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Symmetry — Open Access Journal

Symmetry (ISSN 2073-8994; CODEN: SYMMAM) is an international peer-reviewed open access journal covering research on symmetry phenomena wherever they occur in mathematical and scientific studies. Symmetry is published monthly online by MDPI.

Open Access free for readers, with article processing charges (APC) paid by authors or their institutions.
High visibility: indexed by the Science Citation Index Expanded (Web of Science) [search for "Symmetry-Basel"], Scopus and other databases.
Rapid publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 16 days after submission; acceptance to publication is undertaken in 5.4 days (median values for papers published in the first six months of 2018).
Recognition of reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
Testimonials: See what our authors say about Symmetry.

Impact Factor: 1.256 (2017) ; 5-Year Impact Factor: 1.213 (2017)

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Latest Articles

Open AccessArticle

Random Untargeted Adversarial Example on Deep Neural Network

by Hyun Kwon, Yongchul Kim, Hyunsoo Yoon and Daeseon Choi

Symmetry 2018, 10(12), 738; https://doi.org/10.3390/sym10120738 (registering DOI) - 10 December 2018

Abstract

[...] Read more.

Deep neural networks (DNNs) have demonstrated remarkable performance in machine learning areas such as image recognition, speech recognition, intrusion detection, and pattern analysis. However, it has been revealed that DNNs have weaknesses in the face of adversarial examples, which are created by adding a little noise to an original sample to cause misclassification by the DNN. Such adversarial examples can lead to fatal accidents in applications such as autonomous vehicles and disease diagnostics. Thus, the generation of adversarial examples has attracted extensive research attention recently. An adversarial example is categorized as targeted or untargeted. In this paper, we focus on the untargeted adversarial example scenario because it has a faster learning time and less distortion compared with the targeted adversarial example. However, there is a pattern vulnerability with untargeted adversarial examples: Because of the similarity between the original class and certain specific classes, it may be possible for the defending system to determine the original class by analyzing the output classes of the untargeted adversarial examples. To overcome this problem, we propose a new method for generating untargeted adversarial examples, one that uses an arbitrary class in the generation process. Moreover, we show that our proposed scheme can be applied to steganography. Through experiments, we show that our proposed scheme can achieve a 100% attack success rate with minimum distortion (1.99 and 42.32 using the MNIST and CIFAR10 datasets, respectively) and without the pattern vulnerability. Using a steganography test, we show that our proposed scheme can be used to fool humans, as demonstrated by the probability of their detecting hidden classes being equal to that of random selection. Full article

Open AccessArticle

On the Role of Unitary-Symmetry for the Foundation of Probability and Time in a Realist Approach to Quantum Physics

by Andreas Schlatter

Symmetry 2018, 10(12), 737; https://doi.org/10.3390/sym10120737 (registering DOI) - 10 December 2018

Abstract

We show that probabilities in quantum physics can be derived from permutation-symmetry and the principle of indifference. We then connect unitary-symmetry to the concept of “time” and define a thermal time-flow by symmetry breaking. Finally, we discuss the coexistence of quantum physics and

[...] Read more.

Open AccessArticle

Cutting Pattern Identification for Coal Mining Shearer through Sound Signals Based on a Convolutional Neural Network

by Jing Xu, Zhongbin Wang, Chao Tan, Daohua Lu, Baigong Wu, Zhen Su and Yanbing Tang

Symmetry 2018, 10(12), 736; https://doi.org/10.3390/sym10120736 (registering DOI) - 10 December 2018

Abstract

[...] Read more.

