Symmetry doi: 10.3390/sym9080128

Authors: Ivana Bianchi Marco Bertamini Roberto Burro Ugo Savardi

Symmetry is a salient aspect of biological and man-made objects, and has a central role in perceptual organization. Two studies investigate the role of opposition and identicalness in shaping adults’ naïve idea of “symmetry”. In study 1, both verbal descriptions of symmetry (either provided by the participants or selected from among alternatives presented by the experimenter) and configurations drawn as exemplars of symmetry were studied. In study 2, a pair comparison task was used. Both studies focus on configurations formed by two symmetrical shapes (i.e., between-objects symmetry). Three main results emerged. The explicit description of symmetry provided by participants generally referred to features relating to the relationship perceived between the two shapes and not to geometrical point-by-point transformations. Despite the fact that people tended to avoid references to opposition in their verbal definition of symmetry in study 1, the drawings that they did to represent their prototypical idea of symmetry manifested opposition as a basic component. This latter result was confirmed when the participants were asked to select the definition (in study 1) or the configuration (in study 2) that best fitted with their idea of symmetry. In conclusion, identicalness is an important component in people’s naïve idea of symmetry, but it does not suffice: opposition complements it.

]]>Symmetry doi: 10.3390/sym9080130

Authors: Dong Qiu Yumei Xing Shuqiao Chen

In this article, we put forward the multi-objective matrix game model based on fuzzy payoffs. In order to solve the game model, we first discuss the relationship of two fuzzy numbers via the lower limit - 1 2 of the possibility degree. Then, utilizing this relationship, we conclude that the equilibrium solution of this game model and the optimal solution of multicriteria linear optimization problems are of equal value. Finally, to illustrate the effectiveness and correctness of the obtained model, an example is provided.

]]>Symmetry doi: 10.3390/sym9080129

Authors: Qianhui Dong Yibing Li Qian Sun Ya Zhang

As a typical navigation system, the strapdown inertial navigation system (SINS) is crucial for autonomous underwater vehicles (AUVs) since the SINS accuracy determines the performance of AUVs. Initial alignment is one of the key technologies in SINS, and initial alignment time and initial alignment accuracy affect the performance of SINS directly. As actual systems are nonlinear, the nonlinear filter is widely used to improve the accuracy of the initial alignment. Due to its higher precision and lower computational load, the cubature Kalman filter (CKF) has done well in state estimation. However, the noise characteristics need to be known exactly as prior knowledge, which is difficult or even impossible to achieve. Thus, the adaptive filter should be introduced in the initial alignment algorithm to suppress the uncertainty effect caused by the unknown system noise. Therefore, taking the nonlinearity and uncertainty into account, a novel initial alignment algorithm for AUVs is proposed in this manuscript, based on CKF and the adaptive variance components estimation (VCE) filter (VCKF). Additionally, the simulation and experiment results show that not only the accuracy, but also the convergence speed can be improved with this proposed method. The validity and superiority of this novel adaptive initial alignment algorithm based on VCKF are verified.

]]>Symmetry doi: 10.3390/sym9080127

Authors: Wen Jiang Yehang Shou

The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems. The key to using neutrosophic sets in decision-making applications is to make a similarity measure between single-valued neutrosophic sets. In this paper, a new method to measure the similarity between single-valued neutrosophic sets using Dempster–Shafer evidence theory is proposed, and it is applied in multicriteria decision-making. Finally, some examples are given to show the reasonable and effective use of the proposed method.

]]>Symmetry doi: 10.3390/sym9070124

Authors: Jingyuan Jia Aiwu Zhao Shuang Guan

Most existing fuzzy forecasting models partition historical training time series into fuzzy time series and build fuzzy-trend logical relationship groups to generate forecasting rules. The determination process of intervals is complex and uncertain. In this paper, we present a novel fuzzy forecasting model based on high-order fuzzy-fluctuation trends and the fuzzy-fluctuation logical relationships of the training time series. Firstly, we compare each piece of data with the data of theprevious day in a historical training time series to generate a new fluctuation trend time series (FTTS). Then, we fuzzify the FTTS into a fuzzy-fluctuation time series (FFTS) according to the up, equal, or down range and orientation of the fluctuations. Since the relationship between historical FFTS and the fluctuation trend of the future is nonlinear, a particle swarm optimization (PSO) algorithm is employed to estimate the proportions for the lagged variables of the fuzzy AR (n) model. Finally, we use the acquired parameters to forecast future fluctuations. In order to compare the performance of the proposed model with that of the other models, we apply the proposed method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) time series datasets. The experimental results and the comparison results show that the proposed method can be successfully applied in stock market forecasting or similarkinds of time series. We also apply the proposed method to forecast Shanghai Stock Exchange Composite Index (SHSECI) and DAX30 index to verify its effectiveness and universality.

]]>Symmetry doi: 10.3390/sym9070126

Authors: Chao Zhang Deyu Li Arun Sangaiah Said Broumi

As a significant business activity, merger and acquisition (M&amp;A) generally means transactions in which the ownership of companies, other business organizations or their operating units are transferred or combined. In a typical M&amp;A procedure, M&amp;A target selection is an important issue that tends to exert an increasingly significant impact on different business areas. Although some research works based on fuzzy methods have been explored on this issue, they can only deal with incomplete and uncertain information, but not inconsistent and indeterminate information that exists universally in the decision making process. Additionally, it is advantageous to solve M&amp;A problems under the group decision making context. In order to handle these difficulties in M&amp;A target selection background, we introduce a novel rough set model by combining interval neutrosophic sets (INSs) with multigranulation rough sets over two universes, called an interval neutrosophic (IN) multigranulation rough set over two universes. Then, we discuss the definition and some fundamental properties of the proposed model. Finally, we establish decision making rules and computing approaches for the proposed model in M&amp;A target selection background, and the effectiveness of the decision making approach is demonstrated by an illustrative case analysis.

]]>Symmetry doi: 10.3390/sym9070125

Authors: Hsiao-Ting Tseng Hsin-Ginn Hwang Wei-Yen Hsu Pei-Chin Chou I-Chiu Chang

Population ageing is an important global issue. The Taiwanese government has used various Internet of Things (IoT) applications in the “10-year long-term care program 2.0”. It is expected that the efficiency and effectiveness of long-term care services will be improved through IoT support. Home-delivered meal services for the elderly are important for home-based long-term care services. To ensure that the right meals are delivered to the right recipient at the right time, the runners need to take a picture of the meal recipient when the meal is delivered. This study uses the IoT-based image recognition system to design an integrated service to improve the management of image recognition. The core technology of this IoT-based image recognition system is statistical histogram-based k-means clustering for image segmentation. However, this method is time-consuming. Therefore, we proposed using the statistical histogram to obtain a probability density function of pixels of a figure and segmenting these with weighting for the same intensity. This aims to increase the computational performance and achieve the same results as k-means clustering. We combined histogram and k-means clustering in order to overcome the high computational cost for k-means clustering. The results indicate that the proposed method is significantly faster than k-means clustering by more than 10 times.

]]>Symmetry doi: 10.3390/sym9070123

Authors: Jiqian Chen Jun Ye Shigui Du Rui Yong

In nature, the mechanical properties of geological bodies are very complex, and their various mechanical parameters are vague, incomplete, imprecise, and indeterminate. However, we cannot express them by the crisp values in classical probability and statistics. In geotechnical engineering, we need to try our best to approximate exact values in indeterminate environments because determining the joint roughness coefficient (JRC) effectively is a key parameter in the shear strength between rock joint surfaces. In this original study, we first propose neutrosophic interval probability (NIP) and define the confidence degree based on the cosine measure between NIP and the ideal NIP. Then, we propose a new neutrosophic interval statistical number (NISN) by combining the neutrosophic number with the confidence degree to express indeterminate statistical information. Finally, we apply NISNs to express JRC under indeterminate (imprecise, incomplete, and uncertain, etc.) environments. By an actual case, the results demonstrate that NISNs are suitable and effective for JRC expressions and have the objective advantage.

]]>Symmetry doi: 10.3390/sym9070121

Authors: Zhikang Lu Jun Ye

The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.

]]>Symmetry doi: 10.3390/sym9070120

Authors: Paolo Gregorio Sara Bonella Lamberto Rondoni

We derive the quantum analogues of some recently discovered symmetry relations for time correlation functions in systems subject to a constant magnetic field. The symmetry relations deal with the effect of time reversal and do not require—as in the formulations of Casimir and Kubo—that the magnetic field be reversed. It has been anticipated that the same symmetry relations hold for quantum systems. Thus, here we explicitly construct the required symmetry transformations, acting upon the relevant quantum operators, which conserve the Hamiltonian of a system of many interacting spinless particles, under time reversal. Differently from the classical case, parity transformations always reverse the sign of both the coordinates and of the momenta, while time reversal only of the latter. By implementing time reversal in conjunction with ad hoc “incomplete” parity transformations (i.e., transformations that act upon only some of the spatial directions), it is nevertheless possible to achieve the construction of the quantum analogues of the classical maps. The proof that the mentioned symmetry relations apply straightforwardly to quantal time correlation functions is outlined.

]]>Symmetry doi: 10.3390/sym9070122

Authors: Duc Manh Nguyen Sunghwan Kim

In this paper, new construction methods of entanglement-assisted quantum error correction code (EAQECC) from circulant matrices are proposed. We first construct the matrices from two vectors of constraint size, and determine the isotropic subgroup. Then, we also propose a method for calculation of the entanglement subgroup based on standard forms of binary matrices to satisfy the constraint conditions of EAQECC. With isotropic and entanglement subgroups, we determine all the parameters and the minimum distance of the EAQECC. The proposed EAQECC with small lengths are presented to explain the practicality of this construction of EAQECC. Comparison with some earlier constructions of EAQECC shows that the proposed EAQECC is better.

]]>Symmetry doi: 10.3390/sym9070119

Authors: Zhi-Lian Guo Yan-Ling Liu Hai-Long Yang

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment. Firstly, based on the ( α , β , γ ) -cut relation R ˜ { ( α , β , γ ) } , we propose a rough set model in generalized single-valued neutrosophic approximation spaces. Then, some properties of the new rough set model are discussed. Furthermore, we obtain two extended models of the new rough set model—the degree rough set model and the variable precision rough set model—and study some of their properties. Finally, we explore an example to illustrate the validity of the new rough set model.

]]>Symmetry doi: 10.3390/sym9070118

Authors: Boliang Lin Siqi Liu Ruixi Lin Jianping Wu Jiaxi Wang Chang Liu

China’s railway network is one of the largest railway networks in the world. By the end of 2016, the total length of railway in operation reached 124,000 km and the annual freight volume exceeded 3.3 billion tons. However, the structure of network does not completely match transportation demand, i.e., there still exist a few bottlenecks in the network, which forces some freight flows to travel along non-shortest paths. At present, due to the expansion of the high-speed railway network, more passengers will travel by electric multiple unit (EMU) trains running on the high-speed railway. Therefore, fewer passenger trains will move along the regular medium-speed lines, resulting in more spare capacity for freight trains. In this context, some shipments flowing on non-shortest paths can shift to shorter paths. And consequently, a combinatorial optimization problem concerning which origin-destination (O-D) pairs should be adjusted to their shortest paths will arise. To solve it, mathematical models are developed to adjust freight flows between their shortest paths and non-shortest paths based on the 0-1 knapsack problem. We also carry out computational experiments using the commercial software Gurobi and a greedy algorithm (GA), respectively. The results indicate that the proposed models are feasible and effective.

]]>Symmetry doi: 10.3390/sym9070117

Authors: Washington Encalada José Sequera

In recent years, we have seen a significant number of new technological ideas appearing in literature discussing the future of education. For example, E-learning, cloud computing, social networking, virtual laboratories, virtual realities, virtual worlds, massive open online courses (MOOCs), and bring your own device (BYOD) are all new concepts of immersive and global education that have emerged in educational literature. One of the greatest challenges presented to e-learning solutions is the reproduction of the benefits of an educational institution’s physical laboratory. For a university without a computing lab, to obtain hands-on IT training with software, operating systems, networks, servers, storage, and cloud computing similar to that which could be received on a university campus computing lab, it is necessary to use a combination of technological tools. Such teaching tools must promote the transmission of knowledge, encourage interaction and collaboration, and ensure students obtain valuable hands-on experience. That, in turn, allows the universities to focus more on teaching and research activities than on the implementation and configuration of complex physical systems. In this article, we present a model for implementing ecosystems which allow universities to teach practical Information Technology (IT) skills. The model utilizes what is called a “social cloud”, which utilizes all cloud computing services, such as Software as a Service (SaaS), Platform as a Service (PaaS), and Infrastructure as a Service (IaaS). Additionally, it integrates the cloud learning aspects of a MOOC and several aspects of social networking and support. Social clouds have striking benefits such as centrality, ease of use, scalability, and ubiquity, providing a superior learning environment when compared to that of a simple physical lab. The proposed model allows students to foster all the educational pillars such as learning to know, learning to be, learning to live together, and, primarily, learning to do, through hands-on IT training from a MOOCs. An aspect of the model has been verified experimentally and statistically through a course of computer operating systems.

