Previous Issue
Volume 11, September

Table of Contents

Symmetry, Volume 11, Issue 10 (October 2019)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Select all
Export citation of selected articles as:
Open AccessArticle
Lie Symmetries, Conservation Laws and Exact Solutions for Jaulent-Miodek Equations
Symmetry 2019, 11(10), 1319; https://doi.org/10.3390/sym11101319 (registering DOI) - 21 Oct 2019
Abstract
In this paper, the Lie symmetries of the Jaulent-Miodek (JM) equations are calculated and one dimensional optimal systems of Lie algebra are obtained. Furthermore, the conservation laws are constructed by using the adjoint equation method. Finally, the exact solutions of the equations are [...] Read more.
In this paper, the Lie symmetries of the Jaulent-Miodek (JM) equations are calculated and one dimensional optimal systems of Lie algebra are obtained. Furthermore, the conservation laws are constructed by using the adjoint equation method. Finally, the exact solutions of the equations are obtained by the conservation laws. Full article
Show Figures

Figure 1

Open AccessArticle
Modifications to Plane Gravitational Waves from Minimal Lorentz Violation
Symmetry 2019, 11(10), 1318; https://doi.org/10.3390/sym11101318 (registering DOI) - 21 Oct 2019
Abstract
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from [...] Read more.
General Relativity predicts two modes for plane gravitational waves. When a tiny violation of Lorentz invariance occurs, the two gravitational wave modes are modified. We use perturbation theory to study the detailed form of the modifications to the two gravitational wave modes from the minimal Lorentz-violation coupling. The perturbation solution for the metric fluctuation up to the first order in Lorentz violation is discussed. Then, we investigate the motions of test particles under the influence of the plane gravitational waves with Lorentz violation. First-order deviations from the usual motions are found. Full article
(This article belongs to the Special Issue Symmetry in Special and General Relativity)
Open AccessArticle
Paediatric Orthopaedic Surgery with 3D Printing: Improvements and Cost Reduction
Symmetry 2019, 11(10), 1317; https://doi.org/10.3390/sym11101317 - 20 Oct 2019
Viewed by 129
Abstract
This paper presents a a novel alghorithm of diagnosis and treatment of rigid flatfoot due to tarsal coalition. It introduces a workflow based on 3D printed models, that ensures more efficiency, not only by reducing costs and time, but also by improving procedures [...] Read more.
This paper presents a a novel alghorithm of diagnosis and treatment of rigid flatfoot due to tarsal coalition. It introduces a workflow based on 3D printed models, that ensures more efficiency, not only by reducing costs and time, but also by improving procedures in the preoperative clinical phase. Since this paper concerns the development of a new methodology that integrates both engineering and medical fields, it highlights symmetry. An economic comparison is made between the traditional method and the innovative one; the results demonstrate a reduction in costs with the latter. The current, traditional method faces critical issues in diagnosing the pathologies of a limb (such as the foot) and taking decisions for further treatment of the same limb. The proposed alternative methodology thus uses new technologies that are part of the traditional workflow, only replacing the most obsolete ones. In fact, it is increasingly becoming necessary to introduce new technologies in orthopedics, as in other areas of medicine, to offer improved healthcare services for patients. Similar clinical treatments can be performed using the aforementioned technologies, offering greater effectiveness, more simplicity of approach, shorter times, and lower costs. An important technology that fits into this proposed methodology is 3D printing. Full article
Open AccessArticle
Inaudibility of k-D’Atri Properties
Symmetry 2019, 11(10), 1316; https://doi.org/10.3390/sym11101316 - 20 Oct 2019
Viewed by 100
Abstract
Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that [...] Read more.
Working on closed Riemannian manifolds the first author and Schueth gave a list of curvature properties which cannot be determined by the eigenvalue spectrum of the Laplace–Beltrami operator. Following Kac, it is said that such properties are inaudible. Here, we add to that list the dimension of the manifold minus three new properties namely k-D’Atri for k = 3 , , dim M 1 . Full article
(This article belongs to the Special Issue Geometry of Submanifolds and Homogeneous Spaces)
Open AccessArticle
Security-Oriented Architecture for Managing IoT Deployments
Symmetry 2019, 11(10), 1315; https://doi.org/10.3390/sym11101315 - 19 Oct 2019
Viewed by 231
Abstract
Assuring security and privacy is one of the key issues affecting the Internet of Things (IoT), mostly due to its distributed nature. Therefore, for the IoT to thrive, this problem needs to be tackled and solved. This paper describes a security-oriented architecture for [...] Read more.
Assuring security and privacy is one of the key issues affecting the Internet of Things (IoT), mostly due to its distributed nature. Therefore, for the IoT to thrive, this problem needs to be tackled and solved. This paper describes a security-oriented architecture for managing IoT deployments. Our main goal was to deal with a fine-grained control in the access to IoT data and devices, to prevent devices from being manipulated by attackers and to avoid information leaking from IoT devices to unauthorized recipients. The access control is split: the management of authentication and access control policies is centered on special components (Authentication, Authorization, and Accounting Controllers), which can be distributed or centralized, and the actual enforcement of access control decisions happens on the entities that stay in the path to the IoT devices (Gateways and Device Drivers). The authentication in the entire system uses asymmetric cryptography and pre-distributed unique identifiers derived from public keys; no Public Key Infrastructure (PKI) is used. A Kerberos-like ticket-based approach is used to establish secure sessions. Full article
Open AccessFeature PaperArticle
A Hybrid Data Hiding Method for Strict AMBTC Format Images with High-Fidelity
Symmetry 2019, 11(10), 1314; https://doi.org/10.3390/sym11101314 - 19 Oct 2019
Viewed by 166
Abstract
With the rapid development of smartphones, cloud storage, and wireless communications, protecting the security of compressed images through data transmission on the Internet has become a critical contemporary issue. A series of data hiding methods for AMBTC compressed images has been proposed to [...] Read more.
With the rapid development of smartphones, cloud storage, and wireless communications, protecting the security of compressed images through data transmission on the Internet has become a critical contemporary issue. A series of data hiding methods for AMBTC compressed images has been proposed to solve this problem. However, most of these methods either change the file size of the final compressed code or exchange the order of two quantization values in some blocks. To reverse this situation, this paper proposes a data hiding method for strict AMBTC format images using a hybrid strategy: replacement, matrix encoding, and symmetric quantization value embedding for three block types i.e., smooth blocks, less complex blocks and highly complex blocks. According to the hybrid strategy, an efficient data hiding order is designed to achieve higher-fidelity. Experimental results show that our proposed method provides an excellent balance between image quality and hiding capacity and has no error blocks in the final stego-compressed code. Full article
Show Figures

