Splitting games over finite sets

Early Access MAY 2022National audienceThis paper studies zero-sum splitting games with finite sets of states. Players dynamically choose a pair of martingales {pt,qt}t, in order to control a terminal payoff u(p∞,q∞). A first part introduces the notion of “Mertens–Zamir transform" of a real-valued matrix and use it to approximate the solution of the Mertens–Zamir system for continuous functions on the square [0,1]2. A second part considers the general case of finite splitting games with arbitrary correspondences containing the Dirac mass on the current state: building on Laraki and Renault (Math Oper Res 45:1237–1257, 2020), we show that the value exists by constructing non Markovian ε-optimal strategies and we characterize it as the unique concave-convex function satisfying two new conditions

Production Function Estimation with Multi-Destination Firms

We develop a procedure to estimate production functions, elasticities of demand, and productivity when firms endogenously select into multiple destination markets where they compete imperfectly, and when researchers observe output denominated only in value. We show that ignoring the multi-destination dimension (i.e., exporting) yields biased and inconsistent inference. Our estimator extends the two-stage procedure of Gandhi et al. (2020) to this setting, which allows for cross-market complementarities. In Monte Carlo simulations, we show that our estimator is consistent and performs well in finite samples. Using French manufacturing data, we find aver- age total returns to scale greater than 1, average returns to variable inputs less than 1, price elasticities of demand between -21.5 and -3.4, and learning-by-exporting effects between 0 and 4% per year. Alternative estimation procedures yield unrealistic estimates of returns to scale, demand elasticities, or both

COVID-19 scaling dynamics in growth and decline phases

The definition of optimal COVID-19 mitigation strategies remains worldwide on the top of public health agendas, particularly when facing a second wave. It requires a better understanding and a refined modelling of its dynamics. We emphasise the fact that epidemic models are phenomenologically based on the paradigm of a cascade of contacts that propagates infection. However, the introduction of ad-hoc characteristic times and corresponding rates spuriously break their scale symmetry.Here we theoretically argue and empirically demonstrate that COVID-19 dynamics, during both growth and decline phases, is a cascade with a rather universal scale symmetry whose power-law statistics drastically differ from those of an exponential process. This involves slower but longer phases which are furthermore linked by a fairly simple symmetry. These results explain biases of epidemic models and help to improve them. Due to their generality, these results pave the way to a renewed approach to epidemics, and more generally to growth phenomena

Effect of pore size polydispersity on the acoustic properties of high-porosity solid foams

International audienceThis study investigates the influence of pore size polydispersity on the acoustic behavior of high-porosity solid foams using numerical simulations. The effect of the size of the periodic unit cell (PUC) on the transport parameters is first examined. It is found that the size of the PUC required for properly estimating the acoustic properties of random foams depends on both the analyzed transport parameter(s) and level of polydispersity. Assuming identical and constant aperture ratio of membranes, the results indicate that (i) the viscous permeability is a reliable indicator regarding the size of the PUC (a more constraining property than the other transport parameters), and (ii) high-polydispersity foams require a larger number of pores in the PUC to achieve convergence with respect to morphological characteristics and acoustic properties. The influence of polydispersity on dimensionless transport parameters is then analyzed. It is found that polydispersity has a negligible effect on the high-frequency tortuosity but induces substantial variations in the remaining macroscopic parameters. Simulations further show that the ratio of the dimensionless transport parameters does not depend on membrane aperture ratio. This important result allows us to propose a fast method to estimate the acoustic properties of a random foam from the transport parameters of monodisperse foams with different pore sizes, for each studied transport parameter. The proposed method is finally employed to characterize the pore size and polydispersity in two real foams (with and without membranes), solving an inverse problem

Evaluating the cost-emissions trade-offs of a modal shift in intermodal and synchromodal transportation planning

International audienceIntermodal transportation planning combines road with more sustainable transportation modes to encour- age a modal shift. To evaluate the impact of a modal shift on transportation cost and emissions, we propose an intermodal transportation planning model to provide transparency in the cost-emissions trade-off. The model incorporates minimum load requirements, time windows, freight consolidation, and stochastic travel times to generate alternative transportation options. It also includes order consolidation to facilitate the utilization of transportation modes that would otherwise be infeasible due to, for instance, minimum load requirements. We also propose a synchromodal planning tool to evaluate re-planning and re-consolidation options in response to disruptions. We numerically illustrate the working of our model using a represen- tative network setting and quantify the trade-offs concerning costs and emissions by evaluating different transportation route options

Comparative Microplastic Analysis in Urban Waters Using μ-FTIR And Py-GC-MS: A Case Study in Amsterdam

