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The Koopman operator theory provides a global linearization framework for general nonlinear dynamics, offering significant advantages for system analysis and control. However, practical applications typically involve approximating the infinite-dimensional Koopman operator in a lifted space spanned by a finite set of observable functions. The accuracy of this approximation is the key to effective Koopman operator-based analysis and control methods, generally improving as the dimension of the observables increases. Nonetheless, this increase in dimensionality significantly escalates both storage requirements and computational complexity, particularly for high-dimensional systems, thereby limiting the applicability of these methods in real-world problems. In this paper, we address this problem by reformulating the Koopman operator in tensor format to break the curse of dimensionality associated with its approximation through tensor decomposition techniques. This effective reduction in complexity enables the selection of high-dimensional observable functions and the handling of large-scale datasets, which leads to a precise linear prediction model utilizing the tensor-based Koopman operator. Furthermore, we propose an optimal control framework with the tensor-based Koopman operator, which adeptly addresses the nonlinear dynamics and constraints by linear reformulation in the lifted space and significantly reduces the computational complexity through separated representation of the tensor structure. 

Abstract Turbulent energy dissipation is a fundamental process in plasma physics that has not been settled. It is generally believed that the turbulent energy is dissipated at electron scales leading to electron energization in magnetized plasmas. Here, we propose a micro accelerator which could transform electrons from isotropic distribution to trapped, and then to stream (Strahl) distribution. From the MMS observations of an electron-scale coherent structure in the dayside magnetosheath, we identify an electron flux enhancement region in this structure collocated with an increase of magnetic field strength, which is also closely associated with a non-zero parallel electric field. We propose a trapping model considering a field-aligned electric potential together with the mirror force. The results are consistent with the observed electron fluxes from ~50 eV to ~200 eV. It further demonstrates that bidirectional electron jets can be formed by the hourglass-like magnetic configuration of the structure. 

Abstract The morphology and motion of auroras have been widely studied due to their indications on magnetospheric processes. Here, we report a new kind of “auroral curls,” which have wavelengths in the mesoscale (∼100 km) and propagate azimuthally. Utilizing data from the Chinese Antarctic Zhongshan Station (the all‐sky imager and the high‐frequency radar), the Active Magnetosphere and Planetary Electrodynamics Response Experiment and the Defense Meteorological Satellite Program, we analyze an event occurred on 23 April 2019. We find these curls are fine structures in the poleward boundary of multiple arcs. Corresponding field‐aligned currents manifest as a series of longitudinally arranged pairs, while ionospheric flow velocities nearby oscillate with periods in the Pc 5 band. Observational evidence suggests these curls are connected with ultra‐low frequency (ULF) waves, which opens the possibility of using auroras to globally image ULF waves. 

In this work, we consider the popular tree-based search strategy within the framework of reinforcement learning, the Monte Carlo tree search (MCTS), in the context of the infinite-horizon discounted cost Markov decision process (MDP). Although MCTS is believed to provide an approximate value function for a given state with enough simulations, the claimed proof of this property is incomplete. This is because the variant of MCTS, the upper confidence bound for trees (UCT), analyzed in prior works, uses “logarithmic” bonus term for balancing exploration and exploitation within the tree-based search, following the insights from stochastic multiarm bandit (MAB) literature. In effect, such an approach assumes that the regret of the underlying recursively dependent nonstationary MABs concentrates around their mean exponentially in the number of steps, which is unlikely to hold, even for stationary MABs. As the key contribution of this work, we establish polynomial concentration property of regret for a class of nonstationary MABs. This in turn establishes that the MCTS with appropriate polynomial rather than logarithmic bonus term in UCB has a claimed property. Interestingly enough, empirically successful approaches use a similar polynomial form of MCTS as suggested by our result. Using this as a building block, we argue that MCTS, combined with nearest neighbor supervised learning, acts as a “policy improvement” operator; that is, it iteratively improves value function approximation for all states because of combining with supervised learning, despite evaluating at only finitely many states. In effect, we establish that to learn an ε approximation of the value function with respect to [Formula: see text] norm, MCTS combined with nearest neighbor requires a sample size scaling as [Formula: see text], where d is the dimension of the state space. This is nearly optimal because of a minimax lower bound of [Formula: see text], suggesting the strength of the variant of MCTS we propose here and our resulting analysis. 

ABSTRACT One of the most promising tools for the control of fungal plant diseases is spray‐induced gene silencing (SIGS). In SIGS, small interfering RNA (siRNA) or double‐stranded RNA (dsRNA) targeting essential or virulence‐related pathogen genes are exogenously applied to plants and postharvest products to trigger RNA interference (RNAi) of the targeted genes, inhibiting fungal growth and disease. However, SIGS is limited by the unstable nature of RNA under environmental conditions. The use of layered double hydroxide or clay particles as carriers to deliver biologically active dsRNA, a formulation termed BioClay™, can enhance RNA durability on plants, prolonging its activity against pathogens. Here, we demonstrate that dsRNA delivered as BioClay can prolong protection against Botrytis cinerea , a major plant fungal pathogen, on tomato leaves and fruit and on mature chickpea plants. BioClay increased the protection window from 1 to 3 weeks on tomato leaves and from 5 to 10 days on tomato fruits, when compared with naked dsRNA. In flowering chickpea plants, BioClay provided prolonged protection for up to 4 weeks, covering the critical period of poding, whereas naked dsRNA provided limited protection. This research represents a major step forward for the adoption of SIGS as an eco‐friendly alternative to traditional fungicides.