Symmetry doi: 10.3390/sym10050129

Authors: Sunmi Lee

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

]]>Symmetry doi: 10.3390/sym10050128

Authors: Fengyong Li Kui Wu Xinpeng Zhang Jingsheng Lei Mi Wen

This work tackles a recent challenge in digital image processing: how to identify the steganographic images from a steganographer, who is unknown among multiple innocent actors. The method does not need a large number of samples to train classification model, and thus it is significantly different from the traditional steganalysis. The proposed scheme consists of textural features and clustering ensembles. Local ternary patterns (LTP) are employed to design low-dimensional textural features which are considered to be more sensitive to steganographic changes in texture regions of image. Furthermore, we use the extracted low-dimensional textural features to train a number of hierarchical clustering results, which are integrated as an ensemble based on the majority voting strategy. Finally, the ensemble is used to make optimal decision for suspected image. Extensive experiments show that the proposed scheme is effective and efficient and outperforms the state-of-the-art steganalysis methods with an average gain from 4 % to 6 % .

]]>Symmetry doi: 10.3390/sym10040127

Authors: Yushui Geng Xingang Wang Xuemei Li Kun Yu Peide Liu

There are many practical decision-making problems in people&rsquo;s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance. Therefore, we introduce interval neutrosophic linguistic numbers (INLNs) to represent the less clear and uncertain information and give their operational rules and comparison methods. In addition, since the Maclaurin symmetric mean (MSM) operator has the special characteristic of capturing the interrelationships among multi-input arguments, we further propose an MSM operator for INLNs (INLMSM). Furthermore, considering the weights of attributes are the important parameters and they can influence the decision results, we also propose a weighted INLMSM (WINLMSM) operator. Based on the WINLMSM operator, we develop a multiple attribute decision making (MADM) method with INLNs and some examples are used to show the procedure and effectiveness of the proposed method. Compared with the existing methods, the proposed method is more convenient to express the complex and unclear information. At the same time, it is more scientific and flexible in solving the MADM problems by considering the interrelationships among multi-attributes.

]]>Symmetry doi: 10.3390/sym10040126

Authors: Mikail Bal Moges Mekonnen Shalla Necati Olgun

In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.

]]>Symmetry doi: 10.3390/sym10040125

Authors: Carlos Jiménez de Parga Sebastián Rubén Gómez Palomo

This paper presents several new techniques for volumetric cloud rendering using efficient algorithms and data structures based on ray-tracing methods for cumulus generation, achieving an optimum balance between realism and performance. These techniques target applications such as flight simulations, computer games, and educational software, even with conventional graphics hardware. The contours of clouds are defined by implicit mathematical expressions or triangulated structures inside which volumetric rendering is performed. Novel techniques are used to reproduce the asymmetrical nature of clouds and the effects of light-scattering, with low computing costs. The work includes a new method to create randomized fractal clouds using a recursive grammar. The graphical results are comparable to those produced by state-of-the-art, hyper-realistic algorithms. These methods provide real-time performance, and are superior to particle-based systems. These outcomes suggest that our methods offer a good balance between realism and performance, and are suitable for use in the standard graphics industry.

]]>Symmetry doi: 10.3390/sym10040124

Authors: Martin Gilje Jaatun Inger Anne Tøndel Nils Brede Moe Daniela Soares Cruzes Karin Bernsmed Børge Haugset

In order to be responsible stewards of other people&rsquo;s data, cloud providers must be accountable for their data handling practices. The potential long provider chains in cloud computing introduce additional accountability challenges, with many stakeholders involved. Symmetry is very important in any requirements&rsquo; elicitation activity, since input from diverse stakeholders needs to be balanced. This article ventures to answer the question &ldquo;How can one create an accountable cloud service?&rdquo; by examining requirements which must be fulfilled to achieve an accountability-based approach, based on interaction with over 300 stakeholders.

]]>Symmetry doi: 10.3390/sym10040123

Authors: Roman Cherniha Mykola Serov Oleksii Pliukhin

This review is devoted to search for Lie and Q-conditional (nonclassical) symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

]]>Symmetry doi: 10.3390/sym10040122

Authors: Omid Sharifi Maryam Eskandari

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

]]>Symmetry doi: 10.3390/sym10040121

Authors: Ioannis K. Dassios

Motivated by dynamical models describing phase separation and the motion of interfaces separating phases, we study the stability of dynamical networks in planar domains formed by triple junctions. We take into account symmetry, angle-intersection conditions at the junctions and at the points at which the curves intersect with the boundary. Firstly, we focus on the case of a network where two triple junctions have all their branches unattached to the boundary and then on the case of a network of hexagons, with one of them having all its branches unattached to the boundary. For both type of networks, we introduce the evolution problem, identify the steady states and study their stability in terms of the geometry of the boundary.

]]>Symmetry doi: 10.3390/sym10040120

Authors: XiaoMin Wang SuDao Bilige

In this paper, the numerical solutions of von K a &acute; rm a &acute; n swirling viscous flow are obtained based on the effective combination of the symmetry method and the Runge-Kutta method. Firstly, the multi-parameter symmetry of von K a &acute; rm a &acute; n swirling viscous flow is determined based on the differential characteristic set algorithm. Secondly, we used the symmetry to reduce von K a &acute; rm a &acute; n swirling viscous flow to an initial value problem of the original differential equations. Finally, we numerically solve the initial value problem of the original differential equations by using the Runge-Kutta method.

]]>Symmetry doi: 10.3390/sym10040119

Authors: Yanhui Guo Amira S. Ashour Florentin Smarandache

This paper proposes novel skin lesion detection based on neutrosophic clustering and adaptive region growing algorithms applied to dermoscopic images, called NCARG. First, the dermoscopic images are mapped into a neutrosophic set domain using the shearlet transform results for the images. The images are described via three memberships: true, indeterminate, and false memberships. An indeterminate filter is then defined in the neutrosophic set for reducing the indeterminacy of the images. A neutrosophic c-means clustering algorithm is applied to segment the dermoscopic images. With the clustering results, skin lesions are identified precisely using an adaptive region growing method. To evaluate the performance of this algorithm, a public data set (ISIC 2017) is employed to train and test the proposed method. Fifty images are randomly selected for training and 500 images for testing. Several metrics are measured for quantitatively evaluating the performance of NCARG. The results establish that the proposed approach has the ability to detect a lesion with high accuracy, 95.3% average value, compared to the obtained average accuracy, 80.6%, found when employing the neutrosophic similarity score and level set (NSSLS) segmentation approach.

]]>Symmetry doi: 10.3390/sym10040118

Authors: Peijian Shi Xiao Zheng David A. Ratkowsky Yang Li Ping Wang Liang Cheng

Many plant leaves exhibit bilateral symmetry, but such symmetry has rarely been measured because of the lack of practical methods. We propose a simple method for achieving the above objective. A leaf is divided into left and right sides, and several equally-sized strips are generated to intersect each side of that leaf to generate pairwise left and right sub-regions. A standardized index (SI) for measuring bilateral symmetry is built based on the left&ndash;right areal differences of those sub-regions. The leaves of 10 species of plants were sampled for testing the method&rsquo;s validity. Based on the experimental data, we compared the root-mean-squared error (RMSE), SI, and areal ratio (AR) of the left side to the right side of the leaf. The SI measures the bilateral symmetry of plant leaves well, and it is better than the RMSE and AR for eliminating the effect of leaf size on the goodness of fit. The SI proposed here is the best indicator for evaluating the degree of bilateral symmetry and can be potentially used for comparing the difference in the bilateral symmetry of leaves of different plants.

]]>Symmetry doi: 10.3390/sym10040117

Authors: Stefan Van Dongen

(1) Background: The link between behavioral lateralization and bodily asymmetry in humans is studied to investigate the reliability of fluctuating asymmetry as a measure of developmental instability; (2) Methods: Morphological asymmetries of arms and legs, obtained from 3D body scans, were correlated with different measures of behavioral lateralization; (3) Results: Observed associations were in the directions expected, showing that more asymmetric use of the body increases asymmetry, especially in the arms, and more symmetric body use appears to have a symmetrizing effect; and (4) Conclusions: The results presented here question the suitability of human bodily asymmetry in arms and legs&mdash;or at least part of them&mdash;as a measure of developmental instability. There is a need for future research that identifies regions of the body that are not affected by behavioral lateralization and can reliably reflect developmental instability.

]]>Symmetry doi: 10.3390/sym10040116

Authors: Mohamed Abdel-Basset Mai Mohamed Florentin Smarandache

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

]]>Symmetry doi: 10.3390/sym10040115

Authors: Wei Yang Yongfeng Pang

Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among attributes can be modeled, and attribute weights are determined. The normalized Euclidean distance and the normalized Hamming distance between multi-valued interval neutrosophic fuzzy values are defined. Alternatives are ranked by using the TOPSIS method based on the distance measures. The truck selection problem in the logistics industry is presented to illustrate the feasibility and practical advantages of the proposed method. Some comparisons of the new method with other methods are also made.

]]>Symmetry doi: 10.3390/sym10040114

Authors: Jungil Kim Eunjoo Lee

The code reviewer assignment problem affects the reviewing time of a source code change. To effectively perform the code review process of a software project, the code reviewer assignment problem must be dealt with. Reviewer recommendation can reduce the time required for finding appropriate reviewers for a given source code change. In this paper, we propose a reviewer recommendation approach based on latent Dirichlet allocation (LDA). The proposed reviewer recommendation approach consists of a review expertise generation phase and a reviewer recommendation phase. The review expertise generation phase generates the review expertise of developers for topics of source code changes from the review history of a software project. The reviewer recommendation phase computes the review scores of the developers according to the topic distribution of a given source code change and the review expertise of the developers. In an empirical evaluation of five open source projects, we confirm that the proposed reviewer recommendation approach obtains better average top-10 accuracy than existing reviewer recommendation approaches.

]]>Symmetry doi: 10.3390/sym10040113

Authors: Guang Li Jie Wang Jing Liang Caitong Yue

Since data stream anomaly detection algorithms based on sliding windows are sensitive to the abnormal deviation of individual interference data, this paper presents a sliding nest window chart anomaly detection based on the data stream (SNWCAD-DS) by employing the concept of the sliding window and control chart. By nesting a small sliding window in a large sliding window and analyzing the deviation distance between the small window and the large sliding window, the algorithm increases the out-of-bounds detection ratio and classifies the conceptual drift data stream online. The designed algorithm is simulated on the industrial data stream of drilling engineering. The proposed algorithm SNWCAD is compared with Automatic Outlier Detection for Data Streams (A-ODDS) and Distance-Based Outline Detection for Data Stream (DBOD-DS). The experimental results show that the new algorithm can obtain higher detection accuracy than the compared algorithms. Furthermore, it can shield the influence of individual interference data and satisfy actual engineering needs.

