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We consider the class of (finite) spatial games. We show that the problem of determining whether there exists a Nash equilibrium in which each player has a payoff of at least k is NP-complete as a function of the number of players. When each player has two strategies and the base game is an anti-coordination game, the problem is decidable in polynomial time. more...

We investigated the changes in constant velocity spring-mass behavior after high intensity sprint fatigue in order to better interpret the results recently reported after ultra-long distance (ULD) exercises. Our hypothesis was that after repeated sprints (RS), subjects may likely experience losses of force such as after ULD, but the necessity to modify their running pattern to attenuate the overall impact at each step (such as after ULD) may not be present. Eleven male subjects performed four sets of five 6-s sprints with 24-s recovery between sprints and 3 min between sets, on a sprint treadmill and on a bicycle ergometer. For each session, their running mechanics and spring-mass characteristics were measured at 10 and 20 km h(-1) on an instrumented treadmill before and after RS. Two-way (period and velocity) ANOVAs showed that high-intensity fatigue did not induce any change in the constant velocity running pattern at low or high velocity, after both running and cycling RS, despite significant decreases (P 0.001) in maximal power (-27.1 ± 8.2% after running RS and -15.4 ± 11.5 % after cycling RS) and knee extensors maximal voluntary force (-18.8 ± 6.7 % after running RS and -15.0 ± 7.6 % after cycling RS). These results bring indirect support to the hypothesis put forward in recent ULD studies that the changes in running mechanics observed after ULD are likely not related to the decrease in strength capabilities, but rather to the necessity for subjects to adopt a protective running pattern. more...

A spectral analysis and a multiscale study are performed on the numerical data obtained from direct numerical simulation and large-eddy simulation of the turbulent flow in a cubical lid-driven cavity. The analyzed data or signals are picked at three specific points inside the cavity allowing to investigate three drastically different flow regimes over time: laminar, transitional and turbulent. In comparison with direct numerical simulation, large-eddy simulation not only have a reduced resolution in space but also in time. In this context a wavelet analysis is chosen to study signals from large-eddy simulation, to provide a 'local' analysis of transient turbulent events. A time-scale joint representation is generated by continuous wavelet transform and compared with the time-scale joint representation of the direct numerical simulation. In this framework, the main objective of this study is to confirm the correlation between the computed physical quantities and those expected theoretically. (C) 2010 Elsevier Ltd. All rights reserved. more...

A strategic model of network formation is developed which permits unreliable links and organizational costs. Finding a connected Nash network which guarantees a given payoff to each player proves to be an NP-hard problem. For the associated evolutionary game with asynchronous updating and logit updating rules, the stochastically stable networks are characterized.The organization of agents into networks has an important role in the communication of information within a spatial structure. One goal is to understand how such networks form and evolve over time. Our agents are endowed with some information which can be accessed by other agents forming links with them. Link formation is costly and communication not fully reliable. We model the process of network formation as a non-cooperative game, and we then focus on Nash networks. But, showing existence of a Nash network with particular properties and computing one are two different tasks. The aim of this paper is to show that computing a connected Nash network is a computationally demanding optimization problem. The question then arises what outcomes might be chosen by agents who would like to form a connected Nash network but fail to achieve their goal because of computational limitations. We propose a stochastic evolutionary model. By solving a companion global optimization problem, this model selects a subset of Nash networks referred to as the set of stochastically stable networks. more...

International audience; In the present paper, we are interested in the one-way flow model of Bala and Goyal (2000) [Bala, V., Goyal, S., 2000. A non-cooperative model of network formation, Econometrica, N. 68 (5), 1181-1229]. We generalize this model by relaxing the authors' assumption concerning the relation between the number of resources obtained by an agent and this agent's payoffs. Firstly, we show that Nash networks are line bases and strict Nash networks are minimum line bases. Secondly, we establish that efficient networks are minimum line bases. more...

International audience; We consider vibro-impact problems, i.e. mechanical systems with a finite number of degrees of freedom submitted to perfect unilateral constraints. The dynamics is basically described by a second-order measure differential inclusion for the unknown position completed with a constitutive impact law. Another formulation of the problem as a frictionless sweeping process is possible: the unknown velocity belongs to an appropriate functional space and satisfies a first order measure differential inclusion. The equivalence of these two formulations is studied. They lead to time-discretiza-tions written in terms of positions or in terms of velocities, respectively. We present these different schemes and we compare them on the simple test-problem of a bouncing ball. We recall the convergence results in the single constraint case. Moreover, an example of implementation of the scheme derived from the basic description of the dynamics is presented. Finally, in the multi-constraint case, we point out some theoretical and computational difficulties. more...

