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Entropy
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From Time Series to Stochastic Dynamic Models
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From Time Series to Stochastic Dynamic Models

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (15 August 2021) | Viewed by 13500

Special Issue Editors

Prof. Dr. Mohammad Reza Rahimi Tabar

E-Mail Website
Guest Editor
1. Department of Physics, Sharif University of Technology, Tehran, Iran
2. Department of Physics, Oldenburg University, D-26111 Oldenburg, Germany
Interests: dynamics of the complex systems; stochastic processes; time series analysis; control of complex systems
Prof. Dr. Muhammad Sahimi

E-Mail Website
Guest Editor
Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA
Interests: percolation theory and stochastic processes; transport; adsorption and separation of fluid mixtures in nanoporous membranes; molecular dynamics and Monte Carlo Simulations; discrete stochastic modelling of biological phenomena

Special Issue Information

Dear Colleagues,

When dynamical equations describing a complex system are not known, as, e.g., for many systems considered in real world, we need a top-down approach to understand its complexity and modeling.

We welcome contributions that have focus on the question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data, with a data-based approach how should one analyze the data, assess underlying deterministic trends and nonlinearities, uncover characteristics of the fluctuations and construct a stochastic evolution equation? The answer to this question yields important information on the dynamical properties of the system under consideration.

Historically, this question has been addressed for the case of deterministic dynamical systems by methods in which the fluctuations in a measured time series has been considered as a random variable, additively superimposed on a trajectory generated by a deterministic dynamical system. The problem of dynamical noise, i.e., fluctuations that interfere with the dynamical evolution, has been addressed recently in much details. Such approaches will be relevant to many fields of research across various disciplines; for instance, physics, astrophysics, meteorology, earth science, engineering, finance, medicine, and neurosciences, and will led to many important results.

Foreseen contributions include the following:

  • Construction of a stochastic dynamical equation from time series
  • Data-based construction of a potential function from time series, whose valleys represent stable attractors of the dynamics
  • Characterizations of local (time-dependent) stochastic behaviors of a given nonstationary time series

Prof. Dr. Mohammad Reza Rahimi Tabar
Prof. Muhammad Sahimi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • time series
  • stochastic processes
  • modeling complex dynamical systems
  • stochastic differential equations

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Published Papers (4 papers)

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Research

15 pages, 541 KiB  
Article
Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator
by Leonardo Rydin Gorjão, Dirk Witthaut, Klaus Lehnertz and Pedro G. Lind
Entropy 2021, 23(5), 517; https://doi.org/10.3390/e23050517 - 24 Apr 2021
Cited by 11 | Viewed by 3376
Abstract
With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different [...] Read more.
With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. We arrive at a closed-form solution expressed through conditional moments, which can be extracted directly from time-series data with a finite sampling intervals. We provide all finite-time correction terms for parametric and non-parametric estimation of the Kramers–Moyal coefficients for discontinuous processes which can be easily implemented—employing Bell polynomials—in time-series analyses of stochastic processes. With exemplary cases of insufficiently sampled diffusion and jump-diffusion processes, we demonstrate the advantages of our arbitrary-order finite-time corrections and their impact in distinguishing diffusion and jump-diffusion processes strictly from time-series data. Full article
(This article belongs to the Special Issue From Time Series to Stochastic Dynamic Models)
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9 pages, 2955 KiB  
Article
Testing Jump-Diffusion in Epileptic Brain Dynamics: Impact of Daily Rhythms
by Jutta G. Kurth, Thorsten Rings and Klaus Lehnertz
Entropy 2021, 23(3), 309; https://doi.org/10.3390/e23030309 - 5 Mar 2021
Cited by 3 | Viewed by 2427
Abstract
Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, [...] Read more.
Stochastic approaches to complex dynamical systems have recently provided broader insights into spatial-temporal aspects of epileptic brain dynamics. Stochastic qualifiers based on higher-order Kramers-Moyal coefficients derived directly from time series data indicate improved differentiability between physiological and pathophysiological brain dynamics. It remains unclear, however, to what extent stochastic qualifiers of brain dynamics are affected by other endogenous and/or exogenous influencing factors. Addressing this issue, we investigate multi-day, multi-channel electroencephalographic recordings from a subject with epilepsy. We apply a recently proposed criterion to differentiate between Langevin-type and jump-diffusion processes and observe the type of process most qualified to describe brain dynamics to change with time. Stochastic qualifiers of brain dynamics are strongly affected by endogenous and exogenous rhythms acting on various time scales—ranging from hours to days. Such influences would need to be taken into account when constructing evolution equations for the epileptic brain or other complex dynamical systems subject to external forcings. Full article
(This article belongs to the Special Issue From Time Series to Stochastic Dynamic Models)
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16 pages, 1924 KiB  
Article
Multi-Chaotic Analysis of Inter-Beat (R-R) Intervals in Cardiac Signals for Discrimination between Normal and Pathological Classes
by Oleg Gorshkov and Hernando Ombao
Entropy 2021, 23(1), 112; https://doi.org/10.3390/e23010112 - 15 Jan 2021
Cited by 4 | Viewed by 2808
Abstract
Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm [...] Read more.
Cardiac signals have complex structures representing a combination of simpler structures. In this paper, we develop a new data analytic tool that can extract the complex structures of cardiac signals using the framework of multi-chaotic analysis, which is based on the p-norm for calculating the largest Lyapunov exponent (LLE). Appling the p-norm is useful for deriving the spectrum of the generalized largest Lyapunov exponents (GLLE), which is characterized by the width of the spectrum (which we denote by W). This quantity measures the degree of multi-chaos of the process and can potentially be used to discriminate between different classes of cardiac signals. We propose the joint use of the GLLE and spectrum width to investigate the multi-chaotic behavior of inter-beat (R-R) intervals of cardiac signals recorded from 54 healthy subjects (hs), 44 subjects diagnosed with congestive heart failure (chf), and 25 subjects diagnosed with atrial fibrillation (af). With the proposed approach, we build a regression model for the diagnosis of pathology. Multi-chaotic analysis showed a good performance, allowing the underlying dynamics of the system that generates the heart beat to be examined and expert systems to be built for the diagnosis of cardiac pathologies. Full article
(This article belongs to the Special Issue From Time Series to Stochastic Dynamic Models)
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12 pages, 810 KiB  
Article
Stochastic SIS Modelling: Coinfection of Two Pathogens in Two-Host Communities
by Auwal Abdullahi, Shamarina Shohaimi, Adem Kilicman, Mohd Hafiz Ibrahim and Nader Salari
Entropy 2020, 22(1), 54; https://doi.org/10.3390/e22010054 - 31 Dec 2019
Cited by 4 | Viewed by 3831
Abstract
A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis. Therefore, we studied two susceptible classes [...] Read more.
A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis. Therefore, we studied two susceptible classes S 1 ( t ) and S 2 ( t ) , each of which can be infected when interacting with two different infectious groups I 1 ( t ) and I 2 ( t ) . The stochastic models were formulated through the continuous time Markov chain (CTMC) along with their deterministic analogues. The statistics for the developed model were studied using the multi-type branching process. Since each epidemic class was assumed to transmit only its own type of pathogen, two reproduction numbers were obtained, in addition to the probability-generating functions of offspring. Thus, these, together with the mean number of infections, were used to estimate the probability of extinction. The initial population of infectious classes can influence their probability of extinction. Understanding the disease extinctions and outbreaks could result in rapid intervention by the management for effective control measures. Full article
(This article belongs to the Special Issue From Time Series to Stochastic Dynamic Models)
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