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Symmetry, Volume 9, Issue 12 (December 2017)

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Cover Story (view full-size image) The theory of knotoids can be regarded as a refinement of classical knot theory. Knotoids provide a [...] Read more.
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Open AccessArticle A Design for Genetically Oriented Rules-Based Incremental Granular Models and Its Application
Symmetry 2017, 9(12), 324; https://doi.org/10.3390/sym9120324
Received: 28 November 2017 / Revised: 17 December 2017 / Accepted: 18 December 2017 / Published: 20 December 2017
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Abstract
In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The
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In this paper, we develop a genetically oriented rule-based Incremental Granular Model (IGM). The IGM is designed using a combination of a simple Linear Regression (LR) model and a local Linguistic Model (LM) to predict the modeling error obtained by the LR. The IGM has been successfully applied to various examples. However, the disadvantage of IGM is that the number of clusters in each context is determined, with the same number, by trial and error. Moreover, a weighting exponent is set to the typical value. In order to solve these problems, the goal of this paper is to design an optimized rule-based IGM with the use of a Genetic Algorithm (GA) to simultaneously optimize the number of cluster centers in each context, the number of contexts, and the weighting exponent. The experimental results regarding a coagulant dosing process in a water purification plant, an automobile mpg (miles per gallon) prediction, and a Boston housing data set revealed that the proposed GA-based IGM showed good performance, when compared with the Radial Basis Function Neural Network (RBFNN), LM, Takagi–Sugeno–Kang (TSK)-Linguistic Fuzzy Model (LFM), GA-based LM, and IGM itself. Full article
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Open AccessFeature PaperArticle Boundary Value Problems for Some Important Classes of Recurrent Relations with Two Independent Variables
Symmetry 2017, 9(12), 323; https://doi.org/10.3390/sym9120323
Received: 3 December 2017 / Revised: 17 December 2017 / Accepted: 18 December 2017 / Published: 20 December 2017
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Abstract
It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C={(n,k):0kn,
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It is shown that complex-valued boundary value problems for several classes of recurrent relations with two independent variables, of some considerable interest, are solvable on the following domain: C = { ( n , k ) : 0 k n , k N 0 , n N } , the so called combinatorial domain. The recurrent relations include some of the most important combinatorial ones, which, among other things, serve as a motivation for the investigation. The methods for solving the boundary value problems are presented and explained in detail. Full article
(This article belongs to the Special Issue Symmetry: Feature Papers 2017)
Open AccessArticle Graph Cellular Automata with Relation-Based Neighbourhoods of Cells for Complex Systems Modelling: A Case of Traffic Simulation
Symmetry 2017, 9(12), 322; https://doi.org/10.3390/sym9120322
Received: 5 December 2017 / Revised: 5 December 2017 / Accepted: 17 December 2017 / Published: 19 December 2017
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Abstract
A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to
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A complex system is a set of mutually interacting elements for which it is possible to construct a mathematical model. This article focuses on the cellular automata theory and the graph theory in order to compare various types of cellular automata and to analyse applications of graph structures together with cellular automata. It proposes a graph cellular automaton with a variable configuration of cells and relation-based neighbourhoods (r–GCA). The developed mechanism enables modelling of phenomena found in complex systems (e.g., transport networks, urban logistics, social networks) taking into account the interaction between the existing objects. As an implementation example, modelling of moving vehicles has been made and r–GCA was compared to the other cellular automata models simulating the road traffic and used in the computer simulation process. Full article
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Open AccessArticle A Novel String Grammar Unsupervised Possibilistic C-Medians Algorithm for Sign Language Translation Systems
Symmetry 2017, 9(12), 321; https://doi.org/10.3390/sym9120321
Received: 30 November 2017 / Revised: 13 December 2017 / Accepted: 14 December 2017 / Published: 19 December 2017
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Abstract
Sign language is a basic method for solving communication problems between deaf and hearing people. In order to communicate, deaf and hearing people normally use hand gestures, which include a combination of hand positioning, hand shapes, and hand movements. Thai Sign Language is
