Combinatorial automata theory can be seen as studying reachability in transformation semigroups. An interesting way of generalising this setting is by lifting it up to reachability in finite semigroups of rational matrices. Here, besides finite automata theory, other areas come into play, for example weighted automata, algebraic number theory, and multilinear algebra. I will explain several nice questions (such as mortality and minimum rank) that transfer from transformation semigroups to finite matrix semigroups. I will also explain the lack of mathematical structure that is brought by certain PSPACE-complete transformation semigroup problems.
Tag : Français
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We then give upper and lower bounds of minimal subword entropy for words of fixed length in a fixed alphabet, and also showing that minimal subword entropy per letter has a limit value. A better upper bound of minimal subword entropy for a binary alphabet is then given by looking at certain families of periodic words. We also give some conjectures based on experimental observations.
In this talk, I present results and techniques to measure the Hausdorff dimension of two types of random geometries. The first is a generalization of the mating of trees approach. The original mating of trees encodes Liouville Quantum Gravity on the 2-sphere in terms of a correlated Brownian motion describing a pair of random trees. We extended this approach to higher-dimensional correlated Brownian motions, leading to a family of non-planar random graphs that belong to new universality classes of scale-invariant random geometries. The second example of random geometry is the D-random feuilletage, which for D=2 agrees with a family of planar maps, while for D>2, these represent new universality classes of random geometries. We developed numerical methods to efficiently simulate these random graphs and explore their scaling limits through distance measurements, allowing us to estimate Hausdorff dimensions.
Certains logiciels de gestion de versions comme Git et Mercurial organisent l’historique d’un projet sous la forme d’un graphe orienté acyclique, les sommets représentant les différentes versions du projet et les arêtes indiquant les changements intervenus entre elles.
À l’origine, avec Paul Dorbec et Romain Lecoq (Univ. Caen Normandie), on a analysé la complexité dans le pire des cas d’un algorithme de graphes issu de Git, qui s’appelle git bisect. Cet algorithme sert à débusquer l’introduction d’un bug dans un graphe. Nous avons montré que git bisect avait une stratégie totalement catastrophique pour certains graphes particuliers. Mais qu’en est-il en moyenne ?
Derrière cette épineuse question, il faut d’abord s’interroger sur la forme typique d’un graphe représentant l’historique d’un projet dans un logiciel de gestion de versions. En théorie n’importe quel graphe acyclique peut être obtenu, mais dans la pratique, la forme de ces graphes est contrainte par des conventions de « bonne pratique ».
Je vais donc introduire une famille de graphes à la fois simples et réalistes, qu’on a appelés « graphes de Git ». Je vais alors vous présenter le problème de comptage de ces graphes, ainsi que des générateurs aléatoires. Il s’agit ici d’une collaboration avec Martin Pépin Univ. Caen Normandie.
L’intégration de l’IoT et des réseaux futurs a révolutionné divers secteurs en permettant des environnements intelligents, des communications fiables et en facilitant l’échange massif données en temps réel. Cependant, cette adoption généralisée entraîne également des risques majeurs en matière de sécurité et de vie privée qui doivent être abordés pour garantir des déploiements IoT sûrs et fiables. La présentation explore quelques travaux abordant des problématiques de sécurité et vie privée dans des environnements IoT tels que les applications médicales et les réseaux véhiculaires.
5G is being to be deployed and commercial service already started. The full exploitation of its capabilities is far to be achieved because so far only the physical layer innovations were actually implemented and in limited bandwidth while all the network management capabilities are not yet (fully) enjoyed. The last years have been dedicated to progress in the design and development of innovative services and applications to properly and fruitfully use the satellite to complement the terrestrial component in order to fully satisfy the requirements of 5G. To this aim, the adaption of the communication standard has been pursued. The description and the outcomes of some ESA projects funded in this frame will be briefly presented. Last but not least the advent of megaconstellations seems to be the technical solution but on the basis of available information some considerations will be shared.
The study presents an OpenAirInterface-based 5G-V2X testbed designed for evaluating vehicle-to-everything (V2X) communication scenarios in 5G Standalone (SA) networks. Key components include a 5G Core Network (CN), a gNodeB at the Radio Access Network (RAN), and JetRacer Pro robot cars equipped with NVIDIA Jetson Nano platforms. The testbed integrates network slicing policies and advanced mechanisms like deep learning (DL) and reinforcement learning (RL) for detecting and mitigating network attacks, such as DDoS and radio jamming. It also explores autonomous mobility models using convolutional neural networks (CNNs) to map camera data to vehicle commands, offering a robust framework for testing autonomous V2X solutions in realistic environments.
Les plateformes Bec3 sont des infrastructures innovantes conçues pour répondre aux besoins croissants en matière de calcul distribué, de gestion de données massives et de connectivité avancée. Ce travail explore les caractéristiques clés de ces plateformes, notamment leur modularité, leur interopérabilité et leur capacité à s’adapter à des environnements dynamiques et hétérogènes. En s’appuyant sur des technologies de pointe, les plateformes Bec3 permettent une gestion optimisée des ressources, une fiabilité accrue des systèmes, et un support étendu pour les applications critiques. Ces plateformes ouvrent de nouvelles perspectives dans divers domaines, tels que l’Internet des objets, l’intelligence artificielle, et les systèmes embarqués.
AI applications embedded in a critical system face significant real-time scheduling challenges due to several factors.
One of them is that classic task models are not directly able to model accurately such systems. Another factor is that the
variability of execution time can be influenced by various factors that exceed the variability factors considered in real-
time. Finally, new benchmarks are needed in order to evaluate the performances of real-time models and scheduling algorithms dedicated to embedded AI. In this presentation, we specify research directions in order to be able to deploy real-time CNN inference over NVIDIA GPU.
Ensuring reliable participation in UAV-enabled federated edge learning on non-IID (non-Independent and Identically Distributed) data is a complex challenge due to the variability in data distribution and the mobility of UAVs. This research focuses on developing strategies to enhance the reliability and efficiency of federated learning in such settings. By addressing issues such as data heterogeneity, communication overhead, and resource constraints, the study proposes novel mechanisms to optimize model aggregation and training processes. These advancements aim to enable robust and scalable federated learning frameworks, facilitating real-world applications in distributed, dynamic, and resource-constrained environments.