ALBERT

Description: Symmetry, Vol. 10, Pages 402: Noise-Robust Sound-Event Classification System with Texture Analysis Symmetry doi: 10.3390/sym10090402 Authors: Yongju Choi Othmane Atif Jonguk Lee Daihee Park Yongwha Chung Sound-event classification has emerged as an important field of research in recent years. In particular, investigations using sound data are being conducted in various industrial fields. However, sound-event classification tasks have become more difficult and challenging with the increase in noise levels. In this study, we propose a noise-robust system for the classification of sound data. In this method, we first convert one-dimensional sound signals into two-dimensional gray-level images using normalization, and then extract the texture images by means of the dominant neighborhood structure (DNS) technique. Finally, we experimentally validate the noise-robust approach by using four classifiers (convolutional neural network (CNN), support vector machine (SVM), k-nearest neighbors(k-NN), and C4.5). The experimental results showed superior classification performance in noisy conditions compared with other methods. The F1 score exceeds 98.80% in railway data, and 96.57% in livestock data. Besides, the proposed method can be implemented in a cost-efficient manner (for instance, use of a low-cost microphone) while maintaining high level of accuracy in noisy environments. This approach can be used either as a standalone solution or as a supplement to the known methods to obtain a more accurate solution.

Description: Symmetry, Vol. 10, Pages 404: A New Method to Decision-Making with Fuzzy Competition Hypergraphs Symmetry doi: 10.3390/sym10090404 Authors: Musavarah Sarwar Muhammad Akram Noura Omair Alshehri Hypergraph theory is the most developed tool for demonstrating various practical problems in different domains of science and technology. Sometimes, information in a network model is uncertain and vague in nature. In this paper, our main focus is to apply the powerful methodology of fuzziness to generalize the notion of competition hypergraphs and fuzzy competition graphs. We introduce various new concepts, including fuzzy column hypergraphs, fuzzy row hypergraphs, fuzzy competition hypergraphs, fuzzy k-competition hypergraphs and fuzzy neighbourhood hypergraphs, strong hyperedges, kth strength of competition and symmetric properties. We design certain algorithms for constructing different types of fuzzy competition hypergraphs. We also present applications of fuzzy competition hypergraphs in decision support systems, including predator–prey relations in ecological niche, social networks and business marketing.

Description: Symmetry, Vol. 10, Pages 408: BGPcoin: Blockchain-Based Internet Number Resource Authority and BGP Security Solution Symmetry doi: 10.3390/sym10090408 Authors: Qianqian Xing Baosheng Wang Xiaofeng Wang Without the design for inherent security, the Border Gateway Protocol (BGP) is vulnerable to prefix/subprefix hijacks and other attacks. Though many BGP security approaches have been proposed to prevent or detect such attacks, the unsatisfactory cost-effectiveness frustrates their deployment. In fact, the currently deployed BGP security infrastructure leaves the chance for potential centralized authority misconfiguration and abuse. It actually becomes the critical yield point that demands the logging and auditing of misbehaviors and attacks in BGP security deployments. We propose a blockchain-based Internet number resource authority and trustworthy management solution, named BGPcoin, to facilitate the transparency of BGP security. BGPcoin provides a reliable origin advertisement source for origin authentication by dispensing resource allocations and revocations compliantly against IP prefix hijacking. We perform and audit resource assignments on the tamper-resistant Ethereum blockchain by means of a set of smart contracts, which also interact as one to provide the trustworthy origin route examination for BGP. Compared with RPKI, BGPcoin yields significant benefits in securing origin advertisement and building a dependable infrastructure for the object repository. We demonstrate it through an Ethereum prototype implementation, and we deploy it and do experiment on a locally-simulated network and an official Ethereum test network respectively. The extensive experiment and evaluation demonstrate the incentives to deploy BGPcoin, and the enhanced security provided by BGPcoin is technically and economically feasible.

Description: Symmetry, Vol. 10, Pages 122: Cosmetic Detection Framework for Face and Iris Biometrics Symmetry doi: 10.3390/sym10040122 Authors: Omid Sharifi Maryam Eskandari Cosmetics pose challenges to the recognition performance of face and iris biometric systems due to its ability to alter natural facial and iris patterns. Facial makeup and iris contact lens are considered to be commonly applied cosmetics for the face and iris in this study. The present work aims to present a novel solution for the detection of cosmetics in both face and iris biometrics by the fusion of texture, shape and color descriptors of images. The proposed cosmetic detection scheme combines the microtexton information from the local primitives of texture descriptors with the color spaces achieved from overlapped blocks in order to achieve better detection of spots, flat areas, edges, edge ends, curves, appearance and colors. The proposed cosmetic detection scheme was applied to the YMU YouTube makeup database (YMD) facial makeup database and IIIT-Delhi Contact Lens iris database. The results demonstrate that the proposed cosmetic detection scheme is significantly improved compared to the other schemes implemented in this study.

Description: Symmetry, Vol. 10, Pages 121: Stability of Bounded Dynamical Networks with Symmetry Symmetry doi: 10.3390/sym10040121 Authors: Ioannis K. Dassios Motivated by dynamical models describing phase separation and the motion of interfaces separating phases, we study the stability of dynamical networks in planar domains formed by triple junctions. We take into account symmetry, angle-intersection conditions at the junctions and at the points at which the curves intersect with the boundary. Firstly, we focus on the case of a network where two triple junctions have all their branches unattached to the boundary and then on the case of a network of hexagons, with one of them having all its branches unattached to the boundary. For both type of networks, we introduce the evolution problem, identify the steady states and study their stability in terms of the geometry of the boundary.

Description: Symmetry, Vol. 10, Pages 126: Neutrosophic Triplet Cosets and Quotient Groups Symmetry doi: 10.3390/sym10040126 Authors: Mikail Bal Moges Shalla Necati Olgun In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.

Description: Symmetry, Vol. 10, Pages 123: Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions Symmetry doi: 10.3390/sym10040123 Authors: Roman Cherniha Mykola Serov Oleksii Pliukhin This review is devoted to search for Lie and Q-conditional (nonclassical) symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Description: Symmetry, Vol. 10, Pages 125: Efficient Algorithms for Real-Time GPU Volumetric Cloud Rendering with Enhanced Geometry Symmetry doi: 10.3390/sym10040125 Authors: Carlos Jiménez de Parga Sebastián Rubén Gómez Palomo This paper presents several new techniques for volumetric cloud rendering using efficient algorithms and data structures based on ray-tracing methods for cumulus generation, achieving an optimum balance between realism and performance. These techniques target applications such as flight simulations, computer games, and educational software, even with conventional graphics hardware. The contours of clouds are defined by implicit mathematical expressions or triangulated structures inside which volumetric rendering is performed. Novel techniques are used to reproduce the asymmetrical nature of clouds and the effects of light-scattering, with low computing costs. The work includes a new method to create randomized fractal clouds using a recursive grammar. The graphical results are comparable to those produced by state-of-the-art, hyper-realistic algorithms. These methods provide real-time performance, and are superior to particle-based systems. These outcomes suggest that our methods offer a good balance between realism and performance, and are suitable for use in the standard graphics industry.

Description: Symmetry, Vol. 10, Pages 127: Some Interval Neutrosophic Linguistic Maclaurin Symmetric Mean Operators and Their Application in Multiple Attribute Decision Making Symmetry doi: 10.3390/sym10040127 Authors: Yushui Geng Xingang Wang Xuemei Li Kun Yu Peide Liu There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.

Description: Symmetry, Vol. 10, Pages 129: Dynamics of Trapped Solitary Waves for the Forced KdV Equation Symmetry doi: 10.3390/sym10050129 Authors: Sunmi Lee The forced Korteweg-de Vries equation is considered to investigate the impact of bottom configurations on the free surface waves in a two-dimensional channel flow. In the study of shallow water waves, the bottom topography plays a critical role, which can determine the characteristics of wave motions significantly. The interplay between solitary waves and the bottom topography can exhibit more interesting dynamics of the free surface waves when the bottom configuration is more complex. In the presence of two bumps, there are multiple trapped solitary wave solutions, which remain stable between two bumps up to a finite time when they evolve in time. In this work, various stationary trapped wave solutions of the forced KdV equation are explored as the bump sizes and the distance between two bumps are varied. Moreover, the semi-implicit finite difference method is employed to study their time evolutions in the presence of two-bump configurations. Our numerical results show that the interplay between trapped solitary waves and two bumps is the key determinant which influences the time evolution of those wave solutions. The trapped solitary waves tend to remain between two bumps for a longer time period as the distance between two bumps increases. Interestingly, there exists a nontrivial relationship between the bump size and the time until trapped solitary waves remain stable between two bumps.

Description: Symmetry, Vol. 10, Pages 128: Multi-Source Stego Detection with Low-Dimensional Textural Feature and Clustering Ensembles Symmetry doi: 10.3390/sym10050128 Authors: Fengyong Li Kui Wu Xinpeng Zhang Jingsheng Lei Mi Wen This work tackles a recent challenge in digital image processing: how to identify the steganographic images from a steganographer, who is unknown among multiple innocent actors. The method does not need a large number of samples to train classification model, and thus it is significantly different from the traditional steganalysis. The proposed scheme consists of textural features and clustering ensembles. Local ternary patterns (LTP) are employed to design low-dimensional textural features which are considered to be more sensitive to steganographic changes in texture regions of image. Furthermore, we use the extracted low-dimensional textural features to train a number of hierarchical clustering results, which are integrated as an ensemble based on the majority voting strategy. Finally, the ensemble is used to make optimal decision for suspected image. Extensive experiments show that the proposed scheme is effective and efficient and outperforms the state-of-the-art steganalysis methods with an average gain from 4 % to 6 % .

Description: Symmetry, Vol. 10, Pages 134: Bandwidth-Guaranteed Resource Allocation and Scheduling for Parallel Jobs in Cloud Data Center Symmetry doi: 10.3390/sym10050134 Authors: Zhen Li Bin Chen Xiaocheng Liu Dandan Ning Qihang Wei Yiping Wang Xiaogang Qiu Cloud Computing has emerged as a powerful and promising way for running high performance computing (HPC) jobs. Most HPC jobs are designed under multi-processes paradigm and involve frequent communication and synchronization among parallel processes. However, as the underlying resources of cloud data centers are always shared among multiple tenants, the competition of jobs for limited bandwidth resources lead to unpredictable completion times for jobs in the cloud, which may lead to QoS violation and inefficient utilization of resources when scheduling parallel jobs in the cloud. To tackle the issue, it is essential to provide bandwidth guarantees for parallel jobs running in the cloud. Offering a dedicated virtual cluster (VC) for running applications in the cloud is a popular way to guarantee bandwidth demands. Motivated by these problems, in this paper, we firstly design a time-aware virtual cluster (TVC) request model for parallel jobs and consider how to embed requested TVCs of jobs into cloud efficiently under parallel job scheduling framework. An adaptive bandwidth-aware heuristic algorithm, which is denoted as AdaBa, is proposed to improve the job accept rate by adjusting the priorities of servers to accommodate the VMs of TVC adaptively according to the relative size of requested bandwidth demand. Then, a bandwidth-guaranteed migration and backfilling scheduling algorithm, which is denoted as BgMBF, is designed to schedule parallel jobs and the bandwidth demands are guaranteed by AdaBa. To obtain high job responsiveness performance, a bandwidth-reserved job backfilling strategy is designed when the requested TVC for current scheduled job cannot be allocated in the cloud. The migration cost of BgMBF is also considered and an enhanced version BgMBFSDF is then proposed to minimize the number of migration when the execution time of jobs are known. Through extensive simulation experiments on popular parallel workloads, our proposed TVC embedding algorithm AdaBa achieves up to 15 percent of improvement on accept rate compared with existing algorithms such as Oktupus and greedy algorithm. Our proposed BgMBF and BgMBFSDF also significantly outperform other popular scheduling algorithms integrated with AdaBa on average response time and average bounded slow down.

Description: Symmetry, Vol. 10, Pages 133: Towards Generalized Noise-Level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns Symmetry doi: 10.3390/sym10050133 Authors: Peter Moeck Geometric Akaike Information Criteria (G-AICs) for generalized noise-level dependent crystallographic symmetry classifications of two-dimensional (2D) images that are more or less periodic in either two or one dimensions as well as Akaike weights for multi-model inferences and predictions are reviewed. Such novel classifications do not refer to a single crystallographic symmetry class exclusively in a qualitative and definitive way. Instead, they are quantitative, spread over a range of crystallographic symmetry classes, and provide opportunities for inferences from all classes (within the range) simultaneously. The novel classifications are based on information theory and depend only on information that has been extracted from the images themselves by means of maximal likelihood approaches so that these classifications are objective. This is in stark contrast to the common practice whereby arbitrarily set thresholds or null hypothesis tests are employed to force crystallographic symmetry classifications into apparently definitive/exclusive states, while the geometric feature extraction results on which they depend are never definitive in the presence of generalized noise, i.e., in all real-world applications. Thus, there is unnecessary subjectivity in the currently practiced ways of making crystallographic symmetry classifications, which can be overcome by the approach outlined in this review.

