Symmetry
http://www.mdpi.com/journal/symmetry
Latest open access articles published in Symmetry at http://www.mdpi.com/journal/symmetry<![CDATA[Symmetry, Vol. 9, Pages 78: A Study on Immersion and VR Sickness in Walking Interaction for Immersive Virtual Reality Applications]]>
http://www.mdpi.com/2073-8994/9/5/78
This study analyzes walking interaction to enhance the immersion and minimize virtual reality (VR) sickness of users by conducting experiments. In this study, the walking interaction is composed of three steps using input devices with a simple structure that can be easily used by anyone. The first step consists of a gamepad control method, which is the most popular but has low presence. The second step consists of a hand-based walking control interface, which is mainly used for interaction in VR applications. The last step consists of a march-in-place detection simulator that interacts with the legs—the key body parts for walking. Four experiments were conducted to determine the degree of direct expression of intention by users in the course of walking interactions that can improve immersion, presence, and prevent VR sickness in VR applications. With regard to the experiments in this study, survey experiments were conducted for general users using the Wilcoxon test, a presence questionnaire, and simulator sickness questionnaire (SSQ). In addition, the technical performance of the VR scenes used in the experiment was analyzed. The experimental results showed that higher immersion was achieved when interactions that felt closer to real walking were provided in VR. Furthermore, it was found that even control methods with a simple structure could be used for walking interactions with minimal VR sickness. Finally, a satisfactory presence was found in VR if the user was able interact using his or her own legs.Symmetry2017-05-2295Article10.3390/sym9050078782073-89942017-05-22doi: 10.3390/sym9050078Jiwon LeeMingyu KimJinmo Kim<![CDATA[Symmetry, Vol. 9, Pages 77: Lateralization of the Avian Magnetic Compass: Analysis of Its Early Plasticity]]>
http://www.mdpi.com/2073-8994/9/5/77
In European Robins, Erithacus rubecula, the magnetic compass is lateralized in favor of the right eye/left hemisphere of the brain. This lateralization develops during the first winter and initially shows a great plasticity. During the first spring migration, it can be temporarily removed by covering the right eye. In the present paper, we used the migratory orientation of robins to analyze the circumstances under which the lateralization can be undone. Already a period of 1½ h being monocularly left-eyed before tests began proved sufficient to restore the ability to use the left eye for orientation, but this effect was rather short-lived, as lateralization recurred again within the next 1½ h. Interpretable magnetic information mediated by the left eye was necessary for removing the lateralization. In addition, monocularly, the left eye seeing robins could adjust to magnetic intensities outside the normal functional window, but this ability was not transferred to the “right-eye system”. Our results make it clear that asymmetry of magnetic compass perception is amenable to short-term changes, depending on lateralized stimulation. This could mean that the left hemispheric dominance for the analysis of magnetic compass information depends on lateralized interhemispheric interactions that in young birds can swiftly be altered by environmental effects.Symmetry2017-05-1995Article10.3390/sym9050077772073-89942017-05-19doi: 10.3390/sym9050077Dennis GehringOnur GüntürkünWolfgang WiltschkoRoswitha Wiltschko<![CDATA[Symmetry, Vol. 9, Pages 76: Asymmetry for Symmetry: Right-Hemispheric Superiority in Bi-Dimensional Symmetry Perception]]>
http://www.mdpi.com/2073-8994/9/5/76
A right-hemispheric superiority has been shown for spatial symmetry perception with mono-dimensional stimuli (e.g., bisected lines). Nevertheless, the cerebral imbalance for bi-dimensional stimuli is still controversial, and the aim of the present study is to investigate this issue. Healthy participants and a split-brain patient (D.D.C.) were tested in a divided visual field paradigm, in which a square shape was presented either in the left or right visual field and they were asked to judge whether a dot was placed exactly in the center of the square or off-center, by using the left/right hand in two separate sessions. The performance of healthy participants was better when the stimuli presented in the left visual field (LVF) were on-center rather than off-center. The performance of D.D.C. was higher than chance only when on-center stimuli were presented in the LVF in the left hand session. Only in this condition did his accuracy not differ with respect to that of the control group, whereas in all of the other conditions, it was lower than the controls’ accuracy. We conclude that the right-hemispheric advantage already shown for mono-dimensional stimuli can be extended also to bi-dimensional configurations, confirming the right-hemispheric superiority for spatial symmetry perception.Symmetry2017-05-1895Article10.3390/sym9050076762073-89942017-05-18doi: 10.3390/sym9050076Giulia PreteMara FabriNicoletta FoschiLuca Tommasi<![CDATA[Symmetry, Vol. 9, Pages 75: Neural Networks for Radar Waveform Recognition]]>
http://www.mdpi.com/2073-8994/9/5/75
