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Symmetry
Volume 10
Issue 3
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Symmetry, Volume 10, Issue 3 (March 2018) – 26 articles

Cover Story (view full-size image): Finite Unified Theories (FUTs) are $N=1$ supersymmetric grand unified theories that can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. FUTs correctly predicted the mass of the top and bottom quarks as well as the standard model-like Higgs Boson. This is naturally realized using a heavy SUSY spectrum that escapes current and future LHC searches. Higher-energy $pp$ such as the FCC-hh will be able to test this model. View this paper
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14 pages, 6841 KiB  
Article
A Robust Image Watermarking Technique Based on DWT, APDCBT, and SVD
by Xiao Zhou, Heng Zhang and Chengyou Wang
Symmetry 2018, 10(3), 77; https://doi.org/10.3390/sym10030077 - 19 Mar 2018
Cited by 86 | Viewed by 9957
Abstract
Copyright protection for digital multimedia has become a research hotspot in recent years. As an efficient solution, the digital watermarking scheme has emerged at the right moment. In this article, a highly robust and hybrid watermarking method is proposed. The discrete wavelet transform [...] Read more.
Copyright protection for digital multimedia has become a research hotspot in recent years. As an efficient solution, the digital watermarking scheme has emerged at the right moment. In this article, a highly robust and hybrid watermarking method is proposed. The discrete wavelet transform (DWT) and all phase discrete cosine biorthogonal transform (APDCBT) presented in recent years as well as the singular value decomposition (SVD) are adopted in this method to insert and recover the watermark. To enhance the watermark imperceptibility, the direct current (DC) coefficients after block-based APDCBT in high frequency sub-bands (LH and HL) are modified by using the watermark. Compared with the conventional SVD-based watermarking method and another watermarking technique, the watermarked images obtained by the proposed method have higher image quality. In addition, the proposed method achieves high robustness in resisting various image processing attacks. Full article
(This article belongs to the Special Issue Advanced in Artificial Intelligence and Cloud Computing)
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9 pages, 226 KiB  
Article
Analytic Solutions of Nonlinear Partial Differential Equations by the Power Index Method
by Barbara Abraham-Shrauner
Symmetry 2018, 10(3), 76; https://doi.org/10.3390/sym10030076 - 19 Mar 2018
Cited by 3 | Viewed by 3655
Abstract
An updated Power Index Method is presented for nonlinear differential equations (NLPDEs) with the aim of reducing them to solutions by algebraic equations. The Lie symmetry, translation invariance of independent variables, allows for traveling waves. In addition discrete symmetries, reflection, or [...] Read more.
An updated Power Index Method is presented for nonlinear differential equations (NLPDEs) with the aim of reducing them to solutions by algebraic equations. The Lie symmetry, translation invariance of independent variables, allows for traveling waves. In addition discrete symmetries, reflection, or 180 ° rotation symmetry, are possible. The method tests whether certain hyperbolic or Jacobian elliptic functions are analytic solutions. The method consists of eight steps. The first six steps are quickly applied; conditions for algebraic equations are more complicated. A few exceptions to the Power Index Method are discussed. The method realizes an aim of Sophus Lie to find analytic solutions of nonlinear differential equations. Full article
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II)
15 pages, 2685 KiB  
Article
An Improved Set-Membership Proportionate Adaptive Algorithm for a Block-Sparse System
by Zhan Jin, Yingsong Li and Jianming Liu
Symmetry 2018, 10(3), 75; https://doi.org/10.3390/sym10030075 - 19 Mar 2018
Cited by 13 | Viewed by 3491
Abstract
In this paper, an improved set-membership proportionate normalized least mean square (SM-PNLMS) algorithm is proposed for block-sparse systems. The proposed algorithm, which is named the block-sparse SM-PNLMS (BS-SMPNLMS), is implemented by inserting a penalty of a mixed l 2 , 1 norm of [...] Read more.
In this paper, an improved set-membership proportionate normalized least mean square (SM-PNLMS) algorithm is proposed for block-sparse systems. The proposed algorithm, which is named the block-sparse SM-PNLMS (BS-SMPNLMS), is implemented by inserting a penalty of a mixed l 2 , 1 norm of weight-taps into the cost function of the SM-PNLMS. Furthermore, an improved BS-SMPNLMS algorithm (the (BS-SMIPNLMS algorithm) is also derived and analyzed. The proposed algorithms are well investigated in the framework of network echo cancellation. The results of simulations indicate that the devised BS-SMPNLMS and BS-SMIPNLMS algorithms converge faster and have smaller estimation errors compared with related algorithms. Full article
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10 pages, 789 KiB  
Article
Dispersion Forces Between Fields Confined to Half Spaces
by M. Bordag and I.G. Pirozhenko
Symmetry 2018, 10(3), 74; https://doi.org/10.3390/sym10030074 - 19 Mar 2018
Cited by 2 | Viewed by 2777
Abstract
We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions [...] Read more.
