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  1. In this paper, a distributed swarm control problem is studied for large-scale multi-agent systems (LS-MASs). Different than classical multi-agent systems, an LS-MAS brings new challenges to control design due to its large number of agents. It might be more difficult for developing the appropriate control to achieve complicated missions such as collective swarming. To address these challenges, a novel mixed game theory is developed with a hierarchical learning algorithm. In the mixed game, the LS-MAS is represented as a multi-group, large-scale leader–follower system. Then, a cooperative game is used to formulate the distributed swarm control for multi-group leaders, and a Stackelberg game is utilized to couple the leaders and their large-scale followers effectively. Using the interaction between leaders and followers, the mean field game is used to continue the collective swarm behavior from leaders to followers smoothly without raising the computational complexity or communication traffic. Moreover, a hierarchical learning algorithm is designed to learn the intelligent optimal distributed swarm control for multi-group leader–follower systems. Specifically, a multi-agent actor–critic algorithm is developed for obtaining the distributed optimal swarm control for multi-group leaders first. Furthermore, an actor–critic–mass method is designed to find the decentralized swarm control for large-scale followers. Eventually, a series of numerical simulations and a Lyapunov stability proof of the closed-loop system are conducted to demonstrate the performance of the developed scheme. 
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  2. Abstract

    Pepper (Capsicumspp.) is one of the earliest cultivated crops and includes five domesticated species,C. annuumvar.annuum,C. chinense,C. frutescens,C. baccatumvar.pendulumandC. pubescens. Here, we report a pepper graph pan-genome and a genome variation map of 500 accessions from the five domesticatedCapsicumspecies and close wild relatives. We identify highly differentiated genomic regions among the domesticated peppers that underlie their natural variations in flowering time, characteristic flavors, and unique resistances to biotic and abiotic stresses. Domestication sweeps detected inC. annuumvar.annuumandC. baccatumvar.pendulumare mostly different, and the common domestication traits, including fruit size, shape and pungency, are achieved mainly through the selection of distinct genomic regions between these two cultivated species. Introgressions fromC. baccatumintoC. chinenseandC. frutescensare detected, including those providing genetic sources for various biotic and abiotic stress tolerances.

     
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  3. A bstract We study Ising Field Theory (the scaling limit of Ising model near the Curie critical point) in pure imaginary external magnetic field. We put particular emphasis on the detailed structure of the Yang-Lee edge singularity. While the leading singular behavior is controlled by the Yang-Lee fixed point (= minimal CFT $$ \mathcal{M} $$ M 2 / 5 ), the fine structure of the subleading singular terms is determined by the effective action which involves a tower of irrelevant operators. We use numerical data obtained through the “Truncated Free Fermion Space Approach” to estimate the couplings associated with two least irrelevant operators. One is the operator $$ T\overline{T} $$ T T ¯ , and we use the universal properties of the $$ T\overline{T} $$ T T ¯ deformation to fix the contributions of higher orders in the corresponding coupling parameter α . Another irrelevant operator we deal with is the descendant L_ 4 $$ \overline{L} $$ L ¯ _ 4 ϕ of the relevant primary ϕ in $$ \mathcal{M} $$ M 2 / 5 . The significance of this operator is that it is the lowest dimension operator which breaks integrability of the effective theory. We also establish analytic properties of the particle mass M (= inverse correlation length) as the function of complex magnetic field. 
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