Related papers: On the Dynamical Foundation of Multifractality
A recent method based on the concurrence of complex networks and multifractal analyses is applied for the first time to explore ground-level ozone behavior. Ozone time series are converted into complex networks for their posterior analysis.…
Linear response theory, the backbone of non-equilibrium statistical physics, has recently been extended to explain how and why non-ergodic renewal processes are insensitive to simple perturbations, such as in habituation. It was established…
We show why the amount of information communicated between the past and future--the excess entropy--is not in general the amount of information stored in the present--the statistical complexity. This is a puzzle, and a long-standing one,…
Adaptive dynamical systems arise in a multitude of contexts, e.g., optimization, control, communications, signal processing, and machine learning. A precise characterization of their fundamental limitations is therefore of paramount…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
Among the statistical models employed to approximate nonlinear interactions in biological and psychological processes, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, a…
Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$…
Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions are derived. It is shown that interactions retardation leads to irreversible behaviour of many-body…
Economic transformation -- change in what an economy produces -- is foundational to development and rising standards of living. Our understanding of this process has been propelled recently by two branches of work in the field of economic…
Multivariate time series (MTS) analysis prevails in real-world applications such as finance, climate science and healthcare. The various self-attention mechanisms, the backbone of the state-of-the-art Transformer-based models, efficiently…
Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…
We investigate the scaling of the cross-correlations calculated for two-variable time series containing vertex properties in the context of complex networks. Time series of such observables are obtained by means of stationary, unbiased…
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be…
As a quantification of the main bottleneck to flow over a graph, the network property of conductance plays an important role in the process of synchronization of network-coupled dynamical systems. Diffusive coupling terms serve not only to…
The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific…
Weighted networks capture the structure of complex systems where interaction strength is meaningful. This information is essential to a large number of processes, such as threshold dynamics, where link weights reflect the amount of…