Open AccessArticle
Two-Dimensional Hermite Filters Simplify the Description of High-Order Statistics of Natural Images
Symmetry 2016, 8(9), 98; doi:10.3390/sym8090098 -
Abstract
Natural image statistics play a crucial role in shaping biological visual systems, understanding their function and design principles, and designing effective computer-vision algorithms. High-order statistics are critical for conveying local features but they are challenging to study, largely because their number and [...] Read more.
Natural image statistics play a crucial role in shaping biological visual systems, understanding their function and design principles, and designing effective computer-vision algorithms. High-order statistics are critical for conveying local features but they are challenging to study, largely because their number and variety is large. Here, via the use of two-dimensional Hermite (TDH) functions, we identify a covert symmetry in high-order statistics of natural images that simplifies this task. This emerges from the structure of TDH functions, which are an orthogonal set of functions that are organized into a hierarchy of ranks. Specifically, we find that the shape (skewness and kurtosis) of the distribution of filter coefficients depends only on the projection of the function onto a one-dimensional subspace specific to each rank. The characterization of natural image statistics provided by TDH filter coefficients reflects both their phase and amplitude structure, and we suggest an intuitive interpretation for the special subspace within each rank. Full article
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Open AccessArticle
M-Polynomial and Related Topological Indices of Nanostar Dendrimers
Symmetry 2016, 8(9), 97; doi:10.3390/sym8090097 -
Abstract
Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with [...] Read more.
Dendrimers are highly branched organic macromolecules with successive layers of branch units surrounding a central core. The M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices. These indices are invariants of the topology of graphs associated with molecular structure of nanomaterials to correlate certain physicochemical properties like boiling point, stability, strain energy, etc. of chemical compounds. In this paper, we first determine M-polynomials of some nanostar dendrimers and then recover many degree-based topological indices. Full article
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Open AccessArticle
ANFIS-Based Modeling for Photovoltaic Characteristics Estimation
Symmetry 2016, 8(9), 96; doi:10.3390/sym8090096 -
Abstract
Due to the high cost of photovoltaic (PV) modules, an accurate performance estimation method is significantly valuable for studying the electrical characteristics of PV generation systems. Conventional analytical PV models are usually composed by nonlinear exponential functions and a good number of [...] Read more.
Due to the high cost of photovoltaic (PV) modules, an accurate performance estimation method is significantly valuable for studying the electrical characteristics of PV generation systems. Conventional analytical PV models are usually composed by nonlinear exponential functions and a good number of unknown parameters must be identified before using. In this paper, an adaptive-network-based fuzzy inference system (ANFIS) based modeling method is proposed to predict the current-voltage characteristics of PV modules. The effectiveness of the proposed modeling method is evaluated through comparison with Villalva’s model, radial basis function neural networks (RBFNN) based model and support vector regression (SVR) based model. Simulation and experimental results confirm both the feasibility and the effectiveness of the proposed method. Full article
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Open AccessArticle
Lorentz Transformations from Intrinsic Symmetries
Symmetry 2016, 8(9), 94; doi:10.3390/sym8090094 -
Abstract
We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination [...] Read more.
We reveal the frame-exchange space-inversion (FESI) symmetry and the frame-exchange time-inversion (FETI) symmetry in the Lorentz transformation and propose a symmetry principle stating that the space-time transformation between two inertial frames is invariant under the FESI or the FETI transformation. In combination with the principle of relativity and the presumed nature of Euclidean space and time, the symmetry principle is employed to derive the proper orthochronous Lorentz transformation without assuming the constancy of the speed of light and specific mathematical requirements (such as group property) a priori. We explicitly demonstrate that the constancy of the speed of light in all inertial frames can be derived using the velocity reciprocity property, which is a deductive consequence of the space–time homogeneity and the space isotropy. The FESI or the FETI symmetry remains to be preserved in the Galilean transformation at the non-relativistic limit. Other similar symmetry operations result in either trivial transformations or improper and/or non-orthochronous Lorentz transformations, which do not form groups. Full article
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Open AccessArticle
Approach to Multi-Criteria Group Decision-Making Problems Based on the Best-Worst-Method and ELECTRE Method
Symmetry 2016, 8(9), 95; doi:10.3390/sym8090095 -
Abstract
This paper proposes a novel approach to cope with the multi-criteria group decision-making problems. We give the pairwise comparisons based on the best-worst-method (BWM), which can decrease comparison times. Additionally, our comparison results are determined with the positive and negative aspects. In [...] Read more.
