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Symmetry
Volume 11
Issue 5
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Symmetry, Volume 11, Issue 5 (May 2019) – 128 articles

Cover Story (view full-size image): We derive a scalar junction condition and a generalized Lanczos equation across lightlike shock waves in cosmologically viable scalar–tensor gravity theories. The first constrains the energy density, current, and pressure of the shock wave, while the second relates them to the jumps in the geometry and transverse derivative of the scalar. We thank Cecília Gergely for contributing the cover figure. View this paper.
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15 pages, 1461 KiB  
Article
LPI Radar Waveform Recognition Based on CNN and TPOT
by Jian Wan, Xin Yu and Qiang Guo
Symmetry 2019, 11(5), 725; https://doi.org/10.3390/sym11050725 - 27 May 2019
Cited by 31 | Viewed by 4802
Abstract
The electronic reconnaissance system is the operational guarantee and premise of electronic warfare. It is an important tool for intercepting radar signals and providing intelligence support for sensing the battlefield situation. In this paper, a radar waveform automatic identification system for detecting, tracking [...] Read more.
The electronic reconnaissance system is the operational guarantee and premise of electronic warfare. It is an important tool for intercepting radar signals and providing intelligence support for sensing the battlefield situation. In this paper, a radar waveform automatic identification system for detecting, tracking and locating low probability interception (LPI) radar is studied. The recognition system can recognize 12 different radar waveform: binary phase shift keying (Barker codes modulation), linear frequency modulation (LFM), Costas codes, polytime codes (T1, T2, T3, and T4), and polyphase codes (comprising Frank, P1, P2, P3 and P4). First, the system performs time–frequency transform on the LPI radar signal to obtain a two-dimensional time–frequency image. Then, the time–frequency image is preprocessed (binarization and size conversion). The preprocessed time–frequency image is then sent to the convolutional neural network (CNN) for training. After the training is completed, the features of the fully connected layer are extracted. Finally, the feature is sent to the tree structure-based machine learning process optimization (TPOT) classifier to realize offline training and online recognition. The experimental results show that the overall recognition rate of the system reaches 94.42% when the signal-to-noise ratio (SNR) is −4 dB. Full article
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12 pages, 267 KiB  
Article
On r-Central Incomplete and Complete Bell Polynomials
by Dae San Kim, Han Young Kim, Dojin Kim and Taekyun Kim
Symmetry 2019, 11(5), 724; https://doi.org/10.3390/sym11050724 - 27 May 2019
Cited by 3 | Viewed by 2194
Abstract
Here we would like to introduce the extended r-central incomplete and complete Bell polynomials, as multivariate versions of the recently studied extended r-central factorial numbers of the second kind and the extended r-central Bell polynomials, and also as multivariate versions [...] Read more.
Here we would like to introduce the extended r-central incomplete and complete Bell polynomials, as multivariate versions of the recently studied extended r-central factorial numbers of the second kind and the extended r-central Bell polynomials, and also as multivariate versions of the r- Stirling numbers of the second kind and the extended r-Bell polynomials. In this paper, we study several properties, some identities and various explicit formulas about these polynomials and their connections as well. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)
13 pages, 2938 KiB  
Article
Infrared Dim Target Detection Using Shearlet’s Kurtosis Maximization under Non-Uniform Background
by Lingbing Peng, Tianfang Zhang, Yuhan Liu, Meihui Li and Zhenming Peng
Symmetry 2019, 11(5), 723; https://doi.org/10.3390/sym11050723 - 27 May 2019
Cited by 18 | Viewed by 2501
Abstract
A novel method based on multiscale and multidirectional feature fusion in the shearlet transform domain and kurtosis maximization for detecting the dim target in infrared images with a low signal-to-noise ratio (SNR) and serious interference caused by a cluttered and non-uniform background is [...] Read more.
A novel method based on multiscale and multidirectional feature fusion in the shearlet transform domain and kurtosis maximization for detecting the dim target in infrared images with a low signal-to-noise ratio (SNR) and serious interference caused by a cluttered and non-uniform background is presented in this paper. First, an original image is decomposed using the shearlet transform with translation invariance. Second, various directions of high-frequency subbands are fused and the corresponding kurtosis of fused image is computed. The targets can be enhanced by strengthening the column with maximum kurtosis. Then, processed high-frequency subbands on different scales of images are merged. Finally, the dim targets are detected by an adaptive threshold with a maximum contrast criterion (MCC). The experimental results show that the proposed method has good performance for infrared target detection in comparison with the nonsubsampled contourlet transform (NSCT) method. Full article
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21 pages, 362 KiB  
Article
Strong Convergence of a System of Generalized Mixed Equilibrium Problem, Split Variational Inclusion Problem and Fixed Point Problem in Banach Spaces
by Mujahid Abbas, Yusuf Ibrahim, Abdul Rahim Khan and Manuel de la Sen
Symmetry 2019, 11(5), 722; https://doi.org/10.3390/sym11050722 - 27 May 2019
Cited by 10 | Viewed by 2326
Abstract
The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable [...] Read more.
