On power corrections to the event shape distributions in QCD

We study power corrections to the differential thrust, heavy jet mass and C-parameter distributions in the two-jet kinematical region in e^+e^- annihilation. We argue that away from the end-point region, e>> \Lambda_{QCD}/Q, the leading 1/Q-power corrections are parameterized by a single nonperturbative scale while for e \Lambda_{QCD}/Q one encounters a novel regime in which power corrections of the form 1/(Qe)^n have to be taken into account for arbitrary n. These nonperturbative corrections can be resummed and factor out into a universal nonperturbative distribution, the shape function, and the differential event shape distributions are given by convolution of the shape function with perturbative cross-sections. Choosing a simple ansatz for the shape function we demonstrate a good agreement of the obtained QCD predictions for the distributions and their lowest moments with the existing data over a wide energy interval.Comment: 18 pages, LaTeX style, 4 figure

Infinite Boltzmann Samplers and Applications to Branching Processes

National audienceIn this short note, we extend the Boltzmann model for combinatorial random sampling [8] to allow for infinite size objects; in particular, this extension now fully includes Galton-Watson processes. We then illustrate our idea with two examples, one of which is the generation of prefixes of infinite Cayley trees

Perturbative application of next-to-leading order pionless EFT for A≤3A\le3 nuclei in a finite volume

Lattice quantum chromodynamics (LQCD) calculations with physical pion mass would revolutionize nuclear physics by enabling predictions based on the fundamental theory of the strong force. To bridge the gap between finite-volume LQCD results and free-space physical observables, two primary extrapolation methods have been employed so far. The traditional approach relies on the L\"{u}scher formula and its extensions, while a recent alternative employs effective field theories (EFTs) fitted directly to the finite volume data. In this study, we fit pionless EFT with perturbative inclusion of the next-to-leading order to finite-volume energies generated from a phenomenological $NN$ interaction. The theory is then used to extrapolate the finite-volume results into free space as well as to predict new few-body observables. As a benchmark, we also apply the L\"{u}scher formalism directly to the finite-volume data. Through a comprehensive analysis, we explore the characteristics of order-by-order predictions of the pionless EFT fitted within a finite volume, investigate the limitations of the different extrapolation techniques used, and derive recommended box sizes required for reliable predictions

On the diversity of pattern distributions in rational language

International audienceIt is well known that, under some aperiodicity and irreducibility conditions, the number of occurrences of local patterns within a Markov chain (and, more generally, within the languages generated by weighted regular expressions/automata) follows a Gaussian distribu- tion with both variance and mean in (n). By contrast, when these conditions no longer hold, it has been denoted that the limiting distribution may follow a whole diversity of distributions, including the uniform, power-law or even multimodal distribution, arising as tradeo s between structural properties of the regular expression and the weight/probabilities associated with its transitions/letters. However these cases only partially cover the full diversity of behaviors induced within regular expressions, and a characterization of attainable distributions remained to be provided. In this article, we constructively show that the limiting distribution of the simplest foresee- able motif (a single letter!) may already follow an arbitrarily complex continuous distribution (or cadlag process). We also give applications in random generation (Boltzmann sampling) and bioinformatics (parsimonious segmentation of DNA)

Binary Heaps Formally Verified in Why3

The VACID-0 benchmarks is a set of small programs which pose challenges for formal verification of their functional behavior. This paper reports on the formal verification of one of these challenges: binary heaps. The solution given here is performed using the Why3 environment for program verification. The expected behavior of the program is specified in Why3 logic, structured using the constructs for building hierarchies of theories provided by Why3. The proofs are achieved by a significant amount of automation, using SMT solvers for a large majority of the verification conditions generated, whereas the remaining verification conditions are discharged by interactive constructions of proof scripts using the Coq proof assistant. The general aim of this case study is to demonstrate the usability and efficiency of both the Why3 specification language and the accompanying tools, which offer a fairly advanced environment for specification while keeping a significant amount of automation of proofs.Les benchmarks VACID-0 forment une collection de petits programmes qui posent des défis pour la vérification formelle de leur comportement fonctionnel. Ce rapport présente la vérification formelle de l'un de ces exemples: les tas binaires. La solution présentée utilise l'environnement pour la vérification Why3. Le comportement attendu est spécifié dans la logique de Why3, de façon structurée grâce aux constructions hiérarchiques de théories proposées par Why3. Les preuves sont effectuées de façon largement automatiques, car les prouveurs SMT disponibles en sortie de Why3 résolvent un pourcentage significatif des obligations de preuves engendrées, le reste étant prouvé interactivement avec l'assistant de preuve Coq. La motivation de cette étude de cas est de démontrer l'utilisabilité et l'efficacité à la fois du langage de spécification de Why3 et des outils associés, qui fournissent un langage puissant de spécification tout en permettant une automatisation importante des preuves