]]>Symmetry doi: 10.3390/sym10040112

Authors: Jianping Zhou Yuan Wang Yang Wang Zhilian Yan Zhen Wang

The compatibility method is used for a generalized variable-coefficient Gardner equation (GVGE) with a forcing term. By the compatibility of the considered equation and a non-classical symmetry of a given form, four types of symmetry are obtained. Then, by solving the characteristic equations of symmetry, the GVGE is reduced to variable coefficients ordinary differential equations, and rich varieties of new similarity solutions are presented. Our results show that the compatibility method can be employed for variable coefficients nonlinear evolution equations with forcing terms.

]]>Symmetry doi: 10.3390/sym10040111

Authors: Yuval Ben-Abu Ira Wolfson Haim Eshach Hezi Yizhaq

The cycloid is one of the most intriguing objects in the classical physics world, at once solving the brachistochrone and isochronous curve problems. Historically, the cycloid shape has been employed to great success in many physical contexts. We discuss one such case, presenting the longitude problem as a pathway into an in-depth discussion of the analytical solution of a point mass motion along a cycloid. The classical solution is presented, and the modifications needed for a rolling ball along a cycloid rail are made. A comparison is then made between the two cases, and we show that the difference in most physical cases between the point mass and the rolling ball is at most ~7%. Next, an experiment is presented in which the isochronous nature of the cycloid path is tested, to different degrees of success. The results are discussed and several possible origins of the discrepancy between the theory and the experimental results are identified. We conclude with a discussion of skidding and slipless rolling.

]]>Symmetry doi: 10.3390/sym10040110

Authors: Wontaek Hong Jeonghoon Moon Woojin Seok Jinwook Chung

The rapid transfer of massive data in the cloud environment is required to prepare for unexpected situations like disaster recovery. With regard to this requirement, we propose a new approach to transferring cloud virtual machine images rapidly in the cloud environment utilizing dedicated Data Transfer Nodes (DTNs). The overall procedure is composed of local/remote copy processes and a DTN-to-DTN transfer process. These processes are coordinated and executed based on a fork system call in the proposed algorithm. In addition, we especially focus on the local copy process between a cloud controller and DTNs and improve data transfer performance through the well-tuned mount techniques in Network File System (NFS)-based connections. Several experiments have been performed considering the combination of synchronous/asynchronous modes and the network buffer size. We show the results of throughput in all the experiment cases and compare them. Consequently, the best throughput in write operations has been obtained in the case of an NFS server in a DTN and an NFS client in a cloud controller running entirely in the asynchronous mode.

]]>Symmetry doi: 10.3390/sym10040109

Authors: Mingyu Kim Jiwon Lee Changhun Kim Jinmo Kim

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

]]>Symmetry doi: 10.3390/sym10040108

Authors: Jeon Kang Chan Kim Young Lee Se Cho Kang Park

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

]]>Symmetry doi: 10.3390/sym10040107

Authors: Boyuan Ma Xiaojuan Ban Haiyou Huang Yulian Chen Wanbo Liu Yonghong Zhi

Quantitative analysis through image processing is a key step to gain information regarding the microstructure of materials. In this paper, we develop a deep learning-based method to address the task of image segmentation for microscopic images using an Al–La alloy. Our work makes three key contributions. (1) We train a deep convolutional neural network based on DeepLab to achieve image segmentation and have significant results. (2) We adopt a local processing method based on symmetric overlap-tile strategy which makes it possible to analyze the microscopic images with high resolution. Additionally, it achieves seamless segmentation. (3) We apply symmetric rectification to enhance the accuracy of results with 3D information. Experimental results showed that our method outperforms existing segmentation methods.

]]>Symmetry doi: 10.3390/sym10040106

Authors: Mohamed Abdel-Basset Mai Mohamed Florentin Smarandache Victor Chang

Big Data is a large-sized and complex dataset, which cannot be managed using traditional data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold. The classical association rules can only be extracted from binary data where an item exists in a transaction, but it fails to deal effectively with quantitative attributes, through decreasing the quality of generated association rules due to sharp boundary problems. In order to overcome the drawbacks of classical association rule mining, we propose in this research a new neutrosophic association rule algorithm. The algorithm uses a new approach for generating association rules by dealing with membership, indeterminacy, and non-membership functions of items, conducting to an efficient decision-making system by considering all vague association rules. To prove the validity of the method, we compare the fuzzy mining and the neutrosophic mining. The results show that the proposed approach increases the number of generated association rules.

]]>Symmetry doi: 10.3390/sym10040105

Authors: Jolanta Dzwierzynska Aleksandra Prokopska

The aim of the study is to develop an original, methodical, and practical approach to the early stages of parametric design of roof shells formed by repetitive modules of Catalan surfaces. It is presented on the example of designing the roof shells compound of four concrete elements. The designing process proposed by us consists in linking geometric shaping of roofs’ models with their structural analysis and optimization. Contrary to other methods, which use optimization process in order to find free roof forms, we apply it in order to explore and improve design alternatives. It is realized with the application of designing tools working in Rhinoceros 3D software. The flexible scripts elaborated by us, in order to achieve roofs’ models of regular and symmetrical shapes, are converted into simulation models to perform structural analysis. It is mainly focused on how the roof shells perform dependently on their geometric characteristics. The simulation enables one to evaluate various roof shells’ shapes, as well as to select an optimal design solution. The proposed approach to the conceptual design process may drive the designing to achieve geometric and structural forms which not only follow the design intentions but also target better results.

]]>Symmetry doi: 10.3390/sym10040104

Authors: Huimin Zhao Weitong Gao Wu Deng Meng Sun

The ant colony optimization (ACO) algorithm has the characteristics of positive feedback, essential parallelism, and global convergence, but it has the shortcomings of premature convergence and slow convergence speed. The co-evolutionary algorithm (CEA) emphasizes the existing interaction among different sub-populations, but it is overly formal, and does not form a very strict and unified definition. Therefore, a new adaptive co-evolutionary ant colony optimization (SCEACO) algorithm based on the complementary advantages and hybrid mechanism is proposed in this paper. Firstly, the pheromone update formula is improved and the pheromone range of the ACO algorithm is limited in order to achieve the adaptive update of the pheromone. The elitist strategy and co-evolutionary idea are used for reference, the symbiotic mechanism and hybrid mechanism are introduced to better utilize the advantages of the CEA and ACO. Then the multi-objective optimization problem is divided into several sub-problems, each sub-problem corresponds to one population. Each ant colony is divided into multiple sub-populations in a common search space, and each sub-population performs the search activity and pheromone updating strategy. The elitist strategy is used to retain the elitist individuals within the population and the min-max ant strategy is used to set pheromone concentration for each path. Next, the selection, crossover, and mutation operations of individuals are introduced to adaptively adjust the parameters and implement the information sharing of the population and the co-evolution. Finally, the gate assignment problem of a hub airport is selected to verify the optimization performance of the SCEACO algorithm. The experiment results show that the SCEACO algorithm can effectively solve the gate assignment problem of a hub airport and obtain the effective assignment result. The SCEACO algorithm improves the convergence speed, and enhances the local search ability and global search capability.

]]>Symmetry doi: 10.3390/sym10040103

Authors: Oleg Epstein

From studies on the effects of “high dilutions” on organisms, it was found that their administration induces a delicate physiological (molecular and cellular) response. Occasionally, physiological reactions can become atypical (pathological) individual reactions. To resolve this paradox, the spatial homeostasis hypothesis has been proposed. It considers pathological processes as tools used by living systems, in order to retain their spatial integrity (symmetry), allowing them to properly reflect the geometry of the surrounding world and thus, to be a part of the evolutionary process. This article addresses an interdisciplinary subject and is aimed at natural scientists (physicists, chemists, and biologists) as well as philosophers.

]]>Symmetry doi: 10.3390/sym10040102

Authors: Antonio Belmonte Juan Garrido Jorge Jiménez Francisco Vázquez

This paper presents a new algorithm for the resolution of over-constrained lumped process systems, where partial differential equations of a continuous time and space model of the system are reduced into ordinary differential equations with a finite number of parameters and where the model equations outnumber the unknown model variables. Our proposal is aimed at the study and improvement of the algorithm proposed by Hangos-Szerkenyi-Tuza. This new algorithm improves the computational cost and solves some of the internal problems of the aforementioned algorithm in its original formulation. The proposed algorithm is based on parameter relaxation that can be modified easily. It retains the necessary information of the lumped process system to reduce the time cost after introducing changes during the system formulation. It also allows adjustment of the system formulations that change its differential index between simulations.

]]>Symmetry doi: 10.3390/sym10040101

Authors: Guomin Sun Jinsong Leng Carlo Cattani

In this paper, we will construct a new multilevel system in the Fourier domain using the harmonic wavelet. The main advantages of harmonic wavelet are that its frequency spectrum is confined exactly to an octave band, and its simple definition just as Haar wavelet. The constructed multilevel system has the circular shape, which forms a partition of the frequency domain by shifting and scaling the basic wavelet functions. To possess the circular shape, a new type of sampling grid, the circular-polar grid (CPG), is defined and also the corresponding modified Fourier transform. The CPG consists of equal space along rays, where different rays are equally angled. The main difference between the classic polar grid and CPG is the even sampling on polar coordinates. Another obvious difference is that the modified Fourier transform has a circular shape in the frequency domain while the polar transform has a square shape. The proposed sampling grid and the new defined Fourier transform constitute a completely Fourier transform system, more importantly, the harmonic wavelet based multilevel system defined on the proposed sampling grid is more suitable for the distribution of general images in the Fourier domain.

]]>Symmetry doi: 10.3390/sym10040100

Authors: Daniel Arrigo Andrea Weaver

It is generally known that classical point and potential Lie symmetries of differential equations can be different. In a recent paper, we were able to show for a class of nonlinear diffusion equation that the nonclassical potential symmetries possess all nonclassical symmetries of the original equation. We question whether this is true for the power law Harry Dym equation. In this paper, we show that the nonclassical symmetries of the power law Harry Dym equation and an equivalent system still possess special separate symmetries. However, we will show that we can extend the nonclassical method so that all nonclassical symmetries of the original power law Harry Dym equation can be obtained through the equivalent system.

