar results obtained by Rong at al (arXiv:2007.04698 [cs.DM]
Comparator automata in quantitative verification
No full textThe notion of comparison between system runs is fundamental in formalverification. This concept is implicitly present in the verification ofqualitative systems, and is more pronounced in the verification of quantitativesystems. In this work, we identify a novel mode of comparison in quantitativesystems: the online comparison of the aggregate values of two sequences ofquantitative weights. This notion is embodied by comparator automata(comparators, in short), a new class of automata that read two infinitesequences of weights synchronously and relate their aggregate values. We show that aggregate functions that can be represented with B\"uchiautomaton result in comparators that are finite-state and accept by the B\"uchicondition as well. Such -regular comparators further lead to genericalgorithms for a number of well-studied problems, including the quantitativeinclusion and winning strategies in quantitative graph games with incompleteinformation, as well as related non-decision problems, such as obtaining afinite representation of all counterexamples in the quantitative inclusionproblem. We study comparators for two aggregate functions: discounted-sum andlimit-average. We prove that the discounted-sum comparator is -regulariff the discount-factor is an integer. Not every aggregate function, however,has an -regular comparator. Specifically, we show that the language ofsequence-pairs for which limit-average aggregates exist is neither-regular nor -context-free. Given this result, we introduce thenotion of prefix-average as a relaxation of limit-average aggregation, and showthat it admits -context-free comparators i.e. comparator automataexpressed by B\"uchi pushdown automata
Impacts sociaux et environnementaux résultant de l'élimination irrégulière des déchets solides dans le Bairro Passaré, à Fortaleza – Ceará – Brésil
No full textAsynchronous wreath product and cascade decompositions for concurrent behaviours
No full textWe develop new algebraic tools to reason about concurrent behaviours modelledas languages of Mazurkiewicz traces and asynchronous automata. These toolsreflect the distributed nature of traces and the underlying causality andconcurrency between events, and can be said to support true concurrency. Theygeneralize the tools that have been so efficient in understanding, classifyingand reasoning about word languages. In particular, we introduce an asynchronousversion of the wreath product operation and we describe the trace languagesrecognized by such products (the so-called asynchronous wreath productprinciple). We then propose a decomposition result for recognizable tracelanguages, analogous to the Krohn-Rhodes theorem, and we prove thisdecomposition result in the special case of acyclic architectures. Finally, weintroduce and analyze two distributed automata-theoretic operations. One, thelocal cascade product, is a direct implementation of the asynchronous wreathproduct operation. The other, global cascade sequences, although conceptuallyand operationally similar to the local cascade product, translates to a morecomplex asynchronous implementation which uses the gossip automaton of Mukundand Sohoni. This leads to interesting applications to the characterization oftrace languages definable in first-order logic: they are accepted by arestricted local cascade product of the gossip automaton and 2-stateasynchronous reset automata, and also by a global cascade sequence of 2-stateasynchronous reset automata. Over distributed alphabets for which theasynchronous Krohn-Rhodes theorem holds, a local cascade product of suchautomata is sufficient and this, in turn, leads to the identification of asimple temporal logic which is expressively complete for such alphabets
Autour de la conjecture de Tate enti\`ere pour certains produits de dimension sur un corps fini
No full textLet be the product of a surface satisfying and of a curve overa finite field. We study a strong form of the integral Tate conjecture for-cycles on . We generalize and give unconditional proofs of severalresults of our previous paper with J.-L. Colliot-Th\'el\`ene.Comment: in French. Improves on the results of arXiv:2001.10515. Final versio