Symmetry doi: 10.3390/sym10100533

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

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.

]]>Symmetry doi: 10.3390/sym10100532

Authors: Jawdat Alebraheem

The paradox of the enrichment phenomenon, considered one of the main counterintuitive observations in ecology, likely destabilizes predator&ndash;prey dynamics by increasing the nutrition of the prey. We use two systems to study the occurrence of the paradox of enrichment: The prey&ndash;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.

]]>Symmetry doi: 10.3390/sym10100531

Authors: Jun Ye Zebo Fang Wenhua Cui

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.

]]>Symmetry doi: 10.3390/sym10100530

Authors: Wanmeng Ding Kesheng Liu Xuehu Yan Huaixi Wang Lintao Liu Qinghong Gong

Most of today&rsquo;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&rsquo;s polynomial-based SS scheme. In this paper, matrix theory is used to analyze Shamir&rsquo;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&rsquo;s polynomial-based SS scheme is a special case of our proposed scheme.

]]>Symmetry doi: 10.3390/sym10100529

Authors: Ying-Che Hung Ping Chen Liang-Yü Chen

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&ndash;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.

]]>Symmetry doi: 10.3390/sym10100528

Authors: Ruperto Menayo Aarón Manzanares Francisco Segado

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&rsquo; functional behavior, based on complexity and stability, which has been associated with the ability of human beings to adapt to the environment.

]]>Symmetry doi: 10.3390/sym10100527

Authors: Adem Kilicman Rathinavel Silambarasan

The generalized Kuramoto&ndash;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.

]]>Symmetry doi: 10.3390/sym10100526

Authors: Piasecki Łyczkowska-Hanćkowiak

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&rsquo;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.

]]>Symmetry doi: 10.3390/sym10100525

Authors: Habtamu Zegeye Alemu Wei Wu Junhong Zhao

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.

]]>Symmetry doi: 10.3390/sym10100524

Authors: Fernando Olivar-Romero Oscar Rosas-Ortiz

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 &le; &alpha; &le; 2 in time, and order 1 &le; &beta; &le; 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 &alpha; = 2 and &beta; = 1 . Unlike the above conventional cases, the latter equation permits the presence of nodes in its solutions.

]]>Symmetry doi: 10.3390/sym10100523

Authors: Ying Xu Zefeng Lu Xin Shan Wenhao Jia Bo Wei Yingqing Wang

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.

]]>Symmetry doi: 10.3390/sym10100522

Authors: Merve Temizer Ersoy Hasan Furkan

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 , &tau; ) ( T x ) ( &tau; ) d &tau; , 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 H&ouml;lder 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.

]]>Symmetry doi: 10.3390/sym10100521

Authors: Yuan Xie Kan Xie Junjie Yang Shengli Xie

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.

]]>Symmetry doi: 10.3390/sym10100520

Authors: Emma Kun Zoltán Keresztes Saurya Das László Á. Gergely

We confront a non-relativistic Bose&ndash;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 &minus; 26 eV / c 2 , three orders of magnitude stronger than the limit derived from recent gravitational wave detections.

]]>Symmetry doi: 10.3390/sym10100519

Authors: Defang Zhao Dandan Zhu Jianwei Lu Ye Luo Guokai Zhang

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&amp;BGAN), which can generate high-quality synthetic medical images. F&amp;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&amp;BGAN in generating medical images and the effectiveness of M-VGG16 in classifying malignant and benign nodules.

]]>Symmetry doi: 10.3390/sym10100518

Authors: Alessandro Sergi Gabriel Hanna Roberto Grimaudo Antonino Messina

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 Nos&eacute;&ndash;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.

]]>Symmetry doi: 10.3390/sym10100517

Authors: Wanxiao Tang Fanchao Zhou Peibiao Zhao

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.

]]>Symmetry doi: 10.3390/sym10100516

Authors: Pei Li Chaofan Dai Wenqian Wang

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 CFDPs 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 CFDPs 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.

]]>Symmetry doi: 10.3390/sym10100515

Authors: Aykut Emniyet Memet Şahin

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.

]]>Symmetry doi: 10.3390/sym10100514

Authors: Miekyung Choi Young Ho Kim

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.

]]>Symmetry doi: 10.3390/sym10100513

Authors: Arbab I. Arbab Mudhahir Al Ajmi

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, viz. &psi; &tilde; = ( i c &psi; 0 , &psi; &rarr; ) , 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 &psi; &rarr; , points in an opposite direction of L &rarr; . 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&ndash;Bohm and Aharonov&ndash;Casher effects.

]]>Symmetry doi: 10.3390/sym10100512

Authors: Erdal Karapınar Panda Sumati Kumari Durdana Lateef

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&ndash;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.

]]>Symmetry doi: 10.3390/sym10100511

Authors: Jeong-Yup Lee Shigeki Akiyama Yasushi Nagai

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 &isin; 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.

]]>Symmetry doi: 10.3390/sym10100510

Authors: Mumtaz Ali Huma Khan Le Hoang Son Florentin Smarandache W. B. Vasantha Kandasamy

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.

]]>Symmetry doi: 10.3390/sym10100509

Authors: Yunyun Qu Jiwen Zeng Yongfeng Cao

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 &le; max { a , b , c } &le; d .

]]>Symmetry doi: 10.3390/sym10100508

Authors: Hari M. Srivastava Ahmed M. A. El-Sayed Fatma M. Gaafar

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.

]]>Symmetry doi: 10.3390/sym10100507

Authors: Waleed Shahjehan Syed Waqar Shah Jaime Lloret Antonio Leon

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.

]]>Symmetry doi: 10.3390/sym10100506

Authors: Andreas Henrici

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.

]]>Symmetry doi: 10.3390/sym10100505

Authors: Zengxian Li Guiwu Wei Mao Lu

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.

]]>Symmetry doi: 10.3390/sym10100504

Authors: Fabian Ball Andreas Geyer-Schulz

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&rsquo;s and von Neumann&rsquo;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.

]]>Symmetry doi: 10.3390/sym10100503

Authors: Junsheng Duan Lian Chen

In this paper, solutions for systems of linear fractional differential equations are considered. For the commensurate order case, solutions in terms of matrix Mittag&ndash;Leffler functions were derived by the Picard iterative process. For the incommensurate order case, the system was converted to a commensurate order case by newly introducing unknown functions. Computation of matrix Mittag&ndash;Leffler functions was considered using the methods of the Jordan canonical matrix and minimal polynomial or eigenpolynomial, respectively. Finally, numerical examples were solved using the proposed methods.

]]>Symmetry doi: 10.3390/sym10100502

Authors: Jong-Hyun Kim Wook Kim Young Bin Kim Jung Lee

When we perform particle-based water simulation, water particles are often increased dramatically because of particle splitting around breaking holes to maintain the thin fluid sheets. Because most of the existing approaches do not consider the volume of the water particles, the water particles must have a very low mass to satisfy the law of the conservation of mass. This phenomenon smears the motion of the water, which would otherwise result in splashing, thereby resulting in artifacts such as numerical dissipation. Thus, we propose a new fluid-implicit, particle-based framework for maintaining and representing the thin sheets and turbulent flows of water. After splitting the water particles, the proposed method uses the ghost density and ghost mass to redistribute the difference in mass based on the volume of the water particles. Next, small-scale turbulent flows are formed in local regions and transferred in a smooth manner to the global flow field. Our results show us the turbulence details as well as the thin sheets of water, thereby obtaining an aesthetically pleasing improvement compared with existing methods.

]]>Symmetry doi: 10.3390/sym10100501

Authors: Hai-Yan Zhang Huo Tang Xiao-Meng Niu

Let S l * denote the class of analytic functions f in the open unit disk D = { z : | z | &lt; 1 } normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , which is subordinate to exponential function, z f ′ ( z ) f ( z ) ≺ e z ( z ∈ D ) . In this paper, we aim to investigate the third-order Hankel determinant H 3 ( 1 ) for this function class S l * associated with exponential function and obtain the upper bound of the determinant H 3 ( 1 ) . Meanwhile, we give two examples to illustrate the results obtained.

