Symmetry

15 pages, 5848 KiB

Open AccessArticle

Use of Bone Marrow Aspirate Concentrate (BMAC) Associated with Hyperbaric Oxygenation Therapy in Maxillary Appositional Bone Reconstruction. A Randomized Clinical Trial

by Antonio Carlos Aloise, Paulo Pasquali, Marcelo Sperandio, Luis Guilherme Scavone de Macedo, Marcelo Lucchesi Teixeira, André Antonio Pelegrine and José Luis Calvo-Guirado

Symmetry 2018, 10(10), 533; https://doi.org/10.3390/sym10100533 - 22 Oct 2018

Viewed by 4316

Abstract

Objectives: The objective of this study was to evaluate bone reconstruction using xenograft alone and associated with bone marrow aspirate concentrate (BMAC) and hyperbaric oxygen therapy. Material and Methods: Twenty-four maxillary edentulous patients were randomly assigned into three groups: Control group (CG)—xenograft bone [...] Read more.

Objectives: The objective of this study was to evaluate bone reconstruction using xenograft alone and associated with bone marrow aspirate concentrate (BMAC) and hyperbaric oxygen therapy. Material and Methods: Twenty-four maxillary edentulous patients were randomly assigned into three groups: Control group (CG)—xenograft bone alone (n = 8); Group 1 (G1)—xenogeneic bone block combined with BMAC (n = 8), and Group 2 (G2)—xenogeneic bone block combined with BMAC and hyperbaric oxygenation (n = 8). Bone biopsies were harvested 6 months after grafting. Vital Mineralized Tissue (VMT), Non-vital Mineralized Tissue (NVMT), and Non-Mineralized Tissue (NMT) were measured. Computed tomography was also performed on three occasions T0 (preoperative), T4 (4 months postoperative), and T8 (8 months postoperative). The difference between T4 and T8 values with respect to T0 was used to determine the thickness level gain after 4 and 8 months, respectively. Results: The tomographic evaluation did not show significant differences between the groups either at 4 or at the 8 months postoperatively. Regarding the histomorphometric analysis, CG had the lowest percentages of VMT (36.58 ± 9.56%), whereas G1 and G2 had similar results (55.64 ± 2.83% and 55.30 ± 1.41%, respectively). Concerning NMT and NVMT levels, the opposite was observed, with CG levels of 51.21 ± 11.54% and 11.16 ± 2.37%, G1 of 39.76 ± 11.48% and 3.65 ± 0.87%, and G2 of 40.3 ± 11.48% and 4.10 ± 0.87%, respectively. Conclusions: The use of bone block xenograft associated with BMAC resulted in a significant increase of bone neoformation when compared to the xenograft alone, though hyperbaric oxygenation did not enhance the results. Full article

(This article belongs to the Special Issue Biomaterials and Symmetry)

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18 pages, 3817 KiB

Open AccessArticle

Relationship between the Paradox of Enrichment and the Dynamics of Persistence and Extinction in Prey-Predator Systems

by Jawdat Alebraheem

Symmetry 2018, 10(10), 532; https://doi.org/10.3390/sym10100532 - 22 Oct 2018

Cited by 7 | Viewed by 3702

Abstract

The paradox of the enrichment phenomenon, considered one of the main counterintuitive observations in ecology, likely destabilizes predator–prey dynamics by increasing the nutrition of the prey. We use two systems to study the occurrence of the paradox of enrichment: The prey–predator system and [...] Read more.

The paradox of the enrichment phenomenon, considered one of the main counterintuitive observations in ecology, likely destabilizes predator–prey dynamics by increasing the nutrition of the prey. We use two systems to study the occurrence of the paradox of enrichment: The prey–predator system and the one prey, two predators system, with Holling type I and type II functional and numerical responses. We introduce a new approach that involves the connection between the occurrence of the enrichment paradox and persistence and extinction dynamics. We apply two main analytical techniques to study the persistence and extinction dynamics of two and three trophics, respectively. The linearity and nonlinearity of functional and numerical responses plays important roles in the occurrence of the paradox of enrichment. We derive the persistence and extinction conditions through the carrying capacity parameter, and perform some numerical simulations to demonstrate the effects of the paradox of enrichment when increasing carrying capacity. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications)

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9 pages, 259 KiB

Open AccessArticle

by Jun Ye, Zebo Fang and Wenhua Cui

Symmetry 2018, 10(10), 531; https://doi.org/10.3390/sym10100531 - 22 Oct 2018

Cited by 9 | Viewed by 2132

Abstract

Since language is used for thinking and expressing habits of humans in real life, the linguistic evaluation for an objective thing is expressed easily in linguistic terms/values. However, existing linguistic concepts cannot describe linguistic arguments regarding an evaluated object in two-dimensional universal sets [...] Read more.