]]>Symmetry doi: 10.3390/sym9070116

Authors: Kim-Phung Truong Ming-Hung Shu Thanh-Lam Nguyen Bi-Min Hsu

The inevitability of measurement errors and/or humans of subjectivity in data collection processes make accumulated data imprecise, and are thus called fuzzy data. To adapt to this fuzzy domain in a manufacturing process, a traditional u control chart for monitoring the average number of nonconformities per unit is required to extend. In this paper, we first generalize the u chart, named fuzzy u-chart, whose control limits are built on the basis of resolution identity, which is a well-known fuzzy set theory. Then, an approach to fuzzy-logic reasoning, incorporating the decision-maker’s varying levels of optimism towards the online process, is proposed to categorize the manufacturing conditions. In addition, we further develop a condition-based classification mechanism, where the process conditions can be discriminated into intermittent states between in-control and out-of-control. As anomalous conditions are monitored to some extent, this condition-based classification mechanism can provide the critical information to deliberate the cost of process intervention with respect to the gain of quality improvement. Finally, the proposed fuzzy u-chart is implemented in the Vietnam textile dyeing industry to replace its conventional u-chart. The results demonstrate that the industry can effectively evade unnecessary adjustments to its current processes; thus, the industry can substantially reduce its operational cost and potential loss.

]]>Symmetry doi: 10.3390/sym9070115

Authors: Dingjiang Huang Xiangxiang Li Shunchang Yu

In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.

]]>Symmetry doi: 10.3390/sym9070114

Authors: Hyoseok Yoon Se-Ho Park Kyung-Taek Lee Jung Park Anind Dey SeungJun Kim

Wearable devices are being explored and investigated as a promising computing platform as well as a source of personal big data for the post smartphone era. To deal with a series of rapidly developed wearable prototypes, a well-structured strategy is required to assess the prototypes at various development stages. In this paper, we first design and develop variants of advanced wearable user interface prototypes, including joystick-embedded, potentiometer-embedded, motion-gesture and contactless infrared user interfaces for rapidly assessing hands-on user experience of potential futuristic user interfaces. To achieve this goal systematically, we propose a conceptual test framework and present a case study of using the proposed framework in an iterative cyclic process to prototype, test, analyze, and refine the wearable user interface prototypes. We attempt to improve the usability of the user interface prototypes by integrating initial user feedback into the leading phase of the test framework. In the following phase of the test framework, we track signs of improvements through the overall results of usability assessments, task workload assessments and user experience evaluation of the prototypes. The presented comprehensive and in-depth case study demonstrates that the iterative approach employed by the test framework was effective in assessing and enhancing the prototypes, as well as gaining insights on potential applications and establishing practical guidelines for effective and usable wearable user interface development.

]]>Symmetry doi: 10.3390/sym9070113

Authors: Hui-Fei Lin Chi-Hua Chen

An intelligent tour service system including an augmented reality (AR) tour-sharing Application (APP) and a query-answering server was developed in this study to promote tourist attractions involving local Hakka culture in Thailand. Subsequently, use of this APP to navigate Hakka culture tourist attractions in Thailand was observed. The novel random neural networks (RNNs) were proposed to obtain query-answering services, and the practical experimental results showed that the accuracy of RNNs was 99.51%. This study also integrated the Technology Acceptance Model with Uses and Gratifications Theory to predict the gratification, usage intention, and user attitudes toward marketed attractions of the AR tour-sharing APP. A questionnaire survey was conducted, and 446 valid questionnaires were returned. The following results were obtained: (a) self-presentation and perceived usefulness (PU) directly influenced gratification; (b) perceived entertainment indirectly influenced gratification through perceived ease of use and PU, and information sharing indirectly influenced gratification through PU; and (c) gratification was significantly and positively related to usage intention and attitude toward attractions. Based on these results, suggestions that new technology marketing can be used to promote causes other than Hakka tourist attractions established in Thailand can be contrived. For example, the tour-sharing APP developed in this study could be applied to emphasize the characteristics of Thai Hakka culture; users’ fondness for self-presentation and information sharing can be used for word-of-mouth marketing to attract additional visitors. In addition, this research provides a reference for enterprises and marketers regarding the use of AR tour-sharing APPs to market tourist attractions, and also for future related studies.

]]>Symmetry doi: 10.3390/sym9070112

Authors: Jing Li Guoqing He Peibiao Zhao

In this paper, we study submanifolds in a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection on a submanifold is also semi-symmetric non-metric connection. We consider the total geodesicness and minimality of a submanifold with respect to the semi-symmetric non-metric connection. We obtain the Gauss, Cadazzi, and Ricci equations for submanifolds with respect to the semi-symmetric non-metric connection.

]]>Symmetry doi: 10.3390/sym9070111

Authors: Zebo Fang Jun Ye

Existing intuitionistic linguistic variables can describe the linguistic information of both the truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information. To deal with the issue, this paper originally proposes the concept of a linguistic neutrosophic number (LNN), which is characterized independently by the truth, indeterminacy, and falsity linguistic variables. Then, we define the basic operational laws of LNNs and the score and accuracy functions of LNN for comparing LNNs. Next, we develop an LNN-weighted arithmetic averaging (LNNWAA) operator and an LNN-weighted geometric averaging (LNNWGA) operator to aggregate LNN information and investigate their properties. Further, a multiple attribute group decision-making method based on the proposed LNNWAA or LNNWGA operator is established under LNN environment. Finally, an illustrative example about selecting problems of investment alternatives is presented to demonstrate the application and effectiveness of the developed approach.

]]>Symmetry doi: 10.3390/sym9070109

Authors: Xinhua Liu Yao Shi Jing Xu

In order to improve the response performance of a proportion integration differentiation (PID) controller for magnetorheological fluids (MRF) brake and to reduce the braking fluctuation rate, an improved fruit fly optimization algorithm for PID controller parameters tuning of MRF brake is proposed. A data acquisition system for MRF brake is designed and the transfer function of MRF brake is identified. Moreover, an improved fruit fly optimization algorithm (IFOA) through integration of PID control strategy and cloud model algorithm is proposed to design a PID controller for MRF brake. Finally, the simulation and experiment are carried out. The results show that IFOA, with a faster response output and no overshoot, is superior to the conventional PID and fruit fly optimization algorithm (FOA) PID controller.

]]>Symmetry doi: 10.3390/sym9070110

Authors: Linbo Zhai Hua Wang

This paper studies cooperative spectrum sensing based on crowdsourcing in cognitive radio networks. Since intelligent mobile users such as smartphones and tablets can sense the wireless spectrum, channel sensing tasks can be assigned to these mobile users. This is referred to as the crowdsourcing method. However, there may be some malicious mobile users that send false sensing reports deliberately, for their own purposes. False sensing reports will influence decisions about channel state. Therefore, it is necessary to classify mobile users in order to distinguish malicious users. According to the sensing reports, mobile users should not just be divided into two classes (honest and malicious). There are two reasons for this: on the one hand, honest users in different positions may have different sensing outcomes, as shadowing, multi-path fading, and other issues may influence the sensing results; on the other hand, there may be more than one type of malicious users, acting differently in the network. Therefore, it is necessary to classify mobile users into more than two classes. Due to the lack of prior information of the number of user classes, this paper casts the problem of mobile user classification as a dynamic clustering problem that is NP-hard. The paper uses the interdistance-to-intradistance ratio of clusters as the fitness function, and aims to maximize the fitness function. To cast this optimization problem, this paper proposes a distributed algorithm for user classification in order to obtain bounded close-to-optimal solutions, and analyzes the approximation ratio of the proposed algorithm. Simulations show the distributed algorithm achieves higher performance than other algorithms.

]]>Symmetry doi: 10.3390/sym9070108

Authors: Sungju Lee Taikyeong Jeong

The goal of this paper is to compare and analyze the forecasting performance of two artificial neural network models (i.e., MLP (multi-layer perceptron) and DNN (deep neural network)), and to conduct an experimental investigation by data flow, not economic flow. In this paper, we investigate beyond the scope of simple predictions, and conduct research based on the merits and data of each model, so that we can predict and forecast the most efficient outcomes based on analytical methodology with fewer errors. In particular, we focus on identifying two models of neural networks (NN), a multi-layer perceptron (i.e., MLP) model and an excellent model between the neural network (i.e., DNN) model. At this time, predictability and accuracy were found to be superior in the DNN model, and in the MLP model, it was found to be highly correlated and accessible. The major purpose of this study is to analyze the performance of MLP and DNN through a practical approach based on an artificial neural network stock forecasting method. Although we do not limit S&amp;P (i.e., Standard&amp;Poor’s 500 index) to escape other regional exits in order to see the proper flow of capital, we first measured S&amp;P data for 100 months (i.e., 407 weeks) and found out the following facts: First, the traditional artificial neural network (ANN) model, according to the specificity of each model and depending on the depth of the layer, shows the model of the prediction well and is sensitive to the index data; Second, comparing the two models, the DNN model showed better accuracy in terms of data accessibility and prediction accuracy than MLP, and the error rate was also shown in the weekly and monthly data; Third, the difference in the prediction accuracy of each model is not statistically significant. However, these results are correlated with each other, and are considered robust because there are few error rates, thanks to the accessibility to various other prediction accuracy measurement methodologies.

]]>Symmetry doi: 10.3390/sym9070107

Authors: Yibing Li Xueying Diao Qianhui Dong Chunrui Tang

In this paper, we focus on the interference management in the cognitive radio (CR) network comprised of multiple primary users (PUs) and multiple secondary users (SUs). Firstly, two interference alignment (IA) schemes are proposed to mitigate the interference among PUs. The first one is an interference rank minimization (IRM) scheme, which aims to minimize the rank of the joint interference matrix via alternating between the forward and reverse communication links. Considering the overhead of information exchanged between the transmitters and receivers in the IRM scheme, we further develop an interference subspace distance minimization (ISDM) scheme which runs at the transmitters only. The ISDM scheme focuses on aligning the subspaces spanned by interference with an aligned subspace introduced in this paper. For the secondary network, though IRM and ISDM mitigate the received interference at secondary receivers, they make no attempt to eliminate the interference from SUs to PUs. To address this, we improve the IRM and ISDM schemes by putting a rank constraint into their optimizations, where the rank constraint forces the ranks of the interference matrices from SUs to PUs to be zero. Simulation results validate the effectiveness of the proposed schemes in terms of the average sum rate.

]]>Symmetry doi: 10.3390/sym9070106

Authors: Ru-xin Nie Jian-qiang Wang Hong-yu Zhang

As one of the promising renewable energy resources, solar-wind energy has increasingly become a regional engine in leading the economy and raising competitiveness. Selecting a solar-wind power station location can contribute to efficient utilization of resource and instruct long-term development of socio-economy. Since the selection procedure consists of several location alternatives and many influential criteria factors, the selection can be recognized as a multiple criteria decision-making (MCDM) problem. To better express multiple uncertainty information during the selection procedure, fuzzy set theory is introduced to manage that issue. Interval neutrosophic sets (INSs), which are characterized by truth-membership, indeterminacy-membership and falsity-membership functions in the interval numbers (INs) form, are feasible in modeling more uncertainty of reality. In this paper, a newly extended weighted aggregated sum product assessment (WASPAS) technique, which involves novel three procedures, is utilized to handle MCDM issues under INSs environment. Some modifications are conducted in the extended method comparing with the classical WASPAS method. The most obvious improvement of the extended method relies on that it can generate more realistic criteria weight information by an objective and subjective integrated criteria weight determination method. A case study concerning solar-wind power station location selection is implemented to demonstrate the applicability and rationality of the proposed method in practice. Its validity and feasibility are further verified by a sensitivity analysis and a comparative analysis. These analyses effectively reveal that the extended WASPAS technique can well match the reality and appropriately handle the solar-wind power station location selection problem.