]]>Symmetry doi: 10.3390/sym10100500

Authors: Bo Wu Wei Li Fan Jiang

Guide rails are amongst the most important components of mine hoist systems, and faults in them must be detected as early as possible to avoid fatal breakdowns in mine production. Presently, guide rail inspection is performed visually in most situations. In this paper, we examine a more efficient approach based on multi-time scale and dynamic time warping (DTW) to diagnose guide rail faults including embossment, bumps, and clearance. Firstly, vibration signals collected from operational conveyance under different fault categories are analyzed and the corresponding characteristic waveforms (CWs) are extracted. Embossment faults are identified with priority according to visible disparities in CW patterns on a large time scale. Then, templates for bump and clearance faults are established through processing the CWs on a small time scale. Subsequently, the distances of DTW (DDTWs) between test samples and the selected templates are calculated. Finally, the remaining fault conditions are classified according to the DDTW results since the same fault category has the smallest distance. Experiments are conducted on a guide rail fault simulator to demonstrate the reliability of the proposed method. The resultant diagnosis accuracies are 100%, 90.40%, and 84.53%, respectively, for embossment, bump, and clearance faults, which indicates that the proposed approach is feasible and effective for diagnosing guide rail faults under variable operating conditions and different fault severities.

]]>Symmetry doi: 10.3390/sym10100499

Authors: Chih Ping Tso Chee Hao Hor Gooi Mee Chen Chee Kuang Kok

The heat induced by viscous dissipation in a microchannel fluid, due to a small oscillating motion of the lower plate, is investigated for the first time. The methodology is by applying the momentum and energy equations and solving them for three cases of standard thermal boundary conditions. The first two cases involve symmetric boundary conditions of constant surface temperature on both plates and both plates insulated, respectively. The third case has the asymmetric conditions that the lower plate is insulated while the upper plate is maintained at constant temperature. Results reveal that, although the fluid velocity is only depending on the oscillation rate of the plate, the temperature field for all three cases show that the induced heating is dependent on the oscillation rate of the plate, but strongly dependent on the parameters Brinkman number and Prandtl number. All three cases prove that the increasing oscillation rate or Brinkman number and decreasing Prandtl number, when it is less than unity, will significantly increase the temperature field. The present model is applied to the synovial fluid motion in artificial hip implant and results in heat induced by viscous dissipation for the second case shows remarkably close agreement with the experimental literature.

]]>Symmetry doi: 10.3390/sym10100498

Authors: Sahar Shah Anwar Khan Ihsan Ali Kwang-Man Ko Hasan Mahmood

Mitigation of channel unfavorable circumstances during data routing in underwater wireless sensor networks (UWSNs) has utmost significance. It guarantees saving packet corruption along unfavorable channels so that vital data is not lost or become meaningless. This paper proposes two routing protocols for UWSNs: localization free energy efficient routing (LFEER) and its improved version, localization free energy efficient cooperative routing (Co-LFEER). The LFEER makes decision of choosing a relay based on its maximum residual energy, number of hops and the bit error rate of the link over which packets are transmitted. These metrics are chosen to save packets from corruption to the maximum limit and maintain stable paths (where nodes do not die soon). Since a single link is used in the LFEER for packets forwarding, the link may become worse with changing circumstances of the channel. To deal with this issue, cooperative routing is added to the LFFER to construct the Co-LFEER protocol, in which some copies of packets are received by destination to decide about packets quality. Converse to some prevalent protocols, both LFEER and Co-LFEER are independent of knowing the sensor nodes&rsquo; positions, which increases computational complexity and wasteful utilization of resources. Based on extensive simulations, the proposed schemes are better than Co-DBR in reducing energy utilization and advancing packets to the desired destination.

]]>Symmetry doi: 10.3390/sym10100497

Authors: Jie Wang Guiwu Wei Mao Lu

In this article, we combine the original VIKOR model with a triangular fuzzy neutrosophic set to propose the triangular fuzzy neutrosophic VIKOR method. In the extended method, we use the triangular fuzzy neutrosophic numbers (TFNNs) to present the criteria values in multiple criteria group decision making (MCGDM) problems. Firstly, we summarily introduce the fundamental concepts, operation formulas and distance calculating method of TFNNs. Then we review some aggregation operators of TFNNs. Thereafter, we extend the original VIKOR model to the triangular fuzzy neutrosophic environment and introduce the calculating steps of the TFNNs VIKOR method, our proposed method which is more reasonable and scientific for considering the conflicting criteria. Furthermore, a numerical example for potential evaluation of emerging technology commercialization is presented to illustrate the new method, and some comparisons are also conducted to further illustrate advantages of the new method.

]]>Symmetry doi: 10.3390/sym10100496

Authors: Saman Hanif Shahbaz Khushnoor Khan Muhammad Qaiser Shahbaz

In this paper, we have developed single and double acceptance sampling plans when the product life length follows the power Lindley distribution. The sampling plans have been developed by assuming infinite and finite lot sizes. We have obtained the operating characteristic curves for the resultant sampling plans. The sampling plans have been obtained for various values of the parameters. It has been found that for a finite lot size, the sampling plans provide smaller values of the parameters to achieve the specified acceptance probabilities.

]]>Symmetry doi: 10.3390/sym10100495

Authors: Ling Wang Dongfang Zhou Hao Zhang Wei Zhang Jing Chen

Fault prognosis of electronic circuits is the premise of guaranteeing normal operation of a system and carrying out on-condition maintenance. In this work, the remaining useful life (RUL) of electronic elements was estimated by selecting fault features based on variance, measuring fault severity based on relative entropy distance, and conducting fault prognosis based on the gradient boosting decision tree (GBDT) model. At first, the corresponding voltages of amplitude-frequency response, under conditions of changing full-band element parameters, were extracted, and then the frequency bands with large change amplitude were further selected based on variance. Afterwards, using relative entropy distance, the degradation of element parameters was measured, and then the RUL of electronic elements was diagnosed through regression analysis by GBDT. By comparing the data with those arising from the use of other distance-measuring methods, the relative entropy distance shows a larger change range and less apt to suffer interference from noise, which is favorable to subsequent regression prediction. The regression analysis through GBDT is easy to understand and conveniently applied in engineering practice. The application of the method proposed in the study in two examples of electronic circuits indicates that the prediction accuracy of the method for RUL of electronic elements is higher than that of the other distance-measuring methods, and its application in engineering practice is convenient.

]]>Symmetry doi: 10.3390/sym10100494

Authors: Luis Sánchez-Soto Juan Monzón

We reelaborate on the basic properties of PT symmetry from a geometrical perspective. The transfer matrix associated with these systems induces a Möbius transformation in the complex plane. The trace of this matrix classifies the actions into three types that represent rotations, translations, and parallel displacements. We find that a PT invariant system can be pictured as a complex conjugation followed by an inversion in a circle. We elucidate the physical meaning of these geometrical operations and link them with measurable properties of the system.

]]>Symmetry doi: 10.3390/sym10100493

Authors: Adem Kiliçman Wedad Saleh

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality constrained programming are discussed under the sub-b-s-preinvexity. Moreover, some new inequalities of the Hermite&mdash;Hadamard type for differentiable sub-b-s-preinvex functions are presented. Examples of applications of these inequalities are shown.

]]>Symmetry doi: 10.3390/sym10100492

Authors: Shulong Chen Yuxing Peng

Top-N recommendation is an important recommendation technique that delivers a ranked top-N item list to each user. Data sparsity is a great challenge for top-N recommendation. In order to tackle this problem, in this paper, we propose a semi-supervised model called Semi-BPR (Semi-Supervised Bayesian Personalized Ranking). Our approach is based on the assumption that, for a given model, users always prefer items ranked higher in the generated recommendation list. Therefore, we select a certain number of items ranked higher in the recommendation list to construct an intermediate set and optimize the metric Area Under the Curve (AUC). In addition, we treat the intermediate set as a teaching set and design a semi-supervised self-training model. We conduct a series of experiments on three popular datasets to compare the proposed approach with several state-of-the-art baselines. The experimental results demonstrate that our approach significantly outperforms the other methods for all evaluation metrics, especially for sparse datasets.

]]>Symmetry doi: 10.3390/sym10100491

Authors: Lincheng Jiang Yumei Jing Shengze Hu Bin Ge Weidong Xiao

Due to the cost limitation of camera sensors, images captured in low-light environments often suffer from low contrast and multiple types of noise. A number of algorithms have been proposed to improve contrast and suppress noise in the input low-light images. In this paper, a deep refinement network, LL-RefineNet, is built to learn from the synthetical dark and noisy training images, and perform image enhancement for natural low-light images in symmetric—forward and backward—pathways. The proposed network utilizes all the useful information from the down-sampling path to produce the high-resolution enhancement result, where global features captured from deeper layers are gradually refined using local features generated by earlier convolutions. We further design the training loss for mixed noise reduction. The experimental results show that the proposed LL-RefineNet outperforms the comparative methods both qualitatively and quantitatively with fast processing speed on both synthetic and natural low-light image datasets.

