Symmetry doi: 10.3390/sym10060230

Authors: Connah Kendrick Kevin Tan Kevin Walker Moi Hoon 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.

]]>Symmetry doi: 10.3390/sym10060229

Authors: Yao Chen Jian Feng

In recent years, group theory has been gradually adopted for computational problems of solid and structural mechanics. This paper reviews the advances made in the application of group theory in areas such as stability, form-finding, natural vibration and bifurcation of novel prestressed structures. As initial prestress plays an important role in prestressed structures, its contribution to structural stiffness has been considered. General group-theoretic approaches for several problems are presented, where certain stiffness matrices and equilibrium matrices are expressed in symmetry-adapted coordinate system and block-diagonalized neatly. Illustrative examples on structural stability analysis, force-finding analysis, and generalized eigenvalue analysis on cable domes and cable-strut structures are drawn from recent studies by the authors. It shows how group theory, through symmetry spaces for irreducible representations and matrix decompositions, enables remarkable simplifications and reductions in the computational effort to be achieved. More importantly, before any numerical computations are performed, group theory allows valuable and effective insights on the behavior or intrinsic properties of a prestressed structure to be gained.

]]>Symmetry doi: 10.3390/sym10060228

Authors: Matthias Zschornak Tilmann Leisegang Falk Meutzner Hartmut Stöcker Theresa Lemser Tobias Tauscher Claudia Funke Charaf Cherkouk Dirk C. 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&rsquo;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&rsquo;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.

]]>Symmetry doi: 10.3390/sym10060227

Authors: Boliang Lin Jianping Wu Jiaxi Wang Jingsong Duan Yinan Zhao

Service network design is fundamentally crucial for railway express cargo transportation. The main challenge is to strike a balance between two conflicting objectives: low network setup costs and high expected operational incomes. Different configurations of these objectives will have different impacts on the quality of freight transportation services. In this paper, a bi-level programming model for the railway express cargo service network design problem is proposed. The upper-level model forms the optimal decisions in terms of the service characteristics, and the low-level model selects the service arcs for each commodity. The rail express cargo is strictly subject to the service commitment, the capacity restriction, flow balance constraints, and logical relationship constraints among the decisions variables. Moreover, linearization techniques are used to convert the lower-level model to a linear one so that it can be directly solved by a standard optimization solver. Finally, a real-world case study based on the Beijing&ndash;Guangzhou Railway Line is carried out to demonstrate the effectiveness and efficiency of the proposed solution approach.

]]>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.

]]>Symmetry doi: 10.3390/sym10060225

Authors: Wenhua Cui Jun Ye

This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings. Then, the sine entropy measures of SNSs are presented to establish a sine entropy weight model for solving the criteria weights in decision-making. Based on the improved weighted SMs of SNSs and the sine entropy weight model, a multi-criteria decision-making (MCDM) method with unknown criteria weights (an improved MCDM method) is established in the SNS setting. In the MCDM process, corresponding to the criteria weights obtained by the sine entropy model, the ranking order of all alternatives and the best one are given by means of the improved weighted SMs between the ideal solution and each alternative. Lastly, the improved MCDM method is applied to an actual decision example in single-valued and interval neutrosophic settings to indicate the feasibility of the improved MCDM method. By comparative analysis with existing MCDM methods, the improved SMs and the sine entropy weight model not only provide a simpler and more effective method for MCDM problems with unknown criteria weights in the SNS setting, but can also overcome the insufficiency of the existing SMs and MCDM method.

]]>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&ndash;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&rsquo;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.

]]>Symmetry doi: 10.3390/sym10060223

Authors: Dan-Ping Li Ji-Qun He Peng-Fei Cheng Jian-Qiang Wang Hong-Yu Zhang

Gastric cancer results in malignant tumors with high morbidity and mortality, and seriously affects the health and life quality of patients. Early detection and appropriate treatment for early-stage gastric cancer patients are very helpful to reducing the recurrence rate and improving survival rates. Hence, the selection of a suitable surgical treatment is an important part. At present, surgical treatment selection has been researched in numerous studies, but there is no study integrating fuzzy decision-making theory with quantitative analysis, considering the patient&rsquo;s conditions with other relative conditions, and which can handle multisource heterogeneous information at the same time. Hence, this paper proposes a novel selection model of surgical treatments for early gastric cancer based on heterogeneous multiple-criteria group decision-making (MCGDM), which is helpful to selecting the most appropriate surgery in the case of asymmetric information between doctors and patients. Subjective and objective criteria are comprehensively taken into account in the index system of the selection model for early gastric cancer, which combines fuzzy theory with quantitative data analysis. Moreover, the evaluation information obtained from the patient&rsquo;s conditions, the surgery, and the hospital&rsquo;s medical status, etc., including crisp numbers, interval numbers, neutrosophic numbers, and probabilistic linguistic labels, is more complete and real, so the surgical treatment selection is accurate and reliable. Furthermore, the technique for order of preference by similarity to ideal solution (TOPSIS) method is employed to solve the prioritization of early gastric cancer surgical treatments. Finally, an empirical study of surgical treatment selection for early gastric cancer surgery is conducted, and the results of sensitivity analysis and comparative analysis suggest that the proposed selection model of surgical treatments for early gastric cancer patients is reliable and effective.

]]>Symmetry doi: 10.3390/sym10060221

Authors: Chia–Nan Wang Van Thanh Nguyen Duy Hung Duong Hanh Tuong Do

In the market economy, competition is typically due to the difficulty in selecting the most suitable supplier, one that is capable to help a business to develop a profit to the highest value threshold and capable to meet sustainable development features. In addition, this research discusses a wide range of consequences from choosing an effective supplier, including reducing production cost, improving product quality, delivering the product on time, and responding flexibly to customer requirements. Therefore, the activities noted above are able to increase an enterprise&rsquo;s competitiveness. It can be seen that selecting a supplier is complex in that decision-makers must have an understanding of the qualitative and quantitative features for assessing the symmetrical impact of the criteria to reach the most accurate result. In this research, the multi-criteria group decision-making (MCGDM) approach was proposed to solve supplier selection problems. The authors collected data from 25 potential suppliers, and the four main criteria within contain 15 sub-criteria to define the most effective supplier, which has viewed factors, including financial efficiency guarantee, quality of materials, ability to deliver on time, and the conditioned response to the environment to improve the efficiency of the industry supply chain. Initially, fuzzy analytic network process (ANP) is used to evaluate and rank these criteria, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. Subsequently, data envelopment analysis (DEA) models, including the Charnes Cooper Rhodes model (CCR model), Banker Charnes Cooper model (BCC model), and slacks-based measure model (SBM model), were proposed to rank suppliers. The result of the model has proposed 7/25 suppliers, which have a condition response to the enterprises&rsquo; supply requirements.

]]>Symmetry doi: 10.3390/sym10060222

Authors: Yizheng Liu Chengyou Wang Hongming Zhao Jiayang Song Shiyue Chen

In this paper, we propose a new demosaicking algorithm which uses eight-directional weights based on the gradient of color difference (EWGCD) for Bayer image demosaicking. To obtain the interpolation of green (G) pixels, the eight-directional G pixel values are first estimated in red (R)/blue (B) pixels. This estimate is used to calculate the color difference in R/B pixels of the Bayer image in diagonal directions. However, in horizontal and vertical directions, the new estimated G pixels are defined to obtain the color difference. The eight-directional weights of estimated G pixels can be obtained by considering the gradient of the color difference and the gradient of the RGB pixels of the Bayer image. Therefore, the eight-directional weighted values and the first estimated G pixel values are combined to obtain the full G image. Compared with six similar algorithms using the same eighteen McMaster images, the results of the experiment demonstrate that the proposed algorithm has a better performance not only in the subjective visual measurement but also in the assessments of peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) index measurement.