Recently, sound-based diagnosis systems have been given much attention in many fields due to the advantages of their simple structure, non-touching measurement style, and low-power dissipation. In order to improve the efficiency of coal production and the safety of the coal mining process, accurate information is always essential. It is indicated that the sound signal produced during the cutting process of the coal mining shearer contains much cutting pattern identification information. In this paper, the original acoustic signal is first collected through an industrial microphone. To analyze the signal deeply, an adaptive Hilbert–Huang transform (HHT) was applied to decompose the sound to several intrinsic mode functions (IMFs) to subsequently acquire 1024 Hilbert marginal spectrum points. The 1024 time-frequency nodes were reorganized as a 32 × 32 feature map. Moreover, the LeNet-5 convolutional neural network (CNN), with three convolution layers and two sub-sampling layers, was used as the cutting pattern recognizer. A simulation example, with 10,000 training samples and 2000 testing samples, was conducted to prove the effectiveness of the proposed method. Finally, 1971 testing sound series were recognized accurately through the trained CNN and the proposed method achieved an identification rate of 98.55%. Full article

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Open AccessReview

Dispersion Interactions between Neutral Atoms and the Quantum Electrodynamical Vacuum

by Roberto Passante

Symmetry 2018, 10(12), 735; https://doi.org/10.3390/sym10120735 (registering DOI) - 10 December 2018

Abstract

[...] Read more.

Dispersion interactions are long-range interactions between neutral ground-state atoms or molecules, or polarizable bodies in general, due to their common interaction with the quantum electromagnetic field. They arise from the exchange of virtual photons between the atoms, and, in the case of three or more atoms, are not additive. In this review, after having introduced the relevant coupling schemes and effective Hamiltonians, as well as properties of the vacuum fluctuations, we outline the main properties of dispersion interactions, both in the nonretarded (van der Waals) and retarded (Casimir–Polder) regime. We then discuss their deep relation with the existence of the vacuum fluctuations of the electromagnetic field and vacuum energy. We describe some transparent physical models of two- and three-body dispersion interactions, based on dressed vacuum field energy densities and spatial field correlations, which stress their deep connection with vacuum fluctuations and vacuum energy. These models give a clear insight of the physical origin of dispersion interactions, and also provide useful computational tools for their evaluation. We show that this aspect is particularly relevant in more complicated situations, for example when macroscopic boundaries are present. We also review recent results on dispersion interactions for atoms moving with noninertial motions and the strict relation with the Unruh effect, and on resonance interactions between entangled identical atoms in uniformly accelerated motion. Full article

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Open AccessArticle

Background Augmentation Generative Adversarial Networks (BAGANs): Effective Data Generation Based on GAN-Augmented 3D Synthesizing

by Yan Ma, Kang Liu, Zhibin Guan, Xinkai Xu, Xu Qian and Hong Bao

Symmetry 2018, 10(12), 734; https://doi.org/10.3390/sym10120734 - 8 December 2018

Abstract

[...] Read more.

Augmented Reality (AR) is crucial for immersive Human–Computer Interaction (HCI) and the vision of Artificial Intelligence (AI). Labeled data drives object recognition in AR. However, manually annotating data is expensive, labor-intensive, and data distribution asymmetry . Scantily labeled data limits the application of AR. Aiming at solving the problem of insufficient and asymmetry training data in AR object recognition, an automated vision data synthesis method, i.e., background augmentation generative adversarial networks (BAGANs), is proposed in this paper based on 3D modeling and the Generative Adversarial Network (GAN) algorithm. Our approach has been validated to have better performance than other methods through image recognition tasks with respect to the natural image database ObjectNet3D. This study can shorten the algorithm development time of AR and expand its application scope, which is of great significance for immersive interactive systems. Full article

Open AccessArticle

A New Representation for Srivastava’s λ-Generalized Hurwitz-Lerch Zeta Functions

by Asifa Tassaddiq

Symmetry 2018, 10(12), 733; https://doi.org/10.3390/sym10120733 - 8 December 2018

Abstract

[...] Read more.