]]>Symmetry doi: 10.3390/sym10100490

Authors: Michael Seifert

Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a &ldquo;Lorentz-violating&rdquo; (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an &ldquo;effective equation&rdquo; for the metric perturbations alone. The resulting effective equation may depend on the metric in a gauge-invariant way, or it may be gauge-dependent. The only two known models yielding gauge-invariant effective equations involve differential forms; I show in this work that the obvious generalizations of these models do not yield gauge-invariant effective equations. Meanwhile, I show that a gauge-dependent effective equation may be obtained from any &ldquo;tensor Klein&ndash;Gordon&rdquo; model under similar assumptions. Finally, I discuss the implications of this work in the search for Lorentz-violating gravitational effects.

]]>Symmetry doi: 10.3390/sym10100489

Authors: Ke Ruan Qi Zhang

With reference to the hospitalizing trips made by the elderly, the impedance of these trips that require the use of public transportation, is introduced. An evaluation model that can accurately detect the accessibility of high order urban hospitals (HOUHs) for the elderly is established with the help of Geographic Information System (GIS) technology. Furthermore, the established model is employed to detect the accessibility of first-level hospitals in Xi&rsquo;an City. Results showed that the traffic connection between hospitals and their service objects is an important factor for the feasibility and effectiveness of an accessibility evaluation. It is suggested that special evaluations of the accessibility of hospitals for the elderly are needed to achieve the human-oriented goal of urban traffic planning. The well-served spatial pattern of hospitalizing accessibility for the elderly in Xi&rsquo;an City has been established in recent years because of the strategies for public transit metropolis. The accessibility constraints can be divided into three types: The imprisonment, the antagonism and the running-in, for which the corresponding countermeasures to settle the low accessibility of hospitals will be taken by the planning administration. Attention is paid to specific population groups during their hospitalizing trips in the accessibility research, which is beneficial for enabling the improvement of the current traditional method which is mainly based on travel facilities.

]]>Symmetry doi: 10.3390/sym10100488

Authors: Wei Fan Hong Lu Xinbao Zhang Yongquan Zhang Rong Zeng Qi Liu

The position synchronous control of multi-axis gantry-type feed stage is crucial in precision machine tools. Industrial position control which aims to widen the bandwidth and improve disturbance rejection of single axis is not enough to achieve precise synchronization in a dual-driving feed stage. The characteristics diversity, transmission-mechanism deformation, and mechanical coupling effect between dual axes will degrade the control accuracy. Hence, the novel two-degree-of-freedom (2-DOF) dynamic model-based terminal sliding mode control (TSMC) with disturbance and state observer is proposed in this paper for the synchronous control of a 2-DOF dual-driving feed stage. The 2-DOF dynamic model, based on Lagrange equation, is established along with the parameters identification method. The predictive natural frequencies and vibration modes frequencies by the proposed dynamic model are compared by a modal experiment. Then, the 2-DOF dynamic model-based TSMC is provided to satisfy the tracking and synchronization control. In order to reduce the chattering and to increase the robustness against the mechanical coupling, the disturbance and state observer is designed. Moreover, Lyapunov stability criterion is used to analyze the stability of the proposed control scheme. Finally, an industrial application of 2-DOF dual-driving feed stage is utilized to validate the effectiveness of the proposed control scheme. The proposed 2-DOF dynamic model-based TSMC with observer has been effectively demonstrated to improve synchronous performance and tracking accuracy.

]]>Symmetry doi: 10.3390/sym10100487

Authors: Yeong-Hyeon Byeon Jae-Neung Lee Sung-Bum Pan Keun-Chang Kwak

In this study, we present a third-order tensor-based multilinear eigenECG (MEECG) and multilinear Fisher ECG (MFECG) for individual identification based on the information obtained by an electrocardiogram (ECG) sensor. MEECG and MFECG are based on multilinear principal component analysis (MPCA) and multilinear linear discriminant analysis (MLDA) in the field of multilinear subspace learning (MSL), respectively. MSL directly extracts features without the vectorization of input data, while MSL extracts features without vectorizing the input data while maintaining most of the correlations shown in the original structure. In contrast with unsupervised linear subspace learning (LSL) techniques such as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis), it is less susceptible to small-data problems because it learns more compact and potentially useful representations, and it can efficiently handle large tensors. Here, the third-order tensor is formed by reordering the one-dimensional ECG signal into a two-dimensional matrix, considering the time frame. The MSL consists of four steps. The first step is preprocessing, in which input samples are centered. The second step is initialization, in which eigen decomposition is performed and the most significant eigenvectors are selected. The third step is local optimization, in which input data is applied by eigenvectors from the second step, and new eigenvectors are calculated using the applied input data. The final step is projection, in which the resultant feature tensors after projection are obtained. The experiments are performed on two databases for performance evaluation. The Physikalisch-Technische Bundesanstalt (PTB)-ECG is a well-known database, and Chosun University (CU)-ECG is directly built for this study using the developed ECG sensor. The experimental results revealed that the tensor-based MEECG and MFECG showed good identification performance in comparison to PCA and LDA of LSL.

]]>Symmetry doi: 10.3390/sym10100486

Authors: Jie Wang Guiwu Wei Mao Lu

In this article, we extend the original TODIM (Portuguese acronym for Interactive Multi-Criteria Decision Making) method to the 2-tuple linguistic neutrosophic fuzzy environment to propose the 2TLNNs TODIM method. In the extended method, we use 2-tuple linguistic neutrosophic numbers (2TLNNs) to present the criteria values in multiple attribute group decision making (MAGDM) problems. Firstly, we briefly introduce the definition, operational laws, some aggregation operators and the distance calculating method of 2TLNNs. Then, the calculation steps of the original TODIM model are presented in simplified form. Thereafter, we extend the original TODIM model to the 2TLNNs environment to build the 2TLNNs TODIM model, our proposed method, which is more reasonable and scientific in considering the subjectivity of DM&rsquo;s behaviors and the dominance of each alternative over others. Finally, a numerical example for the safety assessment of a construction project is proposed to illustrate the new method, and some comparisons are also conducted to further illustrate the advantages of the new method.

]]>Symmetry doi: 10.3390/sym10100485

Authors: Muhammad Ashfaq Khan Md. Rezaul Karim Yangwoo Kim

Every day we experience unprecedented data growth from numerous sources, which contribute to big data in terms of volume, velocity, and variability. These datasets again impose great challenges to analytics framework and computational resources, making the overall analysis difficult for extracting meaningful information in a timely manner. Thus, to harness these kinds of challenges, developing an efficient big data analytics framework is an important research topic. Consequently, to address these challenges by exploiting non-linear relationships from very large and high-dimensional datasets, machine learning (ML) and deep learning (DL) algorithms are being used in analytics frameworks. Apache Spark has been in use as the fastest big data processing arsenal, which helps to solve iterative ML tasks, using distributed ML library called Spark MLlib. Considering real-world research problems, DL architectures such as Long Short-Term Memory (LSTM) is an effective approach to overcoming practical issues such as reduced accuracy, long-term sequence dependency, and vanishing and exploding gradient in conventional deep architectures. In this paper, we propose an efficient analytics framework, which is technically a progressive machine learning technique merged with Spark-based linear models, Multilayer Perceptron (MLP) and LSTM, using a two-stage cascade structure in order to enhance the predictive accuracy. Our proposed architecture enables us to organize big data analytics in a scalable and efficient way. To show the effectiveness of our framework, we applied the cascading structure to two different real-life datasets to solve a multiclass and a binary classification problem, respectively. Experimental results show that our analytical framework outperforms state-of-the-art approaches with a high-level of classification accuracy.

]]>Symmetry doi: 10.3390/sym10100484

Authors: Yanlan Mei Yingying Liang Yan Tu

Quality function deployment (QFD) is an effective approach to satisfy the customer requirements (CRs). Furthermore, accurately prioritizing the engineering characteristics (ECs) as the core of QFD is considered as a group decision making (GDM) problem. In order to availably deal with various preferences and the vague information of different experts on a QFD team, multi-granularity 2-tuple linguistic representation is applied to elucidate the relationship and correlation between CRs and ECs without loss of information. In addition, the importance of CRs is determined using the best worst method (BWM), which is more applicable and has good consistency. Furthermore, we propose considering the relationship matrix and correlation matrix method to prioritize ECs. Finally, an example about evaluating emergency routes of metro station is proposed to illustrate the validity of the proposed methodology.

]]>Symmetry doi: 10.3390/sym10100483

Authors: Sinan ERCAN

The aim of the present work is to introduce notions of statistical convergence, strongly p-Ces&agrave;ro summability and the statistically Cauchy sequence of order &alpha; in paranormed spaces. Some certain topological properties of these new concepts are examined. Furthermore, we introduce the some inclusion relations among them.

]]>Symmetry doi: 10.3390/sym10100482

Authors: Huidong Qiao Haihe Ba Huaizhe Zhou Zhiying Wang Jiangchun Ren Ying Hu

Cryptographic cloud storage (CCS) is a secure architecture built in the upper layer of a public cloud infrastructure. In the CCS system, a user can define and manage the access control of the data by himself without the help of cloud storage service provider. The ciphertext-policy attribute-based encryption (CP-ABE) is considered as the critical technology to implement such access control. However, there still exists a large security obstacle to the implementation of CP-ABE in CCS. That is, how to identify the malicious cloud user who illegally shares his private keys with others or applies his keys to construct a decryption device/black-box, and provides the decryption service. Although several CP-ABE schemes with black-box traceability have been proposed to address the problem, most of them are not practical in CCS systems, due to the absence of scalability and expensive computation cost, especially the cost of tracing. Thus, we present a new black-box traceable CP-ABE scheme that is scalable and high efficient. To achieve a much better performance, our work is designed on the prime order bilinear groups that results in a great improvement in the efficiency of group operations, and the cost of tracing is reduced greatly to O ( N ) or O ( 1 ) , where N is the number of users of a system. Furthermore, our scheme is proved secure in a selective standard model. To the best of our knowledge, this work is the first such practical and provably secure CP-ABE scheme for CCS, which is black-box traceable.

]]>Symmetry doi: 10.3390/sym10100481

Authors: Buthinah A. Bin Dehaish Mohamed A Khamsi

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci&ndash;Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by x n + 1 = t n T ϕ ( n ) ( x n ) + ( 1 &minus; t n ) x n , for n &isin; N , when T is a monotone asymptotically nonexpansive self-mapping.

]]>Symmetry doi: 10.3390/sym10100480

Authors: Quentin G. Bailey Charles D. Lane

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) ★ symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) ★ model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.

]]>Symmetry doi: 10.3390/sym10100479

Authors: Yadong Yang Xiaofeng Wang Hengzheng Zhang

Compared with ordinary image classification tasks, fine-grained image classification is closer to real-life scenes. Its key point is how to find the local areas with sufficient discrimination and perform effective feature learning. Based on a bilinear convolutional neural network (B-CNN), this paper designs a local importance representation convolutional neural network (LIR-CNN) model, which can be divided into three parts. Firstly, the super-pixel segmentation convolution method is used for the input layer of the model. It allows the model to receive images of different sizes and fully considers the complex geometric deformation of the images. Then, we replaced the standard convolution of B-CNN with the proposed local importance representation convolution. It can score each local area of the image using learning to distinguish their importance. Finally, channelwise convolution is proposed and it plays an important role in balancing lightweight network and classification accuracy. Experimental results on the benchmark datasets (e.g., CUB-200-2011, FGVC-Aircraft, and Stanford Cars) showed that the LIR-CNN model had good performance in fine-grained image classification tasks.

]]>Symmetry doi: 10.3390/sym10100478

Authors: Zafar Hussain Mobeen Munir Shazia Rafique Shin Min Kang

Topological indices and connectivity polynomials are invariants of molecular graphs. These invariants have the tendency of predicting the properties of the molecular structures. The honeycomb network structure is an important type of benzene network. In the present article, new topological characterizations of honeycomb networks are given in the form of degree-based descriptors. In particular, we compute Zagreb and Forgotten polynomials and some topological indices such as the hyper-Zagreb index, first and second multiple Zagreb indices and the Forgotten index, F. We, for the first time, determine some regularity indices such as the Albert index, Bell index and I R M ( G ) index, as well as the F-index of the complement of the honeycomb network and several co-indices related to this network without considering the graph of its complement or even the line graph. These indices are useful for correlating the physio-chemical properties of the honeycomb network. We also give a graph theoretic analysis of some indices against the dimension of this network.

]]>Symmetry doi: 10.3390/sym10100477

Authors: Jianqiang Hao Jianzhi Sun Yi Chen Qiang Cai Li Tan

This paper provides a full theoretical and experimental analysis of a serial algorithm for the point-in-polygon test, which requires less running time than previous algorithms and can handle all degenerate cases. The serial algorithm can quickly determine whether a point is inside or outside a polygon and accurately determine the contours of input polygon. It describes all degenerate cases and simultaneously provides a corresponding solution to each degenerate case to ensure the stability and reliability. This also creates the prerequisites and basis for our novel boolean operations algorithm that inherits all the benefits of the serial algorithm. Using geometric probability and straight-line equation F ( P ) = ( y i &minus; y i + 1 ) ( x p &minus; x i ) &minus; ( y i &minus; y p ) ( x i + 1 &minus; x i ) , it optimizes our two algorithms that avoid the division operation and do not need to compute any intersection points. Our algorithms are applicable to any polygon that may be self-intersecting or with holes nested to any level of depth. They do not have to sort the vertices clockwise or counterclockwise beforehand. Consequently, they process all edges one by one in any order for input polygons. This allows a parallel implementation of each algorithm to be made very easily. We also prove several theorems guaranteeing the correctness of algorithms. To speed up the operations, we assign each vector a number code and derive two iterative formulas using differential calculus. However, the experimental results as well as the theoretical proof show that our serial algorithm for the point-in-polygon test is optimal and the time complexities of all algorithms are linear. Our methods can be extended to three-dimensional space, in particular, they can be applied to 3D printing to improve its performance.

]]>Symmetry doi: 10.3390/sym10100476

Authors: Zi-Xin Zhang Liang Wang Ying-Ming Wang

Because of the continuous burst of emergency events (EEs) recently, emergency decision making (EDM) has become an active research topic due to its crucial role in relieving and reducing various losses and damages (property, lives, environment, etc.) caused by EEs. Current EDM studies based on prospect theory (PT) have considered decision maker&rsquo;s (DM&rsquo;s) psychological behavior, which is very important in the EDM process because it affects DM&rsquo;s decision behavior directly, particularly under the uncertainty decision environment. However, those studies neglected an important fact that different emergency situations should be handled by different measures to show the pertinence and effectiveness of the emergency response in the real world, which has been taken into consideration in EDM studies based on game theory (GT). Different behavior experiments show that DMs usually have limited rationality when involved in risk and an uncertain decision environment, in which their psychological behavior has distinct impacts on their decision choice and behavior. Nevertheless, the existing studies of EDM based on GT build on an assumption that DMs are totally rational; however, it is obvious that such an assumption is unreasonable and far from the real-world situation. Motivated by these limitations pointed out previously, this study proposes a novel EDM method combining GT and PT that considers not only the DM&rsquo;s psychological behavior, but also takes different situations&rsquo; handling for EEs into account, which is closer to the EDM problems in reality. An example and comparison with other methods are provided to demonstrate the validity and rationality of the proposed method for coping with real-world EDM problems.

]]>Symmetry doi: 10.3390/sym10100475

Authors: Ying Tian Zhong Yin Miao Huang

Traditional outlier detection methods assume that the sampling time and interval are the same. However, for plant-wide processes, since the signal change rate of different devices may vary by several orders of magnitude, the measured data in real-world systems usually have different sampling rates, resulting in missing data. To achieve reliable outlier detection, a missing data probability estimation-based Bayesian outlier detection method is adopted. In this strategy, the expectation&ndash;maximization (EM) algorithm is first used to estimate the likelihood probability of different evidence under different process statuses by using the history dataset which contains complete and incomplete samplings. Secondly, the realization of unavailable parts in the monitoring point is estimated as a probability through historical data and online moving horizon data. Bayesian theory and likelihood probability are then used to calculate the outlier posterior probability of different realization. Finally, the outlier probability of the monitoring sampling is calculated by the probability of different realizations and the corresponding outlier probability. Using the Tennessee Eastman (TE) dataset, a simulation indicates that the proposed method exhibits a significant improvement over the complete data method.

]]>Symmetry doi: 10.3390/sym10100474

Authors: Yujun Zeng Lilin Qian Junkai Ren

Extreme learning machine (ELM), characterized by its fast learning efficiency and great generalization ability, has been applied to various object recognition tasks. When extended to the stacked autoencoder network, which is a typical symmetrical representation learning model architecture, ELM manages to realize hierarchical feature extraction and classification, which is what deep neural networks usually do, but with much less training time. Nevertheless, the input weights and biases of the hidden nodes in ELM are generated according to a random distribution and may lead to the occurrence of non-optimal and redundant parameters that deteriorate discriminative features, which will have a bad influence on the final classification effect. In this paper, a novel sparse autoencoder derived from ELM and differential evolution is proposed and integrated into a hierarchical hybrid autoencoder network to accomplish the end-to-end learning with raw visible light camera sensor images and applied to several typical object recognition problems. Experimental results show that the proposed method is able to obtain competitive or better performance than current relevant methods with acceptable or less time consumption.