]]>Symmetry doi: 10.3390/sym10060220

Authors: Rebecca J. Sharman Elena Gheorghiu

Recent studies have shown that limiting the lifetime of pattern elements improves symmetry detection, potentially by increasing the number of element locations. Here, we investigate how spatial relocation, luminance contrast modulation and lifetime duration of elements affect symmetry perception in dynamic stimuli. Stimuli were dynamic dot-patterns containing varying amounts of symmetry about a vertical axis. Symmetrical matched-pairs were: (i) relocated to multiple successive, but random locations (i.e., multiple locations condition); (ii) relocated between the same two locations (i.e., two locations condition); (iii) not, relocated, but their luminance contrast was modulated at different temporal frequencies (i.e., one location condition), and (iv) not relocated, but a single pattern was presented at full contrast (i.e., static condition). In the dynamic conditions, we varied the elements&rsquo; lifetime duration and temporal frequency of contrast modulation. We measured symmetry detection thresholds using a two-interval forced choice procedure. Our results show improved performance for the multiple locations condition compared to two-location and static conditions, suggesting a cumulative process whereby weak symmetry information is integrated by spatiotemporal filters to increase overall symmetry signal strength. Performance also improved for the static, contrast modulated patterns, but this was explained by a reduction in perceived density. This suggests that different mechanisms mediate symmetry detection in dynamic stimuli and static contrast modulated patterns.

]]>Symmetry doi: 10.3390/sym10060219

Authors: Taekyun Kim Dae San Kim Gwan-Woo Jang Jongkyum Kwon

We represent the generating function of w-torsion Fubini polynomials by means of a fermionic p-adic integral on Zp. Then we investigate a quotient of such p-adic integrals on Zp, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

]]>Symmetry doi: 10.3390/sym10060218

Authors: Sun Jung Young Kim

We study ruled submanifolds in Minkowski space in regard to the Gauss map satisfying some partial differential equation. As a generalization of usual cylinders, cones and null scrolls in a three-dimensional Minkowski space, a cylinder over a space curve, a product manifold of a right cone and a k-plane, a product manifold of a hyperbolic cone and a k-plane which look like kinds of cylinders over cones in 3-space, and the generalized B-scroll kind in Minkowski space are characterized with the partial differential equation regarding the Gauss map, where k is a positive integer.

]]>Symmetry doi: 10.3390/sym10060217

Authors: Parimala Mani Karthika Muthusamy Saeid Jafari Florentin Smarandache Udhayakumar Ramalingam

The concept of interval neutrosophic sets has been studied and the introduction of a new kind of set in topological spaces called the interval valued neutrosophic support soft set has been suggested. We study some of its basic properties. The main purpose of this paper is to give the optimum solution to decision-making in real life problems the using interval valued neutrosophic support soft set.

]]>Symmetry doi: 10.3390/sym10060216

Authors: Jin Zhang Zhaohui Tang Mingxi Ai Weihua Gui

Froth flotation is a vital mineral concentration process. Froth surface behavior is the knowledge about flotation working condition. However, in computer vision aided froth surface behavior control, there are still two challenges that need to be tackled seriously. Against the difficulty in the froth surface behavior representation, this paper proposes to combine the bubble size distribution (BSD) and froth velocity distribution. As far as we know, this is the first time that the froth velocity distribution is presented. Against the difficulty in the adaptive generation of the optimal froth surface behavior feature (optimal setpoint), this paper introduces the fuzzy apriori to mine the association rule between the current working condition and the optimal setpoint. Then, a fuzzy inference module is constructed to generate optimal setpoint for current working condition adaptively. Many validation experiments and comparison experiments demonstrate the superiority and robustness of the proposed methods.

]]>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.

]]>Symmetry doi: 10.3390/sym10060214

Authors: Qing Li Steven Y. Liang

The ability to accurately track the degradation trajectories of rotating machinery components is arguably one of the challenging problems in prognostics and health management (PHM). In this paper, an intelligent prediction approach based on asymmetric penalty sparse decomposition (APSD) algorithm combined with wavelet neural network (WNN) and autoregressive moving average-recursive least squares algorithm (ARMA-RLS) is proposed for degradation prognostics of rotating machinery, taking the accelerated life test of rolling bearings as an example. Specifically, the health indicators time series (e.g., peak-to-peak value and Kurtosis) is firstly decomposed into low frequency component (LFC) and high frequency component (HFC) using the APSD algorithm; meanwhile, the resulting non-convex regularization problem can be efficiently solved using the majorization-minimization (MM) method. In particular, the HFC part corresponds to the stable change around the zero line of health indicators which most extensively occurs; in contrast, the LFC part is essentially related to the evolutionary trend of health indicators. Furthermore, the nonparametric-based method, i.e., WNN, and parametric-based method, i.e., ARMA-RLS, are respectively introduced to predict the LFC and HFC that focus on abrupt degradation regions (e.g., last 100 points). Lastly, the final predicted data could be correspondingly obtained by integrating the predicted LFC and predicted HFC. The proposed methodology is tested using degradation health indicator time series from four rolling bearings. The proposed approach performed favorably when compared to some state-of-the-art benchmarks such as WNN and largest Lyapunov (LLyap) methods.

]]>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.

]]>Symmetry doi: 10.3390/sym10060212

Authors: Marija Maksimović

One of the main problems in the theory of strongly regular graphs (SRGs) is constructing and classifying SRGs with given parameters. Strongly regular graphs with parameters (37,18,8,9), (41,20,9,10), (45,22,10,11), (49,24,11,12), (49,18,7,6) and (50,21,8,9) are the only strongly regular graphs on up to 50 vertices that still have to be classified. In this paper, we give the enumeration of SRGs with these parameters having S3 as an automorphism group. The construction of SRGs in this paper is a step in the classification of SRGs on up to 50 vertices.

]]>Symmetry doi: 10.3390/sym10060211

Authors: Chung-Chuan Chen J. Alberto Conejero Marko Kostić Marina Murillo-Arcila

The existence of chaos and the quest of dense orbits have been recently considered for dynamical systems given by multivalued linear operators. We consider the notions of topological transitivity, topologically mixing property, hypercyclicity, periodic points, and Devaney chaos in the general case of binary relations on topological spaces, and we analyze how they can be particularized when they are represented with graphs and digraphs. The relations of these notions with different types of connectivity and with the existence of Hamiltonian paths are also exposed. Special attention is given to the study of dynamics over tournaments. Finally, we also show how disjointness can be introduced in this setting.

