Symmetry doi: 10.3390/sym10080342

Authors: Behrooz Hosseini Kourosh Kiani

Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on some of the prevalent datasets. In the first step of this algorithm, the input data is divided into partitions using a Bayesian type of Locality Sensitive Hashing (LSH). Partitioning makes the processing fully parallel and much simpler by avoiding unneeded calculations. Each of the proposed algorithm steps is completely independent of the others and no serial bottleneck exists all over the clustering procedure. Locality preservation also filters out the outliers and enhances the robustness of the proposed approach. Density is defined on the basis of Ordered Weighted Averaging (OWA) distance which makes clusters more homogenous. According to the density of each node, the local density peaks will be detected adaptively. By merging the local peaks, final cluster centers will be obtained and other data points will be a member of the cluster with the nearest center. The proposed method has been implemented and compared with similar recently published researches. Cluster validity indexes achieved from the proposed method shows its superiorities in precision and noise robustness in comparison with recent researches. Comparison with similar approaches also shows superiorities of the proposed method in scalability, high performance, and low computation cost. The proposed method is a general clustering approach and it has been used in gene expression clustering as a sample of its application.

]]>Symmetry doi: 10.3390/sym10080341

Authors: Aliyu Isa Aliyu Mustafa Inc Abdullahi Yusuf Dumitru Baleanu

In this work, we study the completely integrable sixth-order nonlinear Ramani equation. By applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system of one-dimensional sub-algebras of the equation are derived. The optimal system is further used to derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli sub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary differential equations (ODEs) obtained from the symmetry reduction. We show that the equation is nonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries by invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical interpretations of the acquired results.

]]>Symmetry doi: 10.3390/sym10080340

Authors: Jinrui Chen Kesheng Liu Xuehu Yan Lintao Liu Xuan Zhou Longdan Tan

Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all random factors of an SIS scheme are utilized for achieving small sizes of shadow images. Most of the studies in this area suffer from an inevitable problem: auxiliary encryption is crucial in ensuring the security of those schemes. In this paper, an SIS scheme with small-sized shadow images based on the Chinese remainder theorem (CRT) is proposed. The size of shadow images can be reduced to nearly 1 / k of the original secret image. By adding random bits to binary representations of the random factors in the CRT, auxiliary encryption is not necessary for this scheme. Additionally, reasonable modifications of the random factors make it possible to incorporate all advantages of the CRT as well, including a ( k , n ) threshold, lossless recovery, and low computation complexity. Analyses and experiments are provided to demonstrate the effectiveness of the proposed scheme.

]]>Symmetry doi: 10.3390/sym10080339

Authors: Yi-Fang Chen Hui-Chin Tang

We consider the constrained ordered weighted averaging (OWA) aggregation problem with a single constraint and lower bounded variables. For the three-dimensional constrained OWA aggregation problem with lower bounded variables, we present four types of solution(x1',x2',x3') depending on the number of zero elements. According to the computerized experiment we perform, the lower bounds can affect the solution(x1',x2',x3') types, thereby affecting the optimal solution of the three-dimensional constrained OWA aggregation problem with lower bounded variables.

]]>Symmetry doi: 10.3390/sym10080338

Authors: Kanghuai Liu Zhigang Chen Jia Wu Leilei Wang

At the dawn of big data and 5G networks, end-to-end communication with large amounts of data between mobile devices is difficult to be implemented through the traditional face-to-face transmission mechanism in social networks. Consequently, opportunistic social networks proposed that message applications should choose proper relay nodes to perform effective data transmission processes. At present, several routing algorithms, based on node similarity, attempt to use the contextual information related to nodes and the special relationships between them to select a suitable relay node among neighbors. However, when evaluating the similarity degree between a pair of nodes, most existing algorithms in opportunistic social networks pay attention to only a few similar factors, and even ignore the importance of mobile similarity in the data transmission process. To improve the transmission environment, this study establishes a fuzzy routing-forwarding algorithm (FCNS) exploiting comprehensive node similarity (the mobile and social similarities) in opportunistic social networks. In our proposed scheme, the transmission preference of the node is determined through the fuzzy evaluation of mobile and social similarities. The suitable message delivery decision is made by collecting and comparing the transmission preference of nodes, and the sustainable and stable data transmission process is performed through the feedback mechanism. Through simulations and the comparison of social network algorithms, the delivery ratio in the proposed algorithm is 0.85 on average, and the routing delay and network overhead of this algorithm are always the lowest.

]]>Symmetry doi: 10.3390/sym10080337

Authors: Chiu Shih Li

A novel global harmony search (NGHS) algorithm, as proposed in 2010, is an improved algorithm that combines the harmony search (HS), particle swarm optimization (PSO), and a genetic algorithm (GA). Moreover, the fixed parameter of mutation probability was used in the NGHS algorithm. However, appropriate parameters can enhance the searching ability of a metaheuristic algorithm, and their importance has been described in many studies. Inspired by the adjustment strategy of the improved harmony search (IHS) algorithm, a dynamic adjusting novel global harmony search (DANGHS) algorithm, which combines NGHS and dynamic adjustment strategies for genetic mutation probability, is introduced in this paper. Moreover, extensive computational experiments and comparisons are carried out for 14 benchmark continuous optimization problems. The results show that the proposed DANGHS algorithm has better performance in comparison with other HS algorithms in most problems. In addition, the proposed algorithm is more efficient than previous methods. Finally, different strategies are suitable for different situations. Among these strategies, the most interesting and exciting strategy is the periodic dynamic adjustment strategy. For a specific problem, the periodic dynamic adjustment strategy could have better performance in comparison with other decreasing or increasing strategies. These results inspire us to further investigate this kind of periodic dynamic adjustment strategy in future experiments.

]]>Symmetry doi: 10.3390/sym10080336

Authors: Jie Liu Hui Tian Chin-Chen Chang Tian Wang Yonghong Chen Yiqiao Cai

This paper concentrates on the detection of steganography in inactive frames of low bit rate audio streams in Voice over Internet Protocol (VoIP) scenarios. Both theoretical and experimental analyses demonstrate that the distribution of 0 and 1 in encoding parameter bits becomes symmetric after a steganographic process. Moreover, this symmetry affects the frequency of each subsequence of parameter bits, and accordingly changes the poker test statistical features of encoding parameter bits. Employing the poker test statistics of each type of encoding parameter bits as detection features, we present a steganalysis method based on a support vector machine. We evaluate the proposed method with a large quantity of speech samples encoded by G.723.1 and compare it with the entropy test. The experimental results show that the proposed method is effective, and largely outperforms the entropy test in any cases.

]]>Symmetry doi: 10.3390/sym10080335

Authors: J. A. López-Campos A. Segade E. Casarejos J. R. Fernández J. A. Vilán P. Izquierdo

This paper studies the stress state of a threaded fastening by using Finite Element (FE) models, applied to surgical screws in cortical bone. There is a general interest in studying the stress states induced in the different elements of a joint caused by the thread contact. Analytical models were an initial approach, and later FE models allowed detailed studies of the complex phenomena related to these joints. Different studies have evaluated standard threaded joints in machinery and structures, being the thread symmetric. However, surgical screws employ asymmetric thread geometry, selected to improve the stress level generated in the bone. Despite the interest and widespread use, there is scarce documentation on the actual effect of this thread type. In this work, we discuss the results provided by FE models with detailed descriptions of the contacts comparing differences caused by the materials of the joint, the thread geometry and the thread&rsquo;s three-dimensional helical effects. The complex contacts at the threaded surfaces cause intense demand on computational resources that often limits the studies including these joints. We analyze the results provided by one commercial software package to simplify the threaded joints. The comparison with detailed FE models allows a definition of the level of uncertainty and possible limitations of this type of simplifications, and helps in making suitable choices for complex applications.

]]>Symmetry doi: 10.3390/sym10080334

Authors: Francesco Naddeo Alessandro Naddeo Nicola Cappetti Emilio Cataldo Riccardo Militio

In this article, the authors propose a novel procedure for designing a customized 3D-printed surgical template to guide surgeons in inserting screws into the sacral zone during arthrodesis surgeries. The template is characterized by two cylindrical guides defined by means of trajectories identified, based on standard procedure, via an appropriate Computer-Aided-Design (CAD)-based procedure. The procedure is based on the definition of the insertion direction by means of anatomical landmarks that enable the screws to take advantage of the maximum available bone path. After 3D printing, the template adheres perfectly to the bone surface, showing univocal positioning by exploiting the foramina of the sacrum, great maneuverability due to the presence of an ergonomic handle, as well as a break system for the two independent guides. These features make the product innovative. Thanks to its small size and the easy anchoring, the surgeon can simply position the template on the insertion area and directly insert the screws, without alterations to standard surgical procedures. This has the effect of reducing the overall duration of the surgery and the patient&rsquo;s exposure to X-rays, and increasing both the safety of the intervention and the quality of the results.

]]>Symmetry doi: 10.3390/sym10080333

Authors: Jinyan Wang Guoqing Cai Chen Liu Jingli Wu Xianxian Li

Nowadays, more and more applications are dependent on storage and management of semi-structured information. For scientific research and knowledge-based decision-making, such data often needs to be published, e.g., medical data is released to implement a computer-assisted clinical decision support system. Since this data contains individuals’ privacy, they must be appropriately anonymized before to be released. However, the existing anonymization method based on l-diversity for hierarchical data may cause serious similarity attacks, and cannot protect data privacy very well. In this paper, we utilize fuzzy sets to divide levels for sensitive numerical and categorical attribute values uniformly (a categorical attribute value can be converted into a numerical attribute value according to its frequency of occurrences), and then transform the value levels to sensitivity levels. The privacy model ( α l e v h , k)-anonymity for hierarchical data with multi-level sensitivity is proposed. Furthermore, we design a privacy-preserving approach to achieve this privacy model. Experiment results demonstrate that our approach is obviously superior to existing anonymous approach in hierarchical data in terms of utility and security.