]]>Symmetry doi: 10.3390/sym9070105

Authors: Chi-Lun Lo Chi-Hua Chen Ta-Sheng Kuan Kuen-Rong Lo Hsun-Jung Cho

This study proposes a fuel consumption estimation system and method with lower cost. On-board units can report vehicle speed, and user devices can send fuel information to a data analysis server. Then the data analysis server can use the proposed fuel consumption estimation method to estimate the fuel consumption based on driver behaviours without fuel sensors for cost savings. The proposed fuel consumption estimation method is designed based on a genetic algorithm which can generate gene sequences and use crossover and mutation for retrieving an adaptable gene sequence. The adaptable gene sequence can be applied as the set of fuel consumption in accordance with the pattern of driver behaviour. The practical experimental results indicated that the accuracy of the proposed fuel consumption estimation method was about 95.87%.

]]>Symmetry doi: 10.3390/sym9070104

Authors: Qiang Guo Guoqing Ruan Yanping Liao

This paper considers the underdetermined blind separation of multiple input multiple output (MIMO) radar signals that are insufficiently sparse in both time and frequency domains under noisy conditions, while traditional algorithms are usually applied in the ideal sparse environment. An effective separation method based on single source point (SSP) identification and time-frequency smoothed l 0 norm (TF-SL0) is proposed. Firstly, a preprocessing step of the moving average filter and a novel argument-based time-frequency SSPs detection are employed to improve the signal-to-noise ratio and signal sparsity of the observed signals, respectively. Then, the mixing matrix is obtained by using clustering algorithms. Secondly, to obtain the optimal solution of underdetermined sparse component analysis, the smoothed l 0 norm (SL0) is introduced to preliminarily achieve signal separation in the time-frequency domain. Finally, time-frequency ridge estimation is proposed to jointly enhance the reconstruction accuracy of the MIMO radar signals, and the time domain waveforms are recovered by the model of the signals. Simulations illustrate the validity of the method and show that the proposed method outperforms the traditional methods in source separation, especially in the non-cooperative electromagnetic case where the prior information is unknown.

]]>Symmetry doi: 10.3390/sym9070103

Authors: Yunna Wu Chuanbo Xu Haobo Zhang Jianwei Gao

We propose a new class of aggregation operator based on utility function and apply them to group decision-making problem. First of all, based on an optimal deviation model, a new operator called the interval generalized ordered weighted utility multiple averaging (IGOWUMA) operator is proposed, it incorporates the risk attitude of decision-makers (DMs) in the aggregation process. Some desirable properties of the IGOWUMA operator are studied afterward. Subsequently, under the hyperbolic absolute risk aversion (HARA) utility function, another new operator named as interval generalized ordered weighted hyperbolic absolute risk aversion utility multiple averaging-HARA (IGOWUMA-HARA) operator is also defined. Then, we discuss its families and find that it includes a wide range of aggregation operators. To determine the weights of the IGOWUMA-HARA operator, a preemptive nonlinear objective programming model is constructed, which can determine a uniform weighting vector to guarantee the uniform standard comparison between the alternatives and measure their fair competition under the condition of valid comparison between various alternatives. Moreover, a new approach for group decision-making is developed based on the IGOWUMA-HARA operator. Finally, a comparison analysis is carried out to illustrate the superiority of the proposed method and the result implies that our operator is superior to the existing operator.

]]>Symmetry doi: 10.3390/sym9070101

Authors: Jihun Kim Jonghee Youn

Thanks to the development of Internet of Things (IoT) technologies, wearable markets have been growing rapidly. Smartwatches can be said to be the most representative product in wearable markets, and involve various hardware technologies in order to overcome the limitations of small hardware. Motion recognition sensors are a representative example of those hardware technologies. However, smartwatches and motion recognition sensors that can be worn by users may pose security threats of password pattern leakage. In the present paper, passwords are inferred through experiments to obtain password patterns inputted by users using motion recognition sensors, and verification of the results and the accuracy of the results is shown.

]]>Symmetry doi: 10.3390/sym9070102

Authors: Kwan Lee Hyung Hong Kang Park

The application of user emotion recognition for fear is expanding in various fields, including the quantitative evaluation of horror movies, dramas, advertisements, games, and the monitoring of emergency situations in convenience stores (i.e., a clerk threatened by a robber), in addition to criminal psychology. Most of the existing methods for the recognition of fear involve referring to a single physiological signal or recognizing circumstances in which users feel fear by selecting the most informative one among multiple physiological signals. However, the level of accuracy as well as the credibility of these study methods is low. Therefore, in this study, data with high credibility were obtained using non-intrusive multimodal sensors of near-infrared and far-infrared light cameras and selected based on t-tests and Cohen’s d analysis considering the symmetrical characteristics of face and facial feature points. The selected data were then combined into a fuzzy system using the input and output membership functions of symmetrical shape to ultimately derive a new method that can quantitatively show the level of a user’s fear. The proposed method is designed to enhance conventional subjective evaluation (SE) by fuzzy system based on multi-modalities. By using four objective features except for SE and combining these four features into a fuzzy system, our system can produce an accurate level of fear without being affected by the physical, psychological, or fatigue condition of the participants in SE. After conducting a study on 20 subjects of various races and genders, the results indicate that the new method suggested in this study has a higher level of credibility for the recognition of fear than the methods used in previous studies.

]]>Symmetry doi: 10.3390/sym9070100

Authors: Fei Hao Doo-Soon Park Zheng Pei

In social networking analysis, there exists a fundamental problem called maximal cliques enumeration(MCE), which has been extensively investigated in many fields, including social networks, biological science, etc. As a matter of fact, the formation principle of maximal cliques that can help us to speed up the detection of maximal cliques from social networks is often ignored by most existing research works. Aiming to exploit the formation of maximal cliques in social networks, this paper pioneers a creative research issue on the detection of bases of maximal cliques in social networks. We propose a formal concept analysis-based approach for detecting the bases of maximal cliques and detection theorem. It is believed that our work can provide a new research solution and direction for future topological structure analysis in various complex networking systems.

]]>Symmetry doi: 10.3390/sym9070099

Authors: Gisela Kaplan

The neural processes of bird song and song development have become a model for research relevant to human acquisition of language, but in fact, very few avian species have been tested for lateralization of the way in which their audio-vocal system is engaged in perception, motor output and cognition. Moreover, the models that have been developed have been premised on birds with strong vocal dimorphism, with a tendency to species with complex social and/or monomorphic song systems. The Australian magpie (Gymnorhina tibicen) is an excellent model for the study of communication and vocal plasticity with a sophisticated behavioural repertoire, and some of its expression depends on functional asymmetry. This paper summarizes research on vocal mechanisms and presents field-work results of behavior in the Australian magpie. For the first time, evidence is presented and discussed about lateralized behaviour in one of the foremost songbirds in response to specific and specialized auditory and visual experiences under natural conditions. It presents the first example of auditory lateralization evident in the birds’ natural environment by describing an extractive foraging event that has not been described previously in any avian species. It also discusses the first example of auditory behavioral asymmetry in a songbird tested under natural conditions.

]]>Symmetry doi: 10.3390/sym9070098

Authors: Nicholas Grebe Rachael Falcon Steven Gangestad

Fluctuating asymmetry is hypothesized to predict developmental instability (DI) and fitness outcomes. While published studies largely support this prediction, publication bias remains an issue. Biologists have increasingly turned to meta-analysis to estimate true support for an effect. Van Dongen and Gangestad (VD&amp;G) performed a meta-analysis on studies of fluctuating asymmetry (FA) and fitness-related qualities in humans. They found an average robust effect size, but estimates varied widely. Recently, psychologists have identified limitations in traditional meta-analyses and popular companion adjustments, and have advocated for alternative meta-analytic techniques. P-curve estimates true mean effects using significant published effects; it also detects the presence of p-hacking (where researchers exploit researcher “degrees of freedom”), not just publication bias. Alternative selection methods also provide a means to estimate average effect size correcting for publication bias, but may better account for heterogeneity in effect sizes and publication decisions than p-curve. We provide a demonstration by performing p-curve and selection method analyses on the set of effects from VD&amp;G. We estimate an overall effect size range (r = 0.08–0.15) comparable to VD&amp;G, but with notable differences between domains and techniques. Results from alternative estimation methods can provide corroborating evidence for, as well as insights beyond, traditional meta-analytic estimates.

]]>Symmetry doi: 10.3390/sym9070097

Authors: Sibel Başkal Young Kim Marilyn Noz

Wigner’s little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathematical forms for massive and for massless particles. However, it is shown possible to construct one unified representation using a graphical description. This graphical approach allows us to describe vividly parity, time reversal, and charge conjugation of the internal symmetry groups. As for the language of group theory, the two-by-two representation is used throughout the paper. While this two-by-two representation is for spin-1/2 particles, it is shown possible to construct the representations for spin-0 particles, spin-1 particles, as well as for higher-spin particles, for both massive and massless cases. It is shown also that the four-by-four Dirac matrices constitute a two-by-two representation of Wigner’s little group.

]]>Symmetry doi: 10.3390/sym9070096

Authors: Mansoor Siddiqui Shahid Butt Omer Gilani Mohsin Jamil Adnan Maqsood Faping Zhang

This research work is aimed at optimizing the availability of a framework comprising of two units linked together in series configuration utilizing Markov Model and Monte Carlo (MC) Simulation techniques. In this article, effort has been made to develop a maintenance model that incorporates three distinct states for each unit, while taking into account their different levels of deterioration. Calculations are carried out using the proposed model for two distinct cases of corrective repair, namely perfect and imperfect repairs, with as well as without opportunistic maintenance. Initially, results are accomplished using an analytical technique i.e., Markov Model. Validation of the results achieved is later carried out with the help of MC Simulation. In addition, MC Simulation based codes also work well for the frameworks that follow non-exponential failure and repair rates, and thus overcome the limitations offered by the Markov Model.

]]>Symmetry doi: 10.3390/sym9060095

Authors: Shuwei Wang Jia Liu

Practical decision situations are becoming increasingly complicated. It is common for a person to select or rank alternatives with respect to multiple attributes, and the TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method, which is one of the first multiple attribute decision making (MADM) methods based on prospect theory, has received more attention due to its great performance in considering the bounded rationality of decision makers (DMs). However, the classical TODIM method can only handle the MADM problems with crisp numbers. In this paper, considering that intuitionistic linguistic variables are convenient to describe uncertain or imprecise information, we propose the intuitionistic linguistic TODIM (IL-TODIM) method and intuitionistic uncertain linguistic TODIM (IUL-TODIM) method to solve uncertain MADM problems with IL and IUL variables, respectively. Additionally, a novel distance measure for IUL numbers is developed, based on which we can obtain the corresponding dominance degree of one alternative over another. Finally, examples are provided to show the validity of the proposed methods, and we also conduct a comparison of the results between the IL-TODIM method and the existing intuitionistic fuzzy MADM methods to illustrate the effectiveness of our proposed methods.

]]>Symmetry doi: 10.3390/sym9060094

Authors: Qian Sun Ming Diao Ya Zhang Yibing Li

The Multiple Mobile Robot (MMR) cooperative system is becoming a focus of study in various fields due to its advantages, such as high efficiency and good fault tolerance. However, the uncertainty and nonlinearity problems severely limit the cooperative localization accuracy of the MMR system. Thus, to solve the problems mentioned above, this manuscript presents a cooperative localization algorithm for MMR systems based on Cubature Kalman Filter (CKF) and adaptive Variance Component Estimation (VCE) methods. In this novel algorithm, a nonlinear filter named CKF is used to enhance the cooperative localization accuracy and reduce the computational load. On the other hand, the adaptive VCE method is introduced to eliminate the effects of unknown system noise. Furthermore, the performance of the proposed algorithm is compared with that of the cooperative localization algorithm based on normal CKF by utilizing the real experiment data. In addition, the results demonstrate that the proposed algorithm outperforms the CKF cooperative localization algorithm both in accuracy and consistency.

