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1. Learning theory for inferring interaction kernels in second-order interacting agent systems

   https://doi.org/10.1007/s43670-023-00055-9  

   Miller, Jason; Tang, Sui; Zhong, Ming; Maggioni, Mauro (June 2023, Sampling Theory, Signal Processing, and Data Analysis)

   Abstract Modeling the complex interactions of systems of particles or agents is a fundamental problem across the sciences, from physics and biology, to economics and social sciences. In this work, we consider second-order, heterogeneous, multivariable models of interacting agents or particles, within simple environments. We describe a nonparametric inference framework to efficiently estimate the latent interaction kernels which drive these dynamical systems. We develop a learning theory which establishes strong consistency and optimal nonparametric min–max rates of convergence for the estimators, as well as provably accurate predicted trajectories. The optimal rates only depends on intrinsic dimension of interactions, which is typically much smaller than the ambient dimension. Our arguments are based on a coercivity condition which ensures that the interaction kernels can be estimated in stable fashion. The numerical algorithm presented to build the estimators is parallelizable, performs well on high-dimensional problems, and its performance is tested on a variety of complex dynamical systems. 

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2. Eddy-driven Zonal Jet Flows in the Laboratory

   https://doi.org/10.5802/crphys.213  

   Read, Peter; Afanasyev, Yakov; Aurnou, Jonathan; Lemasquerier, Daphné (January 2024, Comptes Rendus. Physique)

   Zonal jets are a ubiquitous feature of the circulation of planetary atmospheres, oceans and interiors. Many of the dynamical mechanisms that lead to the formation and evolution of such jets can be reproduced and studied in laboratory experiments, which have proved to be important sources of insight for understanding the nature of planetary jets. Here we introduce some of the key concepts underlying the production and maintenance of patterns of zonal jets in rotating and/or stratified flows. We then review a broad range of laboratory experiments that have helped to test and verify many of the dynamical mechanisms proposed to interpret geophysical jets involving the interaction of eddies and zonal flows. Laboratory experiments continue to have an important role to play in elucidating a quantitative understanding of zonal jets and their interactions with other aspects of planetary circulation systems. 

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3. Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties

   https://doi.org/10.1093/biomet/asab051  

   Zhao, Anqi; Ding, Peng (October 2021, Biometrika)

   Summary Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism while conditioning on the potential outcomes. To this end, we derive the sampling properties of the regression estimators under a wide range of specifications, and establish the appropriateness of the corresponding robust standard errors for Wald-type inference. The results help to clarify the causal interpretation of the coefficients in these factor-based regressions, and motivate the definition of general factorial effects to unify the definitions of factorial effects in various fields. We also quantify the bias-variance trade-off between the saturated and unsaturated regressions from the design-based perspective. 

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4. Lift in the vertical shear of a southerly jet embedded in a uniform westerly flow

   https://doi.org/10.1002/qj.3982  

   Hu, Qi; Limpert, George (February 2021, Quarterly Journal of the Royal Meteorological Society)

   Abstract A new mechanism is proposed as a potential cause for the one‐third of warm season severe nocturnal convection in the US Great Plains that develops in environments without the presence of air‐mass boundaries of fronts or mesoscale systems. This mechanism is tested in two‐ and three‐dimensional models. Results show strong ascent (∼1.0 m·s⁻¹), sufficient for nocturnal convection initiation, arising from interactions of mean westerly zonal wind with the vertical shear of a northern vortex and also perturbation westerly winds that are created by the Coriolis torque on the Great Plains southerly low‐level jet. The interaction involving the northern vortex results in organized strong ascent on the east side of the vortex from the near‐surface level to the top of the model atmosphere, and also a weak upward acceleration near the centre of the vortex. In simulations with westerly wind perturbations, strong and organized ascent occurs above and on the east side of the westerly perturbation winds. The upward motion in these simulations relies on both mechanical forcing from non‐hydrostatic pressure perturbations and buoyant acceleration caused by interactions of the westerly zonal wind and the vertical shear in the vortex or the perturbation westerly wind. Statistical tests confirm that these interactions, not the northern vortex or westerly perturbation itself and related shear, are essential for the simulated vertical motion. Additional sensitivity analysis indicates robust ascent across a wide range of westerly perturbation or northern vortex strengths. The vertical motion profile is not sensitive to the horizontal grid spacing of the model, at least at or below 4 km, but to the morphology of westerly wind perturbations. The latter suggests where improvement could be made to increase the accuracy of model prediction of nocturnal convective storms in the US Great Plains. 

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5. Blind SNR Estimation and Nonparametric Channel Denoising in Multi-Antenna mmWave Systems

   https://doi.org/10.1109/ICC42927.2021.9500387  

   Gallyas-Sanhueza, Alexandra; Studer, Christoph (June 2021, IEEE International Conference on Communications)

   We propose blind estimators for the average noise power, receive signal power, signal-to-noise ratio (SNR), and mean-square error (MSE), suitable for multi-antenna millimeter wave (mmWave) wireless systems. The proposed estimators can be computed at low complexity and solely rely on beamspace sparsity, i.e., the fact that only a small number of dominant propagation paths exist in typical mmWave channels. Our estimators can be used (i) to quickly track some of the key quantities in multi-antenna mmWave systems while avoiding additional pilot overhead and (ii) to design efficient nonparametric algorithms that require such quantities. We provide a theoretical analysis of the proposed estimators, and we demonstrate their efficacy via synthetic experiments and using a nonparametric channel-vector denoising task with realistic multi-antenna mmWave channels. 

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