Description: Symmetry, Vol. 10, Pages 131: Models for Green Supplier Selection with Some 2-Tuple Linguistic Neutrosophic Number Bonferroni Mean Operators Symmetry doi: 10.3390/sym10050131 Authors: Jie Wang Guiwu Wei Yu Wei In this paper, we extend the Bonferroni mean (BM) operator, generalized Bonferroni mean (GBM) operator, dual generalized Bonferroni mean (DGBM) operator and dual generalized geometric Bonferroni mean (DGGBM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (2TLNNWBM) operator, 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (2TLNNWGBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (G2TLNNWBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (G2TLNNWGBM) operator, dual generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (DG2TLNNWBM) operator, and dual generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (DG2TLNNWGBM) operator. Then, the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

Description: Symmetry, Vol. 10, Pages 137: Symmetry Adaptation of the Rotation-Vibration Theory for Linear Molecules Symmetry doi: 10.3390/sym10050137 Authors: Katy Chubb Per Jensen Sergei Yurchenko A numerical application of linear-molecule symmetry properties, described by the D ∞ h point group, is formulated in terms of lower-order symmetry groups D n h with finite n. Character tables and irreducible representation transformation matrices are presented for D n h groups with arbitrary n-values. These groups can subsequently be used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of “reduced” vibrational eigenvalue problems with simplified Hamiltonians is used as a practical example. It is shown how the solutions of these eigenvalue problems can also be extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator L ^ z . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D n h . 12 C 2 H 2 is used as an example of a linear molecule of D ∞ h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE).

Description: Symmetry, Vol. 10, Pages 140: Multiple Criteria Group Decision-Making Considering Symmetry with Regards to the Positive and Negative Ideal Solutions via the Pythagorean Normal Cloud Model for Application to Economic Decisions Symmetry doi: 10.3390/sym10050140 Authors: Jinming Zhou Weihua Su Tomas Baležentis Dalia Streimikiene Pythagorean fuzzy sets are highly appealing in dealing with uncertainty as they allow for greater flexibility in regards to the membership and non-membership degrees by extending the set of possible values. In this paper, we propose a multi-criteria group decision-making approach based on the Pythagorean normal cloud. Some cloud aggregation operators are presented in this paper to facilitate the appraisal of the underlying utilities of the alternatives under consideration. The concept and properties of the Pythagorean normal cloud and its backward generation algorithm, aggregation operators and distance measurement are outlined. The proposed approach resembles the TOPSIS technique, which, indeed, considers the symmetry of the distances to the positive and negative ideal solutions. Furthermore, an example from e-commerce is presented to demonstrate and validate the proposed decision-making approach. Finally, the comparative analysis is implemented to check the robustness of the results when the aggregation rules are changed.

Description: Symmetry, Vol. 10, Pages 139: An Exact Analytical Solution for Thermoelastic Response of Clamped Beams Subjected to a Movable Laser Pulse Symmetry doi: 10.3390/sym10050139 Authors: Xianfeng Yang Jingxuan Ma Shoubin Liu Yun Xing Jialing Yang Yuxin Sun The thermoelastic dynamic response of a clamped Bernoulli beam was studied when it was irradiated by a movable, temporally non-Gaussian, laser pulse. Both the energy absorption depth and the time decaying effects were considered. The temperature distribution, deflection, vibration acceleration, and stress of the beam were derived analytically, and the variations of them with time and space were illustrated. It was shown that the vibration frequency is independent of the scanning speed of the laser pulse. It is important to notice that, although the deflection of the beam is small, high vibration acceleration can be induced in microbeams, which is important for failure and fracture of the beam. Moreover, compressive stress is induced in the beam, but the importance of temperature-induced stress and deformation-induced stress may be different according to the duration time and moving speed of the laser pulse.

Description: Symmetry, Vol. 10, Pages 160: Linguistic Neutrosophic Generalized Partitioned Bonferroni Mean Operators and Their Application to Multi-Attribute Group Decision Making Symmetry doi: 10.3390/sym10050160 Authors: Yumei Wang Peide Liu To solve the problems related to inhomogeneous connections among the attributes, we introduce a novel multiple attribute group decision-making (MAGDM) method based on the introduced linguistic neutrosophic generalized weighted partitioned Bonferroni mean operator (LNGWPBM) for linguistic neutrosophic numbers (LNNs). First of all, inspired by the merits of the generalized partitioned Bonferroni mean (GPBM) operator and LNNs, we combine the GPBM operator and LNNs to propose the linguistic neutrosophic GPBM (LNGPBM) operator, which supposes that the relationships are heterogeneous among the attributes in MAGDM. Then, we discuss its desirable properties and some special cases. In addition, aimed at the different importance of each attribute, the weighted form of the LNGPBM operator is investigated, which we call the LNGWPBM operator. Then, we discuss some of its desirable properties and special examples accordingly. In the end, we propose a novel MAGDM method on the basis of the introduced LNGWPBM operator, and illustrate its validity and merit by comparing it with the existing methods.

Description: Symmetry, Vol. 10, Pages 159: The Local Theory for Regular Systems in the Context of t-Bonded Sets Symmetry doi: 10.3390/sym10050159 Authors: Mikhail Bouniaev Nikolay Dolbilin The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are ( r , R ) -systems or, in other words, Delone sets of type ( r , R ) in d-dimensional Euclidean space. In this paper, we will review the recent results of the local theory for a wider class of point sets compared with the Delone sets. We call them t-bonded sets. This theory, in particular, might provide new insight into the case for which the atomic structure of matter is a Delone set of a “microporous” character, i.e., a set that contains relatively large cavities free from points of the set.

Description: Symmetry, Vol. 10, Pages 157: Total Variation Based Neural Network Regression for Nonuniformity Correction of Infrared Images Symmetry doi: 10.3390/sym10050157 Authors: Rui Lai Gaoyu Yue Gangxuan Zhang Many existing scene-adaptive nonuniformity correction (NUC) methods suffer from slow convergence rate together with ghosting effects. In this paper, an improved NUC algorithm based on total variation penalized neural network regression is presented. Our work mainly focuses on solving the overfitting problem in least mean square (LMS) regression of traditional neural network NUC methods, which is realized by employing a total variation penalty in the cost function and redesigning the processing architecture. Moreover, an adaptive gated learning rate is presented to further reduce the ghosting artifacts and guarantee fast convergence. The performance of the proposed algorithm is comprehensively investigated with artificially corrupted test sequences and real infrared image sequences, respectively. Experimental results show that the proposed algorithm can effectively accelerate the convergence speed, suppress ghosting artifacts, and promote correction precision.

Description: Symmetry, Vol. 10, Pages 163: An Online Algorithm for Dynamic NFV Placement in Cloud-Based Autonomous Response Networks Symmetry doi: 10.3390/sym10050163 Authors: Leonardo Ochoa-Aday Cristina Cervelló-Pastor Adriana Fernández-Fernández Paola Grosso Autonomous response networks are becoming a reality thanks to recent advances in cloud computing, Network Function Virtualization (NFV) and Software-Defined Networking (SDN) technologies. These enhanced networks fully enable autonomous real-time management of virtualized infrastructures. In this context, one of the major challenges is how virtualized network resources can be effectively placed. Although this issue has been addressed before in cloud-based environments, it is not yet completely resolved for the online placement of virtual machines. For such a purpose, this paper proposes an online heuristic algorithm called Topology-Aware Placement of Virtual Network Functions (TAP-VNF) as a low-complexity solution for such dynamic infrastructures. As a complement, we provide a general formulation of the network function placement using the service function chaining concept. Furthermore, two metrics called consolidation and aggregation validate the efficiency of the proposal in the experimental simulations. We have compared our approach with optimal solutions, in terms of consolidation and aggregation ratios, showing a more suitable performance for dynamic cloud-based environments. The obtained results show that TAP-VNF also outperforms existing approaches based on traditional bin packing schemes.

Description: Symmetry, Vol. 10, Pages 187: New Operations of Totally Dependent-Neutrosophic Sets and Totally Dependent-Neutrosophic Soft Sets Symmetry doi: 10.3390/sym10060187 Authors: Xiaohong Zhang Chunxin Bo Florentin Smarandache Choonkil Park The purpose of the paper is to study new algebraic operations and fundamental properties of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets. First, the in-coordination relationships among the original inclusion relations of totally dependent-neutrosophic sets (called type-1 and typ-2 inclusion relations in this paper) and union (intersection) operations are analyzed, and then type-3 inclusion relation of totally dependent-neutrosophic sets and corresponding type-3 union, type-3 intersection, and complement operations are introduced. Second, the following theorem is proved: all totally dependent-neutrosophic sets (based on a certain universe) determined a generalized De Morgan algebra with respect to type-3 union, type-3 intersection, and complement operations. Third, the relationships among the type-3 order relation, score function, and accuracy function of totally dependent-neutrosophic sets are discussed. Finally, some new operations and properties of totally dependent-neutrosophic soft sets are investigated, and another generalized De Morgan algebra induced by totally dependent-neutrosophic soft sets is obtained.

Description: Symmetry, Vol. 10, Pages 189: Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm Symmetry doi: 10.3390/sym10060189 Authors: Jianghong Zhu Yanlai Li Hesitant fuzzy linguistic (HFL) term set, as a very flexible tool to represent the judgments of decision makers, has attracted the attention of many researchers. In recent years, some HFL aggregation operators have been developed to aggregate the HFL information. However, most of these operators are proposed based on the Algebraic product and Algebraic sum. In this paper, we presented some HFL aggregation operators to handle HFL information based on Hamacher triangle norms. We first define new operational laws on the HFL element according to Hamacher triangle norms. Then we present a family of HFL Hamacher aggregation operators, including the HFL Hamacher weighted averaging, HFL Hamacher weighted geometric, HFL Hamacher power weighted averaging and HFL Hamacher power weighted geometric operators and their generalized forms. We also investigate some special cases and properties of these operators in detail. Furthermore, we develop two approaches based on the proposed operators to deal with the multi-criteria decision-making problem with HFL information. Finally, a numerical example with regard to choosing a suitable city to release sharing car is provided to illustrate the feasibility of the proposed method, and the advantages of the proposed methods are shown by conducting a sensitivity and comparative analysis.

Description: Symmetry, Vol. 10, Pages 195: Vortex Creation without Stirring in Coupled Ring Resonators with Gain and Loss Symmetry doi: 10.3390/sym10060195 Authors: Aleksandr Ramaniuk Nguyen Viet Hung Michael Giersig Krzysztof Kempa Vladimir V. Konotop Marek Trippenbach We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We show that by turning on and off local coupling between rings, one can selectively generate a permanent vortex in one of the rings. We find that due to the modulation instability, it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with an interesting structure of currents flowing between rings, the generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as a single vortex in one of the channels, which later alternates between channels.

Description: Symmetry, Vol. 10, Pages 191: Reflection Negative Kernels and Fractional Brownian Motion Symmetry doi: 10.3390/sym10060191 Authors: Palle E. T. Jorgensen Karl-Hermann Neeb Gestur Ólafsson In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 < H ≤ 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 < H < 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R ) . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E ) .

Description: Symmetry, Vol. 10, Pages 193: Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition Symmetry doi: 10.3390/sym10060193 Authors: Kifayat Ullah Tahir Mahmood Naeem Jan In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.

Description: Symmetry, Vol. 10, Pages 249: Lossless and Efficient Polynomial-Based Secret Image Sharing with Reduced Shadow Size Symmetry doi: 10.3390/sym10070249 Authors: Xuan Zhou Yuliang Lu Xuehu Yan Yongjie Wang Lintao Liu Thien-and-Lin’s polynomial-based secret image sharing (PSIS) is utilized as the basic method to achieve PSISs with better performances, such as meaningful shares, two-in-one property and shares with different priorities. However, this (k,n) threshold PSIS cannot achieve lossless recovery for pixel values more than 250. Furthermore, current solutions to lossless recovery for PSIS have several natural drawbacks, such as large computational costs and random pixel expansion. In this paper, a lossless and efficient (k,n) threshold PSIS scheme with reduced shadow size is presented. For lossless recovery and efficiency, two adjacent pixels are specified as a secret value, the prime in the sharing polynomial is replaced with 65,537, and then the additional screening operation can ensure each shared value in the range [0,65,535]. To reduce shadows size and improve security, only the first k−1 coefficients are embedded with secret values and the last coefficient is assigned randomly. To prevent the leakage of secrets, generalized Arnold permutation with special key generating strategy is performed on the secret image prior to sharing process without key distribution. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.