We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions on the interfaces for the fields in the half spaces and calculate their one-loop contribution to the wave equation for the other field. We perform the ultraviolet renormalization and develop a convenient formalism for the calculation of the vacuum energy in this configuration. Full article
(This article belongs to the Special Issue Casimir Physics and Applications)
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25 pages, 9487 KiB  
Article
Intelligent Image Processing System for Detection and Segmentation of Regions of Interest in Retinal Images
by Dan Popescu and Loretta Ichim
Symmetry 2018, 10(3), 73; https://doi.org/10.3390/sym10030073 - 17 Mar 2018
Cited by 7 | Viewed by 5662
Abstract
The automatic detection, segmentation, localization, and evaluation of the optic disc, macula, exudates, and hemorrhages are very important for diagnosing retinal diseases. One of the difficulties in detecting such regions of interest (RoIs) with computer vision is their symmetries, e.g., between the optic [...] Read more.
The automatic detection, segmentation, localization, and evaluation of the optic disc, macula, exudates, and hemorrhages are very important for diagnosing retinal diseases. One of the difficulties in detecting such regions of interest (RoIs) with computer vision is their symmetries, e.g., between the optic disc and exudates and also between exudates and hemorrhages. This paper proposes an original, intelligent, and high-performing image processing system for the simultaneous detection and segmentation of retinal RoIs. The basic principles of the method are image decomposition in small boxes and local texture analysis. The processing flow contains three phases: preprocessing, learning, and operating. As a first novelty, we propose proper feature selection based on statistical analysis in confusion matrices for different feature types (extracted from a co-occurrence matrix, fractal type, and local binary patterns). Mainly, the selected features are chosen to differentiate between similar RoIs. The second novelty consists of local classifier fusion. To this end, the local classifiers associated with features are grouped in global classifiers corresponding to the RoIs. The local classifiers are based on minimum distances to the representatives of classes and the global classifiers are based on confidence intervals, weights, and a voting scheme. A deep convolutional neural network, based on supervised learning, for blood vessel segmentation is proposed in order to improve the RoI detection performance. Finally, the experimental results on real images from different databases demonstrate the rightness of our methodologies and algorithms. Full article
(This article belongs to the Special Issue Advances in Medical Image Segmentation)
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18 pages, 1258 KiB  
Article
Nonclassical Symmetry Solutions for Fourth-Order Phase Field Reaction–Diffusion
by Philip Broadbridge, Dimetre Triadis, Dilruk Gallage and Pierluigi Cesana
Symmetry 2018, 10(3), 72; https://doi.org/10.3390/sym10030072 - 17 Mar 2018
Cited by 8 | Viewed by 3737
Abstract
Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing [...] Read more.
Using the nonclassical symmetry of nonlinear reaction–diffusion equations, some exact multi-dimensional time-dependent solutions are constructed for a fourth-order Allen–Cahn–Hilliard equation. This models a phase field that gives a phenomenological description of a two-phase system near critical temperature. Solutions are given for the changing phase of cylindrical or spherical inclusion, allowing for a “mushy” zone with a mixed state that is controlled by imposing a pure state at the boundary. The diffusion coefficients for transport of one phase through the mixture depend on the phase field value, since the physical structure of the mixture depends on the relative proportions of the two phases. A source term promotes stability of both of the pure phases but this tendency may be controlled or even reversed through the boundary conditions. Full article
(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models, II)
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15 pages, 4297 KiB  
Article
Ensemble Genetic Fuzzy Neuro Model Applied for the Emergency Medical Service via Unbalanced Data Evaluation
by Muammar Sadrawi, Wei-Zen Sun, Matthew Huei-Ming Ma, Yu-Ting Yeh, Maysam F. Abbod and Jiann-Shing Shieh
Symmetry 2018, 10(3), 71; https://doi.org/10.3390/sym10030071 - 17 Mar 2018
Cited by 11 | Viewed by 3739
Abstract
Equally partitioned data are essential for prediction. However, in some important cases, the data distribution is severely unbalanced. In this study, several algorithms are utilized to maximize the learning accuracy when dealing with a highly unbalanced dataset. A linguistic algorithm is applied to [...] Read more.