Figure 1

Open AccessArticle
Group Decision-Making Based on the VIKOR Method with Trapezoidal Bipolar Fuzzy Information
Symmetry 2019, 11(10), 1313; https://doi.org/10.3390/sym11101313 - 19 Oct 2019
Viewed by 84
Abstract
The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on [...] Read more.
The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented. Full article
Show Figures

Figure 1

Open AccessArticle
Symmetry Breaking in Interacting Ring-Shaped Superflows of Bose–Einstein Condensates
Symmetry 2019, 11(10), 1312; https://doi.org/10.3390/sym11101312 - 19 Oct 2019
Viewed by 94
Abstract
We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction [...] Read more.
We demonstrate that the evolution of superflows in interacting persistent currents of ultracold gases is strongly affected by symmetry breaking of the quantum vortex dynamics. We study counter-propagating superflows in a system of two parallel rings in regimes of weak (a Josephson junction with tunneling through the barrier) and strong (rings merging across a reduced barrier) interactions. For the weakly interacting toroidal Bose–Einstein condensates, formation of rotational fluxons (Josephson vortices) is associated with spontaneous breaking of the rotational symmetry of the tunneling superflows. The influence of a controllable symmetry breaking on the final state of the merging counter-propagating superflows is investigated in the framework of a weakly dissipative mean-field model. It is demonstrated that the population imbalance between the merging flows and the breaking of the underlying rotational symmetry can drive the double-ring system to final states with different angular momenta. Full article
(This article belongs to the Special Issue Symmetry Breaking in Bose-Einstein Condensates)
Show Figures

