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Symmetry, Volume 8, Issue 6 (June 2016) – 15 articles

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281 KiB  
Article
Parity-Time Symmetry and the Toy Models of Gain-Loss Dynamics near the Real Kato’s Exceptional Points
by Miloslav Znojil
Symmetry 2016, 8(6), 52; https://doi.org/10.3390/sym8060052 - 20 Jun 2016
Cited by 12 | Viewed by 4722
Abstract
For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a [...] Read more.
For a given operator D ( t ) of an observable in theoretical parity-time symmetric quantum physics (or for its evolution-generator analogues in the experimental gain-loss classical optics, etc.) the instant t c r i t i c a l of a spontaneous breakdown of the parity-time alias gain-loss symmetry should be given, in the rigorous language of mathematics, the Kato’s name of an “exceptional point”, t c r i t i c a l = t ( E P ) . In the majority of conventional applications the exceptional point (EP) values are not real. In our paper, we pay attention to several exactly tractable toy-model evolutions for which at least some of the values of t ( E P ) become real. These values are interpreted as “instants of a catastrophe”, be it classical or quantum. In the classical optical setting the discrete nature of our toy models might make them amenable to simulations. In the latter context the instant of Big Bang is mentioned as an illustrative sample of possible physical meaning of such an EP catastrophe in quantum cosmology. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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775 KiB  
Article
On Classification of Symmetry Reductions for the Eikonal Equation
by Vasyl Fedorchuk and Volodymyr Fedorchuk
Symmetry 2016, 8(6), 51; https://doi.org/10.3390/sym8060051 - 17 Jun 2016
Cited by 8 | Viewed by 3709
Abstract
We study the relationship between the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P ( 1 , 4 ) and the types of symmetry reduction of the eikonal equation to ordinary differential equations (ODEs). [...] Read more.
We study the relationship between the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group P ( 1 , 4 ) and the types of symmetry reduction of the eikonal equation to ordinary differential equations (ODEs). Full article
493 KiB  
Article
Exact and Numerical Solutions of a Spatially-Distributed Mathematical Model for Fluid and Solute Transport in Peritoneal Dialysis
by Roman Cherniha, Kateryna Gozak and Jacek Waniewski
Symmetry 2016, 8(6), 50; https://doi.org/10.3390/sym8060050 - 16 Jun 2016
Cited by 8 | Viewed by 4838
Abstract
The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a [...] Read more.
The nonlinear mathematical model for solute and fluid transport induced by the osmotic pressure of glucose and albumin with the dependence of several parameters on the hydrostatic pressure is described. In particular, the fractional space available for macromolecules (albumin was used as a typical example) and fractional fluid void volume were assumed to be different functions of hydrostatic pressure. In order to find non-uniform steady-state solutions analytically, some mathematical restrictions on the model parameters were applied. Exact formulae (involving hypergeometric functions) for the density of fluid flux from blood to tissue and the fluid flux across tissues were constructed. In order to justify the applicability of the analytical results obtained, a wide range of numerical simulations were performed. It was found that the analytical formulae can describe with good approximation the fluid and solute transport (especially the rate of ultrafiltration) for a wide range of values of the model parameters. Full article
(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)
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948 KiB  
Article
Neutrino Signals in Electron-Capture Storage-Ring Experiments
by Avraham Gal
Symmetry 2016, 8(6), 49; https://doi.org/10.3390/sym8060049 - 15 Jun 2016
Cited by 6 | Viewed by 6802
Abstract
Neutrino signals in electron-capture decays of hydrogen-like parent ions P in storage-ring experiments at GSI are reconsidered, with special emphasis placed on the storage-ring quasi-circular motion of the daughter ions D in two-body decays P D + ν e . It is [...] Read more.