This paper proposes a novel approach to cope with the multi-criteria group decision-making problems. We give the pairwise comparisons based on the best-worst-method (BWM), which can decrease comparison times. Additionally, our comparison results are determined with the positive and negative aspects. In order to deal with the decision matrices effectively, we consider the elimination and choice translation reality (ELECTRE III) method under the intuitionistic multiplicative preference relations environment. The ELECTRE III method is designed for a double-automatic system. Under a certain limitation, without bothering the decision-makers to reevaluate the alternatives, this system can adjust some special elements that have the most influence on the group’s satisfaction degree. Moreover, the proposed method is suitable for both the intuitionistic multiplicative preference relation and the interval valued fuzzy preference relations through the transformation formula. An illustrative example is followed to demonstrate the rationality and availability of the novel method. Full article
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Open AccessArticle
Modeling and Optimization of a Tree Based on Virtual Reality for Immersive Virtual Landscape Generation
Symmetry 2016, 8(9), 93; doi:10.3390/sym8090093 -
Abstract
This study proposes a modeling method that can effectively generate multiple diverse digital trees for creating immersive virtual landscape based on virtual reality and an optimization method for real-time rendering. The proposed method simplifies a process of procedures from growth of tree [...] Read more.
This study proposes a modeling method that can effectively generate multiple diverse digital trees for creating immersive virtual landscape based on virtual reality and an optimization method for real-time rendering. The proposed method simplifies a process of procedures from growth of tree models to the generation of the three-dimensional branch geometric model. Here, the procedural branch graph (PBG) algorithm is proposed, which simultaneously and effectively generates diverse trees that have a similar branch pattern. Moreover, the optimization method is designed in a polygon-based branch model which controls the resolution of tree models according to the distance from the camera to generate a tree model structure that is appropriate for an immersive system based on virtual reality. Finally, a virtual reality system is established based on the Oculus SDK (Software Development Kit) and Unity3D engine. In this process, the image processing-based pixel to tree (PTT) method is proposed as a technique for easily and efficiently generating a virtual landscape by allocating multiple trees on terrain. An immersive virtual landscape that has a stereoscopic perception and spatial impression is created through the proposed method and whether it can deliver experience of nature in virtual reality to the users was checked through an experiment. Full article
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Open AccessArticle
Energy Conservation Law in Industrial Architecture: An Approach through Geometric Algebra
Symmetry 2016, 8(9), 92; doi:10.3390/sym8090092 -
Abstract
Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. [...] Read more.
Since 1892, the electrical engineering scientific community has been seeking a power theory for interpreting the power flow within electric networks under non-sinusoidal conditions. Although many power theories have been proposed regarding non-sinusoidal operation, an adequate solution is yet to be found. Using the framework based on complex algebra in non-sinusoidal circuit analysis (frequency domain), the verification of the energy conservation law is only possible in sinusoidal situations. In this case, reactive energy turns out to be proportional to the energy difference between the average electric and magnetic energies stored in the loads and its cancellation is mathematically trivial. However, in industrial architecture, apparent power definition of electric loads (non-sinusoidal conditions) is inconsistent with the energy conservation law. Up until now, in the classical complex algebra approach, this goal is only valid in the case of purely resistive loads. Thus, in this paper, a new circuit analysis approach using geometric algebra is used to develop the most general proof of energy conservation in industrial building loads. In terms of geometric objects, this powerful tool calculates the voltage, current, and apparent power in electrical systems in non-sinusoidal, linear/nonlinear situations. In contrast to the traditional method developed by Steinmetz, the suggested powerful tool extends the concept of phasor to multivector-phasors and is performed in a new Generalized Complex Geometric Algebra structure (CGn), where Gn is the Clifford algebra in n-dimensional real space and C is the complex vector space. To conclude, a numerical example illustrates the clear advantages of the approach suggested in this paper. Full article
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Open AccessArticle
The Combination of a Fuzzy Analytical Hierarchy Process and the Taguchi Method to Evaluate the Malaysian Users’ Willingness to Pay for Public Transportation
Symmetry 2016, 8(9), 90; doi:10.3390/sym8090090 -
Abstract
This study is an attempt to overcome the lack of reliable estimates on the willingness of Malaysian users to pay for public transportation (particularly buses) through a combined analysis of a fuzzy analytical hierarchy process (F-AHP) and the Taguchi method. This is [...] Read more.
