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随机微分方程的广义坐标理论AI 解读

Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some non-trivial temporal correlation structure, which renders the SDE non-Markovian; a phenomenon commonly known as ``colored'' noise. Thus, an important objective is to develop effective tools for mathematically and numerically studying (possibly non-Markovian) SDEs. In this report, we formalise a…

利用核密度估计选择非线性指标计算中的半径AI 解读

When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which quantifies the probability of finding neighbors, i.e. pair of points spaced by less than the radius parameter. While each nonlinear measure comes with several specific empirical rules to select a radius value, we provide a systematic selection…

时间序列相关性的显著性评估：参数方法及生理信号应用AI 解读

Correlation coefficients play a pivotal role in quantifying linear relationships between random variables. Yet, their application to time series data is very challenging due to temporal dependencies. This paper introduces a novel approach to estimate the statistical significance of correlation coefficients in time series data, addressing the limitations of traditional methods based on the concept of effective degrees of freedom (or effective sample size, ESS). These…