]]>Symmetry doi: 10.3390/sym10100473

Authors: Ravi Agarwal Snezhana Hristova Donal O’Regan

The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag&ndash;Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

]]>Symmetry doi: 10.3390/sym10100472

Authors: Yuan Xu Xiaopu Shang Jun Wang Wen Wu Huiqun Huang

The q-rung orthopair fuzzy sets (q-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of q-ROFSs are q-rung orthopair fuzzy numbers (q-ROFNs), which are constructed by membership and nonmembership degrees. As realistic decision-making is very complicated, decision makers (DMs) may be hesitant among several values when determining membership and nonmembership degrees. By incorporating dual hesitant fuzzy sets (DHFSs) into q-ROFSs, we propose a new technique to deal with uncertainty, called q-rung dual hesitant fuzzy sets (q-RDHFSs). Subsequently, we propose a family of q-rung dual hesitant fuzzy Heronian mean operators for q-RDHFSs. Further, the newly developed aggregation operators are utilized in multiple attribute group decision-making (MAGDM). We used the proposed method to solve a most suitable supplier selection problem to demonstrate its effectiveness and usefulness. The merits and advantages of the proposed method are highlighted via comparison with existing MAGDM methods. The main contribution of this paper is that a new method for MAGDM is proposed.

]]>Symmetry doi: 10.3390/sym10100471

Authors: YunJae Kim Byung Moon Kim Lee-Chae Jang Jongkyum Kwon

Kim-Kim studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace transformation and investigate some properties and formulas related to them.

]]>Symmetry doi: 10.3390/sym10100470

Authors: Marko Hölbl Marko Kompara Aida Kamišalić Lili Nemec Zlatolas

Blockchain technology enables a decentralized and distributed environment with no need for a central authority. Transactions are simultaneously secure and trustworthy due to the use of cryptographic principles. In recent years, blockchain technology has become very trendy and penetrated different domains, mostly due to the popularity of cryptocurrencies. One field where blockchain technology has tremendous potential is healthcare, due to the need for a more patient-centric approach to healthcare systems and to connect disparate systems and increase the accuracy of electronic healthcare records (EHRs). In this systematic review, an analysis of state-of-the-art blockchain research in the field of healthcare is conducted. The aim is to reveal the potential applications of the technology and to highlight the challenges and possible directions of blockchain research in healthcare. First, background information is discussed, followed by a description of the exact methodology used in this paper. Next, an analysis of the results is given, which includes a bibliometric overview, an analysis of gathered data and its properties, and the results of a literature quality assessment. Lastly, there is a discussion of the results from the analysis. The findings indicate that blockchain technology research in healthcare is increasing and it is mostly used for data sharing, managing health records and access control. Other scenarios are very rare. Most research is aimed at presenting novel structural designs in the form of frameworks, architectures or models. Findings also show that technical details about the used blockchain elements are not given in most of the analyzed publications and that most research does not present any prototype implementation or implementation details. Often even with a prototype implementation, no details about blockchain elements are given.

]]>Symmetry doi: 10.3390/sym10100469

Authors: Yan Zhao Yuki Endo Yoshihiro Kanamori Jun Mitani

Three-dimensional (3D) origami, which can generate a structure through folding a crease pattern on a flat sheet of paper, has received considerable attention in art, mathematics, and engineering. With consideration of symmetry, the user can efficiently generate a rational crease pattern and make the fabricated shape stable. In this paper, we focus on a category of axisymmetric origami consisting of triangular facets and edit the origami in 3D space for expanding its variations. However, it is difficult to retain the developability, which requires the sum of the angles around each interior vertex needing to equal 360 degrees, for designing origami. Intersections occur between crease lines when such a value is larger than 360 degrees. On the other hand, blank spaces (unfolded areas) emerge in the crease pattern when the value is less than 360 degrees. The former case is difficult to generate a realizable shape due to the crease lines are intersected with each other. For the latter case, however, blank spaces can be filled with crease lines and become a part of the origami through tucking. Here, we propose a computational method to add flaps or tucks on the 3D shape, which contains non-developable interior vertices, for achieving the resulting origami. Finally, on the application side, we describe a load-bearing experiment on a stool shape-like origami to demonstrate the potential usage.

]]>Symmetry doi: 10.3390/sym10100468

Authors: Venkataraman Yegnanarayanan Gayathri Narayana Yegnanarayanan Marius M. Balas

A vertex coloring of a graph G is a mapping that allots colors to the vertices of G. Such a coloring is said to be a proper vertex coloring if two vertices joined by an edge receive different colors. The chromatic number &chi; ( G ) is the least number of colors used in a proper vertex coloring. In this paper, we compute the &chi; of certain distance graphs whose distance set elements are (a) a finite set of Catalan numbers, (b) a finite set of generalized Catalan numbers, (c) a finite set of Hankel transform of a transformed sequence of Catalan numbers. Then while discussing the importance of minimizing interference in wireless networks, we probe how a vertex coloring problem is related to minimizing vertex collisions and signal clashes of the associated interference graph. Then when investigating the &chi; of certain G ( V , D ) and graphs with interference, we also compute certain lower and upper bound for &chi; of any given simple graph in terms of the average degree and Laplacian operator. Besides obtaining some interesting results we also raised some open problems.

]]>Symmetry doi: 10.3390/sym10100466

Authors: Qingqing Hu Xiaohong Zhang

Cut sets, decomposition theorem and representation theorem have a great influence on the realization of the transformation of fuzzy sets and classical sets, and the single-valued neutrosophic multisets (SVNMSs) as the generalization of fuzzy sets, which cut sets, decomposition theorem and representation theorem have the similar effects, so they need to be studied in depth. In this paper, the decomposition theorem, representation theorem and the application of a new similarity measures of SVNMSs are studied by using theoretical analysis and calculations. The following are the main results: (1) The notions, operation and operational properties of the cut sets and strong cut sets of SVNMSs are introduced and discussed; (2) The decomposition theorem and representation theorem of SVNMSs are established and rigorously proved. The decomposition theorem and the representation theorem of SVNMSs are the theoretical basis for the development of SVNMSs. The decomposition theorem provides a new idea for solving the problem of SVNMSs, and points out the direction for the principle of expansion of SVNMSs. (3) Based on the decomposition theorem and representation theorem of SVNMSs, a new notion of similarity measure of SVNMSs is proposed by applying triple integral. And this new similarity is applied to the practical problem of multicriteria decision-making, which explains the efficacy and practicability of this decision-making method. The new similarity is not only a way to solve the problem of multi-attribute decision-making, but also contains an important mathematical idea, that is, the idea of transformation.

]]>Symmetry doi: 10.3390/sym10100467

Authors: Ke Chen Dandan Zhu Jianwei Lu Ye Luo

Automatic reconstructing of neural circuits in the brain is one of the most crucial studies in neuroscience. Connectomes segmentation plays an important role in reconstruction from electron microscopy (EM) images; however, it is rather challenging due to highly anisotropic shapes with inferior quality and various thickness. In our paper, we propose a novel connectomes segmentation framework called adversarial and densely dilated network (ADDN) to address these issues. ADDN is based on the conditional Generative Adversarial Network (cGAN) structure which is the latest advance in machine learning with power to generate images similar to the ground truth especially when the training data is limited. Specifically, we design densely dilated network (DDN) as the segmentor to allow a deeper architecture and larger receptive fields for more accurate segmentation. Discriminator is trained to distinguish generated segmentation from manual segmentation. During training, such adversarial loss function is optimized together with dice loss. Extensive experimental results demonstrate that our ADDN is effective for such connectomes segmentation task, helping to retrieve more accurate segmentation and attenuate the blurry effects of generated boundary map. Our method obtains state-of-the-art performance while requiring less computation on ISBI 2012 EM dataset and mouse piriform cortex dataset.

]]>Symmetry doi: 10.3390/sym10100465

Authors: Xiaoying Wu Xiaohong Zhang

For mathematical fuzzy logic systems, the study of corresponding algebraic structures plays an important role. Pseudo-BCI algebra is a class of non-classical logic algebras, which is closely related to various non-commutative fuzzy logic systems. The aim of this paper is focus on the structure of a special class of pseudo-BCI algebras in which every element is quasi-maximal (call it QM-pseudo-BCI algebras in this paper). First, the new notions of quasi-maximal element and quasi-left unit element in pseudo-BCK algebras and pseudo-BCI algebras are proposed and some properties are discussed. Second, the following structure theorem of QM-pseudo-BCI algebra is proved: every QM-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an anti-group pseudo-BCI algebra. Third, the new notion of weak associative pseudo-BCI algebra (WA-pseudo-BCI algebra) is introduced and the following result is proved: every WA-pseudo-BCI algebra is a KG-union of a quasi-alternating BCK-algebra and an Abel group.