This study is an attempt to overcome the lack of reliable estimates on the willingness of Malaysian users to pay for public transportation (particularly buses) through a combined analysis of a fuzzy analytical hierarchy process (F-AHP) and the Taguchi method. This is a ground-breaking study in the attempt to evaluate the bus users’ satisfaction factors based on the F-AHP, and find the pattern for the users’ willingness to pay (WTP) characteristic by reducing the travel time with the Taguchi application. The data were collected from the public transportation users’ intentions in Kelang Valley, Kuala Lumpur, Malaysia. The results convinced us that, for complex data, one requires flexible approaches that can adjust their combination methods to the properties of analyzed datasets. This study is interested in initiating the use of a system combination strategy to have a better understanding of the factors that motivate the public transportation users to be willing to pay for the public transportation’s fare. Full article
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Open AccessArticle
Social Content Recommendation Based on Spatial-Temporal Aware Diffusion Modeling in Social Networks
Symmetry 2016, 8(9), 89; doi:10.3390/sym8090089 -
Abstract
User interactions in online social networks (OSNs) enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal [...] Read more.
User interactions in online social networks (OSNs) enable the spread of information and enhance the information dissemination process, but at the same time they exacerbate the information overload problem. In this paper, we propose a social content recommendation method based on spatial-temporal aware controlled information diffusion modeling in OSNs. Users interact more frequently when they are close to each other geographically, have similar behaviors, and fall into similar demographic categories. Considering these facts, we propose multicriteria-based social ties relationship and temporal-aware probabilistic information diffusion modeling for controlled information spread maximization in OSNs. The proposed social ties relationship modeling takes into account user spatial information, content trust, opinion similarity, and demographics. We suggest a ranking algorithm that considers the user ties strength with friends and friends-of-friends to rank users in OSNs and select highly influential injection nodes. These nodes are able to improve social content recommendations, minimize information diffusion time, and maximize information spread. Furthermore, the proposed temporal-aware probabilistic diffusion process categorizes the nodes and diffuses the recommended content to only those users who are highly influential and can enhance information dissemination. The experimental results show the effectiveness of the proposed scheme. Full article
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Open AccessArticle
Higgs Phase in a Gauge U(1) Non-Linear CP1-Model. Two Species of BPS Vortices and Their Zero Modes
Symmetry 2016, 8(9), 91; doi:10.3390/sym8090091 -
Abstract
In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged U(1) nonlinear CP1-model. [...] Read more.
In this paper, zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged U(1) nonlinear CP1-model. If 2πn, nZ, is the quantized magnetic flux of the two species of BPS vortex solutions, 2n linearly-independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension 2n of these stringy topological defects is thus locally shown. Full article
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Open AccessArticle
The Conformal Camera in Modeling Active Binocular Vision
Symmetry 2016, 8(9), 88; doi:10.3390/sym8090088 -
Abstract
Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a [...] Read more.
Primate vision is an active process that constructs a stable internal representation of the 3D world based on 2D sensory inputs that are inherently unstable due to incessant eye movements. We present here a mathematical framework for processing visual information for a biologically-mediated active vision stereo system with asymmetric conformal cameras. This model utilizes the geometric analysis on the Riemann sphere developed in the group-theoretic framework of the conformal camera, thus far only applicable in modeling monocular vision. The asymmetric conformal camera model constructed here includes the fovea’s asymmetric displacement on the retina and the eye’s natural crystalline lens tilt and decentration, as observed in ophthalmological diagnostics. We extend the group-theoretic framework underlying the conformal camera to the stereo system with asymmetric conformal cameras. Our numerical simulation shows that the theoretical horopter curves in this stereo system are conics that well approximate the empirical longitudinal horopters of the primate vision system. Full article
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Open AccessArticle
Facial Feature Movements Caused by Various Emotions: Differences According to Sex
Symmetry 2016, 8(9), 86; doi:10.3390/sym8090086 -
Abstract
Facial muscle micro movements for eight emotions were induced via visual and auditory stimuli and were verified according to sex. Thirty-one main facial features were chosen from the Kinect API out of 121 initially obtained facial features; the average change of pixel [...] Read more.