Taking inspiration principally from some of the latest research, we develop a new series representation for the λ-generalized Hurwitz-Lerch zeta functions. This representation led to important new results. The Fourier transform played a foundational role in this work. The duality property of the Fourier transform became significant for checking the consistency of the results. Some known data has been verified as special cases of the results obtained in this investigation. Full article

Open AccessArticle

Unification of the Fixed Point in Integral Type Metric Spaces

by Panda Sumati Kumari, Badriah A. S. Alamri, Nawab Hussain and Sumit Chandok

Symmetry 2018, 10(12), 732; https://doi.org/10.3390/sym10120732 - 7 December 2018

Abstract

[...] Read more.

In metric fixed point theory, the conditions like “symmetry” and “triangle inequality” play a predominant role. In this paper, we introduce a new kind of metric space by using symmetry, triangle inequality, and other conditions like self-distances are zero. In this paper, we introduce the weaker forms of integral type metric spaces, thereby we establish the existence of unique fixed point theorems. As usual, illustrations and counter examples are provided wherever necessary. Full article

Open AccessArticle

On Some Statistical Approximation by (p,q)-Bleimann, Butzer and Hahn Operators

by Khursheed J. Ansari, Ishfaq Ahmad, M. Mursaleen and Iqtadar Hussain

Symmetry 2018, 10(12), 731; https://doi.org/10.3390/sym10120731 - 7 December 2018

Abstract

In this article, we propose a different generalization of

(p, q)

-BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where

(p, q)

-integers contains symmetric property.

[...] Read more.

In this article, we propose a different generalization of

(p, q)

-BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where

(p, q)

-integers contains symmetric property. We establish a Korovkin approximation theorem in the statistical sense and obtain the statistical rates of convergence. Furthermore, we also introduce a bivariate extension of proposed operators and carry many statistical approximation results. The extra parameter p plays an important role to symmetrize the q-BBH operators. Full article

Open AccessArticle

Rolling Bearing Fault Diagnosis Based on EWT Sub-Modal Hypothesis Test and Ambiguity Correlation Classification

by Mingtao Ge, Jie Wang, Yicun Xu, Fangfang Zhang, Ke Bai and Xiangyang Ren

Symmetry 2018, 10(12), 730; https://doi.org/10.3390/sym10120730 - 7 December 2018

Abstract

[...] Read more.

Because of the cyclic symmetric structure of rolling bearings, its vibration signals are regular when the rolling bearing is working in a normal state. But when the rolling bearing fails, whether the outer race fault or the inner race fault, the symmetry of the rolling bearing is broken and the fault destroys the rolling bearing’s stable working state. Whenever the bearing passes through the fault point, it will send out vibration signals representing the fault characteristics. These signals are often non-linear, non-stationary, and full of Gaussian noise which are quite different from normal signals. According to this, the sub-modal obtained by empirical wavelet transform (EWT), secondary decomposition is tested by the Gaussian distribution hypothesis test. It is regarded that sub-modal following Gaussian distribution is Gaussian noise which is filtered during signal reconstruction. Then by taking advantage of the ambiguity function superiority in non-stationary signal processing and combining correlation coefficient, an ambiguity correlation classifier is constructed. After training, the classifier can recognize vibration signals of rolling bearings under different working conditions, so that the purpose of identifying rolling bearing faults can be achieved. Finally, the method effect was verified by experiments. Full article

Open AccessArticle

Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity

by Lifeng Li and Qinjun Luo

Symmetry 2018, 10(12), 729; https://doi.org/10.3390/sym10120729 - 7 December 2018

Abstract

[...] Read more.

The convexity in triangular norm (for short, ⊗−convexity) is a generalization of Zadeh’s quasiconvexity. The aggregation of two ⊗−convex sets is under the aggregation operator ⊗ is also ⊗−convex, but the aggregation operator ⊗ is not unique. To solve it in complexity, in the present paper, we give some sufficient conditions for aggregation operators preserve ⊗−convexity. In particular, when aggregation operators are triangular norms, we have that several results such as arbitrary triangular norm preserve

\otimes_{D} -

convexity and

\otimes_{a} -

convexity on bounded lattices,

\otimes_{M}

preserves

\otimes_{H} -

convexity in the real unite interval

[0, 1]

. Full article

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Open AccessArticle

Functional Asymmetry and Fingerprint Features of Left-Handed and Right-Handed Young Yakuts (Mongoloid Race, North-Eastern Siberia)

by Elena Shadrina and Yakov Vol’pert

Symmetry 2018, 10(12), 728; https://doi.org/10.3390/sym10120728 - 6 December 2018

Abstract

[...] Read more.