]]>Symmetry doi: 10.3390/sym10080332

Authors: Muhammad Fazil Muhammad Murtaza Zafar Ullah Usman Ali Imran Javaid

Let G 1 and G 2 be disjoint copies of a graph G and g : V ( G 1 ) &rarr; V ( G 2 ) be a function. A functigraph F G consists of the vertex set V ( G 1 ) &cup; V ( G 2 ) and the edge set E ( G 1 ) &cup; E ( G 2 ) &cup; { u v : g ( u ) = v } . In this paper, we extend the study of distinguishing numbers of a graph to its functigraph. We discuss the behavior of distinguishing number in passing from G to F G and find its sharp lower and upper bounds. We also discuss the distinguishing number of functigraphs of complete graphs and join graphs.

]]>Symmetry doi: 10.3390/sym10080331

Authors: Raja Muhammad Hashim Muhammad Gulistan Florentin Smarandache

In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life&rsquo;s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets. After giving the definition we introduce some basic operation of neutrosophic bipolar fuzzy sets and focus on weighted aggregation operators in terms of neutrosophic bipolar fuzzy sets. We define neutrosophic bipolar fuzzy weighted averaging ( N B FWA ) and neutrosophic bipolar fuzzy ordered weighted averaging ( N B FOWA ) operators. Next we introduce different kinds of similarity measures of neutrosophic bipolar fuzzy sets. Finally as an application we give an algorithm for the multiple attribute decision making problems under the neutrosophic bipolar fuzzy environment by using the different kinds of neutrosophic bipolar fuzzy weighted/fuzzy ordered weighted aggregation operators with a numerical example related with HOPE foundation.

]]>Symmetry doi: 10.3390/sym10080330

Authors: Wenhua Cui Jun Ye

Linguistic neutrosophic numbers (LNNs) are a powerful tool for describing fuzzy information with three independent linguistic variables (LVs), which express the degrees of truth, uncertainty, and falsity, respectively. However, existing LNNs cannot depict the hesitancy of the decision-maker (DM). To solve this issue, this paper first defines a hesitant linguistic neutrosophic number (HLNN), which consists of a few LNNs regarding an evaluated object due to DMs&rsquo; hesitancy to represent their hesitant and uncertain information in the decision-making process. Then, based on the least common multiple cardinality (LCMC), we present generalized distance and similarity measures of HLNNs, and then develop a similarity measure-based multiple-attribute decision-making (MADM) method to handle the MADM problem in the HLNN setting. Finally, the feasibility of the proposed approach is verified by an investment decision case.

]]>Symmetry doi: 10.3390/sym10080329

Authors: Jiufei Luo Haitao Xu Kai Zheng Xinyi Li Song Feng

Asymmetric windows are of increasing interest to researchers because of the nonlinear and adjustable phase response, as well as alterable time delay. Short-time phase distortion can provide an essential improvement in speech coding, and also has better performance in speech recognition. The merits of asymmetric windows in the aspect of spectral behaviors have an important function in frequency component detection and parameter estimation. In this paper, the phase response of windows were further studied, and the phase characteristics of symmetric and asymmetric windows are described. The relationship between the barycenter of windows in the time domain, and the phase characteristic at the center of the main lobe in the frequency domain, was established. In light of the relationship, an improved version of the asymmetric window- based frequency estimation algorithm was proposed. The improved algorithm has advantages of straightforward implementation and computational efficiency. The numeric simulation results also indicate that the improved approach is more robust than the traditional method against additive random noise.

]]>Symmetry doi: 10.3390/sym10080328

Authors: Yuxin Sun Shoubin Liu Zhangheng Rao Yuhang Li Jialing Yang

In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green&rsquo;s function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail.

]]>Symmetry doi: 10.3390/sym10080327

Authors: Avishek Chakraborty Sankar Prasad Mondal Ali Ahmadian Norazak Senu Shariful Alam Soheil Salahshour

In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.

]]>Symmetry doi: 10.3390/sym10080326

Authors: Jihyun Choi Jae-Hyouk Lee

In this article, we have an explicit description of the binary isosahedral group as a 600-cell. We introduce a method to construct binary polyhedral groups as a subset of quaternions H via spin map of SO(3). In addition, we show that the binary icosahedral group in H is the set of vertices of a 600-cell by applying the Coxeter&ndash;Dynkin diagram of H4.

]]>Symmetry doi: 10.3390/sym10080325

Authors: Yilun Shang

Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by &lambda;1,&lambda;2,⋯,&lambda;n. The Gaussian Estrada index, denoted by H(G) (Estrada et al., Chaos 27(2017) 023109), can be defined as H(G)=&sum;i=1ne&minus;&lambda;i2. Gaussian Estrada index underlines the eigenvalues close to zero, which plays an important role in chemistry reactions, such as molecular stability and molecular magnetic properties. In a network of particles governed by quantum mechanics, this graph-theoretic index is known to account for the information encoded in the eigenvalues of the Hamiltonian near zero by folding the graph spectrum. In this paper, we establish some new lower bounds for H(G) in terms of the number of vertices, the number of edges, as well as the first Zagreb index.

]]>Symmetry doi: 10.3390/sym10080324

Authors: Dabuxilatu Wang Liang Zhang

Autoregressive moving average (ARMA) models are important in many fields and applications, although they are most widely applied in time series analysis. Expanding the ARMA models to the case of various complex data is arguably one of the more challenging problems in time series analysis and mathematical statistics. In this study, we extended the ARMA model to the case of linguistic data that can be modeled by some symmetric fuzzy sets, and where the relations between the linguistic data of the time series can be considered as the ordinary stochastic correlation rather than fuzzy logical relations. Therefore, the concepts of set-valued or interval-valued random variables can be employed, and the notions of Aumann expectation, Fr&eacute;chet variance, and covariance, as well as standardized process, were used to construct the ARMA model. We firstly determined that the estimators from the least square estimation of the ARMA (1,1) model under some L2 distance between two sets are weakly consistent. Moreover, the justified linguistic data-valued ARMA model was applied to forecast the linguistic monthly Hang Seng Index (HSI) as an empirical analysis. The obtained results from the empirical analysis indicate that the accuracy of the prediction produced from the proposed model is better than that produced from the classical one-order, two-order, three-order autoregressive (AR(1), AR(2), AR(3)) models, as well as the (1,1)-order autoregressive moving average (ARMA(1,1)) model.

]]>Symmetry doi: 10.3390/sym10080323

Authors: V. A. Shestakov M. M. Korshunov O. V. Dolgov

We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the s&plusmn; state with sign-changing gaps. Scattering by nonmagnetic impurities leads to the change of the sign of the smaller gap, resulting in a transition from the s&plusmn; to the s++ state with the sign-preserving gaps. We show here that the transition is temperature-dependent. Thus, there is a line of s&plusmn;&rarr;s++ transition in the temperature&ndash;disorder phase diagram. There is a narrow range of impurity scattering rates, where the disorder-induced s&plusmn;&rarr;s++ transition occurs at low temperatures, but then the low-temperature s++ state transforms back to the s&plusmn; state at higher temperatures. With increasing impurity scattering rate, the temperature of such s++&rarr;s&plusmn; transition shifts to the critical temperature Tc, and only the s++ state is left for higher amounts of disorder.

]]>Symmetry doi: 10.3390/sym10080322

Authors: Raúl M. Falcón Óscar J. Falcón Juan Núñez

In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard.

]]>Symmetry doi: 10.3390/sym10080321

Authors: Mehmet Çelik Moges Mekonnen Shalla Necati Olgun

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

]]>Symmetry doi: 10.3390/sym10080320

Authors: Young Chel Kwun Abaid ur Rehman Virk Waqas Nazeer M. A. Rehman Shin Min Kang

The application of graph theory in chemical and molecular structure research has far exceeded people&rsquo;s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3&minus;I[p,q] and Si2C3&minus;II[p,q] second.

]]>Symmetry doi: 10.3390/sym10080319

Authors: Yuhou Wang Ying Dong Shiyuan Li Hao Wu Mengyao Cui

With the development of wireless sensor networks (WSNs), the problem about how to increase the lifecycle of the WSNs is always a hot discussion point, and some researchers have devoted to the &lsquo;energy saving&rsquo; to decrease the energy consumption of the sensor nodes by different algorithms. However, the fundamental technique is &lsquo;energy acquiring&rsquo; for the battery which can solve the limited capacity problem. In this paper, we study the data gathering and energy charging by a mobile charger (MC) at the same time that most energy consumption can be saved by short communication distance. We have named this as the recharging model-combined recharging and collecting data model on-demand (CRCM). Firstly, the hexagon-based (HB) algorithm is proposed to sort all sensor nodes in the region to make data collecting and energy charging work at the same time. Then we consider both residual energy and geographic position (REGP) of the sensor node to calculate the priority of each cluster. Thirdly, the dynamic mobile charger (DMC) algorithm is proposed to calculate the number of MCs to make sure no sensor node will die in each charging queue. Finally, the simulations show that our REGP algorithm is better than Earliest Deadline First (EDF) and Nearest-Job-Next with Preemption (NJNP), and the DMC plays well when the number of sensor nodes increase.

