Symmetry, Volume 8, Issue 11 (November 2016) – 29 articles

Efficient utilization of human resources is an important force for the sustainable development of society and the economy. Against the backdrop of the development of economic globalization, the Chinese Government is presently implementing the strategy of “Strengthening the Nation with Talent” to assist the exploitation and management of human resources. Overseas talents have recently become an important resource. How to scientifically evaluate and classify overseas talents has become an important research topic, and it is necessary to seek a systematic decision aid. This paper introduces a novel methodology to evaluate and classify overseas talents in China under the intuitionistic relations environment. Firstly, we determine the weighted values of decision makers and criteria through defining geometry consistency. Secondly, we construct a non-linear Best-Worst-Method (BWM) model with intuitionistic preference relations. A highlight of this BWM model for intuitionistic relations is taking both positive and negative aspects into consideration, which is different from the original BWM. Finally, the proposed methodology is applied to an illustrative example of overseas talent evaluation, indicating the simultaneous efficiency and practicability of the method. Full article

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. Full article

The concept of developmental instability (DI) is a well-known indicator of environmental and genetic stress and is often investigated using various indices such as fluctuating asymmetry, directional asymmetry, antisymmetry and phenotypic variance. Investigations dealing with DI are using morphometric traits. The aim of this investigation is to present the novel concept of behavioural instability in which the trait measured is a behavioural trait. We apply the conventional indices used for the estimation of developmental instability on directional movement—clockwise (CW) and counter-clockwise (CCW) movement of 19 highly inbred lines of Drosophila melanogaster tested in a circular arena. We show that it is possible to quantify behavioural instability using the indices traditionally used to investigate DI. Results revealed several significant differences among lines, depending on the index utilized. The perspectives of utilizing the concept in biological research such as toxicology, evolutionary and stress biology are discussed. Full article

Topological indices and polynomials are predicting properties like boiling points, fracture toughness, heat of formation, etc., of different materials, and thus save us from extra experimental burden. In this article we compute many topological indices for the family of circulant graphs. At first, we give a general closed form of M-polynomial of this family and recover many degree-based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family. Our results extend many existing results. Full article

Brain tumor segmentation in magnetic resonance imaging (MRI) is considered a complex procedure because of the variability of tumor shapes and the complexity of determining the tumor location, size, and texture. Manual tumor segmentation is a time-consuming task highly prone to human error. Hence, this study proposes an automated method that can identify tumor slices and segment the tumor across all image slices in volumetric MRI brain scans. First, a set of algorithms in the pre-processing stage is used to clean and standardize the collected data. A modified gray-level co-occurrence matrix and Analysis of Variance (ANOVA) are employed for feature extraction and feature selection, respectively. A multi-layer perceptron neural network is adopted as a classifier, and a bounding 3D-box-based genetic algorithm is used to identify the location of pathological tissues in the MRI slices. Finally, the 3D active contour without edge is applied to segment the brain tumors in volumetric MRI scans. The experimental dataset consists of 165 patient images collected from the MRI Unit of Al-Kadhimiya Teaching Hospital in Iraq. Results of the tumor segmentation achieved an accuracy of 89% ± 4.7% compared with manual processes. Full article

Environmental stressors have the potential to induce perturbations in the development of young individuals, leading to aberrant and unstable development. This may manifest as fluctuating asymmetry (FA; small, non-directional changes in the bilateral symmetry of morphological traits). Although widely regarded as a proxy for stress effects, the use of FA as a biomarker is still a topic of much debate. We investigated the applicability of FA as an indicator of nutritional stress (brought about by energetic constraints) by experimental manipulation of the diet composition and quantity during the growth of Lesser Black-backed Gull (Larus fuscus) chicks. FA as an endpoint was measured across the tarsus, wing and 10th primary feather when chicks reached 30 days of age. Although levels of asymmetry were found to increase with stress in the feather, relationships with tarsus and wing FA were mixed and mostly non-significant. Furthermore, we did not find any correlations in unsigned FA between traits, indicating the absence of organism-wide asymmetry. Our study was therefore unable to find unequivocal evidence in support of the application of FA as a reliable estimator of nutritional stress. Full article