The purpose of this paper is to introduce a new algorithm to approximate a common solution for a system of generalized mixed equilibrium problems, split variational inclusion problems of a countable family of multivalued maximal monotone operators, and fixed-point problems of a countable family of left Bregman, strongly asymptotically non-expansive mappings in uniformly convex and uniformly smooth Banach spaces. A strong convergence theorem for the above problems are established. As an application, we solve a generalized mixed equilibrium problem, split Hammerstein integral equations, and a fixed-point problem, and provide a numerical example to support better findings of our result. Full article
(This article belongs to the Special Issue Symmetry with Operator Theory and Equations)
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13 pages, 1714 KiB  
Article
Fast Calculation Method for Transient Response of Transmission Line Based on Chebyshev Pseudospectral–Two-Step Three-Order Boundary Value Coupled Method
by Zhenhua Li, Tinghe Hu, Yuan Tao, Tao Zhang and Zhenxing Li
Symmetry 2019, 11(5), 721; https://doi.org/10.3390/sym11050721 - 27 May 2019
Cited by 1 | Viewed by 2262
Abstract
A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is [...] Read more.
A Chebyshev pseudospectral–two-step three-order boundary value coupled method is proposed and presented for handling the issue associated with complicated calculation, low precision, and poor stability in the process of transient response of transmission line. The first order differential equation in time domain is obtained via dispersing the telegraph equation in space domain by utilizing the pseudospectral method (PSM) based on Chebyshev polynomial. Then the two-step three-order boundary value method (BVM3) is presented and employed to resolve the obtained differential equation, so the numerical solution of the space discrete points can be obtained. Furthermore, the Chebyshev pseudospectral–two-step three-order boundary value coupled method (PSM-BVM3) is presented and compared with the Chebyshev pseudospectral–two-step two order boundary value coupled method (PSM-BVM2), the pseudospectral–differential quadrature method (PSM-DQM), and the pseudospectral method–trapezoid rule (PSM-TR) to validate the feasibility of the new proposed method. Theoretical analysis and numerical simulation reveal that the proposed Chebyshev PSM-BVM3 has a higher performance than the conventional method. For the proposed Chebyshev PSM-BVM3, the higher precision, efficiency, and numerical stability can be obtained and achieved only with fewer discrete points in the space domain, which is suitable for solving the transient response of transmission line. The proposed PSM-BVM3 can improve the drawback of numerical instability of the PSM and can also improve the disadvantage of the BVM as it is not easy to change the latter’s timestep size. Full article
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19 pages, 1238 KiB  
Article
An Integrated Model for Demand Forecasting and Train Stop Planning for High-Speed Rail
by Guowei Jin, Shiwei He, Jiabin Li, Yubin Li, Xiaole Guo and Hongfei Xu
Symmetry 2019, 11(5), 720; https://doi.org/10.3390/sym11050720 - 27 May 2019
Cited by 5 | Viewed by 3045
Abstract
Studying the interaction between demand forecasting and train stop planning is important, as it ensures the sustainable development of high-speed rail (HSR). Forecasting the demand for high-speed rail (HSR), which refers to modal choice or modal split in this paper, is the first [...] Read more.
Studying the interaction between demand forecasting and train stop planning is important, as it ensures the sustainable development of high-speed rail (HSR). Forecasting the demand for high-speed rail (HSR), which refers to modal choice or modal split in this paper, is the first step in high-speed rail (HSR) planning. Given the travel demand and the number of train trips on each route, the train stop planning problem (TSPP) of line planning involves determining the stations at which each train trip stops, i.e., the stop-schedule of each train trip, so that the demand can be satisfied. To integrate and formulate the two problems, i.e., the modal choice problem (MCP) and train stop planning problem (TSPP), a nonlinear model is presented with the objective of maximizing the total demand captured by a high-speed rail system. To solve the model, a heuristic iterative algorithm is developed. To study the relationship between the demand and the service, the Beijing–Shanghai high-speed rail (HSR) corridor in China is selected. The empirical analysis indicates that combining modal choice and train stop planning should be considered for the sustainable design of high-speed rail (HSR) train services. Furthermore, the model simulates the impact of the number of stops on its mode share by reflecting changes in travelers’ behaviors according to HSR train stop planning, and it also provides a theoretical basis for the evaluation of the adaptability of the service network to travel demand. Full article
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14 pages, 331 KiB  
Article
Geometric Properties of Certain Classes of Analytic Functions Associated with a q-Integral Operator
by Shahid Mahmood, Nusrat Raza, Eman S. A. AbuJarad, Gautam Srivastava, H. M. Srivastava and Sarfraz Nawaz Malik
Symmetry 2019, 11(5), 719; https://doi.org/10.3390/sym11050719 - 27 May 2019
Cited by 63 | Viewed by 3302
Abstract
This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by [...] Read more.
This article presents certain families of analytic functions regarding q-starlikeness and q-convexity of complex order γ ( γ ∈ C \ 0 ) . This introduced a q-integral operator and certain subclasses of the newly introduced classes are defined by using this q-integral operator. Coefficient bounds for these subclasses are obtained. Furthermore, the ( δ , q )-neighborhood of analytic functions are introduced and the inclusion relations between the ( δ , q )-neighborhood and these subclasses of analytic functions are established. Moreover, the generalized hyper-Bessel function is defined, and application of main results are discussed. Full article
(This article belongs to the Special Issue Integral Transformations, Operational Calculus and Their Applications)
13 pages, 3001 KiB  
Article
A Power Control Algorithm Based on Chicken Game Theory in Multi-Hop Networks
by Jinpeng Wang, Ye Zhengpeng, Jeremy Gillbanks, Tarun M. Sanders and Nianyu Zou
Symmetry 2019, 11(5), 718; https://doi.org/10.3390/sym11050718 - 27 May 2019
Cited by 13 | Viewed by 2451
Abstract
With the development of modern society, there are not only many voice calls being made over wireless communication systems, but there is also a great deal of demand for data services. There are increasing demands from the general public for more information data, [...] Read more.
