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Volume 13, November

Symmetry, Volume 13, Issue 12 (December 2021) – 221 articles

Cover Story (view full-size image): Laws of large numbers (LLNs) are theorems of great importance for probability and chance theory. Within chance theory the notion of an uncertain random variable was defined to model phenomena where both uncertainty and randomness are present. This work considers uncertain random variables as functions of random variables and uncertain variables, introduced within uncertainty theory. Sequences of uncertain random variables are defined for a fixed continuous function, strictly monotone with respect to its second argument, as are sequences of pairwise independent or independent, identically distributed random variables and regular, independent, and identically distributed uncertain variables. Some LLNs for such defined sequences of uncertain random variables are formulated and proven. Two of their counterparts for uncertain variables are also discussed. View this paper
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Article
Modelling Artificial Immunization Processes to Counter Cyberthreats
Symmetry 2021, 13(12), 2453; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122453 - 20 Dec 2021
Viewed by 302
Abstract
This paper looks at the problem of cybersecurity in modern cyber-physical and information systems and proposes an immune-like approach to the information security of modern complex systems. This approach is based on the mathematical modeling in information security—in particular, the use of immune [...] Read more.
This paper looks at the problem of cybersecurity in modern cyber-physical and information systems and proposes an immune-like approach to the information security of modern complex systems. This approach is based on the mathematical modeling in information security—in particular, the use of immune methods to protect several critical system nodes from a predetermined range of attacks, and to minimize the success of an attack on the system. The methodological approach is to systematize the tasks, means and modes of immunization to describe how modern systems can counter the spread of computer attacks. The main conclusions and recommendations are that using an immunization approach will not only improve the security of systems, but also define principles for building systems that are resistant to cyber attacks. The immunization approach enables a symmetrical response to an intruder in a protected system to be produced rapidly. This symmetry provides a step-by-step neutralization of all stages of a cyber attack, which, combined with the accumulation of knowledge of the attacker’s actions, allows a base of defensive responses to be generated for various cyber attack scenarios. The theoretical conclusions are supported by practical experiments describing real-world scenarios for the use of immunization tools to protect against cyber threats. Full article
(This article belongs to the Section Computer and Engineering Science and Symmetry/Asymmetry)
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Article
Information Reliability Assessment and Filtering for Decision Making. Case Study of Lithuanian and China Students’ Life Goals Survey Data
Symmetry 2021, 13(12), 2452; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122452 - 20 Dec 2021
Viewed by 230
Abstract
This article presents the methodology and tools to evaluate the reliability of quantitative sociological research data. The problem of filtering unreliable data is usually solved by statistical methods. This article proposes an improved method for filtering unreliable data. In this case, the statistical [...] Read more.
This article presents the methodology and tools to evaluate the reliability of quantitative sociological research data. The problem of filtering unreliable data is usually solved by statistical methods. This article proposes an improved method for filtering unreliable data. In this case, the statistical methods are not applied to the initial data but the value of the distance function between the two preferences. This allows for the disclosure of conflicting or erroneous data. Calculation of the distance between two preferences and prioritisation of life goals are based on binary relation theory, where the properties of symmetry (antisymmetry) are very important. The article presents a case study on 11 life goals evaluation and ranking by Lithuanian and China students. The study revealed that the China student data filtered at least twice as much as the Lithuanian student data, i.e., they are less reliable. The filtered data show that students of both countries ranked the most and the least important life goals in a very similar way with minimum deviations detected in the ranking results. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models, Part II)
Article
Stability Characteristics and Mechanism of U-Shaped Metal Bellows under Symmetrical Cyclic Tension and Compression Process
Symmetry 2021, 13(12), 2451; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122451 - 20 Dec 2021
Viewed by 257
Abstract
The U-shaped metal bellows expansion joint compensates for the pipeline displacement by its own deformation. The compensation performance of the metal bellows in the initial stage of tension and compression deformation is unstable. In this paper, the symmetrical cyclic tension and compression (SCTC) [...] Read more.