For passive radar detection system, radar waveform recognition is an important research area. In this paper, we explore an automatic radar waveform recognition system to detect, track and locate the low probability of intercept (LPI) radars. The system can classify (but not identify) 12 kinds of signals, including binary phase shift keying (BPSK) (barker codes modulated), linear frequency modulation (LFM), Costas codes, Frank code, P1-P4 codesand T1-T4 codeswith a low signal-to-noise ratio (SNR). It is one of the most extensive classification systems in the open articles. A hybrid classifier is proposed, which includes two relatively independent subsidiary networks, convolutional neural network (CNN) and Elman neural network (ENN). We determine the parameters of the architecture to make networks more effectively. Specifically, we focus on how the networks are designed, what the best set of features for classification is and what the best classified strategy is. Especially, we propose several key features for the classifier based on Choi–Williams time-frequency distribution (CWD). Finally, the recognition system is simulated by experimental data. The experiments show the overall successful recognition ratio of 94.5% at an SNR of −2 dB.Symmetry2017-05-1795Article10.3390/sym9050075752073-89942017-05-17doi: 10.3390/sym9050075Ming ZhangMing DiaoLipeng GaoLutao Liu<![CDATA[Symmetry, Vol. 9, Pages 74: Coupling Form and Function: How the Oligomerisation Symmetry of the SAS-6 Protein Contributes to the Architecture of Centriole Organelles]]>
http://www.mdpi.com/2073-8994/9/5/74
Centrioles make up the centrosome and basal bodies in animals and as such play important roles in cell division, signalling and motility. They possess characteristic 9-fold radial symmetry strongly influenced by the protein SAS-6. SAS-6 is essential for canonical centriole assembly as it forms the central core of the organelle, which is then surrounded by microtubules. SAS-6 self-assembles into an oligomer with elongated spokes that emanate towards the outer microtubule wall; in this manner, the symmetry of the SAS-6 oligomer influences centriole architecture and symmetry. Here, we summarise the form and symmetry of SAS-6 oligomers inferred from crystal structures and directly observed in vitro. We discuss how the strict 9-fold symmetry of centrioles may emerge, and how different forms of SAS-6 oligomers may be accommodated in the organelle architecture.Symmetry2017-05-1695Review10.3390/sym9050074742073-89942017-05-16doi: 10.3390/sym9050074Jodie FordPhillip StansfeldIoannis Vakonakis<![CDATA[Symmetry, Vol. 9, Pages 73: Fair Dynamic Spectrum Allocation Using Modified Game Theory for Resource-Constrained Cognitive Wireless Sensor Networks]]>
http://www.mdpi.com/2073-8994/9/5/73
This paper considers the deployment of a cognitive radio scheme in wireless sensor networks to achieve (1) fair spectrum allocation, (2) maximum spectrum utilization, and (3) priority-based sensor transmissions, while (4) avoiding unnecessary spectrum handover (or handoff). This problem is modelled as a bi-objective optimization problem. We apply modified game theory and a cooperative approach to identify an approximate optimal solution in reasonable time. We perform a series of numerical experiments to show that our scheme achieves fair spectrum allocation (in terms of proportional fairness) while observing transmission priorities and minimizing unnecessary spectrum handover.Symmetry2017-05-1695Article10.3390/sym9050073732073-89942017-05-16doi: 10.3390/sym9050073Sang-Seon ByunJoon-Min Gil<![CDATA[Symmetry, Vol. 9, Pages 72: Androgen Levels and Body Size Are Associated with Directional as Well as Fluctuating Asymmetry Patterns in Adult !Kung San and Kavango Males from Northern Namibia]]>
http://www.mdpi.com/2073-8994/9/5/72
Fluctuating asymmetry is mainly interpreted as an indicator of developmental instability, while directional asymmetry of the upper limbs is associated with handedness. The association patterns between adult androgen levels and fluctuating as well directional asymmetry patterns are still unclear. In the present study, the association between adult androgen levels, body size and directional as well as fluctuating asymmetry pattern was tested among !Kung San and Kavango males from northern Namibia. Serum concentrations of testosterone (Tser) and 5α-dihydrotestosterone (DHT) as well as salivary testosterone (Tsal) concentrations were obtained from 114 !Kung San and 136 Kavango men aged 18–40 years. Fluctuating and directional asymmetry were determined from eight paired traits. Signed and unsigned asymmetry, composite fluctuating and directional asymmetry were calculated. !Kung San males surpassed their Kavango counterparts in the directional asymmetry but also in composite directional asymmetry (CDA) significantly. Among !Kung San males, DHT correlated significantly negatively with parameters of fluctuating asymmetry as well as with parameters of directional asymmetry. Free testosterone of the saliva correlated significantly negatively with asymmetry of hand length. Among Kavango males, DHT is negatively associated with foot breadth asymmetry, but positively associated with wrist asymmetry. Although the correlations between asymmetry patterns and androgen levels are weak, it can be concluded that among !Kung San males adult androgen levels are negatively associated with a high quality phenotype.Symmetry2017-05-1595Article10.3390/sym9050072722073-89942017-05-15doi: 10.3390/sym9050072Sylvia KirchengastKerrin Christiansen<![CDATA[Symmetry, Vol. 9, Pages 71: Lateralized Functions in the Dog Brain]]>
http://www.mdpi.com/2073-8994/9/5/71
Understanding the complementary specialisation of the canine brain has been the subject of increasing scientific study over the last 10 years, chiefly due to the impact of cerebral lateralization on dog behaviour. In particular, behavioural asymmetries, which directly reflect different activation of the two sides of the dog brain, have been reported at different functional levels, including motor and sensory. The goal of this review is not only to provide a clear scenario of the experiments carried out over the last decade but also to highlight the relationships between dogs’ lateralization, cognitive style and behavioural reactivity, which represent crucial aspect relevant for canine welfare.Symmetry2017-05-1395Review10.3390/sym9050071712073-89942017-05-13doi: 10.3390/sym9050071Marcello SiniscalchiSerenella d’IngeoAngelo Quaranta<![CDATA[Symmetry, Vol. 9, Pages 70: Urban Traffic Congestion Evaluation Based on Kernel the Semi-Supervised Extreme Learning Machine]]>
http://www.mdpi.com/2073-8994/9/5/70