With the development of modern society, there are not only many voice calls being made over wireless communication systems, but there is also a great deal of demand for data services. There are increasing demands from the general public for more information data, especially for high-speed services with elevated Gbps levels. As is well known, higher sending power is needed once data rates increase. In order to solve this problem, virtual cellular networks (VCNs) can be employed in order to reduce these peak power shifts. If a VCN works well, mobile ports will receive their own wireless signals via individual cells, and then, the signals will access core networks with the help of a central terminal. Power control can improve the power capacity in multi-hop networks. However, the use of power control will also have a negative impact on network connectivity, delay, and capacity. In order to address the problem, this paper compares specific control methods and capacities in multi-hop networks. Distributed chicken game algorithm power control (DCGAPC) methods are presented in order to reach acceptable minimum levels of network delay and maximum network capacity and connectivity. Finally, a computer simulation is implemented, and the results are shown. Full article
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16 pages, 1074 KiB  
Article
A Novel Hybrid Artificial Intelligence Based Methodology for the Inventory Routing Problem
by Aslı Boru, Ayşe Tuğba Dosdoğru, Mustafa Göçken and Rızvan Erol
Symmetry 2019, 11(5), 717; https://doi.org/10.3390/sym11050717 - 27 May 2019
Cited by 4 | Viewed by 3434
Abstract
In this paper, a new hybrid method including simulation optimization and artificial intelligence based simulation is created to solve the inventory routing problem (IRP) in which three different routing strategies are evaluated for uneven demand patterns including intermittent, erratic, and lumpy demand. The [...] Read more.
In this paper, a new hybrid method including simulation optimization and artificial intelligence based simulation is created to solve the inventory routing problem (IRP) in which three different routing strategies are evaluated for uneven demand patterns including intermittent, erratic, and lumpy demand. The proposed method includes two phases. In the first phase, a nondominated sorting genetic algorithm II based simulation is employed to perform a multi-objective search for the IRP where the objectives of the method are total supply chain cost minimization and average service level maximization. In the second phase, artificial neural network based simulation is used to adjust the reorder point and order-up-to-level by forecasting the customer demand at each replenishment time. The results of the study demonstrated that the average service level is at least 98.54% in the supply chain. From this, it can be concluded that the proposed method can provide a tremendous opportunity to improve the average service level under uncertain environments. In addition, it is determined that different routing strategies can be selected for different demand patterns according to the considered performance measures. Full article
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24 pages, 18473 KiB  
Article
Dragonfly Algorithm with Opposition-Based Learning for Multilevel Thresholding Color Image Segmentation
by Xiaoli Bao, Heming Jia and Chunbo Lang
Symmetry 2019, 11(5), 716; https://doi.org/10.3390/sym11050716 - 27 May 2019
Cited by 30 | Viewed by 4153
Abstract
Multilevel thresholding is a very active research field in image segmentation, and has been successfully used in various applications. However, the computational time will increase exponentially as the number of thresholds increases, and for color images which contain more information this is even [...] Read more.
Multilevel thresholding is a very active research field in image segmentation, and has been successfully used in various applications. However, the computational time will increase exponentially as the number of thresholds increases, and for color images which contain more information this is even worse. To overcome the drawback while maintaining segmentation accuracy, a modified version of dragonfly algorithm (DA) with opposition-based learning (OBLDA) for color image segmentation is proposed in this paper. The opposition-based learning (OBL) strategy simultaneously considers the current solution and the opposite solution, which are symmetrical in the search space. With the introduction of OBL, the proposed algorithm has a faster convergence speed and more balanced exploration–exploitation compared with the original DA. In order to clearly demonstrate the outstanding performance of the OBLDA, the proposed method is compared with seven state-of-the-art meta-heuristic algorithms, through experiments on 10 test images. The optimal threshold values are calculated by the maximization of between-class variance and Kapur’s entropy. Meanwhile, some indicators, including peak signal to noise ratio (PSNR), feature similarity index (FSIM), structure similarity index (SSIM), the average fitness values, standard deviation (STD), and computation time are used as evaluation criteria in the experiments. The promising results reveal that proposed method has the advantages of high accuracy and remarkable stability. Wilcoxon’s rank sum test and Friedman test are also performed to verify the superiority of OBLDA in a statistical way. Furthermore, various satellite images are also included for robustness testing. In conclusion, the OBLDA algorithm is a feasible and effective method for multilevel thresholding color image segmentation. Full article
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9 pages, 245 KiB  
Article
A Hybrid Contraction that Involves Jaggi Type
by Erdal Karapınar and Andreea Fulga
Symmetry 2019, 11(5), 715; https://doi.org/10.3390/sym11050715 - 27 May 2019
Cited by 10 | Viewed by 1946
Abstract
In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction [...] Read more.
