A central problem in the study of complex systems is to identify hierarchical and intertwined dynamics. A hierarchical level is defined as an aggregation of the system's variables such that the aggregation induces its own closed dynamics. In this paper, we present an algorithm that finds...

Linear measures such as cross-correlation have been used successfully to determine time delays from the given processes. Such an analysis often precedes identifying possible causal relationships between the observed processes. The present study investigates the impact of a positively correlated...

Several studies have investigated the scaling behavior in naturally occurring biological and physical processes using techniques such as detrended fluctuation analysis (DFA). Data acquisition is an inherent part of these studies and maps the continuous process into digital data. The resulting...

Macroscopic thermodynamics of flowing polymeric liquids in terms of a single conformation tensor is derived from atomistic or mechanical bead-spring models via a systematic coarse-graining procedure. The macroscopic equations derived here are consistent with earlier works where they have been...

We present a method for identifying coarse-grained dynamics through aggregation of variables or states in linear dynamical systems. The condition for aggregation is expressed as a permutation symmetry of a set of dual eigenvectors of the matrix that defines the dynamics. The applicability of the...

We propose a simple mathematical model for lipid bilayer membranes of flexible fluid or solid state. The model consists of interacting coarse-grained particles with two extra variables. One indicates the spontaneous curvature at the particle position, and the other indicates the vector...

A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the...

A recently introduced systematic approach to derivations of the macroscopic dynamics from the underlying microscopic equations of motions in the short-memory approximation (Phys. Rev. E 63 (2001) 066124) is presented in detail. The essence of this method is a consistent implementation of...

We investigate how various coarse-graining (signal quantization) methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i)...

Given a closed system described via an amplitude function ψ(x), what is its level of order? We consider here a quantity R defined by the property that it decreases (or stays constant) after the system is coarse grained. It was recently found that (i) this quantity exhibits a series of...