]]>Symmetry doi: 10.3390/sym10060210

Authors: Wei-zhen Sun Jie-sheng Wang Xian Wei

Whale optimization algorithm (WOA) is a swarm intelligence optimization algorithm inspired by humpback whale hunting behavior. WOA has many similarities with other swarm intelligence algorithms (PSO, GWO, etc.). WOA&rsquo;s unique search mechanism enables it to have a strong global search capability while taking into account the strong global search capabilities. In this work, considering the the deficiency of WOA in local search mechanism, combined with the optimization methods of other group intelligent algorithms, perceptual perturbation mechanism is introduced, which makes the agent perform more detailed searches near the local extreme point. At the same time, since the WOA uses a logarithmic spiral curve, the agent cannot fully search all the spaces within its search range, even though the introduction of the perturbation mechanism may still lead to the algorithm falling into a local optimum. Therefore, the equal pitch Archimedes spiral curve is chosen to replace the classic logarithmic spiral curve. In order to fully verify the effect of the search path on the performance of the algorithm, several other spiral curves have been chosen for experimental comparison. By utilizing the 23 benchmark test functions, the simulation results show that WOA (PDWOA) with perceptual perturbation significantly outperforms the standard WOA. Then, based on the PDWOA, the effect of the search path on the performance of the algorithm has been verified. The simulation results show that the equal pitch of the Archimedean spiral curve is best.

]]>Symmetry doi: 10.3390/sym10060209

Authors: Shahid Imran Muhammad Kamran Siddiqui Muhammad Imran Muhammad Hussain Hafiz Muhammad Bilal Imran Zulfiqar 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 &cong; 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.

]]>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.

]]>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: &Delta; ( r n &Delta; ( x n + p n x n &minus; &tau; ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma.

]]>Symmetry doi: 10.3390/sym10060206

Authors: Shin Kang Muhammad Siddiqui Najma Rehman Muhammad Imran Mehwish Muhammad

The Kirchhoff index, global mean-first passage time, average path length and number of spanning trees are of great importance in the field of networking. The “Kirchhoff index” is known as a structure descriptor index. The “global mean-first passage time” is known as a measure for nodes that are quickly reachable from the whole network. The “average path length” is a measure of the efficiency of information or mass transport on a network, and the “number of spanning trees” is used to minimize the cost of power networks, wiring connections, etc. In this paper, we have selected a complex network based on a categorical product and have used the spectrum approach to find the Kirchhoff index, global mean-first passage time, average path length and number of spanning trees. We find the expressions for the product and sum of reciprocals of all nonzero eigenvalues of a categorical product network with the help of the eigenvalues of the path and cycles.

]]>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&rsquo;s structure, are usually employed. Therefore, the use of the procedures, improving the accuracy of the evaluation of the weights&rsquo; 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.

]]>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.

]]>Symmetry doi: 10.3390/sym10060202

Authors: Tèmítópé Jaíyéolá 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.

]]>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.

]]>Symmetry doi: 10.3390/sym10060201

Authors: Muhammad Imran Muhammad Ali Sarfraz Ahmad Muhammad Siddiqui Abdul Baig

The bismuth tri-iodide ( B i I 3 ) is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of the molecular graph that portray its topology and are normally graph invariants. In 1975, Randic presented, in a bond-added substance, a topological index as a descriptor for portraying subatomic branching. In this paper, we investigate the precious stone structure of bismuth tri-iodide chain and sheet. Moreover, exact formulas of degree-based added-substance topological indices principally the first, second, and hyper Zagreb indices, the general Randic index, the geometric-arithmetic index, the fourth atom-bond connectivity index, and the fifth geometric arithmetic index of the subatomic graph of bismuth tri-iodide for both chain and sheet structures are determined.

]]>Symmetry doi: 10.3390/sym10060200

Authors: Boris A. Kulnitskiy Igor A. Perezhogin Mikhail Yu. Popov Danila A. Ovsyannikov Vladimir D. Blank

The structure of silicon, along with mixtures of silicon and boron carbide (B4C) powders and silicon and diamond powders with different proportions after mechanoactivation, has been studied by transmission electron microscopy (TEM) methods. It was shown that silicon and boron carbide experience twinning according to the known twinning mechanisms. In addition to the initial phase with a diamond lattice, the particles of two other phases were detected for silicon, including: the Kasper phase (SiIII) and lonsdaleite (SiIV). We established that the phase transformations in silicon can happen due to different mechanisms.

]]>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.

]]>Symmetry doi: 10.3390/sym10060198

Authors: Ionel-Alexandru Gal Danut Bucur Luige Vladareanu

In this paper, we present a deciding technique for robotic dexterous hand configurations. This algorithm can be used to decide on how to configure a robotic hand so it can grasp objects in different scenarios. Receiving as input, several sensor signals that provide information on the object&rsquo;s shape, the DSmT decision-making algorithm passes the information through several steps before deciding what hand configuration should be used for a certain object and task. The proposed decision-making method for real time control will decrease the feedback time between the command and grasped object, and can be successfully applied on robot dexterous hands. For this, we have used the Dezert&ndash;Smarandache theory which can provide information even on contradictory or uncertain systems.

]]>Symmetry doi: 10.3390/sym10060197

Authors: Jian-Qiang Wang Chu-Quan Tian Xu Zhang Hong-Yu Zhang Tie-Li Wang

This study introduces simplified neutrosophic linguistic numbers (SNLNs) to describe online consumer reviews in an appropriate manner. Considering the defects of studies on SNLNs in handling linguistic information, the cloud model is used to convert linguistic terms in SNLNs to three numerical characteristics. Then, a novel simplified neutrosophic cloud (SNC) concept is presented, and its operations and distance are defined. Next, a series of simplified neutrosophic cloud aggregation operators are investigated, including the simplified neutrosophic clouds Maclaurin symmetric mean (SNCMSM) operator, weighted SNCMSM operator, and generalized weighted SNCMSM operator. Subsequently, a multi-criteria decision-making (MCDM) model is constructed based on the proposed aggregation operators. Finally, a hotel selection problem is presented to verify the effectiveness and validity of our developed approach.

]]>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. So, this paper mainly focus on the research of the 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 in detail. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is used to aggregate assessment information to obtain the comprehensive risk assessment. 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.

]]>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.

]]>Symmetry doi: 10.3390/sym10060194

Authors: Vasantha Kandasamy W.B. Ilanthenral Kandasamy Florentin Smarandache

In this paper we study the neutrosophic triplet groups for a &isin; Z 2 p and prove this collection of triplets a , n e u t ( a ) , a n t i ( a ) if trivial forms a semigroup under product, and semi-neutrosophic triplets are included in that collection. Otherwise, they form a group under product, and it is of order ( p &minus; 1 ) , with ( p + 1 , p + 1 , p + 1 ) as the multiplicative identity. The new notion of pseudo primitive element is introduced in Z 2 p analogous to primitive elements in Z p , where p is a prime. Open problems based on the pseudo primitive elements are proposed. Here, we restrict our study to Z 2 p and take only the usual product modulo 2 p .

]]>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.

]]>Symmetry doi: 10.3390/sym10060192

Authors: Kai-Qing Zhou Wei-Hua Gui Li-Ping Mo Azlan Mohd Zain

Fuzzy Petri net (FPN) is a powerful tool to execute the fault diagnosis function for various industrial applications. One of the most popular approaches for fault diagnosis is to calculate the corresponding algebra forms which record flow information and three parameters of value of all places and transitions of the FPN model. However, with the rapid growth of the complexity of the real system, the scale of the corresponding FPN is also increased sharply. It indicates that the complexity of the fault diagnosis algorithm is also raised due to the increased scale of vectors and matrix. Focusing on this situation, a bidirectional adaptive fault diagnosis algorithm is presented in this article to reduce the complexity of the fault diagnosis process via removing irrelevant places and transitions of the large-scale FPN, followed by the correctness and algorithm complexity of the proposed approach that are also discussed in detail. A practical example is utilized to show the feasibility and efficacy of the proposed method. The results of the experiments illustrated that the proposed algorithm owns the ability to simplify the inference process and to reduce the algorithm complexity due to the removal of unnecessary places and transitions in the reasoning path of the appointed output place.

