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.

]]>Symmetry doi: 10.3390/sym10070242

Authors: Muhammad Sajid Tamoor Shafique Mirza Jabbar Aziz Baig Imran Riaz Shahid Amin Sohaib Manzoor

Facial palsy caused by nerve damage results in loss of facial symmetry and expression. A reliable palsy grading system for large-scale applications is still missing in the literature. Although numerous approaches have been reported on facial palsy quantification and grading, most employ hand-crafted features on relatively smaller datasets which limit the classification accuracy due to non-optimal face representation. In contrast, convolutional neural networks (CNNs) automatically learn the discriminative features facilitating the accurate classification of underlying tasks. In this paper, we propose to apply a typical deep network on a large dataset to extract palsy-specific features from face images. To prevent the inherent limitation of overfitting frequently occurring in CNNs, a generative adversial network (GAN) is applied to augment the training dataset. The deeply learned features are then used to classify the palsy disease into five benchmarked grades. The experimental results show that the proposed approach offers superior palsy grading performance compared to some existing methods. Such an approach is useful for palsy grading at large scale, such as primary health care.

]]>Symmetry doi: 10.3390/sym10070241

Authors: Xiaohong Zhang Xiaoying Wu Florentin Smarandache Minghao Hu

The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented. As a corollary of these properties, the following important result are proved: for any commutative neutrosophic triplet group, its every element has a unique neutral element. Moreover, some left (right)-quasi neutrosophic triplet structures in BE-algebras and generalized BE-algebras (including CI-algebras and pseudo CI-algebras) are established, and the adjoint semigroups of the BE-algebras and generalized BE-algebras are investigated for the first time.

]]>Symmetry doi: 10.3390/sym10070240

Authors: Memet Şahin Abdullah Kargın Mehmet Ali Çoban

Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM. Also, we show that NTPMS can be defined with each NTMS. Furthermore, we define a contraction for NTPMS and we give a fixed point theory (FPT) for NTPMS. The FPT has been revealed as a very powerful tool in the study of nonlinear phenomena. This study is also part of the &ldquo;Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets&rdquo; which is a special issue.

]]>Symmetry doi: 10.3390/sym10070239

Authors: Junjie Ma Huilan Liu

Lubich&rsquo;s convolution quadrature rule provides efficient approximations to integrals with special kernels. Particularly, when it is applied to computing highly oscillatory integrals, numerical tests show it does not suffer from fast oscillation. This paper is devoted to studying the convergence property of the convolution quadrature rule for highly oscillatory problems. With the help of operational calculus, the convergence rate of the convolution quadrature rule with respect to the frequency is derived. Furthermore, its application to highly oscillatory integral equations is also investigated. Numerical results are presented to verify the effectiveness of the convolution quadrature rule in solving highly oscillatory problems. It is found from theoretical and numerical results that the convolution quadrature rule for solving highly oscillatory problems is efficient and high-potential.

]]>Symmetry doi: 10.3390/sym10070238

Authors: Umar Hayat Daniel López-Aguayo Akhtar Abbas

Let G=Zp&oplus;Zp2, where p is a prime number. Suppose that d is a divisor of the order of G. In this paper, we find the number of automorphisms of G fixing d elements of G and denote it by &theta;(G,d). As a consequence, we prove a conjecture of Checco-Darling-Longfield-Wisdom. We also find the exact number of fixed-point-free automorphisms of the group Zpa&oplus;Zpb, where a and b are positive integers with a&lt;b. Finally, we compute &theta;(D2q,d), where D2q is the dihedral group of order 2q, q is an odd prime, and d&isin;{1,q,2q}.