]]>Symmetry doi: 10.3390/sym10100464

Authors: Ferdous Hossain Tan Kim Geok Tharek Abd Rahman Mhd Nour Hindia Kaharudin Dimyati Azlan Abdaziz

The Millimeter-Wave (mmW) technology is going to mitigate the global higher bandwidth carriers. It will dominate the future network system by the attractive advantages of the higher frequency band. Higher frequency offers a wider bandwidth spectrum. Therefore, its utilizations are rapidly increasing in the wireless communication system. In this paper, an indoor mmW propagation prediction is presented at 38 GHz based on measurements and the proposed Three-Dimensional (3-D) Ray Tracing (RT) simulation. Moreover, an additional simulation performed using 3-D Shooting Bouncing Ray (SBR) method is presented. Simulation using existing SBR and the proposed RT methods have been performed separately on a specific layout where the measurement campaign is conducted. The RT methods simulations results have been verified by comparing with actual measurement data. There is a significant agreement between the simulation and measurement with respect to path loss and received signal strength indication. The analysis result shows that the proposed RT method output has better agreement with measurement output when compared to the SBR method. According to the result of the propagation prediction analysis, it can be stated that the proposed method&rsquo;s ray tracing is capable of predicting the mmW propagation based on a raw sketch of the real environment.

]]>Symmetry doi: 10.3390/sym10100463

Authors: M. Zubair Muhammad Zeeshan Syed Sibet Hasan V. K. Oikonomou

We study the cosmic evolution of non-minimally coupled f ( R , T ) gravity in the presence of matter fluids consisting of collisional self-interacting dark matter and radiation. We study the cosmic evolution in the presence of collisional matter, and we compare the results with those corresponding to non-collisional matter and the &Lambda; -cold-dark-matter ( &Lambda; CDM) model. Particularly, for a flat Friedmann&ndash;Lema i ^ tre&ndash;Robertson&ndash;Walker Universe, we study two non-minimally coupled f ( R , T ) gravity models and we focus our study on the late-time dynamical evolution of the model. Our study is focused on the late-time behavior of the effective equation of the state parameter &omega; e f f and of the deceleration parameter q as functions of the redshift for a Universe containing collisional and non-collisional dark matter fluids, and we compare both models with the &Lambda; CDM model. As we demonstrate, the resulting picture is well accommodated to the latest observational data on the basis of physical parameters.

]]>Symmetry doi: 10.3390/sym10100462

Authors: Jingqian Wang Xiaohong Zhang

Intuitionistic fuzzy rough sets are constructed by combining intuitionistic fuzzy sets with rough sets. Recently, Huang et al. proposed the definition of an intuitionistic fuzzy (IF) β -covering and an IF covering rough set model. In this paper, some properties of IF β -covering approximation spaces and the IF covering rough set model are investigated further. Moreover, we present a novel methodology to the problem of multiple criteria group decision making. Firstly, some new notions and properties of IF β -covering approximation spaces are proposed. Secondly, we study the characterizations of Huang et al.’s IF covering rough set model and present a new IF covering rough set model for crisp sets in an IF environment. The relationships between these two IF covering rough set models and some other rough set models are investigated. Finally, based on the IF covering rough set model, Huang et al. also defined an optimistic multi-granulation IF rough set model. We present a novel method to multiple criteria group decision making problems under the optimistic multi-granulation IF rough set model.

]]>Symmetry doi: 10.3390/sym10100461

Authors: David Luviano-Cruz Francesco Garcia-Luna Luis Pérez-Domínguez S. K. Gadi

A multi-agent system (MAS) is suitable for addressing tasks in a variety of domains without any programmed behaviors, which makes it ideal for the problems associated with the mobile robots. Reinforcement learning (RL) is a successful approach used in the MASs to acquire new behaviors; most of these select exact Q-values in small discrete state space and action space. This article presents a joint Q-function linearly fuzzified for a MAS&rsquo; continuous state space, which overcomes the dimensionality problem. Also, this article gives a proof for the convergence and existence of the solution proposed by the algorithm presented. This article also discusses the numerical simulations and experimental results that were carried out to validate the proposed algorithm.

]]>Symmetry doi: 10.3390/sym10100460

Authors: Zhijian Huang Yongjun Wang

AFL (American Fuzzy Lop) is a powerful fuzzing tool that has discovered hundreds of real-world vulnerabilities. Recent efforts are seen to port AFL to a fuzzing Java program and have shown to be effective in Java testing. However, these tools require humans to write driver classes, which is not plausible for testing large-scale software. In addition, AFL generates files as input, making it limited for testing methods that process files. In this paper, we present JDriver, an automatic driver class generation framework for AFL-based fuzzing tools, which can build driver code for methods&rsquo; processing files as well as ordinary methods not processing files. Our approach consists of three parts: a dependency-analysis based method to generate method sequences that are able to change the instance&rsquo;s status so as to exercise more paths, a knowledge assisted method to make instance for the method sequences, and an input-file oriented driver class assembling method to handle the method parameters for ordinary methods. We evaluate JDriver on commons-imaging, a widely used image library provided by the Apache organization. JDriver has successfully generated 149 helper methods which can be used to make instances for 110 classes. Moreover, 99 driver classes are built to cover 422 methods.

]]>Symmetry doi: 10.3390/sym10100459

Authors: Qaisar Khan Peide Liu Tahir Mahmood Florentin Smarandache Kifayat Ullah

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

]]>Symmetry doi: 10.3390/sym10100458

Authors: María Jose Pérez-Peñalver Esther Sanabria-Codesal Florica Moldoveanu Alin Moldoveanu Victor Asavei Andrei A. Muller Adrian Ionescu

This work describes the geometry behind the Smith chart, recent 3D Smith chart tool and previously reported conceptual Hyperbolic Smith chart. We present the geometrical properties of the transformations used in creating them by means of inversive geometry and basic non-Euclidean geometry. The beauty and simplicity of this perspective are complementary to the classical way in which the Smith chart is taught in the electrical engineering community by providing a visual insight that can lead to new developments. Further we extend our previous work where we have just drawn the conceptual hyperbolic Smith chart by providing the equations for its generation and introducing additional properties.

]]>Symmetry doi: 10.3390/sym10100457

Authors: Dandan Zhu Lei Dai Ye Luo Guokai Zhang Xuan Shao Laurent Itti Jianwei Lu

Previous saliency detection methods usually focused on extracting powerful discriminative features to describe images with a complex background. Recently, the generative adversarial network (GAN) has shown a great ability in feature learning for synthesizing high quality natural images. Since the GAN shows a superior feature learning ability, we present a new multi-scale adversarial feature learning (MAFL) model for image saliency detection. In particular, we build this model, which is composed of two convolutional neural network (CNN) modules: the multi-scale G-network takes natural images as inputs and generates the corresponding synthetic saliency map, and we design a novel layer in the D-network, namely a correlation layer, which is used to determine whether one image is a synthetic saliency map or ground-truth saliency map. Quantitative and qualitative comparisons on several public datasets show the superiority of our approach.

]]>Symmetry doi: 10.3390/sym10100456

Authors: Juan C. Hernández-Gómez J. A. Méndez-Bermúdez José M. Rodríguez José M. Sigarreta

Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, corona product, join, Cartesian sum and lexicographic product. Some upper and lower bounds for the harmonic indices of these operations of graphs, in terms of related indices, are derived from known bounds on the integral of a product on nonnegative convex functions. Besides, we provide an algorithm that computes the harmonic polynomial with complexity O ( n 2 ) .

]]>Symmetry doi: 10.3390/sym10100455

Authors: Young Jae Sim Oh Sang Kwon Nak Eun Cho

In the present paper, we find sufficient conditions for starlikeness and convexity of normalized Lommel functions of the first kind using the admissible function methods. Additionally, we investigate some inclusion relationships for various classes associated with the Lommel functions. The functions belonging to these classes are related to the starlike functions, convex functions, close-to-convex functions and quasi-convex functions.