Equally partitioned data are essential for prediction. However, in some important cases, the data distribution is severely unbalanced. In this study, several algorithms are utilized to maximize the learning accuracy when dealing with a highly unbalanced dataset. A linguistic algorithm is applied to evaluate the input and output relationship, namely Fuzzy c-Means (FCM), which is applied as a clustering algorithm for the majority class to balance the minority class data from about 3 million cases. Each cluster is used to train several artificial neural network (ANN) models. Different techniques are applied to generate an ensemble genetic fuzzy neuro model (EGFNM) in order to select the models. The first ensemble technique, the intra-cluster EGFNM, works by evaluating the best combination from all the models generated by each cluster. Another ensemble technique is the inter-cluster model EGFNM, which is based on selecting the best model from each cluster. The accuracy of these techniques is evaluated using the receiver operating characteristic (ROC) via its area under the curve (AUC). Results show that the AUC of the unbalanced data is 0.67974. The random cluster and best ANN single model have AUCs of 0.7177 and 0.72806, respectively. For the ensemble evaluations, the intra-cluster and the inter-cluster EGFNMs produce 0.7293 and 0.73038, respectively. In conclusion, this study achieved improved results by performing the EGFNM method compared with the unbalanced training. This study concludes that selecting several best models will produce a better result compared with all models combined. Full article
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17 pages, 273 KiB  
Review
Symmetries in Classical and Quantum Treatment of Einstein’s Cosmological Equations and Mini-Superspace Actions
by Theodosios Christodoulakis, Alexandros Karagiorgos and Adamantia Zampeli
Symmetry 2018, 10(3), 70; https://doi.org/10.3390/sym10030070 - 16 Mar 2018
Cited by 13 | Viewed by 3090
Abstract
The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action principle exists, the symmetries of [...] Read more.
The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action principle exists, the symmetries of the configuration mini-supermetric space can also be used, in conjunction with the constraints, to provide local or non-local constants of motion. At the classical level, depending on their number, these integrals can even secure the acquisition of the entire solution space without any further solving of the dynamical equations. At the quantum level, their operator analogues can be used, along with the Wheeler–DeWitt equation, to define unique wave functions that exhibit singularity-free behavior at a semi-classical level. Full article
(This article belongs to the Special Issue Symmetry in Cosmology)
19 pages, 3004 KiB  
Article
Enabling Symmetric Collaboration in Public Spaces through 3D Mobile Interaction
by Mayra Donaji Barrera Machuca, Winyu Chinthammit, Weidong Huang, Rainer Wasinger and Henry Duh
Symmetry 2018, 10(3), 69; https://doi.org/10.3390/sym10030069 - 16 Mar 2018
Cited by 4 | Viewed by 4600
Abstract
Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the [...] Read more.
Collaboration has been common in workplaces in various engineering settings and in our daily activities. However, how to effectively engage collaborators with collaborative tasks has long been an issue due to various situational and technical constraints. The research in this paper addresses the issue in a specific scenario, which is how to enable users to interact with public information from their own perspective. We describe a 3D mobile interaction technique that allows users to collaborate with other people by creating a symmetric and collaborative ambience. This in turn can increase their engagement with public displays. In order to better understand the benefits and limitations of this technique, we conducted a usability study with a total of 40 participants. The results indicate that the 3D mobile interaction technique promotes collaboration between users and also improves their engagement with the public displays. Full article
(This article belongs to the Special Issue Symmetry in Cooperative Applications III)
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10 pages, 397 KiB  
Article
Casimir Energies for Isorefractive or Diaphanous Balls
by Kimball A. Milton and Iver Brevik
Symmetry 2018, 10(3), 68; https://doi.org/10.3390/sym10030068 - 16 Mar 2018
Cited by 4 | Viewed by 3296
Abstract
It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside [...] Read more.
It is known that the Casimir self-energy of a homogeneous dielectric ball is divergent, although a finite self-energy can be extracted through second order in the deviation of the permittivity from the vacuum value. The exception occurs when the speed of light inside the spherical boundary is the same as that outside, so the self-energy of a perfectly conducting spherical shell is finite, as is the energy of a dielectric-diamagnetic sphere with ε μ = 1 , a so-called isorefractive or diaphanous ball. Here we re-examine that example and attempt to extend it to an electromagnetic δ -function sphere, where the electric and magnetic couplings are equal and opposite. Unfortunately, although the energy expression is superficially ultraviolet finite, additional divergences appear that render it difficult to extract a meaningful result in general, but some limited results are presented. Full article
(This article belongs to the Special Issue Casimir Physics and Applications)
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28 pages, 636 KiB  
Article
Construction of Fullerenes and Pogorelov Polytopes with 5-, 6- and one 7-Gonal Face
by Nikolai Erokhovets
Symmetry 2018, 10(3), 67; https://doi.org/10.3390/sym10030067 - 15 Mar 2018
Cited by 7 | Viewed by 4285
Abstract
A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple 3-polytopes with cyclically 5-edge connected graphs. A Pogorelov polytope has no 3- and 4-gons and may have any prescribed [...] Read more.