An ethnically homogeneous group of Yakuts (Mongoloid race, Northeast Asia), aged 18–31, was studied to characterize the diversity of particular features between left- and right-handed individuals. A total of 52 left-handed (32 women and 20 men) and 100 right-handed (50 women and 50 men) individuals were studied. Testing included two sets of questions and tasks, dynamometry of the right and left hand, and fingerprint analysis. Left-handed and right-handed people were found to differ in functional asymmetry of psychophysiological and motor reactions. Right-handers were characterized by higher intragroup similarity, while, among left-handers, greater dispersion of these traits was observed. Asymmetry in hand grip strength was less pronounced in the left-handed people than in the right-handed; this difference was statistically significant, and the difference was greater in men than in women. This suggests that the non-dominant hand in the left-handed people was subjected to a greater load and indicates the forced adaptation of the left-handed people to “dextrastress”. No significant difference between sexes was found when analyzing fingerprint patterns. Left-handers had arches significantly more often than right-handers. Radial loops were most often found on the index finger, and, in the left-handers, their occurrence was significantly higher on three to five fingers of the left hand compared with the right-handers. The levels of fluctuating asymmetry in left-handers and right-handers were similar. Full article

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Open AccessArticle

Binary Locating-Dominating Sets in Rotationally-Symmetric Convex Polytopes

by Hassan Raza, Sakander Hayat and Xiang-Feng Pan

Symmetry 2018, 10(12), 727; https://doi.org/10.3390/sym10120727 - 6 December 2018

Abstract

A convex polytope or simply polytope is the convex hull of a finite set of points in Euclidean space

R^{d}

. Graphs of convex polytopes emerge from geometric structures of convex polytopes by preserving the adjacency-incidence relation between vertices. In this paper,

[...] Read more.

A convex polytope or simply polytope is the convex hull of a finite set of points in Euclidean space

R^{d}

. Graphs of convex polytopes emerge from geometric structures of convex polytopes by preserving the adjacency-incidence relation between vertices. In this paper, we study the problem of binary locating-dominating number for the graphs of convex polytopes which are symmetric rotationally. We provide an integer linear programming (ILP) formulation for the binary locating-dominating problem of graphs. We have determined the exact values of the binary locating-dominating number for two infinite families of convex polytopes. The exact values of the binary locating-dominating number are obtained for two rotationally-symmetric convex polytopes families. Moreover, certain upper bounds are determined for other three infinite families of convex polytopes. By using the ILP formulation, we show tightness in the obtained upper bounds. Full article

Open AccessArticle

Robust Adaptive Full-Order TSM Control Based on Neural Network

by Qianlei Cao, Chongzhen Cao, Fengqin Wang, Dan Liu and Hui Sun

Symmetry 2018, 10(12), 726; https://doi.org/10.3390/sym10120726 - 6 December 2018

Abstract

[...] Read more.

Existing full-order terminal sliding mode (FOTSM) control methods often require a priori knowledge of the system model. To tackle this problem, two novel neural-network-based FOTSM control methods were proposed. The first one was model based but did not require knowledge of the uncertainties’ bounds. The second one was model free and did not require knowledge of the system model. Finite-time convergence of the two schemes was verified by theoretical analysis and simulation cases. Meanwhile, the designed methods avoided singularity as well as chattering. Full article

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Open AccessArticle

Image Feature Matching Based on Semantic Fusion Description and Spatial Consistency

by Wei Zhang and Guoying Zhang

Symmetry 2018, 10(12), 725; https://doi.org/10.3390/sym10120725 - 6 December 2018

Abstract

[...] Read more.