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Sign language is a basic method for solving communication problems between deaf and hearing people. In order to communicate, deaf and hearing people normally use hand gestures, which include a combination of hand positioning, hand shapes, and hand movements. Thai Sign Language is the communication method for Thai hearing-impaired people. Our objective is to improve the dynamic Thai Sign Language translation method with a video captioning technique that does not require prior hand region detection and segmentation through using the Scale Invariant Feature Transform (SIFT) method and the String Grammar Unsupervised Possibilistic C-Medians (sgUPCMed) algorithm. This work is the first to propose the sgUPCMed algorithm to cope with the unsupervised generation of multiple prototypes in the possibilistic sense for string data. In our experiments, the Thai Sign Language data set (10 isolated sign language words) was collected from 25 subjects. The best average result within the constrained environment of the blind test data sets of signer-dependent cases was 89–91%, and the successful rate of signer semi-independent cases was 81–85%, on average. For the blind test data sets of signer-independent cases, the best average classification rate was 77–80%. The average result of the system without a constrained environment was around 62–80% for the signer-independent experiments. To show that the proposed algorithm can be implemented in other sign languages, the American sign language (RWTH-BOSTON-50) data set, which consists of 31 isolated American Sign Language words, is also used in the experiment. The system provides 88.56% and 91.35% results on the validation set alone, and for both the training and validation sets, respectively. Full article
(This article belongs to the Special Issue Emerging Approaches and Advances in Big Data)
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Open AccessArticle Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making
Symmetry 2017, 9(12), 320; https://doi.org/10.3390/sym9120320
Received: 4 November 2017 / Revised: 13 December 2017 / Accepted: 13 December 2017 / Published: 19 December 2017
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Abstract
As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA)
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As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
Open AccessArticle New Applications of m-Polar Fuzzy Matroids
Symmetry 2017, 9(12), 319; https://doi.org/10.3390/sym9120319
Received: 1 November 2017 / Revised: 7 December 2017 / Accepted: 11 December 2017 / Published: 18 December 2017
Cited by 1 | PDF Full-text (386 KB) | HTML Full-text | XML Full-text
Abstract
Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when
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Mathematical modelling is an important aspect in apprehending discrete and continuous physical systems. Multipolar uncertainty in data and information incorporates a significant role in various abstract and applied mathematical modelling and decision analysis. Graphical and algebraic models can be studied more precisely when multiple linguistic properties are dealt with, emphasizing the need for a multi-index, multi-object, multi-agent, multi-attribute and multi-polar mathematical approach. An m-polar fuzzy set is introduced to overcome the limitations entailed in single-valued and two-valued uncertainty. Our aim in this research study is to apply the powerful methodology of m-polar fuzzy sets to generalize the theory of matroids. We introduce the notion of m-polar fuzzy matroids and investigate certain properties of various types of m-polar fuzzy matroids. Moreover, we apply the notion of the m-polar fuzzy matroid to graph theory and linear algebra. We present m-polar fuzzy circuits, closures of m-polar fuzzy matroids and put special emphasis on m-polar fuzzy rank functions. Finally, we also describe certain applications of m-polar fuzzy matroids in decision support systems, ordering of machines and network analysis. Full article
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making) Printed Edition available
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Open AccessArticle Algebraic Aspects of the Supersymmetric Minimal Surface Equation
Symmetry 2017, 9(12), 318; https://doi.org/10.3390/sym9120318
Received: 13 November 2017 / Revised: 8 December 2017 / Accepted: 13 December 2017 / Published: 18 December 2017
Cited by 1 | PDF Full-text (279 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143
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In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is performed, which results in a list of 143 conjugacy classes with respect to action by the supergroup generated by the Lie superalgebra. The symmetry reduction method is used to obtain invariant solutions of the supersymmetric minimal surface equation. The classical minimal surface equation is also examined and its group-theoretical properties are compared with those of the supersymmetric version. Full article
Open AccessArticle Analyzing Spatial Behavior of Backcountry Skiers in Mountain Protected Areas Combining GPS Tracking and Graph Theory
