CNRS Luminy Institute of Mathematics (IML)

Marseille, France

CNRS Luminy Institute of Mathematics (IML)

Marseille, France
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Klimcik C.,CNRS Luminy Institute of Mathematics (IML)
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2017

It turns out that many integrable σ-models on group manifolds belong to the class of the so-called E-models which are relevant in the context of the Poisson–Lie T-duality. We show that this is the case also for the Yang–Baxter σ-model with WZNW term introduced by Delduc, Magro and Vicedo in [5]. © 2017 The Author(s)

Louboutin S.R.,CNRS Luminy Institute of Mathematics (IML)
Proceedings of the American Mathematical Society | Year: 2012

We give a new and short proof of J. Beers, D. Henshaw, C. McCall, S. Mulay and M. Spindler following a recent result: if is a totally real cubic algebraic unit, then there exists a unit η ∈ Z such that { , η} is a system of fundamental units of the group UE of the units of the cubic order Z[E], except for an infinite family for which E is a square in Z[E] and one sporadic exception. Not only is our proof shorter, but it enables us to prove a new result: if the conjugates E' and E" of E are in Z[E], then the subgroup generated by E and E' is of bounded index in UE, and if E > 1 > |E'| ≥ |E" | > 0 and if E' and E" are of opposite sign, then { E', E" } is a system of fundamental units of UE.2. © 2011 American Mathematical Society.

BEFFARA E.,CNRS Luminy Institute of Mathematics (IML)
Mathematical Structures in Computer Science | Year: 2017

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational (in the sense that the internal workings of processes are ignored) and non-interleaving. Constructions on algebras and their subspaces enjoy a good structure that make them (nearly) a model of differential linear logic, showing that the underlying approach to the representation of non-determinism as linear combinations is the same. Copyright © Cambridge University Press 2017

Feher L.,WIGNER RCP | Feher L.,University of Szeged | Klimcik C.,CNRS Luminy Institute of Mathematics (IML)
Nuclear Physics B | Year: 2012

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider III b system from a quasi-Hamiltonian reduction of the internally fused double SU(n)×SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the III b phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the III b system in terms of flat SU(n) connections on the one-holed torus. © 2012 Elsevier B.V.

Troubetzkoy S.,CNRS Luminy Institute of Mathematics (IML)
Journal of Statistical Physics | Year: 2010

We show that the typical wind-tree model, in the sense of Baire, is recurrent and has a dense set of periodic orbits. The recurrence result also holds for the Lorentz gas: the typical Lorentz gas, in the sense of Baire, is recurrent. These Lorentz gases need not be of finite horizon! © 2010 Springer Science+Business Media, LLC.

Girard J.-Y.,CNRS Luminy Institute of Mathematics (IML)
Theoretical Computer Science | Year: 2011

Geometry of Interaction is a transcendental syntax developed in the framework of operator algebras. This fifth installment of the program takes place inside a von Neumann algebra, the hyperfinite factor. It provides a built-in interpretation of cut-elimination as well as an explanation for light, i.e., complexity sensitive, logics. © 2010 Elsevier B.V. All rights reserved.

Squellari R.,CNRS Luminy Institute of Mathematics (IML) | Squellari R.,CNRS Theoretical and High Energy Physics
Nuclear Physics B | Year: 2014

We study the quantum properties at one-loop of the Yang-Baxter σ-models introduced by Klimčík [1,2]. The proof of the one-loop renormalizability is given, the one-loop renormalization flow is investigated and the quantum equivalence is studied. © 2014 The Authors.

Rolland R.,CNRS Luminy Institute of Mathematics (IML)
Cryptography and Communications | Year: 2010

The second weight of the Generalized Reed-Muller code of length q n and order d over the finite field with q elements is now known for d ≤ q and d ≥ (n - 1)(q - 1). In this paper, we determine the second weight for the other values of d which are not multiples of q - 1 plus 1. For the special case d = a(q - 1) + 1 we give an estimate. © 2009 Springer Science + Business Media, LLC.

Girard J.-Y.,CNRS Luminy Institute of Mathematics (IML)
Leibniz International Proceedings in Informatics, LIPIcs | Year: 2013

Whether we deal with foundations or computation, logic relates questions and answers, typically formulas and proofs: a very entangled relation due to the abuse of presuppositions. In order to analyse syntax, we should step out from language, which is quite impossible. However, it is enough to step out from meaning: this is why our first lighting of logic is that of answers: it is possible to deal with them as meaningless artifacts assuming two basic states, implicit and explicit. The process of explicitation (a.k.a. normalisation, execution), which aims at making explicit what is only implicit, is fundamentally hazardous. The second light is that of questions whose choice involves a formatting ensuring the convergence of explicitation, i.e., the existence of "normal forms". This formatting can be seen as the emergence of meaning. It is indeed a necessary nuisance; either too laxist or too coercitive, there is no just format. Logic should avoid the pitfall of Prussian, axiomatic, formats by trying to understand which deontic dialogue is hidden behind logical restrictions. The third lighting, certainty deals with the adequation between answers and questions: how do we know that an answer actually matches a question? Apodictic certainty - beyond a reasonable doubt - is out of reach: we can only hope for epidictic, i.e., limited, reasonable, certainty. Under the second light (questions), we see that the format is made of two opposite parts, namely rights and duties, and that logical deduction relies on a strict balance between these two opposite terms, expressed by the identity group "A is A and conversely". The issue of certainty thus becomes the interrogation: "Can we afford the rights of our duties?", © Jean-Yves Girard.

Didier G.,CNRS Luminy Institute of Mathematics (IML)
Bulletin of Mathematical Biology | Year: 2011

We give a formal study of the relationships between the transition cost parameters and the generalized maximum parsimonious reconstructions of unknown (ancestral) binary character states {0, 1} over a phylogenetic tree. As a main result, we show there are two thresholds λ n 1 and λ n 0 generally confounded, associated to each node n of the phylogenetic tree and such that there exists a maximum parsimonious reconstruction associating state 1 to n (resp. state 0 to n) if the ratio "10-cost"/"01-cost" is smaller than λ n 1. We propose a dynamic programming algorithm computing these thresholds in a quadratic time with the size of tree. We briefly illustrate some possible applications of this work over a biological dataset. In particular, the thresholds provide a natural way to quantify the degree of support for states reconstructed as well as to determine what kind of evolutionary assumptions in terms of costs are necessary to a given reconstruction. © Society for Mathematical Biology 2010.

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