Symmetry
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Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 9, Pages 46: Symmetry in Domination for Hypergraphs with Choice]]>
http://www.mdpi.com/2073-8994/9/3/46
In this paper, we introduce the concept of (pair-wise) domination graphs for hypergraphsendowed with a choice function on edges. We are interested, for instance, in minimal numbers ofedges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge)domination graphs are presented. Several open questions are posed.Symmetry2017-03-2293Article10.3390/sym9030046462073-89942017-03-22doi: 10.3390/sym9030046Kenneth S. BerenhautBrendan P. Lidral-PorterTheodore H. SchoenKyle P. Webb<![CDATA[Symmetry, Vol. 9, Pages 45: Interweaving the Principle of Least Potential Energy in School and Introductory University Physics Courses]]>
http://www.mdpi.com/2073-8994/9/3/45
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.Symmetry2017-03-2293Letter10.3390/sym9030045452073-89942017-03-22doi: 10.3390/sym9030045Yuval Ben-AbuHaim EshachHezi Yizhaq<![CDATA[Symmetry, Vol. 9, Pages 44: Changes of Fluctuating Asymmetry with Age in Human Fetuses and Young Infants]]>
http://www.mdpi.com/2073-8994/9/3/44
(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.Symmetry2017-03-2193Communication10.3390/sym9030044442073-89942017-03-21doi: 10.3390/sym9030044Stefan Van DongenClaartje Ten BroekJessica BotsFrietson Galis<![CDATA[Symmetry, Vol. 9, Pages 42: Two-Way Multi-Antenna Relaying with Simultaneous Wireless Information and Power Transfer]]>
http://www.mdpi.com/2073-8994/9/3/42
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.Symmetry2017-03-1693Article10.3390/sym9030042422073-89942017-03-16doi: 10.3390/sym9030042Thanaphat SrivantanaKiattisak Maichalernnukul<![CDATA[Symmetry, Vol. 9, Pages 43: Reference-Dependent Aggregation in Multi-AttributeGroup Decision-Making]]>
http://www.mdpi.com/2073-8994/9/3/43
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.Symmetry2017-03-1693Article10.3390/sym9030043432073-89942017-03-16doi: 10.3390/sym9030043Jianwei GaoHuihui Liu<![CDATA[Symmetry, Vol. 9, Pages 41: The Roundest Polyhedra with Symmetry Constraints]]>
http://www.mdpi.com/2073-8994/9/3/41
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.Symmetry2017-03-1593Article10.3390/sym9030041412073-89942017-03-15doi: 10.3390/sym9030041András LengyelZsolt GáspárTibor Tarnai<![CDATA[Symmetry, Vol. 9, Pages 40: Age-Dependent Sexually-Dimorphic Asymmetric Development of the Ferret Cerebellar Cortex]]>
http://www.mdpi.com/2073-8994/9/3/40
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.Symmetry2017-03-1493Article10.3390/sym9030040402073-89942017-03-14doi: 10.3390/sym9030040Kazuhiko SawadaIchio Aoki<![CDATA[Symmetry, Vol. 9, Pages 39: Matching Visual and Acoustic Mirror Forms]]>
http://www.mdpi.com/2073-8994/9/3/39
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.Symmetry2017-03-1093Article10.3390/sym9030039392073-89942017-03-10doi: 10.3390/sym9030039Ivana BianchiRoberto BurroRoberta PezzolaUgo Savardi<![CDATA[Symmetry, Vol. 9, Pages 38: Transmission Power Adaption for Full-Duplex Relay-Aided Device-to-Device Communication]]>
http://www.mdpi.com/2073-8994/9/3/38
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.Symmetry2017-03-0993Article10.3390/sym9030038382073-89942017-03-09doi: 10.3390/sym9030038Hui DunFang YeYibing Li<![CDATA[Symmetry, Vol. 9, Pages 37: Multi-Class Disease Classification in Brain MRIs Using a Computer-Aided Diagnostic System]]>
http://www.mdpi.com/2073-8994/9/3/37
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.Symmetry2017-03-0893Article10.3390/sym9030037372073-89942017-03-08doi: 10.3390/sym9030037Muhammad SiddiquiGhulam MujtabaAhmed RezaLiyana Shuib<![CDATA[Symmetry, Vol. 9, Pages 36: Faithworthy Collaborative Spectrum Sensing Based on Credibility and Evidence Theory for Cognitive Radio Networks]]>
http://www.mdpi.com/2073-8994/9/3/36
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.Symmetry2017-03-0493Article10.3390/sym9030036362073-89942017-03-04doi: 10.3390/sym9030036Fang YeXun ZhangYibing LiChunrui Tang<![CDATA[Symmetry, Vol. 9, Pages 35: Detecting Sybil Attacks in Cloud Computing Environments Based on Fail‐Stop Signature]]>
http://www.mdpi.com/2073-8994/9/3/35
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.Symmetry2017-03-0293Article10.3390/sym9030035352073-89942017-03-02doi: 10.3390/sym9030035JongBeom LimHeonChang YuJoon‐Min Gil<![CDATA[Symmetry, Vol. 9, Pages 34: Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet]]>
http://www.mdpi.com/2073-8994/9/3/34
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.Symmetry2017-02-2893Article10.3390/sym9030034342073-89942017-02-28doi: 10.3390/sym9030034Fang YeJing DaiYibing Li<![CDATA[Symmetry, Vol. 9, Pages 29: Generalized Degree-Based Graph Entropies]]>
http://www.mdpi.com/2073-8994/9/3/29
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.Symmetry2017-02-2893Article10.3390/sym9030029292073-89942017-02-28doi: 10.3390/sym9030029Guoxiang Lu<![CDATA[Symmetry, Vol. 9, Pages 33: On the Incompleteness of Ibragimov’s Conservation Law Theorem and Its Equivalence to a Standard Formula Using Symmetries and Adjoint-Symmetries]]>
http://www.mdpi.com/2073-8994/9/3/33
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.Symmetry2017-02-2793Article10.3390/sym9030033332073-89942017-02-27doi: 10.3390/sym9030033Stephen Anco<![CDATA[Symmetry, Vol. 9, Pages 32: Evaluation of Cyber Security and Modelling of Risk Propagation with Petri Nets]]>
http://www.mdpi.com/2073-8994/9/3/32
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.Symmetry2017-02-2693Article10.3390/sym9030032322073-89942017-02-26doi: 10.3390/sym9030032Marcin SzpyrkaBartosz Jasiul<![CDATA[Symmetry, Vol. 9, Pages 30: Intelligent RFID Indoor Localization System Using a Gaussian Filtering Based Extreme Learning Machine]]>
http://www.mdpi.com/2073-8994/9/3/30
Nowadays, the increasing demands of location-based services (LBS) have spurred the rapid development of indoor positioning systems (IPS). However, the performance of IPSs is affected by the fluctuation of the measured signal. In this study, a Gaussian filtering algorithm based on an extreme learning machine (ELM) is proposed to address the problem of inaccurate indoor positioning when significant Received Signal Strength Indication (RSSI) fluctuations happen during the measurement process. The Gaussian filtering method is analyzed and compared, which can effectively filter out the fluctuant signals that were caused by the environment effects in an RFID-based positioning system. Meanwhile, the fast learning ability of the proposed ELM algorithm can reduce the time consumption for the offline and online service, and establishes the network positioning regression model between the signal strengths of the tags and their corresponding positions. The proposed positioning system is tested in a real experimental environment. In addition, system test results demonstrate that the positioning algorithms can not only provide higher positioning accuracy, but also achieve a faster computational efficiency compared with other previous algorithms.Symmetry2017-02-2693Article10.3390/sym9030030302073-89942017-02-26doi: 10.3390/sym9030030Changzhi WangZhicai ShiFei Wu<![CDATA[Symmetry, Vol. 9, Pages 31: BSLIC: SLIC Superpixels Based on Boundary Term]]>
http://www.mdpi.com/2073-8994/9/3/31
A modified method for better superpixel generation based on simple linear iterative clustering (SLIC) is presented and named BSLIC in this paper. By initializing cluster centers in hexagon distribution and performing k-means clustering in a limited region, the generated superpixels are shaped into regular and compact hexagons. The additional cluster centers are initialized as edge pixels to improve boundary adherence, which is further promoted by incorporating the boundary term into the distance calculation of the k-means clustering. Berkeley Segmentation Dataset BSDS500 is used to qualitatively and quantitatively evaluate the proposed BSLIC method. Experimental results show that BSLIC achieves an excellent compromise between boundary adherence and regularity of size and shape. In comparison with SLIC, the boundary adherence of BSLIC is increased by at most 12.43% for boundary recall and 3.51% for under segmentation error.Symmetry2017-02-2693Article10.3390/sym9030031312073-89942017-02-26doi: 10.3390/sym9030031Hai WangXiongyou PengXue XiaoYan Liu<![CDATA[Symmetry, Vol. 9, Pages 28: On the Legibility of Mirror-Reflected and Rotated Text]]>
http://www.mdpi.com/2073-8994/9/3/28
We happened to observe that text that was reflected about either the horizontal or vertical axis was more difficult to read than text that was reflected about first one and then the other, which amounts to a 180-degree rotation. In this article, we review a number of studies that examine the nature of recognizing reflected and inverted letters, and the frequency of mirror reversal errors (e.g., confusing 'b' for 'd') in children and adults. We explore recent ideas linking the acquisition of literacy with the loss of mirror-invariance, not just for text, but for objects in general. We try to connect these various literatures to examine why certain transformations of text are more difficult to read than others for adults.Symmetry2017-02-2393Review10.3390/sym9030028282073-89942017-02-23doi: 10.3390/sym9030028Gennady ErlikhmanLars StrotherIskra BarzakovGideon Caplovitz<![CDATA[Symmetry, Vol. 9, Pages 27: Symmetry Analysis and Conservation Laws of the Zoomeron Equation]]>
http://www.mdpi.com/2073-8994/9/2/27
In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the ﬁrst time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the ﬁrst time, we construct the conservation laws of the underlying equation using the multiplier method.Symmetry2017-02-2192Article10.3390/sym9020027272073-89942017-02-21doi: 10.3390/sym9020027Tanki MotsepaChaudry KhaliqueMaria Gandarias<![CDATA[Symmetry, Vol. 9, Pages 26: A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids]]>
http://www.mdpi.com/2073-8994/9/2/26
In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH) method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient.Symmetry2017-02-1792Article10.3390/sym9020026262073-89942017-02-17doi: 10.3390/sym9020026Yalan ZhangXiaojuan BanXiaokun WangXing Liu<![CDATA[Symmetry, Vol. 9, Pages 25: Deformable Object Matching Algorithm Using Fast Agglomerative Binary Search Tree Clustering]]>
http://www.mdpi.com/2073-8994/9/2/25
Deformable objects have changeable shapes and they require a different method of matching algorithm compared to rigid objects. This paper proposes a fast and robust deformable object matching algorithm. First, robust feature points are selected using a statistical characteristic to obtain the feature points with the extraction method. Next, matching pairs are composed by the feature point matching of two images using the matching method. Rapid clustering is performed using the BST (Binary Search Tree) method by obtaining the geometric similarity between the matching pairs. Finally, the matching of the two images is determined after verifying the suitability of the composed cluster. An experiment with five different image sets with deformable objects confirmed the superior robustness and independence of the proposed algorithm while demonstrating up to 60 times faster matching speed compared to the conventional deformable object matching algorithms.Symmetry2017-02-1092Article10.3390/sym9020025252073-89942017-02-10doi: 10.3390/sym9020025Jaehyup JeongInsu WonHunjun YangBowon LeeDongseok Jeong<![CDATA[Symmetry, Vol. 9, Pages 24: Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression]]>
http://www.mdpi.com/2073-8994/9/2/24
Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR). Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR) is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained.Symmetry2017-02-1092Article10.3390/sym9020024242073-89942017-02-10doi: 10.3390/sym9020024Yungang ZhangJieming Ma<![CDATA[Symmetry, Vol. 9, Pages 23: Erratum: Rauh, A. Coherent States of Harmonic and Reversed Harmonic Oscillator. Symmetry, 2016, 8, 46]]>
http://www.mdpi.com/2073-8994/9/2/23
n/aSymmetry2017-02-0992Erratum10.3390/sym9020023232073-89942017-02-09doi: 10.3390/sym9020023Alexander Rauh<![CDATA[Symmetry, Vol. 9, Pages 22: A Study on Immersion of Hand Interaction for Mobile Platform Virtual Reality Contents]]>
http://www.mdpi.com/2073-8994/9/2/22
This study proposes gaze-based hand interaction, which is helpful for improving the user’s immersion in the production process of virtual reality content for the mobile platform, and analyzes efficiency through an experiment using a questionnaire. First, three-dimensional interactive content is produced for use in the proposed interaction experiment while presenting an experiential environment that gives users a high sense of immersion in the mobile virtual reality environment. This is designed to induce the tension and concentration of users in line with the immersive virtual reality environment. Additionally, a hand interaction method based on gaze—which is mainly used for the entry of mobile virtual reality content—is proposed as a design method for immersive mobile virtual reality environment. The user satisfaction level of the immersive environment provided by the proposed gaze-based hand interaction is analyzed through experiments in comparison with the general method that uses gaze only. Furthermore, detailed analysis is conducted by dividing the effects of the proposed interaction method on user’s psychology into positive factors such as immersion and interest and negative factors such as virtual reality (VR) sickness and dizziness. In this process, a new direction is proposed for improving the immersion of users in the production of mobile platform virtual reality content.Symmetry2017-02-0592Article10.3390/sym9020022222073-89942017-02-05doi: 10.3390/sym9020022Seunghun HanJinmo Kim<![CDATA[Symmetry, Vol. 9, Pages 21: Aesthetic Patterns with Symmetries of the Regular Polyhedron]]>
http://www.mdpi.com/2073-8994/9/2/21
A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regular polyhedra.Symmetry2017-02-0392Article10.3390/sym9020021212073-89942017-02-03doi: 10.3390/sym9020021Peichang OuyangLiying WangTao YuXuan Huang<![CDATA[Symmetry, Vol. 9, Pages 20: Acknowledgement to Reviewers of Symmetry in 2016]]>
http://www.mdpi.com/2073-8994/9/2/20
The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]Symmetry2017-01-2692Editorial10.3390/sym9020020202073-89942017-01-26doi: 10.3390/sym9020020 Symmetry Editorial Office<![CDATA[Symmetry, Vol. 9, Pages 19: Cyclotomic Aperiodic Substitution Tilings]]>
http://www.mdpi.com/2073-8994/9/2/19
The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the 2 n -th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry D n or D 2 n , i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry D n or D 2 n only by iteration of substitution rules on a single tile.Symmetry2017-01-2592Article10.3390/sym9020019192073-89942017-01-25doi: 10.3390/sym9020019Stefan Pautze<![CDATA[Symmetry, Vol. 9, Pages 17: Some Invariants of Jahangir Graphs]]>
http://www.mdpi.com/2073-8994/9/1/17
In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results.Symmetry2017-01-2391Article10.3390/sym9010017172073-89942017-01-23doi: 10.3390/sym9010017Mobeen MunirWaqas NazeerShin KangMuhammad QureshiAbdul NizamiYoul Kwun<![CDATA[Symmetry, Vol. 9, Pages 18: Fully Integrated on-Chip Switched DC–DC Converter for Battery-Powered Mixed-Signal SoCs]]>
http://www.mdpi.com/2073-8994/9/1/18
This paper presents a fully integrated on-chip switched-capacitor (SC) DC–DC converter that supports a programmable regulated power supply ranging from 2.6 to 3.2 V out of a 5 V input supply. The proposed 4-to-3 step-down topology utilizes two conventional 2-to-1 step-down topologies; each of them (2-to-1_up and 2-to-1_dw) has a different flying capacitance to maximize the load current driving capability while minimizing the bottom-plate capacitance loss. The control circuits use a low power supply provided by a small internal low-drop output (LDO) connected to the internal load voltage (VL_dw) from the 2-to-1_dw, and low swing level-shifted gate-driving signals are generated using the internal load voltage (VL_dw). Therefore, the proposed implementation reduces control circuit and switching power consumptions. The programmable power supply voltage is regulated by means of a pulse frequency modulation (PFM) technique with the compensated two-stage operational transconductance amplifier (OTA) and the current-starved voltage controlled oscillator (VCO) to maintain high efficiency over a wide range of load currents. The proposed on-chip SC DC–DC converter is designed and simulated using high-voltage 0.35 μm bipolar, complementary metal-oxide-semiconductor (CMOS) and DMOS (BCDMOS) technology. It achieves a peak efficiency of 74% when delivering an 8 mA load current at a 3.2 V supply voltage level, and it provides a maximum output power of 48 mW (IL = 15 mA at VL_up = 3.2 V) at 70.5% efficiency. The proposed on-chip SC voltage regulator shows better efficiency than the ideal linear regulator over a wide range of output power, from 2.6 mW to 48 mW. The 18-phase interleaving technique enables the worst-case output voltage ripple to be less than 5.77% of the load voltage.Symmetry2017-01-2291Article10.3390/sym9010018182073-89942017-01-22doi: 10.3390/sym9010018Heungjun JeonKyung KimYong-Bin Kim<![CDATA[Symmetry, Vol. 9, Pages 12: Iterative Speedup by Utilizing Symmetric Data in Pricing Options with Two Risky Assets]]>
http://www.mdpi.com/2073-8994/9/1/12
The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of equations resulting from the Crank–Nicolson discretization help us to use the standard pre-conditioner for the iterative matrix solver and reduces the number of iterations to get an accurate option values. In addition, the number of iterations that is required to solve the preconditioned system, resulting from the proposed iterative Crank–Nicolson scheme, does not grow with the size of the system. Thus, we can effectively reduce the order of complexity in multidimensional option pricing. The numerical results are compared to the one with implicit Operator Splitting Method (OSM) to show the effectiveness.Symmetry2017-01-2191Article10.3390/sym9010012122073-89942017-01-21doi: 10.3390/sym9010012Dohyun PakChangkyu HanWon-Tak Hong<![CDATA[Symmetry, Vol. 9, Pages 15: An Orthogonal Multi-Swarm Cooperative PSO Algorithm with a Particle Trajectory Knowledge Base]]>
http://www.mdpi.com/2073-8994/9/1/15
A novel orthogonal multi-swarm cooperative particle swarm optimization (PSO) algorithm with a particle trajectory knowledge base is presented in this paper. Different from the traditional PSO algorithms and other variants of PSO, the proposed orthogonal multi-swarm cooperative PSO algorithm not only introduces an orthogonal initialization mechanism and a particle trajectory knowledge base for multi-dimensional optimization problems, but also conceives a new adaptive cooperation mechanism to accomplish the information interaction among swarms and particles. Experiments are conducted on a set of benchmark functions, and the results show its better performance compared with traditional PSO algorithm in aspects of convergence, computational efficiency and avoiding premature convergence.Symmetry2017-01-2091Article10.3390/sym9010015152073-89942017-01-20doi: 10.3390/sym9010015Jun YangHaihua ZhuYingcong Wang<![CDATA[Symmetry, Vol. 9, Pages 14: Generalized Null 2-Type Surfaces in Minkowski 3-Space]]>
http://www.mdpi.com/2073-8994/9/1/14
For the mean curvature vector field H and the Laplace operator Δ of a submanifold in the Minkowski space, a submanifold satisfying the condition Δ H = f H + g C is known as a generalized null 2-type, where f and g are smooth functions, and C is a constant vector. The notion of generalized null 2-type submanifolds is a generalization of null 2-type submanifolds defined by B.-Y. Chen. In this paper, we study flat surfaces in the Minkowski 3-space L 3 and classify generalized null 2-type flat surfaces. In addition, we show that the only generalized null 2-type null scroll in L 3 is a B-scroll.Symmetry2017-01-2091Article10.3390/sym9010014142073-89942017-01-20doi: 10.3390/sym9010014Dae YoonDong-Soo KimYoung KimJae Lee<![CDATA[Symmetry, Vol. 9, Pages 13: A (1 + 2)-Dimensional Simplified Keller–Segel Model: Lie Symmetry and Exact Solutions. II]]>
http://www.mdpi.com/2073-8994/9/1/13
A simplified Keller–Segel model is studied by means of Lie symmetry based approaches. It is shown that a (1 + 2)-dimensional Keller–Segel type system, together with the correctly-specified boundary and/or initial conditions, is invariant with respect to infinite-dimensional Lie algebras. A Lie symmetry classification of the Cauchy problem depending on the initial profile form is presented. The Lie symmetries obtained are used for reduction of the Cauchy problem to that of (1 + 1)-dimensional. Exact solutions of some (1 + 1)-dimensional problems are constructed. In particular, we have proved that the Cauchy problem for the (1 + 1)-dimensional simplified Keller–Segel system can be linearized and solved in an explicit form. Moreover, additional biologically motivated restrictions were established in order to obtain a unique solution. The Lie symmetry classification of the (1 + 2)-dimensional Neumann problem for the simplified Keller–Segel system is derived. Because Lie symmetry of boundary-value problems depends essentially on geometry of the domain, which the problem is formulated for, all realistic (from applicability point of view) domains were examined. Reduction of the the Neumann problem on a strip is derived using the symmetries obtained. As a result, an exact solution of a nonlinear two-dimensional Neumann problem on a finite interval was found.Symmetry2017-01-2091Article10.3390/sym9010013132073-89942017-01-20doi: 10.3390/sym9010013Roman ChernihaMaksym Didovych<![CDATA[Symmetry, Vol. 9, Pages 16: Data-Filtering System to Avoid Total Data Distortion in IoT Networking]]>
http://www.mdpi.com/2073-8994/9/1/16
In the Internet of Things (IoT) networking, numerous objects are connected to a network. They sense events and deliver the sensed information to the cloud. A lot of data is generated in the IoT network, and servers in the cloud gather the sensed data from the objects. Then, the servers analyze the collected data and provide proper intelligent services to users through the results of the analysis. When the server analyzes the collected data, if there exists malfunctioning data, distortional results of the analysis will be generated. The distortional results lead to misdirection of the intelligent services, leading to poor user experience. In the analysis for intelligent services in IoT, malfunctioning data should be avoided because integrity of the collected data is crucial. Therefore, this paper proposes a data-filtering system for the server in the cloud. The proposed data-filtering system is placed in front of the server and firstly receives the sensed data from the objects. It employs the naïve Bayesian classifier and, by learning, classifies the malfunctioning data from among the collected data. Data with integrity is delivered to the server for analysis. Because the proposed system filters the malfunctioning data, the server can obtain accurate analysis results and reduce computing load. The performance of the proposed data-filtering system is evaluated through computer simulation. Through the simulation results, the efficiency of the proposed data-filtering system is shown.Symmetry2017-01-2091Article10.3390/sym9010016162073-89942017-01-20doi: 10.3390/sym9010016Dae-Young KimYoung-Sik JeongSeokhoon Kim<![CDATA[Symmetry, Vol. 9, Pages 10: Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components]]>
http://www.mdpi.com/2073-8994/9/1/10
In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous Fréchet components in terms of the usual stochastic order, reversed hazard rate order and likelihood ratio order. The partial results established here extend some well-known results in the literature of Gupta et al. Specifically, first, we generalize the result of Theorem 2 from the usual stochastic order to the reversed hazard rate order. Second, we generalize the result of Theorem 3 from the reversed hazard rate order to the likelihood ratio order. Last, we generalize the result of Theorem 4 from the hazard rate order to the likelihood ratio order when shape parameter 0 &lt; α ≤ 1 .Symmetry2017-01-1391Article10.3390/sym9010010102073-89942017-01-13doi: 10.3390/sym9010010Longxiang FangYanqin Wang<![CDATA[Symmetry, Vol. 9, Pages 11: Prognosis Essay Scoring and Article Relevancy Using Multi-Text Features and Machine Learning]]>
http://www.mdpi.com/2073-8994/9/1/11
This study develops a model for essay scoring and article relevancy. Essay scoring is a costly process when we consider the time spent by an evaluator. It may lead to inequalities of the effort by various evaluators to apply the same evaluation criteria. Bibliometric research uses the evaluation criteria to find relevancy of articles instead. Researchers mostly face relevancy issues while searching articles. Therefore, they classify the articles manually. However, manual classification is burdensome due to time needed for evaluation. The proposed model performs automatic essay evaluation using multi-text features and ensemble machine learning. The proposed method is implemented in two data sets: a Kaggle short answer data set for essay scoring that includes four ranges of disciplines (Science, Biology, English, and English language Arts), and a bibliometric data set having IoT (Internet of Things) and non-IoT classes. The efficacy of the model is measured against the Tandalla and AutoP approach using Cohen’s kappa. The model achieves kappa values of 0.80 and 0.83 for the first and second data sets, respectively. Kappa values show that the proposed model has better performance than those of earlier approaches.Symmetry2017-01-1291Article10.3390/sym9010011112073-89942017-01-12doi: 10.3390/sym9010011Arif MehmoodByung-Won OnIngyu LeeGyu Choi<![CDATA[Symmetry, Vol. 9, Pages 8: DIaaS: Resource Management System for the Intra-Cloud with On-Premise Desktops]]>
http://www.mdpi.com/2073-8994/9/1/8
Infrastructure as a service with desktops (DIaaS) based on the extensible mark-up language (XML) is herein proposed to utilize surplus resources. DIaaS is a traditional surplus-resource integrated management technology. It is designed to provide fast work distribution and computing services based on user service requests as well as storage services through desktop-based distributed computing and storage resource integration. DIaaS includes a nondisruptive resource service and an auto-scalable scheme to enhance the availability and scalability of intra-cloud computing resources. A performance evaluation of the proposed scheme measured the clustering performance time for surplus resource utilization. The results showed improvement in computing and storage services in a connection of at least two computers compared to the traditional method for high-availability measurement of nondisruptive services. Furthermore, an artificial server error environment was used to create a clustering delay for computing and storage services and for nondisruptive services. It was compared to the Hadoop distributed file system (HDFS).Symmetry2017-01-0991Article10.3390/sym901000882073-89942017-01-09doi: 10.3390/sym9010008Hyun-Woo KimJaekyung HanJong ParkYoung-Sik Jeong<![CDATA[Symmetry, Vol. 9, Pages 9: Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security]]>
http://www.mdpi.com/2073-8994/9/1/9
The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ) system of equations, which is a system representing a subclass of multivariate quadratic (MQ) systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA) and chosen ciphertext attack (CCA) is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol.Symmetry2017-01-0791Article10.3390/sym901000992073-89942017-01-07doi: 10.3390/sym9010009Eligijus SakalauskasAleksejus MihalkovichAlgimantas Venčkauskas<![CDATA[Symmetry, Vol. 9, Pages 7: First and Second Zagreb Eccentricity Indices of Thorny Graphs]]>
http://www.mdpi.com/2073-8994/9/1/7
The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index ( E 1 ( H ) ) is defined to be the summation of squares of the eccentricity of vertices, i.e., E 1 ( H ) = ∑ u ∈ V ( H ) Ɛ H 2 ( u ) . The second Zagreb eccentricity index ( E 2 ( H ) ) is the summation of product of the eccentricities of the adjacent vertices, i.e., E 2 ( H ) = ∑ u v ∈ E ( H ) Ɛ H ( u ) Ɛ H ( v ) . We obtain the thorny graph of a graph H by attaching thorns i.e., vertices of degree one to every vertex of H . In this paper, we will find closed formulation for the first Zagreb eccentricity index and second Zagreb eccentricity index of different well known classes of thorny graphs.Symmetry2017-01-0691Article10.3390/sym901000772073-89942017-01-06doi: 10.3390/sym9010007Nazeran IdreesMuhammad SaifAsia RaufSaba Mustafa<![CDATA[Symmetry, Vol. 9, Pages 6: Some Computational Aspects of Boron Triangular Nanotubes]]>
http://www.mdpi.com/2073-8994/9/1/6
The recent discovery of boron triangular nanotubes competes with carbon in many respects. The closed form of M‐polynomial of nanotubes produces closed forms of many degree‐based topological indices which are numerical parameters of the structure and, in combination, determine properties of the concerned nanotubes. In this report, we give M‐polynomials of boron triangular nanotubes and recover many important topological degree‐based indices of these nanotubes. We also plot surfaces associated with these nanotubes that show the dependence of each topological index on the parameters of the structure.Symmetry2017-01-0191Article10.3390/sym901000662073-89942017-01-01doi: 10.3390/sym9010006Mobeen MunirWaqas NazeerShazia RafiqueAbdul NizamiShin Kang<![CDATA[Symmetry, Vol. 9, Pages 5: Some Algebraic Polynomials and Topological Indices of Generalized Prism and Toroidal Polyhex Networks]]>
http://www.mdpi.com/2073-8994/9/1/5
A topological index of graph G is a numerical parameter related to G, which characterizes its topology and is preserved under isomorphism of graphs. Properties of the chemical compounds and topological indices are correlated. In this report, we compute closed forms of first Zagreb, second Zagreb, and forgotten polynomials of generalized prism and toroidal polyhex networks. We also compute hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and forgotten index of these networks. Moreover we gave graphical representation of our results, showing the technical dependence of each topological index and polynomial on the involved structural parameters.Symmetry2016-12-2991Article10.3390/sym901000552073-89942016-12-29doi: 10.3390/sym9010005Muhammad AjmalWaqas NazeerMobeen MunirShin KangYoung Kwun<![CDATA[Symmetry, Vol. 9, Pages 4: State of Health Estimation of Li-ion Batteries with Regeneration Phenomena: A Similar Rest Time-Based Prognostic Framework]]>
http://www.mdpi.com/2073-8994/9/1/4
State of health (SOH) prediction in Li-ion batteries plays an important role in intelligent battery management systems (BMS). However, the existence of capacity regeneration phenomena remains a great challenge for accurately predicting the battery SOH. This paper proposes a novel prognostic framework to predict the regeneration phenomena of the current battery using the data of a historical battery. The global degradation trend and regeneration phenomena (characterized by regeneration amplitude and regeneration cycle number) of the current battery are extracted from its raw SOH time series. Moreover, regeneration information of the historical battery derived from corresponding raw SOH data is utilized in this framework. The global degradation trend and regeneration phenomena of the current battery are predicted, and then the prediction results are integrated together to calculate the overall SOH prediction values. Particle swarm optimization (PSO) is employed to obtain an appropriate regeneration threshold for the historical battery. Gaussian process (GP) model is adopted to predict the global degradation trend, and linear models are utilized to predict the regeneration amplitude and the cycle number of each regeneration region. The proposed framework is validated using experimental data from the degradation tests of Li-ion batteries. The results demonstrate that both the global degradation trend and the regeneration phenomena of the testing batteries can be well predicted. Moreover, compared with the published methods, more accurate SOH prediction results can be obtained under this framework.Symmetry2016-12-2491Article10.3390/sym901000442073-89942016-12-24doi: 10.3390/sym9010004Taichun QinShengkui ZengJianbin GuoZakwan Skaf<![CDATA[Symmetry, Vol. 9, Pages 2: Non-Local Meta-Conformal Invariance, Diffusion-Limited Erosion and the XXZ Chain]]>
http://www.mdpi.com/2073-8994/9/1/2
Diffusion-limited erosion is a distinct universality class of fluctuating interfaces. Although its dynamical exponent z = 1 , none of the known variants of conformal invariance can act as its dynamical symmetry. In d = 1 spatial dimensions, its infinite-dimensional dynamic symmetry is constructed and shown to be isomorphic to the direct sum of three loop-Virasoro algebras. The infinitesimal generators are spatially non-local and use the Riesz-Feller fractional derivative. Co-variant two-time response functions are derived and reproduce the exact solution of diffusion-limited erosion. The relationship with the terrace-step-kind model of vicinal surfaces and the integrable XXZ chain are discussed.Symmetry2016-12-2491Article10.3390/sym901000222073-89942016-12-24doi: 10.3390/sym9010002Malte Henkel<![CDATA[Symmetry, Vol. 9, Pages 1: Unmanned Aerial Vehicle Flight Point Classification Algorithm Based on Symmetric Big Data]]>
http://www.mdpi.com/2073-8994/9/1/1
Unmanned aerial vehicles (UAVs) with auto-pilot capabilities are often used for surveillance and patrol. Pilots set the flight points on a map in order to navigate to the imaging point where surveillance or patrolling is required. However, there is the limit denoting the information such as absolute altitudes and angles. Therefore, it is required to set the information accurately. This paper hereby proposes a method to construct environmental symmetric big data using an unmanned aerial vehicle (UAV) during flight by designating the imaging and non-imaging points for surveillance and patrols. The K-Means-based algorithm proposed in this paper is then employed to divide the imaging points, which is set by the pilot, into K clusters, and K imaging points are determined using these clusters. Flight data are then used to set the points to which the UAV will fly. In our experiment, flight records were gathered through an UAV in order to monitor a stadium and the imaging and non-imaging points were set using the proposed method and compared with the points determined by a traditional K-Means algorithm. Through the proposed method, the cluster centroids and cumulative distance of its members were reduced by 87.57% more than with the traditional K-Means algorithm. With the traditional K-Means algorithm, imaging points were not created in the five points desired by the pilot, and two incorrect points were obtained. However, with the proposed method, two incorrect imaging points were obtained. Due to these two incorrect imaging points, the two points desired by the pilot were not generated.Symmetry2016-12-2491Article10.3390/sym901000112073-89942016-12-24doi: 10.3390/sym9010001Jeonghoon KwakJong ParkYunsick Sung<![CDATA[Symmetry, Vol. 9, Pages 3: Reduction Operators and Exact Solutions of Variable Coefficient Nonlinear Wave Equations with Power Nonlinearities]]>
http://www.mdpi.com/2073-8994/9/1/3
Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classification of regular reduction operators is performed with respect to generalized extended equivalence groups. Exact solutions of some nonlinear wave models, which are invariant under certain reduction operators, are also constructed.Symmetry2016-12-2291Article10.3390/sym901000332073-89942016-12-22doi: 10.3390/sym9010003Dingjiang HuangYan ZhuQinmin Yang<![CDATA[Symmetry, Vol. 8, Pages 159: Accurate Dense Stereo Matching Based on Image Segmentation Using an Adaptive Multi-Cost Approach]]>
http://www.mdpi.com/2073-8994/8/12/159
This paper presents a segmentation-based stereo matching algorithm using an adaptive multi-cost approach, which is exploited for obtaining accuracy disparity maps. The main contribution is to integrate the appealing properties of multi-cost approach into the segmentation-based framework. Firstly, the reference image is segmented by using the mean-shift algorithm. Secondly, the initial disparity of each segment is estimated by an adaptive multi-cost method, which consists of a novel multi-cost function and an adaptive support window cost aggregation strategy. The multi-cost function increases the robustness of the initial raw matching costs calculation and the adaptive window reduces the matching ambiguity effectively. Thirdly, an iterative outlier suppression and disparity plane parameters fitting algorithm is designed to estimate the disparity plane parameters. Lastly, an energy function is formulated in segment domain, and the optimal plane label is approximated by belief propagation. The experimental results with the Middlebury stereo datasets, along with synthesized and real-world stereo images, demonstrate the effectiveness of the proposed approach.Symmetry2016-12-21812Article10.3390/sym81201591592073-89942016-12-21doi: 10.3390/sym8120159Ning MaYubo MenChaoguang MenXiang Li<![CDATA[Symmetry, Vol. 8, Pages 156: THD Reduction of Distribution System Based on ASRFC and HVC Method for SVC under EV Charger Condition for Power Factor Improvement]]>
http://www.mdpi.com/2073-8994/8/12/156
