Special Issue "Disordered Systems, Fractals and Chaos"

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

Deadline for manuscript submissions: 31 January 2020.

Special Issue Editor

Prof. Dr. Marcel Ausloos
E-Mail Website
Guest Editor
1. School of Business, University of Leicester, Leicester, LE2 1RQ, United Kingdom
2. Department of Statistics and Econometrics, Bucharest University of Economic Studies, Bucharest, 010552 Sector 1, Romania
Interests: time series analyses; statistical methods; multifractals; socio-eonophysics; models; religion implications; bibliometrics; scientometrics
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Special Issue Information

Dear Colleagues,

It is difficult to know what came first, and which one developed faster, nowadays, with the complex levels that have been reached by the study of disordered systems, fractals, and chaos. Disordered systems likely pre-date the techniques allowing their properties to be described in terms of fractals (and scaling arguments) and, in particular, their chaotic features. The level of complexity is such that in disordered systems, it is hard to disentangle the concepts from the analysis of features.

This allows the two aspects to intermingle without losing their separate identities. In fact, one should not separate, unmix, or disjoin, such features.

Fractal phenomena in disordered systems are, nowadays, of such general knowledge that a Special Issue based on “entropy” is particularly appealing, since one can cover a broad range of both “old” and “new” topics. These include the geometric formulation of aggregates and rough interfaces, as the first applications, in addition to studies of fractal networks and from the very current studies of (multilayered or otherwise) networks up to the study of nonequilibrium processes (generalized classical entropy concepts), multifractals, random multiplicative processes, earthquakes, and, even now, economic, sociological, and medical applications. Indeed, the discovery of “stylized facts” in financial data was concomitant to fractional Brownian motion developments, whence gathering the three items for this issue: disordered systems, fractals, and chaos. I do not discount any test based on scaling ideas, like Benford law. Nowadays, there are also challenges in the medical field, not only EEG, but also taking a much larger perspective on biomedical engineering, neuroscience, and (networked or otherwise) physiology. I would even re-include botany, more generally “ecology”, with regard to population dynamics. A rather relevant field pertaining to the Special Issue theme is “opinion dynamics”—text analyses should also be of renewed interest. Accounting tests can also lead to enthusiastic papers connecting fractals and chaos in a new “natural” way.

As long as we are aware that entropy is a measure of diversity, we should connect with all disordered systems; we should look at power laws, and discuss their validity limit, without any fear; and we should prepare nonlinear (dynamic) equations for obtaining “order from chaos”. We know that part of the challenge stems from “real things”, in measuring properties, thereafter modeling, and, if possible, forecasting. We should be open minded. We are.

Thus, it is proposed that the articles comprising this Special Issue should provide our colleagues with a good sense of the remarkable diversity and important applications of fractals, with theoretical and practical features in any type of disordered system. A huge variety of perspectives can be presented. We wish to be one for all, and all for one. One paper on our beloved investigation topic will serve many. There are no limits.

Prof. Dr. Marcel Ausloos
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

  • entropy
  • fractals
  • chaos
  • networks
  • econophysics
  • sociophysics
  • ecology
  • opinion dynamics
  • aggregates
  • physiology
  • applied linguistics
  • power laws
  • systemic risk
  • nonequilibrium states
  • multifractals
  • fractional Brownian motion
  • time series

Published Papers (3 papers)