Description: Symmetry, Vol. 10, Pages 247: A Local Approximation Approach for Processing Time-Evolving Graphs Symmetry doi: 10.3390/sym10070247 Authors: Shuo Ji Yinliang Zhao To efficiently process time-evolving graphs where new vertices and edges are inserted over time, an incremental computing model, which processes the newly-constructed graph based on the results of the computation on the outdated graph, is widely adopted in distributed time-evolving graph computing systems. In this paper, we first experimentally study how the results of the graph computation on the local graph structure can approximate the results of the graph computation on the complete graph structure in distributed environments. Then, we develop an optimization approach to reduce the response time in bulk synchronous parallel (BSP)-based incremental computing systems by processing time-evolving graphs on the local graph structure instead of on the complete graph structure. We have evaluated our optimization approach using the graph algorithms single-source shortest path (SSSP) and PageRankon the Amazon Elastic Compute Cloud(EC2), a central part of Amazon.com’s cloud-computing platform, with different scales of graph datasets. The experimental results demonstrate that the local approximation approach can reduce the response time for the SSSP algorithm by 22% and reduce the response time for the PageRank algorithm by 7% on average compared to the existing incremental computing framework of GraphTau.

Description: Symmetry, Vol. 10, Pages 248: From Theory to Practice: A Data Quality Framework for Classification Tasks Symmetry doi: 10.3390/sym10070248 Authors: David Camilo Corrales Agapito Ledezma Juan Carlos Corrales The data preprocessing is an essential step in knowledge discovery projects. The experts affirm that preprocessing tasks take between 50% to 70% of the total time of the knowledge discovery process. In this sense, several authors consider the data cleaning as one of the most cumbersome and critical tasks. Failure to provide high data quality in the preprocessing stage will significantly reduce the accuracy of any data analytic project. In this paper, we propose a framework to address the data quality issues in classification tasks DQF4CT. Our approach is composed of: (i) a conceptual framework to provide the user guidance on how to deal with data problems in classification tasks; and (ii) an ontology that represents the knowledge in data cleaning and suggests the proper data cleaning approaches. We presented two case studies through real datasets: physical activity monitoring (PAM) and occupancy detection of an office room (OD). With the aim of evaluating our proposal, the cleaned datasets by DQF4CT were used to train the same algorithms used in classification tasks by the authors of PAM and OD. Additionally, we evaluated DQF4CT through datasets of the Repository of Machine Learning Databases of the University of California, Irvine (UCI). In addition, 84% of the results achieved by the models of the datasets cleaned by DQF4CT are better than the models of the datasets authors.

Description: Symmetry, Vol. 10, Pages 246: Analysis of the Angular Dependence of Time Delay in Gravitational Lensing Symmetry doi: 10.3390/sym10070246 Authors: Nicola Alchera Marco Bonici Roberta Cardinale Alba Domi Nicola Maggiore Chiara Righi Silvano Tosi We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom as the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to the arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in Astrophysics and Cosmology which may be applied to investigate the discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.

Description: Symmetry, Vol. 10, Pages 253: RIM4J: An Architecture for Language-Supported Runtime Measurement against Malicious Bytecode in Cloud Computing Symmetry doi: 10.3390/sym10070253 Authors: Haihe Ba Huaizhe Zhou Huidong Qiao Zhiying Wang Jiangchun Ren While cloud customers can benefit from migrating applications to the cloud, they are concerned about the security of the hosted applications. This is complicated by the customers not knowing whether their cloud applications are working as expected. Although memory-safety Java Virtual Machine (JVM) can alleviate their anxiety due to the control flow integrity, their applications are prone to a violation of bytecode integrity. The analysis of some Java exploits indicates that the violation results primarily from the given excess sandbox permission, loading flaws in Java class libraries and third-party middlewares and the abuse of sun.misc.UnsafeAPI. To such an end, we design an architecture, called RIM4J, to enforce a runtime integrity measurement of Java bytecode within a cloud system, with the ability to attest this to a cloud customer in an unforgeable manner. Our RIM4J architecture is portable, such that it can be quickly deployed and adopted for real-world purposes, without requiring modifications to the underlying systems and access to application source code. Moreover, our RIM4J architecture is the first to measure dynamically-generated bytecode. We apply our runtime measurement architecture to a messaging server application where we show how RIM4J can detect undesirable behaviors, such as uploading arbitrary files and remote code execution. This paper also reports the experimental evaluation of a RIM4J prototype using both a macro- and a micro-benchmark; the experimental results indicate that RIM4J is a practical solution for real-world applications.

Description: Symmetry, Vol. 10, Pages 254: Joint Adaptive Coding and Reversible Data Hiding for AMBTC Compressed Images Symmetry doi: 10.3390/sym10070254 Authors: Wien Hong Xiaoyu Zhou Shaowei Weng This paper proposes a joint coding and reversible data hiding method for absolute moment block truncation coding (AMBTC) compressed images. Existing methods use a predictor to predict the quantization levels of AMBTC codes. Equal-length indicators, secret bits and prediction errors are concatenated to construct the output code stream. However, the quantization levels might not highly correlate with their neighbors for predictive coding, and the use of equal-length indicators might impede the coding efficiency. The proposed method uses reversible integer transform to represent the quantization levels by their means and differences, which is advantageous for predictive coding. Moreover, the prediction errors are better classified into symmetrical encoding cases using the adaptive classification technique. The length of indicators and the bits representing the prediction errors are properly assigned according to the classified results. Experiments show that the proposed method offers the lowest bitrate for a variety of images when compared with the existing state-of-the-art works.

Description: Symmetry, Vol. 10, Pages 255: Probability of Conjunction Estimation for Analyzing the Electromagnetic Environment Based on a Space Object Conjunction Methodology Symmetry doi: 10.3390/sym10070255 Authors: Asad Husnain Baqar Tao Jiang Ishfaq Hussain Ghulam Farid The introduction of the space object conjunction method in electromagnetic compatibility modeling and simulation is quite a novel concept. It is useful for the stochastic analysis of an electromagnetic (EM) environment which is based on the probability of conjunction assessment. The space conjunction methodology is anticipated as the frontline defense for the protection of active satellites in space. EM congestion occurs in an environment with the increase in the number of operational EM devices. In a theoretical sense, this congestion is analogous to the space conjunction. Therefore, the space conjunction model can be applied in the EM scenarios. In this paper, we have investigated the application of the defined conjunction model by using the analytical expression of the probability of electromagnetic conjunction, which is based on the orbital parameters of the system under test. Additionally, we have elaborated the influence of these orbital parameters on the probability of conjunction. The simulations have been performed by considering different EM scenarios and the results are validated by using Monte Carlo simulations. The results show that errors in the analytical and Monte Carlo simulations are within a 1% range, which makes the analytical model effective. Computationally, the proposed analytical model is cost effective as compared to the numerical method, i.e., Monte Carlo. Moreover, from the results, it has been validated that the probability of conjunction increases with the increase in transmitted power and decreases with the compatible threshold limit of the receiving system, thus, making this method useful for analyzing the electromagnetic environment and as a frontline safety tool for electromagnetic systems.

Description: Symmetry, Vol. 10, Pages 250: A Cluster-Based Boosting Algorithm for Bankruptcy Prediction in a Highly Imbalanced Dataset Symmetry doi: 10.3390/sym10070250 Authors: Tuong Le Le Hoang Son Minh Thanh Vo Mi Young Lee Sung Wook Baik Bankruptcy prediction has been a popular and challenging research topic in both computer science and economics due to its importance to financial institutions, fund managers, lenders, governments, as well as economic stakeholders in recent years. In a bankruptcy dataset, the problem of class imbalance, in which the number of bankruptcy companies is smaller than the number of normal companies, leads to a standard classification algorithm that does not work well. Therefore, this study proposes a cluster-based boosting algorithm as well as a robust framework using the CBoost algorithm and Instance Hardness Threshold (RFCI) for effective bankruptcy prediction of a financial dataset. This framework first resamples the imbalance dataset by the undersampling method using Instance Hardness Threshold (IHT), which is used to remove the noise instances having large IHT value in the majority class. Then, this study proposes a Cluster-based Boosting algorithm, namely CBoost, for dealing with the class imbalance. In this algorithm, the majority class will be clustered into a number of clusters. The distance from each sample to its closest centroid will be used to initialize its weight. This algorithm will perform several iterations for finding weak classifiers and combining them to create a strong classifier. The resample set resulting from the previous module, will be used to train CBoost, which will be used to predict bankruptcy for the validation set. The proposed framework is verified by the Korean bankruptcy dataset (KBD), which has a very small balancing ratio in both the training and the testing phases. The experimental results of this research show that the proposed framework achieves 86.8% in AUC (area under the ROC curve) and outperforms several methods for dealing with the imbalanced data problem for bankruptcy prediction such as GMBoost algorithm, the oversampling-based method using SMOTEENN, and the clustering-based undersampling method for bankruptcy prediction in the experimental dataset.

Description: Symmetry, Vol. 10, Pages 251: Complex Fuzzy Geometric Aggregation Operators Symmetry doi: 10.3390/sym10070251 Authors: Lvqing Bi Songsong Dai Bo Hu A complex fuzzy set is an extension of the traditional fuzzy set, where traditional [0,1]-valued membership grade is extended to the complex unit disk. The aggregation operator plays an important role in many fields, and this paper presents several complex fuzzy geometric aggregation operators. We show that these operators possess the properties of rotational invariance and reflectional invariance. These operators are also closed on the upper-right quadrant of the complex unit disk. Based on the relationship between Pythagorean membership grades and complex numbers, these operators can be applied to the Pythagorean fuzzy environment.

Description: Symmetry, Vol. 10, Pages 252: On the Diameter and Incidence Energy of Iterated Total Graphs Symmetry doi: 10.3390/sym10070252 Authors: Eber Lenes Exequiel Mallea-Zepeda María Robbiano Jonnathan Rodríguez The total graph of G, T(G) is the graph whose vertex set is the union of the sets of vertices and edges of G, where two vertices are adjacent if and only if they stand for either incident or adjacent elements in G. For k≥2, the k-th iterated total graph of G, Tk(G), is defined recursively as Tk(G)=T(Tk−1(G)), where T1(G)=T(G) and T0(G)=G. If G is a connected graph, its diameter is the maximum distance between any pair of vertices in G. The incidence energy IE(G) of G is the sum of the singular values of the incidence matrix of G. In this paper, for a given integer k we establish a necessary and sufficient condition under which diam(Tr+1(G))>k−r,r≥0. In addition, bounds for the incidence energy of the iterated graph Tr+1(G) are obtained, provided G is a regular graph. Finally, new families of non-isomorphic cospectral graphs are exhibited.

Description: Symmetry, Vol. 10, Pages 263: A Survey of Methods for Symmetry Detection on 3D High Point Density Models in Biomedicine Symmetry doi: 10.3390/sym10070263 Authors: Chiara Bartalucci Rocco Furferi Lapo Governi Yary Volpe Versatile, cheap and non-invasive 3D acquisition techniques have received attention and interest in the field of biomedicine in recent years as the accuracy of developed devices permits the acquisition of human body shapes in detail. Interest in these technologies derives from the fact that they have the potential to overcome some limitations of invasive techniques (CT, X-rays, etc.) and those based on 2D photographs for the acquisition of 3D geometry. However, the data acquired from the 3D scanner cannot be directly used but need to be processed as they consist of 3D coordinates of the acquired points. Therefore, many researchers have proposed different algorithms which recognise the shape of human body and/or its features when starting from a 3D point cloud. Among all possible human body features to be evaluated, symmetry results the most relevant one. Accordingly, this survey systematically investigates the methods proposed in the literature to recognise 2D symmetry by the symmetry line and bilateral symmetry by the symmetry plane. The paper also analyses qualitative comparisons among the proposed methods to provide a guide for both practitioners and researchers.

Description: Symmetry, Vol. 10, Pages 262: Iterative Group Decomposition for Refining Microaggregation Solutions Symmetry doi: 10.3390/sym10070262 Authors: Laksamee Khomnotai Jun-Lin Lin Zhi-Qiang Peng Arpita Samanta Santra Microaggregation refers to partitioning n given records into groups of at least k records each to minimize the sum of the within-group squared error. Because microaggregation is non-deterministic polynomial-time hard for multivariate data, most existing approaches are heuristic based and derive a solution within a reasonable timeframe. We propose an algorithm for refining the solutions generated using the existing microaggregation approaches. The proposed algorithm refines a solution by iteratively either decomposing or shrinking the groups in the solution. Experimental results demonstrated that the proposed algorithm effectively reduces the information loss of a solution.