]]>Symmetry doi: 10.3390/sym10040099

Authors: David Corrales Juan Corrales Agapito Ledezma

Today, data availability has gone from scarce to superabundant. Technologies like IoT, trends in social media and the capabilities of smart-phones are producing and digitizing lots of data that was previously unavailable. This massive increase of data creates opportunities to gain new business models, but also demands new techniques and methods of data quality in knowledge discovery, especially when the data comes from different sources (e.g., sensors, social networks, cameras, etc.). The data quality process of the data set proposes conclusions about the information they contain. This is increasingly done with the aid of data cleaning approaches. Therefore, guaranteeing a high data quality is considered as the primary goal of the data scientist. In this paper, we propose a process for data cleaning in regression models (DC-RM). The proposed data cleaning process is evaluated through a real datasets coming from the UCI Repository of Machine Learning Databases. With the aim of assessing the data cleaning process, the dataset that is cleaned by DC-RM was used to train the same regression models proposed by the authors of UCI datasets. The results achieved by the trained models with the dataset produced by DC-RM are better than or equal to that presented by the datasets’ authors.

]]>Symmetry doi: 10.3390/sym10040098

Authors: Riina Aav Kamini Mishra

Cucurbituril-type hosts are highly symmetric, but there are means to break their symmetry. This review will present examples from three directions of induction of chirality in or by cucurbituril-type hosts: first, through the incorporation of stereogenic elements into host molecules; second, through complexation with achiral guests, which leads to axial supramolecular chirality and helical structures; third, through the formation of complexes with chiral guests in multi-molecule complexes and induction of supramolecular chirality. In addition, a list of chiral guests used in binding studies with cucurbiturils is collected. We would envision that encouraged by the outlined examples of outstanding applications of chiral cucurbituril-supramolecular systems, the boundaries of chiral applications of cucurbiturils would be widened.

]]>Symmetry doi: 10.3390/sym10040097

Authors: Giao N. Pham Suk-Hwan Lee Oh-Heum Kwon Ki-Ryong Kwon

Nowadays, 3D printing is widely used in many areas of life. This leads to 3D printing models often being used illegally without any payment to the original providers. Therefore, providers need a solution to identify and protect the copyright of 3D printing. This paper presents a novel watermarking method for the copyright protection of 3D printing based on the Menger facet curvature and K-mean clustering. The facets of the 3D printing model are classified into groups based on the value of Menger curvature and the K-mean clustering, and the mean Menger curvature of each group will then be computed for embedding the watermark data. The watermark data are embedded into the groups of facets by changing the mean Menger curvature of each group according to the bit of watermark data. In each group, we select a facet that has the Menger curvature closest to the changed mean Menger curvature, and we then transform the vertices of the selected facet according to the changed Menger curvature for the watermarked 3D printing model generation. Watermark data are extracted from 3D-printed objects, which are printed from the watermarked 3D printing models by the 3D printer. Experimental results after embedding the watermark verified that the proposed method is invisible and robust to geometric attacks such as rotation, scaling and translation. In experiments with an XYZ Printing Pro 3D printer and 3D scanner, the accuracy and performance of the proposed method was higher than the two previous methods in the 3D printing watermarking domain. The proposed method provides a better solution for the copyright protection of 3D printing.

]]>Symmetry doi: 10.3390/sym10040096

Authors: Jucheng Yang Wenhui Sun Na Liu Yarui Chen Yuan Wang Shujie Han

Multimodal biometrics combine a variety of biological features to have a significant impact on identification performance, which is a newly developed trend in biometrics identification technology. This study proposes a novel multimodal biometrics recognition model based on the stacked extreme learning machines (ELMs) and canonical correlation analysis (CCA) methods. The model, which has a symmetric structure, is found to have high potential for multimodal biometrics. The model works as follows. First, it learns the hidden-layer representation of biological images using extreme learning machines layer by layer. Second, the canonical correlation analysis method is applied to map the representation to a feature space, which is used to reconstruct the multimodal image feature representation. Third, the reconstructed features are used as the input of a classifier for supervised training and output. To verify the validity and efficiency of the method, we adopt it for new hybrid datasets obtained from typical face image datasets and finger-vein image datasets. Our experimental results demonstrate that our model performs better than traditional methods.

]]>Symmetry doi: 10.3390/sym10040095

Authors: Yang-Wai Chow Willy Susilo Joseph Tonien Elena Vlahu-Gjorgievska Guomin Yang

Secret sharing is an information security technique where a dealer divides a secret into a collection of shares and distributes these to members of a group. The secret will only be revealed when a predefined number of group members cooperate to recover the secret. The purpose of this study is to investigate a method of distributing shares by embedding them into cover Quick Response (QR) codes in a secure manner using cryptographic keys. The advantage of this approach is that the shares can be disseminated over public channels, as anyone who scans the QR codes will only obtain public information. Only authorized individuals who are in possession of the required keys will be able to recover the shares. This also means that when group members cooperate to recover a secret, the group can determine the presence of an illegitimate participant if the person does not produce a valid share. This study proposes a protocol for accomplishing this and discusses the underlying security of the protocol.

]]>Symmetry doi: 10.3390/sym10040094

Authors: Xiaokun Wang Xiaojuan Ban Runzi He Di Wu Xing Liu Yuting Xu

In order to simulate fluid-solid boundary interaction for non-Newtonian Smoothed Particle Hydrodynamics (SPH) fluids, we present a steady and realistic fluid-solid boundary handling method using symmetrical interaction forces. Firstly, we use the improved SPH method to model the non-Newtonian fluid. Secondly, the density of boundary particle is created into the calculation of fluid-solid interaction forces. Besides, we apply friction conditions to constrain the fluid particles at the boundary. Finally, we apply the predictive-corrective scheme to correct the density deviation and improve boundary computing efficiency. The experiment confirms the feasibility for the interaction between non-Newtonian fluid and solid objects with this method. At the same time, it reflects the viscous characteristics and ensures the physical properties of non-Newtonian fluid. In addition, compared to existing methods, this method is more stable and easier to implement.

]]>Symmetry doi: 10.3390/sym10040093

Authors: Jun-Ho Huh

The obese population is increasing rapidly due to the change of lifestyle and diet habits. Obesity can cause various complications and is becoming a social disease. Nonetheless, many obese patients are unaware of the medical treatments that are right for them. Although a variety of online and offline obesity management services have been introduced, they are still not enough to attract the attention of users and are not much of help to solve the problem. Obesity healthcare and personalized health activities are the important factors. Since obesity is related to lifestyle habits, eating habits, and interests, I concluded that the big data analysis of these factors could deduce the problem. Therefore, I collected big data by applying the machine learning and crawling method to the unstructured citizen health data in Korea and the search data of Naver, which is a Korean portal company, and Google for keyword analysis for personalized health activities. It visualized the big data using text mining and word cloud. This study collected and analyzed the data concerning the interests related to obesity, change of interest on obesity, and treatment articles. The analysis showed a wide range of seasonal factors according to spring, summer, fall, and winter. It also visualized and completed the process of extracting the keywords appropriate for treatment of abdominal obesity and lower body obesity. The keyword big data analysis technique for personalized health activities proposed in this paper is based on individual’s interests, level of interest, and body type. Also, the user interface (UI) that visualizes the big data compatible with Android and Apple iOS. The users can see the data on the app screen. Many graphs and pictures can be seen via menu, and the significant data values are visualized through machine learning. Therefore, I expect that the big data analysis using various keywords specific to a person will result in measures for personalized treatment and health activities.

]]>Symmetry doi: 10.3390/sym10040092

Authors: Geunseok Yang Youngjun Jeong Kyeongsic Min Jung-won Lee Byungjeong Lee

Owing to the high complexity of recent software products, developers cannot avoid major/minor mistakes, and software bugs are generated during the software development process. When developers manually modify a program source code using bug descriptions to fix bugs, their daily workloads and costs increase. Therefore, we need a way to reduce their workloads and costs. In this paper, we propose a novel automatic fault repair method by using similar bug fix information based on genetic programming (GP). First, we searched for similar buggy source codes related to the new given buggy code, and then we searched for a fixed the buggy code related to the most similar source code. Next, we transformed the fixed code into abstract syntax trees for applying GP and generated the candidate program patches. In this step, we verified the candidate patches by using a fitness function based on given test cases to determine whether the patch was valid or not. Finally, we produced program patches to fix the new given buggy code.

]]>Symmetry doi: 10.3390/sym10040091

Authors: Mehdi Keshavarz-Ghorabaee Maghsoud Amiri Edmundas Zavadskas Zenonas Turskis Jurgita Antucheviciene

Determination of subjective weights, which are based on the opinions and preferences of decision-makers, is one of the most important matters in the process of multi-criteria decision-making (MCDM). Step-wise Weight Assessment Ratio Analysis (SWARA) is an efficient method for obtaining the subjective weights of criteria in the MCDM problems. On the other hand, decision-makers may express their opinions with a degree of uncertainty. Using the symmetric interval type-2 fuzzy sets enables us to not only capture the uncertainty of information flexibly but also to perform computations simply. In this paper, we propose an extended SWARA method with symmetric interval type-2 fuzzy sets to determine the weights of criteria based on the opinions of a group of decision-makers. The weights determined by the proposed approach involve the uncertainty of decision-makers’ preferences and the symmetric form of the weights makes them more interpretable. To show the procedure of the proposed approach, it is used to determine the importance of intellectual capital dimensions and components in a company. The results show that the proposed approach is efficient in determining the subjective weights of criteria and capturing the uncertainty of information.

]]>Symmetry doi: 10.3390/sym10040090

Authors: Giao Pham Suk-Hwan Lee Oh-Heum Kwon Ki-Ryong Kwon

With the development of 3D printing, weapons are easily printed without any restriction from the production managers. Therefore, anti-3D weapon model detection is necessary issue in safe 3D printing to prevent the printing of 3D weapon models. In this paper, we would like to propose an anti-3D weapon model detection algorithm to prevent the printing of anti-3D weapon models for safe 3D printing based on the D2 shape distribution and an improved convolutional neural networks (CNNs). The purpose of the proposed algorithm is to detect anti-3D weapon models when they are used in 3D printing. The D2 shape distribution is computed from random points on the surface of a 3D weapon model and their geometric features in order to construct a D2 vector. The D2 vector is then trained by improved CNNs. The CNNs are used to detect anti-3D weapon models for safe 3D printing by training D2 vectors which have been constructed from the D2 shape distribution of 3D weapon models. Experiments with 3D weapon models proved that the D2 shape distribution of 3D weapon models in the same class is the same. Training and testing results also verified that the accuracy of the proposed algorithm is higher than the conventional works. The proposed algorithm is applied in a small application, and it could detect anti-3D weapon models for safe 3D printing.