Figure 1

Open AccessArticle
Structure Learning of Gaussian Markov Random Fields with False Discovery Rate Control
Symmetry 2019, 11(10), 1311; https://doi.org/10.3390/sym11101311 - 18 Oct 2019
Viewed by 111
Abstract
In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted 1 -norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing [...] Read more.
In this paper, we propose a new estimation procedure for discovering the structure of Gaussian Markov random fields (MRFs) with false discovery rate (FDR) control, making use of the sorted 1 -norm (SL1) regularization. A Gaussian MRF is an acyclic graph representing a multivariate Gaussian distribution, where nodes are random variables and edges represent the conditional dependence between the connected nodes. Since it is possible to learn the edge structure of Gaussian MRFs directly from data, Gaussian MRFs provide an excellent way to understand complex data by revealing the dependence structure among many inputs features, such as genes, sensors, users, documents, etc. In learning the graphical structure of Gaussian MRFs, it is desired to discover the actual edges of the underlying but unknown probabilistic graphical model—it becomes more complicated when the number of random variables (features) p increases, compared to the number of data points n. In particular, when p n , it is statistically unavoidable for any estimation procedure to include false edges. Therefore, there have been many trials to reduce the false detection of edges, in particular, using different types of regularization on the learning parameters. Our method makes use of the SL1 regularization, introduced recently for model selection in linear regression. We focus on the benefit of SL1 regularization that it can be used to control the FDR of detecting important random variables. Adapting SL1 for probabilistic graphical models, we show that SL1 can be used for the structure learning of Gaussian MRFs using our suggested procedure nsSLOPE (neighborhood selection Sorted L-One Penalized Estimation), controlling the FDR of detecting edges. Full article
Show Figures

Figure 1

Open AccessEditorial
Symmetry in Quantum Optics Models
Symmetry 2019, 11(10), 1310; https://doi.org/10.3390/sym11101310 - 18 Oct 2019
Viewed by 126
Abstract
This editorial introduces the successful invited submissions [...] Full article
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
Open AccessArticle
Some Chaos Notions on Dendrites
Symmetry 2019, 11(10), 1309; https://doi.org/10.3390/sym11101309 - 17 Oct 2019
Viewed by 143
Abstract
Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is [...] Read more.
Transitivity is a key element in a chaotic dynamical system. In this paper, we present some relations between transitivity, stronger and alternative notions of it on compact and dendrite spaces. The relation between Auslander and Yorke chaos and Devaney chaos on dendrites is also discussed. Moreover, we prove that Devaney chaos implies strong dense periodicity on dendrites while the converse is not true. Full article
(This article belongs to the Special Issue Symmetry and Dynamical Systems)
Show Figures

Graphical abstract

Open AccessArticle
Neural Networks Application for Processing of the Data from the FMICW Radars
Symmetry 2019, 11(10), 1308; https://doi.org/10.3390/sym11101308 - 17 Oct 2019
Viewed by 95
Abstract
In this paper the results of the Neural Networks and machine learning applications for radar signal processing are presented. The radar output from the primary radar signal processing is represented as a 2D image composed from echoes of the targets and noise background. [...] Read more.
In this paper the results of the Neural Networks and machine learning applications for radar signal processing are presented. The radar output from the primary radar signal processing is represented as a 2D image composed from echoes of the targets and noise background. The Frequency Modulated Interrupted Continuous Wave (FMICW) radar PCDR35 (Portable Cloud Doppler Radar at the frequency 35.4 GHz) was used. Presently, the processing is realized via a National Instruments industrial computer. The neural network of the proposed system is using four or five (optional for the user) signal processing steps. These steps are 2D spectrum filtration, thresholding, unification of the target, target area transforming to the rectangular shape (optional step), and target board line detection. The proposed neural network was tested with sets of four cases (100 tests for every case). This neural network provides image processing of the 2D spectrum. The results obtained from this new system are much better than the results of our previous algorithm. Full article
Show Figures

