These seminars are common with the Plume team (ENS Lyon) and are held in the seminar room, second floor of the building Le Chablais, on the Bourget-du-lac (Savoy) site or at ENS Lyon.

Next seminar:

Thursday 12th January 2023 at 10h Andrea Frosini (University of Florence),
TBA

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TBA

The seminar of the team LIMD is under the responsibility of Sebastien Tavenas.
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Other years: 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2023, all years together.

Year 2022

Thursday 1st December 2022 at 10h Sébastien Tavenas (LAMA),
Focus sur les derniers résultats de bornes inférieures pour les circuits algébriques

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TBA

Thursday 10th November 2022 at 10h Peio Borthelle (LAMA),
Vers une sémantique intéractive en théorie des types via la coïnduction

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En sémantique des langages, l'équivalence contextuelle de programmes est une notion clef, mais sa définition se prête mal à la manipulation, on cherche donc des modèles corrects et complets lui donnant une expression plus pratique. Les jeux et la sémantique interactive sont de tels modèles, applicables à beaucoup de langages et donnant une équivalence coïnductivement définie. Dans cette présentation je vais esquisser visuellement et de manière intuitive un formalisme de jeux général qui se prête bien à la formalisation dans un assistant de preuve. Je vais également décrire différents genres d'arbres inductifs et coïnductifs ainsi qu'une manière pratique de construire des jeux à partir de composants plus élémentaires.

Thursday 13th October 2022 at 10h Stéphane Breuils (LAMA),
Conjecture of the Characterisation of Bijective Digitized Reflections and Rotations

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In this seminar, I will focus on the characterisation of bijective digitized rotations and reflections. Although the characterisation of bijective digitized rotations in 2D is well known, the extension to 3D is still an open problem. A certification algorithm exists that allows to verify that a digitized 3D rotation defined by a quaternion is bijective. In this seminar, we show how we use geometric algebra to represent a bijective digitized rotation as a pair of bijective digitized reflections. Visualization of bijective digitized reflections in 3D using geometric algebra leads to a conjectured characterization of 3D bijective digitized reflections and, thus, rotations. So far, any known quaternion that defines a bijective digitized rotation verifies the conjecture. An approximation method of any 3D digitized reflection by a conjectured bijective one is also proposed. Some experimental results will be shown with DGtal.

Thursday 6th October 2022 at 10h Clovis Eberhart (National Institute of Informatics, Tokyo, Japon),
A Compositional Approach to Graph Games

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We introduce open parity games, which is a compositional approach to parity games. This is achieved by adding open ends to the usual notion of parity games. We introduce the category of open parity games, which is defined using standard definitions for graph games. We also define a graphical language for open parity games as a prop, which have recently been used in many applications as graphical languages. We introduce a suitable semantic category inspired by the work by Grellois and Melliès on the semantics of higher-order model checking. Computing the set of winning positions in open parity games yields a functor to the semantic category. Finally, by interpreting the graphical language in the semantic category, we show that this computation can be carried out compositionally. We also discuss current work on an efficient implementation of a compositional solver of graph games.

Thursday 29th September 2022 at 10h Yannick Zakowski (ENS Lyon),
Monadic Definitional Interpreters as Formal Semantic Models of Computations

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Monadic interpreters have been used for a long time as a mean to embed arbitrary computations in purely functional contexts. At its core, the idea is elementary: the object language of interest is implemented as an executable interpreter in the host language, and monads are simply the abstraction used to embed features such as side effects, failure, non-determinism. By building these interpreters on top of the free monad, the approach has offered a comfortable design point notably enabling an extensible syntax, reusable modular components, structural compositional definitions, as well as algebraic reasoning. The approach has percolated beyond its programming roots: it is also used as a way to formalize the semantics of computational systems, programming languages notably, in proof assistants based on dependently typed theories. In such assistants, the host language is even more restricted: programs are all pure, but also provably terminating. Divergent programs can nonetheless be embedded using for instance the Capretta monad: intuitively, a lazy, infinite (coinductive) tree models the dynamic of the computation. Interaction trees are a specific implementation, in the Coq proof assistant, of a set of tools realizing this tradition. They provide a coinductive implementation of the iterative free monad, equipped with a set of combinators, allowing notably for general recursion. Each iterator comes with its equational theory established with respect to a notion of weak bisimulation --- i.e. termination sensitive, but ignoring the amount of fuel consumed --- and practical support for equational reasoning. Further effects are implemented into richer monads via a general notion of interpretation, allowing one to introduce the missing algebras required for proper semantic reasoning. Beyond program equivalence, support for arbitrary heterogeneous relational reasoning is provided, typically allowing one to prove a compilation pass correct. Introduced in 2020, the project has spawned realistic applications --- they are used to model LLVM IR's semantics notably ---, as well as extensions to reduce the necessary boilerplate, or to offer proper support for non-determinism. In this talk, I will attempt to paint an illustrative overview of the core ideas and contributions constitutive of this line of work.

Thursday 7th July 2022 at 10h Jacques-Olivier Lachaud (LAMA),
An alternative definition for digital convexity

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This talk proposes full convexity as an alternative definition of digital convexity, which is valid in arbitrary dimension. It solves many problems related to its usual definitions, like possible non connectedness or non simple connectedness, while encompassing its desirable features. Fully convex sets are digitally convex, but are also connected and simply connected. They have a morphological characterisation, which induces a simple convexity test algorithm. Arithmetic planes are fully convex too. Full convexity implies local full convexity, hence it enables local shape analysis, with an unambiguous definition of convex, concave and planar points. We propose also a natural definition of tangent subsets to a digital set. It gives rise to the tangential cover in 2D, and to consistent extensions in arbitrary dimension. We present two applications of tangency: the first one is a simple algorithm for building a polygonal mesh from a set of digital points, with reversibility property, the second one is the definition and computation of shortest paths within digital sets. In a second part of the talk, we study the problem of building a fully convex hull. We propose an iterative operator for this purpose, which computes a fully convex enveloppe in finite time. We can even build a fully convex enveloppe within another fully convex set (a kind of relative convex hull). We show how it induces several natural digital polyhedral models, whose cells of different dimensions are all fully convex sets. As perspective to this work, we study the problem of fully convex set intersection, which is the last step toward a full digital analogue of continuous convexity.