A Pogorelov polytope is a combinatorial simple 3-polytope realizable in the Lobachevsky (hyperbolic) space as a bounded right-angled polytope. These polytopes are exactly simple 3-polytopes with cyclically 5-edge connected graphs. A Pogorelov polytope has no 3- and 4-gons and may have any prescribed numbers of k-gons, k ≥ 7 . Any simple polytope with only 5-, 6- and at most one 7-gon is Pogorelov. For any other prescribed numbers of k-gons, k ≥ 7 , we give an explicit construction of a Pogorelov and a non-Pogorelov polytope. Any Pogorelov polytope different from k-barrels (also known as Löbel polytopes, whose graphs are biladders on 2 k vertices) can be constructed from the 5- or the 6-barrel by cutting off pairs of adjacent edges and connected sums with the 5-barrel along a 5-gon with the intermediate polytopes being Pogorelov. For fullerenes, there is a stronger result. Any fullerene different from the 5-barrel and the ( 5 , 0 ) -nanotubes can be constructed by only cutting off adjacent edges from the 6-barrel with all the intermediate polytopes having 5-, 6- and at most one additional 7-gon adjacent to a 5-gon. This result cannot be literally extended to the latter class of polytopes. We prove that it becomes valid if we additionally allow connected sums with the 5-barrel and 3 new operations, which are compositions of cutting off adjacent edges. We generalize this result to the case when the 7-gon may be isolated from 5-gons. Full article
(This article belongs to the Special Issue Mathematical Crystallography)
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16 pages, 1364 KiB  
Article
Carbon Oxides Gases for Occupancy Counting and Emergency Control in Fog Environment
by Kairong Duan, Simon Fong, Yan Zhuang and Wei Song
Symmetry 2018, 10(3), 66; https://doi.org/10.3390/sym10030066 - 15 Mar 2018
Cited by 3 | Viewed by 4201
Abstract
The information of human occupancy plays a crucial role in building management. For instance, fewer people, less demand for heat and electricity supply, and vice versa. Moreover, when there is a fire in a building, it is convenient to know how many persons [...] Read more.
The information of human occupancy plays a crucial role in building management. For instance, fewer people, less demand for heat and electricity supply, and vice versa. Moreover, when there is a fire in a building, it is convenient to know how many persons in a single room there are in order to plan a more efficient rescue strategy. However, currently most buildings have not installed adequate devices that can be used to count the number of people, and the most popular embedded fire alarm system triggers a warning only when a fire breaks out with plenty of smoke. In view of this constraint, in this paper we propose a carbon oxides gases based warning system to detect potential fire breakouts and to estimate the number of people in the proximity. In order to validate the efficiency of the devised system, we simulate its application in the Fog Computing environment. Furthermore, we also improve the iFogSim by giving data analytics capacity to it. Based on this framework, energy consumption, latency, and network usage of the designed system obtained from iFogSim are compared with those obtained from Cloud environment. Full article
(This article belongs to the Special Issue Emerging Approaches and Advances in Big Data)
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22 pages, 1129 KiB  
Article
Spectrum Graph Coloring and Applications to Wi-Fi Channel Assignment
by David Orden, Jose Manuel Gimenez-Guzman, Ivan Marsa-Maestre and Enrique De la Hoz
Symmetry 2018, 10(3), 65; https://doi.org/10.3390/sym10030065 - 14 Mar 2018
Cited by 27 | Viewed by 6155
Abstract
We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the [...] Read more.
We introduce and explore a family of vertex-coloring problems, which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of interferences between each pair of colors, the Threshold Spectrum Coloring problem fixes the number of colors available and aims to minimize the interference threshold, i.e., the maximum of the interferences at the vertices. Conversely, the Chromatic Spectrum Coloring problem fixes a threshold and aims to minimize the number of colors for which respecting that threshold is possible. As the main theoretical results, we prove tight upper bounds for the solutions to each problem. Since both problems turn out to be NP-hard, we complete the scene with experimental results. We propose a DSATUR-based heuristic and study its performance to minimize the maximum vertex interference in Wi-Fi channel assignment, both for randomly-generated graphs and for a real-world scenario. Further, for all these graphs, we experimentally check the goodness of the theoretical bounds. Full article
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18 pages, 2699 KiB  
Article
Vision-Based Parking-Slot Detection: A Benchmark and A Learning-Based Approach
by Lin Zhang, Xiyuan Li, Junhao Huang, Ying Shen and Dongqing Wang
Symmetry 2018, 10(3), 64; https://doi.org/10.3390/sym10030064 - 13 Mar 2018
Cited by 22 | Viewed by 9036
Abstract
Recent years have witnessed a growing interest in developing automatic parking systems in the field of intelligent vehicles. However, how to effectively and efficiently locating parking-slots using a vision-based system is still an unresolved issue. Even more seriously, there is no publicly available [...] Read more.