In this manuscript, we aim to provide a new hybrid type contraction that is a combination of a Jaggi type contraction and interpolative type contraction in the framework of complete metric spaces. We investigate the existence and uniqueness of such a hybrid contraction in separate theorems. We consider a solution to certain fractional differential equations as an application of the given results. In addition, we provide an example to indicate the genuineness of the given results. Full article
13 pages, 277 KiB  
Article
Dual Extended Hesitant Fuzzy Sets
by José Carlos R. Alcantud, Gustavo Santos-García, Xindong Peng and Jianming Zhan
Symmetry 2019, 11(5), 714; https://doi.org/10.3390/sym11050714 - 26 May 2019
Cited by 24 | Viewed by 2506
Abstract
Hesitant fuzzy sets extend fuzzy sets by considering many-valued sets of membership degrees. Real applications validate this model and decision making approaches of various forms permit to act in a flexible manner. If we can avail ourselves of hesitant information on non-membership degrees [...] Read more.
Hesitant fuzzy sets extend fuzzy sets by considering many-valued sets of membership degrees. Real applications validate this model and decision making approaches of various forms permit to act in a flexible manner. If we can avail ourselves of hesitant information on non-membership degrees too, then dual hesitant fuzzy sets provide a natural extension of both hesitant fuzzy sets and intuitionistic fuzzy sets. This article defines the concept of dual extended hesitant fuzzy set as the combination of extended hesitant fuzzy sets with dual hesitant fuzzy sets. Its basic algebraic properties are set forth, and the model is linked to other successful models in the literature. We also define a comparison law for the prioritization of elements described in this new framework. Moreover, we present an algorithm to solve the dual extended hesitant fuzzy decision making problem by a weight score function. Finally, the feasibility of this approach is demonstrated by the evaluation of big data industries with an effectiveness test. Full article
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17 pages, 3130 KiB  
Article
Low-Complexity Channel Estimation in 5G Massive MIMO-OFDM Systems
by Omar A. Saraereh, Imran Khan, Qais Alsafasfeh, Salem Alemaishat and Sunghwan Kim
Symmetry 2019, 11(5), 713; https://doi.org/10.3390/sym11050713 - 25 May 2019
Cited by 20 | Viewed by 4402
Abstract
Pilot contamination is the reuse of pilot signals, which is a bottleneck in massive multi-input multi-output (MIMO) systems as it varies directly with the numerous antennas, which are utilized by massive MIMO. This adversely impacts the channel state information (CSI) due to too [...] Read more.
Pilot contamination is the reuse of pilot signals, which is a bottleneck in massive multi-input multi-output (MIMO) systems as it varies directly with the numerous antennas, which are utilized by massive MIMO. This adversely impacts the channel state information (CSI) due to too large pilot overhead outdated feedback CSI. To solve this problem, a compressed sensing scheme is used. The existing algorithms based on compressed sensing require that the channel sparsity should be known, which in the real channel environment is not the case. To deal with the unknown channel sparsity of the massive MIMO channel, this paper proposes a structured sparse adaptive coding sampling matching pursuit (SSA-CoSaMP) algorithm that utilizes the space–time common sparsity specific to massive MIMO channels and improves the CoSaMP algorithm from the perspective of dynamic sparsity adaptive and structural sparsity aspects. It has a unique feature of threshold-based iteration control, which in turn depends on the SNR level. This approach enables us to determine the sparsity in an indirect manner. The proposed algorithm not only optimizes the channel estimation performance but also reduces the pilot overhead, which saves the spectrum and energy resources. Simulation results show that the proposed algorithm has improved channel performance compared with the existing algorithm, in both low SNR and low pilot overhead. Full article
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22 pages, 341 KiB  
Article
On Cauchy’s Interlacing Theorem and the Stability of a Class of Linear Discrete Aggregation Models Under Eventual Linear Output Feedback Controls
by Manuel De la Sen
Symmetry 2019, 11(5), 712; https://doi.org/10.3390/sym11050712 - 24 May 2019
Cited by 2 | Viewed by 2358
Abstract
This paper links the celebrated Cauchy’s interlacing theorem of eigenvalues for partitioned updated sequences of Hermitian matrices with stability and convergence problems and results of related sequences of matrices. The results are also applied to sequences of factorizations of semidefinite matrices with their [...] Read more.
This paper links the celebrated Cauchy’s interlacing theorem of eigenvalues for partitioned updated sequences of Hermitian matrices with stability and convergence problems and results of related sequences of matrices. The results are also applied to sequences of factorizations of semidefinite matrices with their complex conjugates ones to obtain sufficiency-type stability results for the factors in those factorizations. Some extensions are given for parallel characterizations of convergent sequences of matrices. In both cases, the updated information has a Hermitian structure, in particular, a symmetric structure occurs if the involved vector and matrices are complex. These results rely on the relation of stable matrices and convergent matrices (those ones being intuitively stable in a discrete context). An epidemic model involving a clustering structure is discussed in light of the given results. Finally, an application is given for a discrete-time aggregation dynamic system where an aggregated subsystem is incorporated into the whole system at each iteration step. The whole aggregation system and the sequence of aggregated subsystems are assumed to be controlled via linear-output feedback. The characterization of the aggregation dynamic system linked to the updating dynamics through the iteration procedure implies that such a system is, generally, time-varying. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)
17 pages, 1232 KiB  
Article
Pilot-Based Adaptive Channel Estimation for Underwater Spatial Modulation Technologies
by Naveed Ur Rehman Junejo, Hamada Esmaiel, Haixin Sun, Zeyad A. H. Qasem and Junfeng Wang
Symmetry 2019, 11(5), 711; https://doi.org/10.3390/sym11050711 - 24 May 2019
Cited by 13 | Viewed by 2939
Abstract
Spatial Modulation Technologies (SMTs) are schemes that reduce inter-carrier interference (ICI), inter-channel interference, inter-antenna synchronization (IAS), and system complexity for multiple-input multiple-output (MIMO) communication systems. Moreover, high spectral and energy efficiency have rendered SMTs attractive to underwater acoustic (UWA) MIMO communication systems. Consequently, [...] Read more.