]]>Symmetry doi: 10.3390/sym10070237

Authors: Shin Min Kang Zahid Iqbal Muhammad Ishaq Rabia Sarfraz Adnan Aslam Waqas Nazeer

In the study of the quantitative structure&ndash;activity relationship and quantitative structure-property relationships, the eccentric-connectivity index has a very important place among the other topological descriptors due to its high degree of predictability for pharmaceutical properties. In this paper, we compute the exact formulas of the eccentric-connectivity index and its corresponding polynomial, the total eccentric-connectivity index and its corresponding polynomial, the first Zagreb eccentricity index, the augmented eccentric-connectivity index, and the modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

]]>Symmetry doi: 10.3390/sym10070236

Authors: Ganeshsree Selvachandran Shio Gai Quek Florentin Smarandache Said Broumi

A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model. An integrated weight measure approach that takes into consideration both the objective and subjective weights of the attributes is used. The maximizing deviation method is used to compute the objective weight of the attributes, and the non-linear weighted comprehensive method is used to determine the combined weights for each attributes. The use of the maximizing deviation method allows our proposed method to handle situations in which information pertaining to the weight coefficients of the attributes are completely unknown or only partially known. The proposed method is then applied to a multi-attribute decision-making (MADM) problem. Lastly, a comprehensive comparative studies is presented, in which the performance of our proposed algorithm is compared and contrasted with other recent approaches involving SVNSs in literature.

]]>Symmetry doi: 10.3390/sym10070235

Authors: Jianjun Li Kangjian Peng Chin-Chen Chang

For a long time, object detection has been a popular but difficult research problem in the field of pattern recognition. In recent years, object detection algorithms based on convolutional neural networks have achieved excellent results. However, neural networks are computationally intensive and parameter redundant, so they are difficult to deploy on resource-limited embedded devices. Especially for two-stage detectors, operations and parameters are mainly clustered on feature fusion of proposals after the region of interest (ROI) pooling layer, and they are enormous. In order to deal with these problems, we propose a subnetwork&mdash;efficient feature fusion module (EFFM) to reduce the number of operations and parameters for a two-stage detector. In addition, we propose a multi-scale dilation region proposal network (RPN) to further improve detection accuracy. Finally, our accuracy is higher than Faster RCNN based on VGG16, the number of operations is only half of the latter, and the number of parameters is only one third.

]]>Symmetry doi: 10.3390/sym10070234

Authors: Zhen-Hua Li Yao Wang Zheng-Tian Wu Zhen-Xing Li

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

]]>Symmetry doi: 10.3390/sym10070233

Authors: Michael Tsamparlis Andronikos Paliathanasis

The purpose of the current article is to present a brief albeit accurate presentation of the main tools used in the study of symmetries of Lagrange equations for holonomic systems and subsequently to show how these tools are applied in the major models of modern cosmology in order to derive exact solutions and deal with the problem of dark matter/energy. The key role in this approach are the first integrals of the field equations. We start with the Lie point symmetries and the first integrals defined by them, that is, the Hojman integrals. Subsequently, we discuss the Noether point symmetries and the well-known method for deriving the Noether integrals. By means of the Inverse Noether Theorem, we show that, to every Hojman quadratic first integral, it is possible to associate a Noether symmetry whose Noether integral is the original Hojman integral. It is emphasized that the point transformation generating this Noether symmetry need not coincide with the point transformation defining the Lie symmetry which produces the Hojman integral. We discuss the close connection between the Lie point and the Noether point symmetries with the collineations of the metric defined by the kinetic energy of the Lagrangian. In particular, the generators of Noether point symmetries are elements of the homothetic algebra of that metric. The key point in the current study of cosmological models is the introduction of the mini superspace, which is the space that is defined by the physical variables of the model, which is not the spacetime where the model evolves. The metric in the mini superspace is found from the kinematic part of the Lagrangian and we call it the kinetic metric. The rest part of the Lagrangian is the effective potential. We consider coordinate transformations of the original mini superspace metric in order to bring it to a form where we know its collineations, that is, the Killing vectors, the homothetic vector, etc. Then, we write the field equations of the cosmological model and we use the connection of these equations with the collineations of the mini superspace metric to compute the first integrals and subsequently to obtain analytic solutions for various allowable potentials and finally draw conclusions about the problem of dark energy. We consider the &Lambda;CDM cosmological model, the scalar field cosmology, the Brans&ndash;Dicke cosmology, the f(R) gravity, the two scalar fields cosmology with interacting scalar fields and the Galilean cosmology. In each case, we present the relevant results in the form of tables for easy reference. Finally, we discuss briefly the higher order symmetries (the contact symmetries) and show how they are applied in the cases of scalar field cosmology and in the f(R) gravity.