Recent years have witnessed a growing interest in developing automatic parking systems in the field of intelligent vehicles. However, how to effectively and efficiently locating parking-slots using a vision-based system is still an unresolved issue. Even more seriously, there is no publicly available labeled benchmark dataset for tuning and testing parking-slot detection algorithms. In this paper, we attempt to fill the above-mentioned research gaps to some extent and our contributions are twofold. Firstly, to facilitate the study of vision-based parking-slot detection, a large-scale parking-slot image database is established. This database comprises 8600 surround-view images collected from typical indoor and outdoor parking sites. For each image in this database, the marking-points and parking-slots are carefully labeled. Such a database can serve as a benchmark to design and validate parking-slot detection algorithms. Secondly, a learning-based parking-slot detection approach, namely P S D L , is proposed. Using P S D L , given a surround-view image, the marking-points will be detected first and then the valid parking-slots can be inferred. The efficacy and efficiency of P S D L have been corroborated on our database. It is expected that P S D L can serve as a baseline when the other researchers develop more sophisticated methods. Full article
(This article belongs to the Special Issue Advanced in Artificial Intelligence and Cloud Computing)
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17 pages, 1342 KiB  
Article
Symmetric Agency Graphs Facilitate and Improve the Quality of Virtual Network Embedding
by Chenggui Zhao and Behrooz Parhami
Symmetry 2018, 10(3), 63; https://doi.org/10.3390/sym10030063 - 11 Mar 2018
Cited by 4 | Viewed by 3416
Abstract
Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of network symmetry are well known in the design of load-balanced routing algorithms and in network performance analysis. Our work in this paper shows that benefits of graph symmetry also extend [...] Read more.
Virtual network embedding (VNE) is a key technology in network virtualization. Advantages of network symmetry are well known in the design of load-balanced routing algorithms and in network performance analysis. Our work in this paper shows that benefits of graph symmetry also extend to the domain of network embedding. Specifically, we propose an efficient VNE method based on modular and structured agency guidance, a regular graph function. The proposed method, which is based on symmetric intermediate graphs, offers two main advantages. Firstly, characteristics of the intermediate structures enhance the computational efficiency of the VNE process. Secondly, the static agency network modeled with such intermediate structures improves the quality of the resulting embedding. These two advantages of our method are elaborated upon and verified by examples and simulations, respectively. In addition, we present a theoretical analysis explaining the reasons behind the benefits offered by such middleware. Full article
(This article belongs to the Special Issue Advances in Future Internet and Industrial Internet of Things)
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26 pages, 1733 KiB  
Article
The LHC Higgs Boson Discovery: Updated Implications for Finite Unified Theories and the SUSY Breaking Scale
by Sven Heinemeyer, Myriam Mondragón, Gregory Patellis, Nicholas Tracas and George Zoupanos
Symmetry 2018, 10(3), 62; https://doi.org/10.3390/sym10030062 - 7 Mar 2018
Cited by 13 | Viewed by 3186
Abstract
Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among [...] Read more.
Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories, which can be made finite to all orders in perturbation theory, based on the principle of the reduction of couplings. The latter consists of searching for renormalization group invariant relations among parameters of a renormalizable theory holding to all orders in perturbation theory. FUTs have proven very successful so far. In particular, they predicted the top quark mass one and half years before its experimental discovery, while around five years before the Higgs boson discovery, a particular FUT was predicting the light Higgs boson in the mass range ∼121–126 GeV, in striking agreement with the discovery at LHC. Here, we review the basic properties of the supersymmetric theories and in particular finite theories resulting from the application of the method of reduction of couplings in their dimensionless and dimensionful sectors. Then, we analyze the phenomenologically-favored FUT, based on SU(5). This particular FUT leads to a finiteness constrained version of the Minimal SUSY Standard Model (MSSM), which naturally predicts a relatively heavy spectrum with colored supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, and large parts of the allowed spectrum of the lighter might be accessible at CLIC. The FCC-hhwill be able to fully test the predicted spectrum. Full article
(This article belongs to the Special Issue Symmetry in Quantum Field Theory)
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14 pages, 3049 KiB  
Article
The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force
by Gang Deng, Ling Pei, Ni Hu, Yang Liu and Jin-Rong Zhu
Symmetry 2018, 10(3), 61; https://doi.org/10.3390/sym10030061 - 7 Mar 2018
Cited by 3 | Viewed by 3131
Abstract
Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that [...] Read more.