International audienceThe contamination of freshwater with microplastics (MPs) has been established globally. While the analysis of MPs has predominantly involved spectroscopic methods for revealing particle numbers, the potential of employing spectroscopy for mass estimation has been underutilized. Consequently, there is a need to enhance our understanding of the mass loads of MPs and ensure the complementarity and comparability of various techniques for accurate quantification. This study presents the first comparative results on urban water samples using micro Fourier-transform infrared (μ-FTIR) imaging and pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS) to identify and quantify MPs in both particle numbers and mass concentration. Two sampling campaigns in summer and winter were conducted at 11 locations within the Amsterdam canal network. An advanced in-situ volume-reducing sampling pump was employed to collect MPs from the surface water within the size fraction of 10-300 μm. The analysis revealed MP concentrations within the range of 16 -107 MP/m3, estimated to be 2.0-789 μg/m3 by μ-FTIR imaging and 8.5-754 μg/m3 by Py-GC-MS. The results of the two analysis techniques showed good comparability in terms of the general trends of MP abundances, with variations in polymer compositions due to the inherent inter-methodological differences. Elevated MP concentrations were observed in the city center compared to the suburban areas. In addition, seasonal differences in MP abundances were noted at the locations with high human activity

Different Approaches to the Impacts of Climate Change, with a Common Goal: a Healthy Planet

International audienceThis work has benefited from a multidisciplinary scientific and technical contributions geared by the HM&Co Lab of the Ecole des Ponts ParisTech (hmco.enpc.fr) towards the sustainable, desirable, and resilient city. The deepening of the Universal Multifractal (UM) concepts and the encouragement of their operational applications have been linked to several initiatives launched in recent years to better integrate the heterogeneity/intermittency into public policy practices. Considering the complex, dynamic interactions between geophysical and anthropogenic fields within a conurbation such as the Ile de France region, a transition towards the shared value economy has been considered to best stimulate sober and collaborative development, and there exist at least 3 ways to approach today’s discussions about future transformations. Their intercomparison is the core of this presentation. Following the United Nations 2030 Agenda, the first most conventional approach is based on notions of sustainable development, supported by appropriate adaptation and mitigation of climate change. Combining the notions of extreme variability and complexity would require linking together geophysical and urban scales within extreme variability, and therefore considering geosciences, and not just geophysics! Such a synergistic and integrative approach would help move beyond traditional silo thinking, addressing the complexity of data- and/or theory-driven urban geosciences. Finaly, combining the notions of scaling and nonlinear variability would ultimately require linking cascades, multiplicative chaos, and multifractals. This would initiate a break with linear stochastic models towards stronger heterogeneity / intermittency, which would in turn lead to a plausible clustering of field and activity fluctuations. The appearance of multifractal phase transitions then becomes possible, considerably amplifying the impact of any action, and would make future transformations fully efficient, effectively imitating the way in which Nature acts. This will be finally illustrated using several examples of so-called Nature Based Solutions (NBS)

Sylvain Schoonbaert (coord.), Des ponts et des villes : histoire d'un patrimoine urbain, Mérignac, Ville de Bordeaux et Bordeaux Métropole, 2023, 320p. (compte-rendu)

Sylvain Schoonbaert (coord.), Des ponts et des villes : histoire d'un patrimoine urbain, Mérignac, Ville de Bordeaux et Bordeaux Métropole, 2023 (compte rendu)International audienc

Decomposition-Coordination Method for Finite Horizon Bandit Problems

Optimally solving a multi-armed bandit problem suffers the curse of dimensionality. Indeed, resorting to dynamic programming leads to an exponential growth of computing time, as the number of arms and the horizon increase. We introduce a decompositioncoordination heuristic, DeCo, that turns the initial problem into parallelly coordinated one-armed bandit problems. As a consequence, we obtain a computing time which is essentially linear in the number of arms. In addition, the decomposition provides a theoretical lower bound on the regret. For the two-armed bandit case, dynamic programming provides the exact solution, which is almost matched by the DeCo heuristic. Moreover, in numerical simulations with up to 100 rounds and 20 arms, DeCo outperforms classic algorithms (Thompson sampling and Kullback-Leibler upper-confidence bound) and almost matches the theoretical lower bound on the regret for 20 arms

Third-order A-stable alternating implicit Runge-Kutta schemes

We design pairs of six-stage, third-order, alternating implicit Runge--Kutta (RK) schemes that can be used to integrate in time two stiff operators by an operator-split technique. We also design for each pair a companion explicit RK scheme to be used for a third, nonstiff operator in an IMEX fashion. The main application we have in mind are (non)linear parabolic problems, where the two stiff operators represent diffusion processes (for instance, in two spatial directions) and the nonstiff operator represents (non)linear transport. We identify necessary conditions for linear A($\alpha$)-stability by considering a scalar ODE with two (complex) eigenvalues lying in some fixed cone of the half-complex plane with nonpositive real part. We show numerically that it is possible to achieve A(0)-stability when combining two operators with negative eigenvalues, irrespective of their relative magnitude. Finally, we show by numerical examples including two-dimensional nonlinear transport problems discretized in space using finite elements that the proposed schemes behave well