Editorial

2 pages, 655 KiB

Open AccessEditorial

by António M. Lopes and José A. Tenreiro Machado

Symmetry 2020, 12(6), 982; https://doi.org/10.3390/sym12060982 - 08 Jun 2020

Cited by 1 | Viewed by 1689

Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics [...] Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

Research

Jump to: Editorial

14 pages, 262 KiB

Open AccessArticle

Mei Symmetry and Invariants of Quasi-Fractional Dynamical Systems with Non-Standard Lagrangians

by Yi Zhang and Xue-Ping Wang

Symmetry 2019, 11(8), 1061; https://doi.org/10.3390/sym11081061 - 18 Aug 2019

Cited by 23 | Viewed by 2503

Abstract

Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved [...] Read more.

Non-standard Lagrangians play an important role in the systems of non-conservative dynamics or nonlinear differential equations, quantum field theories, etc. This paper deals with quasi-fractional dynamical systems from exponential non-standard Lagrangians and power-law non-standard Lagrangians. Firstly, the definition, criterion, and corresponding new conserved quantity of Mei symmetry in this system are presented and studied. Secondly, considering that a small disturbance is applied on the system, the differential equations of the disturbed motion are established, the definition of Mei symmetry and corresponding criterion are given, and the new adiabatic invariants led by Mei symmetry are proposed and proved. Examples also show the validity of the results. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

12 pages, 464 KiB

Open AccessArticle

Time-Fractional Heat Conduction in Two Joint Half-Planes

by Yuriy Povstenko and Joanna Klekot

Symmetry 2019, 11(6), 800; https://doi.org/10.3390/sym11060800 - 16 Jun 2019

Cited by 3 | Viewed by 1846

Abstract

The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and [...] Read more.

The heat conduction equations with Caputo fractional derivative are considered in two joint half-planes under the conditions of perfect thermal contact. The fundamental solution to the Cauchy problem as well as the fundamental solution to the source problem are examined. The Fourier and Laplace transforms are employed. The Fourier transforms are inverted analytically, whereas the Laplace transform is inverted numerically using the Gaver–Stehfest method. We give a graphical representation of the numerical results. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

► Show Figures

Figure 1

11 pages, 409 KiB

Open AccessArticle

Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading

by Yuriy Povstenko and Tamara Kyrylych

Symmetry 2019, 11(5), 689; https://doi.org/10.3390/sym11050689 - 18 May 2019

Cited by 10 | Viewed by 2059

Abstract

The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the “long-tail” power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with [...] Read more.

The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the “long-tail” power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with two external half-infinite slits with the prescribed heat flux across their surfaces. The integral transform technique is used. The solution is obtained in the form of integrals with integrand being the Mittag–Leffler function. A graphical representation of numerical results is given. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

► Show Figures

Figure 1

9 pages, 265 KiB

Open AccessArticle

Derivative Free Fourth Order Solvers of Equations with Applications in Applied Disciplines

by Ramandeep Behl, Ioannis K. Argyros, Fouad Othman Mallawi and J. A. Tenreiro Machado

Symmetry 2019, 11(4), 586; https://doi.org/10.3390/sym11040586 - 23 Apr 2019

Cited by 1 | Viewed by 2030

Abstract

This paper develops efficient equation solvers for real- and complex-valued functions. An earlier study by Lee and Kim, used the Taylor-type expansions and hypotheses on higher than first order derivatives, but no derivatives appeared in the suggested method. However, we have many cases [...] Read more.

This paper develops efficient equation solvers for real- and complex-valued functions. An earlier study by Lee and Kim, used the Taylor-type expansions and hypotheses on higher than first order derivatives, but no derivatives appeared in the suggested method. However, we have many cases where the calculations of the fourth derivative are expensive, or the result is unbounded, or even does not exist. We only use the first order derivative of function

Ω

in the proposed convergence analysis. Hence, we expand the utilization of the earlier scheme, and we study the computable radii of convergence and error bounds based on the Lipschitz constants. Furthermore, the range of starting points is also explored to know how close the initial guess should be considered for assuring convergence. Several numerical examples where earlier studies cannot be applied illustrate the new technique. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

17 pages, 837 KiB

Open AccessArticle

Extending the Adapted PageRank Algorithm Centrality to Multiplex Networks with Data Using the PageRank Two-Layer Approach

by Taras Agryzkov, Manuel Curado, Francisco Pedroche, Leandro Tortosa and José F. Vicent

Symmetry 2019, 11(2), 284; https://doi.org/10.3390/sym11020284 - 22 Feb 2019

Cited by 19 | Viewed by 3906

Abstract

Usually, the nodes’ interactions in many complex networks need a more accurate mapping than simple links. For instance, in social networks, it may be possible to consider different relationships between people. This implies the use of different layers where the nodes are preserved [...] Read more.