Quantum fluctuations of the electromagnetic field give rise to the force between parallel plates: the Casimir force. We theoretically calculate the Casimir force between two parallel isotropic plates when the space between the plates is filled with anisotropic material. Our result shows that the Casimir force, especially in the direction of the force, can be significantly affected by the anisotropy of the intervening material. We also discuss the combined influence of dispersion and anisotropy, and analyze the impact of the external electric filed on the Casimir force by affecting the anisotropy of the intervening material by Kerr electro-optical effect. Full article
(This article belongs to the Special Issue Casimir Physics and Applications)
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16 pages, 4628 KiB  
Article
Deep Learning as a Tool for Automatic Segmentation of Corneal Endothelium Images
by Karolina Nurzynska
Symmetry 2018, 10(3), 60; https://doi.org/10.3390/sym10030060 - 6 Mar 2018
Cited by 29 | Viewed by 5157
Abstract
The automatic analysis of the state of the corneal endothelium is of much interest in ophthalmology. Up till now, several manual and semi-automatic methods have been introduced, but the need of fully-automatic segmentation of cells in the endothelium is still in search. This [...] Read more.
The automatic analysis of the state of the corneal endothelium is of much interest in ophthalmology. Up till now, several manual and semi-automatic methods have been introduced, but the need of fully-automatic segmentation of cells in the endothelium is still in search. This work addresses the problem of automatic delineation of cells in the corneal endothelium images and suggests to use the convolutional neural network (CNN) to classify between cell center, cell body, and cell border in order to achieve precise segmentation. Additionally, a method to automatically select and split merged cells is given. In order to skeletonize the result, the best-fit method is used. The achieved outcomes are compared to manual annotations in order to define the mutual overlapping. The Dice index, Jaccard coefficient, modified Hausdorff distance, and several other metrics for mosaic overlapping are used. As a final check-up, the visual inspection is shown. The performed experiments revealed the best architecture for CNN. The correctness and precision of the segmentation were evaluated on Endothelial Cell “Alizarine” dataset. According to the Dice index and Jaccard coefficient, the automatically achieved cell delineation overlaps the original one with 93% precision. While modified Hausdorff distance shows 0.14 pixel distance, proving very high accuracy. These findings are confirmed by other metrics and also supported by presented visual inspection of achieved segmentations. To conclude, the methodology to achieve fully-automatic delineation of cell boundaries in the corneal endothelium images was presented. The segmentation obtained as a result of pixel classification with CNN proved very high precision. Full article
(This article belongs to the Special Issue Advances in Medical Image Segmentation)
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14 pages, 2599 KiB  
Article
Microstructure and Properties of the Ferroelectric-Ferromagnetic PLZT-Ferrite Composites
by Dariusz Bochenek, Przemysław Niemiec, Joanna Korzekwa, Bartłomiej Durtka and Zbigniew Stokłosa
Symmetry 2018, 10(3), 59; https://doi.org/10.3390/sym10030059 - 6 Mar 2018
Cited by 20 | Viewed by 4007
Abstract
The paper presents the technology of ferroelectric-ferromagnetic ceramic composites obtained from PLZT powder (the chemical formula Pb0.98La0.02(Zr0.90Ti0.10)0.995O3) and ferrite powder (Ni0.64Zn0.36Fe2O4), as well [...] Read more.
The paper presents the technology of ferroelectric-ferromagnetic ceramic composites obtained from PLZT powder (the chemical formula Pb0.98La0.02(Zr0.90Ti0.10)0.995O3) and ferrite powder (Ni0.64Zn0.36Fe2O4), as well as the results of X-ray powder-diffraction data (XRD) measurement, microstructure, dielectric, ferroelectric, and magnetic properties of the composite samples. The ferroelectric-ferromagnetic composite (P-F) was obtained by mixing and the synthesis of 90% of PLZT and 10% of ferrite powders. The XRD test of the P-F composite shows a two-phase structure derived from the PLZT component (strong peaks) and the ferrite component (weak peaks). The symmetry of PLZT was identified as a rhombohedral ferroelectric phase, while the ferrite was identified as a spinel structure. Scanning electron microscope (SEM) microstructure analysis of the P-F ceramic composites showed that fine grains of the PLZT component surrounded large ferrite grains. At room temperature P-F composites exhibit both ferroelectric and ferromagnetic properties. The P-F composite samples have lower values of the maximum dielectric permittivity at the Curie temperature and a higher dielectric loss compared to the PLZT ceramics, however, the exhibit overall good multiferroic properties. Full article
(This article belongs to the Special Issue Multiferroic Dynamics)
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25 pages, 1287 KiB  
Article
Cuckoo Search Algorithm with Lévy Flights for Global-Support Parametric Surface Approximation in Reverse Engineering
by Andrés Iglesias, Akemi Gálvez, Patricia Suárez, Mikio Shinya, Norimasa Yoshida, César Otero, Cristina Manchado and Valentin Gomez-Jauregui
Symmetry 2018, 10(3), 58; https://doi.org/10.3390/sym10030058 - 3 Mar 2018
Cited by 27 | Viewed by 5076
Abstract
This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric [...] Read more.