Electric vehicles (EVs) have been gaining popularity in recent years due to growing concerns about fuel depletion and increasing petrol prices. Random uncoordinated charging of multiple EVs at residential distribution feeders with moderate penetration levels is expected in the near future. This paper describes a high performance voltage controller for the EVs charging system, and proposes a scheme of asymmetric synchronous reference frame controller (ASRFC) in order to compensate for the voltage distortions and unbalance distribution system due to EVs charger. This paper explores the power factor of distribution and residential network under random EVs charger on the bus load. ASRFC and harmonic voltage compensator (HVC) are employed for static VAR compensator (SVC) in this paper. The proposed scheme can improve the power factor and total harmonic distortion (THD) of the smart grid due to the EVs charger in grid. The effectiveness of the scheme was investigated and verified through computer simulations of a 22.9-kV grid.Symmetry2016-12-20812Article10.3390/sym81201561562073-89942016-12-20doi: 10.3390/sym8120156Saeid FarkoushChang-Hwan KimSang-Bong Rhee<![CDATA[Symmetry, Vol. 8, Pages 155: Noether Symmetries Quantization and Superintegrability of Biological Models]]>
http://www.mdpi.com/2073-8994/8/12/155
It is shown that quantization and superintegrability are not concepts that are inherent to classical Physics alone. Indeed, one may quantize and also detect superintegrability of biological models by means of Noether symmetries. We exemplify the method by using a mathematical model that was proposed by Basener and Ross (2005), and that describes the dynamics of growth and sudden decrease in the population of Easter Island.Symmetry2016-12-20812Article10.3390/sym81201551552073-89942016-12-20doi: 10.3390/sym8120155Maria NucciGiampaolo Sanchini<![CDATA[Symmetry, Vol. 8, Pages 157: The Method of Linear Determining Equations to Evolution System and Application for Reaction-Diffusion System with Power Diffusivities]]>
http://www.mdpi.com/2073-8994/8/12/157
The method of linear determining equations is constructed to study conditional Lie–Bäcklund symmetry and the differential constraint of a two-component second-order evolution system, which generalize the determining equations used in the search for classical Lie symmetry. As an application of the approach, the two-component reaction-diffusion system with power diffusivities is considered. The conditional Lie–Bäcklund symmetries and differential constraints admitted by the reaction-diffusion system are identified. Consequently, the reductions of the resulting system are established due to the compatibility of the corresponding invariant surface conditions and the original system.Symmetry2016-12-20812Article10.3390/sym81201571572073-89942016-12-20doi: 10.3390/sym8120157Lina Ji<![CDATA[Symmetry, Vol. 8, Pages 154: Fluctuating Asymmetry of Human Populations: A Review]]>
http://www.mdpi.com/2073-8994/8/12/154
Fluctuating asymmetry, the random deviation from perfect symmetry, is a widely used population-level index of developmental instability, developmental noise, and robustness. It reflects a population’s state of adaptation and genomic coadaptation. Here, we review the literature on fluctuating asymmetry of human populations. The most widely used bilateral traits include skeletal, dental, and facial dimensions; dermatoglyphic patterns and ridge counts; and facial shape. Each trait has its advantages and disadvantages, but results are most robust when multiple traits are combined into a composite index of fluctuating asymmetry (CFA). Both environmental (diet, climate, toxins) and genetic (aneuploidy, heterozygosity, inbreeding) stressors have been linked to population-level variation in fluctuating asymmetry. In general, these stressors increase average fluctuating asymmetry. Nevertheless, there have been many conflicting results, in part because (1) fluctuating asymmetry is a weak signal in a sea of noise; and (2) studies of human fluctuating asymmetry have not always followed best practices. The most serious concerns are insensitive asymmetry indices (correlation coefficient and coefficient of indetermination), inappropriate size scaling, unrecognized mixture distributions, inappropriate corrections for directional asymmetry, failure to use composite indices, and inattention to measurement error. Consequently, it is often difficult (or impossible) to compare results across traits, and across studies.Symmetry2016-12-16812Review10.3390/sym81201541542073-89942016-12-16doi: 10.3390/sym8120154John GrahamBariş Özener<![CDATA[Symmetry, Vol. 8, Pages 152: Continuous Learning Graphical Knowledge Unit for Cluster Identification in High Density Data Sets]]>
http://www.mdpi.com/2073-8994/8/12/152
Big data are visually cluttered by overlapping data points. Rather than removing, reducing or reformulating overlap, we propose a simple, effective and powerful technique for density cluster generation and visualization, where point marker (graphical symbol of a data point) overlap is exploited in an additive fashion in order to obtain bitmap data summaries in which clusters can be identified visually, aided by automatically generated contour lines. In the proposed method, the plotting area is a bitmap and the marker is a shape of more than one pixel. As the markers overlap, the red, green and blue (RGB) colour values of pixels in the shared region are added. Thus, a pixel of a 24-bit RGB bitmap can code up to 224 (over 1.6 million) overlaps. A higher number of overlaps at the same location makes the colour of this area identical, which can be identified by the naked eye. A bitmap is a matrix of colour values that can be represented as integers. The proposed method updates this matrix while adding new points. Thus, this matrix can be considered as an up-to-time knowledge unit of processed data. Results show cluster generation, cluster identification, missing and out-of-range data visualization, and outlier detection capability of the newly proposed method.Symmetry2016-12-14812Article10.3390/sym81201521522073-89942016-12-14doi: 10.3390/sym8120152K.K.L.B. AdikaramMohamed HusseinMathias EffenbergerThomas Becker<![CDATA[Symmetry, Vol. 8, Pages 153: A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method]]>
http://www.mdpi.com/2073-8994/8/12/153
Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modified ranking method is presented. In comparison with the HFS lexicographical ordering method, the modified ranking method is more reasonable in more general cases.Symmetry2016-12-14812Comment10.3390/sym81201531532073-89942016-12-14doi: 10.3390/sym8120153Xiaodi LiuZengwen WangShitao Zhang<![CDATA[Symmetry, Vol. 8, Pages 151: An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks]]>
http://www.mdpi.com/2073-8994/8/12/151
Heterogeneous networks (HetNets) give users the opportunity to access different access points(APs), which will simultaneously affect user performance and system performance, so user association in HetNets plays a critical role in enhancing the load balancing and the system sum-throughput of networks. Meanwhile, the incremental sum-throughput currently fails to meet the escalating data demands. Besides, ensuring fairness amongst users constitutes another urgent issue in the radio resource management (RRM) of HetNets. What is more, few works consider the maximum service user number constraint in femtocell access points (FAPs). To solve the aforementioned problem, this paper associates users to APs by considering system sum-throughput and fairness at the same time in HetNets under a maximum service user number constraint of FAPs; accordingly, the user association problem is formulated. By releasing constraint, the optimal user association algorithm is obtained by Lagrangian function, and based on this optimal solution, a low complexity suboptimal user association algorithm is proposed. At last, this paper investigates the relationship between system sum-throughput and maximum service user number of FAPs. Numerical simulation results show that the proposed algorithm can improve sum-throughput and fairness at the same time at a specific maximum service user number of FAPs.Symmetry2016-12-10812Article10.3390/sym81201511512073-89942016-12-10doi: 10.3390/sym8120151Fang YeChunxia SuYibing Li<![CDATA[Symmetry, Vol. 8, Pages 150: Morphometric Asymmetry of Frustule Outlines in the Pennate Diatom Luticola poulickovae (Bacillariophyceae)]]>
http://www.mdpi.com/2073-8994/8/12/150
Side orientation of cells is usually ambiguous in unicellular organisms, making it impossible to separate components of directional asymmetry (DA) and fluctuating asymmetry (FA). However, frustules of the diatom Luticola poulickovae have biradially symmetric outlines, and their central areas bear ornamentation that is asymmetric across the apical axis. The goal of this study was to explore differentiation of morphometric asymmetry across the apical axis into DA and FA components. Is there detectable DA of the valve outlines of two L. poulickovae strains that may be related to the asymmetric central areas? Given that the life cycle of diatoms involves cell-size diminution, and cell shape is strongly affected by allometry, we also explored the question of whether asymmetry is correlated with cell size. The extent of symmetric variation among individuals in each strain, as well as DA and FA across the apical axis, were quantified using two Procrustes ANOVA models. The results revealed no correlation of either total asymmetry or FA with valve size. DA was significant and considerably more pronounced than FA in both strains, indicating that there is previously unknown systematic asymmetry of valve outlines of L. poulickovae, which may be related to the asymmetry of its central area.Symmetry2016-12-07812Article10.3390/sym81201501502073-89942016-12-07doi: 10.3390/sym8120150Kateřina WoodardJiří Neustupa<![CDATA[Symmetry, Vol. 8, Pages 149: M-Polynomial and Degree-Based Topological Indices of Polyhex Nanotubes]]>
http://www.mdpi.com/2073-8994/8/12/149
The discovery of new nanomaterials adds new dimensions to industry, electronics, and pharmaceutical and biological therapeutics. In this article, we first find closed forms of M-polynomials of polyhex nanotubes. We also compute closed forms of various degree-based topological indices of these tubes. These indices are numerical tendencies that often depict quantitative structural activity/property/toxicity relationships and correlate certain physico-chemical properties, such as boiling point, stability, and strain energy, of respective nanomaterial. To conclude, we plot surfaces associated to M-polynomials and characterize some facts about these tubes.Symmetry2016-12-06812Article10.3390/sym81201491492073-89942016-12-06doi: 10.3390/sym8120149Mobeen MunirWaqas NazeerShazia RafiqueShin Kang<![CDATA[Symmetry, Vol. 8, Pages 148: EMG Pattern Classification by Split and Merge Deep Belief Network]]>
http://www.mdpi.com/2073-8994/8/12/148
In this paper; we introduce an enhanced electromyography (EMG) pattern recognition algorithm based on a split-and-merge deep belief network (SM-DBN). Generally, it is difficult to classify the EMG features because the EMG signal has nonlinear and time-varying characteristics. Therefore, various machine-learning methods have been applied in several previously published studies. A DBN is a fast greedy learning algorithm that can identify a fairly good set of weights rapidly—even in deep networks with a large number of parameters and many hidden layers. To reduce overfitting and to enhance performance, the adopted optimization method was based on genetic algorithms (GA). As a result, the performance of the SM-DBN was 12.06% higher than conventional DBN. Additionally, SM-DBN results in a short convergence time, thereby reducing the training epoch. It is thus efficient in reducing the risk of overfitting. It is verified that the optimization was improved using GA.Symmetry2016-12-06812Article10.3390/sym81201481482073-89942016-12-06doi: 10.3390/sym8120148Hyeon-min ShimHongsub AnSanghyuk LeeEung LeeHong-ki MinSangmin Lee<![CDATA[Symmetry, Vol. 8, Pages 147: Comprehensive Reputation-Based Security Mechanism against Dynamic SSDF Attack in Cognitive Radio Networks]]>
http://www.mdpi.com/2073-8994/8/12/147
Collaborative spectrum sensing (CSS) was envisioned to improve the reliability of spectrum sensing in centralized cognitive radio networks (CRNs). However, secondary users (SUs)’ changeable environment and ease of compromise make CSS vulnerable to security threats, which further mislead the global decision making and degrade the overall performance. A popular attack in CSS is the called spectrum sensing data falsification (SSDF) attack. In the SSDF attack, malicious cognitive users (MUs) send false sensing results to the fusion center, which significantly degrades detection accuracy. In this paper, a comprehensive reputation-based security mechanism against dynamic SSDF attack for CRNs is proposed. In the mechanism, the reliability of SUs in collaborative sensing is measured with comprehensive reputation values in accordance with the SUs’ current and historical sensing behaviors. Meanwhile a punishment strategy is presented to revise the reputation, in which a reward factor and a penalty factor are introduced to encourage SUs to engage in positive and honest sensing activities. The whole mechanism focuses on ensuring the correctness of the global decision continuously. Specifically, the proposed security scheme can effectively alleviate the effect of users’ malicious behaviors on network decision making, which contributes greatly to enhancing the fairness and robustness of CRNs. Considering that the attack strategy adopted by MUs has been gradually transforming from simplicity, fixedness and singleness into complexity, dynamic and crypticity, we introduce two dynamic behavior patterns (true to false and then to true (TFT) and false to true and then to false (FTF)) to further validate the effectiveness of our proposed defense mechanism. Abundant simulation results verify the rationality and validity of our proposed mechanism.Symmetry2016-12-03812Article10.3390/sym81201471472073-89942016-12-03doi: 10.3390/sym8120147Fang YeXun ZhangYibing Li<![CDATA[Symmetry, Vol. 8, Pages 145: On Center, Periphery and Average Eccentricity for the Convex Polytopes]]>