]]>Symmetry doi: 10.3390/sym10080318

Authors: Wien Hong Xiaoyu Zhou Der-Chyuan Lou Xiaoqin Huang Cancan Peng

Since digital media is gaining popularity nowadays, people are more concerned about its integrity protection and authentication since tampered media may result in unexpected problems. Considering a better media protection technique, this paper proposes an efficient tamper detection scheme for absolute moment block truncation coding (AMBTC) compressed images. In AMBTC, each image block is represented by two quantization levels (QLs) and a bitmap. Requiring insignificant computation cost, it attracts not only a wide range of application developers, but also a variety of studies to investigate the authentication of its codes. While the existing methods protect the AMBTC codes to a large extent, the leakage of some unprotected codes may be insensitive to intentional tampering. The proposed method fully protects the AMBTC codes by embedding authentication codes (ACs) into QLs. Meanwhile, the most significant bits of QLs are symmetrically perturbed to generate the candidates of ACs. The ACs that cause the minimum distortion are embedded into the least significant bits of QLs to minimize the distortion. When compared with prior works, the experimental results reveal that the proposed method offers a significant sensitivity-of-tamper property while providing a comparable image quality.

]]>Symmetry doi: 10.3390/sym10080317

Authors: Muhammad Hanif Zhong Hua Hou Kottakkaran Sooppy Nisar

Recently, extensive research has been done on evolute curves in Minkowski space-time. However, the special characteristics of curves demand advanced level observations that are lacking in existing well-known literature. In this study, a special kind of generalized evolute and involute curve is considered in four-dimensional Minkowski space. We consider (1,3)-evolute curves with respect to the casual characteristics of the (1,3)-normal plane that are spanned by the principal normal and the second binormal of the vector fields and the (0,2)-evolute curve that is spanned by the tangent and first binormal of the given curve. We restrict our investigation of (1,3)-evolute curves to the (1,3)-normal plane in four-dimensional Minkowski space. This research contribution obtains a necessary and sufficient condition for the curve possessing the generalized evolute as well as the involute curve. Furthermore, the Cartan null curve is also discussed in detail.

]]>Symmetry doi: 10.3390/sym10080316

Authors: Yongquan Zhang Hong Lu He Ling Yang Lian Mingtian Ma

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

]]>Symmetry doi: 10.3390/sym10080315

Authors: Huatao Chen Dengqing Cao Jingfei Jiang Xiaoming Fan

Without the assumption that the coefficient of weak damping is large enough, the existence of the global random attractors for simplified Von Karman plate without rotational inertia driven by either additive white noise or multiplicative white noise are proved. Instead of the classical splitting method, the techniques to verify the asymptotic compactness rely on stabilization estimation of the system. Furthermore, a clear relationship between in-plane components of the external force that act on the edge of the plate and the expectation of radius of the global random attractors can be obtained from the theoretical results. Based on the relationship between global random attractor and random probability invariant measure, the global dynamics of the plates are analyzed numerically. With increasing the in-plane components of the external force that act on the edge of the plate, global D-bifurcation, secondary global D-bifurcation and complex local dynamical behavior occur in motion of the system. Moreover, increasing the intensity of white noise leads to the dynamical behavior becoming simple. The results on global dynamics reveal that random snap-through which seems to be a complex dynamics intuitively is essentially a simple dynamical behavior.

]]>Symmetry doi: 10.3390/sym10080314

Authors: Mohsin Khan Le Hoang Son Mumtaz Ali Hoang Thi Minh Chau Nguyen Thi Nhu Na Florentin Smarandache

The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail.

]]>Symmetry doi: 10.3390/sym10080313

Authors: Hidemasa Yamane Satoshi Tanaka

We studied the high-harmonic generation (HHG) of a two-level-system (TLS) driven by an intense monochromatic phase-locked laser based on complex spectral analysis with the Floquet method. In contrast with phenomenological approaches, this analysis deals with the whole process as a coherent quantum process based on microscopic dynamics. We have obtained the time-frequency resolved spectrum of spontaneous HHG single-photon emission from an excited TLS driven by a laser field. Characteristic spectral features of the HHG, such as the plateau and cutoff, are reproduced by the present model. Because the emitted high-harmonic photon is represented as a superposition of different frequencies, the Fano profile appears in the long-time spectrum as a result of the quantum interference of the emitted photon. We reveal that the condition of the quantum interference depends on the initial phase of the driving laser field. We have also clarified that the change in spectral features from the short-time regime to the long-time regime is attributed to the interference between the interference from the Floquet resonance states and the dressed radiation field.

]]>Symmetry doi: 10.3390/sym10080312

Authors: Wei-Shu Hou

The 125 GeV boson is quite consistent with the Higgs boson of the Standard Model (SM), but there is a challenge from Anderson as to whether this particle is in the Lagrangian. As Large Hadron Collider (LHC) Run 2 enters its final year of running, we ought to reflect and make sure we have gotten everything right. The ATLAS and CMS combined Run 1 analysis claimed a measurement of 5.4&sigma; vector boson fusion (VBF) production which is consistent with SM, which seemingly refutes Anderson. However, to verify the source of electroweak symmetry breaking (EWSB), we caution that VBF measurement is too important for us to be imprudent in any way, and gluon&ndash;gluon fusion (ggF) with similar tag jets must be simultaneous measured, which should be achievable in LHC Run 2. The point is to truly test the dilaton possibility&mdash;the pseudo-Goldstone boson of scale invariance violation. We illustrate EWSB by dynamical mass generation of a sequential quark doublet (Q) via its ultrastrong Yukawa coupling and argue how this might be consistent with a 125 GeV dilaton, D. The ultraheavy 2mQ≳4&ndash;5 TeV scale explains the absence of New Physics so far, while the mass generation mechanism shields us from the UV theory for the strong Yukawa coupling. Collider and flavor physics implications are briefly touched upon. Current Run 2 analyses show correlations between the ggF and VBF measurements, but the newly observed tt&macr;H production at LHC poses a challenge.

]]>Symmetry doi: 10.3390/sym10080311

Authors: Lee-Chae Jang Taekyun Kim Dae San Kim Dmitry Victorovich Dolgy

We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Zp and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on Zp of the two variable q-Bernstein polynomials, recently introduced by Kim, and demonstrate that they can be written in terms of the q-analogues of Euler numbers. Further, from such p-adic integrals we will derive some identities for the q-analogues of Euler numbers.

]]>Symmetry doi: 10.3390/sym10080310

Authors: Liangliang Ding Zhenduo Li Fangyun Lu Xiangyu Li

The casing of deformable warheads warps under the action of deforming charges. The deformation profiles may be concave-, convex-, or D-shaped, but they are all symmetrical. The D-shape is considered the optimal deformation profile. The width of the deformed surface affects the number of fragments in the target area. In order to evaluate the deformable surface width of the cylindrical casing, a criterion &alpha; was established and its optimum range was determined as 20 to 30%. Based on our previous theoretical analysis, a MATLAB program that can rapidly evaluate the projectile deformation surface was compiled, which was verified using LS-DYNA and experiments. The laws influencing the deforming charge width on the deformed surface of the filled cylindrical casing were also studied using the MATLAB rapid evaluation program. As the deforming charge width increased, the deformation profile of the casing gradually transferred from &ldquo;inner-concave&rdquo; to the &ldquo;outer-convex&rdquo;. In addition, a formula that can better reflect the relationship between the deforming charge width &phi; and the criterion value &alpha; was fitted and verified. The conclusions obtained in this paper provide rapid guidance for the structural design of deformable warheads.

]]>Symmetry doi: 10.3390/sym10080308

Authors: Kai Wang Xi Zhao Wanshun Gao Jianhua Zou

Facial landmarking locates the key facial feature points on facial data, which provides not only information on semantic facial structures, but also prior knowledge for other kinds of facial analysis. However, most of the existing works still focus on the 2D facial image which may suffer from lighting condition variations. In order to address this limitation, this paper presents a coarse-to-fine approach to accurately and automatically locate the facial landmarks by using deep feature fusion on 3D facial geometry data. Specifically, the 3D data is converted to 2D attribute maps firstly. Then, the global estimation network is trained to predict facial landmarks roughly by feeding the fused CNN (Convolutional Neural Network) features extracted from facial attribute maps. After that, input the local fused CNN features extracted from the local patch around each landmark estimated previously, and other local models are trained separately to refine the locations. Tested on the Bosphorus and BU-3DFE datasets, the experimental results demonstrated effectiveness and accuracy of the proposed method for locating facial landmarks. Compared with existed methods, our results have achieved state-of-the-art performance.

]]>Symmetry doi: 10.3390/sym10080309

Authors: Lambert Jorba Romà Adillon

In this paper, we bring together two concepts related to uncertainty and vagueness: fuzzy numbers and intervals. With them, we build a new structure whose elements we call interval fuzzy segments. We have undertaken this based on the conviction that the fuzzy numbers are a correct representation of the real numbers under situations of indeterminacy. We also believe that if it makes sense to consider the set of real numbers between two real bounds, then it also makes sense to consider the set of all the fuzzy numbers between two fuzzy number bounds. In this way, we extend the concept of real interval to the concept of interval fuzzy segment defined by two fuzzy bounds and a transition mapping that leads from the lower fuzzy bound to the upper fuzzy bound and this transition mapping generates the set of all the fuzzy numbers comprised between those fuzzy bounds. At the same time, this transition mapping brings the concept of interval fuzzy segment closer to the concept of line segment.

]]>Symmetry doi: 10.3390/sym10080307

Authors: Francisco Mesa Raúl Rodríguez-Berral Francisco Medina

A critical discussion on the computation of the dispersion diagram of electromagnetic guiding/radiating structures with one-dimensional periodicity using general-purpose electromagnetic simulation software is presented in this work. In these methods, full-wave simulations of finite sections of the periodic structure are combined with appropriate simplifying network models. In particular, we analyze the advantages and limitations of two different combined methods, with emphasis on the determination of their range of validity. Our discussion is complemented with several selected numerical examples in order to show the most relevant aspects that a potential user of these methods should be aware of. Special attention is paid to the relevant role played by the high-order coupling between adjacent unit cells and between the two halves of unit cells exhibiting reflection, inversion, and glide symmetries.

