Tropical linear algebra with the Lukasiewicz T-norm

The max-Lukasiewicz semiring is defined as the unit interval [0,1] equipped with the arithmetics "a+b"=max(a,b) and "ab"=max(0,a+b-1). Linear algebra over this semiring can be developed in the usual way. We observe that any problem of the max-Lukasiewicz linear algebra can be equivalently formulated as a problem of the tropical (max-plus) linear algebra. Based on this equivalence, we develop a theory of the matrix powers and the eigenproblem over the max-Lukasiewicz semiring.Comment: 27 page

(K,L)-eigenvectors in max-min algebra

Using the concept of (K,L)-eigenvector, we investigate the structure of the max-min eigenspace associated with a given eigenvalue of a matrix in the max-min algebra (also known as fuzzy algebra). In our approach, the max-min eigenspace is split into several regions according to the order relations between the eigenvalue and the components of x. The resulting theory of (K,L)-eigenvectors, being based on the fundamental results of Gondran and Minoux, allows to describe the whole max-min eigenspace explicitly and in more detail.Comment: New title and abstract, several minor correction

Unsupervised video indexing on audiovisual characterization of persons

Cette thèse consiste à proposer une méthode de caractérisation non-supervisée des intervenants dans les documents audiovisuels, en exploitant des données liées à leur apparence physique et à leur voix. De manière générale, les méthodes d'identification automatique, que ce soit en vidéo ou en audio, nécessitent une quantité importante de connaissances a priori sur le contenu. Dans ce travail, le but est d'étudier les deux modes de façon corrélée et d'exploiter leur propriété respective de manière collaborative et robuste, afin de produire un résultat fiable aussi indépendant que possible de toute connaissance a priori. Plus particulièrement, nous avons étudié les caractéristiques du flux audio et nous avons proposé plusieurs méthodes pour la segmentation et le regroupement en locuteurs que nous avons évaluées dans le cadre d'une campagne d'évaluation. Ensuite, nous avons mené une étude approfondie sur les descripteurs visuels (visage, costume) qui nous ont servis à proposer de nouvelles approches pour la détection, le suivi et le regroupement des personnes. Enfin, le travail s'est focalisé sur la fusion des données audio et vidéo en proposant une approche basée sur le calcul d'une matrice de cooccurrence qui nous a permis d'établir une association entre l'index audio et l'index vidéo et d'effectuer leur correction. Nous pouvons ainsi produire un modèle audiovisuel dynamique des intervenants.This thesis consists to propose a method for an unsupervised characterization of persons within audiovisual documents, by exploring the data related for their physical appearance and their voice. From a general manner, the automatic recognition methods, either in video or audio, need a huge amount of a priori knowledge about their content. In this work, the goal is to study the two modes in a correlated way and to explore their properties in a collaborative and robust way, in order to produce a reliable result as independent as possible from any a priori knowledge. More particularly, we have studied the characteristics of the audio stream and we have proposed many methods for speaker segmentation and clustering and that we have evaluated in a french competition. Then, we have carried a deep study on visual descriptors (face, clothing) that helped us to propose novel approches for detecting, tracking, and clustering of people within the document. Finally, the work was focused on the audiovisual fusion by proposing a method based on computing the cooccurrence matrix that allowed us to establish an association between audio and video indexes, and to correct them. That will enable us to produce a dynamic audiovisual model for each speaker

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book