]]>Symmetry doi: 10.3390/sym10100452

Authors: Xing Sun Zhe Tian Reza Malekian Zhixiong Li

Exhaust emissions from vessels have increasingly attracted attention in the continuously growing marine transport world trade market. The International Maritime Organization (IMO) has introduced a number of measures designed to reduce exhaust emissions from global shipping. As one of the busiest ports in the world, Qingdao port has been studied to propose possible support to the development of efficient emission reduction. In this study, a large amount data of emissions inventory in Qingdao port was used to predict its annual exhaust emissions, and hence, to help understand maritime pollution in Qingdao port. Bigdata analysis methodology was employed to perform accurate predictions on vessel emissions. The analysis results show that the emissions were dominated by container ships, oil tankers, and bulk cargo ships. The comparison between Qingdao port and other ports in emission control areas demonstrates the necessity of control measures for exhaust emissions. The adoption of shore power and efficient cargo handling seems to be a potential solution to reduce exhaust emissions. The findings of this study are meaningful for maritime safety administration to understand the current emission situation in Qingdao port, propose corresponding control measures, and perform pollution prevention.

]]>Symmetry doi: 10.3390/sym10100453

Authors: Francisco Cavas-Martínez David Piñero Daniel Fernández-Pacheco Jorge Mira Francisco Cañavate Jorge Alió

Purpose: The aim of this study was to assess bilateral symmetry in normal fellow eyes by using optical and geometric morphometric parameters. Methods: All participants underwent complete biocular examinations. Scheimpflug tomography data from 66 eyes of 33 patients were registered. The interocular symmetry was based on five patterns: morphogeometric symmetry, axial symmetry at the corneal vertex, angular-spatial symmetry, direct symmetry (equal octants), and enantiomorphism (mirror octants). Results: No statistically significant differences were found between right and left eyes in corneal morphogeometric (p ≥ 0.488) and aberrometric parameters (p ≥ 0.102). Likewise, no statistically significant differences were found in any of the axial symmetry parameters analyzed (p ≥ 0.229), except in the surface rotation angle beta (p = 0.102) and translation coordinates X0 and Y0 (p &lt; 0.001) for the anterior corneal surface, and the rotation angle gamma (p &lt; 0.001) for the posterior surface. Similarly, no statistically significant differences were identified for direct symmetry (p ≥ 0.20) and enantiomorphism (p ≥ 0.75), except for some elevation data in the posterior surface (p &lt; 0.01). Conclusions: The level of symmetry of both corneas of a healthy individual is high, with only some level of disparity between fellow corneas in rotation and translation references. Abnormalities in this pattern of interocular asymmetry may be useful as a diagnostic tool.

]]>Symmetry doi: 10.3390/sym10100451

Authors: Dae Kim Taekyun Kim Cheon Ryoo Yonghong Yao

The q-Bernoulli numbers and polynomials can be given by Witt’s type formulas as p-adic invariant integrals on Z p . We investigate some properties for them. In addition, we consider two variable q-Bernstein polynomials and operators and derive several properties for these polynomials and operators. Next, we study the evaluation problem for the double integrals on Z p of two variable q-Bernstein polynomials and show that they can be expressed in terms of the q-Bernoulli numbers and some special values of q-Bernoulli polynomials. This is generalized to the problem of evaluating any finite product of two variable q-Bernstein polynomials. Furthermore, some identities for q-Bernoulli numbers are found.

]]>Symmetry doi: 10.3390/sym10100454

Authors: Kai-Qing Zhou Li-Ping Mo Lei Ding Wei-Hua Gui

Fuzzy Petri net (FPN) is widely used to repre sent, model and analyse knowledge-based systems (KBSs). Meanwhile, a reachability tree is an important tool to fully represent the flow relationship of FPN and is widely applied to implement inference in industrial areas. However, the traditional reachability ignores recording the dependence relationships (&lsquo;and/or&rsquo; relationship) among the places in the neighbouring layers. This paper develops a modified reachability tree based on an and/or graph and presents a three-phase generation algorithm to model the reachability tree for the corresponding FPN automatically via fuzzy production rules (FPRs). Four cases are used to verify the correctness and feasibility of the proposed algorithm from different viewpoints, such as general FPRs, FPRs with a condition-sharing situation, FPRs with a conclusion-sharing situation, and FPRs with multi-conclusions. Simulation results reveal that the proposed approach has the ability to automatically generate the reachability tree for the corresponding FPN correctly.

]]>Symmetry doi: 10.3390/sym10100450

Authors: Han-ye Zhang Wei-ming Lin Ai-xia Chen

Good path planning technology of mobile robot can not only save a lot of time, but also reduce the wear and capital investment of mobile robot. Several methodologies have been proposed and reported in the literature for the path planning of mobile robot. Although these methodologies do not guarantee an optimal solution, they have been successfully applied in their works. The purpose of this paper is to review the modeling, optimization criteria and solution algorithms for the path planning of mobile robot. The survey shows GA (genetic algorithm), PSO (particle swarm optimization algorithm), APF (artificial potential field), and ACO (ant colony optimization algorithm) are the most used approaches to solve the path planning of mobile robot. Finally, future research is discussed which could provide reference for the path planning of mobile robot.

]]>Symmetry doi: 10.3390/sym10100449

Authors: Chang Liu Jun Qiu

In this paper, we propose the symmetric structure of the reconstructed points discretization model to partition and order the subsets of Ordered Subset Expectation Maximum (OSEM) algorithms for image reconstruction and then simplify the calculation of the projection coefficient matrix while satisfying the balancing properties of subsets. The reconstructed points discretization model was utilized to describe the forward and inverse relationships between the reconstructed points and the projection data according to the distance from the point to the ray rather than the intersection length between the square pixel and the ray. This discretization model provides new approaches for improving and constructing the reconstruction algorithms on the basis of the geometry of the model. The experimental results show that the OSEM algorithms based on the reconstructed points discretization model and its geometric symmetry structure can effectively improve the imaging speed and the imaging precision.

]]>Symmetry doi: 10.3390/sym10100448

Authors: Caili Sang Jianxing Zhao

Firstly, the relationships among strictly diagonally dominant ( S D D ) matrices, doubly strictly diagonally dominant ( D S D D ) matrices, eventually S D D matrices and eventually D S D D matrices are considered. Secondly, by excluding some proper subsets of an existing eigenvalue inclusion set for matrices, which do not contain any eigenvalues of matrices, a tighter eigenvalue inclusion set of matrices is derived. As its application, a sufficient condition of determining non-singularity of matrices is obtained. Finally, the infinity norm estimation of the inverse of eventually D S D D matrices is derived.

]]>Symmetry doi: 10.3390/sym10100447

Authors: Qing Yang Zengtai You Xinshang You

Let P be a planar point set with no three points collinear, k points of P be a k-hole of P if the k points are the vertices of a convex polygon without points of P. This article proves 13 is the smallest integer such that any planar points set containing at least 13 points with no three points collinear, contains a 3-hole, a 4-hole and a 5-hole which are pairwise disjoint.

]]>Symmetry doi: 10.3390/sym10100445

Authors: Yuge Du Yu Guo Wenhao Gui

In recent years, information entropy has been studied and developed rapidly across disciplines as a measure of information value. In this article, the maximum likelihood estimation and EM algorithm are used to estimate the parameters of the log-logistic distribution for progressive type-I interval censored data, and the hypothesis testing algorithm of information entropy is proposed. Finally, Monte Carlo numerical simulations are conducted to justify the feasibility of the algorithm.

]]>Symmetry doi: 10.3390/sym10100446

Authors: Zhan-ao Xue Min-jie Lv Dan-jie Han Xian-wei Xin

From the perspective of the degrees of classification error, we proposed graded rough intuitionistic fuzzy sets as the extension of classic rough intuitionistic fuzzy sets. Firstly, combining dominance relation of graded rough sets with dominance relation in intuitionistic fuzzy ordered information systems, we designed type-I dominance relation and type-II dominance relation. Type-I dominance relation reduces the errors caused by single theory and improves the precision of ordering. Type-II dominance relation decreases the limitation of ordering by single theory. After that, we proposed graded rough intuitionistic fuzzy sets based on type-I dominance relation and type-II dominance relation. Furthermore, from the viewpoint of multi-granulation, we further established multi-granulation graded rough intuitionistic fuzzy sets models based on type-I dominance relation and type-II dominance relation. Meanwhile, some properties of these models were discussed. Finally, the validity of these models was verified by an algorithm and some relative examples.

]]>Symmetry doi: 10.3390/sym10100444

Authors: Qaisar Khan Nasruddin Hassan Tahir Mahmood

The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.

]]>Symmetry doi: 10.3390/sym10100443

Authors: Adrian Clingher Jae-Hyouk Lee

We consider certain E n -type root lattices embedded within the standard Lorentzian lattice Z n + 1 ( 3 &le; n &le; 8 ) and study their discrete geometry from the point of view of del Pezzo surface geometry. The lattice Z n + 1 decomposes as a disjoint union of affine hyperplanes which satisfy a certain periodicity. We introduce the notions of line vectors, rational conic vectors, and rational cubics vectors and their relations to E-polytopes. We also discuss the relation between these special vectors and the combinatorics of the Gosset polytopes of type ( n &minus; 4 ) 21 .