Usually, the nodes’ interactions in many complex networks need a more accurate mapping than simple links. For instance, in social networks, it may be possible to consider different relationships between people. This implies the use of different layers where the nodes are preserved and the relationships are diverse, that is, multiplex networks or biplex networks, for two layers. One major issue in complex networks is the centrality, which aims to classify the most relevant elements in a given system. One of these classic measures of centrality is based on the PageRank classification vector used initially in the Google search engine to order web pages. The PageRank model may be understood as a two-layer network where one layer represents the topology of the network and the other layer is related to teleportation between the nodes. This approach may be extended to define a centrality index for multiplex networks based on the PageRank vector concept. On the other hand, the adapted PageRank algorithm (APA) centrality constitutes a model to obtain the importance of the nodes in a spatial network with the presence of data (both real and virtual). Following the idea of the two-layer approach for PageRank centrality, we can consider the APA centrality under the perspective of a two-layer network where, on the one hand, we keep maintaining the layer of the topological connections of the nodes and, on the other hand, we consider a data layer associated with the network. Following a similar reasoning, we are able to extend the APA model to spatial networks with different layers. The aim of this paper is to propose a centrality measure for biplex networks that extends the adapted PageRank algorithm centrality for spatial networks with data to the PageRank two-layer approach. Finally, we show an example where the ability to analyze data referring to a group of people from different aspects and using different sets of independent data are revealed. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

► Show Figures

Figure 1

21 pages, 2441 KiB

Open AccessArticle

A Transmission Prediction Neighbor Mechanism Based on a Mixed Probability Model in an Opportunistic Complex Social Network

by Genghua Yu, Zhigang Chen, Jia Wu and Jian Wu

Symmetry 2018, 10(11), 600; https://doi.org/10.3390/sym10110600 - 06 Nov 2018

Cited by 5 | Viewed by 2831

Abstract

The amount of data has skyrocketed in Fifth-generation (5G) networks. How to select an appropriate node to transmit information is important when we analyze complex data in 5G communication. We could sophisticate decision-making methods for more convenient data transmission, and opportunistic complex social [...] Read more.

The amount of data has skyrocketed in Fifth-generation (5G) networks. How to select an appropriate node to transmit information is important when we analyze complex data in 5G communication. We could sophisticate decision-making methods for more convenient data transmission, and opportunistic complex social networks play an increasingly important role. Users can adopt it for information sharing and data transmission. However, the encountering of nodes in mobile opportunistic network is random. The latest probabilistic routing method may not consider the social and cooperative nature of nodes, and could not be well applied to the large data transmission problem of social networks. Thus, we quantify the social and cooperative relationships symmetrically between the mobile devices themselves and the nodes, and then propose a routing algorithm based on an improved probability model to predict the probability of encounters between nodes (PEBN). Since our algorithm comprehensively considers the social relationship and cooperation relationship between nodes, the prediction result of the target node can also be given without encountering information. The neighbor nodes with higher probability are filtered by the prediction result. In the experiment, we set the node’s selfishness randomly. The simulation results show that compared with other state-of-art transmission models, our algorithm has significantly improved the message delivery rate, hop count, and overhead. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

► Show Figures

Figure 1

18 pages, 1057 KiB

Open AccessArticle

Multi-Agent Reinforcement Learning Using Linear Fuzzy Model Applied to Cooperative Mobile Robots

by David Luviano-Cruz, Francesco Garcia-Luna, Luis Pérez-Domínguez and S. K. Gadi

Symmetry 2018, 10(10), 461; https://doi.org/10.3390/sym10100461 - 03 Oct 2018

Cited by 10 | Viewed by 2832

Abstract

A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire [...] Read more.

A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire new behaviors; most of these select exact Q-values in small discrete state space and action space. This article presents a joint Q-function linearly fuzzified for a MAS’ continuous state space, which overcomes the dimensionality problem. Also, this article gives a proof for the convergence and existence of the solution proposed by the algorithm presented. This article also discusses the numerical simulations and experimental results that were carried out to validate the proposed algorithm. Full article

(This article belongs to the Special Issue Symmetry in Complex Systems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry in Complex Systems

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (8 papers)

Editorial

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI