Special Issue "Symmetry and Complexity 2019"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: 31 October 2019.

Special Issue Editor

Prof. Dr. Carlo Cattani
E-Mail Website
Guest Editor
1. Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
2. Ton Duc Thang University, HCMC, Vietnam
Tel. +39 3207406560
Interests: wavelets; fractals; fractional calculus; dynamical systems; data analysis; time series analysis; image analysis; computer science; computational methods; composite materials; elasticity; nonlinear waves
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetry and complexity are two fundamental features of almost all phenomena in nature and science. Any complex physical model is characterized by the existence of some symmetry groups at different scales. On the other hand, breaking the symmetry of a scientific model has always been considered as the most challenging direction for new discoveries. Modelling complexity has recently become an increasingly popular subject, with an impressive growth in applications. The main goal of modelling complexity is to search for hidden or broken symmetries.

Usually, complexity is modelled by dealing with Big Data or dynamical systems, depending on a large number of parameters. Nonlinear dynamical systems and chaotic dynamical systems are also used for modelling complexity. Complex models are often represented by un-smooth objects, non-differentiable objects, fractals, pseudo-random phenomena, and stochastic process.

The discovery of complexity and symmetry in mathematics, physics, engineering, economics, biology, and medicine have opened new challenging fields of research. Therefore, new mathematical tools have been developed in order to obtain quantitative information from models, newly reformulated in terms of nonlinear differential equations.

This Special Issue focuses on the most recent advances in calculus, applied to dynamical problems, linear and nonlinear (fractional, stochastic) ordinary and partial differential equations, integral differential equations, and stochastic integral problems, arising in all fields of science, engineering applications, and other applied fields dealing with complexity.

We are soliciting contributions covering a broad range of topics on symmetry and complexity in:

  • mathematics
  • chemistry
  • physics
  • fluid dynamics and aerodynamics
  • unified physical theory
  • biology
  • nonlinear dynamical systems
  • nonlinear science
  • engineering application
  • chaos
  • fractals
  • image and data analysis
  • computational systems
  • artificial intelligence, neural networks
  • history of science, philosophy, semantic structures

Prof. Dr. Carlo Cattani
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. Symmetry 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 1400 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

  • mathematics
  • physics
  • mathematical physics
  • mechanics
  • fractal
  • differential equations
  • dynamical systems
  • chaos
  • computational methods
  • stochastic process
  • stochastic differential equations
  • pattern recognition
  • data analysis

Published Papers (10 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Open AccessArticle
Proposal for the Identification of Information Technology Services in Public Organizations
Symmetry 2019, 11(10), 1269; https://doi.org/10.3390/sym11101269 - 10 Oct 2019
Abstract
Handling complexity and symmetry in the identification of services for the management of information technology (IT) emerged as a serious challenge in recent times. One of the most important elements that must be defined in the management of information technology services is the [...] Read more.
Handling complexity and symmetry in the identification of services for the management of information technology (IT) emerged as a serious challenge in recent times. One of the most important elements that must be defined in the management of information technology services is the construction and management of a service catalog. However, in order to create this catalog, it is necessary to correctly identify the services to be formed. So far, there are several proposals that serve to identify information technology services in public organizations. However, there are several inherent drawbacks to these processes, whereby many organizations are yet to adapt to the services. The main objective of this research is to present a proposal for the identification of information technology services and the construction of an information technology catalog. For this, the following methodology was applied: (a) a review of the literature, identifying the research that addressed the process of the identification of services; (b) a proposal based on automatic learning to identify information technology services in public organizations, adapting the catalog of services and taking as its main input the history of requests and incidents accredited by the department of information technologies in public organizations in the Republic of Ecuador. In conclusion, this work leads to satisfactory results for the identification of technology services used to construct its catalog. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Graphical abstract