Symmetry 2017, 9(12), 317; https://doi.org/10.3390/sym9120317
Received: 15 November 2017 / Revised: 10 December 2017 / Accepted: 11 December 2017 / Published: 14 December 2017
Cited by 3 | PDF Full-text (4600 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an
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Mountain protected areas (PAs) aim to preserve vulnerable environments and at the same time encourage numerous outdoor leisure activities. Understanding the way people use natural environments is crucial to balance the needs of visitors and site capacities. This study aims to develop an approach to evaluate the structure and use of designated skiing zones in PAs combining Global Positioning System (GPS) tracking and analytical methods based on graph theory. The study is based on empirical data (n = 609 GPS tracks of backcountry skiers) collected in Tatra National Park (TNP), Poland. The physical structure of the entire skiing zones system has been simplified into a graph structure (structural network; undirected graph). In a second step, the actual use of the area by skiers (functional network; directed graph) was analyzed using a graph-theoretic approach. Network coherence (connectivity indices: β, γ, α), movement directions at path segments, and relative importance of network nodes (node centrality measures: degree, betweenness, closeness, and proximity prestige) were calculated. The system of designated backcountry skiing zones was not evenly used by the visitors. Therefore, the calculated parameters differ significantly between the structural and the functional network. In particular, measures related to the actually used trails are of high importance from the management point of view. Information about the most important node locations can be used for planning sign-posts, on-site maps, interpretative boards, or other tourist infrastructure. Full article
(This article belongs to the Special Issue Graph Theory)
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Open AccessArticle Tangible Visualization Table for Intuitive Data Display
Symmetry 2017, 9(12), 316; https://doi.org/10.3390/sym9120316
Received: 18 October 2017 / Revised: 7 December 2017 / Accepted: 9 December 2017 / Published: 13 December 2017
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Abstract
We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture
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We propose a new tangible visualization table for intuitive and effective visualization of terrain data transferred from a remote server in real time. The shape display approximating the height field of remote terrain data is generated by linear actuators, and the corresponding texture image is projected onto the shape display. To minimize projection distortions, we present a sophisticated technique for projection mapping. Gesture-based user interfaces facilitate intuitive manipulations of visualization results. We demonstrate the effectiveness of our system by displaying and manipulating various terrain data using gesture-based interfaces. Full article
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Open AccessFeature PaperArticle Knotoids, Braidoids and Applications
Symmetry 2017, 9(12), 315; https://doi.org/10.3390/sym9120315
Received: 27 September 2017 / Revised: 7 December 2017 / Accepted: 8 December 2017 / Published: 12 December 2017
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Abstract
This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to
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This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to the study of proteins. Full article
(This article belongs to the Special Issue Knot Theory and Its Applications)
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Open AccessFeature PaperArticle The Exact Evaluation of Some New Lattice Sums
Symmetry 2017, 9(12), 314; https://doi.org/10.3390/sym9120314
Received: 14 November 2017 / Revised: 6 December 2017 / Accepted: 6 December 2017 / Published: 11 December 2017
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Abstract
New q-series in the spirit of Jacobi have been found in a publication first published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely
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New q-series in the spirit of Jacobi have been found in a publication first published in 1884 written in Russian and translated into English in 1928. This work was found by chance and appears to be almost totally unknown. From these entirely new q-series, fresh lattice sums have been discovered and are presented here. Full article
(This article belongs to the Special Issue Mathematical Crystallography)
Open AccessArticle Detection of Double-Compressed H.264/AVC Video Incorporating the Features of the String of Data Bits and Skip Macroblocks
Symmetry 2017, 9(12), 313; https://doi.org/10.3390/sym9120313
Received: 21 October 2017 / Revised: 9 December 2017 / Accepted: 11 December 2017 / Published: 11 December 2017
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Abstract
Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be
[...] Read more.
