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From tropical linear algebra to zero-sum games
No full textInvited Plenary TalkInternational audienceRecently, some relations have appeared between tropicalalgebra, linear programming, Perron-Frobenius theory, and zero-sumgames. This talk is devoted to these relations and to theirconsequences. In particular, we shall make a connection between twowell known unsolved questions. The first is the existence of astrongly polynomial pivoting rule in linear programming. Such a rulewould allow us to solve a linear program in a number of arithmeticoperations bounded only by the number of variables and the number ofconstraints. The second question is the existence of a polynomialalgorithm to solve mean payoff games. In work with Allamigeon,Benchimol, and Joswig, we showed that a positive answer to the firstquestion would yield a positive answer to the second, provided thepivoting rule satisfies certain conditions. This uses the equivalencebetween mean payoff games and tropical linear programs, established inan earlier work with Akian and Guterman. The proof of these resultswill give us the opportunity to see at work non-linearPerron-Frobenius theory, as well as a number of basic tropical tools:tropical eigenvalues, extensions or symmetrization of semirings,tropical analogues of Cramer theorem
The MARs Boundary Layer LIDAR (MARBLL) observation strategies and corresponding performance predictions.
No full textInternational audienceThe MARBLL instrument is the first Martian LIDAR concept providing simultaneous wind speed and aerosol density measurements. Its design, validated with a prototype, relies on a Mach-Zehnder interferometer as well as on the laser inherited from the ChemCam instrument. Whereas the aerosol density profile is classically determined by measuring the amount of backscattered light along the line of sight (LOS), the wind speed measurement uses the Doppler shift created by the velocity of the particles along this LOS. Its performances for a Martian configuration have been simulated. Because, the lidar is only able to measure the wind-speed projected along the line of sight, various observation strategies have been tested. Whereas the vertical sounding allows the direct determination of altitude profiles of aerosols and vertical wind-speed, the measurement of the horizontal wind vector requires specific techniques. The "conical scan" that has been tested consists in sounding the envelope of a cone with the laser, shooting at a given elevation (typically 45) for a selected range of azimuths. The vertical and horizontal wind speed at every altitude can then be deconvolved by fitting a sinusoid on the azimuthal data. The same method can be used at low elevations, for a high vertical resolution measurement near the surface. Eventually, the instrument performances have been predicted using two models. On the one hand, an end-to-end instrument model, describing the whole optical line, interferometer and electronics noises and performances, enabling us the obtain the signal-to-noise ratio (SNR) for each shot as well as the one-sigma error expected for the LOS wind-speed measurement at a given altitude. On the other hand, the Large-Eddy Simulation (LES) model developed at Laboratoire de Météorologie Dynamique, is used to set up the actual measured LOS wind-speed resulting from the combination of the project wind vector components along the lidar LOS. The error on the aerosol density measurement is easily obtained thanks to the SNR whereas the one-sigma error on horizontal and/or vertical wind speed for a given measurement strategy is then determined by propagating the LOS one-sigma error through the employed method (directly for the vertical shot, and through least square fits for the conical scan). A Monte-Carlo method is then used with time, space and observation parameters (the simulated measurement is done at various start times, positions in the simulation box and starting azimuths) in order to finally compute the one-sigma error for one measurement strategy, with a particular set of parameters, therefore allowing us to choose the optimal ones for the instrument design
Understanding and validation of the polarimetric scattering of a forest for bistatic P-band SAR measurements
No full textInternational audienceThe objective of this paper is to propose an alternative measurement device at optical scale to help understanding of bistatic polarimetric SAR images of forests. The device is employed to measure nanoscale trunk forests with a 106 scale factor. Considering the scale invariant rule in electromagnetic scattering this device would enable to predict the Mueller matrix of a whole tree forest for P band radar measurements. The device presents the advantages to be low cost and to get a complete set of bistatic configurations at once. Moreover, the measurements are very fast and would potentially be done on infinitely diverse and well controlled forest structures. Multiplicative decompositions of the Mueller matrix are presented. We underline the trunk density influence for an entire scope of bistatic configuration