]]>Symmetry doi: 10.3390/sym10040089

Authors: Shaojun Bian Anzong Zheng Ehtzaz Chaudhry Lihua You Jian Zhang

Since non-automatic rigging requires heavy human involvements, and various automatic rigging algorithms are less efficient in terms of computational efficiency, especially for current curve-based skin deformation methods, identifying the iso-parametric curves and creating the animation skeleton requires tedious and time-consuming manual work. Although several automatic rigging methods have been developed, but they do not aim at curve-based models. To tackle this issue, this paper proposes a new rigging algorithm for automatic generation of dynamic skin deformation to quickly identify iso-parametric curves and create an animation skeleton in a few milliseconds, which can be seamlessly used in curve-based skin deformation methods to make the rigging process fast enough for highly efficient computer animation applications.

]]>Symmetry doi: 10.3390/sym10040087

Authors: Baidaa Al-Bander Bryan Williams Waleed Al-Nuaimy Majid Al-Taee Harry Pratt Yalin Zheng

Glaucoma is a group of eye diseases which can cause vision loss by damaging the optic nerve. Early glaucoma detection is key to preventing vision loss yet there is a lack of noticeable early symptoms. Colour fundus photography allows the optic disc (OD) to be examined to diagnose glaucoma. Typically, this is done by measuring the vertical cup-to-disc ratio (CDR); however, glaucoma is characterised by thinning of the rim asymmetrically in the inferior-superior-temporal-nasal regions in increasing order. Automatic delineation of the OD features has potential to improve glaucoma management by allowing for this asymmetry to be considered in the measurements. Here, we propose a new deep-learning-based method to segment the OD and optic cup (OC). The core of the proposed method is DenseNet with a fully-convolutional network, whose symmetric U-shaped architecture allows pixel-wise classification. The predicted OD and OC boundaries are then used to estimate the CDR on two axes for glaucoma diagnosis. We assess the proposed method’s performance using a large retinal colour fundus dataset, outperforming state-of-the-art segmentation methods. Furthermore, we generalise our method to segment four fundus datasets from different devices without further training, outperforming the state-of-the-art on two and achieving comparable results on the remaining two.

]]>Symmetry doi: 10.3390/sym10040088

Authors: Manuel Arrayás José Trueba

We calculate analytically the spin-orbital decomposition of the angular momentum using completely nonparaxial fields that have a certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behavior of the local angular momentum density is rather different. By taking cases with constant and non-constant electric and magnetic helicities, we show that the total angular momentum density presents different characteristics during time evolution.

]]>Symmetry doi: 10.3390/sym10040086

Authors: Sinuo Liu Xiaojuan Ban Ben Wang Xiaokun Wang

We present a symmetric particle simulation scheme for diffuse fluids based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, the generation of diffuse particles is determined by the entropy of fluid particles, and it is calculated by the velocity difference and kinetic energy. Diffuse particles are generated near the qualified diffuse particle emitters whose diffuse material generation rate is greater than zero. Our method fits the laws of physics better, as it abandons the common practice of adding diffuse materials at the crest empirically. The coupling between diffuse materials and fluid is a post-processing step achieved by the velocity field, which enables the avoiding of the time-consuming process of cross finding neighbors. The influence weights of the fluid particles are assigned based on the degree of coupling. Therefore, it improved the accuracy of the diffuse particle position and made the simulation results more realistic. The approach is appropriate for large scale diffuse fluid, as it can be easily integrated in existing SPH simulation methods and the computational overhead is negligible.

]]>Symmetry doi: 10.3390/sym10040085

Authors: Xin Li Xiaohong Zhang Choonkil Park

The interval neutrosophic set (INS) is a subclass of the neutrosophic set (NS) and a generalization of the interval-valued intuitionistic fuzzy set (IVIFS), which can be used in real engineering and scientific applications. This paper aims at developing new generalized Choquet aggregation operators for INSs, including the generalized interval neutrosophic Choquet ordered averaging (G-INCOA) operator and generalized interval neutrosophic Choquet ordered geometric (G-INCOG) operator. The main advantages of the proposed operators can be described as follows: (i) during decision-making or analyzing process, the positive interaction, negative interaction or non-interaction among attributes can be considered by the G-INCOA and G-INCOG operators; (ii) each generalized Choquet aggregation operator presents a unique comprehensive framework for INSs, which comprises a bunch of existing interval neutrosophic aggregation operators; (iii) new multi-attribute decision making (MADM) approaches for INSs are established based on these operators, and decision makers may determine the value of &lambda; by different MADM problems or their preferences, which makes the decision-making process more flexible; (iv) a new clustering algorithm for INSs are introduced based on the G-INCOA and G-INCOG operators, which proves that they have the potential to be applied to many new fields in the future.

]]>Symmetry doi: 10.3390/sym10040084

Authors: Chao-Liang Liu Wang-Jui Tsai Ting-Yi Chang Ta-Ming Liu

A three-party Authenticated Key Agreement (AKA) protocol in the distributed computing environment is a client that requests services from an application server through an authentication server. The authentication server is responsible for authenticating the participating entities and helping them to construct a common session key. Adopting the Key Transfer Authentication Protocol (KTAP) in such an environment, the authentication server is able to monitor the communication messages to prevent and trace network crime. However, the session key in the KTAP setting is created only by the authentication server and is vulnerable to the resilience of key control. On the other hand, with the rapid growth of network technologies, mobile devices are widely used by people to access servers in the Internet. Many AKA protocols for mobile devices have been proposed, however, most protocols are vulnerable to Ephemeral Secret Leakage (ESL) attacks which compromise the private keys of clients and the session key by an adversary from eavesdropped messages. This paper proposes a novel ESL-secure ID-based three-party AKA protocol for mobile distributed computing environments based on ESL-secure ID-based Authenticated Key Exchange (ID-AKE) protocol. The proposed protocol solves the key control problem in KTAP while retaining the advantages of preventing and tracing network crime in KTAP and also resists ESL attacks. The AVISPA tool simulation results confirm the correctness of the protocol security analysis. Furthermore, we present a parallel version of the proposed ESL-secure ID-based three-party AKA protocol that is communication-efficient.

]]>Symmetry doi: 10.3390/sym10040083

Authors: Phuong Chu Seoungjae Cho Sungdae Sim Kiho Kwak Kyungeun Cho

Nowadays, unmanned ground vehicles (UGVs) are widely used for many applications. UGVs have sensors including multi-channel laser sensors, two-dimensional (2D) cameras, Global Positioning System receivers, and inertial measurement units (GPS–IMU). Multi-channel laser sensors and 2D cameras are installed to collect information regarding the environment surrounding the vehicle. Moreover, the GPS–IMU system is used to determine the position, acceleration, and velocity of the vehicle. This paper proposes a fast and effective method for modeling nonground scenes using multiple types of sensor data captured through a remote-controlled robot. The multi-channel laser sensor returns a point cloud in each frame. We separated the point clouds into ground and nonground areas before modeling the three-dimensional (3D) scenes. The ground part was used to create a dynamic triangular mesh based on the height map and vehicle position. The modeling of nonground parts in dynamic environments including moving objects is more challenging than modeling of ground parts. In the first step, we applied our object segmentation algorithm to divide nonground points into separate objects. Next, an object tracking algorithm was implemented to detect dynamic objects. Subsequently, nonground objects other than large dynamic ones, such as cars, were separated into two groups: surface objects and non-surface objects. We employed colored particles to model the non-surface objects. To model the surface and large dynamic objects, we used two dynamic projection panels to generate 3D meshes. In addition, we applied two processes to optimize the modeling result. First, we removed any trace of the moving objects, and collected the points on the dynamic objects in previous frames. Next, these points were merged with the nonground points in the current frame. We also applied slide window and near point projection techniques to fill the holes in the meshes. Finally, we applied texture mapping using 2D images captured using three cameras installed in the front of the robot. The results of the experiments prove that our nonground modeling method can be used to model photorealistic and real-time 3D scenes around a remote-controlled robot.

]]>Symmetry doi: 10.3390/sym10040082

Authors: Artyom Yurov Valerian Yurov

In this article we present a new method for construction of exact solutions of the Landau-Lifshitz-Gilbert equation (LLG) for ferromagnetic nanowires. The method is based on the established relationship between the LLG and the nonlinear Schrödinger equation (NLS), and is aimed at resolving an old problem: how to produce multiple-rogue wave solutions of NLS using just the Darboux-type transformations. The solutions of this type—known as P-breathers—have been proven to exist by Dubard and Matveev, but their technique heavily relied on using the solutions of yet another nonlinear equation, the Kadomtsev-Petviashvili I equation (KP-I), and its relationship with NLS. We have shown that in fact one doesn’t have to use KP-I but can instead reach the same results just with NLS solutions, but only if they are dressed via the binary Darboux transformation. In particular, our approach allows us to construct all the Dubard-Matveev P-breathers. Furthermore, the new method can lead to some completely new, previously unknown solutions. One particular solution that we have constructed describes two “positon”-like waves, colliding with each other and in the process producing a new, short-lived rogue wave. We called this unusual solution (in which a rogue wave is begotten after the impact of two solitons) the “impacton”.

]]>Symmetry doi: 10.3390/sym10040081

Authors: Peide Liu Hui Gao

In multicriteria decision making (MCDM), multi-hesitant fuzzy linguistic term sets (MHFLTSs) can eliminate the limitations of hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic sets (HFLSs), and emphasize the importance of a repeated linguistic term (LT). Meanwhile, there is usually an interrelation between criteria. The Maclaurin symmetric mean (MSM) operator can capture the interrelationships among multi-input arguments. The purpose of this paper is to integrate MHFLTSs with MSM operators and to solve MCDM problems. Firstly, we develop the generalized MSM operator for MHFLTSs (MHFLGMSM), the generalized geometric MSM operator for MHFLTSs (MHFLGGMSM), the weighted generalized MSM operator for MHFLTSs (WMHFLGMSM) and the weighted generalized geometric MSM operator for MHFLTSs (WMHFLGGMSM), respectively. Then, we discuss their properties and some special cases. Further, we present a novel method to deal with MCDM problems with the MHFLTSs based on the proposed MSM operators. Finally, an illustrative example about how to select the best third-party logistics service provider is supplied to demonstrate the practicality and reliability of the proposed approaches in comparison with some existing approaches.

]]>Symmetry doi: 10.3390/sym10040080

Authors: Marco Faccioli Luca Salasnich

We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at a finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. We analyze similarities and differences in the two equations and, in particular, in the phase and amplitude modes (i.e., Goldstone and Higgs modes) of the bosonic matter field. We show that the coupling between phase and amplitude modes gives rise to a single gapless Bogoliubov spectrum in the non-relativistic case. Instead, in the relativistic case the spectrum has two branches: one is gapless and the other is gapped. In the non-relativistic limit we find that the relativistic spectrum reduces to the Bogoliubov one. Finally, as an application of the above analysis, we consider the Bose-Hubbard model close to the superfluid-Mott quantum phase transition and we investigate the elementary excitations of its effective action, which contains both non-relativistic and relativistic terms.