Since language is used for thinking and expressing habits of humans in real life, the linguistic evaluation for an objective thing is expressed easily in linguistic terms/values. However, existing linguistic concepts cannot describe linguistic arguments regarding an evaluated object in two-dimensional universal sets (TDUSs). To describe linguistic neutrosophic arguments in decision making problems regarding TDUSs, this study proposes a Q-linguistic neutrosophic variable set (Q-LNVS) for the first time, which depicts its truth, indeterminacy, and falsity linguistic values independently corresponding to TDUSs, and vector similarity measures of Q-LNVSs. Thereafter, a linguistic neutrosophic multi-attribute decision-making (MADM) approach by using the presented similarity measures, including the cosine, Dice, and Jaccard measures, is developed under Q-linguistic neutrosophic setting. Lastly, the applicability and effectiveness of the presented MADM approach is presented by an illustrative example under Q-linguistic neutrosophic setting. Full article

(This article belongs to the Special Issue Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets)

16 pages, 1243 KiB

Open AccessArticle

An Image Secret Sharing Method Based on Matrix Theory

by Wanmeng Ding, Kesheng Liu, Xuehu Yan, Huaixi Wang, Lintao Liu and Qinghong Gong

Symmetry 2018, 10(10), 530; https://doi.org/10.3390/sym10100530 - 22 Oct 2018

Cited by 13 | Viewed by 2708

Abstract

Most of today’s secret image sharing technologies are based on the polynomial-based secret sharing scheme proposed by shamir. At present, researchers mostly focus on the development of properties such as small shadow size and lossless recovery, instead of the principle of Shamir’s polynomial-based [...] Read more.

Most of today’s secret image sharing technologies are based on the polynomial-based secret sharing scheme proposed by shamir. At present, researchers mostly focus on the development of properties such as small shadow size and lossless recovery, instead of the principle of Shamir’s polynomial-based SS scheme. In this paper, matrix theory is used to analyze Shamir’s polynomial-based scheme, and a general (k, n) threshold secret image sharing scheme based on matrix theory is proposed. The effectiveness of the proposed scheme is proved by theoretical and experimental results. Moreover, it has been proved that the Shamir’s polynomial-based SS scheme is a special case of our proposed scheme. Full article

(This article belongs to the Special Issue Emerging Data Hiding Systems in Image Communications)

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11 pages, 2273 KiB

Open AccessArticle

Advanced Classification of Coffee Beans with Fatty Acids Profiling to Block Information Loss

by Ying-Che Hung, Ping Chen and Liang-Yü Chen

Symmetry 2018, 10(10), 529; https://doi.org/10.3390/sym10100529 - 22 Oct 2018

Cited by 6 | Viewed by 4012

Abstract

Classification is a kernel process in the standardization, grading, and sensory aspects of coffee industries. The chemometric data of fatty acids and crude fat are used to characterize the varieties of coffee. Two category classifiers were used to distinguish the species and roasting [...] Read more.

Classification is a kernel process in the standardization, grading, and sensory aspects of coffee industries. The chemometric data of fatty acids and crude fat are used to characterize the varieties of coffee. Two category classifiers were used to distinguish the species and roasting degree of coffee beans. However, the fatty acid profiling with normalized data gave a bad discriminant result in the classification study with mixed dimensions in species and roasted degree. The result of the predictive model is in conflict with the context of human cognition, since roasted coffee beans are easily visually distinguished from green coffee beans. By exploring the effects of error analysis and information processing technologies, the lost information was identified as a bias–variance tradeoff derived from the percentile normalization. The roasting degree as extensive information was attenuated by the percentile normalization, but the cultivars as intensive information were enhanced. An informational spiking technique is proposed to patch the dataset and block the information loss. The identified blocking of informational loss could be available for multidimensional classification systems based on the chemometric data. Full article

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14 pages, 2082 KiB

Open AccessArticle

Complexity, Regularity and Non-Linear Behavior in Human Eye Movements: Analyzing the Dynamics of Gaze in Virtual Sailing Programs

by Ruperto Menayo, Aarón Manzanares and Francisco Segado

Symmetry 2018, 10(10), 528; https://doi.org/10.3390/sym10100528 - 22 Oct 2018

Cited by 3 | Viewed by 2369

Abstract

The non-linear analysis of the behavior of biological signals in humans is studied from different scientific disciplines. The aim of this study was to analyze the possible non-linear behavior present in eye movements during eye-tracking tasks in simulated sailing. Thirty young sailors were [...] Read more.