The IEEE Std 802.15.6 is an international standard for wireless body area networks (WBANs). It contains many aspects of communications, and also provides security services, since some communications in WBANs can carry sensitive information. In this standard, the password authenticated association is a protocol for two participants to identify each other and establish a new master key based on a pre-shared short password. However, recent research shows that this protocol is vulnerable to several attacks. In this paper, we propose an improved protocol which can resist all of these attacks. Moreover, the improved protocol alleviates computational burden on one side of the two participants, the node, which is usually less powerful compared with the other side, the hub. Full article

This paper first analyzes the one-dimensional Gabor function and expands it to a two-dimensional one. The two-dimensional Gabor function generates the two-dimensional Gabor wavelet through measure stretching and rotation. At last, the two-dimensional Gabor wavelet transform is employed to extract the image feature information. Based on the back propagation (BP) neural network model, the image intelligent test model based on the Gabor wavelet and the neural network model is built. The human face image detection is adopted as an example. Results suggest that, although there are complex textures and illumination variations on the images of the face database named AT&T, the detection accuracy rate of the proposed method can reach above 0.93. In addition, extensive simulations based on the Yale and extended Yale B datasets further verify the effectiveness of the proposed method. Full article

In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators. Full article

Due to the development of information technology (IT), it has been applied to various fields such as the smart home, medicine, healthcare, and the smart car. For these fields, IT has been providing continuous prevention and management, including health conditions beyond the mere prevention of disease, improving the quality of life. e-Healthcare is a health management and medical service to provide prevention, diagnosis, treatment, and the follow-up management of diseases at any time and place in connection with information communication technology, without requiring patients to visit hospitals. However, e-Healthcare has been exposed to eavesdropping, manipulation, and the forgery of information that is personal, biological, medical, etc., and is a security threat from malicious attackers. This study suggests a security service model to exchange personal health records (PHRs) for e-Healthcare environments. To be specific, this study suggests a scheme in which communicators are able to securely authorize and establish security channels by constituting the infrastructure each organization relies on. In addition, the possibility of establishing a security service model is indicated by suggesting an e-Healthcare system for a secure e-Healthcare environment as a secure personal health record system. This is anticipated to provide securer communication in e-Healthcare environments in the future through the scheme suggested in this study. Full article

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. Full article

In the present paper, we study helicoidal surfaces in the three-dimensional isotropic space $I^3$ and construct helicoidal surfaces satisfying a linear equation in terms of the Gaussian curvature and the mean curvature of the surface. Full article

Morphological analysis of the scoliotic spine is based on two-dimensional X-rays: coronal and sagittal. The three-dimensional character of scoliosis has raised the necessity for analyzing scoliosis in three planes. We proposed a new user-friendly method of graphical presentation of the spine in the third plane–the Spine Axial Presentation (SAP). Eighty-five vertebrae of patients with scoliosis were analyzed. Due to different positions during X-rays (standing) and computer tomography (CT) (supine), the corresponding measurements cannot be directly compared. As a solution, a software creating Digital Reconstructed Radiographs (DRRs) from CT scans was developed to replace regular X-rays with DRRs. Based on the measurements performed on DRRs, the coordinates of vertebral bodies central points were defined. Next, the geometrical centers of vertebral bodies were determined on CT scans. The reproducibility of measurements was tested with Intraclass Correlation Coefficient (ICC), using p = 0.05. The intra-observer reproducibility and inter-observer reliability for vertebral body central point’s coordinates (x, y, z) were high for results obtained based on DRRs and CT scans, as well as for comparison results obtained based on DRR and CT scans. Based on two standard radiographs, it is possible to localize vertebral bodies in 3D space. The position of vertebral bodies can be present in the Spine Axial Presentation. Full article

