Algebraic coherent confluence and higher-dimensional globular Kleene algebras

We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent proofs by confluence. To this end, we introduce the structure of modal higher-dimensional globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We give a calculation of a coherent Church-Rosser theorem and Newman's lemma in higher-dimensional Kleene algebras. We interpret these results in the context of higher-dimensional rewriting systems described by polygraphs.Comment: Pre-print (second version

Increase of precuneus metabolism correlates with reduction of PTSD symptoms after EMDR therapy in military veterans: an 18F-FDG PET study during virtual reality exposure to war

International audienc

Algebraic coherent confluence and higher globular Kleene algebras

We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and concurrent Kleene algebra. We calculate a coherent Church-Rosser theorem and a coherent Newman's lemma in higher Kleene algebras by equational reasoning. We instantiate these results in the context of higher rewriting systems modelled by polygraphs

Relaxation en réalité virtuelle (une étude pilote dans le trouble anxieux généralisé)

De nouvelles stratégies thérapeutiques sont désormais disponibles pour le traitement du trouble anxieux généralisé (TAG), une pathologie fréquente et invalidante, difficile à traiter. L'objectif principal a été d'étudier l'efficacité de la relaxation en thérapie par réalité virtuelle sur les scores d'anxiété chez des patients souffrrant de TAG. Les objectifs secondaires ont été d'évaluer ses effets sur la dépression, la qualité de vie et l'interaction dans les environnements virtuels spécifiques (niveau de présence et cybermalaise ). Sept patients souffrant de TAG ont participé à cette étude prospective, et avaient la possibilité de choisir parmi six environnements virtuels relaxants pour s'entraîner à trois techniques de relaxation différentes. Plusieurs échelles psychométriques ont été utilisées pour évaluer l'effet du traitement sur les variables principales. Un enregistrement continu du rythme cardiaque a été réalisé durant chaque séance. Cette étude pilote montre une efficacité thérapeutique de la relaxation en réalité virtuelle pour les patients souffrant de TAG, avec une amélioration statistiquement significative des scores d'anxiété, de dépression et de qualité de vie. Ces résultats permettront de proposer d'autres recherches en relaxation par réalité virtuelle dans le TAGAIX-MARSEILLE2-BU Méd/Odontol. (130552103) / SudocSudocFranceF

Les nouveaux appuis technologiques de la psychothérapie cognitivo-comportementale (la réalité virtuelle)

AIX-MARSEILLE2-BU Méd/Odontol. (130552103) / SudocPARIS-BIUM (751062103) / SudocSudocFranceF

Virtual Reality and Fear of Shark Attack: A Case Study for the Treatment of Squalophobia

International audienceResearch treatment protocols are rare regarding an unusual anxiety disorder, namely the fear of sharks (squalophobia). As a possible solution, the effectiveness of virtual reality (VR) exposure therapy for this phobia was tested. The advantage of using VR becomes clearer when a real life set up is impractical, such as exposing a phobic patient to a feared large marine organism, the shark. The effects were evaluated in a single case study involving multiple context-graded aquatic virtual environments with a virtual shark and using affordable VR apparatus and software. Assessment was based on self-report questionnaires. Scores the psychometric instruments exhibited a discernable reduction in fear toward sharks. Such gains were maintained at a 12-month follow-up. Presence rates indicated immersion when confronted to a three-dimensional (3D) virtual shark. This initial study revealed the potential of VR for the treatment of marine biota phobia and its potential to recreate diverse situations for exposure therapy

Convergent presentations and polygraphic resolutions of associative algebras

International audienceSeveral constructive homological methods based on noncommutative Gröbner bases are known to compute free resolutions of associative algebras. In particular, these methods relate the Koszul property for an associative algebra to the existence of a quadratic Gröbner basis of its ideal of relations. In this article, using a higher-dimensional rewriting theory approach, we give several improvements of these methods. We define polygraphs for associative algebras as higher-dimensional linear rewriting systems that generalise the notion of noncommutative Gröbner bases, and allow more possibilities of termination orders than those associated to monomial orders. We introduce polygraphic resolutions of associative algebras, giving a categorical description of higher-dimensional syzygies for presentations of algebras. We show how to compute polygraphic resolutions starting from a convergent presentation, and how these resolutions can be linked with the Koszul property

Persistent homology of directed spaces

In this work, we explore links between natural homology and persistent homology for the classification of directed spaces. The former is an algebraic invariant of directed spaces, a semantic model of concurrent programs. The latter was developed in the context of topological data analysis, in which topological properties of point-cloud data sets are extracted while eliminating noise. In both approaches, the evolution homological properties are tracked through a sequence of inclusions of usual topological spaces. Exploiting this similarity, we show that natural homology may be considered a persistence object, and may be calculated as a colimit of uni-dimensional persistent homologies along traces. Finally, we suggest further links and avenues of future work in this direction