Neutrino signals in electron-capture decays of hydrogen-like parent ions P in storage-ring experiments at GSI are reconsidered, with special emphasis placed on the storage-ring quasi-circular motion of the daughter ions D in two-body decays P D + ν e . It is argued that, to the extent that daughter ions are detected, these detection rates might exhibit modulations with periods of order seconds, similar to those reported in the GSI storage-ring experiments for two-body decay rates. New dedicated experiments in storage rings, or using traps, could explore these modulations. Full article
(This article belongs to the Special Issue Symmetry in Hadrons and Nuclei)
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3010 KiB  
Article
Optimal Face-Iris Multimodal Fusion Scheme
by Omid Sharifi and Maryam Eskandari
Symmetry 2016, 8(6), 48; https://doi.org/10.3390/sym8060048 - 15 Jun 2016
Cited by 28 | Viewed by 6991
Abstract
Multimodal biometric systems are considered a way to minimize the limitations raised by single traits. This paper proposes new schemes based on score level, feature level and decision level fusion to efficiently fuse face and iris modalities. Log-Gabor transformation is applied as the [...] Read more.
Multimodal biometric systems are considered a way to minimize the limitations raised by single traits. This paper proposes new schemes based on score level, feature level and decision level fusion to efficiently fuse face and iris modalities. Log-Gabor transformation is applied as the feature extraction method on face and iris modalities. At each level of fusion, different schemes are proposed to improve the recognition performance and, finally, a combination of schemes at different fusion levels constructs an optimized and robust scheme. In this study, CASIA Iris Distance database is used to examine the robustness of all unimodal and multimodal schemes. In addition, Backtracking Search Algorithm (BSA), a novel population-based iterative evolutionary algorithm, is applied to improve the recognition accuracy of schemes by reducing the number of features and selecting the optimized weights for feature level and score level fusion, respectively. Experimental results on verification rates demonstrate a significant improvement of proposed fusion schemes over unimodal and multimodal fusion methods. Full article
(This article belongs to the Special Issue Symmetry in Complex Networks II)
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1405 KiB  
Article
A Data Mining Approach for Cardiovascular Disease Diagnosis Using Heart Rate Variability and Images of Carotid Arteries
by Hyeongsoo Kim, Musa Ibrahim M. Ishag, Minghao Piao, Taeil Kwon and Keun Ho Ryu
Symmetry 2016, 8(6), 47; https://doi.org/10.3390/sym8060047 - 13 Jun 2016
Cited by 31 | Viewed by 6867
Abstract
In this paper, we proposed not only an extraction methodology of multiple feature vectors from ultrasound images for carotid arteries (CAs) and heart rate variability (HRV) of electrocardiogram signal, but also a suitable and reliable prediction model useful in the diagnosis of cardiovascular [...] Read more.
In this paper, we proposed not only an extraction methodology of multiple feature vectors from ultrasound images for carotid arteries (CAs) and heart rate variability (HRV) of electrocardiogram signal, but also a suitable and reliable prediction model useful in the diagnosis of cardiovascular disease (CVD). For inventing the multiple feature vectors, we extract a candidate feature vector through image processing and measurement of the thickness of carotid intima-media (IMT). As a complementary way, the linear and/or nonlinear feature vectors are also extracted from HRV, a main index for cardiac disorder. The significance of the multiple feature vectors is tested with several machine learning methods, namely Neural Networks, Support Vector Machine (SVM), Classification based on Multiple Association Rule (CMAR), Decision tree induction and Bayesian classifier. As a result, multiple feature vectors extracted from both CAs and HRV (CA+HRV) showed higher accuracy than the separative feature vectors of CAs and HRV. Furthermore, the SVM and CMAR showed about 89.51% and 89.46%, respectively, in terms of diagnosing accuracy rate after evaluating the diagnosis or prediction methods using the finally chosen multiple feature vectors. Therefore, the multiple feature vectors devised in this paper can be effective diagnostic indicators of CVD. In addition, the feature vector analysis and prediction techniques are expected to be helpful tools in the decisions of cardiologists. Full article
(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)
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266 KiB  
Article
Coherent States of Harmonic and Reversed Harmonic Oscillator
by Alexander Rauh
Symmetry 2016, 8(6), 46; https://doi.org/10.3390/sym8060046 - 13 Jun 2016
Cited by 3 | Viewed by 4455
Abstract
A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart [...] Read more.