This paper concerns several important topics of the Symmetry journal, namely, computer-aided design, computational geometry, computer graphics, visualization, and pattern recognition. We also take advantage of the symmetric structure of the tensor-product surfaces, where the parametric variables u and v play a symmetric role in shape reconstruction. In this paper we address the general problem of global-support parametric surface approximation from clouds of data points for reverse engineering applications. Given a set of measured data points, the approximation is formulated as a nonlinear continuous least-squares optimization problem. Then, a recent metaheuristics called Cuckoo Search Algorithm (CSA) is applied to compute all relevant free variables of this minimization problem (namely, the data parameters and the surface poles). The method includes the iterative generation of new solutions by using the Lévy flights to promote the diversity of solutions and prevent stagnation. A critical advantage of this method is its simplicity: the CSA requires only two parameters, many fewer than any other metaheuristic approach, so the parameter tuning becomes a very easy task. The method is also simple to understand and easy to implement. Our approach has been applied to a benchmark of three illustrative sets of noisy data points corresponding to surfaces exhibiting several challenging features. Our experimental results show that the method performs very well even for the cases of noisy and unorganized data points. Therefore, the method can be directly used for real-world applications for reverse engineering without further pre/post-processing. Comparative work with the most classical mathematical techniques for this problem as well as a recent modification of the CSA called Improved CSA (ICSA) is also reported. Two nonparametric statistical tests show that our method outperforms the classical mathematical techniques and provides equivalent results to ICSA for all instances in our benchmark. Full article
(This article belongs to the Special Issue Advances in Computer Graphics, Geometric Modeling, and Virtual and Augmented Reality)
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13 pages, 4200 KiB  
Article
Towards Shape-Changing Devices: Physical Interface Control with an Active Contour Model
by Byung-Kil Han, Seung-Chan Kim and Dong-Soo Kwon
Symmetry 2018, 10(3), 57; https://doi.org/10.3390/sym10030057 - 1 Mar 2018
Cited by 2 | Viewed by 3533
Abstract
This paper proposes a novel tangible interface system to enhance the immersive experience in virtual reality environments. The proposed system allows representing physical properties of the tool, such as the deflection of the elastic rods, which users handle in a virtual and physical [...] Read more.
This paper proposes a novel tangible interface system to enhance the immersive experience in virtual reality environments. The proposed system allows representing physical properties of the tool, such as the deflection of the elastic rods, which users handle in a virtual and physical environment. This system is composed of two parts; one is an articulated interface to visually represent the physical behavior and the other is a computational algorithm that can compute a set of 6-DOF positions of the links. The proposed computational algorithm extends an active contour model, which is used primarily in computer vision and image processing, incorporating a spring and damping constraint energy functional. An elastic rod is modeled as a series of rigid line segments with a symmetric relationship between neighboring segments, and its shape is modeled to be influenced by energies that are induced by a user, and the external deformation of the spline. The symmetric and sparse properties of the proposed model enable an efficient energy minimization process, and the modification of a number of the line segments. Based on this configuration, we construct an energy generation method based on the positional displacement of the base element to generate the deflection behavior of the contour according to the user’s motion in the space. Therefore, the physical device can simulate a variety of deformable objects by modulating energy parameters during the energy minimization process. Experimental results demonstrate the feasibility of emulating various behaviors of deformable splines, and applying to virtual reality system without interfering with the motion-to-photon latency. We also discuss the method’s limitations and explore its potential. Full article
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9 pages, 1023 KiB  
Review
Organophosphines in Cis-PtP2CCl Derivatives Structural Aspects
by Milan Melnik, Peter Mikus and Clive Edward Holloway
Symmetry 2018, 10(3), 56; https://doi.org/10.3390/sym10030056 - 28 Feb 2018
Viewed by 2930
Abstract
This manuscript summarizes and analyzes X-ray data of monomeric cis-PtP2CCl derivatives. These complexes crystallize in the following crystal systems: tetragonal, P42/n (3), triclinic, Pī (10), orthorhombic, P212121 (prevails)(16), and monoclinic, P21/c (prevails) [...] Read more.
