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Modified double brackets and a conjecture of S. Arthamonov
No full textAround 20 years ago, M. Van den Bergh introduced double Poisson brackets asoperations on associative algebras inducing Poisson brackets under therepresentation functor. Weaker versions of these operations, called modifieddouble Poisson brackets, were later introduced by S. Arthamonov in order toinduce a Poisson bracket on moduli spaces of representations of thecorresponding associative algebras. Moreover, he defined two operations that heconjectured to be modified double Poisson brackets. The first case of thisconjecture was recently proved by M. Goncharov and V. Gubarev motivated by thetheory of Rota-Baxter operators of nonzero weight. We settle the conjecture byrealising the second case as part of a new family of modified double Poissonbrackets. These are obtained from mixed double Poisson algebras, a new class ofalgebraic structures that are introduced and studied in the present work.Comment: v4: Journal versio
A cone-theoretic barycenter existence theorem
No full textWe show that every continuous valuation on a locally convex, locallyconvex-compact, sober topological cone has a barycenter. Thisbarycenter is unique, and the barycenter map is continuous, hence isthe structure map of a -algebra, i.e., anEilenberg-Moore algebra of the extended valuation monad on the category of topological spaces; it is, in fact, the unique \mathbf V_{\mathrmw}-algebra that induces the cone structure on
History-deterministic Timed Automata
No full textWe explore the notion of history-determinism in the context of timed automata(TA) over infinite timed words. History-deterministic (HD) automata are thosein which nondeterminism can be resolved on the fly, based on the runconstructed thus far. History-determinism is a robust property that admitsdifferent game-based characterisations, and HD specifications allow forgame-based verification without an expensive determinization step. We show that the class of timed -languages recognized by HD timedautomata strictly extends that of deterministic ones, and is strictly includedin those recognised by fully non-deterministic TA. For non-deterministic timed automata it is known that universality is alreadyundecidable for safety/reachability TA. For history-deterministic TA witharbitrary parity acceptance, we show that timed universality, inclusion, andsynthesis all remain decidable and are EXPTIME-complete. For the subclass of TA with safety or reachability acceptance, one can decide(in EXPTIME) whether such an automaton is history-deterministic. If so, it caneffectively determinized without introducing new automaton states
Asynchronous Session-Based Concurrency: Deadlock-freedom in Cyclic Process Networks
No full textWe tackle the challenge of ensuring the deadlock-freedom property formessage-passing processes that communicate asynchronously in cyclic processnetworks. Our contributions are twofold. First, we present AsynchronousPriority-based Classical Processes (APCP), a session-typed process frameworkthat supports asynchronous communication, delegation, and recursion in cyclicprocess networks. Building upon the Curry-Howard correspondences between linearlogic and session types, we establish essential meta-theoretical results forAPCP, most notably deadlock freedom. Second, we present a new concurrent-calculus with asynchronous session types, dubbed LASTn. We illustrateLASTn by example and establish its meta-theoretical results; in particular, weshow how to soundly transfer the deadlock-freedom guarantee from APCP. To thisend, we develop a translation of terms in LASTn into processes in APCP thatsatisfies a strong formulation of operational correspondence
Contribution à la définition de la notion de port territorial : l’approche juridique
No full textFrom a legal point of view, a territorial port seems to be similar to a decentralised port. Unfortunately, the concept of local public interest, which justifies the exercise of port powers by local authorities, is difficult to define. We will therefore rely on the mirror concept of state port to try to identify the criteria for defining decentralised ports. This analysis will lead us to question the relevance of understanding territorial ports as ports of lesser importance in terms of economic development or territorial planning.Du point de vue juridique, la notion de port territorial semble s’assimiler à celle de port décentralisé. L’intérêt public local qui justifie l’exercice de compétences portuaires par les collectivités territoriales apparait toutefois difficile à conceptualiser, si bien que l’on préfèrera s’appuyer sur la notion miroir de port étatique pour tenter d’identifier, en négatif, les critères de définition des ports décentralisés. Cette analyse conduira à s’interroger sur la pertinence de l’appréhension des ports territoriaux comme des ports de moindre importance au regard des enjeux nationaux de développement économique ou d’aménagement du territoire
Préface
No full textLe volume que nous proposons ici à l'attention des universitaires et plus généralement de toutes celles et ceux qui s'intéressent à la culture russe est à la fois une collection d'études consacrées aux médiatrices — traductrices, hôtesses de salon, éditrices, rédactrices en chef, membres des comités de rédaction, critiques, journalistes, correctrices, auxquelles on peut ajouter les préceptrices ou les enseignantes — et un hommage collectif à ces « petites mains » toujours négligées, parfois anonymes, qui ont pourtant participé pleinement à la construction de la littérature classique russe du XIXe siècle et de sa future historiographie
Representing Matroids over the Reals is -complete
No full textA matroid is an ordered pair , where is a finite set calledthe ground set and a collection called the independent setswhich satisfy the conditions: (i) , (ii) implies , and (iii) and implies thatthere is an such that . The rank of amatroid is the maximum size of an independent set. We say that a matroid is representable over the reals if there is a map such that if and only if forms a linearly independent set. We study the problem of matroid realizability over the reals. Given a matroid, we ask whether there is a set of points in the Euclidean spacerepresenting . We show that matroid realizability is \exists \mathbbR-complete, already for matroids of rank 3. The complexity class can be defined as the family of algorithmic problems that ispolynomial-time is equivalent to determining if a multivariate polynomial withintegers coefficients has a real root. Our methods are similar to previous methods from the literature. Yet, theresult itself was never pointed out and there is no proof readily available inthe language of computer science.Comment: v2 and v3: Minor changes v4: Final version, to appear in DMTC
On equationally Noetherian predicate structures
No full textIn this paper, we prove a criterion for a predicate structure to beequationally Noetherian.Comment: 13 pages, 4 figures. Published in the journal of Groups, Complexity, Cryptolog
Executable First-Order Queries in the Logic of Information Flows
No full textThe logic of information flows (LIF) has recently been proposed as a generalframework in the field of knowledge representation. In this framework, tasks ofprocedural nature can still be modeled in a declarative, logic-based fashion.In this paper, we focus on the task of query processing under limited accesspatterns, a well-studied problem in the database literature. We show that LIFis well-suited for modeling this task. Toward this goal, we introduce a variantof LIF called "forward" LIF (FLIF), in a first-order setting. FLIF takes anovel graph-navigational approach; it is an XPath-like language thatnevertheless turns out to be equivalent to the "executable" fragment offirst-order logic defined by Nash and Lud\"ascher. One can also classify thevariables in FLIF expressions as inputs and outputs. Expressions where inputsand outputs are disjoint, referred to as io-disjoint FLIF expressions, allow aparticularly transparent translation into algebraic query plans that respectthe access limitations. Finally, we show that general FLIF expressions canalways be put into io-disjoint form
On the free metabelian Novikov and metabelian Lie-admissible algebras
No full textIn this paper, we consider Lie-admissible algebras, which are free Novikovand free Lie-admissible algebras with an additional metabelian identity. Weconstruct a linear basis for both free metabelian Novikov and free metabelianLie-admissible algebras. Additionally, we describe a space of symmetricpolynomials for both the free metabelian Novikov algebra and the freemetabelian Lie-admissible algebra.Comment: 10 p, Journal versio