The non-linear analysis of the behavior of biological signals in humans is studied from different scientific disciplines. The aim of this study was to analyze the possible non-linear behavior present in eye movements during eye-tracking tasks in simulated sailing. Thirty young sailors were selected. Fuzzy entropy and detrended fluctuation analyses were applied to quantify the regularity and complexity of eye movements. The results show that neither experience nor ranking affect the regularity or the complexity of eye movement positions or velocities. Younger age is related to more regular visual behavior. At younger ages, eye positions present more complex behavior. Eye positions show more complex behavior than eye velocities. This complexity would allow for a more functional exploration of the environment by sailors. Eye movement velocity presents the greatest irregularity, with significantly higher values than eye movement position. This irregularity would facilitate the visual perception of the environment. All these findings could be related to the sailors’ functional behavior, based on complexity and stability, which has been associated with the ability of human beings to adapt to the environment. Full article

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15 pages, 630 KiB

Open AccessArticle

Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

by Adem Kilicman and Rathinavel Silambarasan

Symmetry 2018, 10(10), 527; https://doi.org/10.3390/sym10100527 - 21 Oct 2018

Cited by 26 | Viewed by 3752

Abstract

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems [...] Read more.

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems yields the analytical solution. By this way, various exact solutions including complex structures are found, and their behavior is drawn in the 2D plane by Maple to compare the uniqueness and wave traveling of the solutions. Full article

(This article belongs to the Special Issue Integral Transforms and Operational Calculus)

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22 pages, 581 KiB

Open AccessArticle

On Approximation of Any Ordered Fuzzy Number by A Trapezoidal Ordered Fuzzy Number

by Krzysztof Piasecki and Anna Łyczkowska-Hanćkowiak

Symmetry 2018, 10(10), 526; https://doi.org/10.3390/sym10100526 - 21 Oct 2018

Cited by 5 | Viewed by 2060

Abstract

In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means [...] Read more.

In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko’s entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model. Full article

(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)

18 pages, 1196 KiB

Open AccessArticle

Feedforward Neural Networks with a Hidden Layer Regularization Method

by Habtamu Zegeye Alemu, Wei Wu and Junhong Zhao

Symmetry 2018, 10(10), 525; https://doi.org/10.3390/sym10100525 - 19 Oct 2018

Cited by 23 | Viewed by 5022

Abstract

In this paper, we propose a group Lasso regularization term as a hidden layer regularization method for feedforward neural networks. Adding a group Lasso regularization term into the standard error function as a hidden layer regularization term is a fruitful approach to eliminate [...] Read more.

In this paper, we propose a group Lasso regularization term as a hidden layer regularization method for feedforward neural networks. Adding a group Lasso regularization term into the standard error function as a hidden layer regularization term is a fruitful approach to eliminate the redundant or unnecessary hidden layer neurons from the feedforward neural network structure. As a comparison, a popular Lasso regularization method is introduced into standard error function of the network. Our novel hidden layer regularization method can force a group of outgoing weights to become smaller during the training process and can eventually be removed after the training process. This means it can simplify the neural network structure and it minimizes the computational cost. Numerical simulations are provided by using K-fold cross-validation method with

K = 5

to avoid overtraining and to select the best learning parameters. The numerical results show that our proposed hidden layer regularization method prunes more redundant hidden layer neurons consistently for each benchmark dataset without loss of accuracy. In contrast, the existing Lasso regularization method prunes only the redundant weights of the network, but it cannot prune any redundant hidden layer neurons. Full article

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23 pages, 1191 KiB

Open AccessArticle

Transition from the Wave Equation to Either the Heat or the Transport Equations through Fractional Differential Expressions

by Fernando Olivar-Romero and Oscar Rosas-Ortiz

Symmetry 2018, 10(10), 524; https://doi.org/10.3390/sym10100524 - 19 Oct 2018

Cited by 8 | Viewed by 2483

Abstract

We present a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that nonlocal differential expressions are required to [...] Read more.