http://www.mdpi.com/2073-8994/8/12/145
A vertex v is a peripheral vertex in G if its eccentricity is equal to its diameter, and periphery P ( G ) is a subgraph of G induced by its peripheral vertices. Further, a vertex v in G is a central vertex if e ( v ) = r a d ( G ) , and the subgraph of G induced by its central vertices is called center C ( G ) of G . Average eccentricity is the sum of eccentricities of all of the vertices in a graph divided by the total number of vertices, i.e., a v e c ( G ) = { 1 n ∑ e G ( u ) ; u ∈ V ( G ) } . If every vertex in G is central vertex, then C ( G ) = G , and hence, G is self-centered. In this report, we find the center, periphery and average eccentricity for the convex polytopes.Symmetry2016-12-02812Article10.3390/sym81201451452073-89942016-12-02doi: 10.3390/sym8120145Waqas NazeerShin KangSaima NazeerMobeen MunirImrana KousarAmmara SeharYoung Kwun<![CDATA[Symmetry, Vol. 8, Pages 146: Design of a Sustainable and Efficient Transportation Station (SETS) Based on Renewable Sources and Efficient Electric Drives]]>
http://www.mdpi.com/2073-8994/8/12/146
The need for reduction in power consumption for public facilities has increased after the occurrences of multiple blackout events. In an effort to enable the development of green and smart social infrastructure, this paper introduces a design for a sustainable and efficient transportation system (SETS). For this design, renewable power sources and efficient electric drives are considered to be crucial technologies. Considering the subway station as an illustrative example, a power system design that uses wind and solar energy as major power sources is studied. The adjustable speed electric drive system that uses synchronous reluctance machines for ventilation systems contributes to increasing the overall power consumption efficiency. The effectiveness of the proposed SETS system is verified through a set of various field measurement data and simulation results. While the verification results demonstrate that operation of SETS is enabled by effective integration of renewable sources and efficient ventilation systems, future research directions have also been identified.Symmetry2016-12-02812Article10.3390/sym81201461462073-89942016-12-02doi: 10.3390/sym8120146Myungchin KimJeongtae KimSungwoo Bae<![CDATA[Symmetry, Vol. 8, Pages 144: Using Convolutional Neural Network Filters to Measure Left-Right Mirror Symmetry in Images]]>
http://www.mdpi.com/2073-8994/8/12/144
We propose a method for measuring symmetry in images by using filter responses from Convolutional Neural Networks (CNNs). The aim of the method is to model human perception of left/right symmetry as closely as possible. Using the Convolutional Neural Network (CNN) approach has two main advantages: First, CNN filter responses closely match the responses of neurons in the human visual system; they take information on color, edges and texture into account simultaneously. Second, we can measure higher-order symmetry, which relies not only on color, edges and texture, but also on the shapes and objects that are depicted in images. We validated our algorithm on a dataset of 300 music album covers, which were rated according to their symmetry by 20 human observers, and compared results with those from a previously proposed method. With our method, human perception of symmetry can be predicted with high accuracy. Moreover, we demonstrate that the inclusion of features from higher CNN layers, which encode more abstract image content, increases the performance further. In conclusion, we introduce a model of left/right symmetry that closely models human perception of symmetry in CD album covers.Symmetry2016-12-01812Article10.3390/sym81201441442073-89942016-12-01doi: 10.3390/sym8120144Anselm BrachmannChristoph Redies<![CDATA[Symmetry, Vol. 8, Pages 143: A New Bayesian Edge-Linking Algorithm Using Single-Target Tracking Techniques]]>
http://www.mdpi.com/2073-8994/8/12/143
This paper proposes novel edge-linking algorithms capable of producing a set of edge segments from a binary edge map generated by a conventional edge-detection algorithm. These proposed algorithms transform the conventional edge-linking problem into a single-target tracking problem, which is a well-known problem in object tracking. The conversion of the problem enables us to apply sophisticated Bayesian inference to connect the edge points. We test our proposed approaches on real images that are corrupted with noise.Symmetry2016-12-01812Article10.3390/sym81201431432073-89942016-12-01doi: 10.3390/sym8120143Ji Yoon<![CDATA[Symmetry, Vol. 8, Pages 142: Fluctuating Asymmetry of Craniological Features of Small Mammals as a Reflection of Heterogeneity of Natural Populations]]>
http://www.mdpi.com/2073-8994/8/12/142
Fluctuating asymmetry (FA) in nine species of small mammals (Insectivora and Rodentia) was estimated using 10 cranial features (foramina for nerves and blood vessels). The main criterion was the occurrence of the fluctuating asymmetry manifestations (OFAM). A total of 2300 skulls collected in the taiga and forest-tundra of Yakutia (Northeast Asia) were examined. The examined species are characterized by comparable OFAM values in the vast territories of the taiga zone; on the ecological periphery of the range an increased FA level is registered. Asymmetric manifestations in analyzed features are equally likely to occur in males and females. OFAM values in juveniles are higher than in adults; this difference is more pronounced on the periphery of the geographic range. Among juveniles, lower FA levels are observed in individuals that have bred. It can be surmised that the risk of elimination of individuals with high FA levels increases in stressful periods (active reproduction and winter). In conditions that are close to optimal, populations demonstrate relatively homogeneous FA levels, while on the periphery of the area an increase in occurrence of disturbances in developmental stability is observed, which leads, on one hand, to higher average FA for the population and, on the other hand, to heterogeneity of the population in this parameter.Symmetry2016-11-29812Article10.3390/sym81201421422073-89942016-11-29doi: 10.3390/sym8120142Elena ShadrinaYakov Vol’pert<![CDATA[Symmetry, Vol. 8, Pages 141: Comparing Bayesian and Maximum Likelihood Predictors in Structural Equation Modeling of Children’s Lifestyle Index]]>
http://www.mdpi.com/2073-8994/8/12/141
Several factors may influence children’s lifestyle. The main purpose of this study is to introduce a children’s lifestyle index framework and model it based on structural equation modeling (SEM) with Maximum likelihood (ML) and Bayesian predictors. This framework includes parental socioeconomic status, household food security, parental lifestyle, and children’s lifestyle. The sample for this study involves 452 volunteer Chinese families with children 7–12 years old. The experimental results are compared in terms of root mean square error, coefficient of determination, mean absolute error, and mean absolute percentage error metrics. An analysis of the proposed causal model suggests there are multiple significant interconnections among the variables of interest. According to both Bayesian and ML techniques, the proposed framework illustrates that parental socioeconomic status and parental lifestyle strongly impact children’s lifestyle. The impact of household food security on children’s lifestyle is rejected. However, there is a strong relationship between household food security and both parental socioeconomic status and parental lifestyle. Moreover, the outputs illustrate that the Bayesian prediction model has a good fit with the data, unlike the ML approach. The reasons for this discrepancy between ML and Bayesian prediction are debated and potential advantages and caveats with the application of the Bayesian approach in future studies are discussed.Symmetry2016-11-28812Article10.3390/sym81201411412073-89942016-11-28doi: 10.3390/sym8120141Che RadziHuang HuiHashem Salarzadeh Jenatabadi<![CDATA[Symmetry, Vol. 8, Pages 139: Attribute Control Chart Construction Based on Fuzzy Score Number]]>
http://www.mdpi.com/2073-8994/8/12/139
There is much uncertainty and fuzziness in product quality attributes or quality parameters of a manufacturing process, so the traditional quality control chart can be difficult to apply. This paper proposes a fuzzy control chart. The plotted data was obtained by transforming expert scores into fuzzy numbers. Two types of nonconformity judgment rules—necessity and possibility measurement rules—are proposed. Through graphical analysis, the nonconformity judging method (i.e., assessing directly based on the shape feature of a fuzzy control chart) is proposed. For four different widely used membership functions, control levels were analyzed and compared by observing gaps between the upper and lower control limits. The result of the case study validates the feasibility and reliability of the proposed approach.Symmetry2016-11-26812Article10.3390/sym81201391392073-89942016-11-26doi: 10.3390/sym8120139Shiwang HouHui WangShunxiao Feng<![CDATA[Symmetry, Vol. 8, Pages 140: Nonclassical Symmetries of a Nonlinear Diffusion–Convection/Wave Equation and Equivalents Systems]]>
http://www.mdpi.com/2073-8994/8/12/140
It is generally known that classical point and potential Lie symmetries of differential equations (the latter calculated as point symmetries of an equivalent system) can be different. We question whether this is true when the symmetries are extended to nonclassical symmetries. In this paper, we consider two classes of nonlinear partial differential equations; the first one is a diffusion–convection equation, the second one a wave, where we will show that the majority of the nonclassical point symmetries are included in the nonclassical potential symmetries. We highlight a special case were the opposite is true.Symmetry2016-11-26812Article10.3390/sym81201401402073-89942016-11-26doi: 10.3390/sym8120140Daniel ArrigoBrandon AshleySeth BloombergThomas Deatherage<![CDATA[Symmetry, Vol. 8, Pages 138: Data Aggregation Gateway Framework for CoAP Group Communications]]>
http://www.mdpi.com/2073-8994/8/12/138
In this paper, a data aggregation gateway framework (DA-GW) for constrained application protocol (CoAP) group communications is proposed. The DA-GW framework is designed to improve the throughput performance and energy efficiency of group communication to monitor and control multiple sensor devices collectively with a single user terminal. The DA-GW consists of four function blocks—the message analyzer, group manager, message scheduler and data handler—and three informative databases—the client database, resource database and information database. The DA-GW performs group management and group communication through each functional block and stores resources in the informative databases. The DA-GW employs international standard-based data structures and provides the interoperability of heterogeneous devices used in various applications. The DA-GW is implemented using a Java-based open source framework called jCoAP to evaluate the functions and performance of the DA-GW. The experiment results showed that the DA-GW framework revealed better performance than existing group communication methods in terms of throughput and energy consumption.Symmetry2016-11-24812Article10.3390/sym81201381382073-89942016-11-24doi: 10.3390/sym8120138Minki ChaJung-Hyok KwonSungJin KimTaeshik ShonEui-Jik Kim<![CDATA[Symmetry, Vol. 8, Pages 136: Big Bounce Genesis and Possible Experimental Tests: A Brief Review]]>
http://www.mdpi.com/2073-8994/8/11/136