]]>Symmetry doi: 10.3390/sym10040079

Authors: Tuong Le Mi Lee Jun Park Sung Baik

In recent years, weakened by the fall of economic growth, many enterprises fell into the crisis caused by financial difficulties. Bankruptcy prediction, a machine learning model, is a great utility for financial institutions, fund managers, lenders, governments, and economic stakeholders. Due to the number of bankrupt companies compared to that of non-bankrupt companies, bankruptcy prediction faces the problem of imbalanced data. This study first presents the bankruptcy prediction framework. Then, five oversampling techniques are used to deal with imbalance problems on the experimental dataset which were collected from Korean companies in two years from 2016 to 2017. Experimental results show that using oversampling techniques to balance the dataset in the training stage can enhance the performance of the bankruptcy prediction. The best overall Area Under the Curve (AUC) of this framework can reach 84.2%. Next, the study extracts more features by combining the financial dataset with transaction dataset to increase the performance for bankruptcy prediction and achieves 84.4% AUC.

]]>Symmetry doi: 10.3390/sym10040078

Authors: Lin Zhang Zaixi Cheng Ying Shen Dongqing Wang

Among the members of biometric identifiers, the palmprint and the palmvein have received significant attention due to their stability, uniqueness, and non-intrusiveness. In this paper, we investigate the problem of palmprint/palmvein recognition and propose a Deep Convolutional Neural Network (DCNN) based scheme, namely P a l m R CNN (short for palmprint/palmvein recognition using CNNs). The effectiveness and efficiency of P a l m R CNN have been verified through extensive experiments conducted on benchmark datasets. In addition, though substantial effort has been devoted to palmvein recognition, it is still quite difficult for the researchers to know the potential discriminating capability of the contactless palmvein. One of the root reasons is that a large-scale and publicly available dataset comprising high-quality, contactless palmvein images is still lacking. To this end, a user-friendly acquisition device for collecting high quality contactless palmvein images is at first designed and developed in this work. Then, a large-scale palmvein image dataset is established, comprising 12,000 images acquired from 600 different palms in two separate collection sessions. The collected dataset now is publicly available.

]]>Symmetry doi: 10.3390/sym10030077

Authors: Xiao Zhou Heng Zhang Chengyou Wang

Copyright protection for digital multimedia has become a research hotspot in recent years. As an efficient solution, the digital watermarking scheme has emerged at the right moment. In this article, a highly robust and hybrid watermarking method is proposed. The discrete wavelet transform (DWT) and all phase discrete cosine biorthogonal transform (APDCBT) presented in recent years as well as the singular value decomposition (SVD) are adopted in this method to insert and recover the watermark. To enhance the watermark imperceptibility, the direct current (DC) coefficients after block-based APDCBT in high frequency sub-bands (LH and HL) are modified by using the watermark. Compared with the conventional SVD-based watermarking method and another watermarking technique, the watermarked images obtained by the proposed method have higher image quality. In addition, the proposed method achieves high robustness in resisting various image processing attacks.

]]>Symmetry doi: 10.3390/sym10030076

Authors: Barbara Abraham-Shrauner

An updated Power Index Method is presented for nonlinear differential equations (NLPDEs) with the aim of reducing them to solutions by algebraic equations. The Lie symmetry, translation invariance of independent variables, allows for traveling waves. In addition discrete symmetries, reflection, or 180 ° rotation symmetry, are possible. The method tests whether certain hyperbolic or Jacobian elliptic functions are analytic solutions. The method consists of eight steps. The first six steps are quickly applied; conditions for algebraic equations are more complicated. A few exceptions to the Power Index Method are discussed. The method realizes an aim of Sophus Lie to find analytic solutions of nonlinear differential equations.

]]>Symmetry doi: 10.3390/sym10030075

Authors: Zhan Jin Yingsong Li Jianming Liu

In this paper, an improved set-membership proportionate normalized least mean square (SM-PNLMS) algorithm is proposed for block-sparse systems. The proposed algorithm, which is named the block-sparse SM-PNLMS (BS-SMPNLMS), is implemented by inserting a penalty of a mixed l 2 , 1 norm of weight-taps into the cost function of the SM-PNLMS. Furthermore, an improved BS-SMPNLMS algorithm (the (BS-SMIPNLMS algorithm) is also derived and analyzed. The proposed algorithms are well investigated in the framework of network echo cancellation. The results of simulations indicate that the devised BS-SMPNLMS and BS-SMIPNLMS algorithms converge faster and have smaller estimation errors compared with related algorithms.

]]>Symmetry doi: 10.3390/sym10030074

Authors: M. Bordag I.G. Pirozhenko

We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions on the interfaces for the fields in the half spaces and calculate their one-loop contribution to the wave equation for the other field. We perform the ultraviolet renormalization and develop a convenient formalism for the calculation of the vacuum energy in this configuration.

]]>Symmetry doi: 10.3390/sym10030073

Authors: Dan Popescu Loretta Ichim

The automatic detection, segmentation, localization, and evaluation of the optic disc, macula, exudates, and hemorrhages are very important for diagnosing retinal diseases. One of the difficulties in detecting such regions of interest (RoIs) with computer vision is their symmetries, e.g., between the optic disc and exudates and also between exudates and hemorrhages. This paper proposes an original, intelligent, and high-performing image processing system for the simultaneous detection and segmentation of retinal RoIs. The basic principles of the method are image decomposition in small boxes and local texture analysis. The processing flow contains three phases: preprocessing, learning, and operating. As a first novelty, we propose proper feature selection based on statistical analysis in confusion matrices for different feature types (extracted from a co-occurrence matrix, fractal type, and local binary patterns). Mainly, the selected features are chosen to differentiate between similar RoIs. The second novelty consists of local classifier fusion. To this end, the local classifiers associated with features are grouped in global classifiers corresponding to the RoIs. The local classifiers are based on minimum distances to the representatives of classes and the global classifiers are based on confidence intervals, weights, and a voting scheme. A deep convolutional neural network, based on supervised learning, for blood vessel segmentation is proposed in order to improve the RoI detection performance. Finally, the experimental results on real images from different databases demonstrate the rightness of our methodologies and algorithms.

]]>Symmetry doi: 10.3390/sym10030072

Authors: Philip Broadbridge Dimetre Triadis Dilruk Gallage Pierluigi Cesana

Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions.

]]>Symmetry doi: 10.3390/sym10030071

Authors: Muammar Sadrawi Wei-Zen Sun Matthew Ma Yu-Ting Yeh Maysam Abbod Jiann-Shing Shieh

Equally partitioned data are essential for prediction. However, in some important cases, the data distribution is severely unbalanced. In this study, several algorithms are utilized to maximize the learning accuracy when dealing with a highly unbalanced dataset. A linguistic algorithm is applied to evaluate the input and output relationship, namely Fuzzy c-Means (FCM), which is applied as a clustering algorithm for the majority class to balance the minority class data from about 3 million cases. Each cluster is used to train several artificial neural network (ANN) models. Different techniques are applied to generate an ensemble genetic fuzzy neuro model (EGFNM) in order to select the models. The first ensemble technique, the intra-cluster EGFNM, works by evaluating the best combination from all the models generated by each cluster. Another ensemble technique is the inter-cluster model EGFNM, which is based on selecting the best model from each cluster. The accuracy of these techniques is evaluated using the receiver operating characteristic (ROC) via its area under the curve (AUC). Results show that the AUC of the unbalanced data is 0.67974. The random cluster and best ANN single model have AUCs of 0.7177 and 0.72806, respectively. For the ensemble evaluations, the intra-cluster and the inter-cluster EGFNMs produce 0.7293 and 0.73038, respectively. In conclusion, this study achieved improved results by performing the EGFNM method compared with the unbalanced training. This study concludes that selecting several best models will produce a better result compared with all models combined.

]]>Symmetry doi: 10.3390/sym10030070

Authors: Theodosios Christodoulakis Alexandros Karagiorgos Adamantia Zampeli

The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action principle exists, the symmetries of the configuration mini-supermetric space can also be used, in conjunction with the constraints, to provide local or non-local constants of motion. At the classical level, depending on their number, these integrals can even secure the acquisition of the entire solution space without any further solving of the dynamical equations. At the quantum level, their operator analogues can be used, along with the Wheeler–DeWitt equation, to define unique wave functions that exhibit singularity-free behavior at a semi-classical level.

]]>Symmetry doi: 10.3390/sym10030069

Authors: Mayra Machuca Winyu Chinthammit Weidong Huang Rainer Wasinger Henry Duh

Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the issue in a specific scenario, which is how to enable users to interact with public information from their own perspective. We describe a 3D mobile interaction technique that allows users to collaborate with other people by creating a symmetric and collaborative ambience. This in turn can increase their engagement with public displays. In order to better understand the benefits and limitations of this technique, we conducted a usability study with a total of 40 participants. The results indicate that the 3D mobile interaction technique promotes collaboration between users and also improves their engagement with the public displays.

]]>Symmetry doi: 10.3390/sym10030068

Authors: Kimball Milton Iver Brevik

It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with ε μ = 1 , a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic δ -function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented.

]]>Symmetry doi: 10.3390/sym10030067

Authors: Nikolai Erokhovets

A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple 3-polytopes with cyclically 5-edge connected graphs. A Pogorelov polytope has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7 . Any simple polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7 , we give an explicit construction of a Pogorelov and a non-Pogorelov polytope. Any Pogorelov polytope different from k-barrels (also known as Löbel polytopes, whose graphs are biladders on 2 k vertices) can be constructed from the 5- or the 6-barrel by cutting off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes, there is a stronger result. Any fullerene different from the 5-barrel and the ( 5 , 0 ) -nanotubes can be constructed by only cutting off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result cannot be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cutting off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons.

]]>Symmetry doi: 10.3390/sym10030066

Authors: Kairong Duan Simon Fong Yan Zhuang Wei Song

The information of human occupancy plays a crucial role in building management. For instance, fewer people, less demand for heat and electricity supply, and vice versa. Moreover, when there is a fire in a building, it is convenient to know how many persons in a single room there are in order to plan a more efficient rescue strategy. However, currently most buildings have not installed adequate devices that can be used to count the number of people, and the most popular embedded fire alarm system triggers a warning only when a fire breaks out with plenty of smoke. In view of this constraint, in this paper we propose a carbon oxides gases based warning system to detect potential fire breakouts and to estimate the number of people in the proximity. In order to validate the efficiency of the devised system, we simulate its application in the Fog Computing environment. Furthermore, we also improve the iFogSim by giving data analytics capacity to it. Based on this framework, energy consumption, latency, and network usage of the designed system obtained from iFogSim are compared with those obtained from Cloud environment.