Deviations in bilateral symmetry or fluctuating asymmetry of an organism may result under environmental stressors that reduce developmental homeostasis and stability. Anthropogenic stressors such as increased urbanization can negatively impact environmental quality of aquatic ecosystems. Researchers have stressed the value in finding easy, accurate and inexpensive methods for assessing potential stress within ecosystems. Here we use fluctuating asymmetry (FA) as a useful quantitative tool in assessing the environmental quality and potential urban-based stressors within eight creeks of the Bull and Upatoi Creeks Watershed within the larger watershed of the Middle Chattahoochee. Using Geographic Information System (GIS), we characterize land-use patterns and a decreasing urbanization gradient as related to each creek’s eastward position from Columbus, Georgia. We collected two common fishes (redbreast sunfish; Lepomis auritus and bluegill; Lepomis macrochirus), measured both metric and meristic traits and investigated if the degree of FA in these two common fishes correlated with the urbanization gradient across creeks. We found significant differences in FA among creeks with one of the highest FA measures for the most urban creek. Principal component analysis (PCA) scores of urbanization and water chemistry were regressed against FA scores. We found no significant relationship between urbanization and FA nor environmental water chemistry and FA among creeks. We comment on the use of FA as a potential response variable and biological indicator of environmental stress within this watershed. Full article

Fluctuating asymmetry (FA), random deviation from perfect bilateral symmetry, is an indicator of developmental stability. Examining the ontogeny of FA can illustrate whether symmetry is actively maintained as the organism grows or breaks down as perturbations accumulate with age. Previous studies of changes in human FA with age have been cross-sectional studies and give conflicting results. We analyzed data from a longitudinal study of bodily FA in Jamaicans, using a composite index of seven paired traits. In addition, 288 children (ages 5–12) were first measured in 1996, and many were re-measured in 2002 and 2006 (maximum age = 22 years). Both within-individual longitudinal comparisons and between-individual comparisons across age groups demonstrate changes in FA with age. In males and females, FA increased until around age 13, but the pattern of change differed between the sexes. In males, FA increased rapidly approaching adolescence and then slightly declined into early adulthood. The increase in female FA was more gradual and then leveled off. The patterns observed likely reflect accumulation of developmental errors over time, rapid physical changes during puberty (especially in boys), and then regulation of symmetry when transitioning into adulthood. Although most changes in symmetry over time probably reflect random processes, the magnitude and direction of asymmetry in an individual at one point in time tended to be positively (though weakly) related to asymmetry in later years, pointing to underlying differences among individuals in developmental stability. Full article

We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes. Full article

We facilitate the editing of hierarchical B-spline curves at multiple resolutions by expressing a displacement function at each level in rotation minimizing frames (RMFs) on the curve at the next lower level. When the curve is edited at a particular level, RMFs at all the higher levels are updated, and the control points of the displacement function at each higher level are obtained from these new RMFs. This transfers details created at the current level to higher levels. Our method presents a hundred-fold faster way to reflect editing results compared to the traditional approach using Frenet frames. We demonstrate the effectiveness of our technique by showing several examples of editing curves with fine details. Full article

This study proposes a method of effectively creating mobile virtual reality scenes centered at events for the purpose of providing new experiences in virtual reality environment to users. For this purpose, this paper uses Prim’s maze generation algorithm to automatically create maze environments that have different patterns every time and to compute mazes with finite paths. This paper designs a scheme of creating virtual reality scenes based on event-centered mazes to maximize users’ tension and immersion. Here, event components that are appropriate for the maze environment are defined and maze patterns are created centered at the event point where events that are appropriate for the maze pattern are automatically created. Finally, the paper analyzes whether the proposed virtual reality scene based on event-centered mazes is helpful in enhancing users’ immersion and arousing their interest through diverse experiments. Full article