Spatial Modulation Technologies (SMTs) are schemes that reduce inter-carrier interference (ICI), inter-channel interference, inter-antenna synchronization (IAS), and system complexity for multiple-input multiple-output (MIMO) communication systems. Moreover, high spectral and energy efficiency have rendered SMTs attractive to underwater acoustic (UWA) MIMO communication systems. Consequently, this paper focuses on SMTs such as spatial modulation (SM), generalized spatial modulation (GSM), and fully generalized spatial modulation (FGSM) in which one constant number and one multiple number of antennas are active to transmit data symbols in any time interval for underwater acoustic communication (UWAC). In SMTs, the receiver requires perfect channel state information (P-CSI) for accurate data detection. However, it is impractical that the perfect channel knowledge is available at the receiver. Therefore, channel estimation is of critical importance to obtain the CSI. This paper proposes the pilot-based recursive least-square (RLS) adaptive channel estimation method over the underwater time-varying MIMO channel. Furthermore, maximum likelihood (ML) decoder is used to detect the transmitted data and antennas indices from the received signal and the estimated UWA-MIMO channel. The numerical computation of mean square error (MSE) and bit error rate (BER) performance are computed for different SMTs like SM, GSM and FSGM using Monte Carlo iterations. Simulation results demonstrate that the RLS channel estimation method achieves the nearly same BER performance as P-CSI. Full article
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16 pages, 2941 KiB  
Article
Applying Event-Related Potentials to Measure Perceptual Experience toward the Navigation Interface of a Mobile Game for Improving the Design
by Fu Guo, Jun-Yi Jiang, Xiao-Hui Tian and Jia-Hao Chen
Symmetry 2019, 11(5), 710; https://doi.org/10.3390/sym11050710 - 24 May 2019
Cited by 12 | Viewed by 2658
Abstract
High-level user experience has become the key factor that one game can be successful in the game market. The home page of mobile games, especially the design of the navigation interface, has a significant impact on users’ initial experience, which is an important [...] Read more.
High-level user experience has become the key factor that one game can be successful in the game market. The home page of mobile games, especially the design of the navigation interface, has a significant impact on users’ initial experience, which is an important determent to users’ preferences and purchase decision. Hence, measuring users’ perceptual experiences of the navigation interface can help designers understand real demands from users. Previous studies primarily used self-report scales or interviews to measure gamers’ perceptual experiences. However, it may not reflect gamers’ real perceptions that they are feeling as most of time the feeling is short-lived and implicit. To fill this gap, the current study attempted to combine subjective evaluation with event-related potentials (ERP) to objectively measure gamers’ perceptual experience evoked by the navigation interface of the mobile game. The navigation interfaces of mobile games with low, medium, and high perceptual experience were developed and the ERP experiment was conducted to detect the differences in users’ electroencephalograph (EEG) components when subjects were exposed to the different design levels of navigation interface. The results showed that N1 reaction showed asymmetry in brain regions, and P2 and N2 showed symmetry, and relative to the navigation interface with low and medium perceptual experiences, the high level of navigation interface induced a larger amplitude of N2 in the anterior scalp and P2 in the frontal scalp. These EEG components can, therefore, be regarded as significant indicators reflecting gamers’ perceptions of the navigation interface. The findings benefit game companies of navigation interface designs. Full article
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11 pages, 231 KiB  
Article
Some Identities of Fully Degenerate Bernoulli Polynomials Associated with Degenerate Bernstein Polynomials
by Jeong Gon Lee, Wonjoo Kim and Lee-Chae Jang
Symmetry 2019, 11(5), 709; https://doi.org/10.3390/sym11050709 - 24 May 2019
Viewed by 1719
Abstract
In this paper, we investigate some properties and identities for fully degenerate Bernoulli polynomials in connection with degenerate Bernstein polynomials by means of bosonic p-adic integrals on Z p and generating functions. Furthermore, we study two variable degenerate Bernstein polynomials and the [...] Read more.
In this paper, we investigate some properties and identities for fully degenerate Bernoulli polynomials in connection with degenerate Bernstein polynomials by means of bosonic p-adic integrals on Z p and generating functions. Furthermore, we study two variable degenerate Bernstein polynomials and the degenerate Bernstein operators. Full article
(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with Their Applications Ⅱ)
14 pages, 5529 KiB  
Article
Ellipse Coefficient Map-Based Geomagnetic Fingerprint Considering Azimuth Angles
by Ju-Hyeon Seong, Seung-Hyun Lee, Kyoung-Kuk Yoon and Dong-Hoan Seo
Symmetry 2019, 11(5), 708; https://doi.org/10.3390/sym11050708 - 23 May 2019
Cited by 3 | Viewed by 2353
Abstract
Geomagnetic fingerprint has been actively studied because of the high signal stability and positioning resolution even when the time has elapsed. However, since the measured three-axis geomagnetism signals at one position are irregular according to the change of the azimuth angle, a large-sized [...] Read more.