]]>Symmetry doi: 10.3390/sym10030065

Authors: David Orden Jose Gimenez-Guzman Ivan Marsa-Maestre Enrique de la Hoz

We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the Threshold Spectrum Coloring problem fixes the number of colors available and aims to minimize the interference threshold, i.e., the maximum of the interferences at the vertices. Conversely, the Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As the main theoretical results, we prove tight upper bounds for the solutions to each problem. Since both problems turn out to be NP-hard, we complete the scene with experimental results. We propose a DSATUR-based heuristic and study its performance to minimize the maximum vertex interference in Wi-Fi channel assignment, both for randomly-generated graphs and for a real-world scenario. Further, for all these graphs, we experimentally check the goodness of the theoretical bounds.

]]>Symmetry doi: 10.3390/sym10030064

Authors: Lin Zhang Xiyuan Li Junhao Huang Ying Shen Dongqing Wang

Recent years have witnessed a growing interest in developing automatic parking systems in the field of intelligent vehicles. However, how to effectively and efficiently locating parking-slots using a vision-based system is still an unresolved issue. Even more seriously, there is no publicly available labeled benchmark dataset for tuning and testing parking-slot detection algorithms. In this paper, we attempt to fill the above-mentioned research gaps to some extent and our contributions are twofold. Firstly, to facilitate the study of vision-based parking-slot detection, a large-scale parking-slot image database is established. This database comprises 8600 surround-view images collected from typical indoor and outdoor parking sites. For each image in this database, the marking-points and parking-slots are carefully labeled. Such a database can serve as a benchmark to design and validate parking-slot detection algorithms. Secondly, a learning-based parking-slot detection approach, namely P S D L , is proposed. Using P S D L , given a surround-view image, the marking-points will be detected first and then the valid parking-slots can be inferred. The efficacy and efficiency of P S D L have been corroborated on our database. It is expected that P S D L can serve as a baseline when the other researchers develop more sophisticated methods.

]]>Symmetry doi: 10.3390/sym10030063

Authors: Chenggui Zhao Behrooz Parhami

Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of network symmetry are well known in the design of load-balanced routing algorithms and in network performance analysis. Our work in this paper shows that benefits of graph symmetry also extend to the domain of network embedding. Specifically, we propose an efficient VNE method based on modular and structured agency guidance, a regular graph function. The proposed method, which is based on symmetric intermediate graphs, offers two main advantages. Firstly, characteristics of the intermediate structures enhance the computational efficiency of the VNE process. Secondly, the static agency network modeled with such intermediate structures improves the quality of the resulting embedding. These two advantages of our method are elaborated upon and verified by examples and simulations, respectively. In addition, we present a theoretical analysis explaining the reasons behind the benefits offered by such middleware.

]]>Symmetry doi: 10.3390/sym10030062

Authors: Sven Heinemeyer Myriam Mondragón Gregory Patellis Nicholas Tracas George Zoupanos

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among parameters of a renormalizable theory holding to all orders in perturbation theory. FUTs have proven very successful so far. In particular, they predicted the top quark mass one and half years before its experimental discovery, while around five years before the Higgs boson discovery, a particular FUT was predicting the light Higgs boson in the mass range ∼121–126 GeV, in striking agreement with the discovery at LHC. Here, we review the basic properties of the supersymmetric theories and in particular finite theories resulting from the application of the method of reduction of couplings in their dimensionless and dimensionful sectors. Then, we analyze the phenomenologically-favored FUT, based on SU(5). This particular FUT leads to a finiteness constrained version of the Minimal SUSY Standard Model (MSSM), which naturally predicts a relatively heavy spectrum with colored supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, and large parts of the allowed spectrum of the lighter might be accessible at CLIC. The FCC-hhwill be able to fully test the predicted spectrum.

]]>Symmetry doi: 10.3390/sym10030061

Authors: Gang Deng Ling Pei Ni Hu Yang Liu Jin-Rong Zhu

Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that the Casimir force, especially in the direction of the force, can be significantly affected by the anisotropy of the intervening material. We also discuss the combined influence of dispersion and anisotropy, and analyze the impact of the external electric filed on the Casimir force by affecting the anisotropy of the intervening material by Kerr electro-optical effect.

]]>Symmetry doi: 10.3390/sym10030060

Authors: Karolina Nurzynska

The automatic analysis of the state of the corneal endothelium is of much interest in ophthalmology. Up till now, several manual and semi-automatic methods have been introduced, but the need of fully-automatic segmentation of cells in the endothelium is still in search. This work addresses the problem of automatic delineation of cells in the corneal endothelium images and suggests to use the convolutional neural network (CNN) to classify between cell center, cell body, and cell border in order to achieve precise segmentation. Additionally, a method to automatically select and split merged cells is given. In order to skeletonize the result, the best-fit method is used. The achieved outcomes are compared to manual annotations in order to define the mutual overlapping. The Dice index, Jaccard coefficient, modified Hausdorff distance, and several other metrics for mosaic overlapping are used. As a final check-up, the visual inspection is shown. The performed experiments revealed the best architecture for CNN. The correctness and precision of the segmentation were evaluated on Endothelial Cell “Alizarine” dataset. According to the Dice index and Jaccard coefficient, the automatically achieved cell delineation overlaps the original one with 93% precision. While modified Hausdorff distance shows 0.14 pixel distance, proving very high accuracy. These findings are confirmed by other metrics and also supported by presented visual inspection of achieved segmentations. To conclude, the methodology to achieve fully-automatic delineation of cell boundaries in the corneal endothelium images was presented. The segmentation obtained as a result of pixel classification with CNN proved very high precision.

]]>Symmetry doi: 10.3390/sym10030059

Authors: Dariusz Bochenek Przemysław Niemiec Joanna Korzekwa Bartłomiej Durtka Zbigniew Stokłosa

The paper presents the technology of ferroelectric-ferromagnetic ceramic composites obtained from PLZT powder (the chemical formula Pb0.98La0.02(Zr0.90Ti0.10)0.995O3) and ferrite powder (Ni0.64Zn0.36Fe2O4), as well as the results of X-ray powder-diffraction data (XRD) measurement, microstructure, dielectric, ferroelectric, and magnetic properties of the composite samples. The ferroelectric-ferromagnetic composite (P-F) was obtained by mixing and the synthesis of 90% of PLZT and 10% of ferrite powders. The XRD test of the P-F composite shows a two-phase structure derived from the PLZT component (strong peaks) and the ferrite component (weak peaks). The symmetry of PLZT was identified as a rhombohedral ferroelectric phase, while the ferrite was identified as a spinel structure. Scanning electron microscope (SEM) microstructure analysis of the P-F ceramic composites showed that fine grains of the PLZT component surrounded large ferrite grains. At room temperature P-F composites exhibit both ferroelectric and ferromagnetic properties. The P-F composite samples have lower values of the maximum dielectric permittivity at the Curie temperature and a higher dielectric loss compared to the PLZT ceramics, however, the exhibit overall good multiferroic properties.

]]>Symmetry doi: 10.3390/sym10030058

Authors: Andrés Iglesias Akemi Gálvez Patricia Suárez Mikio Shinya Norimasa Yoshida César Otero Cristina Manchado Valentin Gomez-Jauregui

This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark.

]]>Symmetry doi: 10.3390/sym10030057

Authors: Byung-Kil Han Seung-Chan Kim Dong-Soo Kwon

This paper proposes a novel tangible interface system to enhance the immersive experience in virtual reality environments. The proposed system allows representing physical properties of the tool, such as the deflection of the elastic rods, which users handle in a virtual and physical environment. This system is composed of two parts; one is an articulated interface to visually represent the physical behavior and the other is a computational algorithm that can compute a set of 6-DOF positions of the links. The proposed computational algorithm extends an active contour model, which is used primarily in computer vision and image processing, incorporating a spring and damping constraint energy functional. An elastic rod is modeled as a series of rigid line segments with a symmetric relationship between neighboring segments, and its shape is modeled to be influenced by energies that are induced by a user, and the external deformation of the spline. The symmetric and sparse properties of the proposed model enable an efficient energy minimization process, and the modification of a number of the line segments. Based on this configuration, we construct an energy generation method based on the positional displacement of the base element to generate the deflection behavior of the contour according to the user’s motion in the space. Therefore, the physical device can simulate a variety of deformable objects by modulating energy parameters during the energy minimization process. Experimental results demonstrate the feasibility of emulating various behaviors of deformable splines, and applying to virtual reality system without interfering with the motion-to-photon latency. We also discuss the method’s limitations and explore its potential.

]]>Symmetry doi: 10.3390/sym10030056

Authors: Milan Melnik Peter Mikus Clive Holloway

This manuscript summarizes and analyzes X-ray data of monomeric cis-PtP2CCl derivatives. These complexes crystallize in the following crystal systems: tetragonal, P42/n (3), triclinic, Pī (10), orthorhombic, P212121 (prevails)(16), and monoclinic, P21/c (prevails) (36) examples. There are three sub-groups of the respective complexes: Pt(η1-PL)2(η1-CL)(η1-Cl); Pt(η2-P2L)(η1-CL)(η1-Cl) and Pt(η1-PL)(η2-P,CL)(η1-Cl). The chelating P,P-donor ligands form: four-(POP, PCP), five-(PC2P), six-(PC3P, PCNCP), seven-(PC4P) and even ten-(PCNCNCNCP) membered rings. The chelating P.C-donor ligands create three-(PC), four-(PCC) and five-(PC2C) membered rings. The mean Pt-L bond distance elongates in the sequence: 2.10 Å (C, trans to P) &lt; 2.222 Å (P, trans to Cl) &lt; 2.312 Å (P, trans to C) &lt; 2.360 Å (Cl, trans to P). There are examples which exist in two isomeric forms, of the distortion isomer type.

]]>Symmetry doi: 10.3390/sym10030055

Authors: Mao-Ting Chien Hiroshi Nakazato

Let A be an n × n complex matrix. Assume the determinantal curve V A = { [ ( x , y , z ) ] ∈ CP 2 : F A ( x , y , z ) = det ( x ℜ ( A ) + y ℑ ( A ) + z I n ) = 0 } is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying F S ( x , y , z ) = F A ( x , y , z ) . It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of 4 × 4 nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from F A ( x , y , z ) associated to the specific 4 × 4 nilpotent Toeplitz matrices.

]]>Symmetry doi: 10.3390/sym10030054

Authors: Stephen Fulling Thomas Settlemyre Kimball Milton

The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential.