]]>Symmetry doi: 10.3390/sym10080306

Authors: Francisco Cavas-Martínez Daniel G. Fernández-Pacheco Francisco J. F. Cañavate Jose S. Velázquez-Blázquez Jose M. Bolarín Jorge L. Alió

The validation of new methods for the diagnosis of incipient cases of Keratoconus (KC) with mild visual limitation is of great interest in the field of ophthalmology. During the asymmetric progression of the disease, the current diagnostic indexes do not record the geometric decompensation of the corneal curvature nor the variation of the spatial profile that occurs in singular points of the cornea. The purpose of this work is to determine the structural characterization of the asymmetry of the disease by using morpho-geometric parameters in KC eyes with mild visual limitation including using an analysis of a patient-specific virtual model with the aid of computer-aided design (CAD) tools. This comparative study included 80 eyes of patients classified as mild KC according to the degree of visual limitation and a control group of 122 eyes of normal patients. The metric with the highest area under the receiver operating characteristic (ROC) curve was the posterior apex deviation. The most prominent correlation was found between the anterior and posterior deviations of the thinnest point for the mild keratoconic cases. This new custom computational approach provides the clinician with a three-dimensional view of the corneal architecture when the visual loss starts to impair.

]]>Symmetry doi: 10.3390/sym10080305

Authors: Siniša Sremac Željko Stević Dragan Pamučar Miloš Arsić Bojan Matić

For companies active in various sectors, the implementation of transport services and other logistics activities has become one of the key factors of efficiency in the total supply chain. Logistics outsourcing is becoming more and more important, and there is an increasing number of third party logistics providers. In this paper, logistics providers were evaluated using the Rough SWARA (Step-Wise Weight Assessment Ratio Analysis) and Rough WASPAS (Weighted Aggregated Sum Product Assessment) models. The significance of the eight criteria on the basis of which evaluation was carried out was determined using the Rough SWARA method. In order to allow for a more precise consensus in group decision-making, the Rough Dombi aggregator was developed in order to determine the initial rough matrix of multi-criteria decision-making. A total of 10 logistics providers dealing with the transport of dangerous goods for chemical industry companies were evaluated using the Rough WASPAS approach. The obtained results demonstrate that the first logistics provider is also the best one, a conclusion confirmed by a sensitivity analysis comprised of three parts. In the first part, parameter &rho; was altered through 10 scenarios in which only alternatives four and five change their ranks. In the second part of the sensitivity analysis, a calculation was performed using the following approaches: Rough SAW (Simple Additive Weighting), Rough EDAS (Evaluation Based on Distance from Average Solution), Rough MABAC (MultiAttributive Border Approximation Area Comparison), and Rough TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). They showed a high correlation of ranks determined by applying Spearman&rsquo;s correlation coefficient in the third part of the sensitivity analysis.

]]>Symmetry doi: 10.3390/sym10080304

Authors: Shanqing Zhang Pengcheng Li Xianghua Xu Li Li Ching-Chun Chang

Blur is an important factor affecting the image quality. This paper presents an efficient no-reference (NR) image blur assessment method based on a response function of singular values. For an image, the grayscale image is computed to the acquire spatial information. In the meantime, the gradient map is computed to acquire the shape information, and the saliency map can be obtained by using scale-invariant feature transform (SIFT). Then, the grayscale image, the gradient map, and the saliency map are divided into blocks of the same size. The blocks of the gradient map are converted into discrete cosine transform (DCT) coefficients, from which the response function of singular values (RFSV) are generated. The sum of the RFSV are then utilized to characterize the image blur. The variance of the grayscale image and the DCT domain entropy of the gradient map are used to reduce the impact of the image content. The SIFT-dependent weights are calculated in the saliency map, which are assigned to the image blocks. Finally, the blur score is the normalized sum of the RFSV. Extensive experiments are conducted on four synthetic databases and two real blur databases. The experimental results indicate that the blur scores produced by our method are highly correlated with the subjective evaluations. Furthermore, the proposed method is superior to six state-of-the-art methods.

]]>Symmetry doi: 10.3390/sym10080303

Authors: Zhao Jianhong Chen Zhuoyu

The aim of this paper is to use elementary methods and the recursive properties of a special sequence to study the computational problem of one kind symmetric sums involving Fubini polynomials and Euler numbers, and give an interesting computational formula for it. At the same time, we also give a recursive calculation method for the general case.

]]>Symmetry doi: 10.3390/sym10080302

Authors: Frederico Santos Manoel Ferreira

In this work, we reassess two known processes of Quantum Electrodynamics involving electrons and muons. The photon propagator is modified by a CPT-even Lorentz-violating (LV) tensor, while fermion lines and the vertex interaction are not altered. Using the Feynman rules, the associated cross sections for unpolarized scatterings are evaluated, revealing the usual energy dependence and Lorentz-violating contributions that induce space anisotropy. A possible route to constraining the LV coefficients is presented and the results properly commented.

]]>Symmetry doi: 10.3390/sym10080301

Authors: Yuyan Luo Lu Yin Yong Qin Zhong Wang Yanfeng Gong

This paper evaluated the water use efficiency in 12 Chinese western provinces from 2005 to 2015. Based on data availability and the index selection rationality and the slacks-based measure (SBM)-undesirable Window analysis model and the Malmquist productivity index, the water resource inputs and outputs were measured to analyze water use efficiency. Total investment in fixed assets for the whole society and total water, made up of total agricultural water, total industrial water, and total domestic water, were used as the input indexes, and regional GDP and waste water discharge were the output indexes, with the waste water discharge being regarded as an undesirable output. The data from different years and different provinces in the same period, and data from the same year and the same provinces in different periods were compared in order to derive the water resource efficiency and technical changes over time and space. It was found that the total water resource factor productivity in the 12 provinces grew slowly in the study period, that water resource technical progress positively affected water use efficiency, and that a lack of technical efficiency restricted water use efficiency growth. Several suggestions are given to optimize water use efficiency in the 12 provinces. The research findings and suggestions provide valuable reference for studies in related fields.

]]>Symmetry doi: 10.3390/sym10080300

Authors: Zafar Hussain Mobeen Munir Maqbool Chaudhary Shin Min Kang

Concepts of resolving set and metric basis has enjoyed a lot of success because of multi-purpose applications both in computer and mathematical sciences. For a connected graph G(V,E) a subset W of V(G) is a resolving set for G if every two vertices of G have distinct representations with respect to W. A resolving set of minimum cardinality is called a metric basis for graph G and this minimum cardinality is known as metric dimension of G. Boron nanotubes with different lattice structures, radii and chirality&rsquo;s have attracted attention due to their transport properties, electronic structure and structural stability. In the present article, we compute the metric dimension and metric basis of 2D lattices of alpha-boron nanotubes.

]]>Symmetry doi: 10.3390/sym10080299

Authors: Muhammad Asif Shafi Ullah Khan Rashid Ahmad Dhananjay Singh

In recent years, global mobile data traffic has seen an unprecedented increase. This is due to worldwide usage of smart devices, availability of fast internet connections, and the popularity of social media. The Mobile Network Operators (MNOs) are, therefore, facing problems in handling this huge traffic flow. Each type of traffic, including real-time video, audio, and text has its own Quality of Services (QoS) requirements which, if not met, may cause a sufficient loss of profit. Offloading of these traffics can be made more efficient so that values of QoS parameters are enhanced. In this work, we propose an incentive-based game-theoretic frame work for downloading data. The download of each type of data will get an incentive determined by the two-stage Stackelberg game. We model the communication among single Mobile Base Station (MBS) and multiple Access Points (APs) in a crowded metropolitan environment. The leader offers an economic incentive based on the traffic type and followers respond to the incentive and offload traffic accordingly. The model optimizes strategies of both the MBS and APs in order to make the best use of their utilities. For the analysis, we have used a combination of analytical and experimental methods. The numerical outcome characterized a direct process of the best possible offloading ratio and legalized the efficiency of the proposed game. Optimal incentives and optimal offloading was the achievement of our proposed game-theoretic approach. We have implemented the model in MATLAB, and the experimental results show a maximum payoff was achieved and the proposed scheme achieved Nash Equilibria.

]]>Symmetry doi: 10.3390/sym10070298

Authors: David L. Andrews

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

]]>Symmetry doi: 10.3390/sym10070297

Authors: Hee Sik Kim J. Neggers Sun Shin Ahn

In this paper, we discuss some relations between the semigroup, Bin(X), of all groupoids (X,&lowast;) and graphs. We discuss mimimum (mutual) covering sets in several groupoids and discuss distances of graphs with groupoids. Finally, we obtain some results on frame graphs with groupoids.

]]>Symmetry doi: 10.3390/sym10070296

Authors: Chunxin Bo Xiaohong Zhang Songtao Shao Florentin Smarandache

It is an interesting direction to study rough sets from a multi-granularity perspective. In rough set theory, the multi-particle structure was represented by a binary relation. This paper considers a new neutrosophic rough set model, multi-granulation neutrosophic rough set (MGNRS). First, the concept of MGNRS on a single domain and dual domains was proposed. Then, their properties and operators were considered. We obtained that MGNRS on dual domains will degenerate into MGNRS on a single domain when the two domains are the same. Finally, a kind of special multi-criteria group decision making (MCGDM) problem was solved based on MGNRS on dual domains, and an example was given to show its feasibility.