Description: Symmetry, Vol. 10, Pages 260: Schützenberger Symmetries in Network Structures Symmetry doi: 10.3390/sym10070260 Authors: Allen D. Parks It is known that the set of all networks of fixed order form a semigroup. This fact provides for the Green’s L, R, H and D  equivalence equivalence classifications of all such networks. These classifications reveal certain structural invariants common to all networks within a Green’s equivalence class and enables the computation of the associated invariant preserving symmetries that transform a network into another network within a Green’s equivalence class. Here, the notion of Schützenberger symmetries in network structures is introduced. These are computable symmetries which transform any network within an H-equivalence class into another network within that class in a manner that preserves the associated structural invariants. Useful applications of Schützenberger symmetries include enabling the classification and analysis of biological network data, identifying important relationships in social networks, and understanding the consequences of link reconfiguration in communication and sensor networks.

Description: Symmetry, Vol. 10, Pages 269: Denoising of Magnetocardiography Based on Improved Variational Mode Decomposition and Interval Thresholding Method Symmetry doi: 10.3390/sym10070269 Authors: Yanping Liao Congcong He Qiang Guo Recently, magnetocardiography (MCG) has attracted increasing attention as a non-invasive and non-contact technique for detecting electrocardioelectric functions. However, the severe background noise makes it difficult to extract information. Variational Mode Decomposition (VMD), which is an entirely non-recursive model, is used to decompose the non-stationary signal into the intrinsic mode functions (IMFs). Traditional VMD algorithms cannot control the bandwidth of each IMF, whose quadratic penalty lacks adaptivity. As a result, baseline drift noise is still present or medical information is lost. In this paper, to overcome the unadaptable quadratic penalty problem, an improved VMD model via correlation coefficient and new update formulas are proposed to decompose MCG signals. To improve the denoising precision, this algorithm is combined with the interval threshold algorithm. First, the correlation coefficient is calculated, to determine quadratic penalty, in order to extract the first IMF made up of baseline drift. Then, the new update formulas derived from the variance that describes the noise level are used, to perform decomposition on the rest signal. Finally, the Interval thresholding algorithm is performed on each IMF. Theoretical analysis and experimental results show that this algorithm can effectively improve the output signal-to-noise ratio and has superior performance.

Description: Symmetry, Vol. 10, Pages 271: An Effective Dual-Image Reversible Hiding for UAV’s Image Communication Symmetry doi: 10.3390/sym10070271 Authors: Yung-I Lin Ying-Hsuan Huang Chih-Cheng Chen Compared with traditional hiding methods, dual-image reversible data hiding methods have a higher embedding rate and a better quality stego image. Also, this is a special case of secret sharing, because secret data cannot be extracted from any stego image. In the literature, the frequencies of occurrence of secret data were used as reference information for data encoding, in which most digits were transformed into smaller ones. The encoding strategy can effectively decrease the modification level of the pixel. However, only limited literature has analyzed the relationship between the adjacent secret data. In this paper, we proposed an exclusive-or (XOR)-based encoding method to convert the neighboring values, thereby reducing the distortion. Since there are significant similarities between the two stego images and the original image, the first stego image is stored on an unmanned aerial vehicle (UAV) to avoid a hacker’s interception attack. The second stego image on the UAV is sent to the command station. After completion of the UAV mission, the proposed method extracts the secret data from the two stego images to identify whether the second stego image has been tampered with.

Description: Symmetry, Vol. 10, Pages 279: Hyperbolicity of Direct Products of Graphs Symmetry doi: 10.3390/sym10070279 Authors: Walter Carballosa Amauris de la Cruz Alvaro Martínez-Pérez José M. Rodríguez It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several types of product graphs (Cartesian, strong, join, corona and lexicographic products). However, the problem with the direct product is more complicated. The symmetry of this product allows us to prove that, if the direct product G1×G2 is hyperbolic, then one factor is bounded and the other one is hyperbolic. Besides, we prove that this necessary condition is also sufficient in many cases. In other cases, we find (not so simple) characterizations of hyperbolic direct products. Furthermore, we obtain good bounds, and even formulas in many cases, for the hyperbolicity constant of the direct product of some important graphs (as products of path, cycle and even general bipartite graphs).

Description: Symmetry, Vol. 10, Pages 280: Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment Symmetry doi: 10.3390/sym10070280 Authors: Harish Garg Nancy The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

Description: Symmetry, Vol. 10, Pages 282: Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model Symmetry doi: 10.3390/sym10070282 Authors: Michał Szymczyk Marcin Nowak Wojciech Sumelka The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

Description: Symmetry, Vol. 10, Pages 284: Adaptive and Blind Audio Watermarking Algorithm Based on Chaotic Encryption in Hybrid Domain Symmetry doi: 10.3390/sym10070284 Authors: Qiuling Wu Meng Wu An adaptive and blind audio watermarking algorithm is proposed based on chaotic encryption in discrete cosine transform (DCT) and discrete wavelet transform (DWT) hybrid domain. Since human ears are not sensitive to small changes in the high-frequency components of the audio media, the encrypted watermark can be embedded into the audio signal according to the special embedding rules. The embedding depth of each audio segment is controlled by the overall average amplitude to effectively improve the robustness and imperceptibility. The watermark is encrypted by a chaotic sequence to improve the security of watermark, so only users who hold the correct key can accurately extract the watermark without the original audio signal. Experimental results show that the proposed algorithm has larger capacity, higher imperceptibility, better security, and stronger robustness when combating against signal-processing attacks than the involved audio watermarking algorithms in recent years.

Description: Symmetry, Vol. 10, Pages 285: A Step-by-Step Solution Methodology for Mathematical Expressions Symmetry doi: 10.3390/sym10070285 Authors: Hosseinpour Milani Pehlivan In this paper, we propose a methodology for the step-by-step solution of problems, which can be incorporated into a computer algebra system. Our main aim is to show all the intermediate evaluation steps of mathematical expressions from the start to the end of the solution. The first stage of the methodology covers the development of a formal grammar that describes the syntax and semantics of mathematical expressions. Using a compiler generation tool, the second stage produces a parser from the grammar description. The parser is used to convert a particular mathematical expression into an Abstract Syntax Tree (AST), which is evaluated in the third stage by traversing al its nodes. After every evaluation of some nodes, which corresponds to an intermediate solution step of the related expression, the resulting AST is transformed into the corresponding mathematical expression and then displayed. Many other algebra-related issues such as simplification, factorization, distribution and substitution can be covered by the solution methodology. We currently focuses on the solutions of various problems associated with the subject of derivative, equations, single variable polynomials, and operations on functions. However, it can easily be extended to cover the other subjects of general mathematics.

Description: Symmetry, Vol. 10, Pages 291: Flight Stability Analysis of a Symmetrically-Structured Quadcopter Based on Thrust Data Logger Information Symmetry doi: 10.3390/sym10070291 Authors: Endrowednes Kuantama Ioan Tarca Simona Dzitac Ioan Dzitac Radu Tarca Quadcopter flight stability is achieved when all of the rotors–propellers generate equal thrust in hover and throttle mode. It requires a control system algorithm for rotor speed adjustment, which is related with the translational vector and rotational angle. Even with an identical propeller and speed, the thrusts generated are not necessarily equal on all rotors–propellers. Therefore, this study focuses on developing a data logger to measure thrust and to assist in flight control on a symmetrically-structured quadcopter. It is developed with a four load cells sensor with two-axis characterizations and is able to perform real-time signal processing. The process includes speed adjustment for each rotor, trim calibration, and a proportional integral derivative (PID) control tuning system. In the data retrieval process, a quadcopter was attached with data logger system in a parallel axis position. Various speeds between 1200 rpm to 4080 rpm in throttle mode were analyzed to determine the stability of the resulting thrust. Adjustment result showed that the thrust differences between the rotors were less than 0.5 N. The data logger showed the consistency of the thrust value and was proved by repeated experiments with 118 s of sampling time for the same quadcopter control condition. Finally, the quadcopter flight stability as the result of tuning process by the thrust data logger was validated by the flight controller data.

Description: Symmetry, Vol. 10, Pages 293: Ultrathin Terahertz Dual-Band Perfect Metamaterial Absorber Using Asymmetric Double-Split Rings Resonator Symmetry doi: 10.3390/sym10070293 Authors: Taiguo Lu Dawei Zhang Peizhen Qiu Jiqing Lian Ming Jing Binbin Yu Jing Wen In this article, an ultrathin terahertz dual band metamaterial absorber made up of patterned asymmetrical double-split rings and a continuous metal layer separated by a thin FR-4 layer is designed. Simulation results show that two almost identical strong absorption peaks appear in the terahertz band. When the incident electric field is perpendicular to the ring gaps located at 11 μm asymmetrically, the absorptivity of 98.6% at 4.48 THz and 98.5% at 4.76 THz can be obtained. The absorption frequency and the absorptivity of the absorber can be modulated by the asymmetric distribution of the gaps. The perfect metamaterial absorber is expected to provide important reference for the design of terahertz modulator, filters, absorbers, and polarizers.

Description: Symmetry, Vol. 10, Pages 294: Vegetation Greening for Winter Oblique Photography Using Cycle-Consistence Adversarial Networks Symmetry doi: 10.3390/sym10070294 Authors: Xiaowei Xue Chunxue Wu Ze Sun Yan Wu Neal N. Xiong A 3D city model is critical for the construction of a digital city. One of the methods of building a 3D city model is tilt photogrammetry. In this method, oblique photography is crucial for generating the model because the visual quality of photography directly impacts the model’s visual effect. Yet, sometimes, oblique photography does not have good visual quality due to a bad season or defective photographic equipment. For example, for oblique photography taken in winter, vegetation is brown. If this photography is employed to generate the 3D model, the result would be bad visually. Yet, common methods for vegetation greening in oblique photography rely on the assistance of the infrared band, which is not available sometimes. Thus, a method for vegetation greening in winter oblique photography without the infrared band is required, which is proposed in this paper. The method was inspired by the work on CycleGAN (Cycle-consistence Adversarial Networks). In brief, the problem of turning vegetation green in winter oblique photography is considered as a style transfer problem. Summer oblique photography generally has green vegetation. By applying CycleGAN, winter oblique photography can be transferred to summer oblique photography, and the vegetation can turn green. Yet, due to the existence of “checkerboard artifacts”, the original result cannot be applied for real production. To reduce artifacts, the generator of CycleGAN is modified. As the final results suggest, the proposed method unlocks the bottleneck of vegetation greening when the infrared band is not available and artifacts are reduced.

Description: Symmetry, Vol. 10, Pages 298: Symmetries, Conserved Properties, Tensor Representations, and Irreducible Forms in Molecular Quantum Electrodynamics Symmetry doi: 10.3390/sym10070298 Authors: David L. Andrews In the wide realm of applications of quantum electrodynamics, a non-covariant formulation of theory is particularly well suited to describing the interactions of light with molecular matter. The robust framework upon which this formulation is built, fully accounting for the intrinsically quantum nature of both light and the molecular states, enables powerful symmetry principles to be applied. With their origins in the fundamental transformation properties of the electromagnetic field, the application of these principles can readily resolve issues concerning the validity of mechanisms, as well as facilitate the identification of conditions for widely ranging forms of linear and nonlinear optics. Considerations of temporal, structural, and tensorial symmetry offer significant additional advantages in correctly registering chiral forms of interaction. More generally, the implementation of symmetry principles can considerably simplify analysis by reducing the number of independent quantities necessary to relate to experimental results to a minimum. In this account, a variety of such principles are drawn out with reference to applications, including recent advances. Connections are established with parity, duality, angular momentum, continuity equations, conservation laws, chirality, and spectroscopic selection rules. Particular attention is paid to the optical interactions of molecules as they are commonly studied, in fluids and randomly organised media.

Description: Symmetry, Vol. 10, Pages 203: A Study on Neutrosophic Cubic Graphs with Real Life Applications in Industries Symmetry doi: 10.3390/sym10060203 Authors: Muhammad Gulistan Naveed Yaqoob Zunaira Rashid Florentin Smarandache Hafiz Abdul Wahab Neutrosophic cubic sets are the more generalized tool by which one can handle imprecise information in a more effective way as compared to fuzzy sets and all other versions of fuzzy sets. Neutrosophic cubic sets have the more flexibility, precision and compatibility to the system as compared to previous existing fuzzy models. On the other hand the graphs represent a problem physically in the form of diagrams, matrices etc. which is very easy to understand and handle. So the authors applied the Neutrosophic cubic sets to graph theory in order to develop a more general approach where they can model imprecise information through graphs. We develop this model by introducing the idea of neutrosophic cubic graphs and introduce many fundamental binary operations like cartesian product, composition, union, join of neutrosophic cubic graphs, degree and order of neutrosophic cubic graphs and some results related with neutrosophic cubic graphs. One of very important futures of two neutrosophic cubic sets is the R-union that R-union of two neutrosophic cubic sets is again a neutrosophic cubic set, but here in our case we observe that R-union of two neutrosophic cubic graphs need not be a neutrosophic cubic graph. Since the purpose of this new model is to capture the uncertainty, so we provide applications in industries to test the applicability of our defined model based on present time and future prediction which is the main advantage of neutrosophic cubic sets.

