Zeta Functions and the (Linear) Logic of Markov Processes

The author introduced models of linear logic known as ''Interaction Graphs''which generalise Girard's various geometry of interaction constructions. Inthis work, we establish how these models essentially rely on a deep connectionbetween zeta functions and the execution of programs, expressed as a cocycle.This is first shown in the simple case of graphs, before begin lifted todynamical systems. Focussing on probabilistic models, we then explain how thenotion of graphings used in Interaction Graphs captures a natural class ofsub-Markov processes. We then extend the realisability constructions and thenotion of zeta function to provide a realisability model of second-order linearlogic over the set of all (discrete-time) sub-Markov processes

Representing Matroids over the Reals is ∃R\exists \mathbb R-complete

A matroid $M$ is an ordered pair $(E,I)$, where $E$ is a finite set calledthe ground set and a collection $I\subset 2^{E}$ called the independent setswhich satisfy the conditions: (i) $\emptyset \in I$, (ii) $I'\subset I \in I$implies $I'\in I$, and (iii) $I_1,I_2 \in I$ and $|I_1| < |I_2|$ implies thatthere is an $e\in I_2$ such that $I_1\cup \{e\} \in I$. The rank $rank(M)$ of amatroid $M$ is the maximum size of an independent set. We say that a matroid$M=(E,I)$ is representable over the reals if there is a map $\varphi \colon E\rightarrow \mathbb{R}^{rank(M)}$ such that $I\in I$ if and only if$\varphi(I)$ forms a linearly independent set. We study the problem of matroid realizability over the reals. Given a matroid$M$, we ask whether there is a set of points in the Euclidean spacerepresenting $M$. We show that matroid realizability is \exists \mathbbR-complete, already for matroids of rank 3. The complexity class $\exists\mathbb R$ 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

Solitons in 4d Wess-Zumino-Witten models -- Towards unification of integrable systems --

We construct soliton solutions of the four-dimensional Wess-Zumino-Witten(4dWZW) model in the context of a unified theory of integrable systems withrelation to the 4d/6d Chern-Simons theory. We calculate the action density ofthe solutions and find that the soliton solutions behave as the KP-typesolitons, that is, the one-soliton solution has a localized action/energydensity on a 3d hyperplane in 4-dimensions (soliton wall) and the n-solitonsolution describes n intersecting soliton walls with phase shifts. We note thatthe Ward conjecture holds mostly in the split signature (+,+,-,-). Furthermore,the 4dWZW model describes the string field theory action of the open N=2 stringtheory in the four-dimensional space-time with the split signature and henceour soliton solutions would describe a new-type of physical objects in the N=2string theory. We discuss instanton solutions in the 4dWZW model as well.Noncommutative extension and quantization of the unified theory of integrablesystems are also discussed.Comment: 19 pages, 2 figures; typos corrected, references added, version to appear in Proceedings of the OCNMP-2024 Conference: Bad Ems, 23-29 June 202

Advanced Model Consistency Restoration with Higher-Order Short-Cut Rules

Sequential model synchronisation is the task of propagating changes from onemodel to another correlated one to restore consistency. It is challenging toperform this propagation in a least-changing way that avoids unnecessarydeletions (which might cause information loss). From a theoretical point ofview, so-called short-cut (SC) rules have been developed that enable provablycorrect propagation of changes while avoiding information loss. However, to beable to react to every possible change, an infinite set of such rules might benecessary. Practically, only small sets of pre-computed basic SC rules havebeen used, severely restricting the kind of changes that can be propagatedwithout loss of information. In this work, we close that gap by developing anapproach to compute more complex required SC rules on-the-fly duringsynchronisation. These higher-order SC rules allow us to cope with more complexscenarios when multiple changes must be handled in one step. We implemented ourapproach in the model transformation tool eMoflon. An evaluation shows that theoverhead of computing higher-order SC rules on-the-fly is tolerable and attimes even improves the overall performance. Above that, completely newscenarios can be dealt with without the loss of information

Женщины издательницы и редакторы русскоязычной периодической печати в России XIX века: к постановке вопроса

The participation of women in the development of periodicals in 19th-century Russia has not been ignored by researchers. Many works were devoted to this subject at the turn of the 21st century. However, only a tiny minority were specifically dedicated to female publishers and editors-in-chief. The purpose of our research is to give an overview of the matter, presenting the most complete list possible of pre-1890 women editors and publishers of periodicals in Russia, to examine the dynamics of the evolution of the number of publisher and editor-in-chief positions that they occupied, and to analyse the diachronic aspect of the periodicals’ geographical distribution. In addition, the question of the typology of periodicals is raised and a first attempt is made to assess the impact of women publishers and editors-in-chief of periodicals on the literary process in 19th-century Russia.La participation des femmes au développement de la presse périodique écrite dans la Russie du XIXe siècle n’est pas ignorée des chercheurs. Au tournant du XXIe siècle, de nombreux travaux consacrés à ce sujet ont vu le jour. Cependant, seule une infime minorité d’entre eux est spécifiquement dédiée aux éditrices et rédactrices en chef. La visée de mon étude est de constituer une liste, lа plus exhaustive possible à ce jour, des noms des éditrices et rédactrices en chef, d’examiner la dynamique de l’évolution du nombre de postes qu’elles occupèrent, et d’analyser l’aspect diachronique de la répartition géographique de ces périodiques. La question de la typologie des périodiques est soulevée, et une première estimation chiffrée de l’influence des éditrices et rédactrices en chef de la presse périodique sur le processus littéraire dans la Russie du XIXe siècle est entreprise.Участие женщин в развитии периодической печати перестало быть белым пятном на карте российской журналистики XIX века. На пороге XXI века появилось немало работ, посвященных этому вопросу. Тем не менее, деятельность женщин редакторов и издателей стала предметом специфического анализа лишь в очень малой их части. Задача нашего исследования – дать общее состояние дела, представив, по возможности, наиболее полный список женщин редакторов и издателей периодики в России до 1890 г. К обсуждению представлена динамика эволюции количества мест, занятых женщинами в этой области, и диахроника географического распределения периодических издательств, в которых они работали. Помимо этого, затронут вопрос типологии печатных органов и предпринята первая попытка оценить воздействие женщин-руководителей периодики на литературный процесс в России XIX века