]]>Symmetry doi: 10.3390/sym10070232

Authors: Muhammad Sajid Tamoor Shafique Imran Riaz Muhammad Imran Mirza Jabbar Aziz Baig Shahbaz Baig Sohaib Manzoor

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

]]>Symmetry doi: 10.3390/sym10070231

Authors: José Manuel Carmona José Luis Cortés José Javier Relancio

It is plausible that quantum gravity effects may lead us to a description of Nature beyond the framework of special relativity. In this case, either the relativity principle is broken or it is maintained. These two scenarios (a violation or a deformation of special relativity) are very different, both conceptually and phenomenologically. We discuss some of their implications on the description of events for different observers and the notion of spacetime.

]]>Symmetry doi: 10.3390/sym10060230

Authors: Connah Kendrick Kevin Tan Kevin Walker Moi Hoon Yap

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

]]>Symmetry doi: 10.3390/sym10060229

Authors: Yao Chen Jian Feng

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

]]>Symmetry doi: 10.3390/sym10060228

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

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

]]>Symmetry doi: 10.3390/sym10060227

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

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

]]>Symmetry doi: 10.3390/sym10060226

Authors: Mohamed Abdel-Basset Mai Mohamed Florentin Smarandache

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

]]>Symmetry doi: 10.3390/sym10060225

Authors: Wenhua Cui Jun Ye

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

]]>Symmetry doi: 10.3390/sym10060224

Authors: José María Pérez–Sánchez Emilio Gómez–Déniz Nancy Dávila–Cárdenes

The target of this paper is to study the relevant factors affecting the victories away from home of football teams in order to fit the probability of winning an away match. The paper addressed the following research issues: (a) Is the identification of the significant variables underlying the results plausible? (b) Can information of these factors increase the probability of winning away from home and assist coaches in their decisions? Empirically, it is shown that there are more home victories and draws than away victories in the professional football leagues in Europe and this fact has to be taken into account. Thus, the classical logistic and Bayesian regression models do not seem to be adequate in this case and an asymmetric logistic regression model is therefore considered. This paper analyses 380 games played in the First Division of the Spanish Football League during the 2013&ndash;2014 season. Asymmetric logistic regression from a Bayesian point of view is chosen as the best model. This model detects new relevant factors undetected by standard logistic regressions. In view of the paper&rsquo;s findings, various practical recommendations were made in order to improve decision-making in this field. The Asymmetric logit link is a helpful device that can assist coaches in their game strategies.

]]>Symmetry doi: 10.3390/sym10060223

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

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

]]>Symmetry doi: 10.3390/sym10060221

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

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

]]>Symmetry doi: 10.3390/sym10060222

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

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

]]>Symmetry doi: 10.3390/sym10060220

Authors: Rebecca J. Sharman Elena Gheorghiu

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

]]>Symmetry doi: 10.3390/sym10060219

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

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

]]>Symmetry doi: 10.3390/sym10060218

Authors: Sun Mi Jung Young Ho Kim

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

]]>Symmetry doi: 10.3390/sym10060217

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

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

]]>Symmetry doi: 10.3390/sym10060216

Authors: Jin Zhang Zhaohui Tang Mingxi Ai Weihua Gui

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

]]>Symmetry doi: 10.3390/sym10060215

Authors: Angyan Tu Jun Ye Bing Wang

In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information. However, a few researchers have studied neutrosophic cubic decision-making problems, where the similarity measure of NCSs is one of the useful measure methods. For this work, we propose the Dice, cotangent, and Jaccard measures between NCSs, and indicate their properties. Then, under an NCS environment, the similarity measures-based decision-making method of multiple attributes is developed. In the decision-making process, all the alternatives are ranked by the similarity measure of each alternative and the ideal solution to obtain the best one. Finally, two practical examples are applied to indicate the feasibility and effectiveness of the developed method.

