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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: closed (30 June 2020) | Viewed by 12596

Special Issue Editor

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland
Interests: modeling of complex systems; multiagent systems; reinforcement learning; emergence and evolution of language; complex networks; statistical mechanics in complex networks; population dynamics; opinion formation; applications of statistical mechanics to computer sciences
Special Issues, Collections and Topics in MDPI journals

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 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

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

Published Papers (5 papers)

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Research

11 pages, 892 KiB  
Article
Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds
by Adam Lipowski, António L. Ferreira and Dorota Lipowska
Entropy 2020, 22(11), 1319; https://0-doi-org.brum.beds.ac.uk/10.3390/e22111319 - 19 Nov 2020
Cited by 1 | Viewed by 1565
Abstract
Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our [...] Read more.
Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
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11 pages, 2923 KiB  
Article
Driver Countries in Global Banking Network
by Farzaneh Atyabi, Olha Buchel and Leila Hedayatifar
Entropy 2020, 22(8), 810; https://0-doi-org.brum.beds.ac.uk/10.3390/e22080810 - 23 Jul 2020
Cited by 3 | Viewed by 2491
Abstract
We analyze the network of cross-border bank lending connections among countries from 1977 to 2018. The network includes core countries that lend money and peripheral countries that borrow money from core countries. In nowadays highly connected banking network, financial crisis that start from [...] Read more.
We analyze the network of cross-border bank lending connections among countries from 1977 to 2018. The network includes core countries that lend money and peripheral countries that borrow money from core countries. In nowadays highly connected banking network, financial crisis that start from a country can spread to other countries very fast and cause global affects. We use principal component analysis (PCA) to find the influential lending (core) countries in this network over the years and clusters of borrowing (peripheral) countries related to these impactful core countries. We find three clusters of peripheral countries, with some constant and some changing members over time. This can be a sign of changes in the financial or political interactions among countries. The changes in the role of core countries and how these roles get affected by the important financial crisis in the past decades is investigated. Among 31 of core countries, 7 countries have a partially or constantly important role in the network including France, United Kingdom, United States, Japan, Germany, Chinese Taipei and Switzerland. Full article
(This article belongs to the Special Issue Statistical Mechanics of Complex Systems)
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16 pages, 2188 KiB  
Article
Taylor’s Law in Innovation Processes
by Francesca Tria, Irene Crimaldi, Giacomo Aletti and Vito D. P. Servedio
Entropy 2020, 22(5), 573; https://0-doi-org.brum.beds.ac.uk/10.3390/e22050573 - 19 May 2020
Cited by 4 | Viewed by 3420
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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16 pages, 2400 KiB  
Article
Analysis of the Stochastic Population Model with Random Parameters
by Adeeb Noor, Ahmed Barnawi, Redhwan Nour, Abdullah Assiri and Mohamed El-Beltagy
Entropy 2020, 22(5), 562; https://0-doi-org.brum.beds.ac.uk/10.3390/e22050562 - 18 May 2020
Cited by 7 | Viewed by 2168
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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12 pages, 385 KiB  
Article
Generalized Independence in the q-Voter Model: How Do Parameters Influence the Phase Transition?
by Angelika Abramiuk and Katarzyna Sznajd-Weron
Entropy 2020, 22(1), 120; https://0-doi-org.brum.beds.ac.uk/10.3390/e22010120 - 19 Jan 2020
Cited by 7 | Viewed by 2486
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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