Quality function deployment (QFD) is a widely used quality system tool for translating customer requirements (CRs) into the engineering design requirements (DRs) of products or services. The conventional QFD analysis, however, has been criticized as having some limitations such as in the assessment of relationships between CRs and DRs, the determination of CR weights and the prioritization of DRs. This paper aims to develop a new hybrid group decision-making model based on hesitant 2-tuple linguistic term sets and an extended QUALIFLEX (qualitative flexible multiple criteria method) approach for handling QFD problems with incomplete weight information. First, hesitant linguistic term sets are combined with interval 2-tuple linguistic variables to express various uncertainties in the assessment information of QFD team members. Borrowing the idea of grey relational analysis (GRA), a multiple objective optimization model is constructed to determine the relative weights of CRs. Then, an extended QUALIFLEX approach with an inclusion comparison method is suggested to determine the ranking of the DRs identified in QFD. Finally, an analysis of a market segment selection problem is conducted to demonstrate and validate the proposed QFD approach. Full article

Craniofacial asymmetry is a convergent trait widely distributed across animals that colonize the extreme cave environment. Although craniofacial asymmetry can be discerned easily, other complex phenotypes (such as sensory organ position and numerical variation) are challenging to score and compare. Certain bones of the craniofacial complex demonstrate substantial asymmetry, and co-localize to regions harboring dramatically expanded numbers of mechanosensory neuromasts. To determine if a relationship exists between this expansion and bone fragmentation in cavefish, we developed a quantitative measure of positional symmetry across the left-right axis. We found that three different cave-dwelling populations were significantly more asymmetric compared to surface-dwelling fish. Moreover, cave populations did not differ in the degree of neuromast asymmetry. This work establishes a method for quantifying symmetry of a complex phenotype, and demonstrates that facial bone fragmentation mirrors the asymmetric distribution of neuromasts in different cavefish populations. Further developmental studies will provide a clearer picture of the developmental and cellular changes that accompany this extreme phenotype, and help illuminate the genetic basis for facial asymmetry in vertebrates. Full article

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO₂) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO₂) nanotubes. Full article

In this review paper, several new results towards the explanation of the accelerated expansion of the large-scale universe is discussed. On the other hand, inflation is the early-time accelerated era and the universe is symmetric in the sense of accelerated expansion. The accelerated expansion of is one of the long standing problems in modern cosmology, and physics in general. There are several well defined approaches to solve this problem. One of them is an assumption concerning the existence of dark energy in recent universe. It is believed that dark energy is responsible for antigravity, while dark matter has gravitational nature and is responsible, in general, for structure formation. A different approach is an appropriate modification of general relativity including, for instance, $f(R)$ and $f(T)$ theories of gravity. On the other hand, attempts to build theories of quantum gravity and assumptions about existence of extra dimensions, possible variability of the gravitational constant and the speed of the light (among others), provide interesting modifications of general relativity applicable to problems of modern cosmology, too. In particular, here two groups of cosmological models are discussed. In the first group the problem of the accelerated expansion of large-scale universe is discussed involving a new idea, named the varying ghost dark energy. On the other hand, the second group contains cosmological models addressed to the same problem involving either new parameterizations of the equation of state parameter of dark energy (like varying polytropic gas), or nonlinear interactions between dark energy and dark matter. Moreover, for cosmological models involving varying ghost dark energy, massless particle creation in appropriate radiation dominated universe (when the background dynamics is due to general relativity) is demonstrated as well. Exploring the nature of the accelerated expansion of the large-scale universe involving generalized holographic dark energy model with a specific Nojiri-Odintsov cut-off is presented to finalize the paper. Full article

While stress is expected to increase developmental instability (DI), not all studies confirm this. This heterogeneity could in part be due to the use of subtle differences between the left and right side of bilateral symmetrical organisms to quantify DI, leading to large sampling error obscuring associations with DI. Traits that develop simultaneously more than twice (such as flower petals or bird feathers) reflect individual DI more reliably, such that stronger associations are expected to emerge. Furthermore, some studies have shown differences in strengths of associations among populations. We studied the association between individual genetic diversity and DI in flower petals within three Opuntia echios populations inhabiting Galápagos. Quantifying individual DI through variation in length and width of a high number of petals within individual cacti, lead to a strong association between DI and genetic diversity in one population. We conclude that associations between individual DI and genetic diversity can be more easily revealed by measuring traits that develop repeatedly. Full article