]]>Symmetry doi: 10.3390/sym10060214

Authors: Qing Li Steven Y. Liang

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

]]>Symmetry doi: 10.3390/sym10060213

Authors: Chao Zhang Deyu Li Said Broumi Arun Kumar Sangaiah

In real-world diagnostic procedures, due to the limitation of human cognitive competence, a medical expert may not conveniently use some crisp numbers to express the diagnostic information, and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information. To deal with medical diagnosis problems based on generalized fuzzy sets (FSs), the notion of single-valued neutrosophic multisets (SVNMs) is firstly used to express the diagnostic information in this article. Then the model of probabilistic rough sets (PRSs) over two universes is applied to analyze SVNMs, and the concepts of single-valued neutrosophic rough multisets (SVNRMs) over two universes and probabilistic rough single-valued neutrosophic multisets (PRSVNMs) over two universes are introduced. Based on SVNRMs over two universes and PRSVNMs over two universes, single-valued neutrosophic probabilistic rough multisets (SVNPRMs) over two universes are further established. Next, a three-way decisions model by virtue of SVNPRMs over two universes in the context of medical diagnosis is constructed. Finally, a practical case study along with a comparative study are carried out to reveal the accuracy and reliability of the constructed three-way decisions model.

]]>Symmetry doi: 10.3390/sym10060212

Authors: Marija Maksimović

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

]]>Symmetry doi: 10.3390/sym10060211

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

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

]]>Symmetry doi: 10.3390/sym10060210

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

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

]]>Symmetry doi: 10.3390/sym10060209

Authors: Shahid Imran Muhammad Kamran Siddiqui Muhammad Imran Muhammad Hussain Hafiz Muhammad Bilal Imran Zulfiqar Cheema Ali Tabraiz Zeeshan Saleem

Let G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J2n,m be a m-level gear graph obtained by m-level wheel graph W2n,m &cong; mC2n + k1 by alternatively deleting n spokes of each copy of C2n and J3n be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W3n. In this paper, the metric dimension of certain gear graphs J2n,m and J3n generated by wheel has been computed. Also this study extends the previous result given by Tomescu et al. in 2007.

]]>Symmetry doi: 10.3390/sym10060208

Authors: Bingyan Lin Weihua Xu

A relation is viewed as a granularity from a granular computing perspective. A classic rough set contains only one granularity. A multi-granulation rough set contains multiple granularities, which promotes the applications of classical rough set. Firstly, this paper uses the incomplete interval-valued decision information system (IIVDIS) as research object and constructs two rough set models in the light of single granularity rough set model for applying the rough set theory to real life more widely, which are optimistic multi-granulation rough set (OMGRS) model and pessimistic multi-granulation rough set (PMGRS) model in the IIVDIS. Secondly, we design two algorithms to compute the roughness and the degree of dependence that are two tools for measuring uncertainty of rough set. Finally, several experiments are performed on six UCI data sets to verify the validity of the proposed theorems.

]]>Symmetry doi: 10.3390/sym10060207

Authors: Małgorzata Migda Janusz Migda

We study asymptotic behavior of nonoscillatory solutions to second-order neutral difference equation of the form: &Delta; ( r n &Delta; ( x n + p n x n &minus; &tau; ) ) = a n f ( n , x n ) + b n . The obtained results are based on the discrete Bihari type lemma and a Stolz type lemma.