]]>Symmetry doi: 10.3390/sym9060093

Authors: Lei Si Zhongbin Wang Rongxin Xu Chao Tan Xinhua Liu, Jing Xu

Surveillance videos of coal mining faces have close relation to the safety of coal miners and mining efficiency. However, surveillance videos are always disturbed by some severe conditions such as atomization, low illumination, glare, and so on. Therefore, this paper proposed a hybrid algorithm (SSR-BF) based on the integration of single-scale Retinex (SSR) and bilateral filtering (BF) to enhance the image quality of surveillance videos. BF was coupled with SSR to reduce the noises and perfect the edge information in the image. The schematic diagram and pseudocode of SSR-BF was designed, and the parameters were set rationally to ensure the enhancement effects through some simulations. Finally, some comparisons with other methods were carried out, and the simulation results demonstrated that the proposed algorithm was superior to others and could be applied to image enhancement for poormonochrome images, especially the surveillance video of a coal mining face.

]]>Symmetry doi: 10.3390/sym9060092

Authors: Hung-Jr. Shiu Bor-Shing Lin Chia-Wei Cheng Chien-Hung Huang Chin-Laung Lei

This work proposes a new and non-blind steganographic scheme for synthesized pitches. Synthesized music is popularly used to demonstrate early versions of compositions conveniently and at low-cost. They can also be utilized to pass secrets or obtain digital rights. The method consists of two procedures, of which the first is the realistic simulation of synthesized pitches using a computer and the second is the hiding of secrets during the generated simulated pitches. The first part of this paper reviews attempts to discover the fundamental patterns of synthesized pitches and to develop a strategy for generating approximate pitches using a computer. The component frequencies are used to generate a pitch in which to hide secrets. Legal receivers receive the referenced composition and frequencies, enabling them to generate the synthesized pitches according to the main frequencies of the referenced composition. Finally, the generated and received pitches are compared to identify the secret bits. As more frequencies are used to hide secret bits, more secret bits can be embedded in the synthesized pitches. The use of more frequencies makes synthesized pitches more realistic compared to real ones. The performance of the proposed method is also compared with that of competing methods and under common attacks.

]]>Symmetry doi: 10.3390/sym9060087

Authors: Primož Jelušič Bojan Žlender

The primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist. In this paper, heuristic fuzzy rules were used with the intention of improving the performance of optimization models, introducing experiential rules acquired from experts and utilizing recommendations. The aim of this paper was to define soft constraints using an adaptive network-based fuzzy inference system (ANFIS). This newly-developed soft constraint was applied to discrete optimization for obtaining optimal solutions. Even though the computational model is based on advanced computational technologies including fuzzy logic, neural networks and discrete optimization, it can be used to solve real-world problems of great interest for design engineers. The proposed computational model was used to find the minimum weight solutions for simply-supported laterally-restrained beams.

]]>Symmetry doi: 10.3390/sym9060089

Authors: Hanshu Hong Yunhao Xia Zhixin Sun

Searchable encryption mechanism and attribute-based encryption (ABE) are two effective tools for providing fine-grained data access control in the cloud. Researchers have also taken their advantages to present searchable encryption schemes based on ABE and have achieved significant results. However, most of the existing key word search schemes based on ABE lack the properties of key exposure protection and highly efficient key updating when key leakage happens. To better tackle these problems, we present a key insulated attribute-based data retrieval scheme with key word search (KI-ABDR-KS) for multi-tenant architecture. In our scheme, a data owner can make a self-centric access policy of the encrypted data. Only when the possessing attributes match with the policy can a receiver generate a valid trapdoor and search the ciphertext. The proposed KI-ABDR-KS also provides full security protection when key exposure happens, which can minimize the damage brought by key exposure. Furthermore, the system public parameters remain unchanged during the process of key updating; this will reduce the considerable overheads brought by parameters synchronization. Finally, our KI-ABDR-KS is proven to be secure under chosen-keyword attack and achieves better efficiency compared to existing works.

]]>Symmetry doi: 10.3390/sym9060091

Authors: Tao Jiang Xianfeng Yang Xufei Cui

To improve the accuracy of indoor pedestrian positioning, an indoor pedestrian positioning system with two-order Bayesian estimation based on Extended Kalman Filter (EKF) and Particle Filter (PF) is proposed in this paper. The presented system combines a foot-mounted inertial sensor, a Wi-Fi propagation model and building structure to make good use of these information resources. There are two updates in this system in order to limit the accumulative errors of inertial sensors. In the first update, the inertial navigation system (INS) is the main system in the calculation of pedestrian positioning, and Zero-velocity update (ZUPT) is introduced as the reference to correct the accumulative errors of INS based on EKF. To further limit the accumulative errors of inertial sensors, the estimated results obtained from the first update, including horizontal position information, are introduced as the observations based on PF in the second update; Pedestrian Dead Reckoning (PDR) is the main system in the calculation of pedestrian positioning, and the weight of particles is determined by the Wi-Fi propagation model, building structure information and output of the first update. The results show that the accuracy of positioning is effectively increased.

]]>Symmetry doi: 10.3390/sym9060090

Authors: Yao Ouyang Jun Li Radko Mesiar

In this note, we discuss when the concave integral coincides with the pan- integral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equality. We show also another sufficient condition, which, in the case of finite spaces, is necessary, too.

]]>Symmetry doi: 10.3390/sym9060088

Authors: Felix Held Kerstin Stingl Svetlana Tsogoeva

The first organocatalyzed sulfoxidation reaction towards enantioenriched (R)-modafinil (Armodafinil®), a drug against narcolepsy, is reported here. A series of chiral organocatalysts, e.g., different chiral BINOL-phosphates, or a fructose-derived N-substituted oxazolidinone ketone (Shi catalyst) were applied for the sulfoxidation reaction with environmentally friendly H2O2 as a convenient oxygen transferring agent. Furthermore, the potential of a biomimetic catalytic system consisting of FeCl3 and a dipeptide-based chiral ligand was demonstrated, which constitutes the most successful asymmetric non-heme iron-catalyzed synthesis of (R)-modafinil so far.

]]>Symmetry doi: 10.3390/sym9060086

Authors: Duc Luong Jeon Kang Phong Nguyen Min Lee Kang Park

In order to capture an eye image of high quality in a gaze-tracking camera, an auto-focusing mechanism is used, which requires accurate focus assessment. Although there has been previous research on focus assessment in the spatial or wavelet domains, there are few previous studies that combine all of the methods of spatial and wavelet domains. Since all of the previous focus assessments in the spatial or wavelet domain methods have disadvantages, such as being affected by illumination variation, etc., we propose a new focus assessment method by combining the spatial and wavelet domain methods for the gaze-tracking camera. This research is novel in the following three ways, in comparison with the previous methods. First, the proposed focus assessment method combines the advantages of spatial and wavelet domain methods by using ε-support vector regression (SVR) with a symmetrical Gaussian radial basis function (RBF) kernel. In order to prevent the focus score from being affected by a change in image brightness, both linear and nonlinear normalizations are adopted in the focus score calculation. Second, based on the camera optics, we mathematically prove the reason for the increase in the focus score in the case of daytime images or a brighter illuminator compared to nighttime images or a darker illuminator. Third, we propose a new criterion to compare the accuracies of the focus measurement methods. This criterion is based on the ratio of relative overlapping amount (standard deviation of focus score) between two adjacent positions along the Z-axis to the entire range of focus score variety between these two points. Experimental results showed that the proposed method outperforms other methods.

]]>Symmetry doi: 10.3390/sym9060085

Authors: Simon Newstead

The POT family of proton coupled oligopeptide transporters belong to the Major Facilitator Superfamily of secondary active transporters and are found widely distributed in bacterial, plant, fungal and animal genomes. POT transporters use the inwardly directed proton electrochemical gradient to drive the concentrative uptake of di- and tri-peptides across the cell membrane for metabolic assimilation. Mammalian members of the family, PepT1 and PepT2, are responsible for the uptake and retention of dietary protein in the human body, and due to their promiscuity in ligand recognition, play important roles in the pharmacokinetics of drug transport. Recent crystal structures of bacterial and plant members have revealed the overall architecture for this protein family and provided a framework for understanding proton coupled transport within the POT family. An interesting outcome from these studies has been the discovery of symmetrically equivalent structural and functional sites. This review will highlight both the symmetry and asymmetry in structure and function within the POT family and discuss the implications of these considerations in understanding transport and regulation.

]]>Symmetry doi: 10.3390/sym9060084

Authors: Cinzia Chiandetti Bastien Lemaire Elisabetta Versace Giorgio Vallortigara

Chicks (Gallus gallus) learned to run from a starting box to a target located at the end of a runway. At test, colourful and bright distractors were placed just outside the starting box. Dark incubated chicks (maintained in darkness from fertilization to hatching) stopped significantly more often, assessing more the left-side distractor than chicks hatched after late (for 42 h during the last three days before hatching) or early (for 42 h after fertilization) exposure to light. The results show that early embryonic light stimulation can modulate this particular behavioural lateralization comparably to the late application of it, though via a different route.

]]>Symmetry doi: 10.3390/sym9060083

Authors: Shen Yuan Travis Goron Liying Huang Lilian Wu Fei Wang

Rice leaves display lateral asymmetry around the midrib, and the narrow side exhibits higher leaf area-based nitrogen concentration (Na) and soil plant analysis development (SPAD) values than the wider side. However, the difference in the relationship between the SPAD of each side and Na of the corresponding lateral half, and the optimal position along the leaf blade for SPAD measurements are not known. In this study, the relationship between SPAD and Na of both sides of the top three leaves was determined with 17 rice varieties grown over three growing seasons in two locations. The relationship between SPAD and Na displayed leaf lateral asymmetry, in which the wide side reflected a higher coefficient of determination than the narrow side. The ability to estimate Na of the whole leaf was slightly improved by averaging SPAD values across the leaf sides and measured points for the top two leaves. Apparently, it was more accurate and easier to measure SPAD readings on the wide side than the narrow side of rice leaf blade with respect to estimating plant N status. Due to the relatively poor relationship of the upper leaf, and the structural limit for SPAD measurements of the base, this study suggests that the most suitable and representative position for SPAD meter measurement on the leaf blade of rice is the lower-middle part from the leaf apex on the wide side.

]]>Symmetry doi: 10.3390/sym9060082

Authors: Jiqian Chen Jun Ye

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach.

]]>Symmetry doi: 10.3390/sym9060081

Authors: Hasibur Chayon Kaharudin Dimyati Harikrishnan Ramiah Ahmed Reza

Long Term Evolution (LTE) is the prominent technology in Fourth Generation (4G) communication standards, which provides higher throughput and better Quality of Service (QoS) to all users. However, users in the cell-edge area are receiving comparatively low QoS due to the distance from eNodeB (eNB) and bad channel conditions. The Conventional Modified Largest Weighted Delay First (MLWDF) algorithm is unable to resolve this issue, as it does not consider the location of the user. This paper proposes an extended MLWDF (EMLWDF) downlink scheduling algorithm to provide better services to the cell-edge user as well as to the cell-center user. The proposed algorithm divides the eNB cell area into inner and outer regions. It includes the distance of the user from attached eNB, received Signal to Interference plus Noise Ratio (SINR) and error probability into the original algorithm. The simulated results are compared with other well-known algorithms and the comparison shows that the proposed algorithm enhances overall 56.23% of cell-edge user throughput and significantly improves the average user throughput, fairness index, and spectral efficiency.

]]>Symmetry doi: 10.3390/sym9060080

Authors: Jun Ye

The normal distribution is a usual one of various distributions in the real world. A normal neutrosophic set (NNS) is composed of both a normal fuzzy number and a neutrosophic number, which a significant tool for describing the incompleteness, indeterminacy, and inconsistency of the decision-making information. In this paper, we propose two correlation coefficients between NNSs based on the score functions of normal neutrosophic numbers (NNNs) (basic elements in NNSs) and investigate their properties. Then, we develop a multiple attribute decision-making (MADM) method with NNSs under normal neutrosophic environments, where, by correlation coefficient values between each alternative (each evaluated NNS) and the ideal alternative (the ideal NNS), the ranking order of alternatives and the best one are given in the normal neutrosophic decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to demonstrate the application and feasibility of the developed decision-making method. Compared to the existing MADM approaches based on aggregation operators of NNNs, the proposed MADM method based on the correlation coefficients of NNSs shows the advantage of its simple decision-making process.