Figure 1

Open AccessArticle
Certain Results for the Twice-Iterated 2D q-Appell Polynomials
Symmetry 2019, 11(10), 1307; https://doi.org/10.3390/sym11101307 - 16 Oct 2019
Viewed by 202
Abstract
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated [...] Read more.
In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of this polynomial class are established. The determinant expression for the twice-iterated 2D q-Appell polynomials is also derived. Further, certain twice-iterated 2D q-Appell and mixed type special q-polynomials are considered as members of this polynomial class. The determinant expressions and some other properties of these associated members are also obtained. The graphs and surface plots of some twice-iterated 2D q-Appell and mixed type 2D q-Appell polynomials are presented for different values of indices by using Matlab. Moreover, some areas of potential applications of the subject matter of, and the results derived in, this paper are indicated. Full article
(This article belongs to the Special Issue Polynomials: Special Polynomials and Number-Theoretical Applications)
Show Figures

Figure 1

Open AccessArticle
A Prediction Model for the Potential Plastic Zone Induced by Tunnel Excavation Adjacent to a Pile Foundation in a Gravity Field
Symmetry 2019, 11(10), 1306; https://doi.org/10.3390/sym11101306 - 16 Oct 2019
Viewed by 126
Abstract
The construction of metro tunnels in urban areas often encounters existing underground structures, such as the pile foundations of adjacent existing buildings. Under the mutual effects and impacts of pile foundation load and tunnel excavation, the soil around tunnel and pile foundations can [...] Read more.
The construction of metro tunnels in urban areas often encounters existing underground structures, such as the pile foundations of adjacent existing buildings. Under the mutual effects and impacts of pile foundation load and tunnel excavation, the soil around tunnel and pile foundations can experience stress redistribution or even yield prior to support installation, which could adversely affect and even damage the adjacent pile foundations. This paper proposes an effective prediction model consisted of axisymmetric tunnel and pile foundation to investigate the shape and range of potential plastic zones induced by tunnel excavation adjacent to pile foundations. Then the results obtained from the proposed method are compared with the existing approaches and numerical simulations, which shows that the shape of the potential plastic zone develops towards a butterfly shape in a gravity field, similar to those from numerical simulations. Finally, a parametric analysis is performed to investigate the influences of different parameters, such as soil parameters, axisymmetric boundary conditions, and pile parameters on the boundaries of the potential plastic zone. This proposed prediction model might provide a certain basis for making protective measures for existing pile foundations influenced by tunnel excavation, and provide a quick estimate of the boundaries of the potential plastic zone induced by tunnel excavation adjacent to pile foundations in a gravity field, thus resulting in time and cost savings. Full article
Show Figures

Figure 1

Open AccessArticle
Flexible Birnbaum–Saunders Distribution
Symmetry 2019, 11(10), 1305; https://doi.org/10.3390/sym11101305 - 16 Oct 2019
Viewed by 99
Abstract
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are [...] Read more.
In this paper, we propose a bimodal extension of the Birnbaum–Saunders model by including an extra parameter. This new model is termed flexible Birnbaum–Saunders (FBS) and includes the ordinary Birnbaum–Saunders (BS) and the skew Birnbaum–Saunders (SBS) model as special cases. Its properties are studied. Parameter estimation is considered via an iterative maximum likelihood approach. Two real applications, of interest in environmental sciences, are included, which reveal that our proposal can perform better than other competing models. Full article
Show Figures