Description: Symmetry, Vol. 10, Pages 202: Some Results on Neutrosophic Triplet Group and Their Applications Symmetry doi: 10.3390/sym10060202 Authors: Tèmítp Jaíyéọlá Florentin Smarandache This article is based on new developments on a neutrosophic triplet group (NTG) and applications earlier introduced in 2016 by Smarandache and Ali. NTG sprang up from neutrosophic triplet set X: a collection of triplets ( b , n e u t ( b ) , a n t i ( b ) ) for an b ∈ X that obeys certain axioms (existence of neutral(s) and opposite(s)). Some results that are true in classical groups were investigated in NTG and were shown to be either universally true in NTG or true in some peculiar types of NTG. Distinguishing features between an NTG and some other algebraic structures such as: generalized group (GG), quasigroup, loop and group were investigated. Some neutrosophic triplet subgroups (NTSGs) of a neutrosophic triplet group were studied. In particular, for any arbitrarily fixed a ∈ X , the subsets X a = { b ∈ X : n e u t ( b ) = n e u t ( a ) } and ker f a = { b ∈ X | f ( b ) = n e u t ( f ( a ) ) } of X, where f : X → Y is a neutrosophic triplet group homomorphism, were shown to be NTSG and normal NTSG, respectively. Both X a and ker f a were shown to be a-normal NTSGs and found to partition X. Consequently, a Lagrange-like formula was found for a finite NTG X ; | X | = ∑ a ∈ X [ X a : ker f a ] | ker f a | based on the fact that | ker f a | | | X a | . The first isomorphism theorem X / ker f ≅ Im f was established for NTGs. Using an arbitrary non-abelian NTG X and its NTSG X a , a Bol structure was constructed. Applications of the neutrosophic triplet set, and our results on NTG in relation to management and sports, are highlighted and discussed.

Description: Symmetry, Vol. 10, Pages 205: The Recalculation of the Weights of Criteria in MCDM Methods Using the Bayes Approach Symmetry doi: 10.3390/sym10060205 Authors: Irina Vinogradova Valentinas Podvezko Edmundas Kazimieras Zavadskas The application of multiple criteria decision-making methods (MCDM) is aimed at choosing the best alternative out of the number of available versions in the absence of the apparently dominant alternative. One of the two major components of multiple criteria decision-making methods is represented by the weights of the criteria describing the considered process. The weights of the criteria quantitatively express their significance and influence on the evaluation result. The criterion weights can be subjective, i.e., based on the estimates assigned by the experts, and the so-called objective, i.e., those which assess the structure of the data array at the time of evaluation. Several groups of experts, representing the opinions of various interested parties may take part in the evaluation of criteria. The evaluation data on the criterion weights also depend on the mathematical methods used for calculations and the estimation scales. In determining the objective weights, several methods, assessing various properties or characteristics of the data array’s structure, are usually employed. Therefore, the use of the procedures, improving the accuracy of the evaluation of the weights’ values and the integration of the obtained data into a single value, is often required. The present paper offers a new approach to more accurate evaluation of the criteria weights obtained by using various methods based on the idea of the Bayes hypothesis. The performed investigation shows that the suggested method is symmetrical and does not depend on the fact whether a priori or posterior values of the weights are recalculated. This result is the theoretical basis for practical use of the method of combining the weights obtained by various approaches as the geometric mean of various estimates. The ideas suggested by the authors have been repeatedly used in the investigation for combining the objective weights, for recalculating the criteria weights after obtaining the estimates of other groups of experts and for combining the subjective and the objective weights. The recalculated values of the weights of the criteria are used in the work for evaluating the quality of the distant courses taught to the students.

Description: Symmetry, Vol. 10, Pages 204: Intrinsic Metrics on Sierpinski-Like Triangles and Their Geometric Properties Symmetry doi: 10.3390/sym10060204 Authors: Mustafa Saltan The classical Sierpinski Gasket defined on the equilateral triangle is a typical example of fractals. Sierpinski-like triangles can also be constructed on isosceles or scalene triangles. An explicit formula for the intrinsic metric on the classical Sierpinski Gasket via code representation of its points is given. The aim of this paper is to generalize this formula to the Sierpinski-like triangles. We also investigate geometrical properties of these triangles with respect to the intrinsic metric. Moreover, we describe certain properties of the classical Sierpinski gasket which are not shared by all of its analogues.

Description: Symmetry, Vol. 10, Pages 208: Multi-Granulation Rough Set for Incomplete Interval-Valued Decision Information Systems Based on Multi-Threshold Tolerance Relation Symmetry doi: 10.3390/sym10060208 Authors: Bingyan Lin Weihua Xu A relation is viewed as a granularity from a granular computing perspective. A classic rough set contains only one granularity. A multi-granulation rough set contains multiple granularities, which promotes the applications of classical rough set. Firstly, this paper uses the incomplete interval-valued decision information system (IIVDIS) as research object and constructs two rough set models in the light of single granularity rough set model for applying the rough set theory to real life more widely, which are optimistic multi-granulation rough set (OMGRS) model and pessimistic multi-granulation rough set (PMGRS) model in the IIVDIS. Secondly, we design two algorithms to compute the roughness and the degree of dependence that are two tools for measuring uncertainty of rough set. Finally, several experiments are performed on six UCI data sets to verify the validity of the proposed theorems.

Description: Symmetry, Vol. 10, Pages 209: Computing the Metric Dimension of Gear Graphs Symmetry doi: 10.3390/sym10060209 Authors: Shahid Imran Muhammad Siddiqui Muhammad Imran Muhammad Hussain Hafiz Bilal Imran Cheema Ali Tabraiz Zeeshan Saleem Let G=(V,E) be a connected graph and d(u,v) denote the distance between the vertices u and v in G.A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J2n,m be a m-level gear graph obtained by m-level wheel graph W2n,m≅mC2n+k1 by alternatively deleting n spokes of each copy of C2n and J3n be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W3n. In this paper, the metric dimension of certain gear graphs J2n,m and J3n generated by wheel has been computed. Also this study extends the previous result given by Tomescu et.al in 2007.

Description: Symmetry, Vol. 10, Pages 207: Nonoscillatory Solutions to Second-Order Neutral Difference Equations Symmetry doi: 10.3390/sym10060207 Authors: Małgorzata Migda Janusz Migda We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: Δ ( r n Δ ( x n + p n x n − τ ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma.

Description: Symmetry, Vol. 10, Pages 199: Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application Symmetry doi: 10.3390/sym10060199 Authors: Guofang Zhang Zhiming Zhang Hang Kong Hamacher operation is a generalization of the algebraic and Einstein operation and expresses a family of binary operation in the unit interval [0,1]. Heronian mean can deal with correlations of different criteria or input arguments and does not bring out repeated calculation. The normal intuitionistic fuzzy numbers (NIFNs) can depict normal distribution information in practical decision making. A decision-making problem was researched under the NIFN environment in this study, and a new multi-criteria group decision-making (MCGDM) approach is herein introduced on the basis of Hamacher operation. Firstly, according to Hamacher operation, some operational laws of NIFNs are presented. Secondly, it is noted that Heronian mean not only takes into account mutuality between the attribute values once, but also considers the correlation between input argument and itself. Therefore, in order to aggregate NIFN information, we developed some operators and studied their properties. These operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM), and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we applied the proposed operators to the MCGDM problem and developed a new MCGDM approach. The characteristics of this new approach are that: (1) it is suitable for making a decision under the NIFN environment and it is more reasonable for aggregating the normal distribution data; (2) it utilizes Hamacher operation to provide an effective and powerful MCGDM algorithm and to make more reliable and more flexible decisions under the NIFN circumstance; (3) it uses the Heronian mean operator to deal with interrelations between the attributes or input arguments, and it does not bring about repeated calculation. Therefore, the proposed method can describe the interaction of the different criteria or input arguments and offer some reasonable and reliable MCGDM aggregation operators, which can open avenues for decision making and broaden perspectives of the decision experts. Lastly, an application is given for showing the effectiveness and feasibility of the approach presented in this paper.

Description: Symmetry, Vol. 10, Pages 196: Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation Symmetry doi: 10.3390/sym10060196 Authors: Ruipu Tan Wende Zhang Shengqun Chen In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass of a neutrosophic set (NS). However, the existing exponential operations and their aggregation methods are primarily for the intuitionistic fuzzy set and the single-valued neutrosophic set (SVNS). So, this paper defines new exponential operational laws of interval neutrosophic numbers (INNs) in which the bases are positive real numbers and the exponents are interval neutrosophic numbers. Several properties based on the exponential operational law are discussed. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is proposed. Finally, a multiple attribute decision making (MADM) approach based on the INWEA operator is introduced and applied to the evaluation of typhoon disasters in Fujian Province, China. Results show that the proposed new approach is feasible and effective in practical applications.

Description: Symmetry, Vol. 10, Pages 215: Multiple Attribute Decision-Making Method Using Similarity Measures of Neutrosophic Cubic Sets Symmetry doi: 10.3390/sym10060215 Authors: Angyan Tu Jun Ye Bing Wang In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information. However, a few researchers have studied neutrosophic cubic decision-making problems, where the similarity measure of NCSs is one of the useful measure methods. For this work, we propose the Dice, cotangent, and Jaccard measures between NCSs, and indicate their properties. Then, under an NCS environment, the similarity measures-based decision-making method of multiple attributes is developed. In the decision-making process, all the alternatives are ranked by the similarity measure of each alternative and the ideal solution to obtain the best one. Finally, two practical examples are applied to indicate the feasibility and effectiveness of the developed method.

Description: Symmetry, Vol. 10, Pages 213: Medical Diagnosis Based on Single-Valued Neutrosophic Probabilistic Rough Multisets over Two Universes Symmetry doi: 10.3390/sym10060213 Authors: Chao Zhang Deyu Li Said Broumi Arun Kumar Sangaiah In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information. To deal with medical diagnosis problems based on generalized fuzzy sets (FSs), the notion of single-valued neutrosophic multisets (SVNMs) is firstly used to express the diagnostic information in this article. Then the model of probabilistic rough sets (PRSs) over two universes is applied to analyze SVNMs, and the concepts of single-valued neutrosophic rough multisets (SVNRMs) over two universes and probabilistic rough single-valued neutrosophic multisets (PRSVNMs) over two universes are introduced. Based on SVNRMs over two universes and PRSVNMs over two universes, single-valued neutrosophic probabilistic rough multisets (SVNPRMs) over two universes are further established. Next, a three-way decisions model by virtue of SVNPRMs over two universes in the context of medical diagnosis is constructed. Finally, a practical case study along with a comparative study are carried out to reveal the accuracy and reliability of the constructed three-way decisions model.

Description: Symmetry, Vol. 10, Pages 228: Harmonic Principles of Elemental Crystals—From Atomic Interaction to Fundamental Symmetry Symmetry doi: 10.3390/sym10060228 Authors: Matthias Zschornak Tilmann Leisegang Falk Meutzner Hartmut Stöcker Theresa Lemser Tobias Tauscher Claudia Funke Charaf Cherkouk Dirk Meyer The formation of crystals and symmetry on the atomic scale has persistently attracted scientists through the ages. The structure itself and its subtle dependence on boundary conditions is a reflection of three principles: atomic attraction, repulsion, and the limitations in 3D space. This involves a competition between simplicity and high symmetry on the one hand and necessary structural complexity on the other. This work presents a simple atomistic crystal growth model derived for equivalent atoms and a pair potential. It highlights fundamental concepts, most prominently provided by a maximum number of equilibrium distances in the atom’s local vicinity, to obtain high symmetric structural motifs, among them the Platonic Solids. In this respect, the harmonically balanced interaction during the atomistic nucleation process may be regarded as origin of symmetry. The minimization of total energy is generalized for 3D periodic structures constituting these motifs. In dependence on the pair potential’s short- and long-range characteristics the, by symmetry, rigid lattices relax isotropically within the potential well. The first few coordination shells with lattice-specific fixed distances do not necessarily determine which equilibrium symmetry prevails. A phase diagram calculated on the basis of these few assumptions summarizes stable regions of close-packed fcc and hcp, next to bcc symmetry for predominantly soft short-range and hard long-range interaction. This lattice symmetry, which is evident for alkali metals as well as transition metals of the vanadium and chromium group, cannot be obtained from classical Morse or Lennard-Jones type potentials, but needs the range flexibility within the pair potential.

