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Many stochastic time series can be described by a Langevin equation composed of a deterministic and a stochastic dynamical part. Such a stochastic process can be reconstructed by means of a recently introduced nonparametric method, thus increasing the predictability, i.e. knowledge of the macroscopic drift and the microscopic diffusion functions. If the measurement of a stochastic process is affected by additional strong measurement noise, the reconstruction process cannot be applied. Here, we present a method for the reconstruction of stochastic processes in the presence of strong measurement noise, based on a suitably parametrized ansatz. At the core of the process is the minimization of the functional distance between terms containing the conditional moments taken from measurement data, and the corresponding ansatz functions. It is shown that a minimization of the distance by means of a simulated annealing procedure yields better results than a previously used Levenberg-Marquardt algorithm, which permits a rapid and reliable reconstruction of the stochastic process.
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian posterior probabil
In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential equations t
We present a new benchmarking procedure that is unambiguous and specific to local community-finding methods, allowing one to compare the accuracy of various methods. We apply this to new and existing algorithms. A simple class of synthetic benchmark
Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to
In this work we investigate the origin of the parabolic relation between skewness and kurtosis often encountered in the analysis of experimental time-series. We argue that the numerical values of the coefficients of the curve may provide informations