]]>Symmetry doi: 10.3390/sym10070295

Authors: Rui Wang Yanlai Li

To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations are presented, simultaneously. Second, the generalized picture hesitant fuzzy weighted aggregation operators are developed, and some theorems and reduced operators of them are discussed. Third, the generalized picture hesitant fuzzy prioritized weighted aggregation operators are put forward to solve the MCDM problems that the related criteria are at different priorities. Fourth, two novel MCDM methods combined with the proposed operators are constructed to determine the best alternative in real life. Finally, two numerical examples and an application of web service selection are investigated to illustrate the effectiveness of the proposed methods. The sensitivity analysis shows that the different values of the parameter &lambda; affect the ranking of alternatives, and the proposed operators are compared with several existing MCDM methods to illustrate their advantages.

]]>Symmetry doi: 10.3390/sym10070294

Authors: Xiaowei Xue Chunxue Wu Ze Sun Yan Wu Neal N. Xiong

A 3D city model is critical for the construction of a digital city. One of the methods of building a 3D city model is tilt photogrammetry. In this method, oblique photography is crucial for generating the model because the visual quality of photography directly impacts the model&rsquo;s visual effect. Yet, sometimes, oblique photography does not have good visual quality due to a bad season or defective photographic equipment. For example, for oblique photography taken in winter, vegetation is brown. If this photography is employed to generate the 3D model, the result would be bad visually. Yet, common methods for vegetation greening in oblique photography rely on the assistance of the infrared band, which is not available sometimes. Thus, a method for vegetation greening in winter oblique photography without the infrared band is required, which is proposed in this paper. The method was inspired by the work on CycleGAN (Cycle-consistence Adversarial Networks). In brief, the problem of turning vegetation green in winter oblique photography is considered as a style transfer problem. Summer oblique photography generally has green vegetation. By applying CycleGAN, winter oblique photography can be transferred to summer oblique photography, and the vegetation can turn green. Yet, due to the existence of &ldquo;checkerboard artifacts&rdquo;, the original result cannot be applied for real production. To reduce artifacts, the generator of CycleGAN is modified. As the final results suggest, the proposed method unlocks the bottleneck of vegetation greening when the infrared band is not available and artifacts are reduced.

]]>Symmetry doi: 10.3390/sym10070293

Authors: Taiguo Lu Dawei Zhang Peizhen Qiu Jiqing Lian Ming Jing Binbin Yu Jing Wen

In this article, an ultrathin terahertz dual band metamaterial absorber made up of patterned asymmetrical double-split rings and a continuous metal layer separated by a thin FR-4 layer is designed. Simulation results show that two almost identical strong absorption peaks appear in the terahertz band. When the incident electric field is perpendicular to the ring gaps located at 11 &mu;m asymmetrically, the absorptivity of 98.6% at 4.48 THz and 98.5% at 4.76 THz can be obtained. The absorption frequency and the absorptivity of the absorber can be modulated by the asymmetric distribution of the gaps. The perfect metamaterial absorber is expected to provide important reference for the design of terahertz modulator, filters, absorbers, and polarizers.

]]>Symmetry doi: 10.3390/sym10070292

Authors: Habib Shah Nasser Tairan Harish Garg Rozaida Ghazali

The objective of this work is to present a Quick Gbest Guided artificial bee colony (ABC) learning algorithm to train the feedforward neural network (QGGABC-FFNN) model for the prediction of the trends in the stock markets. As it is quite important to know that nowadays, stock market prediction of trends is a significant financial global issue. The scientists, finance administration, companies, and leadership of a given country struggle towards developing a strong financial position. Several technical, industrial, fundamental, scientific, and statistical tools have been proposed and used with varying results. Still, predicting an exact or near-to-exact trend of the Stock Market values behavior is an open problem. In this respect, in the present manuscript, we propose an algorithm based on ABC to minimize the error in the trend and actual values by using the hybrid technique based on neural network and artificial intelligence. The presented approach has been verified and tested to predict the accurate trend of Saudi Stock Market (SSM) values. The proposed QGGABC-ANN based on bio-inspired learning algorithm with its high degree of accuracy could be used as an investment advisor for the investors and traders in the future of SSM. The proposed approach is based mainly on SSM historical data covering a large span of time. From the simulation findings, the proposed QGGABC-FFNN outperformed compared with other typical computational algorithms for prediction of SSM values.

]]>Symmetry doi: 10.3390/sym10070291

Authors: Endrowednes Kuantama Ioan Tarca Simona Dzitac Ioan Dzitac Radu Tarca

Quadcopter flight stability is achieved when all of the rotors&ndash;propellers generate equal thrust in hover and throttle mode. It requires a control system algorithm for rotor speed adjustment, which is related with the translational vector and rotational angle. Even with an identical propeller and speed, the thrusts generated are not necessarily equal on all rotors&ndash;propellers. Therefore, this study focuses on developing a data logger to measure thrust and to assist in flight control on a symmetrically-structured quadcopter. It is developed with a four load cells sensor with two-axis characterizations and is able to perform real-time signal processing. The process includes speed adjustment for each rotor, trim calibration, and a proportional integral derivative (PID) control tuning system. In the data retrieval process, a quadcopter was attached with data logger system in a parallel axis position. Various speeds between 1200 rpm to 4080 rpm in throttle mode were analyzed to determine the stability of the resulting thrust. Adjustment result showed that the thrust differences between the rotors were less than 0.5 N. The data logger showed the consistency of the thrust value and was proved by repeated experiments with 118 s of sampling time for the same quadcopter control condition. Finally, the quadcopter flight stability as the result of tuning process by the thrust data logger was validated by the flight controller data.

]]>Symmetry doi: 10.3390/sym10070290

Authors: Yuan-Yu Tsai Yu-Shiou Tsai Chia-Chun Chang

Fragile watermarking algorithms for 3D models has attracted extensive research attention in recent years. Although many literatures have proposed lots of solutions on this issue, low embedding capacity and inaccurate located tampered region are still presented. Higher embedding capacity can reduce the probability of false alarms for authentication, while accurate tamper localization can detect all the modified vertices with fewer unaltered ones. This study proposes three strategies to enhance the embedding capacity and the detection accuracy of our previous algorithm. First, the modified message-digit substitution table can increase the embedding capacity by 11.5%. Second, the modified embedding ratio generation method can be integrated to raise the embedding capacity by about 47.74%. Finally, the strategy adopting a reduced number of reference vertices for authentication code generation accompanying the above two ones improves the embedding capacity up to 123.74%. Extensive experiments show that the proposed algorithm can achieve superior performance in terms of embedding capacity and tamper localization accuracy. Further, the model distortion between the original and the marked ones is small.

]]>Symmetry doi: 10.3390/sym10070289

Authors: Xiaohong Zhang Qingqing Hu Florentin Smarandache Xiaogang An

As a new generalization of the notion of the standard group, the notion of the neutrosophic triplet group (NTG) is derived from the basic idea of the neutrosophic set and can be regarded as a mathematical structure describing generalized symmetry. In this paper, the properties and structural features of NTG are studied in depth by using theoretical analysis and software calculations (in fact, some important examples in the paper are calculated and verified by mathematics software, but the related programs are omitted). The main results are obtained as follows: (1) by constructing counterexamples, some mistakes in the some literatures are pointed out; (2) some new properties of NTGs are obtained, and it is proved that every element has unique neutral element in any neutrosophic triplet group; (3) the notions of NT-subgroups, strong NT-subgroups, and weak commutative neutrosophic triplet groups (WCNTGs) are introduced, the quotient structures are constructed by strong NT-subgroups, and a homomorphism theorem is proved in weak commutative neutrosophic triplet groups.

]]>Symmetry doi: 10.3390/sym10070288

Authors: Muhammad Alzweiri Mariam Sallam Walid Al-Zyoud Khaled Aiedeh

Cyclooxygenase-2 (COX-2) is an enzyme responsible for inflammation and pain. Etoricoxib is the most recent selective (COX-2) inhibitor that has a higher COX-2 selectivity than the other COX-2-selective nonsteroidal anti-inflammatory drugs (NSAIDs), which significantly improves its gastric safety profile. The current therapeutic indications of etoricoxib includes the treatment of several painful conditions, such as osteoarthritis, acute gout, ankylosing spondylitis, and rheumatoid arthritis. To the best of found knowledge, no decent method has been reported that can be used for the routine determination of etoricoxib and additives in pharmaceutical suspensions by a single, rapid and cost-effective run of HPLC, using an UV-Vis detector. Earlier reported methods, such as liquid chromatography-mass spectrometry (LC-MS), high performance thin layer chromatography (HPTLC), capillary zone electrophoresis, and ultra performance liquid chromatography (UPLC), are all tedious and time consuming. A reversed phase high performance liquid chromatography (RP-HPLC) was used as a first reported single run method to achieve developed and validated simultaneous determination for sodium saccharin, vanillin, methyl paraben, etoricoxib, and butyl paraben, in prepared oral suspensions of etoricoxib. Reversed phase column of octadecylsilane (ODS) C18 with isocratic mobile phase containing methanol, and phosphate buffer of pH 6 in a ratio of 70:30 (v/v). Celecoxib is used as an internal standard at a detection wavelength of 215 nm. This method separates the analytes in a total running time less than 13 min. Linearity is obtained in the calibration curve for all analytes with a R2 value of &gt; 0.999. Furthermore, beta-cyclodextrin (&beta;-CD) and 2-hydroxypropyl-&beta;-cyclodextrin (HP-&beta;-CD) were added, either alone or combined, to prevent the crystal formation, and any unpleasant taste of etoricoxib in oral formulations. After testing both HP-&beta;-CD and &beta;-CD at 3% w/w for each, the results showed that HP-&beta;-CD is more efficient in preventing the crystal formation of etoricoxib in suspensions at room temperature than &beta;-CD is.