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Research

Open AccessArticle
An Intrinsic Entropy Model for Exchange-Traded Securities
Entropy 2019, 21(12), 1173; https://doi.org/10.3390/e21121173 - 29 Nov 2019
Abstract
This paper introduces an intrinsic entropy model which can be employed as an indicator for gauging investors’ interest in a given exchange-traded security, along with the state of the overall market corroborated by individual security trading data. Although the syntagma of intrinsic entropy [...] Read more.
This paper introduces an intrinsic entropy model which can be employed as an indicator for gauging investors’ interest in a given exchange-traded security, along with the state of the overall market corroborated by individual security trading data. Although the syntagma of intrinsic entropy might sound somehow pleonastic, since entropy itself characterizes the fundamentals of a system, we would like to make a clear distinction between entropy models based on the values that a random variable may take, and the model that we propose, which employs actual stock exchange trading data. The model that we propose for the intrinsic entropy does not include any exogenous factor that could influence the level of entropy. The intrinsic entropy signals if the market is either inclined to buy the security or rather to sell it. We further explore the usage of the intrinsic entropy model for algorithmic trading, in order to demonstrate the value of our model in assisting investors’ intraday stock portfolio selection, along with timely generated signals for supporting the buy/sell decision-making process. The test results provide empirical evidence that the proposed intrinsic entropy model can be used as an indicator for evaluating the direction and the intensity of intraday trading activity of an exchange-traded security. The data employed for testing consisted of historical intraday transactions executed on The Bucharest Stock Exchange (BVB). Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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Open AccessFeature PaperArticle
Ordered Avalanches on the Bethe Lattice
Entropy 2019, 21(10), 968; https://doi.org/10.3390/e21100968 - 03 Oct 2019
Abstract
We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b [...] Read more.
We discuss deterministic sequences of avalanches on a directed Bethe lattice. The approach is motivated by the phenomenon of self-organized criticality. Grains are added only at one node of the network. When the number of grains at any node exceeds a threshold b, each of k out-neighbors gets one grain. The probability of an avalanche of size s is proportional to s τ . When the avalanche mass is conserved ( k = b ), we get τ = 1 . For an application of the model to social phenomena, the conservation condition can be released. Then, the exponent τ is found to depend on the model parameters; τ     l o g ( b ) / l o g ( k ) . The distribution of the time duration of avalanches is exponential. Multifractal analysis of the avalanche sequences reveals their strongly non-uniform fractal organization. Maximal value of the singularity strength α m a x in the bifractal spectrum is found to be 1 / τ . Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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Open AccessArticle
Research about the Characteristics of Chaotic Systems Based on Multi-Scale Entropy
Entropy 2019, 21(7), 663; https://doi.org/10.3390/e21070663 - 06 Jul 2019
Abstract
The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, [...] Read more.
The logistic chaotic system, as a classical complex phenomenon of nonlinear dynamic systems, has received extensive attention in the field of secure communication. It is generally believed that the characteristics of chaos are suitable for the needs of encryption systems. In this paper, a multi-scale entropy theory analysis and statistical analysis are carried out on the chaotic sequences produced by different parameters and different initial values of logistic systems. According to the simulation results, the complexity of the chaotic system represented by the logistic system is mainly decided by parameter μ. Not all characteristic parameters of the chaotic system depend on the initial values. It is possible to make a reasonable estimation and prediction of the chaotic system from a macroscopic level. A variance estimation method for the parameter μ is proposed and applied to a logistic system and to another chaotic system, which is equally effective. Full article
(This article belongs to the Special Issue Disordered Systems, Fractals and Chaos)
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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.

Title: A Generalized Joint Copula-Entropy Approach for Cross Ownerships
Authors: Giulia Rotundo 1, Roy Cerqueti 2
Affiliations:
1 Sapienza University, Roma, IT
2  University of Macerata, Macerata and IT
Abstract: We generalize the Cerqueti R., Rotundo G., Ausloos M., (2018), Investigating the Configurations in Cross-Shareholding: A Joint Copula-Entropy Approach, paper published in Entropy 20(2), 134. We extend the range of application of the former results. The financial interdependencies in the Stock market given by the cross-ownerships and cross-shareholdings have different and non monotonic effect on the propagation of cascades.
Literature evidenced that the presence of a network structure may increase the risk due to the structure of interaction, but it can also have dumping effects. In fact, the diversification of companies' portfolios causes a reduction of the sensitivity to its own investments, and an exposure to the fluctuations of the others; however, large diversification makes the company reduce the overall correlation, and the contagion becomes less likely.
In a specular way, the integration of companies in the market (though the sale of their shares) increases the dependence on the other organizations. The trade-off among diversification and integration has been shown to play a key role in tuning the different patterns propagation of contagions and cascades.
Since many configurations may give rise to similar levels of risk, a probabilistic approach is most needed. This work bases on a copula approach for exploring the risk due to such financial interdependencies and the raise of concentration and control. The matter is of interest to regulatory bodies, in view of the guidelines on mergers and acquisitions. The calibration of the models on a dataset serves to outline the application of the theoretical approach.

Title: Italian Election Days, a Study of the Vote Complexity and Entropy
Authors: Parmjit Kaur 1, Stefano Marmani 2, Valerio Ficcadenti 2, and Gurjeet Dhesi 2
Affiliations: 1 DeMontfort, Leicester
London South Bank University
Abstract: In Italy the elections occur often, indeed almost every year the citizens are called to make a democratic choice for deciding the leaders of the administrative entities. Sometimes the national governments have adopted the formula so called “Election Day”, namely the citizens have voted to elect their representatives in more than one administrative body during the same days. This phenomenon, occurred 91 times after 1946 (Italian Republic foundation); this creates the peculiar condition of having the same sample of people expressing decisions on political bases at the same time. Therefore, Election Days constitute the occasion to measure coherency and chaos in the Italian citizen system of expressing political opinion. So, in this paper we address all the Italian elections occurred after the 1946. We collect their information about the number of votes per list at each administrative level and we treat each year of election as the manifestation of a complex system. Then, we use Entropy measures (e.g. Shannon Entropy) to study the degree of disorder manifested in the different types of election, with a particular focus on the so-called Election Day. We aim to check if such cases implicate different levels of disorder of such a system from an historical point of view.

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