In weighted automata theory, many classical results on formal languages have been extended into a quantitative setting. Here, we investigate weighted context-free languages of infinite words, a generalization of $\omega$-context-free languages (as introduced by Cohen and Gold in 1977) and an extension of weighted context-free languages of finite words (that were already investigated by Chomsky and Schützenberger in 1963). As in the theory of formal grammars, these weighted context-free languages, or $\omega$-algebraic series, can be represented as solutions of mixed $\omega$-algebraic systems of equations and by weighted $\omega$-pushdown automata. In our first main result, we show that (mixed) $\omega$-algebraic systems can be transformed into Greibach normal form. We use the Greibach normal form in our second main result to prove that simple $\omega$-reset pushdown automata recognize all $\omega$-algebraic series. Simple $\omega$-reset automata do not use $\epsilon$-transitions and can change the stack only by at most one symbol. These results generalize fundamental properties of context-free languages to weighted context-free languages.

We introduce posets with interfaces (iposets) and generalise their standard serial composition to a new gluing composition. In the partial order semantics of concurrency, interfaces and gluing allow modelling events that extend in time and across components. Alternatively, taking a decompositional view, interfaces allow cutting through events, while serial composition may only cut through edges of a poset. We show that iposets under gluing composition form a category, which generalises the monoid of posets under serial composition up to isomorphism. They form a 2-category when a subsumption order and a lax tensor in the form of a non-commutative parallel composition are added, which generalises the interchange monoids used for modelling series-parallel posets. We also study the gluing-parallel hierarchy of iposets, which generalises the standard series-parallel one. The class of gluing-parallel iposets contains that of series-parallel posets and the class of interval orders, which are well studied in concurrency theory, too. We also show that it is strictly contained in the class of all iposets by identifying several forbidden substructures.

Bienvenue dans l’âge des données. Nos actions sur Internet sont enregistrées au profit d’entreprises qui valorisent ces données et offrent des services en échange. Pouvons-nous faire de même ? Pouvons-nous utiliser les données de l’état pour améliorer notre démocratie ?Depuis 2016, les données publiques doivent être ouvertes àà tous. Les citoyens peuvent les analyser pour mesurer l’efficacité de l’action publique ou pour leur compte personnel. Les data journalistes les utilisent pour nous éclairer, les chercheurs pour comprendre. Ainsi la transparence permet de lutter contre la corruption et les intox, tout comme elle est source de progrès.Ce changement de paradigme, l’accès aux données de l’état, est surtout une opportunité pour participer. Noter un dysfonctionnement permet de suggérer une amélioration, un manque peut être une opportunité économique, même un jeu de données incomplet est une occasion pour tisser des liens entre l’administration, les associations et les citoyens.À travers cet essai, l’auteur nous propose un voyage optimiste dans le monde des données. Chemin faisant, les liens entre ces données et la transparence ouvrent la voie vers une démocratie plus ouverte, plus interactive et donc plus juste.

The price of electricity on the European market is very volatile. This is due both to its mode of production by different sources, each with its own constraints (volume of production, dependence on the weather, or production inertia), and by the difficulty of its storage. Being able to predict the prices of the next day is an important issue, to allow the development of intelligent uses of electricity. In this article, we investigate the capabilities of different machine learning techniques to accurately predict electricity prices. Specifically, we extend current state-of-the-art approaches by considering previously unused predictive features such as price histories of neighboring countries. We show that these features significantly improve the quality of forecasts, even in the current period when sudden changes are occurring. We also develop an analysis of the contribution of the different features in model prediction using Shap values, in order to shed light on how models make their prediction and to build user confidence in models.

In 2021, Casares, Colcombet, and Fijalkow introduced the Alternating Cycle Decomposition (ACD) to study properties and transformations of Muller automata. We present the first practical implementation of the ACD in two different tools, Owl and Spot, and adapt it to the framework of Emerson-Lei automata, i.e., $\omega$-automata whose acceptance conditions are defined by Boolean formulas. The ACD provides a transformation of Emerson-Lei automata into parity automata with strong optimality guarantees: the resulting parity automaton is minimal among those automata that can be obtained by duplication of states. Our empirical results show that this transformation is usable in practice. Further, we show how the ACD can generalize many other specialized constructions such as deciding typeness of automata and degeneralization of generalized Büchi automata, providing a framework of practical algorithms for $\omega$-automata.