]]>Symmetry doi: 10.3390/sym9060079

Authors: Dan Chen Zhongzhou Lu Zebang Shen Gaofeng Zhang Chong Chen Qingguo Zhou

The balanced hypercube network, which is a novel interconnection network for parallel computation and data processing, is a newly-invented variant of the hypercube. The particular feature of the balanced hypercube is that each processor has its own backup processor and they are connected to the same neighbors. A Hamiltonian bipartite graph with bipartition V 0 &#x0222A; V 1 x &#x02208; V 0 y &#x02208; V 1 . It is known that each edge is on a Hamiltonian cycle of the balanced hypercube. In this paper, we prove that, for an arbitrary edge e in the balanced hypercube, there exists a Hamiltonian path between any two vertices x and y in different partite sets passing through e with e &#x02260; x y . This result improves some known results.

]]>Symmetry doi: 10.3390/sym9050078

Authors: Jiwon Lee Mingyu Kim Jinmo Kim

This study analyzes walking interaction to enhance the immersion and minimize virtual reality (VR) sickness of users by conducting experiments. In this study, the walking interaction is composed of three steps using input devices with a simple structure that can be easily used by anyone. The first step consists of a gamepad control method, which is the most popular but has low presence. The second step consists of a hand-based walking control interface, which is mainly used for interaction in VR applications. The last step consists of a march-in-place detection simulator that interacts with the legs—the key body parts for walking. Four experiments were conducted to determine the degree of direct expression of intention by users in the course of walking interactions that can improve immersion, presence, and prevent VR sickness in VR applications. With regard to the experiments in this study, survey experiments were conducted for general users using the Wilcoxon test, a presence questionnaire, and simulator sickness questionnaire (SSQ). In addition, the technical performance of the VR scenes used in the experiment was analyzed. The experimental results showed that higher immersion was achieved when interactions that felt closer to real walking were provided in VR. Furthermore, it was found that even control methods with a simple structure could be used for walking interactions with minimal VR sickness. Finally, a satisfactory presence was found in VR if the user was able interact using his or her own legs.

]]>Symmetry doi: 10.3390/sym9050077

Authors: Dennis Gehring Onur Güntürkün Wolfgang Wiltschko Roswitha Wiltschko

In European Robins, Erithacus rubecula, the magnetic compass is lateralized in favor of the right eye/left hemisphere of the brain. This lateralization develops during the first winter and initially shows a great plasticity. During the first spring migration, it can be temporarily removed by covering the right eye. In the present paper, we used the migratory orientation of robins to analyze the circumstances under which the lateralization can be undone. Already a period of 1½ h being monocularly left-eyed before tests began proved sufficient to restore the ability to use the left eye for orientation, but this effect was rather short-lived, as lateralization recurred again within the next 1½ h. Interpretable magnetic information mediated by the left eye was necessary for removing the lateralization. In addition, monocularly, the left eye seeing robins could adjust to magnetic intensities outside the normal functional window, but this ability was not transferred to the “right-eye system”. Our results make it clear that asymmetry of magnetic compass perception is amenable to short-term changes, depending on lateralized stimulation. This could mean that the left hemispheric dominance for the analysis of magnetic compass information depends on lateralized interhemispheric interactions that in young birds can swiftly be altered by environmental effects.

]]>Symmetry doi: 10.3390/sym9050076

Authors: Giulia Prete Mara Fabri Nicoletta Foschi Luca Tommasi

A right-hemispheric superiority has been shown for spatial symmetry perception with mono-dimensional stimuli (e.g., bisected lines). Nevertheless, the cerebral imbalance for bi-dimensional stimuli is still controversial, and the aim of the present study is to investigate this issue. Healthy participants and a split-brain patient (D.D.C.) were tested in a divided visual field paradigm, in which a square shape was presented either in the left or right visual field and they were asked to judge whether a dot was placed exactly in the center of the square or off-center, by using the left/right hand in two separate sessions. The performance of healthy participants was better when the stimuli presented in the left visual field (LVF) were on-center rather than off-center. The performance of D.D.C. was higher than chance only when on-center stimuli were presented in the LVF in the left hand session. Only in this condition did his accuracy not differ with respect to that of the control group, whereas in all of the other conditions, it was lower than the controls’ accuracy. We conclude that the right-hemispheric advantage already shown for mono-dimensional stimuli can be extended also to bi-dimensional configurations, confirming the right-hemispheric superiority for spatial symmetry perception.

]]>Symmetry doi: 10.3390/sym9050075

Authors: Ming Zhang Ming Diao Lipeng Gao Lutao Liu

For passive radar detection system, radar waveform recognition is an important research area. In this paper, we explore an automatic radar waveform recognition system to detect, track and locate the low probability of intercept (LPI) radars. The system can classify (but not identify) 12 kinds of signals, including binary phase shift keying (BPSK) (barker codes modulated), linear frequency modulation (LFM), Costas codes, Frank code, P1-P4 codesand T1-T4 codeswith a low signal-to-noise ratio (SNR). It is one of the most extensive classification systems in the open articles. A hybrid classifier is proposed, which includes two relatively independent subsidiary networks, convolutional neural network (CNN) and Elman neural network (ENN). We determine the parameters of the architecture to make networks more effectively. Specifically, we focus on how the networks are designed, what the best set of features for classification is and what the best classified strategy is. Especially, we propose several key features for the classifier based on Choi–Williams time-frequency distribution (CWD). Finally, the recognition system is simulated by experimental data. The experiments show the overall successful recognition ratio of 94.5% at an SNR of −2 dB.

]]>Symmetry doi: 10.3390/sym9050074

Authors: Jodie Ford Phillip Stansfeld Ioannis Vakonakis

Centrioles make up the centrosome and basal bodies in animals and as such play important roles in cell division, signalling and motility. They possess characteristic 9-fold radial symmetry strongly influenced by the protein SAS-6. SAS-6 is essential for canonical centriole assembly as it forms the central core of the organelle, which is then surrounded by microtubules. SAS-6 self-assembles into an oligomer with elongated spokes that emanate towards the outer microtubule wall; in this manner, the symmetry of the SAS-6 oligomer influences centriole architecture and symmetry. Here, we summarise the form and symmetry of SAS-6 oligomers inferred from crystal structures and directly observed in vitro. We discuss how the strict 9-fold symmetry of centrioles may emerge, and how different forms of SAS-6 oligomers may be accommodated in the organelle architecture.

]]>Symmetry doi: 10.3390/sym9050073

Authors: Sang-Seon Byun Joon-Min Gil

This paper considers the deployment of a cognitive radio scheme in wireless sensor networks to achieve (1) fair spectrum allocation, (2) maximum spectrum utilization, and (3) priority-based sensor transmissions, while (4) avoiding unnecessary spectrum handover (or handoff). This problem is modelled as a bi-objective optimization problem. We apply modified game theory and a cooperative approach to identify an approximate optimal solution in reasonable time. We perform a series of numerical experiments to show that our scheme achieves fair spectrum allocation (in terms of proportional fairness) while observing transmission priorities and minimizing unnecessary spectrum handover.

]]>Symmetry doi: 10.3390/sym9050072

Authors: Sylvia Kirchengast Kerrin Christiansen

Fluctuating asymmetry is mainly interpreted as an indicator of developmental instability, while directional asymmetry of the upper limbs is associated with handedness. The association patterns between adult androgen levels and fluctuating as well directional asymmetry patterns are still unclear. In the present study, the association between adult androgen levels, body size and directional as well as fluctuating asymmetry pattern was tested among !Kung San and Kavango males from northern Namibia. Serum concentrations of testosterone (Tser) and 5α-dihydrotestosterone (DHT) as well as salivary testosterone (Tsal) concentrations were obtained from 114 !Kung San and 136 Kavango men aged 18–40 years. Fluctuating and directional asymmetry were determined from eight paired traits. Signed and unsigned asymmetry, composite fluctuating and directional asymmetry were calculated. !Kung San males surpassed their Kavango counterparts in the directional asymmetry but also in composite directional asymmetry (CDA) significantly. Among !Kung San males, DHT correlated significantly negatively with parameters of fluctuating asymmetry as well as with parameters of directional asymmetry. Free testosterone of the saliva correlated significantly negatively with asymmetry of hand length. Among Kavango males, DHT is negatively associated with foot breadth asymmetry, but positively associated with wrist asymmetry. Although the correlations between asymmetry patterns and androgen levels are weak, it can be concluded that among !Kung San males adult androgen levels are negatively associated with a high quality phenotype.

]]>Symmetry doi: 10.3390/sym9050071

Authors: Marcello Siniscalchi Serenella d’Ingeo Angelo Quaranta

Understanding the complementary specialisation of the canine brain has been the subject of increasing scientific study over the last 10 years, chiefly due to the impact of cerebral lateralization on dog behaviour. In particular, behavioural asymmetries, which directly reflect different activation of the two sides of the dog brain, have been reported at different functional levels, including motor and sensory. The goal of this review is not only to provide a clear scenario of the experiments carried out over the last decade but also to highlight the relationships between dogs’ lateralization, cognitive style and behavioural reactivity, which represent crucial aspect relevant for canine welfare.

]]>Symmetry doi: 10.3390/sym9050070

Authors: Qing Shen Xiaojuan Ban Chong Guo

There is always an asymmetric phenomenon between traffic data quantity and unit information content. Labeled data is more effective but scarce, while unlabeled data is large but weaker in sample information. In an urban transportation assessment system, semi-supervised extreme learning machine (SSELM) can unite manual observed data and extensively collected data cooperatively to build connection between congestion condition and road information. In our method, semi-supervised learning can integrate both small-scale labeled data and large-scale unlabeled data, so that they can play their respective advantages, while the ELM can process large scale data at high speed. Optimized by kernel function, Kernel-SSELM can achieve higher classification accuracy and robustness than original SSELM. Both the experiment and the real-time application show that the evaluation system can precisely reflect the traffic condition.

]]>Symmetry doi: 10.3390/sym9050068

Authors: Sanghyuk Lee Jaehoon Cha Nipon Theera-Umpon Kyeong Kim

A similarity measure is a measure evaluating the degree of similarity between two fuzzy data sets and has become an essential tool in many applications including data mining, pattern recognition, and clustering. In this paper, we propose a similarity measure capable of handling non-overlapped data as well as overlapped data and analyze its characteristics on data distributions. We first design the similarity measure based on a distance measure and apply it to overlapped data distributions. From the calculations for example data distributions, we find that, though the similarity calculation is effective, the designed similarity measure cannot distinguish two non-overlapped data distributions, thus resulting in the same value for both data sets. To obtain discriminative similarity values for non-overlapped data, we consider two approaches. The first one is to use a conventional similarity measure after preprocessing non-overlapped data. The second one is to take into account neighbor data information in designing the similarity measure, where we consider the relation to specific data and residual data information. Two artificial patterns of non-overlapped data are analyzed in an illustrative example. The calculation results demonstrate that the proposed similarity measures can discriminate non-overlapped data.

]]>Symmetry doi: 10.3390/sym9050069

Authors: Fang Ye Jie Chen Yibing Li

A new DS (Dempster-Shafer) combination method is presented in this paper. As data detected by a single sensor are characterized by not only fuzziness, but also partial reliability, the development of multi-sensor information fusion becomes extremely indispensable. The DS evidence theory is an effective means of information fusion, which can not only deal with the uncertainty and inconsistency of multi-sensor data, but also handle the inevitably ambiguity and instability under noise or possible interference. However, the application of DS evidence theory has some limitations when multi-sensor data are conflicting. To address this issue, the DS evidence theory is modified in this paper. Adopting the idea of cluster analysis, we firstly introduce the Lance distance function and spectral angle cosine function to revise original evidence separately before the combination of evidence. Then, based on the modifications of original evidence, an improved conflict redistribution strategy is ulteriorly raised to fuse multi-sensor information. Finally, the numerical simulation analyses demonstrate that the improvement of the DS evidence theory available in this paper overcomes the limitations of conventional DS evidence theory, and realizes more reliable fusion with multi-sensor conflicting information compared to the existing methods.