Geomagnetic fingerprint has been actively studied because of the high signal stability and positioning resolution even when the time has elapsed. However, since the measured three-axis geomagnetism signals at one position are irregular according to the change of the azimuth angle, a large-sized database which is stored magnitudes per angles is required for robust and accurate positioning against the change of the azimuth angle. To solve this problem, this paper proposes a novel approach, an elliptic coefficient map based geomagnetic fingerprint. Unlike the general fingerprint, which stores strength or magnitude of the geomagnetism signals depending on the position, the proposed algorithm minimized the size of databased by storing the Ellipse coefficient map through the ellipse equation derived from the characteristics of 2-D magnetic vectors depending on the position. In addition, the curvature bias of ellipse was reduced by applying the normalized linear least-squares method to 2-D geomagnetic characteristics and the positioning accuracy was improved by applying the weighted geomagnetic signal equalization method. Full article
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12 pages, 263 KiB  
Article
Some Refinements of Ostrowski’s Inequality and an Extension to a 2-Inner Product Space
by Nicuşor Minculete
Symmetry 2019, 11(5), 707; https://doi.org/10.3390/sym11050707 - 23 May 2019
Cited by 3 | Viewed by 1910
Abstract
The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space. Finally, some applications which are related to the Chebyshev function and the Grüss [...] Read more.
The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space. Finally, some applications which are related to the Chebyshev function and the Grüss inequality are presented. Full article
14 pages, 267 KiB  
Article
Introduction to Non-Standard Neutrosophic Topology
by Mohammed A. Al Shumrani and Florentin Smarandache
Symmetry 2019, 11(5), 706; https://doi.org/10.3390/sym11050706 - 23 May 2019
Viewed by 2311
Abstract
For the first time we introduce non-standard neutrosophic topology on the extended non-standard analysis space, called non-standard real monad space, which is closed under neutrosophic non-standard infimum and supremum. Many classical topological concepts are extended to the non-standard neutrosophic topology, several theorems and [...] Read more.
For the first time we introduce non-standard neutrosophic topology on the extended non-standard analysis space, called non-standard real monad space, which is closed under neutrosophic non-standard infimum and supremum. Many classical topological concepts are extended to the non-standard neutrosophic topology, several theorems and properties about them are proven, and many examples are presented. Full article
(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)
16 pages, 1335 KiB  
Article
Multi-Criteria Fuzzy-Stochastic Diffusion Model of Groundwater Control System Selection
by Dušan Polomčić, Zoran Gligorić, Dragoljub Bajić, Miloš Gligorić and Milanka Negovanović
Symmetry 2019, 11(5), 705; https://doi.org/10.3390/sym11050705 - 23 May 2019
Cited by 5 | Viewed by 2269
Abstract
When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic [...] Read more.
When considering data and parameters in hydrogeology, there are often questions of uncertainty, vagueness, and imprecision in terms of the quantity of spatial distribution. To overcome such problems, certain data may be subjectively expressed in the form of expert judgment, whereby a heuristic approach and the use of fuzzy logic are required. In this way, decision-making criteria relating to an optimal groundwater control system do not always have a numerical value. Groundwater control scenarios (alternatives) are identified through hydrodynamic modeling of the aquifer, providing an indication of their effectiveness. The paper develops a fuzzy-stochastic multi-criteria decision-making model to deal with a topical problem: selection of the most suitable groundwater control system for an open-cast mine. Both real numerical and linguistic variables are used to express the values of all criteria that affect the final decision. In particular, it should be pointed out that the values of the criteria are varied over a predefined time horizon. For mathematical calculations, fuzzy dynamic TOPSIS and the stochastic diffusion process—geometric Brownian motion—were used. The proposed method is tested in a case study: the selection of an optimal groundwater control system for an open-cast mine. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
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19 pages, 16911 KiB  
Article
Extracting Information from an Urban Network by Combining a Visibility Index and a City Data Set
by Taras Agryzkov, José Luis Oliver, Leandro Tortosa and José F. Vicent
Symmetry 2019, 11(5), 704; https://doi.org/10.3390/sym11050704 - 23 May 2019
Cited by 1 | Viewed by 2376
Abstract
Cities can be represented by spatial networks, and the mathematical structure that defines a spatial network is a graph. Taking into account this premise, this paper is focused on analysing information on an urban scale by combining a new ray-casting visibility index with [...] Read more.