Adaptive and model-based control theory applied to convectively unstable flows
No full textInternational audienceResearch on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review model-based techniques, such as linear-quadratic regulators, and model-free adaptive methods, such as least-mean square filters. The former are supported by a elegant and powerful theoretical basis, whereas the latter may provide a more prac-tical approach in the presence of complex disturbance envi-ronments, that are difficult to model. We compare the meth-ods with a particular focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the one-dimensional linearized Kuramoto-Sivashinsky equation, that shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples are provided. 1 Introduction The key motivation in research on drag reduction is to develop new technology that will result in the design of ve-hicles with a significantly lower fuel consumption. The field is broad, ranging from passive methods, such as coating surfaces with materials that are super-hydrophobic or non-smooth [1], to active methods, such as applying wall suction or using measurement-based closed-loop control [2]. This work positions itself in the field of active control methods for skin-friction drag. In general, the mean skin friction of a turbulent boundary layer on a flat plate is an order of magni-tude larger compared to a laminar boundary layer. One strat-egy to reduce skin-friction drag is thus to push the laminar-turbulent transition on a flat plate downstream [3]. Differ-ent transition scenarios may occur in a boundary layer flows, depending on the intensity of the external disturbances act-ing on the flow, [4]. Under low levels of free-stream turbu-lence and sufficiently far downstream, the transition process is initiated by the linear growth of small perturbations called Tollmien-Schlichting (TS) waves [3]. Eventually, these per-turbations reach finite amplitudes and breakdown to smaller scales via nonlinear mechanisms [5]. However, in presence of stronger free-stream disturbances, the exponential growth of TS waves are bypassed and transition may be directly triggered by the algebraic growth of stream-wise elongated structures, called streaks [4]. One may delay transition by damping the growth of TS waves and/or streaks, and thus postpone their nonlinear breakdown. This strategy enables the use of linear theory for control design. Fluid dynamists noticed in the early 90's, that many of the emerging concepts in hydrodynamic stability theory al-ready existed in linear systems theory [6, 7]. For example, the analysis of a system forced by harmonic excitations is referred to as signalling problem by fluid dynamicists, while control theorists analyze the problem by constructing a Bode diagram, [8]; similarly, a large transient growth of a fluid system corresponds to large norm of a transfer function and matrix with stable eigenvalues can be called either globally stable or Hurtwitz, [5, 9]. However, the systems theoretical approach had taken one step further, by "closing the loop", i.e providing rigorous conditions and tools to modify the linear system at hand. It was realized by fluid dynamists that the extension of hydro-dynamic stability theory to include tools and concepts from linear control theory was natural [10, 11, 12]. A long series of numerical investigations addressing the various aspects of closed-loop control of transitional [13, 14, 15] and turbulent flows [16, 17, 18] followed in the wake of these initial contri-butions. At the same time, research on active control fo
Gender and time allocation of cohabiting and married women and men in France, Italy, and the United States
No full textInternational audienceBackground: Women, who generally do more unpaid and less paid work than men, have greater incentives to stay in marriages than cohabiting unions, which generally carry fewer legal protections for individuals that wish to dissolve their relationship. The extent to which cohabitation is institutionalized, however, is a matter of policy and varies substantially by country. The gender gap in paid and unpaid work between married and cohabiting individuals should be larger in countries where cohabitation is less institutionalized and where those in cohabiting relationships have relatively fewer legal protections should the relationship dissolve, yet few studies have explored this variation.Objective: Using time diary data from France, Italy, and the United States, we assess the time men and women devote to paid and unpaid work in cohabiting and married couples. These three countries provide a useful diversity in marital regimes for examining these expectations: France, where cohabitation is most “marriage like” and where partnerships can be registered and carry legal rights; the United States, where cohabitation is common but is short-lived and unstable and where legal protections vary across states; and Italy, where cohabitation is not common and where such unions are not legally acknowledged and less socially approved than in either France or the United States.Results: Cohabitating men’s and women’s time allocated to market and nonmarket work is generally more similar than married men and women. Our expectations about country differences are only partially borne out by the findings. Greater gender differences in the time allocated to market and nonmarket work are found in Italy relative to either France or the U.S