]]>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 &lt; H &le; 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 &lt; H &lt; 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 ) .

]]>Symmetry doi: 10.3390/sym10060190

Authors: Shio Gai Quek Said Broumi Ganeshsree Selvachandran Assia Bakali Mohamed Talea Florentin Smarandache

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1) and generalized single-valued neutrosophic graphs of type 1 (GSVNG1). The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection.

]]>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.

]]>Symmetry doi: 10.3390/sym10060188

Authors: Chrysoula Mylona Nikolaos Psarros Garyfalos Papaschinopoulos Christos Schinas

In this paper, we study the stability of the zero equilibria of two close-to-symmetric systems of difference equations with exponential terms in the special case in which one of their eigenvalues is equal to − 1 and the other eigenvalue has an absolute value of less than 1. In the present study, we use the approach of center manifold theory.

]]>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.

]]>Symmetry doi: 10.3390/sym10060186

Authors: Xiang Liu Qian Fang Qiushuang Zhou Yan Liu

This paper presents an analytical method using the energy conservation principle to predict ground settlement due to symmetrically shaped tunnel construction in elastic ground conditions. Ground settlement is calculated by balancing the energy in shearing the soil, the work done by gravity, and the negative work done along the tunnel boundary. The proposed method was validated by finite-difference numerical simulations. According to the simulations, it was found that the direction of maximum shear stress under shear strain extension (SSE) was opposite to that under shear strain compression (SSC). The energy in shearing the soil can be obtained by using both the differential of ground displacement, and the fitted expression of maximum shear strain. Subsequently, ground deformation was predicted by the proposed method under three different conditions, and then compared with numerical results. Specific cases of ground settlement due to tunneling can be predicted by the proposed method, using the differential of the proposed empirical solutions. Ground settlements calculated by fitted expressions of maximum shear strain were closer to numerical results than those calculated by differentials. Deriving an empirical equation of maximum engineering shear strain from fitted expressions may be an innovative way for the proposed method to predict ground settlement.

]]>Symmetry doi: 10.3390/sym10060185

Authors: Wenting Zhou Roberto Passante Lucia Rizzuto

We study the resonant dipole&ndash;dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration&ndash;temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.

]]>Symmetry doi: 10.3390/sym10060184

Authors: Catarina Vila Pouca Connor Gervais Joshua Reed Culum Brown

Climate change is warming the world&rsquo;s oceans at an unprecedented rate. Under predicted end-of-century temperatures, many teleosts show impaired development and altered critical behaviors, including behavioral lateralisation. Since laterality is an expression of brain functional asymmetries, changes in the strength and direction of lateralisation suggest that rapid climate warming might impact brain development and function. However, despite the implications for cognitive functions, the potential effects of elevated temperature in lateralisation of elasmobranch fishes are unknown. We incubated and reared Port Jackson sharks at current and projected end-of-century temperatures and measured preferential detour responses to left or right. Sharks incubated at elevated temperature showed stronger absolute laterality and were significantly biased towards the right relative to sharks reared at current temperature. We propose that animals reared under elevated temperatures might have more strongly lateralized brains to cope with deleterious effects of climate change on brain development and growth. However, far more research in elasmobranch lateralisation is needed before the significance of these results can be fully comprehended. This study provides further evidence that elasmobranchs are susceptible to the effects of future ocean warming, though behavioral mechanisms might allow animals to compensate for some of the challenges imposed by climate change.

]]>Symmetry doi: 10.3390/sym10060183

Authors: Naeem Ayoub Zhenguo Gao Bingcai Chen Muwei Jian

Saliency detection is one of the most valuable research topics in computer vision. It focuses on the detection of the most significant objects/regions in images and reduces the computational time cost of getting the desired information from salient regions. Local saliency detection or common pattern discovery schemes were actively used by the researchers to overcome the saliency detection problems. In this paper, we propose a bottom-up saliency fusion method by taking into consideration the importance of the DS-Evidence (Dempster&ndash;Shafer (DS)) theory. Firstly, we calculate saliency maps from different algorithms based on the pixels-level, patches-level and region-level methods. Secondly, we fuse the pixels based on the foreground and background information under the framework of DS-Evidence theory (evidence theory allows one to combine evidence from different sources and arrive at a degree of belief that takes into account all the available evidence). The development inclination of image saliency detection through DS-Evidence theory gives us better results for saliency prediction. Experiments are conducted on the publicly available four different datasets (MSRA, ECSSD, DUT-OMRON and PASCAL-S). Our saliency detection method performs well and shows prominent results as compared to the state-of-the-art algorithms.

]]>Symmetry doi: 10.3390/sym10060182

Authors: Eerdun Buhe G.W. Bluman Chen Alatancang Hu Yulan

This paper applies the direct construction method, symmetry/adjoint symmetry pair method (SA method), symmetry action on a known conservation law method, Ibragimov&rsquo;s conservation theorem (which always yields the same results as the SA method) and a recursion formula to calculate several conservation laws for nonlinear telegraph systems. In addition, a comparison is made between these methods for conservation laws admitted by nonlinear telegraph systems.

]]>Symmetry doi: 10.3390/sym10060181

Authors: Hasil Park Jinho Park Heegwang Kim Sung Q Lee Kang-Ho Park Joonki Paik

This paper presents a novel hybrid sensor-based intrusion detection system for low-power surveillance in an empty, sealed indoor space with or without illumination. The proposed system includes three functional steps: (i) initial detection of an intrusion event using a sound field sensor; (ii) automatic lighting control based on the detected event, and (iii) detection and tracking the intruder using an image sensor. The proposed hybrid sensor-based surveillance system uses a sound field sensor to detect an abnormal event in a very low-light or completely dark environment for 24 h a day to reduce the power consumption. After detecting the intrusion by the sound sensor, a collaborative image sensor takes over an accurate detection and tracking tasks. The proposed hybrid system can be applied to various surveillance environments such as an office room after work, empty automobile, safety room in a bank, and armory room. This paper deals with fusion of computer-aided pattern recognition and physics-based sound field analysis that reflects the symmetric aspect of computer vision and physical analysis

]]>Symmetry doi: 10.3390/sym10050180

Authors: Yang Fang Xiang Zhao Zhen Tan Weidong Xiao

Network embedding (NE) is an important method to learn the representations of a network via a low-dimensional space. Conventional NE models focus on capturing the structural information and semantic information of vertices while neglecting such information for edges. In this work, we propose a novel NE model named BimoNet to capture both the structural and semantic information of edges. BimoNet is composed of two parts; i.e., the bi-mode embedding part and the deep neural network part. For the bi-mode embedding part, the first mode&mdash;named the add-mode&mdash;is used to express the entity-shared features of edges and the second mode&mdash;named the subtract-mode&mdash;is employed to represent the entity-specific features of edges. These features actually reflect the semantic information. For the deep neural network part, we firstly regard the edges in a network as nodes, and the vertices as links, which will not change the overall structure of the whole network. Then, we take the nodes&rsquo; adjacent matrix as the input of the deep neural network, as it can obtain similar representations for nodes with similar structure. Afterwards, by jointly optimizing the objective function of these two parts, BimoNet could preserve both the semantic and structural information of edges. In experiments, we evaluate BimoNet on three real-world datasets and the task of relation extraction, and BimoNet is demonstrated to outperform state-of-the-art baseline models consistently.