There is always an asymmetric phenomenon between traffic data quantity and unit information content. Labeled data is more effective but scarce, while unlabeled data is large but weaker in sample information. In an urban transportation assessment system, semi-supervised extreme learning machine (SSELM) can unite manual observed data and extensively collected data cooperatively to build connection between congestion condition and road information. In our method, semi-supervised learning can integrate both small-scale labeled data and large-scale unlabeled data, so that they can play their respective advantages, while the ELM can process large scale data at high speed. Optimized by kernel function, Kernel-SSELM can achieve higher classification accuracy and robustness than original SSELM. Both the experiment and the real-time application show that the evaluation system can precisely reflect the traffic condition.Symmetry2017-05-1095Article10.3390/sym9050070702073-89942017-05-10doi: 10.3390/sym9050070Qing ShenXiaojuan BanChong Guo<![CDATA[Symmetry, Vol. 9, Pages 68: Analysis of a Similarity Measure for Non-Overlapped Data]]>
http://www.mdpi.com/2073-8994/9/5/68
A similarity measure is a measure evaluating the degree of similarity between two fuzzy data sets and has become an essential tool in many applications including data mining, pattern recognition, and clustering. In this paper, we propose a similarity measure capable of handling non-overlapped data as well as overlapped data and analyze its characteristics on data distributions. We first design the similarity measure based on a distance measure and apply it to overlapped data distributions. From the calculations for example data distributions, we find that, though the similarity calculation is effective, the designed similarity measure cannot distinguish two non-overlapped data distributions, thus resulting in the same value for both data sets. To obtain discriminative similarity values for non-overlapped data, we consider two approaches. The first one is to use a conventional similarity measure after preprocessing non-overlapped data. The second one is to take into account neighbor data information in designing the similarity measure, where we consider the relation to specific data and residual data information. Two artificial patterns of non-overlapped data are analyzed in an illustrative example. The calculation results demonstrate that the proposed similarity measures can discriminate non-overlapped data.Symmetry2017-05-0995Article10.3390/sym9050068682073-89942017-05-09doi: 10.3390/sym9050068Sanghyuk LeeJaehoon ChaNipon Theera-UmponKyeong Kim<![CDATA[Symmetry, Vol. 9, Pages 69: Improvement of DS Evidence Theory for Multi-Sensor Conflicting Information]]>
http://www.mdpi.com/2073-8994/9/5/69
A new DS (Dempster-Shafer) combination method is presented in this paper. As data detected by a single sensor are characterized by not only fuzziness, but also partial reliability, the development of multi-sensor information fusion becomes extremely indispensable. The DS evidence theory is an effective means of information fusion, which can not only deal with the uncertainty and inconsistency of multi-sensor data, but also handle the inevitably ambiguity and instability under noise or possible interference. However, the application of DS evidence theory has some limitations when multi-sensor data are conflicting. To address this issue, the DS evidence theory is modified in this paper. Adopting the idea of cluster analysis, we firstly introduce the Lance distance function and spectral angle cosine function to revise original evidence separately before the combination of evidence. Then, based on the modifications of original evidence, an improved conflict redistribution strategy is ulteriorly raised to fuse multi-sensor information. Finally, the numerical simulation analyses demonstrate that the improvement of the DS evidence theory available in this paper overcomes the limitations of conventional DS evidence theory, and realizes more reliable fusion with multi-sensor conflicting information compared to the existing methods.Symmetry2017-05-0995Article10.3390/sym9050069692073-89942017-05-09doi: 10.3390/sym9050069Fang YeJie ChenYibing Li<![CDATA[Symmetry, Vol. 9, Pages 67: Redundant Symmetry Influences Perceptual Grouping (as Measured by Rotational Linkage)]]>
http://www.mdpi.com/2073-8994/9/5/67
Symmetry detection has long been a major focus of perception research. However, although symmetry is often cited as a “grouping principle”, the effect of symmetry on grouping, an important form of perceptual organization, has been little measured. In past research, we found little spatio-temporal grouping for oblique lines symmetric around a horizontal axis during ambiguous rotary motion in depth. Grouping was measured by the degree to which the ambiguous motion direction was resolved for two elements in common (rotational linkage). We hypothesized that symmetry-based grouping would be stronger if symmetry was redundant i.e., carried by elements of greater complexity. Using the rotational linkage measure, we compared grouping for horizontally symmetric simple oblique lines and for lines composed of multiple conjoined orientations and found greater grouping for the more complex symmetric lines. A control experiment ruled out possible confounding factors and also showed a grouping effect of vertically aligned endpoints. We attribute the stronger grouping effect of redundant symmetry to the fact that it has a lower probability than does simple symmetry of arising from an accidental environmental arrangement.Symmetry2017-05-0995Article10.3390/sym9050067672073-89942017-05-09doi: 10.3390/sym9050067Barbara Gillam<![CDATA[Symmetry, Vol. 9, Pages 66: The Genetics of Asymmetry: Whole Exome Sequencing in a Consanguineous Turkish Family with an Overrepresentation of Left-Handedness]]>
http://www.mdpi.com/2073-8994/9/5/66