]]>Symmetry doi: 10.3390/sym10060206

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

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

]]>Symmetry doi: 10.3390/sym10060205

Authors: Irina Vinogradova Valentinas Podvezko Edmundas Kazimieras Zavadskas

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

]]>Symmetry doi: 10.3390/sym10060204

Authors: Mustafa Saltan

The classical Sierpinski Gasket defined on the equilateral triangle is a typical example of fractals. Sierpinski-like triangles can also be constructed on isosceles or scalene triangles. An explicit formula for the intrinsic metric on the classical Sierpinski Gasket via code representation of its points is given. The aim of this paper is to generalize this formula to the Sierpinski-like triangles. We also investigate geometrical properties of these triangles with respect to the intrinsic metric. Moreover, we describe certain properties of the classical Sierpinski gasket which are not shared by all of its analogues.

]]>Symmetry doi: 10.3390/sym10060202

Authors: Tèmítópé Jaíyéolá Florentin Smarandache

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

]]>Symmetry doi: 10.3390/sym10060203

Authors: Muhammad Gulistan Naveed Yaqoob Zunaira Rashid Florentin Smarandache Hafiz Abdul Wahab

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

]]>Symmetry doi: 10.3390/sym10060201

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

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

]]>Symmetry doi: 10.3390/sym10060200

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

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

]]>Symmetry doi: 10.3390/sym10060199

Authors: Guofang Zhang Zhiming Zhang Hang Kong

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

]]>Symmetry doi: 10.3390/sym10060198

Authors: Ionel-Alexandru Gal Danut Bucur Luige Vladareanu

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

]]>Symmetry doi: 10.3390/sym10060197

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

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

]]>Symmetry doi: 10.3390/sym10060196

Authors: Ruipu Tan Wende Zhang Shengqun Chen

In recent years, typhoon disasters have occurred frequently and the economic losses caused by them have received increasing attention. This study focuses on the evaluation of typhoon disasters based on the interval neutrosophic set theory. An interval neutrosophic set (INS) is a subclass of a neutrosophic set (NS). However, the existing exponential operations and their aggregation methods are primarily for the intuitionistic fuzzy set. So, this paper mainly focus on the research of the exponential operational laws of interval neutrosophic numbers (INNs) in which the bases are positive real numbers and the exponents are interval neutrosophic numbers. Several properties based on the exponential operational law are discussed in detail. Then, the interval neutrosophic weighted exponential aggregation (INWEA) operator is used to aggregate assessment information to obtain the comprehensive risk assessment. Finally, a multiple attribute decision making (MADM) approach based on the INWEA operator is introduced and applied to the evaluation of typhoon disasters in Fujian Province, China. Results show that the proposed new approach is feasible and effective in practical applications.

]]>Symmetry doi: 10.3390/sym10060195

Authors: Aleksandr Ramaniuk Nguyen Viet Hung Michael Giersig Krzysztof Kempa Vladimir V. Konotop Marek Trippenbach

We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We show that by turning on and off local coupling between rings, one can selectively generate a permanent vortex in one of the rings. We find that due to the modulation instability, it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with an interesting structure of currents flowing between rings, the generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as a single vortex in one of the channels, which later alternates between channels.

]]>Symmetry doi: 10.3390/sym10060194

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

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

]]>Symmetry doi: 10.3390/sym10060193

Authors: Kifayat Ullah Tahir Mahmood Naeem Jan

In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.

]]>Symmetry doi: 10.3390/sym10060192

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

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

]]>Symmetry doi: 10.3390/sym10060191

Authors: Palle E. T. Jorgensen Karl-Hermann Neeb Gestur Ólafsson

In this article we study the connection of fractional Brownian motion, representation theory and reflection positivity in quantum physics. We introduce and study reflection positivity for affine isometric actions of a Lie group on a Hilbert space E and show in particular that fractional Brownian motion for Hurst index 0 &lt; H &le; 1 / 2 is reflection positive and leads via reflection positivity to an infinite dimensional Hilbert space if 0 &lt; H &lt; 1 / 2 . We also study projective invariance of fractional Brownian motion and relate this to the complementary series representations of GL 2 ( R ) . We relate this to a measure preserving action on a Gaussian L 2 -Hilbert space L 2 ( E ) .

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