Open AccessArticle
An Efficient Class of Weighted-Newton Multiple Root Solvers with Seventh Order Convergence
Symmetry 2019, 11(8), 1054; https://doi.org/10.3390/sym11081054 - 16 Aug 2019
Abstract
In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. Hence, the name [...] Read more.
In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. Hence, the name of the scheme is ‘weighted-Newton methods’. Theoretical results are studied exhaustively along with the main theorem describing convergence analysis. Stability and convergence domain of the proposed class are also demonstrated by means of using a graphical technique, namely, basins of attraction. Boundaries of these basins are fractal like shapes through which basins are symmetric. Efficacy is demonstrated through numerical experimentation on variety of different functions that illustrates good convergence behavior. Moreover, the theoretical result concerning computational efficiency is verified by computing the elapsed CPU time. The overall comparison of numerical results including accuracy and CPU-time shows that the new methods are strong competitors for the existing methods. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
Directional Thermodynamic Formalism
Symmetry 2019, 11(6), 825; https://doi.org/10.3390/sym11060825 - 21 Jun 2019
Abstract
The usual thermodynamic formalism is uniform in all directions and, therefore, it is not adapted to study multi-dimensional functions with various directional behaviors. It is based on a scaling function characterized in terms of isotropic Sobolev or Besov-type norms. The purpose of the [...] Read more.
The usual thermodynamic formalism is uniform in all directions and, therefore, it is not adapted to study multi-dimensional functions with various directional behaviors. It is based on a scaling function characterized in terms of isotropic Sobolev or Besov-type norms. The purpose of the present paper was twofold. Firstly, we proved wavelet criteria for a natural extended directional scaling function expressed in terms of directional Sobolev or Besov spaces. Secondly, we performed the directional multifractal formalism, i.e., we computed or estimated directional Hölder spectra, either directly or via some Legendre transforms on either directional scaling function or anisotropic scaling functions. We obtained general upper bounds for directional Hölder spectra. We also showed optimal results for two large classes of examples of deterministic and random anisotropic self-similar tools for possible modeling turbulence (or cascades) and textures in images: Sierpinski cascade functions and fractional Brownian sheets. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Open AccessArticle
Reversible Data Hiding Scheme Using Adaptive Block Truncation Coding Based on an Edge-Based Quantization Approach
Symmetry 2019, 11(6), 765; https://doi.org/10.3390/sym11060765 - 05 Jun 2019
Cited by 1
Abstract
In this paper, we provide a novel reversible data hiding method using adaptive block truncation coding based on an edge-based quantization (ABTC-EQ) approach. We exploit the characteristic not being used in ABTC-EQ. To accomplish this, we first utilized a Canny edge detector to [...] Read more.
In this paper, we provide a novel reversible data hiding method using adaptive block truncation coding based on an edge-based quantization (ABTC-EQ) approach. We exploit the characteristic not being used in ABTC-EQ. To accomplish this, we first utilized a Canny edge detector to obtain an edge image and classify each block in a cover image into two versions, edge-block and non-edge-block. Subsequently, k-means clustering was used to obtain three quantization levels and derive the corresponding bit map while the current processing block was the case of an edge-block. Then Zero-Point Fixed Histogram Shifting (ZPF-HS) was applied to embed the secret information into compressed code. The experimental results show that our method provides a high embedding capacity for each test image and performance is better than other methods. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations
Symmetry 2019, 11(4), 530; https://doi.org/10.3390/sym11040530 - 12 Apr 2019
Cited by 1
Abstract
This paper discusses the applications of numerical inversion of the Laplace transform method based on the Bernstein operational matrix to find the solution to a class of fractional differential equations. By the use of Laplace transform, fractional differential equations are firstly converted to [...] Read more.
This paper discusses the applications of numerical inversion of the Laplace transform method based on the Bernstein operational matrix to find the solution to a class of fractional differential equations. By the use of Laplace transform, fractional differential equations are firstly converted to system of algebraic equations then the numerical inverse of a Laplace transform is adopted to find the unknown function in the equation by expanding it in a Bernstein series. The advantages and computational implications of the proposed technique are discussed and verified in some numerical examples by comparing the results with some existing methods. We have also combined our technique to the standard Laplace Adomian decomposition method for solving nonlinear fractional order differential equations. The method is given with error estimation and convergence criterion that exclude the validity of our method. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
On a SIR Model in a Patchy Environment Under Constant and Feedback Decentralized Controls with Asymmetric Parameterizations
Symmetry 2019, 11(3), 430; https://doi.org/10.3390/sym11030430 - 22 Mar 2019
Cited by 2
Abstract
This paper presents a formal description and analysis of an SIR (involving susceptible- infectious-recovered subpopulations) epidemic model in a patchy environment with vaccination controls being constant and proportional to the susceptible subpopulations. The patchy environment is due to the fact that there is [...] Read more.
This paper presents a formal description and analysis of an SIR (involving susceptible- infectious-recovered subpopulations) epidemic model in a patchy environment with vaccination controls being constant and proportional to the susceptible subpopulations. The patchy environment is due to the fact that there is a partial interchange of all the subpopulations considered in the model between the various patches what is modelled through the so-called travel matrices. It is assumed that the vaccination controls are administered at each community health centre of a particular patch while either the total information or a partial information of the total subpopulations, including the interchanging ones, is shared by all the set of health centres of the whole environment under study. In the case that not all the information of the subpopulations distributions at other patches are known by the health centre of each particular patch, the feedback vaccination rule would have a decentralized nature. The paper investigates the existence, allocation (depending on the vaccination control gains) and uniqueness of the disease-free equilibrium point as well as the existence of at least a stable endemic equilibrium point. Such a point coincides with the disease-free equilibrium point if the reproduction number is unity. The stability and instability of the disease-free equilibrium point are ensured under the values of the disease reproduction number guaranteeing, respectively, the un-attainability (the reproduction number being less than unity) and stability (the reproduction number being more than unity) of the endemic equilibrium point. The whole set of the potential endemic equilibrium points is characterized and a particular case is also described related to its uniqueness in the case when the patchy model reduces to a unique patch. Vaccination control laws including feedback are proposed which can take into account shared information between the various patches. It is not assumed that there are in the most general case, symmetry-type constrains on the population fluxes between the various patches or in the associated control gains parameterizations. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