A one-dimensional wave function is assumed whose logarithm is a quadratic form in the configuration variable with time-dependent coefficients. This trial function allows for general time-dependent solutions both of the harmonic oscillator (HO) and the reversed harmonic oscillator (RO). For the HO, apart from the standard coherent states, a further class of solutions is derived with a time-dependent width parameter. The width of the corresponding probability density fluctuates, or "breathes" periodically with the oscillator frequency. In the case of the RO, one also obtains normalized wave packets which, however, show diffusion through exponential broadening with time. At the initial time, the integration constants give rise to complete sets of coherent states in the three cases considered. The results are applicable to the quantum mechanics of the Kepler-Coulomb problem when transformed to the model of a four-dimensional harmonic oscillator with a constraint. In the classical limit, as was shown recently, the wave packets of the RO basis generate the hyperbolic Kepler orbits, and, by means of analytic continuation, the elliptic orbits are also obtained quantum mechanically. Full article
(This article belongs to the Special Issue Harmonic Oscillators In Modern Physics)
2755 KiB  
Article
Fluctuating Charge Order: A Universal Phenomenon in Unconventional Superconductivity?
by Erminald Bertel and Alexander Menzel
Symmetry 2016, 8(6), 45; https://doi.org/10.3390/sym8060045 - 10 Jun 2016
Cited by 5 | Viewed by 6139
Abstract
Unconventional superconductors are characterized by various competing ordering phenomena in the normal state, such as antiferromagnetism, charge order, orbital order or nematicity. According to a widespread view, antiferromagnetic fluctuations are the dominant ordering phenomenon in cuprates and Fe based superconductors and are responsible [...] Read more.
Unconventional superconductors are characterized by various competing ordering phenomena in the normal state, such as antiferromagnetism, charge order, orbital order or nematicity. According to a widespread view, antiferromagnetic fluctuations are the dominant ordering phenomenon in cuprates and Fe based superconductors and are responsible for electron pairing. In contrast, charge order is believed to be subdominant and compete with superconductivity. Here, we argue that fluctuating charge order in the (0,π) direction is a feature shared by the cuprates and the Fe based superconductors alike. Recent data and theoretical models suggest that superconductivity is brought about by charge order excitations independently from spin fluctuations. Thus, quantum fluctuations of charge order may provide an alternative to spin fluctuations as a mechanism of electron pairing in unconventional superconductors. Full article
(This article belongs to the Special Issue Symmetry of the Order Parameter in Iron-Based Superconductors)
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260 KiB  
Article
On a Reduction Formula for a Kind of Double q-Integrals
by Zhi-Guo Liu
Symmetry 2016, 8(6), 44; https://doi.org/10.3390/sym8060044 - 8 Jun 2016
Cited by 8 | Viewed by 3723
Abstract
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us [...] Read more.
Using the q-integral representation of Sears’ nonterminating extension of the q-Saalschütz summation, we derive a reduction formula for a kind of double q-integrals. This reduction formula is used to derive a curious double q-integral formula, and also allows us to prove a general q-beta integral formula including the Askey–Wilson integral formula as a special case. Using this double q-integral formula and the theory of q-partial differential equations, we derive a general q-beta integral formula, which includes the Nassrallah–Rahman integral as a special case. Our evaluation does not require the orthogonality relation for the q-Hermite polynomials and the Askey–Wilson integral formula. Full article
(This article belongs to the Special Issue Symmetry in Orthogonal Polynomials)
5377 KiB  
Article
Investigating the Performance of a Fractal Ultrasonic Transducer Under Varying System Conditions
by Euan Barlow, Ebrahem A. Algehyne and Anthony J. Mulholland
Symmetry 2016, 8(6), 43; https://doi.org/10.3390/sym8060043 - 6 Jun 2016
Cited by 4 | Viewed by 4110
Abstract
As applications become more widespread there is an ever-increasing need to improve the accuracy of ultrasound transducers, in order to detect at much finer resolutions. In comparison with naturally occurring ultrasound systems the man-made systems have much poorer accuracy, and the scope for [...] Read more.