In the context of current smart cities, Cooperative Intelligent Transportation Systems (C-ITS) represent one of the main use case scenarios that aim to improve peoples? daily lives. Thus, during the last few years, numerous standards have been adopted to regulate such networks. Within a C-ITS, a large number of messages are exchanged continuously in order to ensure that the different applications operate efficiently. However, these networks can be the target of numerous attacks. The sybil attack is among the most dangerous ones. In a sybil attack, an attacker creates multiple identities and then disguises as several fake stations in order to interfere with the normal operations of the system or profit from provided services. We analyze recently proposed sybil detection approaches regarding their compliance with the current C-ITS standards as well as their evaluation methods. We provide several recommendations such as network and attack models as well as an urban and highway datasets that can be considered in future research in sybil attack detection.

The integration of mathematical morphology operations within convolutional neural network architectures has received an increasing attention lately. However, replacing standard convolution layers by morphological layers performing erosions or dilations is particularly challenging because the min and max operations are not differentiable. P-convolution layers were proposed as a possible solution to this issue since they can act as smooth differentiable approximation of min and max operations, yielding pseudo-dilation or pseudo-erosion layers. In a recent work, we proposed two novel morphological layers based on the same principle as the p-convolution, while circumventing its principal drawbacks, and showcased their capacity to efficiently learn grayscale morphological operators while raising several edge cases. In this work, we complete those previous results by thoroughly analyzing the behavior of the proposed layers and by investigating and settling the reported edge cases. We also demonstrate the compatibility of one of the proposed morphological layers with binary morphological frameworks.

Anomalies represent rare observations that vary significantly from others. Anomaly detection intended to discover these rare observations has the power to prevent detrimental events, such as financial fraud, network intrusion, and social spam. However, conventional anomaly detection methods cannot handle this problem well because of the complexity of graph data (e.g., irregular structures, relational dependencies, node/edge types/attributes/directions/multiplicities/weights, large scale, etc.) [1]. Thanks to the rise of deep learning in solving these limitations, graph anomaly detection with deep learning has obtained an increasing attention from many scientists recently. However, while deep learning can capture unseen patterns of multi-dimensional Euclidean data, there is a huge number of applications where data are represented in the form of graphs. Graphs have been used to represent the structural relational information, which raises the graph anomaly detection problem - identifying anomalous graph objects (i.e., vertex, edges, sub-graphs, and change detection). These graphs can be constructed as a static graph, or a dynamic graph based on the availability of timestamp. Recent years have observed a huge efforts on static graphs, among which Graph Convolutional Network (GCN) has appeared as a useful class of models. A challenge today is to detect anomalies with dynamic structures. In this chapter, we aim at providing methods used for detecting anomalies in static and dynamic graphs using graph analysis, graph embedding, and graph convolutional neural networks. For static graphs we categorize these methods according to plain and attribute static graphs. For dynamic graphs we categorize existing methods according to the type of anomalies that they can detect. Moreover, we focus on the challenges in this research area and discuss the strengths and weaknesses of various methods in each category. Finally, we provide open challenges for graph anomaly detection using graph convolutional neural networks on dynamic graphs.

The Skolem problem is a long-standing open problem in linear dynamical systems: can a linear recurrence sequence (LRS) ever reach 0 from a given initial configuration? Similarly, the positivity problem asks whether the LRS stays positive from an initial configuration. Deciding Skolem (or positivity) has been open for half a century: The best known decidability results are for LRS with special properties (e.g., low order recurrences). On the other hand, these problems are much easier for "uninitialized" variants, where the initial configuration is not fixed but can vary arbitrarily: checking if there is an initial configuration from which the LRS stays positive can be decided by polynomial time algorithms (Tiwari in 2004, Braverman in 2006).