On the pigeonhole and related principles in deep inference and monotone systems
No full textInternational audienceWe construct quasipolynomial-size proofs of the propositional pigeonhole principle in the deep inference system KS, addressing an open problem raised in previous works and matching the best known upper bound for the more general class of monotone proofs. We make significant use of monotone formulae computing boolean threshold functions, an idea previously considered in works of Atserias et al. The main construction, monotone proofs witnessing the symmetry of such functions, involves an implementation of merge-sort in the design of proofs in order to tame the structural behaviour of atoms, and so the complexity of normalization. Proof transformations from previous work on atomic flows are then employed to yield appropriate KS proofs. As further results we show that our constructions can be applied to provide quasipolynomial-size KS proofs of the parity principle and the generalized pigeonhole principle. These bounds are inherited for the class of monotone proofs, and we are further able to construct n^O(log log n) -size monotone proofs of the weak pigeonhole principle with (1 + ε)n pigeons and n holes for ε = 1/ polylog n, thereby also improving the best known bounds for monotone proofs
Reduced-order minimum time control of advection-reaction-diffusion systems via dynamic programming.
No full textInternational audienceA numerical approach for a time-optimal feedback control problem for an advection-reaction-diffusion model is considered. Our approach is composed by three main building blocks: approximation of the abstract system dynamics, feedback computation based on dynamic programming and state observation. For the approximation of the abstract system dynamics, we consider a finite element semi-discretization in space, leading to a large-scale dynamical system, whose dimension is reduced by means of a Balanced Truncation algorithm. Next, we apply the dynamic programming principle over the reduced dynamics, and characterize the value function of the optimal control problem in terms of viscosity solutions of the resulting Hamilton-Jacobi-Bellman equation, which is solved via a semi-Lagrangian scheme. Finally, the computation of corresponding feedback controls and its insertion into the control loop is performed by implementing a Luenberger observer
Trade, Wages, and Collective Bargaining: Evidence from France
No full textWe estimate the impact of international trade on wages using detailed data for French manufacturing firms. We instrument firm-level trade flows with firm-specific instrumental variables based on world demand and supply shocks. Both export and offshoring shocks have a positive effect on wages. Exports increase wages similarly for all occupational categories while offshoring has heterogeneous effects. The impact of trade shocks on wages is heterogeneous across bargaining regimes. In firms with collective bargaining, the elasticity of wages with respect to both exports and offshoring is higher than in firms with no collective bargaining. The wage gains associated with collective bargaining are similar across worker categories
BEWARE OF BLACK SWANS AND DO NOT IGNORE WHITE ONES?
No full textUncertainty pervades most aspects of life. From selecting a new technology to choosing a career, decision makers often ignore the outcomes of their decisions. In the last decade a new paradigm has emerged in behavioral decision research in which decisions are “experienced” rather than “described”, as in standard decision theory. The dominant finding from studies using the experience-based paradigm is that decisions from experience exhibit "black swan effect", i.e. the tendency to neglect rare events. Under prospect theory, this results in an experience-description gap. We show that several tentative conclusions can be drawn from our interdisciplinary examination of the putative experience-description gap in decision under uncertainty. Several insights are discussed. First, while the major source of under-weighting of rare events may be sampling error, it is argued that a robust experience-description gap remains when these factors are not at play. Second, the residual experience-description gap is not only about experience per se, but also about the way in which information concerning the probability distribution over possible outcomes is learned.Additional econometric and empirical work might be required to fully flech out these tentative conclusions. However, there was a consensus that an initially polemical literature turns out to be constructive in drawing researcher towards greater rapprochements