We suggest a new nonlinear expansion of space-distributed observational time series. The
expansion allows constructing principal nonlinear manifolds holding essential part of …

Quantitative characterization of causal couplings from time series is crucial in studies of
complex systems of different origin. Various statistical tools for that exist and new ones are …

A new data-driven model for analysis and prediction of spatially distributed time series is
proposed. The model is based on a linear dynamical mode (LDM) decomposition of the …

The local approximation prediction model (LPM) is a forecasting approach based on chaos
theory. It uses the Euclidean distance to evaluate the spatial proximity between two phase …

In this work we formulate a consistent Bayesian approach to modeling stochastic (random)
dynamical systems by time series and implement it by means of artificial neural networks …

Currently, causes of the middle Pleistocene transition (MPT)–the onset of large-amplitude
glacial variability with 100 kyr time scale instead of regular 41 kyr cycles before–are a …

In estimation of causal couplings between observed processes, it is important to
characterize coupling roles at various time scales. The widely used Granger causality …

A method for optimal data simulation using random evolution operator is proposed. We
consider a discrete data-driven model of the evolution operator that is a superposition of …

An approach to prognosis of qualitative behavior of an unknown dynamical system (DS)
from weakly nonstationary chaotic time series (TS) containing significant measurement …

Athletes use amphetamines to improve their performance through largely unknown
mechanisms. Considering that body temperature is one of the major determinants of …