International audience; Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the e ffect of each (group of) variable(s) and computing sensitivity indices without recursivity. more...

International audience; Kriging models have been widely used in computer experiments for the analysis of time-consuming computer codes. Based on kernels, they are flexible and can be tuned to many situations. In this paper, we construct kernels that reproduce the computer code complexity by mimicking its interaction structure. While the standard tensor-product kernel implicitly assumes that all interactions are active, the new kernels are suited for a general interaction structure, and will take advantage of the absence of interaction between some inputs. The methodology is twofold. First, the interaction structure is estimated from the data, using a first initial standard Kriging model, and represented by a so-called FANOVA graph. New FANOVA-based sensitivity indices are introduced to detect active interactions. Then this graph is used to derive the form of the kernel, and the corresponding Kriging model is estimated by maximum likelihood. The performance of the overall procedure is illustrated by several 3-dimensional and 6-dimensional simulated and real examples. A substantial improvement is observed when the computer code has a relatively high level of complexity. more...

This paper deals with a three-dimensional mixture model describing materials undergoing phase transition with thermal expansion. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the sow rule with the heat transfer equation. A global solution for this thermodynamically consistent problem is obtained by using a Þxed-point argument combined with global energy estimates (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) more...

We investigated the changes in the technical ability of force application/orientation against the ground vs. the physical capability of total force production after a multiple-set repeated sprints series. Twelve male physical education students familiar with sprint running performed four sets of five 6-s sprints (24s of passive rest between sprints, 3min between sets). Sprints were performed from a standing start on an instrumented treadmill, allowing the computation of vertical (F(V)), net horizontal (F(H)) and total (F(Tot)) ground reaction forces for each step. Furthermore, the ratio of forces was calculated as RF=F(H)F(Tot)(-1), and the index of force application technique (D(RF)) representing the decrement in RF with increase in speed was computed as the slope of the linear RF-speed relationship. Changes between pre- (first two sprints) and post-fatigue (last two sprints) were tested using paired t-tests. Performance decreased significantly (e.g. top speed decreased by 15.7±5.4%; P0.001), and all the mechanical variables tested significantly changed. F(H) showed the largest decrease, compared to F(V) and F(Tot). D(RF) significantly decreased (P0.001, effect size=1.20), and the individual magnitudes of change of D(RF) were significantly more important than those of F(Tot) (19.2±20.9 vs. 5.81±5.76%, respectively; P0.01). During a multiple-set repeated sprint series, both the total force production capability and the technical ability to apply force effectively against the ground are altered, the latter to a larger extent than the former. more...

International audience; This paper introduces some relations about Cayley graphs and G-graphs. We present a sufficient condition to recognize when a G-graph is a Cayley graph. The relation between G-graphs and Cayley graphs allows us to consider some applications to the hamiltonicity of Cayley graphs. In the last section we illustrate our results by showing that some new classes of Cayley graphs are hamiltonian. more...

International audience; The method of asymptotic partial domain decomposition for thin tube structures (finite unions of thin cylinders) is revisited. Its application to the Newtonian and non-Newtonian flows in great systems of vessels is considered. The possibility of a parallelization of its algorithm is discussed for linear and non-linear models. more...

International audience; Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded coefficients) on sets of integers having a positive upper density. more...

International audience; The purpose of this study was to examine the physiological and biomechanical changes occurring in a subject after running 8,500 km in 161 days (i.e. 52.8 km daily). Three weeks before, 3 weeks after (POST) and 5 months after (POST+5) running from Paris to Beijing, energy cost of running (Cr), knee flexor and extensor isokinetic strength and biomechanical parameters (using a treadmill dynamometer) at different velocities were assessed in an experienced ultra-runner. At POST, there was a tendency toward a 'smoother' running pattern, as shown by (a) a higher stride frequency and duty factor, and a reduced aerial time without a change in contact time, (b) a lower maximal vertical force and loading rate at impact and (c) a decrease in both potential and kinetic energy changes at each step. This was associated with a detrimental effect on Cr (+6.2%) and a loss of strength at all angular velocities for both knee flexors and extensors. At POST+5, the subject returned to his original running patterns at low but not at high speeds and maximal strength remained reduced at low angular velocities (i.e. at high levels of force). It is suggested that the running pattern changes observed in the present study were a strategy adopted by the subject to reduce the deleterious effects of long distance running. However, the running pattern changes could partly be linked to the decrease in maximal strength. more...

The aim of this paper is to describe some partial advances in the solution of the following two problems. Find the maximal order of vanishing at infinity of a non-zero Drinfeld quasi-modular form of given weight. Determine differential properties of a Drinfeld quasi-modular form of given weight and depth with maximal order of vanishing at infinity., We have fixed an error in the proof of Theorem 1.6 and corrected several minor typos more...