Lasserre Hierarchy for Graph Isomorphism and Homomorphism Indistinguishability

We show that feasibility of the $t^\text{th}$ level of the Lasserresemidefinite programming hierarchy for graph isomorphism can be expressed as ahomomorphism indistinguishability relation. In other words, we define a class$\mathcal{L}_t$ of graphs such that graphs $G$ and $H$ are not distinguished bythe $t^\text{th}$ level of the Lasserre hierarchy if and only if they admit thesame number of homomorphisms from any graph in $\mathcal{L}_t$. By analysingthe treewidth of graphs in $\mathcal{L}_t$, we prove that the $3t^\text{th}$level of Sherali--Adams linear programming hierarchy is as strong as the$t^\text{th}$ level of Lasserre. Moreover, we show that this is best possiblein the sense that $3t$ cannot be lowered to $3t-1$ for any $t$. The same resultholds for the Lasserre hierarchy with non-negativity constraints, which wesimilarly characterise in terms of homomorphism indistinguishability over afamily $\mathcal{L}_t^+$ of graphs. Additionally, we give characterisations oflevel-$t$ Lasserre with non-negativity constraints in terms of logicalequivalence and via a graph colouring algorithm akin to the Weisfeiler--Lemanalgorithm. This provides a polynomial time algorithm for determining if twogiven graphs are distinguished by the $t^\text{th}$ level of the Lasserrehierarchy with non-negativity constraints.Comment: Full version. 36 pages, 6 figure

Une évaluation expérimentale de choix des paramètres de prévisions SSA

Six time series related to atmospheric phenomena are used as inputs for experiments offorecasting with singular spectrum analysis (SSA). Existing methods for SSA parametersselection are compared throughout their forecasting accuracy relatively to an optimal aposteriori selection and to a naive forecasting methods. The comparison shows that awidespread practice of selecting longer windows leads often to poorer predictions. It alsoconfirms that the choices of the window length and of the grouping are essential. Withthe mean error of rainfall forecasting below 1.5%, SSA appears as a viable alternative forhorizons beyond two weeks.Six séries temporelles ont servi pour des évaluations expérimentales, en fonction des paramètres choisis, d'exactitude de prévisions de phénomènes atmosphériques par la méthode d'analyse de spectre singulier (SSA). Les méthodes les plus connues de sélection automatique des ces paramètres ont été comparées avec une sélection optimale a posteriori et des méthodes de prévision naïves. On constate notamment qu'une pratique répandue d'utiliser des fenêtres plus larges conduit souvent à des prévisions de médiocre qualité. On confirme aussi que le choix du groupement est capital. Avec l'erreur moyenne observée en dessous de 1,5% de prévisions de pluviométrie pour des horizons au delà de deux semaines, la SSA apparaît comme une alternative viable à d'autres méthodes de prévision

Les carrières de trachyte de la chaîne des Puys (Massif central, France). Production et diffusion des sarcophages au premier Moyen Âge (Ve–IXe s.)

Dans le cadre d’un Programme collectif de recherche (PCR), une équipe pluridisciplinaire étudie les conditions d’exploitation, d’utilisation et de diffusion d’une lave, extraite des volcans auvergnats, le trachyte. Au sein de ce collectif, l’étude archéologique de trois carrières de sarcophages du premier Moyen Âge a permis de faire le lien entre les lieux de fabrication et les nécropoles grâce à une signature géologique discriminante entre les carrières. Cette approche renouvelle les problématiques et montre l’exploitation conjointe de plusieurs carrières, dont ont été extraits plusieurs milliers de sarcophages retrouvés en Auvergne mais aussi en Limousin. Leur répartition spatiale montre la proximité des lieux de diffusion avec les anciennes voies romaines, suggérant l’insertion du schéma économique des sarcophages en trachyte dans un réseau déjà en place, soit qu’il ait été réactivé, soit qu’il n’ait jamais réellement disparu

La contribution des environnements technologiques à l’enseignement de la preuve

This contribution discusses the use of a dynamic geometry environment to promote students’ introduction to mathematical proof. Within the framework of semiotic mediation theory, I explore, on the one hand, the link between available computer tools and the personal meanings emerging from their use in classroom activities and, on the other hand, the mathematical notions that are the subject of teaching. The discussion uses three interrelated perspectives – epistemological, cognitive and didactic – to elaborate the outcomes of a number of long-term teaching experiences in secondary classrooms. Illustrative examples are presented, drawn from research studies conducted in previous years and still ongoing.Cette contribution traite de l’utilisation d’un environnement de géométrie dynamique pour favoriser l’introduction des élèves à la preuve mathématique. Dans le cadre de la théorie de la médiation sémiotique, j’explore, d’une part, le lien entre les outils informatiques disponibles et les significations personnelles émergeant de leur utilisation dans les activités en classe et, d’autre part, les notions mathématiques qui font l’objet de l’enseignement. La discussion utilise trois perspectives interdépendantes – épistémologique, cognitive et didactique – pour élaborer les résultats d’un certain nombre d’expériences d’enseignement sur le long terme dans des salles de classe du secondaire. Des exemples illustratifs sont présentés, tirés des études de recherche conduites au cours des années précédentes et toujours en cours