We review the recent status of big bounce genesis as a new possibility of using dark matter particles’ mass and interaction cross-section to test the existence of a bounce universe at the early stage of evolution in our currently-observed universe. To study the dark matter production and evolution inside the bounce universe, called big bounce genesis for short, we propose a model independent approach. We shall present the motivation for proposing big bounce, as well as the model independent predictions, which can be tested by dark matter direct searches. A positive finding shall have profound impact on our understanding of the early universe physics.Symmetry2016-11-23811Review10.3390/sym81101361362073-89942016-11-23doi: 10.3390/sym8110136Yeuk-Kwan CheungChanghong LiJoannis Vergados<![CDATA[Symmetry, Vol. 8, Pages 137: Evaluation and Classification of Overseas Talents in China Based on the BWM for Intuitionistic Relations]]>
http://www.mdpi.com/2073-8994/8/11/137
Efficient utilization of human resources is an important force for the sustainable development of society and the economy. Against the backdrop of the development of economic globalization, the Chinese Government is presently implementing the strategy of “Strengthening the Nation with Talent” to assist the exploitation and management of human resources. Overseas talents have recently become an important resource. How to scientifically evaluate and classify overseas talents has become an important research topic, and it is necessary to seek a systematic decision aid. This paper introduces a novel methodology to evaluate and classify overseas talents in China under the intuitionistic relations environment. Firstly, we determine the weighted values of decision makers and criteria through defining geometry consistency. Secondly, we construct a non-linear Best-Worst-Method (BWM) model with intuitionistic preference relations. A highlight of this BWM model for intuitionistic relations is taking both positive and negative aspects into consideration, which is different from the original BWM. Finally, the proposed methodology is applied to an illustrative example of overseas talent evaluation, indicating the simultaneous efficiency and practicability of the method.Symmetry2016-11-23811Article10.3390/sym81101371372073-89942016-11-23doi: 10.3390/sym8110137Qing YangZaisheng ZhangXinshang YouTong Chen<![CDATA[Symmetry, Vol. 8, Pages 135: The Novel Concept of “Behavioural Instability” and Its Potential Applications]]>
http://www.mdpi.com/2073-8994/8/11/135
The concept of developmental instability (DI) is a well-known indicator of environmental and genetic stress and is often investigated using various indices such as fluctuating asymmetry, directional asymmetry, antisymmetry and phenotypic variance. Investigations dealing with DI are using morphometric traits. The aim of this investigation is to present the novel concept of behavioural instability in which the trait measured is a behavioural trait. We apply the conventional indices used for the estimation of developmental instability on directional movement—clockwise (CW) and counter-clockwise (CCW) movement of 19 highly inbred lines of Drosophila melanogaster tested in a circular arena. We show that it is possible to quantify behavioural instability using the indices traditionally used to investigate DI. Results revealed several significant differences among lines, depending on the index utilized. The perspectives of utilizing the concept in biological research such as toxicology, evolutionary and stress biology are discussed.Symmetry2016-11-18811Article10.3390/sym81101351352073-89942016-11-18doi: 10.3390/sym8110135Cino PertoldiSimon BahrndorffZorana Kurbalija NovicicPalle Duun Rohde<![CDATA[Symmetry, Vol. 8, Pages 132: Segmentation of Brain Tumors in MRI Images Using Three-Dimensional Active Contour without Edge]]>
http://www.mdpi.com/2073-8994/8/11/132
Brain tumor segmentation in magnetic resonance imaging (MRI) is considered a complex procedure because of the variability of tumor shapes and the complexity of determining the tumor location, size, and texture. Manual tumor segmentation is a time-consuming task highly prone to human error. Hence, this study proposes an automated method that can identify tumor slices and segment the tumor across all image slices in volumetric MRI brain scans. First, a set of algorithms in the pre-processing stage is used to clean and standardize the collected data. A modified gray-level co-occurrence matrix and Analysis of Variance (ANOVA) are employed for feature extraction and feature selection, respectively. A multi-layer perceptron neural network is adopted as a classifier, and a bounding 3D-box-based genetic algorithm is used to identify the location of pathological tissues in the MRI slices. Finally, the 3D active contour without edge is applied to segment the brain tumors in volumetric MRI scans. The experimental dataset consists of 165 patient images collected from the MRI Unit of Al-Kadhimiya Teaching Hospital in Iraq. Results of the tumor segmentation achieved an accuracy of 89% ± 4.7% compared with manual processes.Symmetry2016-11-18811Article10.3390/sym81101321322073-89942016-11-18doi: 10.3390/sym8110132Ali HasanFarid MezianeRob AspinHamid Jalab<![CDATA[Symmetry, Vol. 8, Pages 134: Some Invariants of Circulant Graphs]]>
http://www.mdpi.com/2073-8994/8/11/134
Topological indices and polynomials are predicting properties like boiling points, fracture toughness, heat of formation, etc., of different materials, and thus save us from extra experimental burden. In this article we compute many topological indices for the family of circulant graphs. At first, we give a general closed form of M-polynomial of this family and recover many degree-based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family. Our results extend many existing results.Symmetry2016-11-18811Article10.3390/sym81101341342073-89942016-11-18doi: 10.3390/sym8110134Mobeen MunirWaqas NazeerZakia ShahzadiShin Kang<![CDATA[Symmetry, Vol. 8, Pages 133: Nutritional Stress Causes Heterogeneous Relationships with Multi-Trait FA in Lesser Black-Backed Gull Chicks: An Aviary Experiment]]>
http://www.mdpi.com/2073-8994/8/11/133
Environmental stressors have the potential to induce perturbations in the development of young individuals, leading to aberrant and unstable development. This may manifest as fluctuating asymmetry (FA; small, non-directional changes in the bilateral symmetry of morphological traits). Although widely regarded as a proxy for stress effects, the use of FA as a biomarker is still a topic of much debate. We investigated the applicability of FA as an indicator of nutritional stress (brought about by energetic constraints) by experimental manipulation of the diet composition and quantity during the growth of Lesser Black-backed Gull (Larus fuscus) chicks. FA as an endpoint was measured across the tarsus, wing and 10th primary feather when chicks reached 30 days of age. Although levels of asymmetry were found to increase with stress in the feather, relationships with tarsus and wing FA were mixed and mostly non-significant. Furthermore, we did not find any correlations in unsigned FA between traits, indicating the absence of organism-wide asymmetry. Our study was therefore unable to find unequivocal evidence in support of the application of FA as a reliable estimator of nutritional stress.Symmetry2016-11-17811Article10.3390/sym81101331332073-89942016-11-17doi: 10.3390/sym8110133Trisha GuptaCátia SantosAlejandro SotilloLiesbeth De NeveEric StienenWendt MüllerLuc Lens<![CDATA[Symmetry, Vol. 8, Pages 131: An Improved Protocol for the Password Authenticated Association of IEEE 802.15.6 Standard That Alleviates Computational Burden on the Node]]>
http://www.mdpi.com/2073-8994/8/11/131
The IEEE Std 802.15.6 is an international standard for wireless body area networks (WBANs). It contains many aspects of communications, and also provides security services, since some communications in WBANs can carry sensitive information. In this standard, the password authenticated association is a protocol for two participants to identify each other and establish a new master key based on a pre-shared short password. However, recent research shows that this protocol is vulnerable to several attacks. In this paper, we propose an improved protocol which can resist all of these attacks. Moreover, the improved protocol alleviates computational burden on one side of the two participants, the node, which is usually less powerful compared with the other side, the hub.Symmetry2016-11-17811Article10.3390/sym81101311312073-89942016-11-17doi: 10.3390/sym8110131Jie ZhangXin HuangPaul CraigAlan MarshallDawei Liu<![CDATA[Symmetry, Vol. 8, Pages 130: Image Intelligent Detection Based on the Gabor Wavelet and the Neural Network]]>
http://www.mdpi.com/2073-8994/8/11/130
This paper first analyzes the one-dimensional Gabor function and expands it to a two-dimensional one. The two-dimensional Gabor function generates the two-dimensional Gabor wavelet through measure stretching and rotation. At last, the two-dimensional Gabor wavelet transform is employed to extract the image feature information. Based on the back propagation (BP) neural network model, the image intelligent test model based on the Gabor wavelet and the neural network model is built. The human face image detection is adopted as an example. Results suggest that, although there are complex textures and illumination variations on the images of the face database named AT&amp;T, the detection accuracy rate of the proposed method can reach above 0.93. In addition, extensive simulations based on the Yale and extended Yale B datasets further verify the effectiveness of the proposed method.Symmetry2016-11-15811Article10.3390/sym81101301302073-89942016-11-15doi: 10.3390/sym8110130Yajun XuFengmei LiangGang ZhangHuifang Xu<![CDATA[Symmetry, Vol. 8, Pages 128: Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations]]>
http://www.mdpi.com/2073-8994/8/11/128
In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.Symmetry2016-11-15811Article10.3390/sym81101281282073-89942016-11-15doi: 10.3390/sym8110128Chunrong ZhuChangzheng Qu<![CDATA[Symmetry, Vol. 8, Pages 129: The Design and Analysis of a Secure Personal Healthcare System Based on Certificates]]>
http://www.mdpi.com/2073-8994/8/11/129
Due to the development of information technology (IT), it has been applied to various fields such as the smart home, medicine, healthcare, and the smart car. For these fields, IT has been providing continuous prevention and management, including health conditions beyond the mere prevention of disease, improving the quality of life. e-Healthcare is a health management and medical service to provide prevention, diagnosis, treatment, and the follow-up management of diseases at any time and place in connection with information communication technology, without requiring patients to visit hospitals. However, e-Healthcare has been exposed to eavesdropping, manipulation, and the forgery of information that is personal, biological, medical, etc., and is a security threat from malicious attackers. This study suggests a security service model to exchange personal health records (PHRs) for e-Healthcare environments. To be specific, this study suggests a scheme in which communicators are able to securely authorize and establish security channels by constituting the infrastructure each organization relies on. In addition, the possibility of establishing a security service model is indicated by suggesting an e-Healthcare system for a secure e-Healthcare environment as a secure personal health record system. This is anticipated to provide securer communication in e-Healthcare environments in the future through the scheme suggested in this study.Symmetry2016-11-14811Article10.3390/sym81101291292073-89942016-11-14doi: 10.3390/sym8110129Jungho KangHague ChungJeongkyu LeeJong Park<![CDATA[Symmetry, Vol. 8, Pages 127: Affine Geometry, Visual Sensation, and Preference for Symmetry of Things in a Thing]]>
http://www.mdpi.com/2073-8994/8/11/127
Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion.Symmetry2016-11-14811Article10.3390/sym81101271272073-89942016-11-14doi: 10.3390/sym8110127Birgitta Dresp-Langley<![CDATA[Symmetry, Vol. 8, Pages 126: Linear Weingarten Helicoidal Surfaces in Isotropic Space]]>
http://www.mdpi.com/2073-8994/8/11/126
In the present paper, we study helicoidal surfaces in the three-dimensional isotropic space I 3 and construct helicoidal surfaces satisfying a linear equation in terms of the Gaussian curvature and the mean curvature of the surface.Symmetry2016-11-14811Article10.3390/sym81101261262073-89942016-11-14doi: 10.3390/sym8110126Dae YoonJae Lee<![CDATA[Symmetry, Vol. 8, Pages 125: Improvement in Scoliosis Top View: Evaluation of Vertebrae Localization in Scoliotic Spine-Spine Axial Presentation]]>
http://www.mdpi.com/2073-8994/8/11/125