]]>Symmetry doi: 10.3390/sym10050179

Authors: Mingju Zhang Zhenbo Zhang Zheng Li Pengfei Li

On the basis of the circular arc sliding model of the limit equilibrium method, an axisymmetric arc sliding method (AASM) is proposed to analyze the basal heave stability of braced circular excavations. The proposed method considers the stiffness of the enclosure structure and spatial effects. The AASM was applied to check basal heave stability in a design example and provided results that were more reasonable than those obtained using other methods. The radii effects in theory and numerical simulation, and the enclosure structure stiffness effects on the basal heave stability safety factor were discussed. Additionally, the effects of the embedded depth on the basal heave stability of a braced circular excavation were analyzed. The safety factor of basal heave stability for a braced circular excavation will be larger when calculated with the AASM than when calculated with the circular arc sliding method, and the optimized embedded depth of the enclosure structure may therefore be reduced by 4&sim;5 m to lower the cost of the enclosure structure.

]]>Symmetry doi: 10.3390/sym10050178

Authors: Xia Liang Peide Liu Zhengmin Liu

With the remarkable promotion of e-commerce platforms, consumers increasingly prefer to purchase products online. Online ratings facilitate consumers to choose among products. Thus, to help consumers effectively select products, it is necessary to provide decision support methods for consumers to trade online. Considering the decision makers are bounded rational, this paper proposes a novel decision support model for product selection based on online ratings, in which the regret aversion behavior of consumers is formulated. Massive online ratings provided by experienced consumers for alternative products associated with several evaluation attributes are obtained by software finders. Then, the evaluations of alternative products in format of stochastic variables are conducted. To select a desirable alternative product, a novel method is introduced to calculate gain and loss degrees of each alternative over others. Considering the regret behavior of consumers in the product selection process, the regret and rejoice values of alternative products for consumer are computed to obtain the perceived utility values of alternative products. According to the prior order of the evaluation attributes provided by the consumer, the prior weights of attributes are determined based on the perceived utility values of alternative products. Furthermore, the overall perceived utility values of alternative products are obtained to generate a ranking result. Finally, a practical example from Zol.com.cn for tablet computer selection is used to demonstrate the feasibility and practically of the proposed model.

]]>Symmetry doi: 10.3390/sym10050177

Authors: Chenyang Song Zeshui Xu Hua Zhao

The probabilistic hesitant fuzzy element is a common tool to deal with multi-criteria decision-making problems when the decision makers are irresolute in providing their evaluations. The existing methods for ranking probabilistic hesitant fuzzy elements are limited and not reasonable in practical applications. The main purpose of this paper is to find a more precise and appropriate comparison method so that we can deal with multi-criteria decision-making problems more efficiently. We first propose a chart technique to analyze the structure of a probabilistic hesitant fuzzy element. After that, we propose a novel possibility degree formula to rank probabilistic hesitant fuzzy elements. Last but not least, we provide a useful process to solve the actual multi-criteria decision-making problems, and make a real case study which demonstrates that our method is feasible and reliable.

]]>Symmetry doi: 10.3390/sym10050176

Authors: Muhammed Turhan Dönüş Şengür Songül Karabatak Yanhui Guo Florentin Smarandache

In the recent years, school administrators often come across various problems while teaching, counseling, and promoting and providing other services which engender disagreements and interpersonal conflicts between students, the administrative staff, and others. Action learning is an effective way to train school administrators in order to improve their conflict-handling styles. In this paper, a novel approach is used to determine the effectiveness of training in school administrators who attended an action learning course based on their conflict-handling styles. To this end, a Rahim Organization Conflict Inventory II (ROCI-II) instrument is used that consists of both the demographic information and the conflict-handling styles of the school administrators. The proposed method uses the Neutrosophic Set (NS) and Support Vector Machines (SVMs) to construct an efficient classification scheme neutrosophic support vector machine (NS-SVM). The neutrosophic c-means (NCM) clustering algorithm is used to determine the neutrosophic memberships and then a weighting parameter is calculated from the neutrosophic memberships. The calculated weight value is then used in SVM as handled in the Fuzzy SVM (FSVM) approach. Various experimental works are carried in a computer environment out to validate the proposed idea. All experimental works are simulated in a MATLAB environment with a five-fold cross-validation technique. The classification performance is measured by accuracy criteria. The prediction experiments are conducted based on two scenarios. In the first one, all statements are used to predict if a school administrator is trained or not after attending an action learning program. In the second scenario, five independent dimensions are used individually to predict if a school administrator is trained or not after attending an action learning program. According to the obtained results, the proposed NS-SVM outperforms for all experimental works.

]]>Symmetry doi: 10.3390/sym10050175

Authors: Min-jae Kim Whoi-Yul Kim Joonki Paik

Sweat pores on the human fingertip have meaningful patterns that enable individual identification. Although conventional automatic fingerprint identification systems (AFIS) have mainly employed the minutiae features to match fingerprints, there has been minimal research that uses sweat pores to match fingerprints. Recently, high-resolution optical sensors and pore-based fingerprint systems have become available, which motivates research on pore analysis. However, most existing pore-based AFIS methods use the minutia-ridge information and image pixel distribution, which limit their applications. In this context, this paper presents a stable pore matching algorithm which effectively removes both the minutia-ridge and fingerprint-device dependencies. Experimental results show that the proposed pore matching algorithm is more accurate for general fingerprint images and robust under noisy conditions compared with existing methods. The proposed method can be used to improve the performance of AFIS combined with the conventional minutiae-based methods. Since sweat pores can also be observed using various systems, removing of the fingerprint-device dependency will make the pore-based AFIS useful for wide applications including forensic science, which matches the latent fingerprint to the fingerprint image in databases.

]]>Symmetry doi: 10.3390/sym10050174

Authors: Songtao Shao Xiaohong Zhang Chunxin Bo Florentin Smarandache

The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fuzzy filters are proved.

]]>Symmetry doi: 10.3390/sym10050173

Authors: Muhammad Imran Muhammad Kamran Siddiqui Muhammad Naeem Muhammad Azhar Iqbal

The utilizations of graph theory in chemistry and in the study of molecule structures are more than someone&rsquo;s expectations, and, lately, it has increased exponentially. In molecular graphs, atoms are denoted by vertices and bonds by edges. In this paper, we focus on the molecular graph of (2D) silicon-carbon S i 2 C 3 -I and S i 2 C 3 - I I . Moreover, we have computed topological indices, namely general Randić Zagreb types indices, geometric arithmetic index, atom&ndash;bond connectivity index, fourth atom&ndash;bond connectivity and fifth geometric arithmetic index of S i 2 C 3 -I and S i 2 C 3 - I I .

