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Derniers dépôts dans PRUNEL

Large time behavior and asymptotic stability of the two-dimensional Euler and linearized Euler equations

We study the asymptotic behavior and the asymptotic stability of the two-dimensional Euler equations and of the two-dimensional linearized Euler equations close to parallel flows. We focus on spectrally stable jet profiles $U\left(y\right)$ with stationary streamlines $y_{0}$ such that $U'(y_{0})=0$, a case that has not been studied previously. We describe a new dynamical phenomenon: the depletion of the vorticity at the stationary streamlines. An unexpected consequence, is that the velocity decays for large times with power laws, similarly to what happens in the case of the Orr mechanism for base flows without stationary streamlines. The asymptotic behaviors of velocity and the asymptotic profiles of vorticity are theoretically predicted and compared with direct numerical simulations. We argue on the asymptotic stability of these flow velocities even in the absence of any dissipative mechanisms. Lien vers le documentAnnotation of Tribolium nuclear receptors reveals an increase in evolutionary rate of a network controlling the ecdysone cascade

The Tribolium genome contains 21 nuclear receptors, representing all of the six known subfamilies. This first complete set for a coleopteran species reveals a strong conservation of the number and identity of nuclear receptors in holometabolous insects. Two novelties are observed: the atypical NR0 gene knirps is present only in brachyceran flies, while the NR2E6 gene is found only in Tribolium and in Apis. Using a quantitative analysis of the evolutionary rate, we discovered that nuclear receptors could be divided into two groups. In one group of 13 proteins, the rates follow the trend of the Mecopterida genome-wide acceleration. In a second group of five nuclear receptors, all acting early during the ecdysone cascade, we observed an even higher increase of the evolutionary rate during the early divergence of Mecopterida. We thus extended our analysis to the twelve classic ecdysone transcriptional regulators and found that six of them (ECR, USP, HR3, E75, HR4 and Kr-h1) underwent an increase in evolutionary rate at the base of the Mecopterida lineage. By contrast, E74, E93, BR, HR39, FTZ-F1 and E78 do not show this divergence. We suggest that coevolution occurred within a network of regulators that control the ecdysone cascade. The advent of Tribolium as a powerful model should allow a better understanding of this evolutionary event. Lien vers le documentGradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well. Lien vers le documentComputing the throughput of probabilistic and replicated streaming applications

In this paper, we investigate how to compute the throughput of probabilistic and replicated streaming applications. We are given (i) a streaming application whose dependence graph is a linear chain; (ii) a one- to-many mapping of the application onto a fully heterogeneous target, where a processor is assigned at most one application stage, but where a stage can be replicated onto a set of processors; and (iii) a set of I.I.D. (Indepen- dent and Identically-Distributed) variables to model each computation and communication time in the mapping. How can we compute the throughput of the application, i.e., the rate at which data sets can be processed? We consider two execution models, the Strict model where the actions of each processor are sequentialized, and the Overlap model where a processor can compute and communicate in par- allel. The problem is easy when application stages are not replicated, i.e., assigned to a single processor: in that case the throughput is dictated by the critical hardware resource. However, when stages are replicated, i.e., as- signed to several processors, the problem becomes surprisingly complicated: even in the deterministic case, the optimal throughput may be lower than the smallest internal resource throughput. To the best of our knowledge, the problem has never been considered in the probabilistic case. Lien vers le documentGeneral Iteration graphs and Boolean automata circuits

This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done deterministically, at each time step of a discretised time flow and according to a predefined order, we say that the network is updated according to a block-sequential update schedule (blocks of elements are updated sequentially while, within each block, the elements are updated synchronously). Many studies, for the sake of simplicity and with some biologically motivated reasons, have concentrated on networks updated with one particular block-sequential update schedule (more often the synchronous/parallel update schedule or sequential update schedules). The aim of this paper is to give an argument formally proven and inspired by biological considerations in favour of the fact that the choice of a particular update schedule does not matter so much in terms of the possible and likely dynamical behaviours that networks may display. Lien vers le documentBulking I: an Abstract Theory of Bulking

This paper is the first part of a serie of two papers dealing with bulking: a quasiorder on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we discuss the proper components of grouping and study the most general extensions. We identify the most general space-time transforms and give an axiomatization of bulking quasiorder. Finally, we study some properties of intrinsically universal cellular automata obtained by comparing grouping to bulking. Lien vers le documentBulking II: Classifications of Cellular Automata

This paper is the second part of a serie of two papers dealing with bulking: a quasi-order on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we introduce 3 notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools to classify cellular automata. Lien vers le documentAuction-based Bandwidth Allocation Mechanisms for Wireless Future Internet

An important aspect of the Future Internet is the efficient utilization of (wireless) network resources. In order for the - demanding in terms of QoS - Future Internet services to be provided, the current trend is evolving towards an ``integrated'' wireless network access model that enables users to enjoy mobility, seamless access and high quality of service in an all-IP network on an ``Anytime, Anywhere'' basis. The term ``integrated'' is used to denote that the Future Internet wireless ``last mile'' is expected to comprise multiple heterogeneous geographically coexisting wireless networks, each having different capacity and coverage radius. The efficient management of the wireless access network resources is crucial due to their scarcity that renders wireless access a potential bottleneck for the provision of high quality services. In this paper we propose an auction mechanism for allocating the bandwidth of such a network so that efficiency is attained, i.e. social welfare is maximized. In particular, we propose an incentive-compatible, efficient auction-based mechanism of low computational complexity. We define a repeated game to address user utilities and incentives issues. Subsequently, we extend this mechanism so that it can also accommodate multicast sessions. We also analyze the computational complexity and message overhead of the proposed mechanism. We then show how user bids can be replaced from weights generated by the network and transform the auction to a cooperative mechanism capable of prioritizing certain classes of services and emulating DiffServ and time-of-day pricing schemes. The theoretical analysis is complemented by simulations that assess the proposed mechanisms properties and performance. We finally provide some concluding remarks and directions for future research. Lien vers le documentFixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a ``robust'' aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets. Lien vers le documentFormal Proof of a Wave Equation Resolution Scheme: the Method Error

Popular finite difference numerical schemes for the resolution of the one-dimensional acoustic wave equation are well-known to be convergent. We present a comprehensive formalization of the simplest one and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical pen-and-paper proofs. To our knowledge, this is the first time such kind of mathematical proof is machine-checked. Lien vers le document

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