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Related papers: On the Dynamical Foundation of Multifractality

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Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type…

Chaotic Dynamics · Physics 2018-04-18 Paul M. Riechers , James P. Crutchfield

The density matrix yields probabilistic information about the outcome of measurements on a quantum system, but it does not distinguish between classical randomness in the preparation of the system and entanglement with its environment.…

Quantum Physics · Physics 2025-09-11 Julien Pinske , Klaus Mølmer

In this paper we combine two powerful computational techniques, well-tempered metadynamics and time lagged independent component analysis. The aim is to develop a new tool for studying rare events and exploring complex free energy…

Statistical Mechanics · Physics 2017-12-08 James McCarty , Michele Parrinello

We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the…

Physics and Society · Physics 2015-06-12 Lucas Lacasa , Jesus Gomez-Gardeñes

The control of complex systems is an ongoing challenge of complexity research. Recent advances using concepts of structural control deduce a wide range of control related properties from the network representation of complex systems. Here,…

Statistical Mechanics · Physics 2013-12-31 Márton Pósfai , Philipp Hövel

In High Speed Train Communications (HSTC), the most challenging issue is coping with the extremely fast fading channel. Compared with its static counterpart, channel estimation on the move consumes excessive energy and spectrum to achieve…

Information Theory · Computer Science 2014-04-01 Chunxu Jiao , Zhaoyang Zhang , Huazi Zhang , Liangliang Zhu

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…

Methodology · Statistics 2023-02-13 Lujia Bai , Weichi Wu

Recently, ergodic control has been suggested as a means to guide mobile sensors for information gathering tasks. In ergodic control, a mobile sensor follows a trajectory that is ergodic with respect to some information density distribution.…

Systems and Control · Computer Science 2018-08-22 Louis Dressel , Mykel J. Kochenderfer

In this article, we pay attention to transitive dynamical systems having the shadowing property and the entropy functions are upper semicontinuous. As for these dynamical systems, when we consider ergodic optimization restricted on the…

Dynamical Systems · Mathematics 2021-12-24 Wanshan Lin , Xueting Tian

Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…

Quantitative Methods · Quantitative Biology 2023-02-21 Madhur Mangalam , Ralf Metzler , Damian G. Kelty-Stephen

The metriplectic formalism is useful for describing complete dynamical systems which conserve energy and produce entropy. This creates challenges for model reduction, as the elimination of high-frequency information will generally not…

Numerical Analysis · Mathematics 2022-12-28 Anthony Gruber , Max Gunzburger , Lili Ju , Zhu Wang

Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…

Mathematical Physics · Physics 2025-10-07 Tom Hutchcroft

We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that…

Data Analysis, Statistics and Probability · Physics 2009-11-13 R. T. Wicks , S. C. Chapman , R. O. Dendy

In this paper we will try to assess the multifractality displayed by the high-frequency returns of Madrid's Stock Exchange IBEX35 index. A Multifractal Detrended Fluctuation Analysis shows that this index has a wide singularity spectrum…

Statistical Finance · Quantitative Finance 2015-06-16 Pablo Suárez-García , David Gómez-Ullate

Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…

Disordered Systems and Neural Networks · Physics 2026-03-06 Shijie Liu , Jinliang Han , Jianming Liu , Tim Rogers , Yongzheng Sun

We give a thermodynamically consistent description of simultaneous heat and particle transport, as well as of the associated cross-effects, in the framework of a chaotic dynamical system, a generalized multibaker map. Besides the density, a…

chao-dyn · Physics 2009-10-31 Laszlo Matyas , Tamas Tel , Jurgen Vollmer

Causal decomposition depicts a cause-effect relationship that is not based on the concept of prediction, but based on the phase dependence of time series. It has been validated in both stochastic and deterministic systems and is now…

Signal Processing · Electrical Eng. & Systems 2020-08-18 Yi Zhang , Qin Yang , Lifu Zhang , Branko Celler , Steven Su , Peng Xu , Dezhong Yao

We introduce two abstract constructions for building new measurable dynamical systems from existing ones and study their ergodic properties. The first of these constructions, a "reciprocal transformation," produces a type of non-singular…

Dynamical Systems · Mathematics 2025-07-02 Chris Johnson

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

Data Structures and Algorithms · Computer Science 2020-02-04 Kathrin Hanauer , Monika Henzinger , Christian Schulz

In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A {\bf 209} (1995) 321) or the SDL measure (Phys. Rev. E {\bf 59} (1999) 2). All these…

adap-org · Physics 2015-06-30 Ricard V. Sole , Bartolo Luque