Special Issue "Statistical Mechanics of Complex Systems"

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

Deadline for manuscript submissions: 30 June 2020.

Special Issue Editor

Prof. Dr. Adam Lipowski
Website
Guest Editor
Faculty of Physics, Adam Mickiewicz University, Poznań 61-614, Poland
Interests: modeling of complex systems; multi-agent systems; reinforcement learning; emergence and evolution of language; complex networks; statistical mechanics on complex networks; population dynamics; opinion formation; applications of statistical mechanics to computer sciences

Special Issue Information

Dear Colleagues,

Complex systems attract considerable attention of scientists from various disciplines. Examples of these ubiquitous and extremely important systems include financial markets and human economies, highway transportation and telecommunication networks, climate, ecology, social networks, language formation and its development, the immune system, cancer, and many others. It seems that a key feature of any complex system is that while it is composed of a certain number of interacting elements, as a whole, it exhibits new emerging properties that are much different from the properties and behaviors of its components. Consequently, statistical mechanics approaches provide a well-suited and very promising methodology to examine complex systems. Indeed, due to the multitude of such studies, at least certain aspects of some complex systems are now well understood.

The aim of this Special Issue is to collect papers that introduce novel models or develop innovative methods to study complex systems. Papers that examine agent-based models, complex networks, cellular automata, or adaptive systems using computer simulations, stochastic processes, time series analysis, neural networks, or machine learning are particularly welcome.

Prof. Dr. Adam Lipowski
Guest Editor

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 papers will be 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 1600 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

  • complex systems
  • complex networks
  • multiagent systems
  • computational modeling
  • emergent behavior
  • dynamics of interacting systems

Published Papers (3 papers)

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Research

Open AccessFeature PaperArticle
Taylor’s Law in Innovation Processes
Entropy 2020, 22(5), 573; https://doi.org/10.3390/e22050573 - 19 May 2020
Abstract
Taylor’s law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor’s law exponents in such [...] Read more.
Taylor’s law quantifies the scaling properties of the fluctuations of the number of innovations occurring in open systems. Urn-based modeling schemes have already proven to be effective in modeling this complex behaviour. Here, we present analytical estimations of Taylor’s law exponents in such models, by leveraging on their representation in terms of triangular urn models. We also highlight the correspondence of these models with Poisson–Dirichlet processes and demonstrate how a non-trivial Taylor’s law exponent is a kind of universal feature in systems related to human activities. We base this result on the analysis of four collections of data generated by human activity: (i) written language (from a Gutenberg corpus); (ii) an online music website (Last.fm); (iii) Twitter hashtags; (iv) an online collaborative tagging system (Del.icio.us). While Taylor’s law observed in the last two datasets agrees with the plain model predictions, we need to introduce a generalization to fully characterize the behaviour of the first two datasets, where temporal correlations are possibly more relevant. We suggest that Taylor’s law is a fundamental complement to Zipf’s and Heaps’ laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
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Open AccessArticle
Analysis of the Stochastic Population Model with Random Parameters
Entropy 2020, 22(5), 562; https://doi.org/10.3390/e22050562 - 18 May 2020
Abstract
The population models allow for a better understanding of the dynamical interactions with the environment and hence can provide a way for understanding the population changes. They are helpful in studying the biological invasions, environmental conservation and many other applications. These models become [...] Read more.
The population models allow for a better understanding of the dynamical interactions with the environment and hence can provide a way for understanding the population changes. They are helpful in studying the biological invasions, environmental conservation and many other applications. These models become more complicated when accounting for the stochastic and/or random variations due to different sources. In the current work, a spectral technique is suggested to analyze the stochastic population model with random parameters. The model contains mixed sources of uncertainties, noise and uncertain parameters. The suggested algorithm uses the spectral decompositions for both types of randomness. The spectral techniques have the advantages of high rates of convergence. A deterministic system is derived using the statistical properties of the random bases. The classical analytical and/or numerical techniques can be used to analyze the deterministic system and obtain the solution statistics. The technique presented in the current work is applicable to many complex systems with both stochastic and random parameters. It has the advantage of separating the contributions due to different sources of uncertainty. Hence, the sensitivity index of any uncertain parameter can be evaluated. This is a clear advantage compared with other techniques used in the literature. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
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Open AccessArticle
Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?
Entropy 2020, 22(1), 120; https://doi.org/10.3390/e22010120 - 19 Jan 2020
Cited by 1
Abstract
We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the [...] Read more.
We study the q-voter model with flexibility, which allows for describing a broad spectrum of independence from zealots, inflexibility, or stubbornness through noisy voters to self-anticonformity. Analyzing the model within the pair approximation allows us to derive the analytical formula for the critical point, below which an ordered (agreement) phase is stable. We determine the role of flexibility, which can be understood as an amount of variability associated with an independent behavior, as well as the role of the average network degree in shaping the character of the phase transition. We check the existence of the scaling relation, which previously was derived for the Sznajd model. We show that the scaling is universal, in a sense that it does not depend neither on the size of the group of influence nor on the average network degree. Analyzing the model in terms of the rescaled parameter, we determine the critical point, the jump of the order parameter, as well as the width of the hysteresis as a function of the average network degree k and the size of the group of influence q. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

1. Name: Prof. Dr. Adam Lipowski

2. Title: Analysis of the Stochastic Population Models with Random Parameters
Name: M.  El-Beltagy,  A. Noor, A. Bernawi, R. Nour

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