]]>Symmetry doi: 10.3390/sym10030053

Authors: A. Shapovalov V. Obukhov

This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed.

]]>Symmetry doi: 10.3390/sym10030052

Authors: Tiberiu Tudor

In the frame of a generic language extended from the polarization theory—comprising the notions of Poincaré vectors, Poincaré sphere, and P-spheres—a geometric approach to Lorentz transformations alternative to the Minkowskian one is given. Unlike the four-dimensional Minkowskian approach, this new approach operates in the three-dimensional space of Poincaré vectors.

]]>Symmetry doi: 10.3390/sym10020051

Authors: Nilanjan Dey Venkatesan Rajinikanth Amira Ashour João Manuel Tavares

The segmentation of medical images by computational methods has been claimed by the medical community, which has promoted the development of several algorithms regarding different tissues, organs and imaging modalities. Nowadays, skin melanoma is one of the most common serious malignancies in the human community. Consequently, automated and robust approaches have become an emerging need for accurate and fast clinical detection and diagnosis of skin cancer. Digital dermatoscopy is a clinically accepted device to register and to investigate suspicious regions in the skin. During the skin melanoma examination, mining the suspicious regions from dermoscopy images is generally demanded in order to make a clear diagnosis about skin diseases, mainly based on features of the region under analysis like border symmetry and regularity. Predominantly, the successful estimation of the skin cancer depends on the used computational techniques of image segmentation and analysis. In the current work, a social group optimization (SGO) supported automated tool was developed to examine skin melanoma in dermoscopy images. The proposed tool has two main steps, mainly the image pre-processing step using the Otsu/Kapur based thresholding technique and the image post-processing step using the level set/active contour based segmentation technique. The experimental work was conducted using three well-known dermoscopy image datasets. Similarity metrics were used to evaluate the clinical significance of the proposed tool such as Jaccard’s coefficient, Dice’s coefficient, false positive/negative rate, accuracy, sensitivity and specificity. The experimental findings suggest that the proposed tool achieved superior performance relatively to the ground truth images provided by a skin cancer physician. Generally, the proposed SGO based Kapur’s thresholding technique combined with the level set based segmentation technique is very effective for identifying melanoma dermoscopy digital images with high sensitivity, specificity and accuracy.

]]>Symmetry doi: 10.3390/sym10020050

Authors: Xin Li Xiaohong Zhang

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet integral and that it can reflect more correlations of attributes in MADM, two aggregation operators are defined based on the Choquet integral, specifically, the single-valued neutrosophic hesitant fuzzy Choquet ordered averaging (SVNHFCOA) operator and single-valued neutrosophic hesitant fuzzy Choquet ordered geometric (SVNHFCOG) operator, and their properties are also discussed in detail. Then, novel MADM approaches based on the SVNHFCOA and SVNHFCOG operators are established to process single-valued neutrosophic hesitant fuzzy information. Finally, this work provides a numerical example of investment alternatives to validate the application and effectiveness of the proposed approaches.

]]>Symmetry doi: 10.3390/sym10020049

Authors: Xiaokai Niu Dingli Zhang Jie Su Hong Guo

To exploit the influence of the tunnel face and the distance between the diameter and the orifice of a blast pipe on the ventilation effect in symmetric tunnel construction, this paper uses Fluent to establish a three-dimensional model and numerical simulation. Firstly, the accuracy of the numerical simulation is tested and then the distance between the orifice and tunnel face and the influence of the air duct diameter on the ventilation effect are studied, respectively. The results show that the ventilation effect is best when the wind pipe is arranged on one side of the tunnel wall (an asymmetrical layout), although the space in the tunnel is axisymmetric, and that the error of the numerical simulation is less than 5% of the measured value. When the distance between the orifice and tunnel face is 5 m, the uniformity of the air flow field near the tunnel face is poor; when the distance is 10 m and 12 m, an obvious vertex area appears in the tunnel. Furthermore, the uniformity of the wind velocity flow field is optimal when the distance is 8 m. When the air duct diameter is less than 1.4 m, there is a uniformity of the flow field near the tunnel face of the upper and lower benches; when the air duct diameter is more than 1.4 m, the tunnel face of the upper bench near the ground shows more obvious backflow. Therefore, it was determined that taking the air duct diameter as 1.4 m and the distance between the orifice and tunnel face as 8 m was the best combination for the design of ventilation in this project. It was also found that a better ventilation effect can be achieved when the distance between the nozzle of the ventilator and the tunnel face is 6 m–9 m and the wind speed of the nozzle is 6 m/s–8 m/s. In practical engineering, the wind speed and the required air volume should be taken into consideration to determine the diameter of the ventilator.

]]>Symmetry doi: 10.3390/sym10020048

Authors: Laszlo Iantovics Matthias Dehmer Frank Emmert-Streib

Intelligent cooperative multiagent systems are applied for solving a large range of real-life problems, including in domains like biology and healthcare. There are very few metrics able to make an effective measure of the machine intelligence quotient. The most important drawbacks of the designed metrics presented in the scientific literature consist in the limitation in universality, accuracy, and robustness. In this paper, we propose a novel universal metric called MetrIntSimil capable of making an accurate and robust symmetric comparison of the similarity in intelligence of any number of cooperative multiagent systems specialized in difficult problem solving. The universality is an important necessary property based on the large variety of designed intelligent systems. MetrIntSimil makes a comparison by taking into consideration the variability in intelligence in the problem solving of the compared cooperative multiagent systems. It allows a classification of the cooperative multiagent systems based on their similarity in intelligence. A cooperative multiagent system has variability in the problem solving intelligence, and it can manifest lower or higher intelligence in different problem solving tasks. More cooperative multiagent systems with similar intelligence can be included in the same class. For the evaluation of the proposed metric, we conducted a case study for more intelligent cooperative multiagent systems composed of simple computing agents applied for solving the Symmetric Travelling Salesman Problem (STSP) that is a class of NP-hard problems. STSP is the problem of finding the shortest Hamiltonian cycle/tour in a weighted undirected graph that does not have loops or multiple edges. The distance between two cities is the same in each opposite direction. Two classes of similar intelligence denoted IntClassA and IntClassB were identified. The experimental results show that the agent belonging to IntClassA intelligence class is less intelligent than the agents that belong to the IntClassB intelligence class.

]]>Symmetry doi: 10.3390/sym10020047

Authors: Xiao-Zhu Xie Chia-Chen Lin Chin-Chen Chang

Data hiding is a technology that embeds data into a cover carrier in an imperceptible way while still allowing the hidden data to be extracted accurately from the stego-carrier, which is one important branch of computer science and has drawn attention of scholars in the last decade. Turtle shell-based (TSB) schemes have become popular in recent years due to their higher embedding capacity (EC) and better visual quality of the stego-image than most of the none magic matrices based (MMB) schemes. This paper proposes a two-layer turtle shell matrix-based (TTSMB) scheme for data hiding, in which an extra attribute presented by a 4-ary digit is assigned to each element of the turtle shell matrix with symmetrical distribution. Therefore, compared with the original TSB scheme, two more bits are embedded into each pixel pair to obtain a higher EC up to 2.5 bits per pixel (bpp). The experimental results reveal that under the condition of the same visual quality, the EC of the proposed scheme outperforms state-of-the-art data hiding schemes.

]]>Symmetry doi: 10.3390/sym10020046

Authors: Kajal Chatterjee Edmundas Kazimieras Zavadskas Jolanta Tamošaitienė Krishnendu Adhikary Samarjit Kar

Multi-stakeholder based construction projects are subject to potential risk factors due to dynamic business environment and stakeholders’ lack of knowledge. When solving project management tasks, it is necessary to quantify the main risk indicators of the projects. Managing these requires suitable risk mitigation strategies to evaluate and analyse their severity. The existence of information asymmetry also causes difficulties with achieving Pareto efficiency. Hence, to ensure balanced satisfaction of all participants, risk evaluation of these projects can be considered as an important part of the multi-criteria decision-making (MCDM) process. In real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D numbers domain to handle three types of ambiguous information’s, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D numbers based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster–Shafer (D–S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D numbers extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D numbers is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches in D numbers domain. Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed to verify the robustness of the proposed method.

]]>Symmetry doi: 10.3390/sym10020045

Authors: Jalil Dahooie Edmundas Zavadskas Mahdi Abolhasani Amirsalar Vanaki Zenonas Turskis

The beginning of the 21st-century resulted in a more developed multi-attribute decision-making (MADM) tool and inspired new application areas that have resulted in discoveries in sustainable construction and building life cycle analysis. Construction and civil engineering stand for the central axis of a body consisting of a multidisciplinary (multi-dimensional) world with ties to disciplines constituting the surface, and with the disciplines, as a consequence, tied to each other. When dealing with multi-attribute decision-making problems generally multiple solutions exist, especially when there is a large number of attributes, and the concept of Pareto-optimality is inefficient. The symmetry and structural regularity are essential concepts in many natural and man-made objects and play a crucial role in the design, engineering, and development of the world. The complexity and risks inherent in projects along with different effective indicators for success and failure may contribute to the difficulties in performance evaluation. In such situations, increasing the importance of uncertainty is observed. This paper proposes a novel integrated tool to find a balance between sustainable development, environmental impact and human well-being, i. e. to find symmetry axe with respect to goals, risks, and constraints (attributes) to cope with the complicated problems. The concept of “optimal solution” as the maximum degree of implemented goals (attributes) is very important. The model is built using the most relevant variables cited in the reviewed project literature and integrates two methods: the Step-Wise Weight Assessment Ratio Analysis (SWARA) method and a novel interval-valued fuzzy extension of the Additive Ratio Assessment (ARAS) method. This model was used to solve real case study of oil and gas well drilling projects evaluation. Despite the importance of oil and gas well drilling projects, there is lack of literature that describes and evaluates performance in this field projects. On the other hand, no structured assessment methodology has been presented for these types of projects. Given the limited research on performance evaluation in oil &amp; gas well-drilling projects, the research identifies a set of performance criteria and proposes an evaluation model using fuzzy Delphi method. An illustrative example shows that the proposed method is a useful and alternative decision-making method.

]]>Symmetry doi: 10.3390/sym10020044

Authors: Ekkehard Krüger

As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled “superconducting bands” of special symmetry. The formation of Cooper pairs is not only the result of an attractive electron–electron interaction but is additionally the outcome of quantum mechanical constraining forces. There is theoretical and experimental evidence that only these constraining forces operating in superconducting bands may produce eigenstates in which the electrons form Cooper pairs. Here, we report evidence that also the experimentally found superconducting state in bismuth at ambient as well as at high pressure is stabilized by constraining forces.

