The dynamics of an infinite system of point particles in R d , which hop and interact with each other, is described at both micro-and mesoscopic levels. The states of the system are probability measures on the space of configurations of particles. For a bounded time interval [0, T ), the evolution of states μ 0 → μ t is shown to hold in a space of sub-Poissonian measures. This result is obtained by: (a) solving equations for correlation functions, which yields the evolution k 0 → k t , t ∈ [0, T ), in a scale of Banach spaces; (b) proving that each k t is a correlation function for a unique measure μ t . The mesoscopic theory is based on a Vlasov-type scaling, that yields a mean-field-like approximate description in terms of the particles' density which obeys a kinetic equation. The latter equation is rigorously derived from that for the correlation functions by the scaling procedure. We prove that the kinetic equation has a unique solution t , t ∈ [0, +∞).

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We investigate stochastic (conservative) non-equilibrium jump dynamics of interacting particles in continuum. The corresponding evolutions of correlation functions are constructed. The mesoscopic scaling (Vlasov scaling) of the dynamics is studied and the corresponding kinetic equations for the particle densities are derived. Keywords Interacting particle system • Jump dynamics • Non-equilibrium evolution • Vlasov scaling • Kinetic equation 1 Introduction Usually, an infinite group of identical particles with different locations in R d can be characterized by locally finite subset of R d , the points of which are

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Medical coding (MC) is an essential prerequisite for reliable data retrieval and reporting. Given a free-text reported term (RT) such as "pain of right thigh to the knee", the task is to identify the matching lowest-level term (LLT) -in this case "unilateral leg pain"-from a very large and continuously growing repository of standardized medical terms. However, automating this task is challenging due to a large number of LLT codes (as of writing over 80 000), limited availability of training data for long tail/emerging classes, and the general high accuracy demands of the medical domain. With this paper, we introduce the MC task, discuss its challenges, and present a novel approach called XTARS that combines traditional BERT-based classification with a recent zero/few-shot learning approach (TARS). We present extensive experiments that show that our combined approach outperforms strong baselines, especially in the few-shot regime. The approach is developed and deployed at Bayer, live since November 2021. As we believe our approach potentially promising beyond MC, and to ensure reproducibility, we release the code to the research community.