]]>Symmetry doi: 10.3390/sym9050067

Authors: Barbara Gillam

Symmetry detection has long been a major focus of perception research. However, although symmetry is often cited as a “grouping principle”, the effect of symmetry on grouping, an important form of perceptual organization, has been little measured. In past research, we found little spatio-temporal grouping for oblique lines symmetric around a horizontal axis during ambiguous rotary motion in depth. Grouping was measured by the degree to which the ambiguous motion direction was resolved for two elements in common (rotational linkage). We hypothesized that symmetry-based grouping would be stronger if symmetry was redundant i.e., carried by elements of greater complexity. Using the rotational linkage measure, we compared grouping for horizontally symmetric simple oblique lines and for lines composed of multiple conjoined orientations and found greater grouping for the more complex symmetric lines. A control experiment ruled out possible confounding factors and also showed a grouping effect of vertically aligned endpoints. We attribute the stronger grouping effect of redundant symmetry to the fact that it has a lower probability than does simple symmetry of arising from an accidental environmental arrangement.

]]>Symmetry doi: 10.3390/sym9050066

Authors: Sebastian Ocklenburg Ceren Barutçuoğlu Adile Öniz Özgören Murat Özgören Esra Erdal Dirk Moser Judith Schmitz Robert Kumsta Onur Güntürkün

Handedness is the most pronounced behavioral asymmetry in humans. Genome-wide association studies have largely failed to identify genetic loci associated with phenotypic variance in handedness, supporting the idea that the trait is determined by a multitude of small, possibly interacting genetic and non-genetic influences. However, these studies typically are not capable of detecting influences of rare mutations on handedness. Here, we used whole exome sequencing in a Turkish family with history of consanguinity and overrepresentation of left-handedness and performed quantitative trait analysis with handedness lateralization quotient as a phenotype. While rare variants on different loci showed significant association with the phenotype, none was functionally relevant for handedness. This finding was further confirmed by gene ontology group analysis. Taken together, our results add further evidence to the suggestion that there is no major gene or mutation that causes left-handedness.

]]>Symmetry doi: 10.3390/sym9050065

Authors: Byoungwook Kim Hwirim Byun Yoon-A Heo Young-Sik Jeong

The adaptive mobile resource offloading (AMRO) proposed in this paper is a load balancing scheme for processing large-scale jobs using mobile resources without a cloud server. AMRO is applied in a mobile cloud computing environment based on collaborative architecture. A load balancing scheme with efficient job division and optimized job allocation is needed because the resources for mobile devices will not always be provided consistently in this environment. Therefore, a job load balancing scheme is proposed that considers personal usage patterns and the dynamic resource state of the mobile devices. The delay time for computer job processing is minimized through dynamic job reallocation and adaptive job allocation in the disability state that occurs due to unexpected problems and to excessive job allocations by the mobile devices providing the resources for the mobile cloud computing. In order to validate the proposed load balancing scheme, an adaptive mobile resource management without cloud server (AMRM) protocol was designed and implemented, and the improved processing speed was verified in comparison with the existing offloading method. The improved job processing speed in the mobile cloud environment is demonstrated through job allocation based on AMRM and by taking into consideration the idle resources of the mobile devices. Furthermore, the resource waste of the mobile devices is minimized through adaptive offloading and consideration of both insufficient and idle resources.

]]>Symmetry doi: 10.3390/sym9050064

Authors: Aaron Michaux Vikrant Kumar Vijai Jayadevan Edward Delp Zygmunt Pizlo

We present a new algorithm for 3D shape reconstruction from stereo image pairs that uses mirror symmetry as a biologically inspired prior. 3D reconstruction requires some form of prior because it is an ill-posed inverse problem. Psychophysical research shows that mirror-symmetry is a key prior for 3D shape perception in humans, suggesting that a general purpose solution to this problem will have many applications. An approach is developed for finding objects that fit a given shape definition. The algorithm is developed for shapes with two orthogonal planes of symmetry, thus allowing for straightforward recovery of occluded portions of the objects. Two simulations were run to test: (1) the accuracy of 3D recovery, and (2) the ability of the algorithm to find the object in the presence of noise. We then tested the algorithm on the Children’s Furniture Corpus, a corpus of stereo image pairs of mirror symmetric furniture objects. Runtimes and 3D reconstruction errors are reported and failure modes described.

]]>Symmetry doi: 10.3390/sym9050063

Authors: Pietro Roversi Riccardo Destro

Charge density studies utilise a multipolar expansion of the atomic density (and the associated atomic scattering factor) in order to model asphericity. Contributions of the individual multipoles to the atomic density are then refined as multipole population coefficients. Refinement of these coefficients pertaining to odd-order multipoles that are invariant under the crystal point-group symmetry is often problematic, with ill-defined values and correlations plaguing the convergence to a good model. These difficulties have been discussed in generic terms in the literature, but never explicitly analysed in detail. In this communication, we show that the charge density multipolar atomic scattering factor can be partitioned in three contributions that differ in their behaviour under the point group symmetry of the crystal. This partitioning rationalises and predicts the conditions that give rise to ill-conditioning of the charge density refinement of these multipoles.

]]>Symmetry doi: 10.3390/sym9050062

Authors: Byoungwook Kim JaMee Kim Gangman Yi

The setting of standards is a critical process in educational evaluation, but it is time-consuming and expensive because it is generally conducted by an education experts group. The purpose of this paper is to find a suitable cluster validity index that considers the futures of item response data for setting cut-off scores. In this study, nine representative cluster validity indexes were used to evaluate the clustering results. Cohen’s kappa coefficient is used to check the conformity between a set cut-off score using four clustering techniques and a cut-off score set by experts. We compared the cut-off scores by each cluster validity index and by a group of experts. The experimental results show that the entropy-based method considers the features of item response data, so it has a realistic possibility of applying a clustering evaluation method to the setting of standards in criterion referenced evaluation.

]]>Symmetry doi: 10.3390/sym9050061

Authors: Sunghwan Kim

In this paper, reversible data-hiding (RDH) systems with modified fluctuation functions and rate-matched Reed–Solomon (RS) codes are proposed to enhance the data recovery from encrypted images. The modified fluctuation functions are used for estimating embedded codeword bits from the correlation of pixels. Instead of direct data-bit embedding, codeword bits of RS codes are embedded by a data-hider. With the help of the error-correcting capability of RS codes, the encrypted message can be recovered from the weak correlation of adjacent pixels in the image. In the experimental results, bit error rate (BER) and peak signal to noise ratio (PSNR) performances of the proposed system are better than those of referenced data-hiding systems for three images. The proposed schemes based on the modified fluctuation function or rate-matched codes can be applied to various RDH systems with better data transmission and image recovery performance.

]]>Symmetry doi: 10.3390/sym9050060

Authors: Wu Deng Huimin Zhao Xinhua Yang Chang Dong

Roller bearings are the most widely used and easily damaged mechanical parts in rotating machinery. Their running state directly affects rotating machinery performance. Empirical mode decomposition (EMD) easily occurs illusive component and mode mixing problem. From the view of feature extraction, a new feature extraction method based on integrating ensemble empirical mode decomposition (EEMD), the correlation coefficient method, and Hilbert transform is proposed to extract fault features and identify fault states for motor bearings in this paper. In the proposed feature extraction method, the EEMD is used to decompose the vibration signal into a series of intrinsic mode functions (IMFs) with different frequency components. Then the correlation coefficient method is used to select the IMF components with the largest correlation coefficient, which are carried out with the Hilbert transform. The obtained corresponding envelope spectra are analyzed to extract the fault feature frequency and identify the fault state by comparing with the theoretical value. Finally, the fault signal transmission performance of vibration signals of the bearing inner ring and outer ring at the drive end and fan end are deeply studied. The experimental results show that the proposed feature extraction method can effectively eliminate the influence of the mode mixing and extract the fault feature frequency, and the energy of the vibration signal in the bearing outer ring at the fan end is lost during the transmission of the vibration signal. It is an effective method to extract the fault feature of the bearing from the noise with interference.

]]>Symmetry doi: 10.3390/sym9040059

Authors: Yiqi Wu Fazhi He Soonhung Han

One basic issue with collaborative computer aided design (Co-CAD) is how to maintain valid and consistent modeling results across all design sites. Moreover, modeling history is important in parametric CAD modeling. Therefore, different from a typical co-editing approach, this paper proposes a novel method for Co-CAD synchronization, in which all Co-CAD sites maintain symmetric and consistent operating procedures. Consequently, the consistency of both modeling results and history can be achieved. In order to generate a valid, unique, and symmetric queue among collaborative sites, a set of correlated mechanisms is presented in this paper. Firstly, the causal relationship of operations is maintained. Secondly, the operation queue is reconstructed for partial concurrency operation, and the concurrent operation can be retrieved. Thirdly, a symmetric, concurrent operation control strategy is proposed to determine the order of operations and resolve possible conflicts. Compared with existing Co-CAD consistency methods, the proposed method is convenient and flexible in supporting collaborative design. The experiment performed based on the collaborative modeling procedure demonstrates the correctness and applicability of this work.

]]>Symmetry doi: 10.3390/sym9040058

Authors: Byoungwook Kim

The k-means is one of the most popular and widely used clustering algorithm; however, it is limited to numerical data only. The k-prototypes algorithm is an algorithm famous for dealing with both numerical and categorical data. However, there have been no studies to accelerate it. In this paper, we propose a new, fast k-prototypes algorithm that provides the same answers as those of the original k-prototypes algorithm. The proposed algorithm avoids distance computations using partial distance computation. Our k-prototypes algorithm finds minimum distance without distance computations of all attributes between an object and a cluster center, which allows it to reduce time complexity. A partial distance computation uses a fact that a value of the maximum difference between two categorical attributes is 1 during distance computations. If data objects have m categorical attributes, the maximum difference of categorical attributes between an object and a cluster center is m. Our algorithm first computes distance with numerical attributes only. If a difference of the minimum distance and the second smallest with numerical attributes is higher than m, we can find the minimum distance between an object and a cluster center without distance computations of categorical attributes. The experimental results show that the computational performance of the proposed k-prototypes algorithm is superior to the original k-prototypes algorithm in our dataset.

]]>Symmetry doi: 10.3390/sym9040057

Authors: Lesley J. Rogers

Research on a growing number of vertebrate species has shown that the left and right sides of the brain process information in different ways and that lateralized brain function is expressed in both specific and broad aspects of behaviour. This paper reviews the available evidence relating strength of lateralization to behavioural/cognitive performance. It begins by considering the relationship between limb preference and behaviour in humans and primates from the perspectives of direction and strength of lateralization. In birds, eye preference is used as a reflection of brain asymmetry and the strength of this asymmetry is associated with behaviour important for survival (e.g., visual discrimination of food from non-food and performance of two tasks in parallel). The same applies to studies on aquatic species, mainly fish but also tadpoles, in which strength of lateralization has been assessed as eye preferences or turning biases. Overall, the empirical evidence across vertebrate species points to the conclusion that stronger lateralization is advantageous in a wide range of contexts. Brief discussion of interhemispheric communication follows together with discussion of experiments that examined the effects of sectioning pathways connecting the left and right sides of the brain, or of preventing the development of these left-right connections. The conclusion reached is that degree of functional lateralization affects behaviour in quite similar ways across vertebrate species. Although the direction of lateralization is also important, in many situations strength of lateralization matters more. Finally, possible interactions between asymmetry in different sensory modalities is considered.

]]>Symmetry doi: 10.3390/sym9040055

Authors: Phuong Chu Seoungjae Cho Simon Fong Yong Park Kyungeun Cho

This paper proposes a cloud-based framework that optimizes the three-dimensional (3D) reconstruction of multiple types of sensor data captured from multiple remote robots. A working environment using multiple remote robots requires massive amounts of data processing in real-time, which cannot be achieved using a single computer. In the proposed framework, reconstruction is carried out in cloud-based servers via distributed data processing. Consequently, users do not need to consider computing resources even when utilizing multiple remote robots. The sensors’ bulk data are transferred to a master server that divides the data and allocates the processing to a set of slave servers. Thus, the segmentation and reconstruction tasks are implemented in the slave servers. The reconstructed 3D space is created by fusing all the results in a visualization server, and the results are saved in a database that users can access and visualize in real-time. The results of the experiments conducted verify that the proposed system is capable of providing real-time 3D scenes of the surroundings of remote robots.