Facial muscle micro movements for eight emotions were induced via visual and auditory stimuli and were verified according to sex. Thirty-one main facial features were chosen from the Kinect API out of 121 initially obtained facial features; the average change of pixel value was measured after image alignment. The proposed method is advantageous as it allows for comparisons. Facial micro-expressions are analyzed in real time using 31 facial feature points. The amount of micro-expressions for the various emotion stimuli was comparatively analyzed for differences according to sex. Men’s facial movements were similar for each emotion, whereas women’s facial movements were different for each emotion. The six feature positions were significantly different according to sex; in particular, the inner eyebrow of the right eye had a confidence level of p < 0.01. Consequently, discriminative power showed that men’s ability to separate one emotion from the others was lower compared to women’s ability in terms of facial expression, despite men’s average movements being higher compared to women’s. Additionally, the asymmetric phenomena around the left eye region of women appeared more strongly in cases of positive emotions. Full article
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Open AccessArticle
Weyl, Majorana and Dirac Fields from a Unified Perspective
Symmetry 2016, 8(9), 87; doi:10.3390/sym8090087 -
Abstract
A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian methods play no role in the present exposition, [...] Read more.
A self-contained derivation of the formalism describing Weyl, Majorana and Dirac fields from a unified perspective is given based on a concise description of the representation theory of the proper orthochronous Lorentz group. Lagrangian methods play no role in the present exposition, which covers several fundamental aspects of relativistic field theory, which are commonly not included in introductory courses when treating fermionic fields via the Dirac equation in the first place. Full article
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Open AccessReview
A Survey of Public Key Infrastructure-Based Security for Mobile Communication Systems
Symmetry 2016, 8(9), 85; doi:10.3390/sym8090085 -
Abstract
Mobile communication security techniques are employed to guard the communication between the network entities. Mobile communication cellular systems have become one of the most important communication systems in recent times and are used by millions of people around the world. Since the [...] Read more.
Mobile communication security techniques are employed to guard the communication between the network entities. Mobile communication cellular systems have become one of the most important communication systems in recent times and are used by millions of people around the world. Since the 1990s, considerable efforts have been taken to improve both the communication and security features of the mobile communications systems. However, these improvements divide the mobile communications field into different generations according to the communication and security techniques such as A3, A5 and A8 algorithms for 2G-GSM cellular system, 3G-authentication and key agreement (AKA), evolved packet system-authentication and key agreement (EPS-AKA), and long term evolution-authentication and key agreement (LTE-AKA) algorithms for 3rd generation partnership project (3GPP) systems. Furthermore, these generations have many vulnerabilities, and huge security work is involved to solve such problems. Some of them are in the field of the public key cryptography (PKC) which requires a high computational cost and more network flexibility to be achieved. As such, the public key infrastructure (PKI) is more compatible with the modern generations due to the superior communications features. This paper surveys the latest proposed works on the security of GSM, CDMA, and LTE cellular systems using PKI. Firstly, we present the security issues for each generation of mobile communication systems, then we study and analyze the latest proposed schemes and give some comparisons. Finally, we introduce some new directions for the future scope. This paper classifies the mobile communication security schemes according to the techniques used for each cellular system and covers some of the PKI-based security techniques such as authentication, key agreement, and privacy preserving. Full article
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Open AccessArticle
The Algorithm of Continuous Optimization Based on the Modified Cellular Automaton
Symmetry 2016, 8(9), 84; doi:10.3390/sym8090084 -
Abstract
This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, [...] Read more.
This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown. Full article
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Open AccessReview
Revisiting the Optical PT-Symmetric Dimer
Symmetry 2016, 8(9), 83; doi:10.3390/sym8090083 -
Abstract
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical [...] Read more.
Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of PT-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical PT-symmetric dimer, a two-waveguide coupler where the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry-based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar N-waveguide couplers that are the optical realization of the Lorentz group in 2 + 1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of the Ehrenfest theorem. Full article
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Open AccessReview
Cosmological Reflection of Particle Symmetry
Symmetry 2016, 8(8), 81; doi:10.3390/sym8080081 -
Abstract
The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches [...] Read more.