Description: Symmetry, Vol. 10, Pages 226: A Hybrid Neutrosophic Group ANP-TOPSIS Framework for Supplier Selection Problems Symmetry doi: 10.3390/sym10060226 Authors: Mohamed Abdel-Basset Mai Mohamed Florentin Smarandache One of the most significant competitive strategies for organizations is sustainable supply chain management (SSCM). The vital part in the administration of a sustainable supply chain is the sustainable supplier selection, which is a multi-criteria decision-making issue, including many conflicting criteria. The valuation and selection of sustainable suppliers are difficult problems due to vague, inconsistent and imprecise knowledge of decision makers. In the literature on supply chain management for measuring green performance, the requirement for methodological analysis of how sustainable variables affect each other, and how to consider vague, imprecise and inconsistent knowledge, is still unresolved. This research provides an incorporated multi-criteria decision-making procedure for sustainable supplier selection problems (SSSPs). An integrated framework is presented via interval-valued neutrosophic sets to deal with vague, imprecise and inconsistent information that exists usually in real world. The analytic network process (ANP) is employed to calculate weights of selected criteria by considering their interdependencies. For ranking alternatives and avoiding additional comparisons of analytic network processes, the technique for order preference by similarity to ideal solution (TOPSIS) is used. The proposed framework is turned to account for analyzing and selecting the optimal supplier. An actual case study of a dairy company in Egypt is examined within the proposed framework. Comparison with other existing methods is implemented to confirm the effectiveness and efficiency of the proposed approach.

Description: Symmetry, Vol. 10, Pages 224: A Comparative Study of Logistic Models Using an Asymmetric Link: Modelling the Away Victories in Football Symmetry doi: 10.3390/sym10060224 Authors: José María Pérez–Sánchez Emilio Gómez–Déniz Nancy Dávila–Cárdenes The target of this paper is to study the relevant factors affecting the victories away from home of football teams in order to fit the probability of winning an away match. The paper addressed the following research issues: (a) Is the identification of the significant variables underlying the results plausible? (b) Can information of these factors increase the probability of winning away from home and assist coaches in their decisions? Empirically, it is shown that there are more home victories and draws than away victories in the professional football leagues in Europe and this fact has to be taken into account. Thus, the classical logistic and Bayesian regression models do not seem to be adequate in this case and an asymmetric logistic regression model is therefore considered. This paper analyses 380 games played in the First Division of the Spanish Football League during the 2013–2014 season. Asymmetric logistic regression from a Bayesian point of view is chosen as the best model. This model detects new relevant factors undetected by standard logistic regressions. In view of the paper’s findings, various practical recommendations were made in order to improve decision-making in this field. The Asymmetric logit link is a helpful device that can assist coaches in their game strategies.

Description: Symmetry, Vol. 10, Pages 230: Towards Real-Time Facial Landmark Detection in Depth Data Using Auxiliary Information Symmetry doi: 10.3390/sym10060230 Authors: Connah Kendrick Kevin Tan Kevin Walker Moi Yap Modern facial motion capture systems employ a two-pronged approach for capturing and rendering facial motion. Visual data (2D) is used for tracking the facial features and predicting facial expression, whereas Depth (3D) data is used to build a series of expressions on 3D face models. An issue with modern research approaches is the use of a single data stream that provides little indication of the 3D facial structure. We compare and analyse the performance of Convolutional Neural Networks (CNN) using visual, Depth and merged data to identify facial features in real-time using a Depth sensor. First, we review the facial landmarking algorithms and its datasets for Depth data. We address the limitation of the current datasets by introducing the Kinect One Expression Dataset (KOED). Then, we propose the use of CNNs for the single data stream and merged data streams for facial landmark detection. We contribute to existing work by performing a full evaluation on which streams are the most effective for the field of facial landmarking. Furthermore, we improve upon the existing work by extending neural networks to predict into 3D landmarks in real-time with additional observations on the impact of using 2D landmarks as auxiliary information. We evaluate the performance by using Mean Square Error (MSE) and Mean Average Error (MAE). We observe that the single data stream predicts accurate facial landmarks on Depth data when auxiliary information is used to train the network. The codes and dataset used in this paper will be made available.

Description: Symmetry, Vol. 10, Pages 234: Research on Electronic Voltage Transformer for Big Data Background Symmetry doi: 10.3390/sym10070234 Authors: Zhen-Hua Li Yao Wang Zheng-Tian Wu Zhen-Xing Li A new type of electronic voltage transformer is proposed in this study for big data background. By using the conventional inverted SF_6 transformer insulation structure, a coaxial capacitor sensor was constructed by designing a middle coaxial electrode between the high-voltage electrode and the ground electrode. The measurement of the voltage signal could be obtained by detecting the capacitance current i of the SF_6 coaxial capacitor. To improve the accuracy of the integrator, a high-precision digital integrator based on the Romberg algorithm is proposed in this study. This can not only guarantee the accuracy of computation, but also reduce the consumption time; in addition, the sampling point can be reused. By adopting the double shielding effect of the high-voltage shell and the grounding metal shield, the ability and stability of the coaxial capacitor divide could be effectively improved to resist the interference of stray electric fields. The factors that affect the coaxial capacitor were studied, such as position, temperature, and pressure, which will influence the value of the coaxial capacitor. Tests were carried out to verify the performance. The results showed that the voltage transformer based on the SF_6 coaxial capacitor satisfies the requirements of the 0.2 accuracy class. This study can promote the use of new high-performance products for data transmission in the era of big data and specific test analyses.

Description: Symmetry, Vol. 10, Pages 232: Facial Asymmetry-Based Anthropometric Differences between Gender and Ethnicity Symmetry doi: 10.3390/sym10070232 Authors: Muhammad Sajid Tamoor Shafique Imran Riaz Muhammad Imran Mirza Jabbar Aziz Baig Shahbaz Baig Sohaib Manzoor Bilateral facial asymmetry is frequently exhibited by humans but its combined evaluation across demographic traits including gender and ethnicity is still an open research problem. In this study we measure and evaluate facial asymmetry across gender and different ethnic groups and investigate the differences in asymmetric facial dimensions among the subjects from two public face datasets, the MORPH and FERET. To this end, we detect 28 facial asymmetric dimensions from each face image using an anthropometric technique. An exploratory analysis is then performed via a multiple linear regression model to determine the impact of gender and ethnicity on facial asymmetry. Post-hoc Tukey test has been used to validate the results of the proposed method. The results show that out of 28 asymmetric dimensions, females differ in 25 dimensions from males. African, Asian, Hispanic and other ethnic groups have asymmetric dimensions that differ significantly from those of Europeans. These findings could be important to certain applications like the design of facial fits, as well as guidelines for facial cosmetic surgeons. Lastly, we train a neural network classifier that employs asymmetric dimensions for gender and race classification. The experimental results show that our trained classifier outperforms the support vector machine (SVM) and k-nearest neighbors (kNN) classifiers.

Description: Symmetry, Vol. 10, Pages 238: Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group Symmetry doi: 10.3390/sym10070238 Authors: Umar Hayat Daniel López-Aguayo Akhtar Abbas Let G=Zp⊕Zp2, where p is a prime number. Suppose that d is a divisor of the order of G. In this paper, we find the number of automorphisms of G fixing d elements of G and denote it by θ(G,d). As a consequence, we prove a conjecture of Checco-Darling-Longfield-Wisdom. We also find the exact number of fixed-point-free automorphisms of the group Zpa⊕Zpb, where a and b are positive integers with a<b. Finally, we compute θ(D2q,d), where D2q is the dihedral group of order 2q, q is an odd prime, and d∈{1,q,2q}.

Description: Symmetry, Vol. 10, Pages 240: Fixed Point Theorem for Neutrosophic Triplet Partial Metric Space Symmetry doi: 10.3390/sym10070240 Authors: Memet Şahin Abdullah Kargın Mehmet Ali Çoban Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM. Also, we show that NTPMS can be defined with each NTMS. Furthermore, we define a contraction for NTPMS and we give a fixed point theory (FPT) for NTPMS. The FPT has been revealed as a very powerful tool in the study of nonlinear phenomena. This study is also part of the “Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets” which is a special issue.

Description: Symmetry, Vol. 10, Pages 239: On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels Symmetry doi: 10.3390/sym10070239 Authors: Junjie Ma Huilan Liu Lubich’s convolution quadrature rule provides efficient approximations to integrals with special kernels. Particularly, when it is applied to computing highly oscillatory integrals, numerical tests show it does not suffer from fast oscillation. This paper is devoted to studying the convergence property of the convolution quadrature rule for highly oscillatory problems. With the help of operational calculus, the convergence rate of the convolution quadrature rule with respect to the frequency is derived. Furthermore, its application to highly oscillatory integral equations is also investigated. Numerical results are presented to verify the effectiveness of the convolution quadrature rule in solving highly oscillatory problems. It is found from theoretical and numerical results that the convolution quadrature rule for solving highly oscillatory problems is efficient and high-potential.

Description: Symmetry, Vol. 10, Pages 241: Left (Right)-Quasi Neutrosophic Triplet Loops (Groups) and Generalized BE-Algebras Symmetry doi: 10.3390/sym10070241 Authors: Xiaohong Zhang Xiaoying Wu Florentin Smarandache Minghao Hu The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented. As a corollary of these properties, the following important result are proved: for any commutative neutrosophic triplet group, its every element has a unique neutral element. Moreover, some left (right)-quasi neutrosophic triplet structures in BE-algebras and generalized BE-algebras (including CI-algebras and pseudo CI-algebras) are established, and the adjoint semigroups of the BE-algebras and generalized BE-algebras are investigated for the first time.

Description: Symmetry, Vol. 10, Pages 242: Automatic Grading of Palsy Using Asymmetrical Facial Features: A Study Complemented by New Solutions Symmetry doi: 10.3390/sym10070242 Authors: Muhammad Sajid Tamoor Shafique Mirza Jabbar Aziz Baig Imran Riaz Shahid Amin Sohaib Manzoor Facial palsy caused by nerve damage results in loss of facial symmetry and expression. A reliable palsy grading system for large-scale applications is still missing in the literature. Although numerous approaches have been reported on facial palsy quantification and grading, most employ hand-crafted features on relatively smaller datasets which limit the classification accuracy due to non-optimal face representation. In contrast, convolutional neural networks (CNNs) automatically learn the discriminative features facilitating the accurate classification of underlying tasks. In this paper, we propose to apply a typical deep network on a large dataset to extract palsy-specific features from face images. To prevent the inherent limitation of overfitting frequently occurring in CNNs, a generative adversial network (GAN) is applied to augment the training dataset. The deeply learned features are then used to classify the palsy disease into five benchmarked grades. The experimental results show that the proposed approach offers superior palsy grading performance compared to some existing methods. Such an approach is useful for palsy grading at large scale, such as primary health care.

Description: Symmetry, Vol. 10, Pages 316: Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation Symmetry doi: 10.3390/sym10080316 Authors: Yongquan Zhang Hong Lu He Ling Yang Lian Mingtian Ma The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Description: Symmetry, Vol. 10, Pages 303: Some Symmetric Identities Involving Fubini Polynomials and Euler Numbers Symmetry doi: 10.3390/sym10080303 Authors: Zhao Jianhong Chen Zhuoyu The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

Description: Symmetry, Vol. 10, Pages 317: On Special Kinds of Involute and Evolute Curves in 4-Dimensional Minkowski Space Symmetry doi: 10.3390/sym10080317 Authors: Muhammad Hanif Zhong Hua Hou Kottakkaran Sooppy Nisar Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail.

Description: Symmetry, Vol. 10, Pages 109: TPVR: User Interaction of Third Person Virtual Reality for New Presence and Experience Symmetry doi: 10.3390/sym10040109 Authors: Mingyu Kim Jiwon Lee Changhun Kim Jinmo Kim This study proposes the interaction of third-person virtual reality (TPVR) to provide users with a new presence and experience during immersive virtual reality (VR). The proposed TPVR interaction consists of the ability to directly control the virtual environment and objects by utilizing the hands. For this purpose, this study defines the interaction of TPVR from three types: moving inside the virtual environment, selecting virtual objects and using a menu interface that includes a variety of functions and behaviors. Then, it designs its own experimental application that is able to systematically compare and analyze the proposed interaction against traditional first-person perspective VR. Finally, it examines whether the proposed interaction provides new presence and experience to users by conducting survey experiments. Through this process, this study was able to confirm not only that TPVR interaction can provide a sufficient presence, even in comparison with the first-person viewpoint, but also that it causes less VR sickness and offers a differentiated VR experience, suggesting that the proposed interaction can provide an alternative method for utilizing VR technology in a greater variety of fields.