]]>Symmetry doi: 10.3390/sym10050172

Authors: Li Li Runtong Zhang Jun Wang Xiaopu Shang Kaiyuan Bai

The proposed q-rung orthopair fuzzy set (q-ROFS) and picture fuzzy set (PIFS) are two powerful tools for depicting fuzziness and uncertainty. This paper proposes a new tool, called q-rung picture linguistic set (q-RPLS) to deal with vagueness and impreciseness in multi-attribute group decision-making (MAGDM). The proposed q-RPLS takes full advantages of q-ROFS and PIFS and reflects decision-makers&rsquo; quantitative and qualitative assessments. To effectively aggregate q-rung picture linguistic information, we extend the classic Heronian mean (HM) to q-RPLSs and propose a family of q-rung picture linguistic Heronian mean operators, such as the q-rung picture linguistic Heronian mean (q-RPLHM) operator, the q-rung picture linguistic weighted Heronian mean (q-RPLWHM) operator, the q-rung picture linguistic geometric Heronian mean (q-RPLGHM) operator, and the q-rung picture linguistic weighted geometric Heronian mean (q-RPLWGHM) operator. The prominent advantage of the proposed operators is that the interrelationship between q-rung picture linguistic numbers (q-RPLNs) can be considered. Further, we put forward a novel approach to MAGDM based on the proposed operators. We also provide a numerical example to demonstrate the validity and superiorities of the proposed method.

]]>Symmetry doi: 10.3390/sym10050171

Authors: Roman Cherniha Vasyl’ Davydovych John R. King

A generalisation of the Lie symmetry method is applied to classify a coupled system of reaction-diffusion equations wherein the nonlinearities involve arbitrary functions in the limit case in which one equation of the pair is quasi-steady but the other is not. A complete Lie symmetry classification, including a number of the cases characterised as being unlikely to be identified purely by intuition, is obtained. Notably, in addition to the symmetry analysis of the PDEs themselves, the approach is extended to allow the derivation of exact solutions to specific moving-boundary problems motivated by biological applications (tumour growth). Graphical representations of the solutions are provided and a biological interpretation is briefly addressed. The results are generalised on multi-dimensional case under the assumption of the radially symmetrical shape of the tumour.

]]>Symmetry doi: 10.3390/sym10050170

Authors: Yi Zhong Diego Sáez-Chillón Gómez

Mimetic gravity is analysed in the framework of some extensions of general relativity (GR), whereby a function of the Gauss&ndash;Bonnet invariant in four dimensions is considered. By assuming the mimetic condition, the conformal degree of freedom is isolated, and a pressureless fluid naturally arises. Then, the complete set of field equations for mimetic Gauss&ndash;Bonnet gravity is established, and some inflationary models are analysed, for which the corresponding gravitational action is reconstructed. The spectral index and tensor-to-scalar ratio are obtained and compared with observational bounds from Planck and BICEP2/Keck array data. Full agreement with the above data is achieved for several versions of the mimetic Gauss&ndash;Bonnet gravity. Finally, some extensions of Gauss&ndash;Bonnet mimetic gravity are considered, and the possibility of reproducing inflation is also explored.

]]>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&ndash;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&ndash;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).

]]>Symmetry doi: 10.3390/sym10050168

Authors: Kairong Duan Simon Fong Shirley W. I. Siu Wei Song Steven Sheng-Uei Guan

Cloud computing is a new commercial model that enables customers to acquire large amounts of virtual resources on demand. Resources including hardware and software can be delivered as services and measured by specific usage of storage, processing, bandwidth, etc. In Cloud computing, task scheduling is a process of mapping cloud tasks to Virtual Machines (VMs). When binding the tasks to VMs, the scheduling strategy has an important influence on the efficiency of datacenter and related energy consumption. Although many traditional scheduling algorithms have been applied in various platforms, they may not work efficiently due to the large number of user requests, the variety of computation resources and complexity of Cloud environment. In this paper, we tackle the task scheduling problem which aims to minimize makespan by Genetic Algorithm (GA). We propose an incremental GA which has adaptive probabilities of crossover and mutation. The mutation and crossover rates change according to generations and also vary between individuals. Large numbers of tasks are randomly generated to simulate various scales of task scheduling problem in Cloud environment. Based on the instance types of Amazon EC2, we implemented virtual machines with different computing capacity on CloudSim. We compared the performance of the adaptive incremental GA with that of Standard GA, Min-Min, Max-Min , Simulated Annealing and Artificial Bee Colony Algorithm in finding the optimal scheme. Experimental results show that the proposed algorithm can achieve feasible solutions which have acceptable makespan with less computation time.

]]>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.

]]>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 &otimes; Y -modules. Particularly, we examine Kahler modules on X &otimes; Y , and search for the homological size of &Lambda; 2 ( &Omega; 1 ( X &otimes; Y ) ) .

]]>Symmetry doi: 10.3390/sym10050165

Authors: Baoyao Wang Peidong Zhu Yingwen Chen Peng Xun Zhenyu Zhang

The smart grid is a key piece of infrastructure and its security has attracted widespread attention. The false data injection (FDI) attack is one of the important research issues in the field of smart grid security. Because this kind of attack has a great impact on the safe and stable operation of the smart grid, many effective detection methods have been proposed, such as an FDI detector based on the support vector machine (SVM). In this paper, we first analyze the problem existing in the detector based on SVM. Then, we propose a new attack method to reduce the detection effect of the FDI detector based on SVM and give a proof. The core of the method is that the FDI detector based on SVM cannot detect the attack vectors which are specially constructed and can replace the attack vectors into the training set when it is updated. Therefore, the training set is changed and then the next training result will be affected. With the increase of the number of the attack vectors which are injected into the positive space, the hyperplane moves to the side of the negative space, and the detection effect of the FDI detector based on SVM is reduced. Finally, we analyze the impact of different data injection modes for training results. Simulation experiments show that this attack method can impact the effectiveness of the FDI detector based on SVM.

]]>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.

]]>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.

]]>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.

]]>Symmetry doi: 10.3390/sym10050161

Authors: M Ahsan Mohd Idna Bin Idris Ainuddin Bin Abdul Wahab Ihsan Ali Nawsher Khan Mohammed Al-Garwi Atiq Rahman

Cloud computing is intensifying the necessity for searchable encryption (SE) for data protection in cloud storage. SE encrypts data to preserve its confidentiality while offering a secure search facility on the encrypted data. Typical index-based SEs in data sharing scenarios can effectively search secure keyword indexes. However, due to the smaller size of the keyword space, SEs using a public key are susceptible to a Keyword Guessing Attack (KGA) and other statistical information leakage. In this paper, for secure search in a data sharing scenario, we propose Random Searchable enCryption (RanSCrypt) that adds randomness to a transformed keyword to increase its space and aspires to make it irreversible. At the core of the mechanism, two keywords are garbled with randomness, still enabling another party to determine if the two garbled keywords (RanSCrypt’s terms REST and Trapdoor) are the same or not without knowing the actual keywords. As SE in a public key setting suffers from vulnerability to KGA, RanSCrypt transfers into a symmetric key setting with minimum overhead and without losing the features of a data sharing scenario. RanSCrypt also adulterates the search result to add perplexity and provides full control of access only to the data receiver. The receiver can cull out the erroneous results from the search result locally. Finally, we introduce a new type of attack on SE, namely, the Keyword Luring Attack (KLA), and show that RanSCrypt is safe from KLA attack due to adulteration of the result. Our security analysis proves RanSCrypt is invulnerable against KGA and leaks no information.

