Statistical properties for mixing Markov chains with applications to dynamical systems

We establish an abstract, effective large deviations type estimate for Markov systems satisfying a weak form of strong mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product encoding a random torus translation, a model we call a mixed random-quasiperiodic dynamical system. This abstract scheme is applicable to many other types of skew product dynamics.Comment: 46 pages, 1 figure. Revised version corrects some minor errors in the statement of the CLT, adds more results, remarks and reference

A dynamical Thouless formula

In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov exponent and the integrated density of states of a Schr\"odinger operator. Here, the role of the integrated density of states will be played by a more geometrical quantity, the fibered rotation number. As an application of this formula we present limitations on the modulus of continuity of random linear cocycles. Moreover, we derive H\"older-type continuity properties of the fibered rotation number for linear cocycles over various base dynamics.Comment: A couple of references adde

Human induced pluripotent stem cell-derived sensory neurons for fate commitment of bone marrow-derived Schwann cells: Implications for re-myelination therapy

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Fraction Constraint in Partial Wave Analysis

To resolve the non-convex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in both the efficiency of pole searching and the reliability of resonance selection within partial wave analysis

Event Generation and Consistence Test for Physics with Sliced Wasserstein Distance

In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis. Traditional simulation methods often encounter challenges when dealing with complex physical processes and high-dimensional data distributions, resulting in slow performance. To overcome these limitations, we propose a solution based on deep learning with the sliced Wasserstein distance as the loss function. Our method shows its ability on high precision and large-scale simulations, and demonstrates its effectiveness in handling complex physical processes. By employing an advanced transformer learning architecture, we initiate the learning process from a Monte Carlo sample, and generate high-dimensional data while preserving all original distribution features. The generated data samples have passed the consistence test, that is developed to calculate the confidence of the high-dimentional distributions of the generated data samples through permutation tests. This fast simulation strategy, enabled by deep learning, holds significant potential not only for increasing sample sizes and reducing statistical uncertainties but also for applications in numerical integration, which is crucial in partial wave analysis, high-precision sample checks, and other related fields. It opens up new possibilities for improving event simulation in high-energy physics research