International audience; We present a simple algorithm to refine a finite volume bidimensional mesh admissible to solve elliptic or parabolic partial differential equations. The approximation of the Laplace operator reduces to the one of the normal fluxes along the edges of control volumes. These normal fluxes can be computed in a consistent way by a classical two points flux approximation simple if the mesh is admissible in the finite volume sense. The originality of the mesh refinement technique that we propose, is to preserve the admissibility property of the meshes. Therefore it can be used in a wide classic context. more...

International audience; We investigate 2-variable expanders and 3-source extractors in prime fields. We extend previous results of J. Bourgain.

The high order homogenization technique generates the so called infinite order homogenized equation. Its coefficients were widely discussed in composite mechanics literature because they are closely related to the so called high order strain gradients theories. However, it was not clear what is the correct mathematical setting for this equation and what are the asymptotically exact boundary conditions. In the present Note we give a variational formulation for the high order homogenized equation by the projection of the initial problem on the “ansatz subspace”. This formulation generates the appropriate boundary conditions for the high order homogenized equation. The error estimates for the solution of the original problem and the homogenized one are obtained. To cite this article: G. Panasenko, C. R. Mecanique 337 (2009). more...

International audience; Motivated by the problem of vibrations due to joint clearance between components in complex mechanical systems, we study in this paper the motion of a beam between rigid obstacles. We assume that the material is elastic and the motion is planar. The contact is described with a non-penetration condition, which leads to a model of dynamics with unilateral constraints. We propose a family of fully discretised approximations and their convergence is established. Moreover we present some examples of implementation using either finite element or spline space discretisation. more...

We define a finite-horizon repeated network formation game with consent, and study the differences induced by different levels of individual rationality. We prove that perfectly rational players will remain unconnected at the equilibrium, while nonempty equilibrium networks may form when, following Neyman (1985), players are assumed to behave as finite automata. We define two types of equilibria, namely the Repeated Nash Network (RNN), in which the same network forms at each period, and the Repeated Nash Equilibrium (RNE), in which different networks may form. We state a sufficient condition under which a given network may be implemented as a RNN. Then, we provide structural properties of RNE. For instance, players may form totally different networks at each period, or the networks within a given RNE may exhibit a total order relationship. Finally we investigate the question of efficiency for both Bentham and Pareto criteria. more...

International audience; We calculate numerically the motion of a slender bar dropped on a rigid foundation. For the computation the bar is discretized by a system of rigid bodies linked by spiral springs or by a pair of linear springs. We assume that the impact is frictionless and we model it by Newton's law. We compute the motion by using either an event-driven method based on the detection of impacts or a time-stepping scheme avoiding the detection of impacts. We calculate also the apparent restitution coefficient and we compare our results with the experimental and numerical results of Stoianovici and Hurmuzlu. more...

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we first study an accelerator for the i¾? T pairing over $\mathbb{F}_3[x]/(x^{97}+x^{12}+2)$. Our architecture is based on a unified arithmetic operator which performs addition, multiplication, and cubing over $\mathbb{F}_{3^{97}}$. This design methodology allows us to design a compact coprocessor (1888 slices on a Virtex-II Pro 4 FPGA) which compares favorably with other solutions described in the open literature. We then describe ways to extend our approach to any characteristic and any extension field. more...

We give evidence that sums of 3 cubes have a positive density, the value of which, 0.0999425..., is that given by a probabilistic model we developed earlier.

Van Damme and Weibull (1998, 2002) model the noise in games as endogenously determined tremble probabilities, by assuming that with some effort players can control the probability of implementing the intended strategy. Following their methodology, we derive logit-like adjustment rules for games played on quasi-symmetric weighted graphs and explore the properties of the ensuing Markov chain. more...

We consider a 2×2 coordination game where each agent interacts with his neighbors on a ring. Ellison (1993, Econometrica 61, 1047–1071) shows that the discrete dynamical system generated by the myopic best-reply rule converges to a Nash equilibrium or to a two-period limit cycle. Following Young (1993, Econometrica 61, 57–84), we consider a best-reply process with a sampling procedure. Particularly, we introduce a spatial sampling procedure: each agent observes a sample of information in his neighborhood and plays a best reply to it. We show that if the size of the sample of information is not too large, the best-reply process converges almost surely to a Nash equilibrium. If in addition agents experiment with small probabilities, we show that, in most cases, the risk-dominant equilibrium prevails in the long run. Furthermore, it turns out that the convergence is faster than in Ellison. more...