We present a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a form that nonlocal differential expressions are required to describe the time evolution of solutions. Nonlocality was modeled with a space-time fractional differential equation of order

1 \leq α \leq 2

in time, and order

1 \leq β \leq 2

in space. We adopted the notion of Caputo for the time derivative and the Riesz pseudo-differential operator for the space derivative. The corresponding Cauchy problem was solved for zero initial velocity and initial disturbance, represented by either the Dirac delta or the Gaussian distributions. Well-known results for the conventional partial differential equations of wave propagation, diffusion, and (modified) transport processes were recovered as particular cases. In addition, regular solutions were found for the partial differential equation that arises from

α = 2

and

β = 1

. Unlike the above conventional cases, the latter equation permits the presence of nodes in its solutions. Full article

(This article belongs to the Special Issue Symmetry Breaking in Quantum Phenomena)

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13 pages, 6013 KiB

Open AccessArticle

Study on an Automatic Parking Method Based on the Sliding Mode Variable Structure and Fuzzy Logical Control

by Ying Xu, Zefeng Lu, Xin Shan, Wenhao Jia, Bo Wei and Yingqing Wang

Symmetry 2018, 10(10), 523; https://doi.org/10.3390/sym10100523 - 19 Oct 2018

Cited by 15 | Viewed by 3318

Abstract

This paper discusses an automatic parking control method based on the combination of the sliding mode variable structure control (SMVSC) and fuzzy logical control. SMVSC is applied to drive the vehicle from a random initial position and pose, to the designated parking position [...] Read more.

This paper discusses an automatic parking control method based on the combination of the sliding mode variable structure control (SMVSC) and fuzzy logical control. SMVSC is applied to drive the vehicle from a random initial position and pose, to the designated parking position and pose. Then, the vehicle is driven from the designated parking position to the target parking slot using the method of fuzzy logical control, whose rules are limited to the range of the effective initial position. To combine SMVSC with the fuzzy logical control, the experimental results demonstrate that effective parking can be guaranteed, even if the initial position is out of the effective parking area of the fuzzy logical control. Full article

(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)

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13 pages, 257 KiB

Open AccessArticle

On the Existence of the Solutions of a Fredholm Integral Equation with a Modified Argument in Hölder Spaces

by Merve Temizer Ersoy and Hasan Furkan

Symmetry 2018, 10(10), 522; https://doi.org/10.3390/sym10100522 - 19 Oct 2018

Cited by 9 | Viewed by 2227

Abstract

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument, [...] Read more.

This article concerns the entity of solutions of a quadratic integral equation of the Fredholm type with an altered argument,

x (t) = p (t) + x (t) \int_{0}^{1} k (t, τ) (T x) (τ) d τ,

where

p, k

are given functions, T is the given operator satisfying conditions specified later and x is an unknown function. Through the classical Schauder fixed point theorem and a new conclusion about the relative compactness in Hölder spaces, we obtain the existence of solutions under certain assumptions. Our work is more general than the previous works in the Conclusion section. At the end, we introduce several tangible examples where our entity result can be adopted. Full article

(This article belongs to the Special Issue Integral Transforms and Operational Calculus)

20 pages, 2984 KiB

Open AccessArticle

Underdetermined Blind Source Separation Combining Tensor Decomposition and Nonnegative Matrix Factorization

by Yuan Xie, Kan Xie, Junjie Yang and Shengli Xie

Symmetry 2018, 10(10), 521; https://doi.org/10.3390/sym10100521 - 18 Oct 2018

Cited by 12 | Viewed by 3649

Abstract

Underdetermined blind source separation (UBSS) is a hot topic in signal processing, which aims at recovering the source signals from a number of observed mixtures without knowing the mixing system. Recently, expectation-maximization algorithm shows a great potential in the UBSS. However, the final [...] Read more.