As applications become more widespread there is an ever-increasing need to improve the accuracy of ultrasound transducers, in order to detect at much finer resolutions. In comparison with naturally occurring ultrasound systems the man-made systems have much poorer accuracy, and the scope for improvement has somewhat plateaued as existing transducer designs have been iteratively improved over many years. The desire to bridge the gap between the man-made and naturally occurring systems has led to recent investigation of transducers with a more complex geometry, in order to replicate the complex structure of the natural systems. These transducers have structures representing fractal geometries, and these have been shown to be capable of delivering improved performance in comparison with standard transducer designs. This paper undertakes a detailed investigation of the comparative performance of a standard transducer design, and a transducer based on a fractal geometry. By considering how these performances vary with respect to the key system parameters, a robust assessment of the fractal transducer performance is provided. Full article
(This article belongs to the Special Issue Symmetry and Fractals)
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797 KiB  
Article
Low Scale Saturation of Effective NN Interactions and Their Symmetries
by Enrique Ruiz Arriola
Symmetry 2016, 8(6), 42; https://doi.org/10.3390/sym8060042 - 1 Jun 2016
Cited by 12 | Viewed by 3976
Abstract
The Skyrme force parameters can be uniquely determined by coarse graining the Nucleon-Nucleon (NN) interactions at a characteristic momentum scale. We show how exact V lowk potentials to second order in momenta are saturated with physical NN scattering threshold parameters at Center of [...] Read more.
The Skyrme force parameters can be uniquely determined by coarse graining the Nucleon-Nucleon (NN) interactions at a characteristic momentum scale. We show how exact V lowk potentials to second order in momenta are saturated with physical NN scattering threshold parameters at Center of Mass (CM) cut-off scales of about Λ = 250 MeV for the S-waves and Λ = 100 MeV for the P-waves. The pattern of Wigner and Serber symmetries unveiled previously and suggested by Quantum Chromodynamics (QCD) large N c contracted symmetry emerges at these scales. Full article
(This article belongs to the Special Issue Symmetry in Hadrons and Nuclei)
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5121 KiB  
Article
Hybrid Data Hiding Scheme Using Right-Most Digit Replacement and Adaptive Least Significant Bit for Digital Images
by Mehdi Hussain, Ainuddin Wahid Abdul Wahab, Noman Javed and Ki-Hyun Jung
Symmetry 2016, 8(6), 41; https://doi.org/10.3390/sym8060041 - 31 May 2016
Cited by 38 | Viewed by 8591
Abstract
The goal of image steganographic methods considers three main key issues: high embedding capacity, good visual symmetry/quality, and security. In this paper, a hybrid data hiding method combining the right-most digit replacement (RMDR) with an adaptive least significant bit (ALSB) is proposed to [...] Read more.
The goal of image steganographic methods considers three main key issues: high embedding capacity, good visual symmetry/quality, and security. In this paper, a hybrid data hiding method combining the right-most digit replacement (RMDR) with an adaptive least significant bit (ALSB) is proposed to provide not only high embedding capacity but also maintain a good visual symmetry. The cover-image is divided into lower texture (symmetry patterns) and higher texture (asymmetry patterns) areas and these textures determine the selection of RMDR and ALSB methods, respectively, according to pixel symmetry. This paper has three major contributions. First, the proposed hybrid method enhanced the embedding capacity due to efficient ALSB utilization in the higher texture areas of cover images. Second, the proposed hybrid method maintains the high visual quality because RMDR has the closest selection process to generate the symmetry between stego and cover pixels. Finally, the proposed hybrid method is secure against statistical regular or singular (RS) steganalysis and pixel difference histogram steganalysis because RMDR is capable of evading the risk of RS detection attacks due to pixel digits replacement instead of bits. Extensive experimental tests (over 1500+ cover images) are conducted with recent least significant bit (LSB)-based hybrid methods and it is demonstrated that the proposed hybrid method has a high embedding capacity (800,019 bits) while maintaining good visual symmetry (39.00% peak signal-to-noise ratio (PSNR)). Full article
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1353 KiB  
Article
On Solutions for Linear and Nonlinear Schrödinger Equations with Variable Coefficients: A Computational Approach
by Gabriel Amador, Kiara Colon, Nathalie Luna, Gerardo Mercado, Enrique Pereira and Erwin Suazo
Symmetry 2016, 8(6), 38; https://doi.org/10.3390/sym8060038 - 28 May 2016
Cited by 9 | Viewed by 4939
Abstract
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them [...] Read more.
