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The analysis of temporal networks heavily depends on the analysis of time-respecting paths. However, before being able to model and analyze the time-respecting paths, we have to infer the timescales at which the temporal edges influence…

Physics and Society · Physics 2023-01-30 Luka V. Petrović , Anatol Wegner , Ingo Scholtes

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…

Information Theory · Computer Science 2016-02-09 German Gomez-Herrero , Wei Wu , Kalle Rutanen , Miguel C. Soriano , Gordon Pipa , Raul Vicente

This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a…

Information Theory · Computer Science 2025-12-05 Audun Myers , Bill Kay , Iliana Alvarez , Michael Hughes , Cameron Mackenzie , Carlos Ortiz Marrero , Emily Ellwein , Erik Lentz

Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…

Chaotic Dynamics · Physics 2015-05-14 M. S. Baptista , E. J. Ngamga , Paulo R. F. Pinto , Margarida Brito , J. Kurths

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…

Biological Physics · Physics 2018-10-17 Mattia Miotto , Lorenzo Monacelli

Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…

Statistical Mechanics · Physics 2024-02-23 Yunxiang Song , Thomas A. Witten

We introduce Extrema-Segmented Entropy (ExSEnt), a feature-decomposed framework for quantifying time-series complexity that separates temporal from amplitude contributions. The method partitions a signal into monotonic segments by detecting…

Chaotic Dynamics · Physics 2025-09-30 Sara Kamali , Fabiano Baroni , Pablo Varona

Shannon Entropy has been extensively used for characterizing complexity of time series arising from chaotic dynamical systems and stochastic processes such as Markov chains. However, for short and noisy time series, Shannon entropy performs…

Chaotic Dynamics · Physics 2016-12-08 Nithin Nagaraj , Karthi Balasubramanian

In the present work we investigate phase correlations by recourse to the Shannon entropy. Using theoretical arguments we show that the entropy provides an accurate measure of phase correlations in any dynamical system, in particular when…

Chaotic Dynamics · Physics 2019-10-24 P. M. Cincotta , C. M. Giordano

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

Disordered Systems and Neural Networks · Physics 2013-05-30 James West , Lucas Lacasa , Simone Severini , Andrew Teschendorff

We test whether the complexity of cardiac interbeat interval time series is simply a consequence of the wide range of scales characterizing human behavior, especially physical activity, by analyzing data taken from healthy adult subjects…

Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…

The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…

Dynamical Systems · Mathematics 2017-10-19 Karsten Keller , Sergiy Maksymenko , Inga Stolz

Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…

Machine Learning · Statistics 2020-07-03 Stijn de Waele

Most complex systems are intrinsically dynamic in nature. The evolution of a dynamic complex system is typically represented as a sequence of snapshots, where each snapshot describes the configuration of the system at a particular instant…

Physics and Society · Physics 2016-12-30 Richard K. Darst , Clara Granell , Alex Arenas , Sergio Gómez , Jari Saramäki , Santo Fortunato

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

Statistical Mechanics · Physics 2015-06-18 Torbjørn Helvik , Kristian Lindgren

In this work, we introduce metrics to evaluate the use of simplified time series in the context of interpretability of a TSC -- a Time Series Classifier. Such simplifications are important because time series data, in contrast to text and…

Machine Learning · Computer Science 2025-11-04 Brigt Håvardstun , Felix Marti-Perez , Cèsar Ferri , Jan Arne Telle

In this paper we present the concept of description of random processes in complex systems with the discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations…

Statistical Mechanics · Physics 2009-10-31 Renat Yulmetyev , Reter Hanggi , Fail Gafarov

Multiscale entropy (MSE) has been widely used to examine nonlinear systems involving multiple time scales, such as biological and economic systems. Conversely, Allan variance has been used to evaluate the stability of oscillators, such as…

Chaotic Dynamics · Physics 2023-05-03 Naoki Asuke , Tomoki Yamagami , Takatomo Mihana , André Röhm , Ryoichi Horisaki , Makoto Naruse

We present exact results for two complementary measures of spatial structure generated by 1D spin systems with finite-range interactions. The first, excess entropy, measures the apparent spatial memory stored in configurations. The second,…

Statistical Mechanics · Physics 2009-10-30 James P. Crutchfield , David P. Feldman