]]>Symmetry doi: 10.3390/sym10070287

Authors: Claudio Cremaschini Massimo Tessarotto

Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

]]>Symmetry doi: 10.3390/sym10070286

Authors: V. J. García M. Martel-Escobar F. J. Vázquez-Polo

This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.

]]>Symmetry doi: 10.3390/sym10070285

Authors: Sahereh Hosseinpour Mir Mohammad Reza Alavi Milani Hüseyin Pehlivan

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

]]>Symmetry doi: 10.3390/sym10070284

Authors: Qiuling Wu Meng Wu

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

]]>Symmetry doi: 10.3390/sym10070283

Authors: Weizhang Liang Guoyan Zhao Suizhi Luo

Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to solve such problems, a decision making framework based on a new concept, the hesitant linguistic preference relation (HLPR), is constructed. The basic elements in the HLPR are hesitant fuzzy linguistic numbers (HFLNs). At first, new operational laws and aggregation operators of HFLNs are defined to overcome the limitations in existing literature. Subsequently, a novel comparison method based on likelihood is proposed to obtain the order relationship of two HFLNs. Then, a likelihood-based consistency index is introduced to represent the difference between two hesitant linguistic preference relations (HLPRs). It is a new way to express the consistency degree for the reason that the traditional consistency indices are almost exclusively based on distance measures. Meanwhile, a consistency-improving model is suggested to attain acceptable consistent HLPRs. In addition, a method to receive reasonable ranking results from HLPRs with acceptable consistency is presented. At last, this method is used to pick out the best mine ventilation system under uncertain linguistic decision conditions. A comparison and a discussion are conducted to demonstrate the validity of the presented approach. The results show that the proposed method is effective for selecting the optimal mine ventilation system, and provides references for the construction and management of mines.

]]>Symmetry doi: 10.3390/sym10070282

Authors: Michał Szymczyk Marcin Nowak Wojciech Sumelka

The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

]]>Symmetry doi: 10.3390/sym10070281

Authors: Dajun Ye Decui Liang Pei Hu

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

]]>Symmetry doi: 10.3390/sym10070280

Authors: Harish Garg Nancy

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

]]>Symmetry doi: 10.3390/sym10070279

Authors: Walter Carballosa Amauris de la Cruz Alvaro Martínez-Pérez José M. Rodríguez

It is well-known that the different products of graphs are some of the more symmetric classes of graphs. Since we are interested in hyperbolicity, it is interesting to study this property in products of graphs. Some previous works characterize the hyperbolicity of several types of product graphs (Cartesian, strong, join, corona and lexicographic products). However, the problem with the direct product is more complicated. The symmetry of this product allows us to prove that, if the direct product G1&times;G2 is hyperbolic, then one factor is bounded and the other one is hyperbolic. Besides, we prove that this necessary condition is also sufficient in many cases. In other cases, we find (not so simple) characterizations of hyperbolic direct products. Furthermore, we obtain good bounds, and even formulas in many cases, for the hyperbolicity constant of the direct product of some important graphs (as products of path, cycle and even general bipartite graphs).

]]>Symmetry doi: 10.3390/sym10070278

Authors: Dominik Schmidt Katrin Kahlen

Fluctuating asymmetry in plant leaves is a widely used measure in geometric morphometrics for assessing random deviations from perfect symmetry. In this study, we considered the concept of fluctuating asymmetry to improve the prototype leaf shape of the functional-structural plant model L-Cucumber. The overall objective was to provide a realistic geometric representation of the leaves for the light sensitive plant reactions in the virtual plant model. Based on three-dimensional data from several hundred in situ digitized cucumber leaves comparisons of model leaves and measurements were conducted. Robust Bayesian comparison of groups was used to assess statistical differences between leaf halves while respecting fluctuating asymmetries. Results indicated almost no directional asymmetry in leaves comparing different distances from the prototype while detecting systematic deviations shared by both halves. This information was successfully included in an improved leaf prototype and implemented in the virtual plant model L-Cucumber. Comparative virtual plant simulations revealed a slight improvement in plant internode development against experimental data using the novel leaf shape. Further studies can now focus on analyses of stress on the 3D-deformation of the leaf and the development of a dynamic leaf shape model.

]]>Symmetry doi: 10.3390/sym10070277

Authors: Haitao Xu Zhelang Pan Zhihuan Luo Yan Liu Suiyan Tan Zhijie Mai Jun Xu

A new type of discrete soliton, which we call zigzag solitons, is founded in two-component discrete Rabi lattices with long-range hopping. The spontaneous symmetry breaking (SSB) of zigzag solitons is also studied. Through numerical simulation, we found that by enhancing the intensity of the long-range linearly-coupled effect or increasing the total input power, the SSB process from the symmetric soliton to the asymmetric soliton will switch from the supercritical to subcritical type. These results can help us better understand both the discrete solitons and the Rabi coupled effect.

]]>Symmetry doi: 10.3390/sym10070276

Authors: Qingyou Yan Le Yang Tomas Baležentis Dalia Streimikiene Chao Qin

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.

]]>Symmetry doi: 10.3390/sym10070275

Authors: Kokichi Sugihara Masaki Moriguchi

The present paper introduces a method for designing 3D objects that are initially incomplete, but become complete when they are augmented by their mirror reflections. Physically, the mirror image is plane-symmetric with respect to the original object, but the perceived shape is not necessarily symmetric because of optical illusion. In the proposed method, a 2D shape that is not necessarily symmetric is divided into two halves, one of which is used to construct a solid object. When we place the solid object on a plane mirror, the other half is generated by the mirror, and thus, a whole shape is realized. In the present study, the design algorithm and examples are shown, and the condition for constructability is also presented.

]]>Symmetry doi: 10.3390/sym10070274

Authors: Fevzi Yaşar Kuddusi Kayaduman

The main topic in this article is to define and examine new sequence spaces bs(F^(s,r)) and cs(F^(s,r))), where F^(s,r) is generalized difference Fibonacci matrix in which s,r&isin;R\0. Some algebric properties including some inclusion relations, linearly isomorphism and norms defined over them are given. In addition, it is shown that they are Banach spaces. Finally, the &alpha;-, &beta;- and &gamma;-duals of the spaces bs(F^(s,r)) and cs(F^(s,r)) are appointed and some matrix transformations of them are given.

]]>Symmetry doi: 10.3390/sym10070273

Authors: Fan Wang Pengfei Li

Based on the mirror image method and superposition principle, an analytical model of seepage field for symmetrical underwater tunnels is proposed. The condition is assumed as two-dimensional steady water inflow into symmetrical and horizontal underwater tunnels in a fully saturated, homogeneous, isotropic, and semi-infinite aquifer. Analytical solutions of pore water distribution and water inflow into tunnels are obtained. Two different boundary conditions at the perimeter of symmetrical tunnels are considered, constant total hydraulic head and constant water pressure. Taking the subsea tunnels of Xiamen Xiang&rsquo;an in China as an example, comparisons between analytical solutions and numerical solutions are analyzed in the case of zero water pressure at the perimeter of symmetrical tunnels. The results show that the analytical solutions for pore pressure distribution and water inflow match well with the numerical solutions and that the relative deviations are all in an acceptable range. The solutions derived from the analytical model in this paper can analyze the steady seepage field of symmetrical underwater tunnels accurately and reasonably.

]]>Symmetry doi: 10.3390/sym10070272

Authors: Li He Yi Li Xiang Zhang Chuangbin Chen Lei Zhu Chengcai Leng

We propose an incremental spectral clustering method for stream data clustering and apply it to stream image segmentation. The main idea in our work consists of generating the data points in the kernel space by Fastfood features and iteratively calculating the eigendecomposition of data. Compared with the popular Nystr&ouml;m-based approximation, our work accesses each data point only once while Nystr&ouml;m, in particular the sampling scheme, will go through the entire dataset first and calculate the embeddings of data points with a second visit. As a result, our method is able to learn data partitions incrementally and improve eigenvector approximation with more and more data seen from a stream. By contrast, the performance of the standard Nystr&ouml;m is fixed when the sample set is selected. Experimental results show the superiority of our method.

]]>Symmetry doi: 10.3390/sym10070271

Authors: Yung-I Lin Ying-Hsuan Huang Chih-Cheng Chen

Compared with traditional hiding methods, dual-image reversible data hiding methods have a higher embedding rate and a better quality stego image. Also, this is a special case of secret sharing, because secret data cannot be extracted from any stego image. In the literature, the frequencies of occurrence of secret data were used as reference information for data encoding, in which most digits were transformed into smaller ones. The encoding strategy can effectively decrease the modification level of the pixel. However, only limited literature has analyzed the relationship between the adjacent secret data. In this paper, we proposed an exclusive-or (XOR)-based encoding method to convert the neighboring values, thereby reducing the distortion. Since there are significant similarities between the two stego images and the original image, the first stego image is stored on an unmanned aerial vehicle (UAV) to avoid a hacker&rsquo;s interception attack. The second stego image on the UAV is sent to the command station. After completion of the UAV mission, the proposed method extracts the secret data from the two stego images to identify whether the second stego image has been tampered with.