The standard model involves particle symmetry and the mechanism of its breaking. Modern cosmology is based on inflationary models with baryosynthesis and dark matter/energy, which involves physics beyond the standard model. Studies of the physical basis of modern cosmology combine direct searches for new physics at accelerators with its indirect non-accelerator probes, in which cosmological consequences of particle models play an important role. The cosmological reflection of particle symmetry and the mechanisms of its breaking are the subject of the present review. Full article
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Open AccessArticle
Decoration of the Truncated Tetrahedron—An Archimedean Polyhedron—To Produce a New Class of Convex Equilateral Polyhedra with Tetrahedral Symmetry
Symmetry 2016, 8(8), 82; doi:10.3390/sym8080082 -
Abstract
The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from [...] Read more.
The Goldberg construction of symmetric cages involves pasting a patch cut out of a regular tiling onto the faces of a Platonic host polyhedron, resulting in a cage with the same symmetry as the host. For example, cutting equilateral triangular patches from a 6.6.6 tiling of hexagons and pasting them onto the full triangular faces of an icosahedron produces icosahedral fullerene cages. Here we show that pasting cutouts from a 6.6.6 tiling onto the full hexagonal and triangular faces of an Archimedean host polyhedron, the truncated tetrahedron, produces two series of tetrahedral (Td) fullerene cages. Cages in the first series have 28n2 vertices (n ≥ 1). Cages in the second (leapfrog) series have 3 × 28n2. We can transform all of the cages of the first series and the smallest cage of the second series into geometrically convex equilateral polyhedra. With tetrahedral (Td) symmetry, these new polyhedra constitute a new class of “convex equilateral polyhedra with polyhedral symmetry”. We also show that none of the other Archimedean polyhedra, six with octahedral symmetry and six with icosahedral, can host full-face cutouts from regular tilings to produce cages with the host’s polyhedral symmetry. Full article
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Open AccessArticle
Superconducting Gap Symmetry of LaFeP(O,F) Observed by Impurity Doping Effect
Symmetry 2016, 8(8), 80; doi:10.3390/sym8080080 -
Abstract
We have investigated Mn, Co and Ni substitution effects on polycrystalline samples of LaFePO0.95F0.05 by resistivity and magnetoresistance measurements. In LaFe1-xMxPO0.95F0.05 (M = Mn, Co and Ni), the superconducting transition temperature [...] Read more.
We have investigated Mn, Co and Ni substitution effects on polycrystalline samples of LaFePO0.95F0.05 by resistivity and magnetoresistance measurements. In LaFe1-xMxPO0.95F0.05 (M = Mn, Co and Ni), the superconducting transition temperature (Tc) monotonously decreases with increasing the impurity doping level of x. There is a clear difference of Tc suppression rates among Mn, Co and Ni doping cases, and the decreasing rate of Tc by Mn doping as a magnetic impurity is larger than those by the nonmagnetic doping impurities (Co/Ni). This result indicates that in LaFePO0.95F0.05, Tc is rapidly suppressed by the pair-breaking effect of magnetic impurities, and the pairing symmetry is a full-gapped s-wave. In the nonmagnetic impurity-doped systems, the residual resistivity in the normal state has nearly the same value when Tc becomes zero. The residual resistivity value is almost consistent with the universal value of sheet resistance for two-dimensional superconductors, suggesting that Tc is suppressed by electron localization in Co/Ni-doped LaFePO0.95F0.05. Full article
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Open AccessArticle
Modeling Bottom-Up Visual Attention Using Dihedral Group D4
Symmetry 2016, 8(8), 79; doi:10.3390/sym8080079 -
Abstract
In this paper, first, we briefly describe the dihedral group D4 that serves as the basis for calculating saliency in our proposed model. Second, our saliency model makes two major changes in a latest state-of-the-art model known as group-based asymmetry. First, [...] Read more.
In this paper, first, we briefly describe the dihedral group D4 that serves as the basis for calculating saliency in our proposed model. Second, our saliency model makes two major changes in a latest state-of-the-art model known as group-based asymmetry. First, based on the properties of the dihedral group D4, we simplify the asymmetry calculations associated with the measurement of saliency. This results is an algorithm that reduces the number of calculations by at least half that makes it the fastest among the six best algorithms used in this research article. Second, in order to maximize the information across different chromatic and multi-resolution features, the color image space is de-correlated. We evaluate our algorithm against 10 state-of-the-art saliency models. Our results show that by using optimal parameters for a given dataset, our proposed model can outperform the best saliency algorithm in the literature. However, as the differences among the (few) best saliency models are small, we would like to suggest that our proposed model is among the best and the fastest among the best. Finally, as a part of future work, we suggest that our proposed approach on saliency can be extended to include three-dimensional image data. Full article
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