Underdetermined blind source separation (UBSS) is a hot topic in signal processing, which aims at recovering the source signals from a number of observed mixtures without knowing the mixing system. Recently, expectation-maximization algorithm shows a great potential in the UBSS. However, the final separation results depend strongly on the parameter initialization, leading to poor separation performance. In this paper, we propose an effective algorithm that combines tensor decomposition and nonnegative matrix factorization (NMF). In the proposed algorithm, we first employ tensor decomposition to estimate the mixing matrix, and NMF source model is used to estimate the source spectrogram factors. Then a series of iterations are derived to update the model parameters. At the same time, the spatial images of source signals are estimated with Wiener filters constructed from the learned parameters. Therefore, time-domain sources can be obtained through inverse short-time Fourier transform. Finally, plenty of experimental results demonstrate the effectiveness and advantages of our proposed algorithm over the compared algorithms. Full article

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13 pages, 450 KiB

Open AccessFeature PaperArticle

Dark Matter as a Non-Relativistic Bose–Einstein Condensate with Massive Gravitons

by Emma Kun, Zoltán Keresztes, Saurya Das and László Á. Gergely

Symmetry 2018, 10(10), 520; https://doi.org/10.3390/sym10100520 - 17 Oct 2018

Cited by 7 | Viewed by 3412

Abstract

We confront a non-relativistic Bose–Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of 12 dwarf galaxies. The baryonic component is modeled as an axisymmetric exponential disk and its characteristics [...] Read more.

We confront a non-relativistic Bose–Einstein Condensate (BEC) model of light bosons interacting gravitationally either through a Newtonian or a Yukawa potential with the observed rotational curves of 12 dwarf galaxies. The baryonic component is modeled as an axisymmetric exponential disk and its characteristics are derived from the surface luminosity profile of the galaxies. The purely baryonic fit is unsatisfactory, hence a dark matter component is clearly needed. The rotational curves of five galaxies could be explained with high confidence level by the BEC model. For these galaxies, we derive: (i) upper limits for the allowed graviton mass; and (ii) constraints on a velocity-type and a density-type quantity characterizing the BEC, both being expressed in terms of the BEC particle mass, scattering length and chemical potential. The upper limit for the graviton mass is of the order of

10^{- 26}

eV / c^{2}

, three orders of magnitude stronger than the limit derived from recent gravitational wave detections. Full article

(This article belongs to the Special Issue Cosmological Inflation, Dark Matter and Dark Energy)

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16 pages, 3958 KiB

Open AccessArticle

Synthetic Medical Images Using F&BGAN for Improved Lung Nodules Classification by Multi-Scale VGG16

by Defang Zhao, Dandan Zhu, Jianwei Lu, Ye Luo and Guokai Zhang

Symmetry 2018, 10(10), 519; https://doi.org/10.3390/sym10100519 - 17 Oct 2018

Cited by 62 | Viewed by 6374

Abstract

Lung cancer is one of the highest causes of cancer-related death in both men and women. Therefore, various diagnostic methods for lung nodules classification have been proposed to implement the early detection. Due to the limited amount and diversity of samples, these methods [...] Read more.

Lung cancer is one of the highest causes of cancer-related death in both men and women. Therefore, various diagnostic methods for lung nodules classification have been proposed to implement the early detection. Due to the limited amount and diversity of samples, these methods encounter some bottlenecks. In this paper, we intend to develop a method to enlarge the dataset and enhance the performance of pulmonary nodules classification. We propose a data augmentation method based on generative adversarial network (GAN), called Forward and Backward GAN (F&BGAN), which can generate high-quality synthetic medical images. F&BGAN has two stages, Forward GAN (FGAN) generates diverse images, and Backward GAN (BGAN) is used to improve the quality of images. Besides, a hierarchical learning framework, multi-scale VGG16 (M-VGG16) network, is proposed to extract discriminative features from alternating stacked layers. The methodology was evaluated on the Lung Image Database Consortium and Image Database Resource Initiative (LIDC-IDRI) dataset, with the best accuracy of 95.24%, sensitivity of 98.67%, specificity of 92.47% and area under ROC curve (AUROC) of 0.980. Experimental results demonstrate the feasibility of F&BGAN in generating medical images and the effectiveness of M-VGG16 in classifying malignant and benign nodules. Full article

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28 pages, 441 KiB

Open AccessFeature PaperReview

Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

by Alessandro Sergi, Gabriel Hanna, Roberto Grimaudo and Antonino Messina

Symmetry 2018, 10(10), 518; https://doi.org/10.3390/sym10100518 - 16 Oct 2018

Cited by 15 | Viewed by 3115

Abstract

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. [...] Read more.