]]>Symmetry doi: 10.3390/sym10070270

Authors: Nikos Petrellis

Image processing has been extensively used in various (human, animal, plant) disease diagnosis approaches, assisting experts to select the right treatment. It has been applied to both images captured from cameras of visible light and from equipment that captures information in invisible wavelengths (magnetic/ultrasonic sensors, microscopes, etc.). In most of the referenced diagnosis applications, the image is enhanced by various filtering methods and segmentation follows isolating the regions of interest. Classification of the input image is performed at the final stage. The disease diagnosis approaches based on these steps and the common methods are described. The features extracted from a plant/skin disease diagnosis framework developed by the author are used here to demonstrate various techniques adopted in the literature. The various metrics along with the available experimental conditions and results presented in the referenced approaches are also discussed. The accuracy achieved in the diagnosis methods that are based on image processing is often higher than 90%. The motivation for this review is to highlight the most common and efficient methods that have been employed in various disease diagnosis approaches and suggest how they can be used in similar or different applications.

]]>Symmetry doi: 10.3390/sym10070269

Authors: Yanping Liao Congcong He Qiang Guo

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

]]>Symmetry doi: 10.3390/sym10070268

Authors: Jimmy Aurelio Rosales-Huamaní José Luis Castillo-Sequera Juan Carlos Montalvan-Figueroa Joseps Andrade-Choque

The main restriction of the Semantic Web is the difficulty of the SPARQL language, which is necessary for extracting information from the Knowledge Representation also known as ontology. Making the Semantic Web accessible for people who do not know SPARQL is essential for the use of friendlier interfaces, and a good alternative is Natural Language. This paper shows the implementation of a friendly prototype interface activated by voice to query and retrieving information from websites built with Semantic Web tools. In that way, the end users avoid the complicated SPARQL language. To achieve this, the interface recognizes a speech query and converts it into text, it processes the text through a Java program and identifies keywords, generates a SPARQL query, extracts the information from the website and reads it in a voice for the user. In our work, Google Cloud Speech API makes Speech-to-Text conversions and Text-to Speech conversions are made with SVOX Pico. As a result, we have measured three variables: the success rate in queries, the response time of query and a usability survey. The values of the variables allow the evaluation of our prototype. Finally, the interface proposed provides us with a new approach in the problem, using the Cloud like a Service, reducing barriers of access to the Semantic Web for people without technical knowledge of Semantic Web technologies.

]]>Symmetry doi: 10.3390/sym10070267

Authors: Lina Ji Wei Feng

The radially symmetric nonlinear reaction&ndash;diffusion equation with gradient-dependent diffusivity is investigated. We obtain conditions under which the equations admit second-order conditional Lie&ndash;B&auml;cklund symmetries and first-order Hamilton&ndash;Jacobi sign-invariants which preserve both signs (&ge;0 and &le;0) on the solution manifold. The corresponding reductions of the resulting equations are established due to the compatibility of the invariant surface conditions and the governing equations.

]]>Symmetry doi: 10.3390/sym10070266

Authors: Musheer Ahmad Eesa Al Solami Xing-Yuan Wang M. N. Doja M. M. Sufyan Beg Amer Awad Alzaidi

The issues of identity authentication and privacy protection of individuals in body area network (BAN) systems have raised much concern in past few years. To address the challenges of privacy protection in wireless BAN, an image encryption algorithm has been proposed recently by Wang et al. The encryption algorithm utilized two 1D chaotic maps to generate sub-chaotic matrices which are combined to perform encryption. The algorithm has good statistical encryption performance. However, a cautious inquiry finds that it has some underlying security defects. This paper evaluates the security of the Wang et al. encryption algorithm to show that it is totally breakable under proposed cryptanalysis and hence infeasible for privacy protection in BAN. It has been shown that the plain-image data can be recovered without any prior knowledge of secret key and plain-text. Furthermore, this paper also suggests an improved encryption scheme using secure hash algorithm SHA-512 for one-time keys and a 4D hyperchaotic system to subdue the security insufficiencies of the algorithm under study. The simulation results and analysis demonstrate that the improved image encryption scheme has excellent encryption quality, plain-image sensitivity, and resistance to possible cryptanalytic attacks.

]]>Symmetry doi: 10.3390/sym10070265

Authors: Jia-Bao Liu Muhammad Kamran Siddiqui Manzoor Ahmad Zahid Muhammad Naeem Abdul Qudair Baig

Chemical graph theory plays an important role in modeling and designing any chemical structure. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. In this paper, we study the chemical graph of the crystal structure of titanium difluoride TiF2 and the crystallographic structure of cuprite Cu2O. Furthermore, we compute degree-based topological indices, mainly ABC, GA, ABC4, GA5 and general Randić indices. Furthermore, we also give exact results of these indices for the crystal structure of titanium difluoride TiF2 and the crystallographic structure of cuprite Cu2O.

]]>Symmetry doi: 10.3390/sym10070264

Authors: Guang Li Jie Wang Jing Liang Caitong Yue

The effect of the application of machine learning on data streams is influenced by concept drift, drift deviation, and noise interference. This paper proposes a data stream anomaly detection algorithm combined with control chart and sliding window methods. This algorithm is named DCUSUM-DS (Double CUSUM Based on Data Stream), because it uses a dual mean value cumulative sum. The DCUSUM-DS algorithm based on nested sliding windows is proposed to satisfy the concept drift problem; it calculates the average value of the data within the window twice, extracts new features, and then calculates accumulated and controlled graphs to avoid misleading by interference points. The new algorithm is simulated using drilling engineering industrial data. Compared with automatic outlier detection for data streams (A-ODDS) and with sliding nest window chart anomaly detection based on data streams (SNWCAD-DS), the DCUSUM-DS can account for concept drift and shield a small amount of interference deviating from the overall data. Although the algorithm complexity increased from 0.1 second to 0.19 second, the classification accuracy receiver operating characteristic (ROC) increased from 0.89 to 0.95. This meets the needs of the oil drilling industry data stream with a sampling frequency of 1 Hz, and it improves the classification accuracy.

]]>Symmetry doi: 10.3390/sym10070263

Authors: Chiara Bartalucci Rocco Furferi Lapo Governi Yary Volpe

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

]]>Symmetry doi: 10.3390/sym10070262

Authors: Laksamee Khomnotai Jun-Lin Lin Zhi-Qiang Peng Arpita Samanta Santra

Microaggregation refers to partitioning n given records into groups of at least k records each to minimize the sum of the within-group squared error. Because microaggregation is non-deterministic polynomial-time hard for multivariate data, most existing approaches are heuristic based and derive a solution within a reasonable timeframe. We propose an algorithm for refining the solutions generated using the existing microaggregation approaches. The proposed algorithm refines a solution by iteratively either decomposing or shrinking the groups in the solution. Experimental results demonstrated that the proposed algorithm effectively reduces the information loss of a solution.

]]>Symmetry doi: 10.3390/sym10070261

Authors: Zhengmao Li Dechao Sun Shouzhen Zeng

This paper investigates an intuitionistic fuzzy multiple attribute decision-making method based on weighted induced distance and its application to investment selection. Specifically, an intuitionistic fuzzy weighted induced ordered weighted averaging operator is proposed to eliminate the drawbacks of existing methods by extending the functions of the order-induced variables. The main advantage of the proposed operator is its dual roles of the order-inducing variables that can simultaneously induce arguments and moderate associated weights. A further extension of the proposed operator is its adaptation towards measuring intuitionistic fuzzy information more effectively. In addition, a multiple attribute decision-making model based on the proposed distance operators is proposed. Finally, the practicability and validity of the proposed model are illustrated by using a numerical example related to investment selection.

]]>Symmetry doi: 10.3390/sym10070260

Authors: Allen D. Parks

It is known that the set of all networks of fixed order form a semigroup. This fact provides for the Green&rsquo;s L, R, H and D&nbsp; equivalence equivalence classifications of all such networks. These classifications reveal certain structural invariants common to all networks within a Green&rsquo;s equivalence class and enables the computation of the associated invariant preserving symmetries that transform a network into another network within a Green&rsquo;s equivalence class. Here, the notion of Sch&uuml;tzenberger symmetries in network structures is introduced. These are computable symmetries which transform any network within an H-equivalence class into another network within that class in a manner that preserves the associated structural invariants. Useful applications of Sch&uuml;tzenberger symmetries include enabling the classification and analysis of biological network data, identifying important relationships in social networks, and understanding the consequences of link reconfiguration in communication and sensor networks.

]]>Symmetry doi: 10.3390/sym10070259

Authors: Ekkehard Krüger

The nonadiabatic Heisenberg model presents a nonadiabatic mechanism generating Cooper pairs in narrow, roughly half-filled &ldquo;superconducting bands&rdquo; of special symmetry. Here, I show that this mechanism may be understood as the outcome of a special spin structure in the reciprocal space, hereinafter referred to as &ldquo;k-space magnetism&rdquo;. The presented picture permits a vivid depiction of this new mechanism highlighting the height similarity as well as the essential difference between the new nonadiabatic and the familiar Bardeen&ndash;Cooper&ndash;Schrieffer mechanism.

]]>Symmetry doi: 10.3390/sym10070258

Authors: Taekyun Kim Dae San Kim Dolgy Dmitriy Victorovich Cheon Seoung Ryoo

Here, we consider the sums of finite products of Chebyshev polynomials of the third and fourth kinds. Then, we represent each of those sums of finite products as linear combinations of the four kinds of Chebyshev polynomials, which involve the hypergeometric function 3F2.