Image feature description and matching is widely used in computer vision, such as camera pose estimation. Traditional feature descriptions lack the semantic and spatial information, and give rise to a large number of feature mismatches. In order to improve the accuracy of image feature matching, a feature description and matching method, based on local semantic information fusion and feature spatial consistency, is proposed in this paper. Once object detection is used on images, feature points are then extracted, and image patches with various sizes surrounding these points are clipped. These patches are sent into the Siamese convolution network to get their semantic vectors. Then, semantic fusion description of feature points is obtained by weighted sum of the semantic vectors, and their weights optimized by particle swarm optimization (PSO) algorithm. When matching these feature points using their descriptions, feature spatial consistency is calculated based on the spatial consistency of matched objects, and the orientation and distance constraint of adjacent points within matched objects. With the description and matching method, the feature points are matched accurately and effectively. Our experiment results showed the efficiency of our methods. Full article

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Open AccessArticle

Generalized Modified Slash Birnbaum–Saunders Distribution

by Jimmy Reyes, Inmaculada Barranco-Chamorro, Diego I. Gallardo and Héctor W. Gómez

Symmetry 2018, 10(12), 724; https://doi.org/10.3390/sym10120724 - 6 December 2018

Abstract

[...] Read more.

In this paper, a generalization of the modified slash Birnbaum–Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton–Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems. Full article

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Open AccessFeature PaperArticle

Vacuum Constraints for Realistic Strongly Coupled Heterotic M-Theories

by Burt A. Ovrut

Symmetry 2018, 10(12), 723; https://doi.org/10.3390/sym10120723 - 5 December 2018

Abstract

The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific

S U (4)

vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for

[...] Read more.

The compactification from the 11-dimensional Horava-Witten orbifold to 5-dimensional heterotic M-theory on a Schoen Calabi-Yau threefold is reviewed, as is the specific

S U (4)

vector bundle leading to the “heterotic standard model” in the observable sector. A generic formalism for a consistent hidden sector gauge bundle, within the context of strongly coupled heterotic M-theory, is presented. Anomaly cancellation and the associated bulk space 5-branes are discussed in this context. The further compactification to a 4-dimensional effective field theory on a linearized BPS double domain wall is then presented to order

κ_{11}^{4 / 3}

. Specifically, the generic constraints required for anomaly cancellation and by the linearized domain wall solution, restrictions imposed by the vanishing of the D-terms and, finally, the constraints imposed by the necessity for positive, perturbative squared gauge couplings to this order are presented in detail. Full article

Open AccessArticle

An Updated Constraint on Variations of the Fine-Structure Constant Using Wavelengths of Fe II Absorption Line Multiplets

by T. D. Le

Symmetry 2018, 10(12), 722; https://doi.org/10.3390/sym10120722 - 5 December 2018

Abstract

[...] Read more.

A new stringent limit relating to the variation of the fine-structure constant (α= e²/4πε₀ℏc) has been extracted from Ritz wavelengths of 27 quasi_stellar object (QSO) absorption spectra lines of Fe II. The calculation was combined with laboratory wavelengths and QSO spectra to obtain the result ∆α/α=(0.027±0.832)×10^-6. This result suggests how dedicated astrophysical estimations can improve these limits in the future and can also constrain space_time variations. Full article

Open AccessArticle

Antecedents of Symmetry in Physicians’ Prescription Behavior: Evidence from SEM-based Multivariate Approach

by Rizwan Raheem Ahmed, Zahid Ali Channar, Riaz Hussain Soomro, Jolita Vveinhardt, Dalia Streimikiene and Vishnu Parmar

Symmetry 2018, 10(12), 721; https://doi.org/10.3390/sym10120721 - 5 December 2018

Abstract

[...] Read more.