Thursday 30th June 2022 at 10h Aria Gheeraert (LAMA, Université de Bologne),
Une approche multidisciplinaire de l'étude de la dynamique des protéines et de la transmission de signaux

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L'allostérie est un phénomène d'importance fondamentale en biologie qui permet la régulation de la fonction et l'adaptabilité dynamique des enzymes et protéines. Malgré sa découverte il y a plus d'un siècle, l'allostérie reste une énigme biophysique, parfois appelée « second secret de la vie ». La difficulté est principalement associée à la nature complexe des mécanismes allostériques qui se manifestent comme l'altération de la fonction biologique d'une protéine/enzyme (c-à-d. la liaison d'un substrat/ligand au site active) par la liaison d'un « autre objet » (``allos stereos'' en grec) à un site distant (plus d'un nanomètre) du site actif, le site effecteur. Ainsi, au cœur de l'allostérie, il y a une propagation d'un signal du site effecteur au site actif à travers une matrice protéique dense, où l'un des enjeux principal est représenté par l'élucidation des interactions physico-chimiques entre résidus d'acides aminés qui permettent la communication entre les deux sites : les chemins allostériques. Ici, nous proposons une approche multidisciplinaire basée sur la combinaison de méthodes de chimie théorique, impliquant des simulations de dynamique moléculaire de mouvements de protéines, des analyses (bio)physiques des systèmes allostériques, incluant des alignements multiples de séquences de systèmes allostériques connus, et des outils mathématiques basés sur la théorie des graphes et d'apprentissage automatique qui peuvent grandement aider à la compréhension de de la complexité des interactions dynamiques impliquées dans les différents systèmes allostériques. Le projet vise à développer des outils rapides et robustes pour identifier des chemins allostériques inconnus. La caractérisation et les prédictions de points allostériques peuvent élucider et exploiter pleinement la modulation allostérique dans les enzymes et dans les complexes ADN-protéine, avec de potentielles grandes applications dans l'ingénierie des enzymes et dans la découverte de médicaments.

Thursday 16th June 2022 at 10h Diego Thomas (Kyushu University, Fukuoka, Japan),
3D human shape reconstruction and animation using depth cameras and deep learning

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Reconstructing digital humans is a key problem in 3D vision with many applications for autonomous driving, robotics, Virtual and Augmented Reality and has attracted a lot of research for decades. In this talk I will discuss about non-invasive hardware-based solutions to jointly capture human body shape and motion. We will see that efficient modelisation of human body deformation is key to enable real-time tracking. I will also present recent works about AI-based solutions for both human shape reconstruction from a single color images and full body animation with minimum driving signal such as a skeleton. We will see that deep learning opens new perspectives and possibilities to create real digital humans and animate them in the digital spaces.

Thursday 3rd March 2022 at 10h Matteo Acclavio (Université du Luxembourg),
Semantics for Constructive modal logics

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Constructive modal logics are obtained by adding to intuitionistic logic a minimal set of axioms for the box and diamond modalities. During this talk I will present two new semantics for proofs in these logics. The first semantics captures syntactically the proof equivalence enforced by non-duplicating rules permutations, and it is defined by means of the graphical syntax of combinatorial proofs. The second semantics captures a coarse notion of proof equivalence, and it is given by means of winning innocent strategies of a two-player game over graphs encoding formulas. This latter semantics is provided with a notion of compositionality and indeed defines the first concrete model of a denotational semantics for these logics.

Thursday 6th January 2022 at 10h Loïc Pujet (Nantes (INRIA, LS2N)),
L'extensionnalité en théorie des type intensionnelle

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La théorie des types de Martin-Löf compte parmi les instances les plus abouties de la correspondance preuves-programmes : les types dépendants et les types inductifs permettent de spécifier des propriétés complexes aux programmes, et la hiérarchie d'univers fournit une puissance logique suffisante pour encoder l'essentiel des constructions mathématiques -- ce qui en fait un outil de choix pour les assistants de preuves! Toutefois, l'égalité inductive fournie par la théorie n'est pas très adaptée au raisonnement mathématique, car elle encode l'égalité des programmes (``intensionnalité'') et non l'égalité des comportements (``extensionnalité''). Cela implique des conséquences désagréables : il est impossible de prouver que les fonctions qui à n associent respectivement n+2 et 2+n sont égales, il est impossible de quotienter un type par une relation, etc. C'est précisément pour remédier à ça qu'a été développée l'idée de théorie des types observationnelle, qui fournirait ces principes d'extensionnalité souhaitables, tout en préservant la correspondance preuves-programmes et les propriétés qui en font un outil si pratique (normalisation, canonicité, décidabilité du typage…). Dans cet exposé, je présenterai TT^obs, une altération conceptuellement simple de la théorie de Martin-Löf qui en fait une théorie observationnelle complète, je montrerai quelques exemples d'utilisation, et j'ébaucherai sa méta-théorie si le temps le permet.

The seminar of the team LIMD is under the responsibility of Sebastien Tavenas.
Settings: See with increasing date . Hide abstracts
Other years: 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2023, all years together.