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein. Full article

(This article belongs to the Special Issue New Trends in Quantum Electrodynamics)

10 pages, 266 KiB

Open AccessArticle

Harnack Inequality and No-Arbitrage Analysis

by Wanxiao Tang, Fanchao Zhou and Peibiao Zhao

Symmetry 2018, 10(10), 517; https://doi.org/10.3390/sym10100517 - 16 Oct 2018

Cited by 4 | Viewed by 1985

Abstract

The present paper attains a Harnack inequality for the option pricing (or Kolmogorov) equation with gradient estimate arguments. We then perform a no-arbitrage analysis of a financial market. Full article

24 pages, 1451 KiB

Open AccessArticle

Inconsistent Data Cleaning Based on the Maximum Dependency Set and Attribute Correlation

by Pei Li, Chaofan Dai and Wenqian Wang

Symmetry 2018, 10(10), 516; https://doi.org/10.3390/sym10100516 - 16 Oct 2018

Cited by 5 | Viewed by 3174

Abstract

In banks, governments, and Internet companies, inconsistent data problems may often arise when various information systems are collecting, processing, and updating data due to human or equipment reasons. The emergence of inconsistent data makes it impossible to obtain correct information from the data [...] Read more.

In banks, governments, and Internet companies, inconsistent data problems may often arise when various information systems are collecting, processing, and updating data due to human or equipment reasons. The emergence of inconsistent data makes it impossible to obtain correct information from the data and reduces its availability. Such problems may be fatal in data-intensive enterprises, which causes huge economic losses. Moreover, it is very difficult to clean inconsistent data in databases, especially for data containing conditional functional dependencies with built-in predicates (CFDPs), because it tends to contain more candidate repair values. For the inconsistent data containing CFD^Ps to detect incomplete and repair difficult problems in databases, we propose a dependency lifting algorithm (DLA) based on the maximum dependency set (MDS) and a reparation algorithm (C-Repair) based on integrating the minimum cost and attribute correlation, respectively. In detection, we find recessive dependencies from the original dependency set to obtain the MDS and improve the original algorithm by dynamic domain adjustment, which extends the applicability to continuous attributes and improves the detection accuracy. In reparation, we first set up a priority queue (PQ) for elements to be repaired based on the minimum cost idea to select a candidate element; then, we treat the corresponding conflict-free instance (

I_{n v}

) as the training set to learn the correlation among attributes and compute the weighted distance (WDis) between the tuple of the candidate element and other tuples in

I_{n v}

according to the correlation; and, lastly, we perform reparation based on the WDis and re-compute the PQ after each reparation round to improve the efficiency, and use a label, flag, to mark the repaired elements to ensure the convergence at the same time. By setting up a contrast experiment, we compare the DLA with the CFD^Ps based algorithm, and the C-Repair with a cost-based, interpolation-based algorithm on a simulated instance and a real instance. From the experimental results, the DLA and C-Repair algorithms have better detection and repair ability at a higher time cost. Full article

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8 pages, 227 KiB

Open AccessArticle

Fuzzy Normed Rings

by Aykut Emniyet and Memet Şahin

Symmetry 2018, 10(10), 515; https://doi.org/10.3390/sym10100515 - 16 Oct 2018

Cited by 13 | Viewed by 2928

Abstract

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy [...] Read more.

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples. Full article

(This article belongs to the Special Issue Discrete Mathematics and Symmetry)

11 pages, 267 KiB

Open AccessArticle

Extension of Eigenvalue Problems on Gauss Map of Ruled Surfaces

by Miekyung Choi and Young Ho Kim

Symmetry 2018, 10(10), 514; https://doi.org/10.3390/sym10100514 - 16 Oct 2018

Cited by 1 | Viewed by 2071

Abstract

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from the eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of 1-type in the usual sense and pointwise 1-type. We [...] Read more.

A finite-type immersion or smooth map is a nice tool to classify submanifolds of Euclidean space, which comes from the eigenvalue problem of immersion. The notion of generalized 1-type is a natural generalization of 1-type in the usual sense and pointwise 1-type. We classify ruled surfaces with a generalized 1-type Gauss map as part of a plane, a circular cylinder, a cylinder over a base curve of an infinite type, a helicoid, a right cone and a conical surface of G-type. Full article

6 pages, 217 KiB

Open AccessArticle

The Quaternionic Commutator Bracket and Its Implications

by Arbab I. Arbab and Mudhahir Al Ajmi

Symmetry 2018, 10(10), 513; https://doi.org/10.3390/sym10100513 - 16 Oct 2018

Cited by 1 | Viewed by 1784

Abstract

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz.