Figure 1

Open AccessArticle
Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables
Symmetry 2019, 11(10), 1304; https://doi.org/10.3390/sym11101304 - 16 Oct 2019
Viewed by 97
Abstract
Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular [...] Read more.
Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular domain of the space C n . We investigate relations between this family and some of type of Bavrin’s families. We give estimates of G-balance of k-homogeneous polynomial, a distortion type theorem and a sufficient condition for functions belonging to this family. Furthermore, we present some examples of functions from the considered class. Full article
Open AccessArticle
Quantum-Gravitational Trans-Planckian Energy of a Time-Dependent Black Hole
Symmetry 2019, 11(10), 1303; https://doi.org/10.3390/sym11101303 - 16 Oct 2019
Viewed by 94
Abstract
We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, [...] Read more.
We continue our recent endeavor in which a time-dependent black hole solution of a one-loop quantum-corrected Einstein-scalar system was obtained and its near-horizon behavior was analyzed. The energy analysis led to a trans-Planckian scaling behavior near the event horizon. In the present work, the analysis is extended to a rotating black hole solution of an Einstein–Maxwell-scalar system with a Higgs potential. Although the analysis becomes much more complex compared to that of the previous, we observe the same basic features, including the quantum-gravitational trans-Planckian energy near the horizon. Full article
(This article belongs to the Special Issue Modified Theories of Gravity)
Open AccessArticle
A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides
Symmetry 2019, 11(10), 1302; https://doi.org/10.3390/sym11101302 - 16 Oct 2019
Viewed by 114
Abstract
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, [...] Read more.
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms. Full article
Show Figures

Figure 1

Open AccessArticle
A General Principle of Isomorphism: Determining Inverses
Symmetry 2019, 11(10), 1301; https://doi.org/10.3390/sym11101301 - 15 Oct 2019
Viewed by 121
Abstract
The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, [...] Read more.
The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems. Full article
(This article belongs to the Special Issue Recent Advances in the Application of Symmetry Group)
Show Figures

Figure 1

Open AccessArticle
A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms
Symmetry 2019, 11(10), 1300; https://doi.org/10.3390/sym11101300 - 15 Oct 2019
Viewed by 118
Abstract
We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with [...] Read more.
We introduce a new equivalence on graphs, defined by its symmetry-breaking capability. We first present a framework for various backtracking search algorithms, in which the equivalence is used to prune the search tree. Subsequently, we define the equivalence and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential. We also position the optimization problem into the computational-complexity hierarchy. In particular, we show that the verifier lies between P and NP -complete problems. Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles. Full article
Open AccessArticle
Approximation of a Linear Autonomous Differential Equation with Small Delay
Symmetry 2019, 11(10), 1299; https://doi.org/10.3390/sym11101299 - 15 Oct 2019
Viewed by 115
Abstract
A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary [...] Read more.
A linear autonomous differential equation with small delay is considered in this paper. It is shown that under a smallness condition the delay differential equation is asymptotically equivalent to a linear ordinary differential equation with constant coefficients. The coefficient matrix of the ordinary differential equation is a solution of an associated matrix equation and it can be written as a limit of a sequence of matrices obtained by successive approximations. The eigenvalues of the approximating matrices converge exponentially to the dominant characteristic roots of the delay differential equation and an explicit estimate for the approximation error is given. Full article
Open AccessArticle
Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics
Symmetry 2019, 11(10), 1298; https://doi.org/10.3390/sym11101298 - 15 Oct 2019
Viewed by 120
Abstract
In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( [...] Read more.
In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the description of fermions. Here, we choose the description of 3-manifolds by branched covers. Every 3-manifold can be described by a 3-fold branched cover of S 3 branched along a knot. In case of knot complements, one will obtain a 3-fold branched cover of the 3-disk D 3 branched along a 3-braid or 3-braids describing fermions. The whole approach will uncover new symmetries as induced by quantum and discrete groups. Using the Drinfeld–Turaev quantization, we will also construct a quantization so that quantum states correspond to knots. Particle properties like the electric charge must be expressed by topology, and we will obtain the right spectrum of possible values. Finally, we will get a connection to recent models of Furey, Stoica and Gresnigt using octonionic and quaternionic algebras with relations to 3-braids (Bilson–Thompson model). Full article
(This article belongs to the Special Issue Number Theory and Symmetry)
Show Figures

