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1. 2019/20 lessons from τ(Ωc0) and τ(Ξc0) and CP asymmetry in charm decays

   https://doi.org/10.1142/S0217751X20300136  

   Bianco, S. ; Bigi, I. I. ( August 2020 , International Journal of Modern Physics A)

   null (Ed.)

   Our 2003 “Cicerone” had discussed charm dynamics with different directions and levels. 1 Here we focus on two items, where the “landscape” has changed sizably. (a) The lifetimes and semileptonic decays of charm hadrons show the impact of nonperturbative QCD and to which degree one can apply heavy quark expansion (HQE) for charm hadrons. It is more complex as we have learnt from 2019/20 data. (b) CP asymmetry has been established in 2019: 2 [Formula: see text] is quite an achievement by the LHCb collaboration! Our community is at the beginning of a long travel for fundamental dynamics. Can the SM account for these? We discuss the assumptions that were made up to 2018 data and new conclusions from 2019/20 ones. We need more data; however, one has to discuss correlations between different transitions. We give an Appendix, what we have learnt for large CP asymmetry in [Formula: see text]. 

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2. Effect of electron–electron interaction on magnitude of quantum oscillations of dissipative resistance in magnetic fields

   https://doi.org/10.1063/5.0127286  

   Abedi, Sara ; Vitkalov, Sergey ; Bykov, A. A. ; Bakarov, A. K. ( December 2022 , Journal of Applied Physics)

   Magneto-intersubband resistance oscillations (MISOs) of highly mobile 2D electrons in symmetric GaAs quantum wells with two populated subbands are studied in magnetic fields [Formula: see text] tilted from the normal to the 2D electron layer at different temperatures [Formula: see text]. The in-plane component ([Formula: see text]) of the field [Formula: see text] induces magnetic entanglement between subbands, leading to beating in oscillating density of states (DOS) and to MISO suppression. Model of the MISO suppression is proposed. Within the model, a comparison of MISO amplitude in the entangled and disentangled ([Formula: see text]) 2D systems yields both difference frequency of DOS oscillations, [Formula: see text], and strength of the electron–electron interaction, described by parameter [Formula: see text], in the 2D system. These properties are analyzed using two methods, yielding consistent but not identical results for both [Formula: see text] and [Formula: see text]. The analysis reveals an additional angular dependent factor of MISO suppression. The factor is related to spin splitting of quantum levels in magnetic fields. 

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3. Nonasymptotic Analysis of Monte Carlo Tree Search

   https://doi.org/10.1287/opre.2021.2239  

   Shah, Devavrat ; Xie, Qiaomin ; Xu, Zhi ( May 2022 , Operations Research)

   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. 

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4. Formal Safety Envelopes for Provably Accurate State Classification by Data-Driven Flight Models

   https://doi.org/10.2514/1.I011073  

   Cruz-Camacho, Elkin ; Amer, Ahmad ; Kopsaftopoulos, Fotis ; Varela, Carlos A. ( January 2023 , Journal of Aerospace Information Systems)

   Aerospace systems are inherently stochastic and increasingly data-driven, thus hard to formally verify. Data-driven statistical models can be used to estimate the state and classify potentially anomalous conditions of aerospace systems from multiple heterogeneous sensors with high accuracy. In this paper, we consider the problem of precisely bounding the regions in the sensor input space of a stochastic system in which safe state classification can be formally proven. As an archetypal application, we consider a statistical model created to detect aerodynamic stall in a prototype wing retrofitted with piezoelectric sensors and used to generate data in a wind tunnel for different flight states. We formally define safety envelopes as regions parameterized by [Formula: see text] and [Formula: see text], to respectively capture how model-predictable observed sensor values are, and given these values, how likely the model’s accurate state classification is. Safety envelopes are formalized in the Agda proof assistant, used to also generate formally verified runtime monitors for sensor data stream analyses in the Haskell programming language. We further propose a new metric for model classification quality, evaluate it on our wing prototype model, and compare it to the model restricted to two different fixed airspeeds, and enhanced to a continuous Gaussian process regression model. Safety envelopes are an important step in formally verifying precise probabilistic properties of data-driven models used in stochastic aerospace systems and could be used by advanced control algorithms to maintain these systems well within safe operation boundaries.

    

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5. Learning Markov Models Via Low-Rank Optimization

   https://doi.org/10.1287/opre.2021.2115  

   Zhu, Ziwei ; Li, Xudong ; Wang, Mengdi ; Zhang, Anru ( November 2021 , Operations Research)

   Modeling unknown systems from data is a precursor of system optimization and sequential decision making. In this paper, we focus on learning a Markov model from a single trajectory of states. Suppose that the transition model has a small rank despite having a large state space, meaning that the system admits a low-dimensional latent structure. We show that one can estimate the full transition model accurately using a trajectory of length that is proportional to the total number of states. We propose two maximum-likelihood estimation methods: a convex approach with nuclear norm regularization and a nonconvex approach with rank constraint. We explicitly derive the statistical rates of both estimators in terms of the Kullback-Leiber divergence and the [Formula: see text] error and also establish a minimax lower bound to assess the tightness of these rates. For computing the nonconvex estimator, we develop a novel DC (difference of convex function) programming algorithm that starts with the convex M-estimator and then successively refines the solution till convergence. Empirical experiments demonstrate consistent superiority of the nonconvex estimator over the convex one. 

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