Evolution of Conformity Dynamics in Complex Social Networks
Symmetry 2019, 11(3), 299; https://doi.org/10.3390/sym11030299 - 28 Feb 2019
Abstract
Conformity is a common phenomenon among people in social networks. In this paper, we focus on customers’ conformity behaviors in a symmetry market where customers are located in a social network. We establish a conformity model and analyze it in ring network, random [...] Read more.
Conformity is a common phenomenon among people in social networks. In this paper, we focus on customers’ conformity behaviors in a symmetry market where customers are located in a social network. We establish a conformity model and analyze it in ring network, random network, small-world network, and scale-free network. Our simulations shown that topology structure, network size, and initial market share have significant effects on the evolution of customers’ conformity behaviors. The market will likely converge to a monopoly state in small-world networks but will form a duopoly market in scale networks. As the size of the network increases, there is a greater possibility of forming a dominant group of preferences in small-world network, and the market will converge to the monopoly of the product which has the initial selector in the market. Also, network density will become gradually significant in small-world networks. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
A Novel Computational Technique for Impulsive Fractional Differential Equations
Symmetry 2019, 11(2), 216; https://doi.org/10.3390/sym11020216 - 13 Feb 2019
Cited by 1
Abstract
A computational technique for impulsive fractional differential equations is proposed in this paper. Adomian decomposition method plays an efficient role for approximate analytical solutions for ordinary or fractional calculus. Semi-analytical method is proposed by use of the Adomian polynomials. The method successively updates [...] Read more.
A computational technique for impulsive fractional differential equations is proposed in this paper. Adomian decomposition method plays an efficient role for approximate analytical solutions for ordinary or fractional calculus. Semi-analytical method is proposed by use of the Adomian polynomials. The method successively updates the initial values and gives the numerical solutions on different impulsive intervals. As one of the numerical examples, an impulsive fractional logistic differential equation is given to illustrate the method. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
Improved Hydrodynamic Analysis of 3-D Hydrofoil and Marine Propeller Using the Potential Panel Method Based on B-Spline Scheme
Symmetry 2019, 11(2), 196; https://doi.org/10.3390/sym11020196 - 11 Feb 2019
Abstract
In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with [...] Read more.
In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with the interpolation of the corner points and collocation points to ensure accuracy and continuity of the interpolation points. The B-spline interpolation is used for the distribution of the singularity elements on a complex surface to ensure continuity of the results for the intensity of the singular points and to reduce the possibility of abrupt changes in the surface velocity potential to a certain extent. A conventional cubic spline method is also implemented as a comparison of the proposed method. The surface pressure coefficient and lift the performance of 2-D and 3-D hydrofoils of sweepback and dihedral type with different aspect ratios are analyzed to verify the rationality and feasibility of the present method. The surface pressure distribution and coefficients of thrust and torque are calculated for different marine propellers and compared with the experimental data. A parametric study on the propeller wake model was carried out. The validated results show that it is practical to improve the accuracy of hydrodynamic performance prediction using the improved potential panel method proposed. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Open AccessArticle
An Intelligent Approach for Handling Complexity by Migrating from Conventional Databases to Big Data
Symmetry 2018, 10(12), 698; https://doi.org/10.3390/sym10120698 - 03 Dec 2018
Cited by 1
Abstract
Handling complexity in the data of information systems has emerged into a serious challenge in recent times. The typical relational databases have limited ability to manage the discrete and heterogenous nature of modern data. Additionally, the complexity of data in relational databases is [...] Read more.
Handling complexity in the data of information systems has emerged into a serious challenge in recent times. The typical relational databases have limited ability to manage the discrete and heterogenous nature of modern data. Additionally, the complexity of data in relational databases is so high that the efficient retrieval of information has become a bottleneck in traditional information systems. On the side, Big Data has emerged into a decent solution for heterogenous and complex data (structured, semi-structured and unstructured data) by providing architectural support to handle complex data and by providing a tool-kit for efficient analysis of complex data. For the organizations that are sticking to relational databases and are facing the challenge of handling complex data, they need to migrate their data to a Big Data solution to get benefits such as horizontal scalability, real-time interaction, handling high volume data, etc. However, such migration from relational databases to Big Data is in itself a challenge due to the complexity of data. In this paper, we introduce a novel approach that handles complexity of automatic transformation of existing relational database (MySQL) into a Big data solution (Oracle NoSQL). The used approach supports a bi-fold transformation (schema-to-schema and data-to-data) to minimize the complexity of data and to allow improved analysis of data. A software prototype for this transformation is also developed as a proof of concept. The results of the experiments show the correctness of our transformations that outperform the other similar approaches. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2019)
Show Figures

Figure 1

Back to TopTop