Figure 1

Open AccessArticle
DA-OCBA: Distributed Asynchronous Optimal Computing Budget Allocation Algorithm of Simulation Optimization Using Cloud Computing
Symmetry 2019, 11(10), 1297; https://doi.org/10.3390/sym11101297 - 15 Oct 2019
Viewed by 128
Abstract
The ranking and selection of simulation optimization is a very powerful tool in systems engineering and operations research. Due to the influence of randomness, the algorithms for ranking and selection need high and uncertain amounts of computing power. Recent advances in cloud computing [...] Read more.
The ranking and selection of simulation optimization is a very powerful tool in systems engineering and operations research. Due to the influence of randomness, the algorithms for ranking and selection need high and uncertain amounts of computing power. Recent advances in cloud computing provide an economical and flexible platform to execute these algorithms. Among all ranking and selection algorithms, the optimal computing budget allocation (OCBA) algorithm is one of the most efficient. However, because of the lack of sufficient samples that can be executed in parallel at each stage, some features of the cloud-computing platform, such as parallelism, scalability, flexibility, and symmetry, cannot be fully utilized. To solve these problems, this paper proposes a distributed asynchronous OCBA (DA-OCBA) algorithm. Under the framework of parallel asynchronous simulation, this algorithm takes advantage of every idle docker container to run better designs in advance that are selected by an asymptotic allocation rule. The experiment demonstrated that the efficiency of simulation optimization for DA-OCBA was clearly higher than that for the traditional OCBA on the cloud platform with symmetric architecture. As the number of containers grew, the speedup of DA-OCBA was linearly increasing for simulation optimization. Full article
Show Figures

Figure 1

Open AccessArticle
The Use of Structural Symmetries of a U12 Engine in the Vibration Analysis of a Transmission
Symmetry 2019, 11(10), 1296; https://doi.org/10.3390/sym11101296 - 15 Oct 2019
Viewed by 69
Abstract
The paper focuses on the vibration analysis of a vehicle equipped with two identical engines. Such solutions are encountered in practice when less power is needed for a vehicle for a certain period of time and then greater power the rest of the [...] Read more.
The paper focuses on the vibration analysis of a vehicle equipped with two identical engines. Such solutions are encountered in practice when less power is needed for a vehicle for a certain period of time and then greater power the rest of the time. An example of this would be a mobile drilling rig. During transport (a relatively short period of time) only one engine operates and then, in service (most of the operating time), both engines operate. A characteristic of such an aggregate is the existence, within the transmission, of two identical engines. The existence of identical parts in mechanical systems leads to properties that allow the computations to be simplified in order to obtain suggestive and rapid results, with reduced computation effort. These properties refer to the eigenvalues and eigenmodes of vibration for these types of systems and have been stated and demonstrated in the paper. It also allows for a qualitative analysis of the behavior of the system in case of vibrations. The existence of these properties allows for easier calculation and shortening of the design time. The mechanical consequences of the existence of symmetries or identical parts have begun to be studied in more detail in the last decade (see references), and the work is part of these trends. The vibration properties of a transmission of a truck with two identical engines have been stated and proven and a real example is analyzed. Two 215 hp engines were used in the application. In order to establish a useful solution in practice, two constructive variants with a different clutch position in the transmission are analyzed in parallel. Full article
(This article belongs to the Special Issue Symmetry in Mechanical Engineering)
Show Figures

Figure 1

Open AccessArticle
MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel
Symmetry 2019, 11(10), 1295; https://doi.org/10.3390/sym11101295 - 15 Oct 2019
Viewed by 102
Abstract
Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is [...] Read more.
Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model. Full article
(This article belongs to the Special Issue Aero/Hydrodynamics and Symmetry)
Show Figures