Description: Symmetry, Vol. 10, Pages 108: Age Estimation Robust to Optical and Motion Blurring by Deep Residual CNN Symmetry doi: 10.3390/sym10040108 Authors: Jeon Kang Chan Kim Young Lee Se Cho Kang Park Recently, real-time human age estimation based on facial images has been applied in various areas. Underneath this phenomenon lies an awareness that age estimation plays an important role in applying big data to target marketing for age groups, product demand surveys, consumer trend analysis, etc. However, in a real-world environment, various optical and motion blurring effects can occur. Such effects usually cause a problem in fully capturing facial features such as wrinkles, which are essential to age estimation, thereby degrading accuracy. Most of the previous studies on age estimation were conducted for input images almost free from blurring effect. To overcome this limitation, we propose the use of a deep ResNet-152 convolutional neural network for age estimation, which is robust to various optical and motion blurring effects of visible light camera sensors. We performed experiments with various optical and motion blurred images created from the park aging mind laboratory (PAL) and craniofacial longitudinal morphological face database (MORPH) databases, which are publicly available. According to the results, the proposed method exhibited better age estimation performance than the previous methods.

Description: Symmetry, Vol. 10, Pages 107: Deep Learning-Based Image Segmentation for Al-La Alloy Microscopic Images Symmetry doi: 10.3390/sym10040107 Authors: Boyuan Ma Xiaojuan Ban Haiyou Huang Yulian Chen Wanbo Liu Yonghong Zhi Quantitative analysis through image processing is a key step to gain information regarding the microstructure of materials. In this paper, we develop a deep learning-based method to address the task of image segmentation for microscopic images using an Al–La alloy. Our work makes three key contributions. (1) We train a deep convolutional neural network based on DeepLab to achieve image segmentation and have significant results. (2) We adopt a local processing method based on symmetric overlap-tile strategy which makes it possible to analyze the microscopic images with high resolution. Additionally, it achieves seamless segmentation. (3) We apply symmetric rectification to enhance the accuracy of results with 3D information. Experimental results showed that our method outperforms existing segmentation methods.

Description: Symmetry, Vol. 10, Pages 112: New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term Symmetry doi: 10.3390/sym10040112 Authors: Jianping Zhou Yuan Wang Yang Wang Zhilian Yan Zhen Wang The compatibility method is used for a generalized variable-coefficient Gardner equation (GVGE) with a forcing term. By the compatibility of the considered equation and a non-classical symmetry of a given form, four types of symmetry are obtained. Then, by solving the characteristic equations of symmetry, the GVGE is reduced to variable coefficients ordinary differential equations, and rich varieties of new similarity solutions are presented. Our results show that the compatibility method can be employed for variable coefficients nonlinear evolution equations with forcing terms.

Description: Symmetry, Vol. 10, Pages 114: Understanding Review Expertise of Developers: A Reviewer Recommendation Approach Based on Latent Dirichlet Allocation Symmetry doi: 10.3390/sym10040114 Authors: Jungil Kim Eunjoo Lee The code reviewer assignment problem affects the reviewing time of a source code change. To effectively perform the code review process of a software project, the code reviewer assignment problem must be dealt with. Reviewer recommendation can reduce the time required for finding appropriate reviewers for a given source code change. In this paper, we propose a reviewer recommendation approach based on latent Dirichlet allocation (LDA). The proposed reviewer recommendation approach consists of a review expertise generation phase and a reviewer recommendation phase. The review expertise generation phase generates the review expertise of developers for topics of source code changes from the review history of a software project. The reviewer recommendation phase computes the review scores of the developers according to the topic distribution of a given source code change and the review expertise of the developers. In an empirical evaluation of five open source projects, we confirm that the proposed reviewer recommendation approach obtains better average top-10 accuracy than existing reviewer recommendation approaches.

Description: Symmetry, Vol. 10, Pages 113: Application of Sliding Nest Window Control Chart in Data Stream Anomaly Detection Symmetry doi: 10.3390/sym10040113 Authors: Guang Li Jie Wang Jing Liang Caitong Yue Since data stream anomaly detection algorithms based on sliding windows are sensitive to the abnormal deviation of individual interference data, this paper presents a sliding nest window chart anomaly detection based on the data stream (SNWCAD-DS) by employing the concept of the sliding window and control chart. By nesting a small sliding window in a large sliding window and analyzing the deviation distance between the small window and the large sliding window, the algorithm increases the out-of-bounds detection ratio and classifies the conceptual drift data stream online. The designed algorithm is simulated on the industrial data stream of drilling engineering. The proposed algorithm SNWCAD is compared with Automatic Outlier Detection for Data Streams (A-ODDS) and Distance-Based Outline Detection for Data Stream (DBOD-DS). The experimental results show that the new algorithm can obtain higher detection accuracy than the compared algorithms. Furthermore, it can shield the influence of individual interference data and satisfy actual engineering needs.

Description: Symmetry, Vol. 10, Pages 115: New Multiple Attribute Decision Making Method Based on DEMATEL and TOPSIS for Multi-Valued Interval Neutrosophic Sets Symmetry doi: 10.3390/sym10040115 Authors: Wei Yang Yongfeng Pang Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among attributes can be modeled, and attribute weights are determined. The normalized Euclidean distance and the normalized Hamming distance between multi-valued interval neutrosophic fuzzy values are defined. Alternatives are ranked by using the TOPSIS method based on the distance measures. The truck selection problem in the logistics industry is presented to illustrate the feasibility and practical advantages of the proposed method. Some comparisons of the new method with other methods are also made.

Description: Symmetry, Vol. 10, Pages 116: An Extension of Neutrosophic AHP–SWOT Analysis for Strategic Planning and Decision-Making Symmetry doi: 10.3390/sym10040116 Authors: Mohamed Abdel-Basset Mai Mohamed Florentin Smarandache Every organization seeks to set strategies for its development and growth and to do this, it must take into account the factors that affect its success or failure. The most widely used technique in strategic planning is SWOT analysis. SWOT examines strengths (S), weaknesses (W), opportunities (O) and threats (T), to select and implement the best strategy to achieve organizational goals. The chosen strategy should harness the advantages of strengths and opportunities, handle weaknesses, and avoid or mitigate threats. SWOT analysis does not quantify factors (i.e., strengths, weaknesses, opportunities and threats) and it fails to rank available alternatives. To overcome this drawback, we integrated it with the analytic hierarchy process (AHP). The AHP is able to determine both quantitative and the qualitative elements by weighting and ranking them via comparison matrices. Due to the vague and inconsistent information that exists in the real world, we applied the proposed model in a neutrosophic environment. A real case study of Starbucks Company was presented to validate our model.

Description: Symmetry, Vol. 10, Pages 124: Accountability Requirements in the Cloud Provider Chain Symmetry doi: 10.3390/sym10040124 Authors: Martin Gilje Jaatun Inger Anne Tøndel Nils Brede Moe Daniela Soares Cruzes Karin Bernsmed Børge Haugset In order to be responsible stewards of other people’s data, cloud providers must be accountable for their data handling practices. The potential long provider chains in cloud computing introduce additional accountability challenges, with many stakeholders involved. Symmetry is very important in any requirements’ elicitation activity, since input from diverse stakeholders needs to be balanced. This article ventures to answer the question “How can one create an accountable cloud service?” by examining requirements which must be fulfilled to achieve an accountability-based approach, based on interaction with over 300 stakeholders.

Description: Symmetry, Vol. 10, Pages 130: Design and Analysis of Multiple-Input Multiple-Output Radar System Based on RF Single-Link Technology Symmetry doi: 10.3390/sym10050130 Authors: He Yu Guohui Yang Yingsong Li Fanyi Meng Multiple-input multiple-output (MIMO) radar is playing an important role in military and civilian fields. However, radio frequency (RF) multi-links have a large data-processing capacity and the system is bulky and complex. Therefore, a single-link RF MIMO has been the subject of heated discussed in recent years. Single-link technology shares the same regularity with that of the multi-link MIMO system, which makes the MIMO system simpler in structure without affecting its performance. In this study, a 2 × 2 array single RF link MIMO radar at X band was designed by combining MIMO radar with the concept of a single RF link in the communication field, and a simulation platform for studying its properties was established using SystemVue software. The whole system is controlled by the exclusive OR (XOR) operation results of two transmission signals, and one signal can control the antenna-switching signal to form a variety of orthogonal bases. The received two original signals are demodulated and the control signals enter the corresponding matched filters. The signal is processed by fast Fourier transformation (FFT) and the cell-averaging constant false alarm rate algorithm (CA-CFAR) is used to judge the signal. For multiple measurements, the Monte Carlo method was adopted to obtain its mean value as the final result. Compared with the traditional MIMO radar performance in acquiring the target position, speed, and detection probability, the results show that the computation time can be greatly reduced (due to decrease in the number of links in MIMO radar system) without any deterioration in the MIMO radar performance. The single RF link technology provides a broad prospect for the miniaturization of small radar applications.

Description: Symmetry, Vol. 10, Pages 117: Human Bodily Asymmetry Relates to Behavioral Lateralization and May not Reliably Reflect Developmental Instability Symmetry doi: 10.3390/sym10040117 Authors: Stefan Van Dongen (1) Background: The link between behavioral lateralization and bodily asymmetry in humans is studied to investigate the reliability of fluctuating asymmetry as a measure of developmental instability; (2) Methods: Morphological asymmetries of arms and legs, obtained from 3D body scans, were correlated with different measures of behavioral lateralization; (3) Results: Observed associations were in the directions expected, showing that more asymmetric use of the body increases asymmetry, especially in the arms, and more symmetric body use appears to have a symmetrizing effect; and (4) Conclusions: The results presented here question the suitability of human bodily asymmetry in arms and legs—or at least part of them—as a measure of developmental instability. There is a need for future research that identifies regions of the body that are not affected by behavioral lateralization and can reliably reflect developmental instability.

Description: Symmetry, Vol. 10, Pages 136: Reinforcement Learning Based Data Self-Destruction Scheme for Secured Data Management Symmetry doi: 10.3390/sym10050136 Authors: Young Ki Kim Saeed Ullah Kiuk Kwon Yunchul Jang Jongsoo Lee Choong Seon Hong As technologies and services that leverage cloud computing have evolved, the number of businesses and individuals who use them are increasing rapidly. In the course of using cloud services, as users store and use data that include personal information, research on privacy protection models to protect sensitive information in the cloud environment is becoming more important. As a solution to this problem, a self-destructing scheme has been proposed that prevents the decryption of encrypted user data after a certain period of time using a Distributed Hash Table (DHT) network. However, the existing self-destructing scheme does not mention how to set the number of key shares and the threshold value considering the environment of the dynamic DHT network. This paper proposes a method to set the parameters to generate the key shares needed for the self-destructing scheme considering the availability and security of data. The proposed method defines state, action, and reward of the reinforcement learning model based on the similarity of the graph, and applies the self-destructing scheme process by updating the parameter based on the reinforcement learning model. Through the proposed technique, key sharing parameters can be set in consideration of data availability and security in dynamic DHT network environments.

Description: Symmetry, Vol. 10, Pages 138: Clickbait Convolutional Neural Network Symmetry doi: 10.3390/sym10050138 Authors: Hai-Tao Zheng Jin-Yuan Chen Xin Yao Arun Kumar Sangaiah Yong Jiang Cong-Zhi Zhao With the development of online advertisements, clickbait spread wider and wider. Clickbait dissatisfies users because the article content does not match their expectation. Thus, clickbait detection has attracted more and more attention recently. Traditional clickbait-detection methods rely on heavy feature engineering and fail to distinguish clickbait from normal headlines precisely because of the limited information in headlines. A convolutional neural network is useful for clickbait detection, since it utilizes pretrained Word2Vec to understand the headlines semantically, and employs different kernels to find various characteristics of the headlines. However, different types of articles tend to use different ways to draw users’ attention, and a pretrained Word2Vec model cannot distinguish these different ways. To address this issue, we propose a clickbait convolutional neural network (CBCNN) to consider not only the overall characteristics but also specific characteristics from different article types. Our experimental results show that our method outperforms traditional clickbait-detection algorithms and the TextCNN model in terms of precision, recall and accuracy.