Handedness is the most pronounced behavioral asymmetry in humans. Genome-wide association studies have largely failed to identify genetic loci associated with phenotypic variance in handedness, supporting the idea that the trait is determined by a multitude of small, possibly interacting genetic and non-genetic influences. However, these studies typically are not capable of detecting influences of rare mutations on handedness. Here, we used whole exome sequencing in a Turkish family with history of consanguinity and overrepresentation of left-handedness and performed quantitative trait analysis with handedness lateralization quotient as a phenotype. While rare variants on different loci showed significant association with the phenotype, none was functionally relevant for handedness. This finding was further confirmed by gene ontology group analysis. Taken together, our results add further evidence to the suggestion that there is no major gene or mutation that causes left-handedness.Symmetry2017-05-0195Article10.3390/sym9050066662073-89942017-05-01doi: 10.3390/sym9050066Sebastian OcklenburgCeren BarutçuoğluAdile Öniz ÖzgörenMurat ÖzgörenEsra ErdalDirk MoserJudith SchmitzRobert KumstaOnur Güntürkün<![CDATA[Symmetry, Vol. 9, Pages 65: Adaptive Job Load Balancing Scheme on Mobile Cloud Computing with Collaborative Architecture]]>
http://www.mdpi.com/2073-8994/9/5/65
The adaptive mobile resource offloading (AMRO) proposed in this paper is a load balancing scheme for processing large-scale jobs using mobile resources without a cloud server. AMRO is applied in a mobile cloud computing environment based on collaborative architecture. A load balancing scheme with efficient job division and optimized job allocation is needed because the resources for mobile devices will not always be provided consistently in this environment. Therefore, a job load balancing scheme is proposed that considers personal usage patterns and the dynamic resource state of the mobile devices. The delay time for computer job processing is minimized through dynamic job reallocation and adaptive job allocation in the disability state that occurs due to unexpected problems and to excessive job allocations by the mobile devices providing the resources for the mobile cloud computing. In order to validate the proposed load balancing scheme, an adaptive mobile resource management without cloud server (AMRM) protocol was designed and implemented, and the improved processing speed was verified in comparison with the existing offloading method. The improved job processing speed in the mobile cloud environment is demonstrated through job allocation based on AMRM and by taking into consideration the idle resources of the mobile devices. Furthermore, the resource waste of the mobile devices is minimized through adaptive offloading and consideration of both insufficient and idle resources.Symmetry2017-04-2995Article10.3390/sym9050065652073-89942017-04-29doi: 10.3390/sym9050065Byoungwook KimHwirim ByunYoon-A HeoYoung-Sik Jeong<![CDATA[Symmetry, Vol. 9, Pages 64: Binocular 3D Object Recovery Using a Symmetry Prior]]>
http://www.mdpi.com/2073-8994/9/5/64
We present a new algorithm for 3D shape reconstruction from stereo image pairs that uses mirror symmetry as a biologically inspired prior. 3D reconstruction requires some form of prior because it is an ill-posed inverse problem. Psychophysical research shows that mirror-symmetry is a key prior for 3D shape perception in humans, suggesting that a general purpose solution to this problem will have many applications. An approach is developed for finding objects that fit a given shape definition. The algorithm is developed for shapes with two orthogonal planes of symmetry, thus allowing for straightforward recovery of occluded portions of the objects. Two simulations were run to test: (1) the accuracy of 3D recovery, and (2) the ability of the algorithm to find the object in the presence of noise. We then tested the algorithm on the Children’s Furniture Corpus, a corpus of stereo image pairs of mirror symmetric furniture objects. Runtimes and 3D reconstruction errors are reported and failure modes described.Symmetry2017-04-2895Article10.3390/sym9050064642073-89942017-04-28doi: 10.3390/sym9050064Aaron MichauxVikrant KumarVijai JayadevanEdward DelpZygmunt Pizlo<![CDATA[Symmetry, Vol. 9, Pages 63: On the Charge Density Refinement of Odd-Order Multipoles Invariant under Crystal Point Group Symmetry]]>
http://www.mdpi.com/2073-8994/9/5/63
Charge density studies utilise a multipolar expansion of the atomic density (and the associated atomic scattering factor) in order to model asphericity. Contributions of the individual multipoles to the atomic density are then refined as multipole population coefficients. Refinement of these coefficients pertaining to odd-order multipoles that are invariant under the crystal point-group symmetry is often problematic, with ill-defined values and correlations plaguing the convergence to a good model. These difficulties have been discussed in generic terms in the literature, but never explicitly analysed in detail. In this communication, we show that the charge density multipolar atomic scattering factor can be partitioned in three contributions that differ in their behaviour under the point group symmetry of the crystal. This partitioning rationalises and predicts the conditions that give rise to ill-conditioning of the charge density refinement of these multipoles.Symmetry2017-04-2695Article10.3390/sym9050063632073-89942017-04-26doi: 10.3390/sym9050063Pietro RoversiRiccardo Destro<![CDATA[Symmetry, Vol. 9, Pages 62: Analysis of Clustering Evaluation Considering Features of Item Response Data Using Data Mining Technique for Setting Cut-Off Scores]]>
http://www.mdpi.com/2073-8994/9/5/62