]]>Symmetry doi: 10.3390/sym9040056

Authors: Namjung Kim Kyoungju Park

Previous studies on virtual soap bubbles mainly focused on methods for visualizing the physical and geometrical properties of soap bubbles and paid little attention to the possible ways to enhance the interaction between the simulation and the user. In this paper, a user interaction-based giant soap bubble simulation system is proposed in which the free-form shape, size, and position of giant soap bubbles are determined by the user’s hand motions. Our method improves the controllability of soap bubble simulation by correcting the jerky hand trajectory and hand velocity to a smooth and gradual path. Our air flow transfer algorithm can produce detailed deformation and standing wave for soap film in real time. Our novel soap film bursting algorithm represents the process of the bursting phenomenon of soap-film and giant soap bubbles in a unified framework. The results of our experiment demonstrate that the system allows the user to experience the giant soap bubble blowing and bursting process in a virtual environment.

]]>Symmetry doi: 10.3390/sym9040054

Authors: Cheng-Yu Yeh

The adaptive multi-rate wideband (AMR-WB) speech codec is widely used in modern mobile communication systems for high speech quality in handheld devices. Nonetheless, a major disadvantage is that vector quantization (VQ) of immittance spectral frequency (ISF) coefficients takes a considerable computational load in the AMR-WB coding. Accordingly, a binary search space-structured VQ (BSS-VQ) algorithm is adopted to efficiently reduce the complexity of ISF quantization in AMR-WB. This search algorithm is done through a fast locating technique combined with lookup tables, such that an input vector is efficiently assigned to a subspace where relatively few codeword searches are required to be executed. In terms of overall search performance, this work is experimentally validated as a superior search algorithm relative to a multiple triangular inequality elimination (MTIE), a TIE with dynamic and intersection mechanisms (DI-TIE), and an equal-average equal-variance equal-norm nearest neighbor search (EEENNS) approach. With a full search algorithm as a benchmark for overall search load comparison, this work provides an 87% search load reduction at a threshold of quantization accuracy of 0.96, a figure far beyond 55% in the MTIE, 76% in the EEENNS approach, and 83% in the DI-TIE approach.

]]>Symmetry doi: 10.3390/sym9040053

Authors: Yi Zhang Zhichun Mu

Ear detection is an important step in ear recognition approaches. Most existing ear detection techniques are based on manually designing features or shallow learning algorithms. However, researchers found that the pose variation, occlusion, and imaging conditions provide a great challenge to the traditional ear detection methods under uncontrolled conditions. This paper proposes an efficient technique involving Multiple Scale Faster Region-based Convolutional Neural Networks (Faster R-CNN) to detect ears from 2D profile images in natural images automatically. Firstly, three regions of different scales are detected to infer the information about the ear location context within the image. Then an ear region filtering approach is proposed to extract the correct ear region and eliminate the false positives automatically. In an experiment with a test set of 200 web images (with variable photographic conditions), 98% of ears were accurately detected. Experiments were likewise conducted on the Collection J2 of University of Notre Dame Biometrics Database (UND-J2) and University of Beira Interior Ear dataset (UBEAR), which contain large occlusion, scale, and pose variations. Detection rates of 100% and 98.22%, respectively, demonstrate the effectiveness of the proposed approach.

]]>Symmetry doi: 10.3390/sym9040052

Authors: Jianjian Chen Xianjiu Huang

Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of an intuitionistic fuzzy set, and its membership degrees and nonmembership degrees are represented by two sets of possible values; this new theory of fuzzy sets is known today as dual hesitant fuzzy set theory. This work will extend the notion of dual hesitant fuzzy probabilities by representing probabilities through the dual hesitant fuzzy numbers, in the sense of Zhu et al., instead of intuitionistic fuzzy numbers. We also give the concept of dual hesitant fuzzy probability, based on which we provide some main results including the properties of dual hesitant fuzzy probability, dual hesitant fuzzy conditional probability, and dual hesitant fuzzy total probability.

]]>Symmetry doi: 10.3390/sym9040047

Authors: Na Lu Lipin Liang

Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the length of extended hesitant fuzzy elements (EHFEs) and the correlation coefficients without taking into account the length of EHFEs, as a new extension of existing correlation coefficients for hesitant fuzzy sets (HFSs) and apply them to decision making under extended hesitant fuzzy environments. A real-world example based on the energy policy problem is employed to illustrate the actual need for dealing with the difference of evaluation information provided by different experts without information loss in decision making processes.

]]>Symmetry doi: 10.3390/sym9040050

Authors: Fatema-Tuz-Zohra Khanam Sunghwan Kim

Recently, much attention has been paid to reversible data hiding (RDH) in encrypted images, since it preserves the data that the original image can be perfectly recovered after data extraction while protecting the confidentiality of image content. In this paper, we propose joint and separable RDH techniques using an improved embedding pattern and a new measurement function in encrypted images with a high payload. The first problem in recent joint data hiding is that the encrypted image is divided into blocks, and the spatial correlation in the block cannot fully reflect the smoothness of a natural image. The second problem is that half embedding is used to embed data and the prediction error is exploited to calculate the smoothness, which also fails to give good performance. To solve these problems, we divide the encrypted image into four sets, instead of blocks; the actual value of pixels is considered, rather than an estimated value, and the absolute difference between neighboring pixels is used in preference to prediction error to calculate the smoothness. Therefore, it is possible to use spatial correlation of the natural image perfectly. The experimental results show that the proposed joint and separable methods offer better performance over other works.

]]>Symmetry doi: 10.3390/sym9040051

Authors: Clara M. A. ten Broek Jessica Bots Marianna Bugiani Frietson Galis Stefan van Dongen

Fluctuating asymmetry (FA) is the small random deviation from perfect symmetry in bilateral traits and is often used to assess developmental instability (DI) experienced by organisms. In this study, with a unique dataset of 1389 deceased human fetuses, we investigated the relationship between abnormal development and human limb FA in different ways, using a more fundamental approach than usually done. We studied whether there is an underlying developmental basis of DI, as measured by FA, by investigating, first, whether limb FA can be attributed to developmental abnormalities associated with specific organ systems, germ layers or patterning processes, and second, whether limb FA increases with increasing number of developmental abnormalities either gradually, or in a threshold-like fashion. Limb FA was found to increase in fetuses with cardiovascular and nervous system abnormalities. Fetuses with ectoderm-derived abnormalities were also found to have significantly higher limb FA, but no other germ layers were found to be associated. We found no significant correlation between specific developmental processes, such as neural crest development, segmentation, midline and left-right patterning and limb FA. Although only some congenital abnormalities were correlated with limb FA, our results do suggest that limb FA increases when an increasing number of organ systems, germ layers or developmental pathways are disrupted. Therefore, we conclude that limb FA is mainly a good indicator for DI in the case of particularly severe perturbations of development and that FA does not reflect the subtler deviations from developmental stability.

]]>Symmetry doi: 10.3390/sym9040049

Authors: Vacius Jusas Darius Birvinskas Elvar Gahramanov

Digital triage is the first investigative step of the forensic examination. The digital triage comes in two forms, live triage and post-mortem triage. The primary goal of the live triage is a rapid extraction of an intelligence from the potential sources. The live triage raises legitimate concerns. The post-mortem triage is conducted in the laboratory and its main goal is ranking of the seized devices for the possible existence of the relevant evidence. The digital triage has the potential to quickly identify items that are likely to contain the evidential data. Therefore, it is a solution to the problem of case backlogs. However, existing methods and tools of the digital triage have limitations, especially, in the forensic context. Nevertheless, we have no better solution for the time being. In this paper, we critically review published research works and the proposed solutions for digital triage. The review is divided into four sections as follows: live triage, post-mortem triage, mobile device triage, and triage tools. We conclude that many challenges are awaiting for the developers in creating methods and tools of digital triage in order to keep pace with the development of new technologies.

]]>Symmetry doi: 10.3390/sym9040048

Authors: Guofeng Qin Xiaodi Huang Yiling Chen

As a multi-classification problem, classification of moving vehicles has been studied by different statistical methods. These practical applications have various requirements, efficiencies, and performance, such as the size of training sample sets, convergence rate, and inseparable or ambiguous classification issues. With a reduction in its training time,the one-to-many support vector machine (SVM) method has an advantage over the standard SVM method by directly converting the binary classification problem into two multi-classification problems with short time and fast speed. When the number of training samples of a certain type is far less than the total number of samples, the accuracy of training, however, will be significantlydecreased,leading to theproblem of inseparable area. In this paper, the proposed nested one-to-one symmetric classification method on a fuzzy SVM symmetrically transforms the C multi-classification problems into the C(C-1)/2 binary classification problems with C(C-1)/2 classifiers, and solves the problem of inseparable area. According to the best combination factor of kernel function (γ, C) for the radial basis function (RBF) in the comparative experiments of training sample sets among the different algorithms, and the experimental results of many different training sample sets and test samples, the nested one-to-one symmetric classification algorithm on a fuzzy SVM for moving vehicle is able to obtain the best accuracy of recognition.

]]>Symmetry doi: 10.3390/sym9030046

Authors: Kenneth S. Berenhaut Brendan P. Lidral-Porter Theodore H. Schoen Kyle P. Webb

In this paper, we introduce the concept of (pair-wise) domination graphs for hypergraphs endowed with a choice function on edges. We are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. Several open questions are posed.

]]>Symmetry doi: 10.3390/sym9030045

Authors: Yuval Ben-Abu Haim Eshach Hezi Yizhaq

Understanding advanced physical phenomena such as vertically hanging elastic column, soap bubbles, crystals and cracks demands expressing and manipulating a system’s potential energy under equilibrium conditions. However, students at schools and universities are usually required to consider the forces acting on a system under equilibrium conditions, rather than taking into account its potential energy. As a result, they find it difficult to express the system’s potential energy and use it for calculations when they do need to do so. The principle of least potential energy is a powerful idea for solving static equilibrium physics problems in various fields such as hydrostatics, mechanics, and electrostatics. In the current essay, the authors describe this principle and provide examples where students can apply it. For each problem, the authors provide both the force consideration solution approach and the energy consideration solution approach.

]]>Symmetry doi: 10.3390/sym9030044

Authors: Stefan Van Dongen Claartje Ten Broek Jessica Bots Frietson Galis

(1) Background: Developmental instability (DI), often measured by fluctuating asymmetry (FA), increases with stress in humans, yet little is known about how stress affects the changes of asymmetry with age. More specifically, it is unknown if fetuses experiencing a major congenital abnormality will express higher FA already during early development or only at a later age; (2) Methods: We combine two datasets to study associations between age and asymmetry in human fetuses and young infants. One population consists of fetuses from spontaneous abortions and early deceased infants where many experienced major congenital abnormalities, and a second from elicited abortions for social reasons; (3) Results: While the occurrence of major abnormalities did not seem to affect the way asymmetry decreased with age, differences between the two populations were observed; and (4) Conclusions: In one population where fetuses and young infants deceased of natural causes, asymmetry decreased rapidly until 20 weeks of age and then leveled off. Over the entire timespan (week 15–49), individuals with major congenital abnormalities showed higher FA, suggesting that developmental perturbations increase FA rapidly. In the second, more normal population with abortions solicited for social reasons, the decrease in asymmetry with age was less profound and not statistically significant, calling for further research toward understanding regional differences.

]]>Symmetry doi: 10.3390/sym9030042

Authors: Thanaphat Srivantana Kiattisak Maichalernnukul

In this paper, we propose various kinds of two-way multi-antenna relaying with simultaneous wireless information and power transfer (SWIPT) and investigate their performance. Specifically, we first consider a two-way relay network where two single-antenna end nodes communicate with each other through a multi-antenna relay node that is energy constrained. This relay node harvests energy from the two end nodes and use the harvested energy for forwarding their information. Six relaying schemes that support the considered network then build on the power splitting-based relaying and time switching-based relaying protocols. The average bit error rates of these schemes are evaluated and compared by computer simulations considering several network parameters, including the number of relay antennas, power splitting ratio, and energy harvesting time. Such evaluation and comparison provide useful insights into the performance of SWIPT-based two-way multi-antenna relaying.

]]>Symmetry doi: 10.3390/sym9030043

Authors: Jianwei Gao Huihui Liu

To characterize the influence of decision makers’ psychological factors on the group decisionprocess, this paper develops a new class of aggregation operators based on reference-dependentutility functions (RUs) in multi-attribute group decision analysis. We consider two types of RUs:S-shaped, representing decision makers who are risk-seeking for relative losses, and non-S-shaped,representing those that are risk-averse for relative losses. Based on these RUs, we establish twonew classes of reference-dependent aggregation operators; we study their properties and showthat their generality covers a number of existing aggregation operators. To determine the optimalweights for these aggregation operators, we construct an attribute deviation weight model and adecision maker (DM) deviation weight model. Furthermore, we develop a new multi-attribute groupdecision-making (MAGDM) approach based on these RU aggregation operators and weight models.Finally, numerical examples are given to illustrate the application of the approach.