Morphological analysis of the scoliotic spine is based on two-dimensional X-rays: coronal and sagittal. The three-dimensional character of scoliosis has raised the necessity for analyzing scoliosis in three planes. We proposed a new user-friendly method of graphical presentation of the spine in the third plane–the Spine Axial Presentation (SAP). Eighty-five vertebrae of patients with scoliosis were analyzed. Due to different positions during X-rays (standing) and computer tomography (CT) (supine), the corresponding measurements cannot be directly compared. As a solution, a software creating Digital Reconstructed Radiographs (DRRs) from CT scans was developed to replace regular X-rays with DRRs. Based on the measurements performed on DRRs, the coordinates of vertebral bodies central points were defined. Next, the geometrical centers of vertebral bodies were determined on CT scans. The reproducibility of measurements was tested with Intraclass Correlation Coefficient (ICC), using p = 0.05. The intra-observer reproducibility and inter-observer reliability for vertebral body central point’s coordinates (x, y, z) were high for results obtained based on DRRs and CT scans, as well as for comparison results obtained based on DRR and CT scans. Based on two standard radiographs, it is possible to localize vertebral bodies in 3D space. The position of vertebral bodies can be present in the Spine Axial Presentation.Symmetry2016-11-14811Article10.3390/sym81101251252073-89942016-11-14doi: 10.3390/sym8110125Paweł GłówkaDominik GawełBartosz KasprzakMichał NowakTomasz Kotwicki<![CDATA[Symmetry, Vol. 8, Pages 124: Fluctuating Asymmetry in Two Common Freshwater Fishes as a Biological Indicator of Urbanization and Environmental Stress within the Middle Chattahoochee Watershed]]>
http://www.mdpi.com/2073-8994/8/11/124
Deviations in bilateral symmetry or fluctuating asymmetry of an organism may result under environmental stressors that reduce developmental homeostasis and stability. Anthropogenic stressors such as increased urbanization can negatively impact environmental quality of aquatic ecosystems. Researchers have stressed the value in finding easy, accurate and inexpensive methods for assessing potential stress within ecosystems. Here we use fluctuating asymmetry (FA) as a useful quantitative tool in assessing the environmental quality and potential urban-based stressors within eight creeks of the Bull and Upatoi Creeks Watershed within the larger watershed of the Middle Chattahoochee. Using Geographic Information System (GIS), we characterize land-use patterns and a decreasing urbanization gradient as related to each creek’s eastward position from Columbus, Georgia. We collected two common fishes (redbreast sunfish; Lepomis auritus and bluegill; Lepomis macrochirus), measured both metric and meristic traits and investigated if the degree of FA in these two common fishes correlated with the urbanization gradient across creeks. We found significant differences in FA among creeks with one of the highest FA measures for the most urban creek. Principal component analysis (PCA) scores of urbanization and water chemistry were regressed against FA scores. We found no significant relationship between urbanization and FA nor environmental water chemistry and FA among creeks. We comment on the use of FA as a potential response variable and biological indicator of environmental stress within this watershed.Symmetry2016-11-10811Article10.3390/sym81101241242073-89942016-11-10doi: 10.3390/sym8110124William LutterschmidtSamantha MartinJacob Schaefer<![CDATA[Symmetry, Vol. 8, Pages 122: On the Magnetic Evolution in Friedmann Universes and the Question of Cosmic Magnetogenesis]]>
http://www.mdpi.com/2073-8994/8/11/122
We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes.Symmetry2016-11-09811Article10.3390/sym81101221222073-89942016-11-09doi: 10.3390/sym8110122Christos Tsagas<![CDATA[Symmetry, Vol. 8, Pages 123: A Longitudinal Study of Changes in Fluctuating Asymmetry with Age in Jamaican Youth]]>
http://www.mdpi.com/2073-8994/8/11/123
Fluctuating asymmetry (FA), random deviation from perfect bilateral symmetry, is an indicator of developmental stability. Examining the ontogeny of FA can illustrate whether symmetry is actively maintained as the organism grows or breaks down as perturbations accumulate with age. Previous studies of changes in human FA with age have been cross-sectional studies and give conflicting results. We analyzed data from a longitudinal study of bodily FA in Jamaicans, using a composite index of seven paired traits. In addition, 288 children (ages 5–12) were first measured in 1996, and many were re-measured in 2002 and 2006 (maximum age = 22 years). Both within-individual longitudinal comparisons and between-individual comparisons across age groups demonstrate changes in FA with age. In males and females, FA increased until around age 13, but the pattern of change differed between the sexes. In males, FA increased rapidly approaching adolescence and then slightly declined into early adulthood. The increase in female FA was more gradual and then leveled off. The patterns observed likely reflect accumulation of developmental errors over time, rapid physical changes during puberty (especially in boys), and then regulation of symmetry when transitioning into adulthood. Although most changes in symmetry over time probably reflect random processes, the magnitude and direction of asymmetry in an individual at one point in time tended to be positively (though weakly) related to asymmetry in later years, pointing to underlying differences among individuals in developmental stability.Symmetry2016-11-09811Article10.3390/sym81101231232073-89942016-11-09doi: 10.3390/sym8110123Brian PalestisRobert Trivers<![CDATA[Symmetry, Vol. 8, Pages 121: Multilevel Editing of B-Spline Curves with Robust Orientation of Details]]>
http://www.mdpi.com/2073-8994/8/11/121
We facilitate the editing of hierarchical B-spline curves at multiple resolutions by expressing a displacement function at each level in rotation minimizing frames (RMFs) on the curve at the next lower level. When the curve is edited at a particular level, RMFs at all the higher levels are updated, and the control points of the displacement function at each higher level are obtained from these new RMFs. This transfers details created at the current level to higher levels. Our method presents a hundred-fold faster way to reflect editing results compared to the traditional approach using Frenet frames. We demonstrate the effectiveness of our technique by showing several examples of editing curves with fine details.Symmetry2016-11-08811Article10.3390/sym81101211212073-89942016-11-08doi: 10.3390/sym8110121Hae-Do HwangDong-Geun ParkSeung-Hyun Yoon<![CDATA[Symmetry, Vol. 8, Pages 120: Event-Centered Maze Generation Method for Mobile Virtual Reality Applications]]>
http://www.mdpi.com/2073-8994/8/11/120
This study proposes a method of effectively creating mobile virtual reality scenes centered at events for the purpose of providing new experiences in virtual reality environment to users. For this purpose, this paper uses Prim’s maze generation algorithm to automatically create maze environments that have different patterns every time and to compute mazes with finite paths. This paper designs a scheme of creating virtual reality scenes based on event-centered mazes to maximize users’ tension and immersion. Here, event components that are appropriate for the maze environment are defined and maze patterns are created centered at the event point where events that are appropriate for the maze pattern are automatically created. Finally, the paper analyzes whether the proposed virtual reality scene based on event-centered mazes is helpful in enhancing users’ immersion and arousing their interest through diverse experiments.Symmetry2016-11-04811Article10.3390/sym81101201202073-89942016-11-04doi: 10.3390/sym8110120Kisung JeongJinmo Kim<![CDATA[Symmetry, Vol. 8, Pages 119: Uncertain Quality Function Deployment Using a Hybrid Group Decision Making Model]]>
http://www.mdpi.com/2073-8994/8/11/119
Quality function deployment (QFD) is a widely used quality system tool for translating customer requirements (CRs) into the engineering design requirements (DRs) of products or services. The conventional QFD analysis, however, has been criticized as having some limitations such as in the assessment of relationships between CRs and DRs, the determination of CR weights and the prioritization of DRs. This paper aims to develop a new hybrid group decision-making model based on hesitant 2-tuple linguistic term sets and an extended QUALIFLEX (qualitative flexible multiple criteria method) approach for handling QFD problems with incomplete weight information. First, hesitant linguistic term sets are combined with interval 2-tuple linguistic variables to express various uncertainties in the assessment information of QFD team members. Borrowing the idea of grey relational analysis (GRA), a multiple objective optimization model is constructed to determine the relative weights of CRs. Then, an extended QUALIFLEX approach with an inclusion comparison method is suggested to determine the ranking of the DRs identified in QFD. Finally, an analysis of a market segment selection problem is conducted to demonstrate and validate the proposed QFD approach.Symmetry2016-11-04811Article10.3390/sym81101191192073-89942016-11-04doi: 10.3390/sym8110119Ze-Ling WangJian-Xin YouHu-Chen Liu<![CDATA[Symmetry, Vol. 8, Pages 117: M-Polynomials and Topological Indices of Titania Nanotubes]]>
http://www.mdpi.com/2073-8994/8/11/117
Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO2) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO2) nanotubes.Symmetry2016-10-31811Article10.3390/sym81101171172073-89942016-10-31doi: 10.3390/sym8110117Mobeen MunirWaqas NazeerAbdul NizamiShazia RafiqueShin Kang<![CDATA[Symmetry, Vol. 8, Pages 110: On the Phenomenology of an Accelerated Large-Scale Universe]]>
http://www.mdpi.com/2073-8994/8/11/110
In this review paper, several new results towards the explanation of the accelerated expansion of the large-scale universe is discussed. On the other hand, inflation is the early-time accelerated era and the universe is symmetric in the sense of accelerated expansion. The accelerated expansion of is one of the long standing problems in modern cosmology, and physics in general. There are several well defined approaches to solve this problem. One of them is an assumption concerning the existence of dark energy in recent universe. It is believed that dark energy is responsible for antigravity, while dark matter has gravitational nature and is responsible, in general, for structure formation. A different approach is an appropriate modification of general relativity including, for instance, f ( R ) and f ( T ) theories of gravity. On the other hand, attempts to build theories of quantum gravity and assumptions about existence of extra dimensions, possible variability of the gravitational constant and the speed of the light (among others), provide interesting modifications of general relativity applicable to problems of modern cosmology, too. In particular, here two groups of cosmological models are discussed. In the first group the problem of the accelerated expansion of large-scale universe is discussed involving a new idea, named the varying ghost dark energy. On the other hand, the second group contains cosmological models addressed to the same problem involving either new parameterizations of the equation of state parameter of dark energy (like varying polytropic gas), or nonlinear interactions between dark energy and dark matter. Moreover, for cosmological models involving varying ghost dark energy, massless particle creation in appropriate radiation dominated universe (when the background dynamics is due to general relativity) is demonstrated as well. Exploring the nature of the accelerated expansion of the large-scale universe involving generalized holographic dark energy model with a specific Nojiri-Odintsov cut-off is presented to finalize the paper.Symmetry2016-10-31811Review10.3390/sym81101101102073-89942016-10-31doi: 10.3390/sym8110110Martiros Khurshudyan<![CDATA[Symmetry, Vol. 8, Pages 118: Asymmetric Facial Bone Fragmentation Mirrors Asymmetric Distribution of Cranial Neuromasts in Blind Mexican Cavefish]]>
http://www.mdpi.com/2073-8994/8/11/118