The setting of standards is a critical process in educational evaluation, but it is time-consuming and expensive because it is generally conducted by an education experts group. The purpose of this paper is to find a suitable cluster validity index that considers the futures of item response data for setting cut-off scores. In this study, nine representative cluster validity indexes were used to evaluate the clustering results. Cohen’s kappa coefficient is used to check the conformity between a set cut-off score using four clustering techniques and a cut-off score set by experts. We compared the cut-off scores by each cluster validity index and by a group of experts. The experimental results show that the entropy-based method considers the features of item response data, so it has a realistic possibility of applying a clustering evaluation method to the setting of standards in criterion referenced evaluation.Symmetry2017-04-2595Article10.3390/sym9050062622073-89942017-04-25doi: 10.3390/sym9050062Byoungwook KimJaMee KimGangman Yi<![CDATA[Symmetry, Vol. 9, Pages 61: Reversible Data-Hiding Systems with Modified Fluctuation Functions and Reed-Solomon Codes for Encrypted Image Recovery]]>
http://www.mdpi.com/2073-8994/9/5/61
In this paper, reversible data-hiding (RDH) systems with modified fluctuation functions and rate-matched Reed–Solomon (RS) codes are proposed to enhance the data recovery from encrypted images. The modified fluctuation functions are used for estimating embedded codeword bits from the correlation of pixels. Instead of direct data-bit embedding, codeword bits of RS codes are embedded by a data-hider. With the help of the error-correcting capability of RS codes, the encrypted message can be recovered from the weak correlation of adjacent pixels in the image. In the experimental results, bit error rate (BER) and peak signal to noise ratio (PSNR) performances of the proposed system are better than those of referenced data-hiding systems for three images. The proposed schemes based on the modified fluctuation function or rate-matched codes can be applied to various RDH systems with better data transmission and image recovery performance.Symmetry2017-04-2595Article10.3390/sym9050061612073-89942017-04-25doi: 10.3390/sym9050061Sunghwan Kim<![CDATA[Symmetry, Vol. 9, Pages 60: A Fault Feature Extraction Method for Motor Bearing and Transmission Analysis]]>
http://www.mdpi.com/2073-8994/9/5/60
Roller bearings are the most widely used and easily damaged mechanical parts in rotating machinery. Their running state directly affects rotating machinery performance. Empirical mode decomposition (EMD) easily occurs illusive component and mode mixing problem. From the view of feature extraction, a new feature extraction method based on integrating ensemble empirical mode decomposition (EEMD), the correlation coefficient method, and Hilbert transform is proposed to extract fault features and identify fault states for motor bearings in this paper. In the proposed feature extraction method, the EEMD is used to decompose the vibration signal into a series of intrinsic mode functions (IMFs) with different frequency components. Then the correlation coefficient method is used to select the IMF components with the largest correlation coefficient, which are carried out with the Hilbert transform. The obtained corresponding envelope spectra are analyzed to extract the fault feature frequency and identify the fault state by comparing with the theoretical value. Finally, the fault signal transmission performance of vibration signals of the bearing inner ring and outer ring at the drive end and fan end are deeply studied. The experimental results show that the proposed feature extraction method can effectively eliminate the influence of the mode mixing and extract the fault feature frequency, and the energy of the vibration signal in the bearing outer ring at the fan end is lost during the transmission of the vibration signal. It is an effective method to extract the fault feature of the bearing from the noise with interference.Symmetry2017-04-2595Article10.3390/sym9050060602073-89942017-04-25doi: 10.3390/sym9050060Wu DengHuimin ZhaoXinhua YangChang Dong<![CDATA[Symmetry, Vol. 9, Pages 59: Collaborative CAD Synchronization Based on a Symmetric and Consistent Modeling Procedure]]>
http://www.mdpi.com/2073-8994/9/4/59
One basic issue with collaborative computer aided design (Co-CAD) is how to maintain valid and consistent modeling results across all design sites. Moreover, modeling history is important in parametric CAD modeling. Therefore, different from a typical co-editing approach, this paper proposes a novel method for Co-CAD synchronization, in which all Co-CAD sites maintain symmetric and consistent operating procedures. Consequently, the consistency of both modeling results and history can be achieved. In order to generate a valid, unique, and symmetric queue among collaborative sites, a set of correlated mechanisms is presented in this paper. Firstly, the causal relationship of operations is maintained. Secondly, the operation queue is reconstructed for partial concurrency operation, and the concurrent operation can be retrieved. Thirdly, a symmetric, concurrent operation control strategy is proposed to determine the order of operations and resolve possible conflicts. Compared with existing Co-CAD consistency methods, the proposed method is convenient and flexible in supporting collaborative design. The experiment performed based on the collaborative modeling procedure demonstrates the correctness and applicability of this work.Symmetry2017-04-2394Article10.3390/sym9040059592073-89942017-04-23doi: 10.3390/sym9040059Yiqi WuFazhi HeSoonhung Han<![CDATA[Symmetry, Vol. 9, Pages 58: A Fast K-prototypes Algorithm Using Partial Distance Computation]]>
http://www.mdpi.com/2073-8994/9/4/58