The aim of this paper is to examine the direct impact of marketing and medical tools on the symmetry of physicians’ prescription behavior in the context of the Pakistani healthcare sector. This research also investigates the moderating influence of corporate image and customer relationship in an association of marketing & medical tools, and the symmetry of physicians’ prescription behavior. The survey involved a research sample of 740 physicians, comprising 410 general practitioners and 330 specialists. A series of multivariate approaches such as exploratory factor analysis, confirmatory factor analyses, and conditional process analysis are employed. The findings of the study showed that marketing & medical tools have a direct, positive, and significant influence on physicians’ symmetrical prescription behavior. Corporate image and customer relationship have also a significant impact as moderating variables between marketing & medical tools, and the symmetry of prescription behavior of physicians. The outcomes of this research are beneficial to marketers and medical managers in the pharmaceutical industry. Full article

Open AccessArticle

Khovanov Homology of Three-Strand Braid Links

by Young Chel Kwun, Abdul Rauf Nizami, Mobeen Munir, Zaffar Iqbal, Dishya Arshad and Shin Min Kang

Symmetry 2018, 10(12), 720; https://doi.org/10.3390/sym10120720 - 5 December 2018

Abstract

Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some

[...] Read more.

Δ^{2 k + 1} = x_{1}^{2 k + 2} x_{2} x_{1}^{2} x_{2}^{2} x_{1}^{2} \dots x_{2}^{2} x_{1}^{2} x_{1}^{2}

Δ^{2 k + 1} x_{2}

, and

Δ^{2 k + 1} x_{1}

, where

Δ

is the Garside element

x_{1} x_{2} x_{1}

, and which are three out of all six classes of the general braid

x_{1} x_{2} x_{1} x_{2} \dots

with n factors. Full article

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Open AccessArticle

F(R,G) Cosmology through Noether Symmetry Approach

by Ugur Camci

Symmetry 2018, 10(12), 719; https://doi.org/10.3390/sym10120719 - 5 December 2018

Abstract

The

F (R, G)

theory of gravity, where R is the Ricci scalar and G is the Gauss-Bonnet invariant, is studied in the context of existence the Noether symmetries. The Noether symmetries of the point-like Lagrangian of

F (R

[...] Read more.

The

F (R, G)

F (R, G)

gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker cosmological model is investigated. With the help of several explicit forms of the

F (R, G)

function it is shown how the construction of a cosmological solution is carried out via the classical Noether symmetry approach that includes a functional boundary term. After choosing the form of the

F (R, G)

function such as the case

(i) : F (R, G) = f_{0} R^{n} + g_{0} G^{m}

and the case

(i i) : F (R, G) = f_{0} R^{n} G^{m}

, where n and m are real numbers, we explicitly compute the Noether symmetries in the vacuum and the non-vacuum cases if symmetries exist. The first integrals for the obtained Noether symmetries allow to find out exact solutions for the cosmological scale factor in the cases (i) and (ii). We find several new specific cosmological scale factors in the presence of the first integrals. It is shown that the existence of the Noether symmetries with a functional boundary term is a criterion to select some suitable forms of

F (R, G)

. In the non-vacuum case, we also obtain some extra Noether symmetries admitting the equation of state parameters

w \equiv p / ρ

such as

w = - 1, - 2 / 3, 0, 1

etc. Full article

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30 October 2018
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1–7 September 2019 2nd International Conference on Symmetry (Symmetry 2019)

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Special Issue in Symmetry

Emerging Data Hiding Systems in Image Communications Guest Editors: Wien Hong, Tung-Shou Chen, Shaowei Weng
Deadline: 15 December 2018

Special Issue in Symmetry

Symmetry in Cosmology Guest Editor: Michael Tsamparlis
Deadline: 31 December 2018

Special Issue in Symmetry

New Trends in Quantum Optics Guest Editor: Luis L. Sánchez-Soto
Deadline: 15 January 2019

Special Issue in Symmetry

Cosmological Inflation, Dark Matter and Dark Energy Guest Editor: Kazuharu Bamba
Deadline: 31 January 2019

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