Preuves par raffinement de programmes avec pointeurs

Le but de cette thèse est de spécifier et prouver des programmes avec pointeurs, tels que des programmes C, en utilisant des techniques de raffinement. L approche proposée permet de faire un compromis entre les techniques complexes qui existent dans la littérature et ce qui est utilisable dans l industrie, en conciliant légèreté des annotations et restrictions sur les alias. Nous définissons, dans un premier temps, un langage d étude, qui s inspire du langage C, et dans lequel le seul type de données mutable possible est le type des structures, auquel on accède uniquement à travers des pointeurs. Afin de structurer nos programmes, nous munissons notre langage d une notion de module et des concepts issus de la théorie du raffinement tels que les variables abstraites que nous formalisons par des champs modèle, et les invariants de collage. Ceci nous permet d écrire des programmes structurés en composants. L introduction des invariants de données dans notre langage soulève des problématiques liées au partage de pointeurs. En effet, en cas d alias, on risque de ne plus pouvoir garantir la validité de l invariant de données d une structure. Nous interdisons, alors l aliasing (le partage de référence) dans notre langage. Pour contrôler les accès à la mémoire, nous définissons un système de type, basé sur la notion de régions. Cette contribution s inspire de la théorie du raffinement et a pour but, de rendre les programmes les plus modulaires possible et leurs preuves les plus automatiques possible. Nous définissons, sur ce langage, un mécanisme de génération d obligations de preuve en proposant un calcul de plus faible précondition incorporant du raffinement. Nous prouvons ensuite, la correction de ce mécanisme de génération d obligations de preuve par une méthode originale, fondée sur la notion de sémantique bloquante, qui s apparente à une preuve de type soundness et qui consiste donc, à prouver la préservation puis le progrès de ce calcul. Nous étendons, dans un deuxième temps, notre langage en levant partiellement la restriction liée au partage de références. Nous permettons, notamment, le partage de références lorsqu aucun invariant de données n est associé au type structure référencé. De plus, nous introduisons le type des tableaux, ainsi que les variables globales et l affectation qui ne font pas partie du langage noyau. Pour chacune des extensions citées ci-dessus, nous étendons la définition et la preuve de correction du calcul de plus faible précondition en conséquence. Nous proposons enfin, une implantation de cette approche sous forme d un greffon de Frama-C (http://frama-c.com/). Nous expérimentons notre implantation sur des exemples de modules implantant des structures de données complexes, en particulier des défis issus du challenge VACID0 (http://vacid. codeplex.com/), à savoir les tableaux creux (Sparse Array) et les tas binaires.The purpose of this thesis is to specify and prove programs with pointers, such as C programs, using refinement techniques. The proposed approach allows a compromise between the complexe methods that exist in the literature and what is used in industry, reconciling lightness annotations and restrictions on the alias. We define, firstly, a language study, based on the C language, in which the only type of mutable data allowed is the type of structures, which can be accessed only through pointers. In order to structure our programs, we bring our language with a module notion and concepts issue from a refinement theory such as abstract variables that we formalize by model fields and gluing invariants. This allows us to write programs structured by components. Introducing invariants in our language raises issues related to aliasing. Indeed, in presence of alias, we might not be able to guarantee the validity of the invariant data structure. We forbid then the aliasing in our language. To control memory access, we define a type system based on the concept of regions. This contribution is based on the theory and refinement. It aims to make programs as modular as possible and proofs as automatic as possible. We define on this language, a mechanism for generation of proof obligations by proposing a weakest precondition calculus incorporating refinement. Next we prove the correction of this proof obligations generation mechnaism by an original method based on the concept of blocking semantic, which is similar to a proof of type soundness, and consists therefore, to proove the preservation and the progress of the defined calculus. Secondly, we extend our language by, partially, lifting the restrictions related to aliasing. We allow, in particular, sharing when no invariant is associated to the referenced data structure. In addition, we introduce the type of arrays, global variables, and assignment that are not part of the core language. For each of the extensions mentioned above, we extend the definition and correctness proof of the weakest precondition calculus accordingly. Finally, we propose an implementation of this approach as a Frama-C plugin(http ://frama-c.com/). We experimente our implantation on examples of modules implementing complex data structures, especially the challenges from the challenge VACID0 (http ://vacid. Codeplex.com /), namely sparse srrays and binary heaps.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF