Symmetry and Complexity 2020

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 24667

Special Issue Editor


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Guest Editor
Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
Interests: wavelets; fractals; fractional and stochastic equations; numerical and computational methods; mathematical physics; nonlinear systems; artificial intelligence
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Special Issue Information

Dear Colleagues,

Symmetry and complexity are two fundamental features of almost all phenomena in nature and science. Any complex (physical, engineering, biological, economical, and computational) model is characterized by the existence of some symmetries at different scales. On the other hand, breaking the symmetry of a scientific model has always been considered the most challenging taks 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, patterns, and categories.

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

The discovery of complexity and symmetry in mathematics, computer science, physics, engineering, economics, biology, and medicine has presented 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, computer science, 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;

Philosophy, logic, and 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 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. 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 2400 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.

Published Papers (8 papers)

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Research

16 pages, 1303 KiB  
Article
Helical Hypersurfaces in Minkowski Geometry E 1 4
by Erhan Güler
Symmetry 2020, 12(8), 1206; https://doi.org/10.3390/sym12081206 - 23 Jul 2020
Cited by 13 | Viewed by 3045
Abstract
We define helical (i.e., helicoidal) hypersurfaces depending on the axis of rotation in Minkowski four-space E 1 4 . There are three types of helicoidal hypersurfaces. We derive equations for the curvatures (i.e., Gaussian and mean) and give some examples of these hypersurfaces. [...] Read more.
We define helical (i.e., helicoidal) hypersurfaces depending on the axis of rotation in Minkowski four-space E 1 4 . There are three types of helicoidal hypersurfaces. We derive equations for the curvatures (i.e., Gaussian and mean) and give some examples of these hypersurfaces. Finally, we obtain a theorem classifying the helicoidal hypersurface with timelike axes satisfying Δ I H = A H . Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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23 pages, 19076 KiB  
Article
A Framework of Modeling Large-Scale Wireless Sensor Networks for Big Data Collection
by Asside Christian Djedouboum, Ado Adamou Abba Ari, Abdelhak Mourad Gueroui, Alidou Mohamadou, Ousmane Thiare and Zibouda Aliouat
Symmetry 2020, 12(7), 1113; https://doi.org/10.3390/sym12071113 - 3 Jul 2020
Cited by 7 | Viewed by 2556
Abstract
Large Scale Wireless Sensor Networks (LS-WSNs) are Wireless Sensor Networks (WSNs) composed of an impressive number of sensors, with inherent detection and processing capabilities, to be deployed over large areas of interest. The deployment of a very large number of diverse or similar [...] Read more.
Large Scale Wireless Sensor Networks (LS-WSNs) are Wireless Sensor Networks (WSNs) composed of an impressive number of sensors, with inherent detection and processing capabilities, to be deployed over large areas of interest. The deployment of a very large number of diverse or similar sensors is certainly a common practice that aims to overcome frequent sensor failures and avoid any human intervention to replace them or recharge their batteries, to ensure the reliability of the network. However, in practice, the complexity of LS-WSNs pose significant challenges to ensuring quality communications in terms of symmetry of radio links and maximizing network life. In recent years, most of the proposed LS-WSN deployment techniques aim either to maximize network connectivity, increase coverage of the area of interest or, of course, extend network life. Few studies have considered the choice of a good LS-WSN deployment strategy as a solution for both connectivity and energy consumption efficiency. In this paper, we designed a LS-WSN as a tool for collecting big data generated by smart cities. The intrinsic characteristics of big data require the use of heterogeneous sensors. Furthermore, in order to build a heterogeneous LS-WSN, our scientific contributions include a model of quantifying the kinds of sensors in the network and the multi-level architecture for LS-WSN deployment, which relies on clustering for the big data collection. The results simulations show that our proposed LS-WSN architecture is better than some well known WSN protocols in the literature including Low Energy Adaptive Clustering Hierarchy (LEACH), E-LEACH, SEP, DEEC, EECDA, DSCHE and BEENISH. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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15 pages, 444 KiB  
Article
Solving Higher-Order Boundary and Initial Value Problems via Chebyshev–Spectral Method: Application in Elastic Foundation
by Praveen Agarwal, Maryam Attary, Mohammad Maghasedi and Poom Kumam
Symmetry 2020, 12(6), 987; https://doi.org/10.3390/sym12060987 - 9 Jun 2020
Cited by 19 | Viewed by 2511
Abstract
In this work, we introduce an efficient scheme for the numerical solution of some Boundary and Initial Value Problems (BVPs-IVPs). By using an operational matrix, which was obtained from the first kind of Chebyshev polynomials, we construct the algebraic equivalent representation of the [...] Read more.
In this work, we introduce an efficient scheme for the numerical solution of some Boundary and Initial Value Problems (BVPs-IVPs). By using an operational matrix, which was obtained from the first kind of Chebyshev polynomials, we construct the algebraic equivalent representation of the problem. We will show that this representation of BVPs and IVPs can be represented by a sparse matrix with sufficient precision. Sparse matrices that store data containing a large number of zero-valued elements have several advantages, such as saving a significant amount of memory and speeding up the processing of that data. In addition, we provide the convergence analysis and the error estimation of the suggested scheme. Finally, some numerical results are utilized to demonstrate the validity and applicability of the proposed technique, and also the presented algorithm is applied to solve an engineering problem which is used in a beam on elastic foundation. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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10 pages, 840 KiB  
Article
A Numerical Method for Computing the Roots of Non-Singular Complex-Valued Matrices
by Diego Caratelli and Paolo Emilio Ricci
Symmetry 2020, 12(6), 966; https://doi.org/10.3390/sym12060966 - 5 Jun 2020
Cited by 6 | Viewed by 1972
Abstract
A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the [...] Read more.
A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the invariants of the matrix, so circumventing the computation of the relevant eigenvalues. Several worked examples are illustrated to validate the developed algorithm in the case of higher order matrices. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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12 pages, 320 KiB  
Article
On M-Polynomials of Dunbar Graphs in Social Networks
by Santanu Acharjee, Bijit Bora and Robin I. M. Dunbar
Symmetry 2020, 12(6), 932; https://doi.org/10.3390/sym12060932 - 3 Jun 2020
Cited by 10 | Viewed by 3085
Abstract
Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We [...] Read more.
Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the ( m , n , r ) -agent recruitment graph where n > 1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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16 pages, 2292 KiB  
Article
New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach
by Wei Gao, Pundikala Veeresha, Doddabhadrappla Gowda Prakasha, Haci Mehmet Baskonus and Gulnur Yel
Symmetry 2020, 12(3), 478; https://doi.org/10.3390/sym12030478 - 19 Mar 2020
Cited by 76 | Viewed by 4612
Abstract
This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink [...] Read more.
This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink solitary wave interactions arising in nuclear particle physics and biological structures for the last several decades. The proposed technique is composed of Laplace transform and q -homotopy analysis techniques, and fractional derivative defined in the sense of Caputo. For the governing fractional-order model, the Banach’s fixed point hypothesis is studied to establish the existence and uniqueness of the achieved solution. To illustrate and validate the effectiveness of the projected algorithm, we analyze the considered model in terms of arbitrary order with two distinct cases and also introduce corresponding numerical simulation. Moreover, the physical behaviors of the obtained solutions with respect to fractional-order are presented via various simulations. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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23 pages, 3974 KiB  
Article
EMBLR: A High-Performance Optimal Routing Approach for D2D Communications in Large-scale IoT 5G Network
by Valmik Tilwari, Kaharudin Dimyati, MHD Nour Hindia, Tengku Faiz Bin Tengku Mohmed Noor Izam and Iraj Sadegh Amiri
Symmetry 2020, 12(3), 438; https://doi.org/10.3390/sym12030438 - 9 Mar 2020
Cited by 13 | Viewed by 3640
Abstract
Coping with the skyrocketing needs for massive amounts of data for the future Fifth Generation (5G) network, Device-to-Device (D2D) communications technology will provide seamless connectivity, high data rates, extended network coverage, and spectral efficiency. The D2D communications are a prevalent emerging technology to [...] Read more.
Coping with the skyrocketing needs for massive amounts of data for the future Fifth Generation (5G) network, Device-to-Device (D2D) communications technology will provide seamless connectivity, high data rates, extended network coverage, and spectral efficiency. The D2D communications are a prevalent emerging technology to achieve the vision of symmetry in the Internet of Things (IoT) services. However, energy resource constraints, network stability, traffic congestion, and link failure of the devices are the crucial impediments to establish an optimal route in the D2D communications based IoT 5G network. These obstacles induced packet drop, rapid energy depletion, higher end-to-end delay, and unfairness across the network, leading to significant route and network performance degradation. Therefore, in this paper, an energy, mobility, queue length, and link quality-aware routing (EMBLR) approach is proposed to overcome the challenges and boost network performance. Moreover, a multicriteria decision making (MCDM) technique is utilized for the selection of the intermediate device in an optimal route. Extensive simulation has been conducted and proven that the proposed routing approach significantly enhances network performance. Overall, results have been carried out in Quality of Service (QoS) performance metrics and compared with other well-known routing approaches. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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12 pages, 2778 KiB  
Article
Spectral Kurtosis of Choi–Williams Distribution and Hidden Markov Model for Gearbox Fault Diagnosis
by Yufei Li, Wanqing Song, Fei Wu, Enrico Zio and Yujin Zhang
Symmetry 2020, 12(2), 285; https://doi.org/10.3390/sym12020285 - 15 Feb 2020
Cited by 13 | Viewed by 2339
Abstract
A combination of spectral kurtosis (SK), based on Choi–Williams distribution (CWD) and hidden Markov models (HMM), accurately identifies initial gearbox failures and diagnoses fault types of gearboxes. First, using the LMD algorithm, five types of gearbox vibration signals are collected and decomposed into [...] Read more.
A combination of spectral kurtosis (SK), based on Choi–Williams distribution (CWD) and hidden Markov models (HMM), accurately identifies initial gearbox failures and diagnoses fault types of gearboxes. First, using the LMD algorithm, five types of gearbox vibration signals are collected and decomposed into several product function (PF) components and the multicomponent signals are decomposed into single-component signals. Then, the kurtosis value of each component is calculated, and the component with the largest kurtosis value is selected for the CWD-SK analysis. According to the calculated CWD-SK value, the characteristics of the initial failure of the gearbox are extracted. This method not only avoids the difficulty of selecting the window function, but also provides original eigenvalues for fault feature classification. In the end, from the CWD-SK characteristic parameters at each characteristic frequency, the characteristic sequence based on CWD-SK is obtained with HMM training and diagnosis. The experimental results show that this method can effectively identify the initial fault characteristics of the gearbox, and also accurately classify the fault characteristics of different degrees. Full article
(This article belongs to the Special Issue Symmetry and Complexity 2020)
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