\tilde{ψ} = (\frac{i}{c} ψ_{0}, \vec{ψ})

, represents a state of a particle with orbital angular momentum,

L = 3 ℏ

, [...] Read more.

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz.

\tilde{ψ} = (\frac{i}{c} ψ_{0}, \vec{ψ})

, represents a state of a particle with orbital angular momentum,

L = 3 ℏ

, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector

\vec{ψ}

, points in an opposite direction of

\vec{L}

. When a charged particle is placed in an electromagnetic field, the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov–Bohm and Aharonov–Casher effects. Full article

13 pages, 265 KiB

Open AccessArticle

A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

by Erdal Karapınar, Panda Sumati Kumari and Durdana Lateef

Symmetry 2018, 10(10), 512; https://doi.org/10.3390/sym10100512 - 16 Oct 2018

Cited by 34 | Viewed by 3486

Abstract

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of

f (x) = x

. (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the [...] Read more.

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of

f (x) = x

. (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach. Full article

(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)

9 pages, 286 KiB

Open AccessFeature PaperArticle

Cut-and-Project Schemes for Pisot Family Substitution Tilings

by Jeong-Yup Lee, Shigeki Akiyama and Yasushi Nagai

Symmetry 2018, 10(10), 511; https://doi.org/10.3390/sym10100511 - 16 Oct 2018

Cited by 4 | Viewed by 2520

Abstract

We consider Pisot family substitution tilings in

R^{d}

whose dynamical spectrum is pure point. There are two cut-and-project schemes (CPSs) which arise naturally: one from the Pisot family property and the other from the pure point spectrum. The first CPS has an [...] Read more.

We consider Pisot family substitution tilings in

R^{d}

whose dynamical spectrum is pure point. There are two cut-and-project schemes (CPSs) which arise naturally: one from the Pisot family property and the other from the pure point spectrum. The first CPS has an internal space

R^{m}

for some integer

m \in N

defined from the Pisot family property, and the second CPS has an internal space H that is an abstract space defined from the condition of the pure point spectrum. However, it is not known how these two CPSs are related. Here we provide a sufficient condition to make a connection between the two CPSs. For Pisot unimodular substitution tiling in

R

, the two CPSs turn out to be same due to the remark by Barge-Kwapisz. Full article

10 pages, 623 KiB

Open AccessArticle

New Soft Set Based Class of Linear Algebraic Codes

by Mumtaz Ali, Huma Khan, Le Hoang Son, Florentin Smarandache and W. B. Vasantha Kandasamy

Symmetry 2018, 10(10), 510; https://doi.org/10.3390/sym10100510 - 16 Oct 2018

Cited by 14 | Viewed by 2908

Abstract

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers [...] Read more.

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example. Full article

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7 pages, 245 KiB

Open AccessArticle

Fibonacci and Lucas Numbers of the Form 2^a + 3^b + 5^c + 7^d

by Yunyun Qu, Jiwen Zeng and Yongfeng Cao

Symmetry 2018, 10(10), 509; https://doi.org/10.3390/sym10100509 - 16 Oct 2018

Cited by 8 | Viewed by 3093

Abstract

In this paper, we find all Fibonacci and Lucas numbers written in the form

2^{a} + 3^{b} + 5^{c} + 7^{d}

, in non-negative integers

a, b, c, d

, with [...] Read more.

In this paper, we find all Fibonacci and Lucas numbers written in the form

2^{a} + 3^{b} + 5^{c} + 7^{d}

, in non-negative integers

a, b, c, d

, with

0 \leq \max {a, b, c} \leq d

. Full article

(This article belongs to the Special Issue Current Trends in Symmetric Polynomials with their Applications)

13 pages, 278 KiB

Open AccessArticle

A Class of Nonlinear Boundary Value Problems for an Arbitrary Fractional-Order Differential Equation with the Riemann-Stieltjes Functional Integral and Infinite-Point Boundary Conditions

by Hari M. Srivastava, Ahmed M. A. El-Sayed and Fatma M. Gaafar

Symmetry 2018, 10(10), 508; https://doi.org/10.3390/sym10100508 - 16 Oct 2018

Cited by 26 | Viewed by 2741

Abstract

In this paper, we investigate the existence of an absolute continuous solution to a class of first-order nonlinear differential equation with integral boundary conditions (BCs) or with infinite-point BCs. The Liouville-Caputo fractional derivative is involved in the nonlinear function. We first consider the [...] Read more.