One of the most fundamental symmetries in physics is CPT invariance. This article reviews the conditions under which CPT symmetry holds by recalling two proofs of the CPT theorem: The original Lagrangian-based analysis and the more rigorous one in the context of axiomatic quantum field theory. The presentation of the proofs is followed by a discussion of the major physical implications that arise from CPT symmetry. Motivated by recent theoretical and experimental interest in CPT tests, various approaches to the violation of CPT symmetry are mentioned, and it is briefly discussed how they evade the CPT theorem. An attempt has been made to keep this work self-contained and at a level suitable for a wider readership by excising as many technical aspects as possible. Full article

In this paper, we prove some optimal inequalities involving the intrinsic scalar curvature and the extrinsic Casorati curvature of submanifolds in a generalized complex space form with a semi-symmetric non-metric connection and a generalized Sasakian space form with a semi-symmetric non-metric connection. Moreover, we show that in both cases, the equalities hold if and only if submanifolds are invariantly quasi-umbilical. Full article

The Standard-Model Extension (SME) provides a comprehensive effective field-theory framework for the study of CPT and Lorentz symmetry. This work reviews the structure and philosophy of the SME and provides some intuitive examples of symmetry violation. The results of recent gravitational tests performed within the SME are summarized including analysis of results from the Laser Interferometer Gravitational-Wave Observatory (LIGO), sensitivities achieved in short-range gravity experiments, constraints from cosmic-ray data, and results achieved by studying planetary ephemerids. Some proposals and ongoing efforts will also be considered including gravimeter tests, tests of the Weak Equivalence Principle, and antimatter experiments. Our review of the above topics is augmented by several original extensions of the relevant work. We present new examples of symmetry violation in the SME and use the cosmic-ray analysis to place first-ever constraints on 81 additional operators. Full article

Traditional detectors for spectrum sensing in cognitive radio networks always become disabled when noise uncertainty is severe. Shannon entropy-based detection methods have aroused widespread attention in recent years due to the characteristics of effective anti-noise uncertainty. However, in existing entropy-based sensing schemes, the uniform quantization method cannot guarantee the maximum entropy distribution when primary users do not exist, and cannot effectively distinguish between two hypotheses, which severely limits the promotion of detection performance. Moreover, the Shannon entropy-based sensing schemes are prone to misconvergence occurring when estimating entropy values, thus causing failure detection, which leads to system detection inefficiency and resource waste. These are the two major serious defects in Shannon entropy-based detectors, which restrict the performance improvement. In this paper, a novel non-uniform quantized exponential entropy-based (NQEE) detector is proposed for local sensing to deal with the problems of maximum entropy distribution and detection failure. To further improve the reliability of the detection, a collaborative spectrum sensing algorithm based on an NQEE detector with multiple fusion rules is presented. Simulation results verify that the detection performance of the improved local entropy-based detector is superior to the existing Shannon entropy-based detectors and is proved to be robust to noise power uncertainty. In addition, the novel collaborative detection algorithm outperforms the traditional collaborative spectrum detection method to a great degree. Full article

Texture feature description is a remarkable challenge in the fields of computer vision and pattern recognition. Since the traditional texture feature description method, the local binary pattern (LBP), is unable to acquire more detailed direction information and always sensitive to noise, we propose a novel method based on generalized Gabor direction pattern (GGDP) and weighted discrepancy measurement model (WDMM) to overcome those defects. Firstly, a novel patch-structure direction pattern (PDP) is proposed, which can extract rich feature information and be insensitive to noise. Then, motivated by searching for a description method that can explore richer and more discriminant texture features and reducing the local Gabor feature vector’s high dimension problem, we extend PDP to form the GGDP method with multi-channel Gabor space. Furthermore, WDMM, which can effectively measure the feature distance between two images, is presented for the classification and recognition of image samples. Simulated experiments on olivetti research laboratory (ORL), Carnegie Mellon University pose, illumination, and expression (CMUPIE) and Yale B face databases under different illumination or facial expression conditions indicate that the proposed method outperforms other existing classical methods. Full article