In this work, after reviewing two different ways to solve Riccati systems, we are able to present an extensive list of families of integrable nonlinear Schrödinger (NLS) equations with variable coefficients. Using Riccati equations and similarity transformations, we are able to reduce them to the standard NLS models. Consequently, we can construct bright-, dark- and Peregrine-type soliton solutions for NLS with variable coefficients. As an important application of solutions for the Riccati equation with parameters, by means of computer algebra systems, it is shown that the parameters change the dynamics of the solutions. Finally, we test numerical approximations for the inhomogeneous paraxial wave equation by the Crank-Nicolson scheme with analytical solutions found using Riccati systems. These solutions include oscillating laser beams and Laguerre and Gaussian beams. Full article
(This article belongs to the Special Issue Harmonic Oscillators In Modern Physics)
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4790 KiB  
Article
A Methodology and Tool for Investigation of Artifacts Left by the BitTorrent Client
by Algimantas Venčkauskas, Vacius Jusas, Kęstutis Paulikas and Jevgenijus Toldinas
Symmetry 2016, 8(6), 40; https://doi.org/10.3390/sym8060040 - 26 May 2016
Cited by 3 | Viewed by 7037
Abstract
The BitTorrent client application is a popular utility for sharing large files over the Internet. Sometimes, this powerful utility is used to commit cybercrimes, like sharing of illegal material or illegal sharing of legal material. In order to help forensics investigators to fight [...] Read more.
The BitTorrent client application is a popular utility for sharing large files over the Internet. Sometimes, this powerful utility is used to commit cybercrimes, like sharing of illegal material or illegal sharing of legal material. In order to help forensics investigators to fight against these cybercrimes, we carried out an investigation of the artifacts left by the BitTorrent client. We proposed a methodology to locate the artifacts that indicate the BitTorrent client activity performed. Additionally, we designed and implemented a tool that searches for the evidence left by the BitTorrent client application in a local computer running Windows. The tool looks for the four files holding the evidence. The files are as follows: *.torrent, dht.dat, resume.dat, and settings.dat. The tool decodes the files, extracts important information for the forensic investigator and converts it into XML format. The results are combined into a single result file. Full article
(This article belongs to the Special Issue Symmetry in Secure Cyber World)
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1101 KiB  
Article
A PT -Symmetric Dual-Core System with the Sine-Gordon Nonlinearity and Derivative Coupling
by Jesús Cuevas-Maraver, Boris A. Malomed and Panayotis G. Kevrekidis
Symmetry 2016, 8(6), 39; https://doi.org/10.3390/sym8060039 - 26 May 2016
Cited by 7 | Viewed by 4484
Abstract
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling [...] Read more.
As an extension of the class of nonlinear PT -symmetric models, we propose a system of sine-Gordon equations, with the PT symmetry represented by balanced gain and loss in them. The equations are coupled by sine-field terms and first-order derivatives. The sinusoidal coupling stems from local interaction between adjacent particles in coupled Frenkel–Kontorova (FK) chains, while the cross-derivative coupling, which was not considered before, is induced by three-particle interactions, provided that the particles in the parallel FK chains move in different directions. Nonlinear modes are then studied in this system. In particular, kink-kink (KK) and kink-anti-kink (KA) complexes are explored by means of analytical and numerical methods. It is predicted analytically and confirmed numerically that the complexes are unstable for one sign of the sinusoidal coupling and stable for another. Stability regions are delineated in the underlying parameter space. Unstable complexes split into free kinks and anti-kinks that may propagate or become quiescent, depending on whether they are subject to gain or loss, respectively. Full article
(This article belongs to the Special Issue Parity-Time Symmetry in Optics and Photonics)
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