Figure 1

Open AccessArticle
Classical Limit for Dirac Fermions with Modified Action in the Presence of a Black Hole
Symmetry 2019, 11(10), 1294; https://doi.org/10.3390/sym11101294 - 15 Oct 2019
Viewed by 86
Abstract
We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed [...] Read more.
We consider the model of Dirac fermions coupled to gravity as proposed, in which superluminal velocities of particles are admitted. In this model an extra term is added to the conventional Hamiltonian that originates from Planck physics. Due to this term, a closed Fermi surface is formed in equilibrium inside the black hole. In this paper we propose the covariant formulation of this model and analyse its classical limit. We consider the dynamics of gravitational collapse. It appears that the Einstein equations admit a solution identical to that of ordinary general relativity. Next, we consider the motion of particles in the presence of a black hole. Numerical solutions of the equations of motion are found which demonstrate that the particles are able to escape from the black hole. Full article
(This article belongs to the Special Issue Modified Theories of Gravity)
Show Figures

Figure 1

Open AccessArticle
Use of Platelet-Rich Fibrin Associated with Xenograft in Critical Bone Defects: Histomorphometric Study in Rabbits
Symmetry 2019, 11(10), 1293; https://doi.org/10.3390/sym11101293 - 15 Oct 2019
Viewed by 80
Abstract
Platelet-rich fibrin (PRF) is an autologous material used to improve bone regeneration when associated with bone grafts. It affects tissue angiogenesis, increasing the healing process and, theoretically, presenting potential to increase bone neoformation. The aim of this study was to verify, histomorphometrically, the [...] Read more.
Platelet-rich fibrin (PRF) is an autologous material used to improve bone regeneration when associated with bone grafts. It affects tissue angiogenesis, increasing the healing process and, theoretically, presenting potential to increase bone neoformation. The aim of this study was to verify, histomorphometrically, the effects of the association of PRF to a xenograft. Twelve adult white New Zealand rabbits were randomly assigned into two groups containing six animals each. After general anesthesia of the animals, two critical defects of 12 mm were created in the rabbit calvaria, one on each side of the sagittal line. Each defect was filled with the following biomaterials: in the control group (CG), xenograft hydrated with saline solution filling one defect and xenograft hydrated with saline solution covered with collagen membrane on the other side; in the test group (TG), xenograft associated with PRF filling the defect of one side and xenograft associated with PRF covered with collagen membrane on the other side. After eight weeks the animals were euthanized and a histomorphometric analysis was performed. The results showed that in the sites that were covered with collagen membrane, there was no statistically significant difference for all the analyzed parameters. However, when comparing the groups without membrane coverage, a statistically significant difference could be observed for the vital mineralized tissue (VMT) and nonmineralized tissue (NMT) parameters, with more VMT in the test group and more NMT in the control group. Regarding the intragroup comparison, the use of the membrane coverage presented significant outcomes in both groups. Therefore, in this experimental model, PRF did not affect the levels of bone formation when a membrane coverage technique was used. However, higher levels of bone formation were observed in the test group when membrane coverage was not used. Full article
Show Figures