In this paper, we investigate the existence of an absolute continuous solution to a class of first-order nonlinear differential equation with integral boundary conditions (BCs) or with infinite-point BCs. The Liouville-Caputo fractional derivative is involved in the nonlinear function. We first consider the existence of a solution for the first-order nonlinear differential equation with m-point nonlocal BCs. The existence of solutions of our problems is investigated by applying the properties of the Riemann sum for continuous functions. Several examples are given in order to illustrate our results. Full article

(This article belongs to the Special Issue Integral Transforms and Operational Calculus)

15 pages, 1872 KiB

Open AccessArticle

A Low Rank Channel Estimation Scheme in Massive Multiple-Input Multiple-Output

by Waleed Shahjehan, Syed Waqar Shah, Jaime Lloret and Antonio Leon

Symmetry 2018, 10(10), 507; https://doi.org/10.3390/sym10100507 - 16 Oct 2018

Cited by 2 | Viewed by 2370

Abstract

Aiming at the problem of computational complexity of channel estimation, this paper proposes a low-complexity block matching pursuit (BMP) algorithm based on antenna grouping and block sparsity for frequency division duplex (FDD) massive Multiple-input Multiple-output orthogonal frequency division multiplexing (OFDM) systems. The system [...] Read more.

Aiming at the problem of computational complexity of channel estimation, this paper proposes a low-complexity block matching pursuit (BMP) algorithm based on antenna grouping and block sparsity for frequency division duplex (FDD) massive Multiple-input Multiple-output orthogonal frequency division multiplexing (OFDM) systems. The system coherence time may be exceeded as a result of time consumption when adopting an orthogonal pilot symbol in the time domain. To solve this problem, an antenna grouping transmission scheme is proposed to reduce the total channel estimation time by sacrificing the observed data length. The simulation results show that the proposed BMP algorithm has good anti-noise performance, and it can accurately determine the non-zero position of the sparse vector and adaptively determine the sparsity of the channel, which effectively translates to improved channel estimation performance and better overall system performance than the existing algorithms. Full article

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26 pages, 362 KiB

Open AccessArticle

Nekhoroshev Stability for the Dirichlet Toda Lattice

by Andreas Henrici

Symmetry 2018, 10(10), 506; https://doi.org/10.3390/sym10100506 - 16 Oct 2018

Viewed by 1685

Abstract

In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically [...] Read more.

In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one. Full article

34 pages, 406 KiB

Open AccessArticle

Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Group Decision Making and Their Application to Supplier Selection

by Zengxian Li, Guiwu Wei and Mao Lu

Symmetry 2018, 10(10), 505; https://doi.org/10.3390/sym10100505 - 15 Oct 2018

Cited by 101 | Viewed by 3620

Abstract

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, [...] Read more.

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, weighted Pythagorean fuzzy dual Hamy mean (WPFDHM) operator. Then the multiple attribute group decision making (MAGDM) methods are proposed with these operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)

24 pages, 485 KiB

Open AccessArticle

Invariant Graph Partition Comparison Measures

by Fabian Ball and Andreas Geyer-Schulz

Symmetry 2018, 10(10), 504; https://doi.org/10.3390/sym10100504 - 15 Oct 2018

Cited by 3 | Viewed by 4348

Abstract

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a [...] Read more.

Symmetric graphs have non-trivial automorphism groups. This article starts with the proof that all partition comparison measures we have found in the literature fail on symmetric graphs, because they are not invariant with regard to the graph automorphisms. By the construction of a pseudometric space of equivalence classes of permutations and with Hausdorff’s and von Neumann’s methods of constructing invariant measures on the space of equivalence classes, we design three different families of invariant measures, and we present two types of invariance proofs. Last, but not least, we provide algorithms for computing invariant partition comparison measures as pseudometrics on the partition space. When combining an invariant partition comparison measure with its classical counterpart, the decomposition of the measure into a structural difference and a difference contributed by the group automorphism is derived. Full article

(This article belongs to the Special Issue Discrete Mathematics and Symmetry)

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