The k-means is one of the most popular and widely used clustering algorithm; however, it is limited to numerical data only. The k-prototypes algorithm is an algorithm famous for dealing with both numerical and categorical data. However, there have been no studies to accelerate it. In this paper, we propose a new, fast k-prototypes algorithm that provides the same answers as those of the original k-prototypes algorithm. The proposed algorithm avoids distance computations using partial distance computation. Our k-prototypes algorithm finds minimum distance without distance computations of all attributes between an object and a cluster center, which allows it to reduce time complexity. A partial distance computation uses a fact that a value of the maximum difference between two categorical attributes is 1 during distance computations. If data objects have m categorical attributes, the maximum difference of categorical attributes between an object and a cluster center is m. Our algorithm first computes distance with numerical attributes only. If a difference of the minimum distance and the second smallest with numerical attributes is higher than m, we can find the minimum distance between an object and a cluster center without distance computations of categorical attributes. The experimental results show that the computational performance of the proposed k-prototypes algorithm is superior to the original k-prototypes algorithm in our dataset.Symmetry2017-04-2194Article10.3390/sym9040058582073-89942017-04-21doi: 10.3390/sym9040058Byoungwook Kim<![CDATA[Symmetry, Vol. 9, Pages 57: A Matter of Degree: Strength of Brain Asymmetry and Behaviour]]>
http://www.mdpi.com/2073-8994/9/4/57
Research on a growing number of vertebrate species has shown that the left and right sides of the brain process information in different ways and that lateralized brain function is expressed in both specific and broad aspects of behaviour. This paper reviews the available evidence relating strength of lateralization to behavioural/cognitive performance. It begins by considering the relationship between limb preference and behaviour in humans and primates from the perspectives of direction and strength of lateralization. In birds, eye preference is used as a reflection of brain asymmetry and the strength of this asymmetry is associated with behaviour important for survival (e.g., visual discrimination of food from non-food and performance of two tasks in parallel). The same applies to studies on aquatic species, mainly fish but also tadpoles, in which strength of lateralization has been assessed as eye preferences or turning biases. Overall, the empirical evidence across vertebrate species points to the conclusion that stronger lateralization is advantageous in a wide range of contexts. Brief discussion of interhemispheric communication follows together with discussion of experiments that examined the effects of sectioning pathways connecting the left and right sides of the brain, or of preventing the development of these left-right connections. The conclusion reached is that degree of functional lateralization affects behaviour in quite similar ways across vertebrate species. Although the direction of lateralization is also important, in many situations strength of lateralization matters more. Finally, possible interactions between asymmetry in different sensory modalities is considered.Symmetry2017-04-1894Review10.3390/sym9040057572073-89942017-04-18doi: 10.3390/sym9040057Lesley J. Rogers<![CDATA[Symmetry, Vol. 9, Pages 55: 3D Reconstruction Framework for Multiple Remote Robots on Cloud System]]>
http://www.mdpi.com/2073-8994/9/4/55
This paper proposes a cloud-based framework that optimizes the three-dimensional (3D) reconstruction of multiple types of sensor data captured from multiple remote robots. A working environment using multiple remote robots requires massive amounts of data processing in real-time, which cannot be achieved using a single computer. In the proposed framework, reconstruction is carried out in cloud-based servers via distributed data processing. Consequently, users do not need to consider computing resources even when utilizing multiple remote robots. The sensors’ bulk data are transferred to a master server that divides the data and allocates the processing to a set of slave servers. Thus, the segmentation and reconstruction tasks are implemented in the slave servers. The reconstructed 3D space is created by fusing all the results in a visualization server, and the results are saved in a database that users can access and visualize in real-time. The results of the experiments conducted verify that the proposed system is capable of providing real-time 3D scenes of the surroundings of remote robots.Symmetry2017-04-1494Article10.3390/sym9040055552073-89942017-04-14doi: 10.3390/sym9040055Phuong ChuSeoungjae ChoSimon FongYong ParkKyungeun Cho<![CDATA[Symmetry, Vol. 9, Pages 56: Interactive Blow and Burst of Giant Soap Bubbles]]>
http://www.mdpi.com/2073-8994/9/4/56
Previous studies on virtual soap bubbles mainly focused on methods for visualizing the physical and geometrical properties of soap bubbles and paid little attention to the possible ways to enhance the interaction between the simulation and the user. In this paper, a user interaction-based giant soap bubble simulation system is proposed in which the free-form shape, size, and position of giant soap bubbles are determined by the user’s hand motions. Our method improves the controllability of soap bubble simulation by correcting the jerky hand trajectory and hand velocity to a smooth and gradual path. Our air flow transfer algorithm can produce detailed deformation and standing wave for soap film in real time. Our novel soap film bursting algorithm represents the process of the bursting phenomenon of soap-film and giant soap bubbles in a unified framework. The results of our experiment demonstrate that the system allows the user to experience the giant soap bubble blowing and bursting process in a virtual environment.Symmetry2017-04-1494Article10.3390/sym9040056562073-89942017-04-14doi: 10.3390/sym9040056Namjung KimKyoungju Park<![CDATA[Symmetry, Vol. 9, Pages 54: An Efficient VQ Codebook Search Algorithm Applied to AMR-WB Speech Coding]]>
http://www.mdpi.com/2073-8994/9/4/54
