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Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics
No full textInternational audienceWe study the convergence in total variation and -norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to approximatively sample from a target distribution of interest. We show first that, for a very large class of schemes, a minorization condition uniform in the stepsize holds. This class encompasses popular methods such as the Euler-Maruyama scheme and the schemes based on splitting strategies. Second, we provide mild conditions ensuring that the class of schemes that we consider satisfies a geometric Foster--Lyapunov drift condition, again uniform in the stepsize. This allows us to derive geometric convergence bounds, with a convergence rate scaling linearly with the stepsize. This kind of result is of prime interest to obtain estimates on norms of solutions to Poisson equations associated with a given numerical method
Analysis of the impact of vertical variation and temporal frequency of the chlorophyll forcing field on modelled temperature in the Mediterranean Sea and potential implications for regional climate projections
No full textInternational audienceThe urgency of climate change calls for the exploration of a variety of multi-forcing scenarios based on Shared Socio-economic Pathways. Ensuring the reliability of the climate projections is therefore an imperative prerequisite. In this paper, we examined the impact of the vertical variability and temporal frequency of the chlorophyll field used to force the NEMOMED12 ocean circulation model in the absence of a biogeochemical model on some key physical characteristics, mainly seawater temperature. Our analysis reveals that forcing by a chlorophyll field that is homogeneous in the vertical direction favours heat accumulation below the Deep Chlorophyll Maximum, leading to a positive temperature bias increasing with time. The extrapolation of the trend determined over the 11-year simulations leads to a bias in temperature as high as +1 • C after 100 years in the intermediate layer. Comparison with in situ data clearly shows that forcing the model with a realistically varying Chl field over the vertical allows the model to better represent temperature and avoid the presence of this bias. Additionally, we find that using the same chlorophyll field saved at different time frequencies, namely daily, monthly and monthly climatology, to force the NEMOMED12 model also creates temperature differences between simulations that increase with time, especially in the intermediate layer. The simulation forced by the daily chlorophyll is warmer in the surface layers than the two others, and we suggest that this is due to the asymmetric role of chlorophyll extremes on heat distribution. Finally, using a monthly chlorophyll climatology to force the NEMOMED12 ocean circulation model seems to be sufficient for physical modelling of the Mediterranean basin if the vertical variability of the Chl field is realistic.</div
New Principles For Stabilization Policy
No full textIn a broad class of discrete-time rational-expectations models, I consider stabilization-policy rules making the policy instrument react with coefficient φ ∈ R to a (past, current, or expected future) variable at horizon h ∈ Z, possibly among other variables, possibly with inertia. Using two complex-analysis theorems, I establish analytically some simple, easily interpretable, necessary or sufficient conditions on φ and h for these rules to ensure local-equilibrium determinacy. These conditions lead to new, general principles for stabilization policy in terms of whether, and how strongly or weakly, to react to any variable, at any horizon, in any model, with any policy instrument. Building on these conditions, I characterize the scope of validity of (a generalized version of ) the long-run Taylor principle as a condition for determinacy. I apply all these results to standard interest-rate rules in 134 quantitative monetary-policy models, and find the new principles to be (either typically or occasionally) quantitatively relevant
Apollon Real-Time Adaptive Optics (ARTAO) -- Astronomy-Inspired Wavefront Stabilization in Ultraintense Lasers
No full textInternational audienceTraditional wavefront control in high-energy, high-intensity laser systems usually lacks real-time capability, failing to address dynamic aberrations. This limits experimental accuracy due to shot-to-shot fluctuations and necessitates long cool-down phases to mitigate thermal effects, particularly as higher repetition rates become essential, e.g. in Inertial Fusion research. This paper details the development and implementation of a real-time capable adaptive optics system at the Apollon laser facility. Inspired by astronomical adaptive optics, the system uses a fiber-coupled 905 nm laser diode as a pilot beam that allows for spectral separation, bypassing the constraints of pulsed lasers. A GPU-based controller, built on the open-source CACAO framework, manages a loop comprising a bimorph deformable mirror and high-speed Shack-Hartmann sensor. Initial tests showed excellent stability and effective aberration correction. However, integration into the Apollon laser revealed critical challenges unique to the laser environment that must be resolved to ensure safe operation with amplified shots