Today’s H.264/AVC coded videos have a high quality, high data-compression ratio. They also have a strong fault tolerance, better network adaptability, and have been widely applied on the Internet. With the popularity of powerful and easy-to-use video editing software, digital videos can be tampered with in various ways. Therefore, the double compression in the H.264/AVC video can be used as a first step in the study of video-tampering forensics. This paper proposes a simple, but effective, double-compression detection method that analyzes the periodic features of the string of data bits (SODBs) and the skip macroblocks (S-MBs) for all I-frames and P-frames in a double-compressed H.264/AVC video. For a given suspicious video, the SODBs and S-MBs are extracted for each frame. Both features are then incorporated to generate one enhanced feature to represent the periodic artifact of the double-compressed video. Finally, a time-domain analysis is conducted to detect the periodicity of the features. The primary Group of Pictures (GOP) size is estimated based on an exhaustive strategy. The experimental results demonstrate the efficacy of the proposed method. Full article
(This article belongs to the Special Issue Information Technology and Its Applications)
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Open AccessArticle Chaotic Dynamical State Variables Selection Procedure Based Image Encryption Scheme
Symmetry 2017, 9(12), 312; https://doi.org/10.3390/sym9120312
Received: 30 September 2017 / Revised: 22 November 2017 / Accepted: 6 December 2017 / Published: 11 December 2017
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Abstract
Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led
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Nowadays, in the modern digital era, the use of computer technologies such as smartphones, tablets and the Internet, as well as the enormous quantity of confidential information being converted into digital form have resulted in raised security issues. This, in turn, has led to rapid developments in cryptography, due to the imminent need for system security. Low-dimensional chaotic systems have low complexity and key space, yet they achieve high encryption speed. An image encryption scheme is proposed that, without compromising the security, uses reasonable resources. We introduced a chaotic dynamic state variables selection procedure (CDSVSP) to use all state variables of a hyper-chaotic four-dimensional dynamical system. As a result, less iterations of the dynamical system are required, and resources are saved, thus making the algorithm fast and suitable for practical use. The simulation results of security and other miscellaneous tests demonstrate that the suggested algorithm excels at robustness, security and high speed encryption. Full article
(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)
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Open AccessArticle Task-Management Method Using R-Tree Spatial Cloaking for Large-Scale Crowdsourcing
Symmetry 2017, 9(12), 311; https://doi.org/10.3390/sym9120311
Received: 30 September 2017 / Revised: 5 December 2017 / Accepted: 7 December 2017 / Published: 10 December 2017
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Abstract
With the development of sensor technology and the popularization of the data-driven service paradigm, spatial crowdsourcing systems have become an important way of collecting map-based location data. However, large-scale task management and location privacy are important factors for participants in spatial crowdsourcing. In
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With the development of sensor technology and the popularization of the data-driven service paradigm, spatial crowdsourcing systems have become an important way of collecting map-based location data. However, large-scale task management and location privacy are important factors for participants in spatial crowdsourcing. In this paper, we propose the use of an R-tree spatial cloaking-based task-assignment method for large-scale spatial crowdsourcing. We use an estimated R-tree based on the requested crowdsourcing tasks to reduce the crowdsourcing server-side inserting cost and enable the scalability. By using Minimum Bounding Rectangle (MBR)-based spatial anonymous data without exact position data, this method preserves the location privacy of participants in a simple way. In our experiment, we showed that our proposed method is faster than the current method, and is very efficient when the scale is increased. Full article
(This article belongs to the Special Issue Advanced in Artificial Intelligence and Cloud Computing)
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Open AccessArticle Reconstructing Damaged Complex Networks Based on Neural Networks
Symmetry 2017, 9(12), 310; https://doi.org/10.3390/sym9120310
Received: 2 October 2017 / Revised: 22 November 2017 / Accepted: 9 December 2017 / Published: 9 December 2017
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Abstract
Despite recent progress in the study of complex systems, reconstruction of damaged networks due to random and targeted attack has not been addressed before. In this paper, we formulate the network reconstruction problem as an identification of network structure based on much reduced
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Despite recent progress in the study of complex systems, reconstruction of damaged networks due to random and targeted attack has not been addressed before. In this paper, we formulate the network reconstruction problem as an identification of network structure based on much reduced link information. Furthermore, a novel method based on multilayer perceptron neural network is proposed as a solution to the problem of network reconstruction. Based on simulation results, it was demonstrated that the proposed scheme achieves very high reconstruction accuracy in small-world network model and a robust performance in scale-free network model. Full article
(This article belongs to the Special Issue Graph Theory)
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