Description: Symmetry, Vol. 10, Pages 146: Extended Covering Arrays for Sequence Coverage Symmetry doi: 10.3390/sym10050146 Authors: Yunlong Sheng Chao Sun Shouda Jiang Chang’an Wei Although combinatorial testing has been widely studied and used, there are still some situations and requirements that combinatorial testing does not apply to well, such as a system under test whose test cases need to be performed contiguously. For thorough testing, the testing requirements are not only to cover all the interactions among factors but also to cover all the value sequences of every factor. Generally, systems under test always involve constraints and dependencies in or among test cases. The constraints among test cases have not been effectively specified. First, we introduce extended covering arrays that can achieve both t-way combinatorial coverage and t-wise sequence coverage, and propose a clocked computation tree logic-based formal specification method for specifying constraints. Then, Particle Swarm Optimization (PSO) based Extended covering array Generator (PEG) is elaborated. To evaluate the constructed test suites, a method for verifying the constraints’ validity is presented, and kernel functions for measuring the coverage are also introduced. Finally, the performance of the proposed PEG is evaluated using several sets of benchmark experiments for some common constraints, and the feasibility and usefulness of PEG is validated.

Description: Symmetry, Vol. 10, Pages 147: Polarized Light-Induced Molecular Orientation Control of Rigid Schiff Base Ni(II), Cu(II), and Zn(II) Binuclear Complexes as Polymer Composites Symmetry doi: 10.3390/sym10050147 Authors: Hiroyuki Nakatori Tomoyuki Haraguchi Takashiro Akitsu We have investigated linearly polarized UV light-induced molecular orientation due to Weigert effect of composite materials of new six binuclear nickel(II), copper(II), and zinc(II) complexes of two rigid Schiff base ring ligands (L1 and L2) composite materials with methyl orange (MO), an azo-dye, in polyvinylalchol (PVA) cast films. To compare the degree of molecular orientation, two ligands, namely flexible aliphatic cyclohexane (ML1: NiL1, CuL1, ZnL1) and rigid aromatic (ML2: NiL2, CuL2, ZnL2), were synthesized using amine moiety. We have also characterized these complexes by means of elemental analysis, IR, and UV-vis spectra, single crystal or powder X-ray diffraction (XRD) analysis, and so on. Composite materials of ML1 or ML2+MO+PVA were also prepared to separately disperse the solutes in a polymer matrix. For any metal complexes, optical anisotropy (represented as the R parameters) of ML2+MO+PVA was larger than ML1+MO+PVA because of the rigidness of the ligands.

Description: Symmetry, Vol. 10, Pages 145: Another Approach to Roughness of Soft Graphs with Applications in Decision Making Symmetry doi: 10.3390/sym10050145 Authors: Nasir Shah Noor Rehman Muhammad Shabir Muhammad Irfan Ali Fuzzy sets, rough sets and soft sets are different tools for modeling problems involving uncertainty. Graph theory is another powerful tool for representing the information by means of diagrams, matrices or relations. A possible amalgamation of three different concepts rough sets, soft sets and graphs, known as soft rough graphs, is proposed by Noor et al. They introduced the notion of vertex, edge induced soft rough graphs and soft rough trees depending upon the parameterized subsets of vertex set and edge set. In this article, a new framework for studying the roughness of soft graphs in more general way is introduced. This new model is known as the modified soft rough graphs or MSR -graphs. The concept of the roughness membership function of vertex sets, edge sets and of a graph is also introduced. Further, it has been shown that MSR -graphs are more robust than soft rough graphs. Some results, which are not handled by soft rough graphs, can be handled by modified soft rough graphs. The notion of uncertainty measurement associated with MSR -graphs is introduced. All applications related to decision makings are only restricted to the information of individuals only, not their interactions, using this technique we are able to involve the interactions (edges) of individuals with each other that enhanced the accuracy in decisions.

Description: Symmetry, Vol. 10, Pages 144: Symmetry Measures of Simplified Neutrosophic Sets for Multiple Attribute Decision-Making Problems Symmetry doi: 10.3390/sym10050144 Authors: Angyan Tu Jun Ye Bing Wang A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets) are characterized by its truth, falsity, and indeterminacy degrees. Under a simplified neutrosophic environment, therefore, this paper firstly defines simplified neutrosophic asymmetry measures. Then we propose a normalized symmetry measure and a weighted symmetry measure of simplified neutrosophic sets and develop a simplified neutrosophic multiple attribute decision-making method based on the weighted symmetry measure. All alternatives can be ranked through the weighted symmetry measure between the ideal solution/alternative and each alternative, and then the best one can be determined. Finally, an illustrative example on the selection of manufacturing schemes (alternatives) in the flexible manufacturing system demonstrates the applicability of the proposed method in a simplified (interval and single valued) neutrosophic setting, and then the decision-making method based on the proposed symmetry measure is in accord with the ranking order and best choice of existing projection and bidirectional projection-based decision-making methods and strengthens the resolution/discrimination in the decision-making process corresponding to the comparative example.

Description: Symmetry, Vol. 10, Pages 155: Force Loading Tracking Control of an Electro-Hydraulic Actuator Based on a Nonlinear Adaptive Fuzzy Backstepping Control Scheme Symmetry doi: 10.3390/sym10050155 Authors: Xiang Li Zhen-Cai Zhu Guang-Chao Rui Dong Cheng Gang Shen Yu Tang In this article, a nonlinear adaptive fuzzy backstepping controller combined with an adaptive backstepping controller and an adaptive fuzzy controller is proposed for real-time tracking control of an electro-hydraulic force loading system. Firstly, a nonlinear dynamic model for the electro-hydraulic force loading system is built with consideration of parameter uncertainties and external disturbances. Then, the adaptive backstepping controller is employed to obtain desired control output for the force loading control system considering parameter uncertainties and external disturbances. Furthermore, an adaptive fuzzy control scheme is designed to adjust uncertain control parameters based on adaptive fuzzy system to cope with the chattering condition that results from the overwhelming external disturbances. The stability of the overall system with the proposed control algorithm can be proved by Lyapunov stability theory. Finally, an electro-hydraulic force loading experimental system with xPC rapid prototyping technology is carried out to verify the effectiveness of the proposed nonlinear adaptive fuzzy backstepping controller. Experimental results verify that the proposed control method exhibit excellent performances on force loading tracking control of the electro-hydraulic force loading experimental system compared with a conventional proportional-integral-derivative (PID) controller with velocity feedforward and adaptive backstepping control schemes.

Description: Symmetry, Vol. 10, Pages 154: The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making Symmetry doi: 10.3390/sym10050154 Authors: Changxing Fan En Fan Jun Ye Based on the multiplicity evaluation in some real situations, this paper firstly introduces a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to express the multiplicity information and the operational relations of SVNMs. Then, a cosine measure between SVNMs and weighted cosine measure between SVNMs are presented to measure the cosine degree between SVNMs, and their properties are investigated. Based on the weighted cosine measure of SVNMs, a multiple attribute decision-making method under a SVNM environment is proposed, in which the evaluated values of alternatives are taken in the form of SVNMs. The ranking order of all alternatives and the best one can be determined by the weighted cosine measure between every alternative and the ideal alternative. Finally, an actual application on the selecting problem illustrates the effectiveness and application of the proposed method.

Description: Symmetry, Vol. 10, Pages 153: New Holographic Dark Energy Model in Brans-Dicke Theory Symmetry doi: 10.3390/sym10050153 Authors: M. Sharif Syed Asif Ali Shah Kazuharu Bamba We study the cosmic evolution of the Bianchi type I universe by using new holographic dark energy model in the context of the Brans-Dicke theory for both non-interacting and interacting cases between dark energy and dark matter. We evaluate the equation of state for dark energy ω D and draw the ω D − ω ˙ D plane, where the dot denotes the time derivative. It is found that a stage in which the cosmic expansion is accelerating can be realized in both cases. In addition, we investigate the stability of the model by analyzing the sound speed. As a result, it is demonstrated that for both cases, the behavior of the sound speed becomes unstable. Furthermore, with the Om-diagnostic tool, it is shown that the quintessence region of the universe can exist.

Description: Symmetry, Vol. 10, Pages 162: Sampling Based Histogram PCA and Its Mapreduce Parallel Implementation on Multicore Symmetry doi: 10.3390/sym10050162 Authors: Cheng Wang Huiwen Wang Siyang Wang Edwin Diday Richard Emilion In existing principle component analysis (PCA) methods for histogram-valued symbolic data, projection results are approximated based on Moore’s algebra and fail to reflect the data’s true structure, mainly because there is no precise, unified calculation method for the linear combination of histogram data. In this paper, we propose a new PCA method for histogram data that distinguishes itself from various well-established methods in that it can project observations onto the space spanned by principal components more accurately and rapidly by sampling through a MapReduce framework. The new histogram PCA method is implemented under the same assumption of “orthogonal dimensions for every observation” with the existing literatures. To project observations, the method first samples from the original histogram variables to acquire single-valued data, on which linear combination operations can be performed. Then, the projection of observations can be given by linear combination of loading vectors and single-valued samples, which is close to accurate projection results. Finally, the projection is summarized to histogram data. These procedures involve complex algorithms and large-scale data, which makes the new method time-consuming. To speed it up, we undertake a parallel implementation of the new method in a multicore MapReduce framework. A simulation study and an empirical study confirm that the new method is effective and time-saving.

Description: Symmetry, Vol. 10, Pages 164: Integrated Hybrid Second Order Algorithm for Orthogonal Projection onto a Planar Implicit Curve Symmetry doi: 10.3390/sym10050164 Authors: Xiaowu Li Feng Pan Taixia Cheng Zhinan Wu Juan Liang Linke Hou The computation of the minimum distance between a point and a planar implicit curve is a very important problem in geometric modeling and graphics. An integrated hybrid second order algorithm to facilitate the computation is presented. The proofs indicate that the convergence of the algorithm is independent of the initial value and demonstrate that its convergence order is up to two. Some numerical examples further confirm that the algorithm is more robust and efficient than the existing methods.

Description: Symmetry, Vol. 10, Pages 167: Image Denoising via Improved Dictionary Learning with Global Structure and Local Similarity Preservations Symmetry doi: 10.3390/sym10050167 Authors: Shuting Cai Zhao Kang Ming Yang Xiaoming Xiong Chong Peng Mingqing Xiao We proposed a new efficient image denoising scheme, which leads to four important contributions. The first is to integrate both reconstruction and learning based approaches into a single model so that we are able to benefit advantages from both approaches simultaneously. The second is to handle both multiplicative and additive noise removal problems. The third is that the proposed approach introduces a sparse term to reduce non-Gaussian outliers from multiplicative noise and uses a Laplacian Schatten norm to capture the global structure information. In addition, the image is represented by preserving the intrinsic local similarity via a sparse coding method, which allows our model to incorporate both global and local information from the image. Finally, we propose a new method that combines Method of Optimal Directions (MOD) with Approximate K-SVD (AK-SVD) for dictionary learning. Extensive experimental results show that the proposed scheme is competitive against some of the state-of-the-art denoising algorithms.

Description: Symmetry, Vol. 10, Pages 166: On the Second-Degree Exterior Derivation of Kahler Modules on X ⊗ Y Symmetry doi: 10.3390/sym10050166 Authors: Ali Karakuş Necati Olgun Mehmet Şahin This article presents a new approach to stress the properties of Kahler modules. In this paper, we construct the Kahler modules of second-degree exterior derivations and we constitute an exact sequence of X ⊗ Y -modules. Particularly, we examine Kahler modules on X ⊗ Y , and search for the homological size of Λ 2 ( Ω 1 ( X ⊗ Y ) ) .

Description: Symmetry, Vol. 10, Pages 169: Efficient Superpixel-Guided Interactive Image Segmentation Based on Graph Theory Symmetry doi: 10.3390/sym10050169 Authors: Jianwu Long Xin Feng Xiaofei Zhu Jianxun Zhang Guanglei Gou Image segmentation is a challenging task in the field of image processing and computer vision. In order to obtain an accurate segmentation performance, user interaction is always used in practical image-segmentation applications. However, a good segmentation method should not rely on much prior information. In this paper, an efficient superpixel-guided interactive image-segmentation algorithm based on graph theory is proposed. In this algorithm, we first perform the initial segmentation by using the MeanShift algorithm, then a graph is built by taking the pre-segmented regions (superpixels) as nodes, and the maximum flow–minimum cut algorithm is applied to get the superpixel-level segmentation solution. In this process, each superpixel is represented by a color histogram, and the Bhattacharyya coefficient is chosen to calculate the similarity between any two adjacent superpixels. Considering the over-segmentation problem of the MeanShift algorithm, a narrow band is constructed along the contour of objects using a morphology operator. In order to further segment the pixels around edges accurately, a graph is created again for those pixels in the narrow band and, following the maximum flow–minimum cut algorithm, the final pixel-level segmentation is completed. Extensive experimental results show that the presented algorithm obtains much more accurate segmentation results with less user interaction and less running time than the widely used GraphCut algorithm, Lazy Snapping algorithm, GrabCut algorithm and a region merging algorithm based on maximum similarity (MSRM).