Cities can be represented by spatial networks, and the mathematical structure that defines a spatial network is a graph. Taking into account this premise, this paper is focused on analysing information on an urban scale by combining a new ray-casting visibility index with a data set of the urban street network. The visibility index provides information about the most visible buildings or areas. We relate this index with other data extracted from the city, with the aim of generating and analysing information about urban elements. To corroborate this idea, real data are analysed. The dataset is related to the heritage conservation of the buildings of the Villaflora suburb, located in the city of Quito (Ecuador). This information is processed, together with the visibility index, with the aim of determining the conservation degree of the urban areas most visually exposed to pedestrians or visitors. The combination of both values—heritage conservation and visibility index—is carried out by means of two new indices, I P and I N , which are defined using two-variable exponential functions. Full article
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13 pages, 5140 KiB  
Article
A Novel Sketch-Based Three-Dimensional Shape Retrieval Method Using Multi-View Convolutional Neural Network
by Dianhui Mao and Zhihao Hao
Symmetry 2019, 11(5), 703; https://doi.org/10.3390/sym11050703 - 23 May 2019
Cited by 10 | Viewed by 3078
Abstract
Retrieving 3D models by adopting hand-drawn sketches to be the input has turned out to be a popular study topic. Most current methods are based on manually selected features and the best view produced for 3D model calculations. However, there are many problems [...] Read more.
Retrieving 3D models by adopting hand-drawn sketches to be the input has turned out to be a popular study topic. Most current methods are based on manually selected features and the best view produced for 3D model calculations. However, there are many problems with these methods such as distortion. For the purpose of dealing with such issues, this paper proposes a novel feature representation method to select the projection view and adapt the maxout network to the extended Siamese network architecture. In addition, the strategy is able to handle the over-fitting issue of convolutional neural networks (CNN) and mitigate the discrepancies between the 3D shape domain and the sketch. A pre-trained AlexNet was used to sketch the extract features. For 3D shapes, multiple 2D views were compiled into compact feature vectors using pre-trained multi-view CNNs. Then the Siamese convolutional neural networks were learnt for transforming the two domains’ original characteristics into nonlinear feature space, which mitigated the domain discrepancy and kept the discriminations. Two large data sets were used for experiments, and the experimental results show that the method is superior to the prior art methods in accuracy. Full article
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26 pages, 632 KiB  
Article
Fuzzy Multi-objective Programming Approach for Constrained Matrix Games with Payoffs of Fuzzy Rough Numbers
by M. G. Brikaa, Zhoushun Zheng and El-Saeed Ammar
Symmetry 2019, 11(5), 702; https://doi.org/10.3390/sym11050702 - 22 May 2019
Cited by 21 | Viewed by 2761
Abstract
Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs [...] Read more.
Imprecise constrained matrix games (such as fuzzy constrained matrix games, interval-valued constrained matrix games, and rough constrained matrix games) have attracted considerable research interest. This article is concerned with developing an effective fuzzy multi-objective programming algorithm to solve constraint matrix games with payoffs of fuzzy rough numbers (FRNs). For simplicity, we refer to this problem as fuzzy rough constrained matrix games. To the best of our knowledge, there are no previous studies that solve the fuzzy rough constrained matrix games. In the proposed algorithm, it is proven that a constrained matrix game with fuzzy rough payoffs has a fuzzy rough-type game value. Moreover, this article constructs four multi-objective linear programming problems. These problems are used to obtain the lower and upper bounds of the fuzzy rough game value and the corresponding optimal strategies of each player in any fuzzy rough constrained matrix games. Finally, a real example of the market share game problem demonstrates the effectiveness and reasonableness of the proposed algorithm. Additionally, the results of the numerical example are compared with the GAMS software results. The significant contribution of this article is that it deals with constraint matrix games using two types of uncertainties, and, thus, the process of decision-making is more flexible. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
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14 pages, 1712 KiB  
Article
A Dynamic Multi-Reduction Algorithm for Brain Functional Connection Pathways Analysis
by Guangyao Dai, Chao Yang, Yingjie Liu, Tongbang Jiang and Gervas Batister Mgaya
Symmetry 2019, 11(5), 701; https://doi.org/10.3390/sym11050701 - 22 May 2019
Cited by 2 | Viewed by 2506
Abstract
Revealing brain functional connection pathways is of great significance in understanding the cognitive mechanism of the brain. In this paper, we present a novel rough set based dynamic multi-reduction algorithm (DMRA) to analyze brain functional connection pathways. First, a binary discernibility matrix is [...] Read more.
Revealing brain functional connection pathways is of great significance in understanding the cognitive mechanism of the brain. In this paper, we present a novel rough set based dynamic multi-reduction algorithm (DMRA) to analyze brain functional connection pathways. First, a binary discernibility matrix is introduced to obtain a reduction, and a reduction equivalence theorem is proposed and proved to verify the feasibility of reduction algorithm. Based on this idea, we propose a dynamic single-reduction algorithm (DSRA) to obtain a seed reduction, in which two dynamical acceleration mechanisms are presented to reduce the size of the binary discernibility matrix dynamically. Then, the dynamic multi-reduction algorithm is proposed, and multi-reductions can be obtained by replacing the non-core attributes in seed reduction. Comparative performance experiments were carried out on the UCI datasets to illustrate the superiority of DMRA in execution time and classification accuracy. A memory cognitive experiment was designed and three brain functional connection pathways were successfully obtained from brain functional Magnetic Resonance Imaging (fMRI) by employing the proposed DMRA. The theoretical and empirical results both illustrate the potentials of DMRA for brain functional connection pathways analysis. Full article
(This article belongs to the Special Issue Multi-Criteria Decision-Making Techniques for Improvement Sustainability Engineering Processes)
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12 pages, 472 KiB  
Article
Model for the Evaluation of an Angular Slot’s Coupling Impedance
by Dario Assante and Luigi Verolino
Symmetry 2019, 11(5), 700; https://doi.org/10.3390/sym11050700 - 22 May 2019
Cited by 1 | Viewed by 1933
Abstract
In high energy particle accelerators, a careful modeling of the electromagnetic interaction between the particle beam and the structure is essential to ensure the performance of the experiments. Particular interest arises in the presence of angular discontinuities of the structure, due to the [...] Read more.