]]>Symmetry doi: 10.3390/sym9030041

Authors: András Lengyel Zsolt Gáspár Tibor Tarnai

Amongst the convex polyhedra with n faces circumscribed about the unit sphere, which has the minimum surface area? This is the isoperimetric problem in discrete geometry which is addressed in this study. The solution of this problem represents the closest approximation of the sphere, i.e., the roundest polyhedra. A new numerical optimization method developed previously by the authors has been applied to optimize polyhedra to best approximate a sphere if tetrahedral, octahedral, or icosahedral symmetry constraints are applied. In addition to evidence provided for various cases of face numbers, potentially optimal polyhedra are also shown for n up to 132.

]]>Symmetry doi: 10.3390/sym9030040

Authors: Kazuhiko Sawada Ichio Aoki

A three-dimensional (3D) T1-weighted Magnetic Resonance Imaging (MRI) at 7-Tesla system was acquired with a high spatial resolution from fixed brains of male and female ferrets at postnatal days (PDs) 4 to 90, and their age-related sexual difference and laterality were evaluated by MRI-based ex vivo volumetry. The volume of both left and right sides of cerebellar cortex was larger in males than in females on PD 10 and thereafter. When the cerebellar cortex was divided into four transverse domains, i.e., anterior zone (AZ; lobules I–V), central zone (CZ; lobules VI and VII), posterior zone (PZ; lobules VIII–IXa), and nodular zone (NZ; lobules IXb and X), an age-related significantly greater volume in males than in females was detected on either side of all four domains on PD 42 and of the AZ on PD 90, but only on the left side of the PZ on PD 90. Regarding the volume laterality, significant leftward asymmetry was obtained in the CZ and PZ volumes in males, but not in females on PD 90. From asymmetry quotient (AQ) analysis, AQ scores were rightward in the AZ in both sexes already on PD 21, but gradually left-lateralized only in males in the CZ, PZ, and NZ during PDs 42 to 90. The present study suggests that a characteristic counterclockwise torque asymmetry (rostrally right-biased, and caudally left-biased or symmetrical) is acquired in both sexes of ferrets during PDs 42 to 90, although the leftward laterality of the posterior half of the cerebellum was more enhanced in males.

]]>Symmetry doi: 10.3390/sym9030039

Authors: Ivana Bianchi Roberto Burro Roberta Pezzola Ugo Savardi

This paper presents a comparative analysis of the ability to recognize three mirror forms in visual and acoustic tasks: inversion (reflection on a horizontal axis), retrograde (reflection on a vertical axis) and retrograde inversion (reflection on both horizontal and vertical axes). Dynamic patterns consisting of five tones in succession in the acoustic condition and five square dots in succession in the visual condition were presented to 180 non‐musically expert participants. In a yes/no task, they were asked to ascertain whether a comparison stimulus represented the “target” transformation (i.e., inversion, retrograde or retrograde inversion). Three main results emerged. Firstly, the fact that symmetry pertaining to a vertical axis is the most easily perceived does not only apply to static visual configurations (as found in previous literature) but also applies to dynamic visual configurations and acoustic stimuli where it is in fact even more marked. Secondly, however, differences emerged between the facility with which the three mirror forms were recognized in the acoustic and visual tasks. Thirdly, when the five elements in the stimulus were not of the same duration and therefore a rhythmic structure emerged, performance improved not only in the acoustic but also (even more significantly) in the visual task.

]]>Symmetry doi: 10.3390/sym9030038

Authors: Hui Dun Fang Ye Yibing Li

Device-to-device (D2D) communications bring significant improvements of spectral efficiency by underlaying cellular networks. However, they also lead to a more deteriorative interference environment for cellular users, especially the users in severely deep fading or shadowing. In this paper, we investigate a relay-based communication scheme in cellular systems, where the D2D communications are exploited to aid the cellular downlink transmissions by acting as relay nodes with underlaying cellular networks. We modeled two-antenna infrastructure relays employed for D2D relay. The D2D transmitter is able to transmit and receive signals simultaneously over the same frequency band. Then we proposed an efficient power allocation algorithm for the base station (BS) and D2D relay to reduce the loopback interference which is inherent due to the two-antenna infrastructure in full-duplex (FD) mode. We derived the optimal power allocation problem in closed form under the independent power constraint. Simulation results show that the algorithm reduces the power consumption of D2D relay to the greatest extent and also guarantees cellular users’ minimum transmit rate. Moreover, it also outperforms the existing half-duplex (HD) relay mode in terms of achievable rate of D2D.

]]>Symmetry doi: 10.3390/sym9030037

Authors: Muhammad Siddiqui Ghulam Mujtaba Ahmed Reza Liyana Shuib

Background: An accurate and automatic computer-aided multi-class decision support system to classify the magnetic resonance imaging (MRI) scans of the human brain as normal, Alzheimer, AIDS, cerebral calcinosis, glioma, or metastatic, which helps the radiologists to diagnose the disease in brain MRIs is created. Methods: The performance of the proposed system is validated by using benchmark MRI datasets (OASIS and Harvard) of 310 patients. Master features of the images are extracted using a fast discrete wavelet transform (DWT), then these discriminative features are further analysed by principal component analysis (PCA). Different subset sizes of principal feature vectors are provided to five different decision models. The classification models include the J48 decision tree, k-nearest neighbour (kNN), random forest (RF), and least-squares support vector machine (LS-SVM) with polynomial and radial basis kernels. Results: The RF-based classifier outperformed among all compared decision models and achieved an average accuracy of 96% with 4% standard deviation, and an area under the receiver operating characteristic (ROC) curve of 99%. LS-SVM (RBF) also shows promising results (i.e., 89% accuracy) when the least number of principal features was used. Furthermore, the performance of each classifier on different subset sizes of principal features was (80%–96%) for most performance metrics. Conclusion: The presented medical decision support system demonstrates the potential proof for accurate multi-class classification of brain abnormalities; therefore, it has a potential to use as a diagnostic tool for the medical practitioners.

]]>Symmetry doi: 10.3390/sym9030036

Authors: Fang Ye Xun Zhang Yibing Li Chunrui Tang

Cognitive radio (CR) has become a tempting technology that achieves significant improvement in spectrum utilization. To resolve the hidden terminal problem, collaborative spectrum sensing (CSS), which profits from spatial diversity, has been studied intensively in recent years. As CSS is vulnerable to the attacks launched by malicious secondary users (SUs), certain CSS security schemes based on the Dempster–Shafer theory of evidence have been proposed. Nevertheless, the available works only focus on the real-time difference of SUs, like the difference in similarity degree or SNR, to evaluate the credibility of each SU. Since the real-time difference is unilateral and sometimes inexact, the statistical information comprised in SUs’ historical behaviors should not be ignored. In this paper, we propose a robust CSS method based on evidence theory and credibility calculation. It is executed in four consecutive procedures, which are basic probability assignment (BPA), holistic credibility calculation, option and amelioration of BPA and evidence combination via the Dempster–Shafer rule, respectively. Our scheme evaluates the holistic credibility of SUs from both the real-time difference and statistical sensing behavior of SUs. Moreover, considering that the transmitted data increase with the number of SUs increasing, we introduce the projection approximation approach to adjust the evidence theory to the binary hypothesis test in CSS; on this account, both the data volume to be transmitted and the workload at the data fusion center have been reduced. Malicious SUs can be distinguished from genuine ones based on their historical sensing behaviors, and SUs’ real-time difference can be reserved to acquire a superior current performance. Abounding simulation results have proven that the proposed method outperforms the existing ones under the effect of different attack modes and different numbers of malicious SUs.

]]>Symmetry doi: 10.3390/sym9030035

Authors: JongBeom Lim HeonChang Yu Joon‐Min Gil

Due to the loosely coupled property of cloud computing environments, no node has complete knowledge of the system. For this reason, detecting a Sybil attack in cloud computing environments is a non‐trivial task. In such a dynamic system, the use of algorithms based on tree or ring structures for collecting the global state of the system has unfortunate downsides, that is, the structure should be re‐constructed in the presence of node joining and leaving. In this paper, we propose an unstructured Sybil attack detection algorithm in cloud computing environments. Our proposed algorithm uses one‐to‐one communication primitives rather than broadcast primitives and, therefore, the message complexity can be reduced. In our algorithmic design, attacker nodes forging multiple identities are effectively detected by normal nodes with the fail‐stop signature scheme. We show that, regardless of the number of attacker nodes, our Sybil attack detection algorithm is able to reach consensus.

]]>Symmetry doi: 10.3390/sym9030034

Authors: Fang Ye Jing Dai Yibing Li

In order to improve system performance such as throughput, heterogeneous network (HetNet) has become an effective solution in Long Term Evolution-Advanced (LET-A). However, co-channel interference leads to degradation of the HetNet throughput, because femtocells are always arranged to share the spectrum with the macro base station. In this paper, in view of the serious cross-layer interference in double layer HetNet, the Stackelberg game model is adopted to analyze the resource allocation methods of the network. Unlike the traditional system models only focusing on macro base station performance improvement, we take into account the overall system performance and build a revenue function with convexity. System utility functions are defined as the average throughput, which does not adopt frequency spectrum trading method, so as to avoid excessive signaling overhead. Due to the value scope of continuous Nash equilibrium of the built game model, the gradient iterative algorithm is introduced to reduce the computational complexity. As for the solution of Nash equilibrium, one kind of gradient iterative algorithm is proposed, which is able to intelligently choose adjustment factors. The Nash equilibrium can be quickly solved; meanwhile, the step of presetting adjustment factors is avoided according to network parameters in traditional linear iterative model. Simulation results show that the proposed algorithm enhances the overall performance of the system.

]]>Symmetry doi: 10.3390/sym9030029

Authors: Guoxiang Lu

Inspired by the generalized entropies for graphs, a class of generalized degree-based graph entropies is proposed using the known information-theoretic measures to characterize the structure of complex networks. The new entropies depend on assigning a probability distribution about the degrees to a network. In this paper, some extremal properties of the generalized degree-based graph entropies by using the degree powers are proved. Moreover, the relationships among the entropies are studied. Finally, numerical results are presented to illustrate the features of the new entropies.

]]>Symmetry doi: 10.3390/sym9030033

Authors: Stephen Anco

A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law through a well-known Fréchet derivative identity. Furthermore, the connection of this formula (and of Ibragimov’s theorem) to the standard action of symmetries on conservation laws is explained, which accounts for a number of major drawbacks that have appeared in recent work using the formula to generate conservation laws. In particular, the formula can generate trivial conservation laws and does not always yield all non-trivial conservation laws unless the symmetry action on the set of these conservation laws is transitive. It is emphasized that all local conservation laws for any given system of differential equations can be found instead by a general method using adjoint-symmetries. This general method is a kind of adjoint version of the standard Lie method to find all local symmetries and is completely algorithmic. The relationship between this method, Noether’s theorem and the symmetry/adjoint-symmetry formula is discussed.

]]>Symmetry doi: 10.3390/sym9030032

Authors: Marcin Szpyrka Bartosz Jasiul

This article presents a new method of risk propagation among associated elements. On thebasis of coloured Petri nets, a new class called propagation nets is defined. This class providesa formal model of a risk propagation. The proposed method allows for model relations betweennodes forming the network structure. Additionally, it takes into account the bidirectional relationsbetween components as well as relations between isomorphic, symmetrical components in variousbranches of the network. This method is agnostic in terms of use in various systems and it canbe adapted to the propagation model of any systems’ characteristics; however, it is intentionallyproposed to assess the risk of critical infrastructures. In this paper, as a proof of concept example, weshow the formal model of risk propagation proposed within the project Cyberspace Security ThreatsEvaluation System of the Republic of Poland. In the article, the idea of the method is presented aswell as its use case for evaluation of risk for cyber threats. With the adaptation of Petri nets, it ispossible to evaluate the risk for the particular node and assess the impact of this risk for all relatednodes including hierarchic relations of components as well as isomorphism of elements.

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