Craniofacial asymmetry is a convergent trait widely distributed across animals that colonize the extreme cave environment. Although craniofacial asymmetry can be discerned easily, other complex phenotypes (such as sensory organ position and numerical variation) are challenging to score and compare. Certain bones of the craniofacial complex demonstrate substantial asymmetry, and co-localize to regions harboring dramatically expanded numbers of mechanosensory neuromasts. To determine if a relationship exists between this expansion and bone fragmentation in cavefish, we developed a quantitative measure of positional symmetry across the left-right axis. We found that three different cave-dwelling populations were significantly more asymmetric compared to surface-dwelling fish. Moreover, cave populations did not differ in the degree of neuromast asymmetry. This work establishes a method for quantifying symmetry of a complex phenotype, and demonstrates that facial bone fragmentation mirrors the asymmetric distribution of neuromasts in different cavefish populations. Further developmental studies will provide a clearer picture of the developmental and cellular changes that accompany this extreme phenotype, and help illuminate the genetic basis for facial asymmetry in vertebrates.Symmetry2016-10-31811Article10.3390/sym81101181182073-89942016-10-31doi: 10.3390/sym8110118Joshua GrossAndrew GangidineAmanda Powers<![CDATA[Symmetry, Vol. 8, Pages 116: Associations between Floral Asymmetry and Individual Genetic Variability Differ among Three Prickly Pear (Opuntia echios) Populations]]>
http://www.mdpi.com/2073-8994/8/11/116
While stress is expected to increase developmental instability (DI), not all studies confirm this. This heterogeneity could in part be due to the use of subtle differences between the left and right side of bilateral symmetrical organisms to quantify DI, leading to large sampling error obscuring associations with DI. Traits that develop simultaneously more than twice (such as flower petals or bird feathers) reflect individual DI more reliably, such that stronger associations are expected to emerge. Furthermore, some studies have shown differences in strengths of associations among populations. We studied the association between individual genetic diversity and DI in flower petals within three Opuntia echios populations inhabiting Galápagos. Quantifying individual DI through variation in length and width of a high number of petals within individual cacti, lead to a strong association between DI and genetic diversity in one population. We conclude that associations between individual DI and genetic diversity can be more easily revealed by measuring traits that develop repeatedly.Symmetry2016-10-29811Article10.3390/sym81101161162073-89942016-10-29doi: 10.3390/sym8110116Philippe HelsenStefan Van Dongen<![CDATA[Symmetry, Vol. 8, Pages 114: CPT Symmetry and Its Violation]]>
http://www.mdpi.com/2073-8994/8/11/114
One of the most fundamental symmetries in physics is CPT invariance. This article reviews the conditions under which CPT symmetry holds by recalling two proofs of the CPT theorem: The original Lagrangian-based analysis and the more rigorous one in the context of axiomatic quantum field theory. The presentation of the proofs is followed by a discussion of the major physical implications that arise from CPT symmetry. Motivated by recent theoretical and experimental interest in CPT tests, various approaches to the violation of CPT symmetry are mentioned, and it is briefly discussed how they evade the CPT theorem. An attempt has been made to keep this work self-contained and at a level suitable for a wider readership by excising as many technical aspects as possible.Symmetry2016-10-28811Review10.3390/sym81101141142073-89942016-10-28doi: 10.3390/sym8110114Ralf Lehnert<![CDATA[Symmetry, Vol. 8, Pages 115: Regular and Chiral Polyhedra in Euclidean Nets]]>
http://www.mdpi.com/2073-8994/8/11/115
We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose vertex and edge sets are a subset of those of the primitive cubic lattice, the face-centred cubic lattice, or the body-centred cubic lattice.Symmetry2016-10-28811Article10.3390/sym81101151152073-89942016-10-28doi: 10.3390/sym8110115Daniel Pellicer<![CDATA[Symmetry, Vol. 8, Pages 113: Optimal Inequalities for the Casorati Curvatures of Submanifolds in Generalized Space Forms Endowed with Semi-Symmetric Non-Metric Connections]]>
http://www.mdpi.com/2073-8994/8/11/113
In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection. Moreover, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical.Symmetry2016-10-27811Article10.3390/sym81101131132073-89942016-10-27doi: 10.3390/sym8110113Guoqing HeHairong LiuLiang Zhang<![CDATA[Symmetry, Vol. 8, Pages 111: The Standard-Model Extension and Gravitational Tests]]>
http://www.mdpi.com/2073-8994/8/11/111
The Standard-Model Extension (SME) provides a comprehensive effective field-theory framework for the study of CPT and Lorentz symmetry. This work reviews the structure and philosophy of the SME and provides some intuitive examples of symmetry violation. The results of recent gravitational tests performed within the SME are summarized including analysis of results from the Laser Interferometer Gravitational-Wave Observatory (LIGO), sensitivities achieved in short-range gravity experiments, constraints from cosmic-ray data, and results achieved by studying planetary ephemerids. Some proposals and ongoing efforts will also be considered including gravimeter tests, tests of the Weak Equivalence Principle, and antimatter experiments. Our review of the above topics is augmented by several original extensions of the relevant work. We present new examples of symmetry violation in the SME and use the cosmic-ray analysis to place first-ever constraints on 81 additional operators.Symmetry2016-10-27811Article10.3390/sym81101111112073-89942016-10-27doi: 10.3390/sym8110111Jay Tasson<![CDATA[Symmetry, Vol. 8, Pages 112: Collaborative Spectrum Sensing Algorithm Based on Exponential Entropy in Cognitive Radio Networks]]>
http://www.mdpi.com/2073-8994/8/11/112
Traditional detectors for spectrum sensing in cognitive radio networks always become disabled when noise uncertainty is severe. Shannon entropy-based detection methods have aroused widespread attention in recent years due to the characteristics of effective anti-noise uncertainty. However, in existing entropy-based sensing schemes, the uniform quantization method cannot guarantee the maximum entropy distribution when primary users do not exist, and cannot effectively distinguish between two hypotheses, which severely limits the promotion of detection performance. Moreover, the Shannon entropy-based sensing schemes are prone to misconvergence occurring when estimating entropy values, thus causing failure detection, which leads to system detection inefficiency and resource waste. These are the two major serious defects in Shannon entropy-based detectors, which restrict the performance improvement. In this paper, a novel non-uniform quantized exponential entropy-based (NQEE) detector is proposed for local sensing to deal with the problems of maximum entropy distribution and detection failure. To further improve the reliability of the detection, a collaborative spectrum sensing algorithm based on an NQEE detector with multiple fusion rules is presented. Simulation results verify that the detection performance of the improved local entropy-based detector is superior to the existing Shannon entropy-based detectors and is proved to be robust to noise power uncertainty. In addition, the novel collaborative detection algorithm outperforms the traditional collaborative spectrum detection method to a great degree.Symmetry2016-10-26811Article10.3390/sym81101121122073-89942016-10-26doi: 10.3390/sym8110112Fang YeXun ZhangYibing Li<![CDATA[Symmetry, Vol. 8, Pages 109: A Novel Texture Feature Description Method Based on the Generalized Gabor Direction Pattern and Weighted Discrepancy Measurement Model]]>
http://www.mdpi.com/2073-8994/8/11/109
Texture feature description is a remarkable challenge in the fields of computer vision and pattern recognition. Since the traditional texture feature description method, the local binary pattern (LBP), is unable to acquire more detailed direction information and always sensitive to noise, we propose a novel method based on generalized Gabor direction pattern (GGDP) and weighted discrepancy measurement model (WDMM) to overcome those defects. Firstly, a novel patch-structure direction pattern (PDP) is proposed, which can extract rich feature information and be insensitive to noise. Then, motivated by searching for a description method that can explore richer and more discriminant texture features and reducing the local Gabor feature vector’s high dimension problem, we extend PDP to form the GGDP method with multi-channel Gabor space. Furthermore, WDMM, which can effectively measure the feature distance between two images, is presented for the classification and recognition of image samples. Simulated experiments on olivetti research laboratory (ORL), Carnegie Mellon University pose, illumination, and expression (CMUPIE) and Yale B face databases under different illumination or facial expression conditions indicate that the proposed method outperforms other existing classical methods.Symmetry2016-10-25811Article10.3390/sym81101091092073-89942016-10-25doi: 10.3390/sym8110109Ting ChenXiangmo ZhaoLiang DaiLicheng ZhangJiarui Wang<![CDATA[Symmetry, Vol. 8, Pages 108: Planar Harmonic and Monogenic Polynomials of Type A]]>
http://www.mdpi.com/2073-8994/8/10/108
Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on R N . The Dunkl operators are denoted by T j for 1 ≤ j ≤ N , and the Laplacian Δ κ = ∑ j = 1 N T j 2 . This paper finds the homogeneous harmonic polynomials annihilated by all T j for j &gt; 2 . The structure constants with respect to the Gaussian and sphere inner products are computed. These harmonic polynomials are used to produce monogenic polynomials, those annihilated by a Dirac-type operator.Symmetry2016-10-21810Article10.3390/sym81001081082073-89942016-10-21doi: 10.3390/sym8100108Charles Dunkl<![CDATA[Symmetry, Vol. 8, Pages 107: Scenario-Based Digital Forensics Challenges in Cloud Computing]]>
http://www.mdpi.com/2073-8994/8/10/107
The aim of digital forensics is to extract information to answer the 5Ws (Why, When, Where, What, and Who) from the data extracted from the evidence. In order to achieve this, most digital forensic processes assume absolute control of digital evidence. However, in a cloud environment forensic investigation, this is not always possible. Additionally, the unique characteristics of cloud computing create new technical, legal and architectural challenges when conducting a forensic investigation. We propose a hypothetical scenario to uncover and explain the challenges forensic practitioners face during cloud investigations. Additionally, we also provide solutions to address the challenges. Our hypothetical case scenario has shown that, in the long run, better live forensic tools, development of new methods tailored for cloud investigations and new procedures and standards are indeed needed. Furthermore, we have come to the conclusion that forensic investigations biggest challenge is not technical but legal.Symmetry2016-10-20810Article10.3390/sym81001071072073-89942016-10-20doi: 10.3390/sym8100107Erik Miranda LopezSeo MoonJong Park<![CDATA[Symmetry, Vol. 8, Pages 106: Security Scheme Based on Parameter Hiding Technic for Mobile Communication in a Secure Cyber World]]>
http://www.mdpi.com/2073-8994/8/10/106
Long Term Evolution (LTE) and Long Term Evolution-Advanced (LTE-A) support a better data transmission service than 3G dose and are globally commercialized technologies in a cyber world that is essential for constructing a future mobile environment, since network traffics have exponentially increased as people have started to use more than just one mobile device. However, when User Equipment (UE) is executing initial attach processes to access LTE networks, there is a vulnerability in which identification parameters like International Mobile Subscriber Identity (IMSI) and Radio Network Temporary Identities (RNTI) are transmitted as plain texts. It can threat various services that are commercialized therewith in a cyber world. Therefore, a security scheme is proposed in this paper where identification parameters can be securely transmitted and hidden in four cases where initial attach occurs between UE and Mobility Management Entity (MME). The proposed security scheme not only supports encrypted transmission of identification parameters but also mutual authentication between Evolved Node B (eNB) and MME to make a secure cyber world. Additionally, performance analysis results using an OPNET simulator showed the satisfaction of the average delay rate that is specified in LTE standards.Symmetry2016-10-17810Article10.3390/sym81001061062073-89942016-10-17doi: 10.3390/sym8100106Jong ParkHyungjoo KimJungho Kang<![CDATA[Symmetry, Vol. 8, Pages 105: Testing Lorentz and CPT Invariance with Neutrinos]]>
http://www.mdpi.com/2073-8994/8/10/105
Neutrino experiments can be considered sensitive tools to test Lorentz and CPT invariance. Taking advantage of the great variety of neutrino experiments, including neutrino oscillations, weak decays, and astrophysical neutrinos, the generic experimental signatures of the breakdown of these fundamental symmetries in the neutrino sector are presented.Symmetry2016-10-11810Review10.3390/sym81001051052073-89942016-10-11doi: 10.3390/sym8100105Jorge Díaz