The adaptive multi-rate wideband (AMR-WB) speech codec is widely used in modern mobile communication systems for high speech quality in handheld devices. Nonetheless, a major disadvantage is that vector quantization (VQ) of immittance spectral frequency (ISF) coefficients takes a considerable computational load in the AMR-WB coding. Accordingly, a binary search space-structured VQ (BSS-VQ) algorithm is adopted to efficiently reduce the complexity of ISF quantization in AMR-WB. This search algorithm is done through a fast locating technique combined with lookup tables, such that an input vector is efficiently assigned to a subspace where relatively few codeword searches are required to be executed. In terms of overall search performance, this work is experimentally validated as a superior search algorithm relative to a multiple triangular inequality elimination (MTIE), a TIE with dynamic and intersection mechanisms (DI-TIE), and an equal-average equal-variance equal-norm nearest neighbor search (EEENNS) approach. With a full search algorithm as a benchmark for overall search load comparison, this work provides an 87% search load reduction at a threshold of quantization accuracy of 0.96, a figure far beyond 55% in the MTIE, 76% in the EEENNS approach, and 83% in the DI-TIE approach.Symmetry2017-04-1294Article10.3390/sym9040054542073-89942017-04-12doi: 10.3390/sym9040054Cheng-Yu Yeh<![CDATA[Symmetry, Vol. 9, Pages 53: Ear Detection under Uncontrolled Conditions with Multiple Scale Faster Region-Based Convolutional Neural Networks]]>
http://www.mdpi.com/2073-8994/9/4/53
Ear detection is an important step in ear recognition approaches. Most existing ear detection techniques are based on manually designing features or shallow learning algorithms. However, researchers found that the pose variation, occlusion, and imaging conditions provide a great challenge to the traditional ear detection methods under uncontrolled conditions. This paper proposes an efficient technique involving Multiple Scale Faster Region-based Convolutional Neural Networks (Faster R-CNN) to detect ears from 2D profile images in natural images automatically. Firstly, three regions of different scales are detected to infer the information about the ear location context within the image. Then an ear region filtering approach is proposed to extract the correct ear region and eliminate the false positives automatically. In an experiment with a test set of 200 web images (with variable photographic conditions), 98% of ears were accurately detected. Experiments were likewise conducted on the Collection J2 of University of Notre Dame Biometrics Database (UND-J2) and University of Beira Interior Ear dataset (UBEAR), which contain large occlusion, scale, and pose variations. Detection rates of 100% and 98.22%, respectively, demonstrate the effectiveness of the proposed approach.Symmetry2017-04-1094Article10.3390/sym9040053532073-89942017-04-10doi: 10.3390/sym9040053Yi ZhangZhichun Mu<![CDATA[Symmetry, Vol. 9, Pages 52: Dual Hesitant Fuzzy Probability]]>
http://www.mdpi.com/2073-8994/9/4/52
Intuitionistic fuzzy probabilities are an extension of the concept of probabilities with application in several practical problem solving tasks. The former are probabilities represented through intuitionistic fuzzy numbers, to indicate the uncertainty of the membership and nonmembership degrees in the value assigned to probabilities. Moreover, a dual hesitant fuzzy set (DHFS) is an extension of an intuitionistic fuzzy set, and its membership degrees and nonmembership degrees are represented by two sets of possible values; this new theory of fuzzy sets is known today as dual hesitant fuzzy set theory. This work will extend the notion of dual hesitant fuzzy probabilities by representing probabilities through the dual hesitant fuzzy numbers, in the sense of Zhu et al., instead of intuitionistic fuzzy numbers. We also give the concept of dual hesitant fuzzy probability, based on which we provide some main results including the properties of dual hesitant fuzzy probability, dual hesitant fuzzy conditional probability, and dual hesitant fuzzy total probability.Symmetry2017-04-0794Article10.3390/sym9040052522073-89942017-04-07doi: 10.3390/sym9040052Jianjian ChenXianjiu Huang<![CDATA[Symmetry, Vol. 9, Pages 47: Correlation Coefficients of Extended Hesitant Fuzzy Sets and Their Applications to Decision Making]]>
http://www.mdpi.com/2073-8994/9/4/47
Extended hesitant fuzzy sets (EHFSs), which allow the membership degree of an element to a set represented by several possible value-groups, can be considered as a powerful tool to express uncertain information in the process of group decision making. Therefore, we derive some correlation coefficients between EHFSs, which contain two cases, the correlation coefficients taking into account the length of extended hesitant fuzzy elements (EHFEs) and the correlation coefficients without taking into account the length of EHFEs, as a new extension of existing correlation coefficients for hesitant fuzzy sets (HFSs) and apply them to decision making under extended hesitant fuzzy environments. A real-world example based on the energy policy problem is employed to illustrate the actual need for dealing with the difference of evaluation information provided by different experts without information loss in decision making processes.Symmetry2017-03-2994Article10.3390/sym9040047472073-89942017-03-29doi: 10.3390/sym9040047Na LuLipin Liang<![CDATA[Symmetry, Vol. 9, Pages 50: Enhanced Joint and Separable Reversible Data Hiding in Encrypted Images with High Payload]]>
http://www.mdpi.com/2073-8994/9/4/50
Recently, much attention has been paid to reversible data hiding (RDH) in encrypted images, since it preserves the data that the original image can be perfectly recovered after data extraction while protecting the confidentiality of image content. In this paper, we propose joint and separable RDH techniques using an improved embedding pattern and a new measurement function in encrypted images with a high payload. The first problem in recent joint data hiding is that the encrypted image is divided into blocks, and the spatial correlation in the block cannot fully reflect the smoothness of a natural image. The second problem is that half embedding is used to embed data and the prediction error is exploited to calculate the smoothness, which also fails to give good performance. To solve these problems, we divide the encrypted image into four sets, instead of blocks; the actual value of pixels is considered, rather than an estimated value, and the absolute difference between neighboring pixels is used in preference to prediction error to calculate the smoothness. Therefore, it is possible to use spatial correlation of the natural image perfectly. The experimental results show that the proposed joint and separable methods offer better performance over other works.Symmetry2017-03-2894Article10.3390/sym9040050502073-89942017-03-28doi: 10.3390/sym9040050Fatema-Tuz-Zohra KhanamSunghwan Kim<![CDATA[Symmetry, Vol. 9, Pages 51: Developmental Origins of Limb Developmental Instability in Human Fetuses: Many Abnormalities Make the Difference]]>
