Symmetry — Open Access Journal

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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.
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(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. Full article

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.
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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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article

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. Full article