]]>Symmetry doi: 10.3390/sym10100442

Authors: Dongxue Liang Kyoungju Park Przemyslaw Krompiec

With the advent of the deep learning method, portrait video stylization has become more popular. In this paper, we present a robust method for automatically stylizing portrait videos that contain small human faces. By extending the Mask Regions with Convolutional Neural Network features (R-CNN) with a CNN branch which detects the contour landmarks of the face, we divided the input frame into three regions: the region of facial features, the region of the inner face surrounded by 36 face contour landmarks, and the region of the outer face. Besides keeping the facial features region as it is, we used two different stroke models to render the other two regions. During the non-photorealistic rendering (NPR) of the animation video, we combined the deformable strokes and optical flow estimation between adjacent frames to follow the underlying motion coherently. The experimental results demonstrated that our method could not only effectively reserve the small and distinct facial features, but also follow the underlying motion coherently.

]]>Symmetry doi: 10.3390/sym10100441

Authors: Minxia Luo Jingjing Liang

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

]]>Symmetry doi: 10.3390/sym10100440

Authors: Valery G. Rau Igor A. Togunov Tamara F. Rau Sergey V. Polyakov

The work reports the finding and the study of transformation groups with two conditional elements (binary transformations of abstract structures of the finite numerical sets with broken symmetry). The term Broken Symmetry Group (BSG) is introduced. Transformation examples of relevant structures are studied with computer visualization and application in real structure study. A special type of BSG was discovered, which describes the subsets of &ldquo;evolutionary trees&rdquo; with convergent and divergent properties of the oriented graph (orgraph) with structure-development direction edges and &ldquo;growth spirals&rdquo;.

]]>Symmetry doi: 10.3390/sym10100439

Authors: Hemalathaa Subramanian Subramanian Arasappan

Let G = (V, E) be a simple, finite, and connected graph. A subset S = {u1, u2, &hellip;, uk} of V(G) is called a resolving set (locating set) if for any x &isin; V(G), the code of x with respect to S that is denoted by CS (x), which is defined as CS (x) = (d(u1, x), d(u2, x), .., d(uk, x)), is different for different x. The minimum cardinality of a resolving set is called the dimension of G and is denoted by dim(G). A security concept was introduced in domination. A subset D of V(G) is called a dominating set of G if for any v in V &ndash; D, there exists u in D such that u and v are adjacent. A dominating set D is secure if for any u in V &ndash; D, there exists v in D such that (D &ndash; {v}) &cup; {u} is a dominating set. A resolving set R is secure if for any s &isin; V &ndash; R, there exists r &isin; R such that (R &ndash; {r}) &cup; {s} is a resolving set. The secure resolving domination number is defined, and its value is found for several classes of graphs. The characterization of graphs with specific secure resolving domination number is also done.

]]>Symmetry doi: 10.3390/sym10100438

Authors: Jeong-Yup Lee Dong-il Lee SungSoon Kim

We construct a Gr&ouml;bner-Shirshov basis of the Temperley-Lieb algebra T ( d , n ) of the complex reflection group G ( d , 1 , n ) , inducing the standard monomials expressed by the generators { E i } of T ( d , n ) . This result generalizes the one for the Coxeter group of type B n in the paper by Kim and Lee We also give a combinatorial interpretation of the standard monomials of T ( d , n ) , relating to the fully commutative elements of the complex reflection group G ( d , 1 , n ) . More generally, the Temperley-Lieb algebra T ( d , r , n ) of the complex reflection group G ( d , r , n ) is defined and its dimension is computed.

]]>Symmetry doi: 10.3390/sym10100437

Authors: Vakkas Uluçay Memet Şahin Nasruddin Hassan

Smarandache defined a neutrosophic set to handle problems involving incompleteness, indeterminacy, and awareness of inconsistency knowledge, and have further developed it neutrosophic soft expert sets. In this paper, this concept is further expanded to generalized neutrosophic soft expert set (GNSES). We then define its basic operations of complement, union, intersection, AND, OR, and study some related properties, with supporting proofs. Subsequently, we define a GNSES-aggregation operator to construct an algorithm for a GNSES decision-making method, which allows for a more efficient decision process. Finally, we apply the algorithm to a decision-making problem, to illustrate the effectiveness and practicality of the proposed concept. A comparative analysis with existing methods is done and the result affirms the flexibility and precision of our proposed method.

]]>Symmetry doi: 10.3390/sym10100436

Authors: Jae-Myoung Kim Yun-Ho Kim Jongrak Lee

We herein discuss the following elliptic equations: M &int; R N &int; R N | u ( x ) &minus; u ( y ) | p | x &minus; y | N + p s d x d y ( &minus; &Delta; ) p s u + V ( x ) | u | p &minus; 2 u = &lambda; f ( x , u ) in R N , where ( &minus; &Delta; ) p s is the fractional p-Laplacian defined by ( &minus; &Delta; ) p s u ( x ) = 2 lim &epsilon; ↘ 0 &int; R N \ B &epsilon; ( x ) | u ( x ) &minus; u ( y ) | p &minus; 2 ( u ( x ) &minus; u ( y ) ) | x &minus; y | N + p s d y , x &isin; R N . Here, B &epsilon; ( x ) : = { y &isin; R N : | x &minus; y | &lt; &epsilon; } , V : R N &rarr; ( 0 , &infin; ) is a continuous function and f : R N &times; R &rarr; R is the Carath&eacute;odory function. Furthermore, M : R 0 + &rarr; R + is a Kirchhoff-type function. This study has two aims. One is to study the existence of infinitely many large energy solutions for the above problem via the variational methods. In addition, a major point is to obtain the multiplicity results of the weak solutions for our problem under various assumptions on the Kirchhoff function M and the nonlinear term f. The other is to prove the existence of small energy solutions for our problem, in that the sequence of solutions converges to 0 in the L &infin; -norm.

]]>Symmetry doi: 10.3390/sym10100435

Authors: Jianxing Zheng Deyu Li Sangaiah Arun Kumar

How to find a user&rsquo;s interest from similar users a fundamental research problems in socialized recommender systems. Despite significant advances, there exists diversity loss for the majority of recommender systems. With this paper, for expanding the user&rsquo;s interest, we overcome this challenge by using representative and diverse similar users from followees. First, we model a personal user profile vector via word2vec and term frequency mechanisms. According to user profiles and their follow relationships, we compute content interaction similarity and follow interaction similarity. Second, by combining two kinds of interaction similarity, we calculate the social similarity and discover a diverse group with coverage and dissimilarity. The users in a diverse group can distinguish each other and cover the whole followees, which can model a group user profile (GUP). Then, by tracking the changes of followee set, we heuristically adjust the number of diverse group users and construct an adaptive GUP. Finally, we conduct experiments on Sina Weibo datasets for recommendation, and the experimental results demonstrate that the proposed GUP outperforms conventional approaches for diverse recommendation.

]]>Symmetry doi: 10.3390/sym10100434

Authors: Dunja Radović Željko Stević Dragan Pamučar Edmundas Kazimieras Zavadskas Ibrahim Badi Jurgita Antuchevičiene Zenonas Turskis

The success of any business depends fundamentally on the possibility of balancing (symmetry) needs and their satisfaction, that is, the ability to properly define a set of success indicators. It is necessary to continuously monitor and measure the indicators that have the greatest impact on the achievement of previously set goals. Regarding transportation companies, the rationalization of transportation activities and processes plays an important role in ensuring business efficiency. Therefore, in this paper, a model for evaluating performance indicators has been developed and implemented in three different countries: Bosnia and Herzegovina, Libya and Serbia. The model consists of five phases, of which the greatest contribution is the development of a novel rough additive ratio assessment (ARAS) approach for evaluating measured performance indicators in transportation companies. The evaluation was carried out in the territories of the aforementioned countries in a total of nine companies that were evaluated on the basis of 20 performance indicators. The results obtained were verified throughout a three-phase procedure of a sensitivity analysis. The significance of the performance indicators was simulated throughout the formation of 10 scenarios in the sensitivity analysis. In addition, the following approaches were applied: rough WASPAS (weighted aggregated sum product assessment), rough SAW (simple additive weighting), rough MABAC (multi-attributive border approximation area comparison) and rough EDAS (evaluation based on distance from average solution), which showed high correlation of ranks by applying Spearman's correlation coefficient (SCC).

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