In high energy particle accelerators, a careful modeling of the electromagnetic interaction between the particle beam and the structure is essential to ensure the performance of the experiments. Particular interest arises in the presence of angular discontinuities of the structure, due to the asymmetrical behavior. In this case, semi-analytical models allow one to reduce the computational effort and to better understand the physics of the phenomena, with respect to purely numerical models. In the paper, a model for analyzing the electromagnetic interaction between a traveling charge particle and a perfectly conducting angular slot of a negligible thickness is discussed. The particle travels at a constant velocity along a straight line parallel to the axis of symmetry of the strip. The longitudinal and transverse coupling impedances are therefore evaluated for a wide range of parameters. Full article
(This article belongs to the Special Issue Numerical Analysis or Numerical Method in Symmetry)
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12 pages, 4543 KiB  
Article
Numerical Solution of Non-Newtonian Fluid Flow Due to Rotatory Rigid Disk
by Khalil Ur Rehman, M. Y. Malik, Waqar A Khan, Ilyas Khan and S. O. Alharbi
Symmetry 2019, 11(5), 699; https://doi.org/10.3390/sym11050699 - 22 May 2019
Cited by 40 | Viewed by 3483
Abstract
In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced [...] Read more.
In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced above the rotating disk. The magnetized flow field is framed with Navier’s slip assumption. The Von Karman scheme is adopted to transform flow narrating equations in terms of reduced system. For better depiction a self-coded computational algorithm is executed rather than to move-on with build-in array. Numerical observations via magnetic, Lewis numbers, Casson, slip, Brownian motion, and thermophoresis parameters subject to radial, tangential velocities, temperature, and nanoparticles concentration are reported. The validation of numerical method being used is given through comparison with existing work. Comparative values of local Nusselt number and local Sherwood number are provided for involved flow controlling parameters. Full article
(This article belongs to the Special Issue Symmetry and Fluid Mechanics)
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18 pages, 341 KiB  
Article
Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example
by Muhammad Jamil, Saleem Abdullah, Muhammad Yaqub Khan, Florentin Smarandache and Fazal Ghani
Symmetry 2019, 11(5), 698; https://doi.org/10.3390/sym11050698 - 21 May 2019
Cited by 12 | Viewed by 2924
Abstract
The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators [...] Read more.
The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life. Full article
(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)
9 pages, 1601 KiB  
Article
A Novel Generalized Group-Sparse Mixture Adaptive Filtering Algorithm
by Yingsong Li, Aleksey Cherednichenko, Zhengxiong Jiang, Wanlu Shi and Jinqiu Wu
Symmetry 2019, 11(5), 697; https://doi.org/10.3390/sym11050697 - 21 May 2019
Cited by 1 | Viewed by 1893
Abstract
A novel adaptive filtering (AF) algorithm is proposed for group-sparse system identifications. In the devised algorithm, a novel mixed error criterion (MEC) with two-order logarithm error, p-order errors and group sparse constraint method is devised to give a resistant to the impulsive [...] Read more.
A novel adaptive filtering (AF) algorithm is proposed for group-sparse system identifications. In the devised algorithm, a novel mixed error criterion (MEC) with two-order logarithm error, p-order errors and group sparse constraint method is devised to give a resistant to the impulsive noise. The proposed group-sparse MEC can fully use the known group-sparse characteristics in the cluster sparse systems, and it is derived and analyzed in detail. Various simulations are presented and analyzed to give a verification on the effectiveness of the developed group-sparse MEC algorithms, and the simulated results shown that the developed algorithm outperforms the previously developed sparse AF algorithms for identifying the systems. Full article
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15 pages, 462 KiB  
Article
Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers
by Qiaoyan Li, Yingcang Ma, Xiaohong Zhang and Juanjuan Zhang
Symmetry 2019, 11(5), 696; https://doi.org/10.3390/sym11050696 - 21 May 2019
Cited by 9 | Viewed by 2136
Abstract
In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. Moreover, two kinds of degradation algebra systems of neutrosophic quadruple numbers are introduced. In particular, the following results are strictly proved: (1) the set of neutrosophic quadruple numbers with a [...] Read more.
In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. Moreover, two kinds of degradation algebra systems of neutrosophic quadruple numbers are introduced. In particular, the following results are strictly proved: (1) the set of neutrosophic quadruple numbers with a multiplication operation is a neutrosophic extended triplet group; (2) the neutral element of each neutrosophic quadruple number is unique and there are only sixteen different neutral elements in all of neutrosophic quadruple numbers; (3) the set which has same neutral element is closed with respect to the multiplication operator; (4) the union of the set which has same neutral element is a partition of four-dimensional space. Full article
(This article belongs to the Special Issue New types of Neutrosophic Set/Logic/Probability, Neutrosophic Over-/Under-/Off-Set, Neutrosophic Refined Set, and their Extension to Plithogenic Set/Logic/Probability, with Applications)
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