This manuscript summarizes and analyzes X-ray data of monomeric cis-PtP2CCl derivatives. These complexes crystallize in the following crystal systems: tetragonal, P42/n (3), triclinic, Pī (10), orthorhombic, P212121 (prevails)(16), and monoclinic, P21/c (prevails) (36) examples. There are three sub-groups of the respective complexes: Pt(η1-PL)2(η1-CL)(η1-Cl); Pt(η2-P2L)(η1-CL)(η1-Cl) and Pt(η1-PL)(η2-P,CL)(η1-Cl). The chelating P,P-donor ligands form: four-(POP, PCP), five-(PC2P), six-(PC3P, PCNCP), seven-(PC4P) and even ten-(PCNCNCNCP) membered rings. The chelating P.C-donor ligands create three-(PC), four-(PCC) and five-(PC2C) membered rings. The mean Pt-L bond distance elongates in the sequence: 2.10 Å (C, trans to P) < 2.222 Å (P, trans to Cl) < 2.312 Å (P, trans to C) < 2.360 Å (Cl, trans to P). There are examples which exist in two isomeric forms, of the distortion isomer type. Full article
(This article belongs to the Special Issue Symmetry in Coordination Chemistry)
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13 pages, 273 KiB  
Article
Symmetric Representation of Ternary Forms Associated to Some Toeplitz Matrices †
by Mao-Ting Chien and Hiroshi Nakazato
Symmetry 2018, 10(3), 55; https://doi.org/10.3390/sym10030055 - 27 Feb 2018
Viewed by 2692
Abstract
Let A be an n × n complex matrix. Assume the determinantal curve [...] Read more.
Let A be an n × n complex matrix. Assume the determinantal curve V A = { [ ( x , y , z ) ] ∈ CP 2 : F A ( x , y , z ) = det ( x ℜ ( A ) + y ℑ ( A ) + z I n ) = 0 } is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying F S ( x , y , z ) = F A ( x , y , z ) . It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of 4 × 4 nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from F A ( x , y , z ) associated to the specific 4 × 4 nilpotent Toeplitz matrices. Full article
(This article belongs to the Special Issue Selected Papers: Symmetry 2017—The First International Conference on Symmetry)
16 pages, 291 KiB  
Article
Renormalization for a Scalar Field in an External Scalar Potential
by Stephen A. Fulling, Thomas E. Settlemyre and Kimball A. Milton
Symmetry 2018, 10(3), 54; https://doi.org/10.3390/sym10030054 - 27 Feb 2018
Cited by 12 | Viewed by 3482
Abstract
The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background [...] Read more.
The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential. Full article
(This article belongs to the Special Issue Casimir Physics and Applications)
26 pages, 367 KiB  
Article
Some Aspects of Nonlinearity and Self-Organization In Biosystems on Examples of Localized Excitations in the DNA Molecule and Generalized Fisher–KPP Model
by A. V. Shapovalov and V. V. Obukhov
Symmetry 2018, 10(3), 53; https://doi.org/10.3390/sym10030053 - 27 Feb 2018
Cited by 11 | Viewed by 3687
Abstract
This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very [...] Read more.
This review deals with ideas and approaches to nonlinear phenomena, based on different branches of physics and related to biological systems, that focus on how small impacts can significantly change the state of the system at large spatial scales. This problem is very extensive, and it cannot be fully resolved in this paper. Instead, some selected physical effects are briefly reviewed. We consider sine-Gordon solitons and nonlinear Schrodinger solitons in some models of DNA as examples of self-organization at the molecular level, as well as examine features of their formation and dynamics under the influence of external influences. In addition, the formation of patterns in the generalized Fisher–KPP model is viewed as a simple example of self-organization in a system with nonlocal interaction at the cellular level. Symmetries of model equations are employed to analyze the considered nonlinear phenomena. In this context the possible relations between phenomena considered and released activity effect, which is assessed differently in the literature, are discussed. Full article
(This article belongs to the Special Issue Symmetry: Anniversary Feature Papers 2018)
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16 pages, 7600 KiB  
Article
Lorentz Transformation, Poincaré Vectors and Poincaré Sphere in Various Branches of Physics
by Tiberiu Tudor
Symmetry 2018, 10(3), 52; https://doi.org/10.3390/sym10030052 - 26 Feb 2018
Cited by 8 | Viewed by 7692
Abstract
In the frame of a generic language extended from the polarization theory—comprising the notions of Poincaré vectors, Poincaré sphere, and P-spheres—a geometric approach to Lorentz transformations alternative to the Minkowskian one is given. Unlike the four-dimensional Minkowskian approach, this new approach operates in [...] Read more.
In the frame of a generic language extended from the polarization theory—comprising the notions of Poincaré vectors, Poincaré sphere, and P-spheres—a geometric approach to Lorentz transformations alternative to the Minkowskian one is given. Unlike the four-dimensional Minkowskian approach, this new approach operates in the three-dimensional space of Poincaré vectors. Full article
(This article belongs to the Special Issue Modern Trends of Lorentz Symmetry and Lorentz Violation)
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