Figure 1

Open AccessArticle
Impact-Damage Equivalency for Twisted Composite Blades with Symmetrical Configurations
Symmetry 2019, 11(10), 1292; https://doi.org/10.3390/sym11101292 - 15 Oct 2019
Viewed by 97
Abstract
In spite of potential advantages for aircraft structures, composite laminates can be subjected to bird-strike hazard in civil aviation. For purpose of future surrogate experiments, in this study, impact-damage equivalency for twisted composite blades is numerically investigated by Smoothed Particle Hydrodynamics (SPH) and [...] Read more.
In spite of potential advantages for aircraft structures, composite laminates can be subjected to bird-strike hazard in civil aviation. For purpose of future surrogate experiments, in this study, impact-damage equivalency for twisted composite blades is numerically investigated by Smoothed Particle Hydrodynamics (SPH) and finite element method (FEM). Cantilever slender flat plates are usually used for basic impact tests, the impact-damage equivalency is being considered by comparing damage modes and energies of three impact configurations: (1) twisted blade; (2) flat blade (axisymmetric); and (3) inclined flat blade (centrosymmetric). The damage maps and energy variations were comparatively investigated. Results indicate that both symmetrical flat and inclined flat blades can be, to a certain extent, regarded as alternatives for real twisted blades under bird impact; however, both types of blade have their own merits and drawbacks, and hence should be used carefully. These results aim to serve as tentative design guideline for future prototype or model experimental study of laminated blades in real aeronautical structures. Full article
(This article belongs to the Special Issue Symmetry in Applied Continuous Mechanics)
Show Figures

Figure 1

Open AccessArticle
An Improved Pigeon-Inspired Optimisation Algorithm and Its Application in Parameter Inversion
Symmetry 2019, 11(10), 1291; https://doi.org/10.3390/sym11101291 - 15 Oct 2019
Viewed by 103
Abstract
Pre-stack amplitude variation with offset (AVO) elastic parameter inversion is a nonlinear, multi-solution optimisation problem. The techniques that combine intelligent optimisation algorithms and AVO inversion provide an effective identification method for oil and gas exploration. However, these techniques also have shortcomings in solving [...] Read more.
Pre-stack amplitude variation with offset (AVO) elastic parameter inversion is a nonlinear, multi-solution optimisation problem. The techniques that combine intelligent optimisation algorithms and AVO inversion provide an effective identification method for oil and gas exploration. However, these techniques also have shortcomings in solving nonlinear geophysical inversion problems. The evolutionary optimisation algorithms have recognised disadvantages, such as the tendency of convergence to a local optimum resulting in poor local optimisation performance when dealing with multimodal search problems, decreasing diversity and leading to the prematurity of the population as the number of evolutionary iterations increases. The pre-stack AVO elastic parameter inversion is nonlinear with slow convergence, while the pigeon-inspired optimisation (PIO) algorithm has the advantage of fast convergence and better optimisation characteristics. In this study, based on the characteristics of the pre-stack AVO elastic parameter inversion problem, an improved PIO algorithm (IPIO) is proposed by introducing the particle swarm optimisation (PSO) algorithm, an inverse factor, and a Gaussian factor into the PIO algorithm. The experimental comparisons indicate that the proposed IPIO algorithm can achieve better inversion results. Full article
Show Figures

Figure 1

Open AccessArticle
An Optimized Abstractive Text Summarization Model Using Peephole Convolutional LSTM
Symmetry 2019, 11(10), 1290; https://doi.org/10.3390/sym11101290 - 14 Oct 2019
Viewed by 266
Abstract
Abstractive text summarization that generates a summary by paraphrasing a long text remains an open significant problem for natural language processing. In this paper, we present an abstractive text summarization model, multi-layered attentional peephole convolutional LSTM (long short-term memory) (MAPCoL) that automatically generates [...] Read more.
Abstractive text summarization that generates a summary by paraphrasing a long text remains an open significant problem for natural language processing. In this paper, we present an abstractive text summarization model, multi-layered attentional peephole convolutional LSTM (long short-term memory) (MAPCoL) that automatically generates a summary from a long text. We optimize parameters of MAPCoL using central composite design (CCD) in combination with the response surface methodology (RSM), which gives the highest accuracy in terms of summary generation. We record the accuracy of our model (MAPCoL) on a CNN/DailyMail dataset. We perform a comparative analysis of the accuracy of MAPCoL with that of the state-of-the-art models in different experimental settings. The MAPCoL also outperforms the traditional LSTM-based models in respect of semantic coherence in the output summary. Full article
Show Figures

Figure 1

Previous Issue
Back to TopTop