]]>Symmetry doi: 10.3390/sym10020043

Authors: Eligijus Sakalauskas

A new enhanced matrix power function (MPF) is presented for the construction of cryptographic primitives. According to the definition in previously published papers, an MPF is an action of two matrices powering some base matrix on the left and right. The MPF inversion equations, corresponding to the MPF problem, are derived and have some structural similarity with classical multivariate quadratic (MQ) problem equations. Unlike the MQ problem, the MPF problem seems to be more complicated, since its equations are not defined over the field, but are represented as left–right action of two matrices defined over the infinite near-semiring on the matrix defined over the certain infinite, additive, noncommuting semigroup. The main results are the following: (1) the proposition of infinite, nonsymmetric, and noncommuting algebraic structures for the construction of the enhanced MPF, satisfying associativity conditions, which are necessary for cryptographic applications; (2) the proof that MPF inversion is polynomially equivalent to the solution of a certain kind of generalized multivariate quadratic (MQ) problem which can be reckoned as hard; (3) the estimation of the effectiveness of direct MPF value computation; and (4) the presentation of preliminary security analysis, the determination of the security parameter, and specification of its secure value. These results allow us to make a conjecture that enhanced MPF can be a candidate one-way function (OWF), since the effective (polynomial-time) inversion algorithm for it is not yet known. An example of the application of the proposed MPF for the Key Agreement Protocol (KAP) is presented. Since the direct MPF value is computed effectively, the proposed MPF is suitable for the realization of cryptographic protocols in devices with restricted computation resources.

]]>Symmetry doi: 10.3390/sym10020042

Authors: Syahirbanun Isa Zanariah Abdul Majid Fudziah Ismail Faranak Rabiei

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations.

]]>Symmetry doi: 10.3390/sym10020041

Authors: Vasyl’ Davydovych

Lie symmetry classification of the diffusive Lotka–Volterra system with time-dependent coefficients in the case of a single space variable is studied. A set of such symmetries in an explicit form is constructed. A nontrivial ansatz reducing the Lotka–Volterra system with correctly-specified coefficients to the system of ordinary differential equations (ODEs) and an example of the exact solution with a biological interpretation are found.

]]>Symmetry doi: 10.3390/sym10020040

Authors: Ming Li

This article addresses three classes of fractional oscillators named Class I, II and III. It is known that the solutions to fractional oscillators of Class I type are represented by the Mittag-Leffler functions. However, closed form solutions to fractional oscillators in Classes II and III are unknown. In this article, we present a theory of equivalent systems with respect to three classes of fractional oscillators. In methodology, we first transform fractional oscillators with constant coefficients to be linear 2-order oscillators with variable coefficients (variable mass and damping). Then, we derive the closed form solutions to three classes of fractional oscillators using elementary functions. The present theory of equivalent oscillators consists of the main highlights as follows. (1) Proposing three equivalent 2-order oscillation equations corresponding to three classes of fractional oscillators; (2) Presenting the closed form expressions of equivalent mass, equivalent damping, equivalent natural frequencies, equivalent damping ratio for each class of fractional oscillators; (3) Putting forward the closed form formulas of responses (free, impulse, unit step, frequency, sinusoidal) to each class of fractional oscillators; (4) Revealing the power laws of equivalent mass and equivalent damping for each class of fractional oscillators in terms of oscillation frequency; (5) Giving analytic expressions of the logarithmic decrements of three classes of fractional oscillators; (6) Representing the closed form representations of some of the generalized Mittag-Leffler functions with elementary functions. The present results suggest a novel theory of fractional oscillators. This may facilitate the application of the theory of fractional oscillators to practice.

]]>Symmetry doi: 10.3390/sym10020039

Authors: Lidong Wang Yanjun Wang Xiaodong Liu

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness.

]]>Symmetry doi: 10.3390/sym10020038

Authors: Davide Fermi Livio Pizzocchero

The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico and Zerbini have considered some configurations involving delta-type potentials concentrated at points of R 3 ; in particular, the case with an isolated point singularity at the origin can be formulated as a field theory on R 3 \ { 0 } , with self-adjoint boundary conditions at the origin for the Laplacian. However, the above authors have discussed only global aspects of the Casimir effect, focusing their attention on the vacuum expectation value (VEV) of the total energy. In the present paper we analyze the local Casimir effect with a point delta-type potential, computing the renormalized VEV of the stress-energy tensor at any point of R 3 \ { 0 } ; for this purpose we follow the zeta regularization approach, in the formulation already employed for different configurations in previous works of ours.

]]>Symmetry doi: 10.3390/sym10020037

Authors: Romain Guérout Gert-Ludwig Ingold Astrid Lambrecht Serge Reynaud

We take dissipation into account in the derivation of the Casimir energy formula between two objects placed in a surrounding medium. The dissipation channels are considered explicitly in order to take advantage of the unitarity of the full scattering processes. We demonstrate that the Casimir energy is given by a scattering formula expressed in terms of the scattering amplitudes coupling internal channels and taking dissipation into account implicitly. We prove that this formula is also valid when the surrounding medium is dissipative.

]]>Symmetry doi: 10.3390/sym10020036

Authors: Wien Hong

In this paper, an efficient data hiding method that embeds data into absolute moment block truncation coding (AMBTC) codes is proposed. The AMBTC method represents image blocks by trios, and each trio consists of two quantization levels and an asymmetrically distributed bitmap. However, the asymmetric phenomena of bitmaps cause large degradation in image quality during data embedment. With the help of reference tables filled with symmetrical patterns, the proposed method exploits a symmetry adjustment model to modify the quantization levels in those smooth blocks to achieve the smallest distortion. If the block is complex, a lossless embedding method is performed to carry one additional bit. A sophisticated division switching mechanism is also proposed to modify a block from smooth to complex if the solution to the minimal distortion cannot be found. The payload can be adjusted by varying the threshold, or by embedding more bits into the quantization levels. The experiments indicate that the proposed work provides the best stego image quality under various payloads when comparing to the related prior works.

]]>Symmetry doi: 10.3390/sym10020035

Authors: Jean-Guillaume Eon

A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet B n with rotations mostly as voltages. It thus appears that translation, as a symmetry operation in these nets, is no more fundamental than rotations.

]]>Symmetry doi: 10.3390/sym10020034

Authors: Vaibhav N. Khose Marina E. John Anita D. Pandey Victor Borovkov Anil V. Karnik

The majority of biomolecules found in living beings are chiral, therefore chiral molecular recognition in living systems is crucial to life. Following Cram’s seminal work on the crown-based chiral recognition, prominent research groups have reported innumerable chiral receptors with distinctly different geometrical features and asymmetry elements. Main applications of such chiral receptors are found in chiral chromatography, as for analytical purposes and for bulk separation of racemates.Incorporation of heterocyclic rings in these recognition systems added a new dimension to the existing group of receptors. Heterocycles have additional features such as availability of unshared electron pairs, pronounced conformational features, introduction of hydrogen bonding and presence of permanent dipoles as well as specific spectral properties in certain cases. These features are found to enhance binding properties of the receptors and the selectivity factors between opposite enantiomers, allowing them to be effectively separated. The review presents the synthetic approaches towards these heterocyclic receptors and their distinctly different behavior vis-à-vis carbocyclic receptors.

]]>Symmetry doi: 10.3390/sym10020033

Authors: Peter Schuller-Götzburg Thomas Forte Werner Pomwenger Alexander Petutschnigg Franz Watzinger Karl Entacher

Purpose: the aim of the computational 3D-finite element study is to evaluate the influence of an augmented sinus lift with additional inserted bone grafting. The bone graft block stabilizes the implant in conjunction with conventional bone augmentation. Two finite element models were applied: the real geometry based bone models and the simplified geometry models. The bone graft block was placed in three different positions. The implants were loaded first with an axial force and then with forces simulating laterotrusion and protrusion. This study examines whether the calculated stress behavior is symmetrical for both models. Having established a symmetry between the primary axis, the laterotrusion and protrusion behavior reduces calculation efforts, by simplifying the model. Material and Methods: a simplified U-shaped 3D finite element model of the molar region of the upper jaw and a more complex anatomical model of the left maxilla with less cortical bone were created. The bone graft block was placed in the maxillary sinus. Then the von Mises stress distribution was calculated and analyzed at three block positions: at contact with the sinus floor, in the middle of the implant helix and in the upper third of the implant. The two finite element models were then compared to simplify the modelling. Results: the position of the bone graft block significantly influences the magnitude of stress distribution. A bone graft block positioned in the upper third or middle of the implant reduces the quantity of stress compared to the reference model without a bone graft block. The low bone graft block position is clearly associated with lower stress distribution in compact bone. We registered no significant differences in stress in compact bone with regard to laterotrusion or protrusion. Conclusions: maximum values of von Mises stresses in compact bone can be reduced significantly by using a bone graft block. The reduction of stress is nearly the same for positions in the upper third and the middle of the implant. It is much more pronounced when the bone graft block is in the lower third of the implant near the sinus floor, which appeared to be the best position in the present study.

]]>Symmetry doi: 10.3390/sym10010032

Authors: Jose Rodriguez

This book contains the successful invited submissions [1–10] to a special issue of Symmetry on the subject area of ‘graph theory’ [...]

]]>Symmetry doi: 10.3390/sym10010031

Authors: Klaus Kirsten Yoonweon Lee

We provide a completely new perspective for the analysis of Casimir forces in very general piston configurations. To this end, in order to be self-contained, we prove a “gluing formula” well known in mathematics and relate it with Casimir forces in piston configurations. At the center of our description is the Dirichlet-to-Neumann operator, which encodes all the information about those forces. As an application, the results for previously considered piston configurations are reproduced in a streamlined fashion.

]]>Symmetry doi: 10.3390/sym10010030

Authors: JongBeom Lim Joon-Min Gil HeonChang Yu

Many artificial intelligence applications often require a huge amount of computing resources. As a result, cloud computing adoption rates are increasing in the artificial intelligence field. To support the demand for artificial intelligence applications and guarantee the service level agreement, cloud computing should provide not only computing resources but also fundamental mechanisms for efficient computing. In this regard, a snapshot protocol has been used to create a consistent snapshot of the global state in cloud computing environments. However, the existing snapshot protocols are not optimized in the context of artificial intelligence applications, where large-scale iterative computation is the norm. In this paper, we present a distributed snapshot protocol for efficient artificial intelligence computation in cloud computing environments. The proposed snapshot protocol is based on a distributed algorithm to run interconnected multiple nodes in a scalable fashion. Our snapshot protocol is able to deal with artificial intelligence applications, in which a large number of computing nodes are running. We reveal that our distributed snapshot protocol guarantees the correctness, safety, and liveness conditions.

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