Direct measurement of Tan's contact in a one-dimensional Lieb-Liniger gas
No full textInternational audienceThe Tan contact has emerged as a pivotal quantity in characterizing many-body quantum systems, bridging microscopic short-range correlations to thermodynamic behavior. It is defined as the weight of universal fall off in momentum distribution tails, which can be measured directly in ultracold gases. So far, however, its direct measurement has been hindered in Bose gases due to interactions strongly affecting the expansion dynamics. Here, we present the first direct measurement of the Tan contact in a strongly-correlated Lieb-Liniger gas. Leveraging the one-dimensional geometry of our system, we implement a two-stage expansion scheme, yielding interaction-immune time-of-flight imaging. Our results show excellent agreement with theoretical predictions from quantum Monte Carlo calculations, which also provides independent thermometry of the experiment. By varying atom number, temperature, and interaction strength, we obtain results consistent with the universal scaling law predicted for the trapped Lieb-Liniger model. Our work paves the way for further characterization of the Lieb-Liniger gas across broad interaction regimes and holds promise for extension to other correlated quantum gases in confined geometries
Two-way Fixed Effects and Differences-in-Differences in Heterogeneous Adoption Designs without Stayers
No full textThe first version of this paper (Nov 23rd, 2022) circulated under the title "An Optimal Bandwidth For Difference-in-Difference Estimation with a Continuous Treatment and an Heterogeneous Adoption Design".We consider treatment-effect estimation under a parallel trends assumption, in designs where no unit is treated at period one, all units receive a strictly positive dose at period two, and the dose varies across units. There are therefore no true control groups in such cases. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly used two-way fixed-effects estimator is consistent. When this test is rejected or lacks power, we propose alternative estimators, robust to heterogeneous effects. If there are units with a period-two treatment arbitrarily close to zero, the robust estimator is a difference-in-difference using units with a period-two treatment below a bandwidth as controls. Without such units, we propose non-parametric bounds, and an estimator relying on a parametric specification of treatment-effect heterogeneity. We use our results to revisit Pierce and Schott (2016) and Enikolopov et al. (2011)
Universal Waterfall Feature in Cuprate Superconductors: Evidence of a Momentum-Driven Crossover
No full textInternational audienceWe study two related universal anomalies of the spectral function of cuprates, so called waterfall and high-energy kink features, by a combined cellular dynamical mean-field theory and angle-resolved photoemission study for the oxychloride NaCaCuOCl (Na-CCOC). Tracing their origin back to an interplay of spin-polaron and local correlation effects both in undoped and hole-doped (Na-)CCOC, we establish them as a universal crossover between regions differing in the momentum dependence of the coupling and not necessarily in the related quasiparticles' energies. The proposed scenario extends to doping levels coinciding with the cuprate's superconducting dome and motivates further investigations of the fate of spin-polarons in the superconducting phase
Refined Analysis of Federated Averaging's Bias and Federated Richardson-Romberg Extrapolation
No full textInternational audienceIn this paper, we present a novel analysis of FedAvg with constant step size, relying on the Markov property of the underlying process. We demonstrate that the global iterates of the algorithm converge to a stationary distribution and analyze its resulting bias and variance relative to the problem's solution. We provide a first-order bias expansion in both homogeneous and heterogeneous settings. Interestingly, this bias decomposes into two distinct components: one that depends solely on stochastic gradient noise and another on client heterogeneity. Finally, we introduce a new algorithm based on the Richardson-Romberg extrapolation technique to mitigate this bias
Kinetic structure of strong-field QED showers in crossed electromagnetic fields
No full textInternational audienceA complete, kinetic description of electron-seeded strong-field QED showers in crossed electromagnetic fields is derived. The kinetic structure of the shower and its temporal evolution are shown to be a function of two parameters: the initial shower quantum parameter and radiation time. The latter determines the short and long time evolution of the shower. Explicit solutions for the shower multiplicity (number of pairs per seed electron) and the emitted photon spectrum are obtained for both timescales. Our approach is first derived considering showers in a constant, homogeneous magnetic field. We find that our results are valid for any crossed fields and we apply them to laboratory settings for which we obtain fully analytical, predictive scaling laws