]]>Symmetry doi: 10.3390/sym10070257

Authors: Dhimas Arief Dharmawan Boon Poh Ng Susanto Rahardja

In this paper, we present a new unsupervised algorithm for retinal vessels segmentation. The algorithm utilizes a directionally sensitive matched filter bank using a modified Dolph-Chebyshev type II basis function and a new method to combine the matched filter bank&rsquo;s responses. Fundus images from the DRIVE and STARE databases, as well as high-resolution fundus images from the HRF database, are utilized to validate the proposed algorithm. The results that we achieve on the three databases (DRIVE: Sensitivity = 0.748, F1-score = 0.786, G-score = 0.856, Matthews Correlation Coefficient = 0.758; STARE: Sensitivity = 0.793, F1-score = 0.780, G-score = 0.877, Matthews Correlation Coefficient = 0.756; HRF: Sensitivity = 0.804, F1-score = 0.764, G-score = 0.883, Matthews Correlation Coefficient = 0.741) are higher than many other competing methods.

]]>Symmetry doi: 10.3390/sym10070256

Authors: Jieqiong Song Ming Zhao Sifan Long

Images crowdsourcing of mobile devices can be applied to many real-life application scenarios. However, this type of scenario application often faces issues such as the limitation of bandwidth, insufficient storage space, and the processing capability of CPU. These lead to only a few photos that can be crowdsourced. Therefore, it is a great challenge to use a limited number of resources to select photos and make it possible to cover the target area maximally. In this paper, the geographic and geometric information of the photo called data-unit is used to cover the target area as much as possible. Compared with traditional content-based image delivery methods, the network delay and computational costs can be greatly reduced. In the case of resource constraints, this paper uses the utility of photos to measure the coverage of the target area, and improves a photo utility calculation method based on data-unit. In the meantime, this paper proposes the minimum selection problem of images under the coverage requirements, and designs a selection algorithm based on greedy strategies. Compared with other traditional random selection algorithms, the results prove the effectiveness and superiority of the minimum selection algorithm.

]]>Symmetry doi: 10.3390/sym10070255

Authors: Asad Husnain Baqar Tao Jiang Ishfaq Hussain Ghulam Farid

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

]]>Symmetry doi: 10.3390/sym10070254

Authors: Wien Hong Xiaoyu Zhou Shaowei Weng

This paper proposes a joint coding and reversible data hiding method for absolute moment block truncation coding (AMBTC) compressed images. Existing methods use a predictor to predict the quantization levels of AMBTC codes. Equal-length indicators, secret bits and prediction errors are concatenated to construct the output code stream. However, the quantization levels might not highly correlate with their neighbors for predictive coding, and the use of equal-length indicators might impede the coding efficiency. The proposed method uses reversible integer transform to represent the quantization levels by their means and differences, which is advantageous for predictive coding. Moreover, the prediction errors are better classified into symmetrical encoding cases using the adaptive classification technique. The length of indicators and the bits representing the prediction errors are properly assigned according to the classified results. Experiments show that the proposed method offers the lowest bitrate for a variety of images when compared with the existing state-of-the-art works.

]]>Symmetry doi: 10.3390/sym10070253

Authors: Haihe Ba Huaizhe Zhou Huidong Qiao Zhiying Wang Jiangchun Ren

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

]]>Symmetry doi: 10.3390/sym10070252

Authors: Eber Lenes Exequiel Mallea-Zepeda María Robbiano Jonnathan Rodríguez

The total graph of G, T(G) is the graph whose vertex set is the union of the sets of vertices and edges of G, where two vertices are adjacent if and only if they stand for either incident or adjacent elements in G. For k&ge;2, the k-th iterated total graph of G, Tk(G), is defined recursively as Tk(G)=T(Tk&minus;1(G)), where T1(G)=T(G) and T0(G)=G. If G is a connected graph, its diameter is the maximum distance between any pair of vertices in G. The incidence energy IE(G) of G is the sum of the singular values of the incidence matrix of G. In this paper, for a given integer k we establish a necessary and sufficient condition under which diam(Tr+1(G))&gt;k&minus;r,r&ge;0. In addition, bounds for the incidence energy of the iterated graph Tr+1(G) are obtained, provided G is a regular graph. Finally, new families of non-isomorphic cospectral graphs are exhibited.

]]>Symmetry doi: 10.3390/sym10070251

Authors: Lvqing Bi Songsong Dai Bo Hu

A complex fuzzy set is an extension of the traditional fuzzy set, where traditional [0,1]-valued membership grade is extended to the complex unit disk. The aggregation operator plays an important role in many fields, and this paper presents several complex fuzzy geometric aggregation operators. We show that these operators possess the properties of rotational invariance and reflectional invariance. These operators are also closed on the upper-right quadrant of the complex unit disk. Based on the relationship between Pythagorean membership grades and complex numbers, these operators can be applied to the Pythagorean fuzzy environment.

]]>Symmetry doi: 10.3390/sym10070250

Authors: Tuong Le Le Hoang Son Minh Thanh Vo Mi Young Lee Sung Wook Baik

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

]]>Symmetry doi: 10.3390/sym10070249

Authors: Xuan Zhou Yuliang Lu Xuehu Yan Yongjie Wang Lintao Liu

Thien-and-Lin&rsquo;s polynomial-based secret image sharing (PSIS) is utilized as the basic method to achieve PSISs with better performances, such as meaningful shares, two-in-one property and shares with different priorities. However, this (k,n) threshold PSIS cannot achieve lossless recovery for pixel values more than 250. Furthermore, current solutions to lossless recovery for PSIS have several natural drawbacks, such as large computational costs and random pixel expansion. In this paper, a lossless and efficient (k,n) threshold PSIS scheme with reduced shadow size is presented. For lossless recovery and efficiency, two adjacent pixels are specified as a secret value, the prime in the sharing polynomial is replaced with 65,537, and then the additional screening operation can ensure each shared value in the range [0,65,535]. To reduce shadows size and improve security, only the first k&minus;1 coefficients are embedded with secret values and the last coefficient is assigned randomly. To prevent the leakage of secrets, generalized Arnold permutation with special key generating strategy is performed on the secret image prior to sharing process without key distribution. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.

]]>Symmetry doi: 10.3390/sym10070248

Authors: David Camilo Corrales Agapito Ledezma Juan Carlos Corrales

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

]]>Symmetry doi: 10.3390/sym10070247

Authors: Shuo Ji Yinliang Zhao

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

]]>Symmetry doi: 10.3390/sym10070246

Authors: Nicola Alchera Marco Bonici Roberta Cardinale Alba Domi Nicola Maggiore Chiara Righi Silvano Tosi

We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom as the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to the arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in Astrophysics and Cosmology which may be applied to investigate the discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.

]]>Symmetry doi: 10.3390/sym10070245

Authors: Hongjun Guan Jie He Aiwu Zhao Zongli Dai Shuang Guan

Making predictions according to historical values has long been regarded as common practice by many researchers. However, forecasting solely based on historical values could lead to inevitable over-complexity and uncertainty due to the uncertainties inside, and the random influence outside, of the data. Consequently, finding the inherent rules and patterns of a time series by eliminating disturbances without losing important details has long been a research hotspot. In this paper, we propose a novel forecasting model based on multi-valued neutrosophic sets to find fluctuation rules and patterns of a time series. The contributions of the proposed model are: (1) using a multi-valued neutrosophic set (MVNS) to describe the fluctuation patterns of a time series, the model could represent the fluctuation trend of up, equal, and down with degrees of truth, indeterminacy, and falsity which significantly preserve details of the historical values; (2) measuring the similarities of different fluctuation patterns by the Hamming distance could avoid the confusion caused by incomplete information from limited samples; and (3) introducing another related time series as a secondary factor to avoid warp and deviation in inferring inherent rules of historical values, which could lead to more comprehensive rules for further forecasting. To evaluate the performance of the model, we explored the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) as the major factor we forecast, and the Dow Jones Index as the secondary factor to facilitate the predicting of the TAIEX. To show the universality of the model, we applied the proposed model to forecast the Shanghai Stock Exchange Composite Index (SHSECI) as well.

]]>Symmetry doi: 10.3390/sym10070244

Authors: Zehui Shao Muhammad Kamran Siddiqui Mehwish Hussain Muhammad

Topological indices are numbers related to sub-atomic graphs to allow quantitative structure-movement/property/danger connections. These topological indices correspond to some specific physico-concoction properties such as breaking point, security, strain vitality of chemical compounds. The idea of topological indices were set up in compound graph hypothesis in view of vertex degrees. These indices are valuable in the investigation of mitigating exercises of specific Nanotubes and compound systems. In this paper, we discuss Zagreb types of indices and Zagreb polynomials for a few Nanotubes covered by cycles.

]]>Symmetry doi: 10.3390/sym10070243

Authors: Qing Li Steven Y. Liang

It is a primary challenge in the fault diagnosis community of the gearbox to extract the weak fault features under heavy background noise and nonstationary conditions. For this purpose, a novel weak fault detection approach based on majorization&ndash;minimization (MM) and asymmetric convex penalty regularization (ACPR) is proposed in this paper. The proposed objective cost function (OCF) consisting of a signal-fidelity term, and two parameterized penalty terms (i.e., one is an asymmetric nonconvex penalty regularization term, and another is a symmetric nonconvex penalty regularization term).To begin with, the asymmetric and symmetric penalty functions are established on the basis of an L1-norm model, then, according to the splitting idea, the majorizer of the symmetric function and the majorizer of the asymmetric function are respectively calculated via the MM algorithm. Finally, the MM is re-introduced to solve the proposed OCF. As examples, the effectiveness and reliability of the proposed method is verified through simulated data and gearbox experimental real data. Meanwhile, a comparison with the state of-the-art methods is illustrated, including nonconvex penalty regularization (NCPR) and L1-norm fused lasso optimization (LFLO) techniques, the results indicate that the gear chipping characteristic frequency 13.22 Hz and its harmonic (2f, 3f, 4f and 5f) can be identified clearly, which highlights the superiority of the proposed approach.

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