]]>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.

]]>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.

]]>Symmetry doi: 10.3390/sym10050158

Authors: Mohamed Mussa Azrul Mutalib Roszilah Hamid Sudharshan Raman

This study aimed to determine the reliability of the damage criteria that was adopted by the peak particle velocity (PPV) method and the single degree of freedom (SDOF) approach to assess the damage level of a box-shaped underground tunnel. An advanced arbitrary Lagrangian Eulerian (ALE) technique available in LS-DYNA software was used to simulate a symmetrical underground tunnel that was subjected to a surface detonation. The validation results of peak pressure into the soil revealed a good consistency with the TM5-855-1 manual within differences that were much less than previous numerical studies. The pressure contours revealed that the blast waves travelled into the soil in a hemispherical shape and the peak reflected the pressure of the tunnel that occurred immediately before the incident pressure reached its highest value. The assessment results proved that the criteria of the above methods could efficiently predict the damage level of a box-shaped tunnel under different circumstances of explosive charge weight and lining thickness at a depth of 4 m within slight differences that were observed during van and small delivery truck (SDT) explosions. However, the efficiency of both the methods was varied with the increase of burial depth. Whereas, using the PPV method significantly underestimated or overestimated the damage level of the tunnel, especially during SDT and container explosions with a lining thickness of 250 mm at burial depths of 6 and 8 m, respectively, the damage level that was obtained by the SDOF method greatly matched with the observed failure modes of the tunnel. Furthermore, new boundary conditions and equations were proposed for the damage criteria of the PVV method.

]]>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.

]]>Symmetry doi: 10.3390/sym10050156

Authors: Krzysztof B. Zegadlo Nguyen Viet Hung Aleksandr Ramaniuk Marek Trippenbach Boris A. Malomed

We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two-dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries.

]]>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.

]]>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.

]]>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 &omega; D and draw the &omega; D &minus; &omega; ˙ 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.

]]>Symmetry doi: 10.3390/sym10050152

Authors: Jia Wu Yanlin Tan Zhigang Chen Ming Zhao

In many developing or underdeveloped countries, limited medical resources and large populations may affect the survival of mankind. The research for the medical information system and recommendation of effective treatment methods may improve diagnosis and drug therapy for patients in developing or underdeveloped countries. In this study, we built a system model for the drug therapy, relevance parameter analysis, and data decision making in non-small cell lung cancer. Based on the probability analysis and status decision, the optimized therapeutic schedule can be calculated and selected, and then effective drug therapy methods can be determined to improve relevance parameters. Statistical analysis of clinical data proves that the model of the probability analysis and decision making can provide fast and accurate clinical data.

]]>Symmetry doi: 10.3390/sym10050151

Authors: Hwankuk Kim Taeun Kim Daeil Jang

Since 2016, Mirai and Persirai malware have infected hundreds of thousands of Internet of Things (IoT) devices and created a massive IoT botnet, which caused distributed denial of service (DDoS) attacks. IoT malware targets vulnerable IoT devices, which are vulnerable to security risks. Techniques are needed to prevent IoT devices from being exploited by attackers. However, unlike high-performance PCs, IoT devices are lightweight, low-power, and low-cost, having performance limitations regarding processing and memory, which makes it difficult to install security and anti-malware programs. Recently, several studies have been attempted to quickly search for vulnerable internet-connected devices to solve this real issue. Issues yet to be studied still exist regarding these types of internet-wide scan technologies, such as filtering by security devices and a shortage of collected operating system (OS) information. This paper proposes an intelligent internet-wide scan model that improves IP state scanning with advanced internet protocol (IP) randomization, reactive protocol (port) scanning, and OS fingerprinting scanning, applying k* algorithm in order to find vulnerable IoT devices. Additionally, we describe the experiment&rsquo;s results compared to the existing internet-wide scan technologies, such as ZMap and Shodan. As a result, the proposed model experimentally shows improved performance. Although we improved the ZMap, the throughput per minute (TPM) performance is similar to ZMap without degrading the IP scan throughput and the performance of generating a single IP address is about 118% better than ZMap. In the protocol scan performance experiments, it is about 129% better than the Censys based ZMap, and the performance of OS fingerprinting is better than ZMap, with about 50% accuracy.

]]>Symmetry doi: 10.3390/sym10050150

Authors: Jiangbo Feng Min Li Yansong Li

Rooftop distributed photovoltaic projects have been quickly proposed in China because of policy promotion. Before, the rooftops of the shopping mall had not been occupied, and it was urged to have a decision-making framework to select suitable shopping mall photovoltaic plans. However, a traditional multi-criteria decision-making (MCDM) method failed to solve this issue at the same time, due to the following three defects: the interactions problems between the criteria, the loss of evaluation information in the conversion process, and the compensation problems between diverse criteria. In this paper, an integrated MCDM framework was proposed to address these problems. First of all, the compositive evaluation index was constructed, and the application of decision-making trial and evaluation laboratory (DEMATEL) method helped analyze the internal influence and connection behind each criterion. Then, the interval-valued neutrosophic set was utilized to express the imperfect knowledge of experts group and avoid the information loss. Next, an extended elimination et choice translation reality (ELECTRE) III method was applied, and it succeed in avoiding the compensation problem and obtaining the scientific result. The integrated method used maintained symmetry in the solar photovoltaic (PV) investment. Last but not least, a comparative analysis using Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method and VIKOR method was carried out, and alternative plan X1 ranks first at the same. The outcome certified the correctness and rationality of the results obtained in this study.

]]>Symmetry doi: 10.3390/sym10050149

Authors: Zakir Ullah Zhiwei Xu Zhang Lei Libo Zhang

A novel approach is proposed for the path tracking of a Wheeled Mobile Robot (WMR) in the presence of an unknown lateral slip. Much of the existing work has assumed pure rolling conditions between the wheel and ground. Under the pure rolling conditions, the wheels of a WMR are supposed to roll without slipping. Complex wheel-ground interactions, acceleration and steering system noise are the factors which cause WMR wheel slip. A basic research problem in this context is localization and slip estimation of WMR from a stream of noisy sensors data when the robot is moving on a slippery surface, or moving at a high speed. DecaWave based ranging system and Particle Filter (PF) are good candidates to estimate the location of WMR indoors and outdoors. Unfortunately, wheel-slip of WMR limits the ultimate performance that can be achieved by real-world implementation of the PF, because location estimation systems typically partially rely on the robot heading. A small error in the WMR heading leads to a large error in location estimation of the PF because of its cumulative nature. In order to enhance the tracking and localization performance of the PF in the environments where the main reason for an error in the PF location estimation is angular noise, two methods were used for heading estimation of the WMR (1): Reinforcement Learning (RL) and (2): Location-based Heading Estimation (LHE). Trilateration is applied to DecaWave based ranging system for calculating the probable location of WMR, this noisy location along with PF current mean is used to estimate the WMR heading by using the above two methods. Beside the WMR location calculation, DecaWave based ranging system is also used to update the PF weights. The localization and tracking performance of the PF is significantly improved through incorporating heading error in localization by applying RL and LHE. Desired trajectory information is then used to develop an algorithm for extracting the lateral slip along X- and Y-axis from the PF estimated position of the WMR, the lateral slip along X- and Y-axis is then used to take some corrective measures. Lateral slip information is also used to find the direction along which WMR has to move to get back along the desired trajectory. Simulation results show that our proposed LHE and RL heading estimation methods significantly improve the PF localization and tracking performance on a slippery surface in both indoor and outdoor environments. The simulation results also show that the accurate locations of WMR and desired path information are used to estimate and compensate the lateral slip.