http://www.mdpi.com/2073-8994/9/4/51
Fluctuating asymmetry (FA) is the small random deviation from perfect symmetry in bilateral traits and is often used to assess developmental instability (DI) experienced by organisms. In this study, with a unique dataset of 1389 deceased human fetuses, we investigated the relationship between abnormal development and human limb FA in different ways, using a more fundamental approach than usually done. We studied whether there is an underlying developmental basis of DI, as measured by FA, by investigating, first, whether limb FA can be attributed to developmental abnormalities associated with specific organ systems, germ layers or patterning processes, and second, whether limb FA increases with increasing number of developmental abnormalities either gradually, or in a threshold-like fashion. Limb FA was found to increase in fetuses with cardiovascular and nervous system abnormalities. Fetuses with ectoderm-derived abnormalities were also found to have significantly higher limb FA, but no other germ layers were found to be associated. We found no significant correlation between specific developmental processes, such as neural crest development, segmentation, midline and left-right patterning and limb FA. Although only some congenital abnormalities were correlated with limb FA, our results do suggest that limb FA increases when an increasing number of organ systems, germ layers or developmental pathways are disrupted. Therefore, we conclude that limb FA is mainly a good indicator for DI in the case of particularly severe perturbations of development and that FA does not reflect the subtler deviations from developmental stability.Symmetry2017-03-2894Article10.3390/sym9040051512073-89942017-03-28doi: 10.3390/sym9040051Clara M. A. ten BroekJessica BotsMarianna BugianiFrietson GalisStefan van Dongen<![CDATA[Symmetry, Vol. 9, Pages 49: Methods and Tools of Digital Triage in Forensic Context: Survey and Future Directions]]>
http://www.mdpi.com/2073-8994/9/4/49
Digital triage is the first investigative step of the forensic examination. The digital triage comes in two forms, live triage and post-mortem triage. The primary goal of the live triage is a rapid extraction of an intelligence from the potential sources. The live triage raises legitimate concerns. The post-mortem triage is conducted in the laboratory and its main goal is ranking of the seized devices for the possible existence of the relevant evidence. The digital triage has the potential to quickly identify items that are likely to contain the evidential data. Therefore, it is a solution to the problem of case backlogs. However, existing methods and tools of the digital triage have limitations, especially, in the forensic context. Nevertheless, we have no better solution for the time being. In this paper, we critically review published research works and the proposed solutions for digital triage. The review is divided into four sections as follows: live triage, post-mortem triage, mobile device triage, and triage tools. We conclude that many challenges are awaiting for the developers in creating methods and tools of digital triage in order to keep pace with the development of new technologies.Symmetry2017-03-2894Review10.3390/sym9040049492073-89942017-03-28doi: 10.3390/sym9040049Vacius JusasDarius BirvinskasElvar Gahramanov<![CDATA[Symmetry, Vol. 9, Pages 48: Nested One-to-One Symmetric Classification Method on a Fuzzy SVM for Moving Vehicles]]>
http://www.mdpi.com/2073-8994/9/4/48
As a multi-classification problem, classification of moving vehicles has been studied by different statistical methods. These practical applications have various requirements, efficiencies, and performance, such as the size of training sample sets, convergence rate, and inseparable or ambiguous classification issues. With a reduction in its training time,the one-to-many support vector machine (SVM) method has an advantage over the standard SVM method by directly converting the binary classification problem into two multi-classification problems with short time and fast speed. When the number of training samples of a certain type is far less than the total number of samples, the accuracy of training, however, will be significantlydecreased,leading to theproblem of inseparable area. In this paper, the proposed nested one-to-one symmetric classification method on a fuzzy SVM symmetrically transforms the C multi-classification problems into the C(C-1)/2 binary classification problems with C(C-1)/2 classifiers, and solves the problem of inseparable area. According to the best combination factor of kernel function (γ, C) for the radial basis function (RBF) in the comparative experiments of training sample sets among the different algorithms, and the experimental results of many different training sample sets and test samples, the nested one-to-one symmetric classification algorithm on a fuzzy SVM for moving vehicle is able to obtain the best accuracy of recognition.Symmetry2017-03-2694Article10.3390/sym9040048482073-89942017-03-26doi: 10.3390/sym9040048Guofeng QinXiaodi HuangYiling Chen<![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 hypergraphs endowed with a choice function on edges. We are interested, for instance, in minimal numbers of edges for associated domination graphs. Theorems regarding the existence of balanced (zero-edge) domination graphs are presented. Several open questions are posed.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