]]>Symmetry doi: 10.3390/sym10050148

Authors: Muhammad Sajid Tamoor Shafique Sohaib Manzoor Faisal Iqbal Hassan Talal Usama Samad Qureshi Imran Riaz

Demographic estimation of human face images involves estimation of age group, gender, and race, which finds many applications, such as access control, forensics, and surveillance. Demographic estimation can help in designing such algorithms which lead to better understanding of the facial aging process and face recognition. Such a study has two parts—demographic estimation and subsequent face recognition and retrieval. In this paper, first we extract facial-asymmetry-based demographic informative features to estimate the age group, gender, and race of a given face image. The demographic features are then used to recognize and retrieve face images. Comparison of the demographic estimates from a state-of-the-art algorithm and the proposed approach is also presented. Experimental results on two longitudinal face datasets, the MORPH II and FERET, show that the proposed approach can compete the existing methods to recognize face images across aging variations.

]]>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.

]]>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&rsquo; 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.

]]>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.

]]>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.

]]>Symmetry doi: 10.3390/sym10050143

Authors: Li Xu Bing Luo Zheng Pei Keyun Qin

In this paper, we propose a particle-filter-based superpixel (PFS) segmentation method that extends the original tracking problem as a region clustering problem. The basic idea is to approximate superpixel centers by multiple particles to obtain high intra-region similarity. Specifically, we firstly use a density cluster to initialize single-group particles and introduce the association rule for mining other initial candidate particles. In propagation, particles are transferred to neighboring local regions by a moving step aiming to update local candidate particles with a lower energy cost. We evaluate all particles on the basis of their cluster similarity and estimate the largest particles as the final superpixel centers. The proposed method can locate cluster centers in diverse feature space, which alleviates the risk of a local optimum and produces better segmentation performance. Experimental results on the Berkeley segmentation 500 dataset (BSD500) demonstrate that our method outperforms seven state-of-the-art methods.

]]>Symmetry doi: 10.3390/sym10050142

Authors: Lu Wu Quan Liu

Objects in images are characterized by intra-class variation, inter-class diversity, and noisy images. These characteristics pose a challenge to object localization. To address this issue, we present a novel joint Bayesian model for weakly-supervised object localization. The differences compared to previous discriminative methods are evaluated in three aspects: (1) We co-localize the similar object per class through transferring shared parts, which are pooling by modeling object, parts and features within and between-class; (2) Labels are given at class level to provide strong supervision for features and corresponding parts; (3) Noisy images are considered by leveraging a constraint on the detection of shared parts. In addition, our methods are evaluated by extensive experiments. The results indicated outperformance of the state-of-the-art approaches with almost 7% and 1.5% improvements in comparison to the previous methods on PASCAL VOC 2007 6 &times; 2 and Object Discovery datasets, respectively.

]]>Symmetry doi: 10.3390/sym10050141

Authors: Abdul Jaleel Shazia Arshad Muhammad Shoaib

Autonomic computing embeds self-management features in software systems using external feedback control loops, i.e., autonomic managers. In existing models of autonomic computing, adaptive behaviors are defined at the design time, autonomic managers are statically configured, and the running system has a fixed set of self-* capabilities. An autonomic computing design should accommodate autonomic capability growth by allowing the dynamic configuration of self-* services, but this causes security and integrity issues. A secure, scalable and elastic autonomic computing system (SSE-ACS) paradigm is proposed to address the runtime inclusion of autonomic managers, ensuring secure communication between autonomic managers and managed resources. Applying the SSE-ACS concept, a layered approach for the dynamic adaptation of self-* services is presented with an online &lsquo;Autonomic_Cloud&rsquo; working as the middleware between Autonomic Managers (offering the self-* services) and Autonomic Computing System (requiring the self-* services). A stock trading and forecasting system is used for simulation purposes. The security impact of the SSE-ACS paradigm is verified by testing possible attack cases over the autonomic computing system with single and multiple autonomic managers running on the same and different machines. The common vulnerability scoring system (CVSS metric) shows a decrease in the vulnerability severity score from high (8.8) for existing ACS to low (3.9) for SSE-ACS. Autonomic managers are introduced into the system at runtime from the Autonomic_Cloud to test the scalability and elasticity. With elastic AMs, the system optimizes the Central Processing Unit (CPU) share resulting in an improved execution time for business logic. For computing systems requiring the continuous support of self-management services, the proposed system achieves a significant improvement in security, scalability, elasticity, autonomic efficiency, and issue resolving time, compared to the state-of-the-art approaches.

]]>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.

]]>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.

]]>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&rsquo; 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.

]]>Symmetry doi: 10.3390/sym10050137

Authors: Katy L. Chubb Per Jensen Sergei N. Yurchenko

A numerical application of linear-molecule symmetry properties, described by the D &infin; 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 Schr&ouml;dinger equations of linear molecules. Their implementation into the symmetrisation procedure based on a set of &ldquo;reduced&rdquo; 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 &infin; h point group symmetry to illustrate the symmetrisation procedure of the variational nuclear motion program Theoretical ROVibrational Energies (TROVE).

]]>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.

]]>Symmetry doi: 10.3390/sym10050135

Authors: Siqi Liu Boliang Lin Jiaxi Wang Jianping Wu

Classification yards are crucial nodes of railway freight transportation network, which plays a vital role in car flow reclassification and new train formation. Generally, a modern yard covers an expanse of several square kilometers and costs billions of Chinese Yuan (CNY), i.e., hundreds of millions of dollars. The determination of location and size of classification yards in multiple periods is not only related to yard establishment or improvement cost, but also involved with train connection service (TCS) plan. This paper proposes a bi-level programming model for the multi-period and multi-classification-yard location (MML) problem. The upper-level is intended to find an optimal combinatorial investment strategy for candidate nodes throughout the planning horizon, and the lower-level aims to obtain a railcar reclassification plan with minimum operation cost on the basis of the strategy given by the upper-level. The model is constrained by budget, classification capacity, the number of available tracks, etc. A numerical study is then performed to evaluate the validity and effectiveness of the model.

]]>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.

]]>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.

]]>Symmetry doi: 10.3390/sym10050132

Authors: Muhammad Aslam

The theory of classical statistics assumes crisp, certain, and clear observations/parameters in engineering applications. However, in such engineering applications, due to their complex functions, it may not possible to obtain clear or crisp values of certain parameters. So, there is a chance of obtaining indeterminate, imprecise, vague, and incomplete parameters. In this situation, neutrosophic statistics can be applied, which is the generalization of classical statistics. This is reduced to classical statistics when no parameters are found to be indeterminate, imprecise, vague, or incomplete in actual practice. In this paper, we design a new sampling plan using the neutrosophic approach for the process loss function. The neutrosophic non-linear problem is given and applied to determine the neutrosophic plan parameters of the proposed sampling plan. A table is given and discussed with the help of factory data.

]]>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.

]]>