The U-shaped metal bellows expansion joint compensates for the pipeline displacement by its own deformation. The compensation performance of the metal bellows in the initial stage of tension and compression deformation is unstable. In this paper, the symmetrical cyclic tension and compression (SCTC) process of metal bellows was simulated by ABAQUS software. Then, the SCTC process experiment of metal bellows was completed on the universal material testing machine. The distribution law of axial load with displacement and that of axial stiffness and yield load with cycles of metal bellows were obtained. Finally, the X-ray diffraction peak confirmed the deformation-induced martensite in the wave trough and proved that the plastic strain and hardness values of metal bellows increased with the displacement amplitude. The microstructure in the wave trough area was observed by a Zeiss microscope, and the stability characteristics mechanism of the metal bellows was revealed. The martensite in the wave trough increases the grain boundary area under SCTC loading. The forward movement of the slip band in the grain caused by large deformation reached an equilibrium state with the resistance at the grain boundary, which promotes the macroscopic mechanical properties of the metal bellows to be stable characteristics under SCTC loading. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Metal Forming)
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Article
A Dynamically Adjusted Subspace Gradient Method and Its Application in Image Restoration
Symmetry 2021, 13(12), 2450; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122450 - 20 Dec 2021
Viewed by 369
Abstract
In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm [...] Read more.
In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace. The obtained algorithm has the ability to automatically adjust the search direction according to the feedback from experiments. Under some mild assumptions, we use the generalized line search with non-monotonicity to obtain remarkable results, which not only establishes the global convergence of the algorithm for general functions, but also R-linear convergence for uniformly convex functions is further proved. The numerical performance for both the traditional test functions and image restoration problems show that the proposed algorithm is efficient. Full article
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Article
On Baryogenesis from a Complex Inflaton
Symmetry 2021, 13(12), 2449; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122449 - 20 Dec 2021
Viewed by 336
Abstract
We derive the particle asymmetry due to inflationary baryogenesis involving a complex inflaton, obtaining a different result to that in the literature. While asymmetries were found to be significantly smaller than previously calculated, in certain parameter regions, baryogenesis can still be achieved. Full article
(This article belongs to the Special Issue Current Issues in Particle Physics)
Article
Radius of Star-Likeness for Certain Subclasses of Analytic Functions
Symmetry 2021, 13(12), 2448; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122448 - 19 Dec 2021
Viewed by 427
Abstract
In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition fzgz>0, for some analytic function, g, with [...] Read more.
In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition fzgz>0, for some analytic function, g, with z+12nzgz>0,nN. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp. Full article
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis II)
Article
Stabilization of Periodical Discrete Feedback Control for Markov Jumping Stochastic Systems
Symmetry 2021, 13(12), 2447; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122447 - 19 Dec 2021
Viewed by 306
Abstract
Motivated by the two strategies of intermittent control and discrete feedback control, this paper aims to introduce a periodically intermittent discrete feedback control in the drift part to stabilize an unstable Markov jumping stochastic differential system. It is illustrated that, by the approach [...] Read more.
Motivated by the two strategies of intermittent control and discrete feedback control, this paper aims to introduce a periodically intermittent discrete feedback control in the drift part to stabilize an unstable Markov jumping stochastic differential system. It is illustrated that, by the approach of comparison principle, this can be achieved in the sense of almost sure exponential stability. Further, the stabilization theory is applied to Markov jumping stochastic recurrent neural networks. Full article
Article
A Design of Multi-Purpose Image-Based QR Code
Symmetry 2021, 13(12), 2446; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122446 - 18 Dec 2021
Viewed by 325
Abstract
A multi-purpose image-based QR code is designed in this paper. There are four purposes for the generated image-based QR code. In the first purpose, the basic image-based QR code with the look of a host image is with an ingenious layout to be [...] Read more.
A multi-purpose image-based QR code is designed in this paper. There are four purposes for the generated image-based QR code. In the first purpose, the basic image-based QR code with the look of a host image is with an ingenious layout to be identified easier. In the second one, a saliency region detection method is adopted for enhancing the quality of the image-based QR code. In the third one, the host image is embedded into the image-based QR code for further access to the host image; Finally, the visual cryptography-based watermarking method is applied to the host image embedded image-based QR code. In the case that the specific users need verification from the image-based QR code, the binary verified image can be retrieved when the public share is available. The experimental results demonstrate that the generated image-based QR code not only looked better than some previous works but also had high quality host image embedded and identification ability. Full article
(This article belongs to the Special Issue Symmetry in Image Processing and Visualization)
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Article
Coherence Trapping in Open Two-Qubit Dynamics
Symmetry 2021, 13(12), 2445; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122445 - 17 Dec 2021
Viewed by 315
Abstract
In this manuscript, we examine the dynamical behavior of the coherence in open quantum systems using the l1 norm. We consider a two-qubit system that evolves in the framework of Kossakowski-type quantum dynamical semigroups (KTQDSs) of completely positive maps (CPMs). We find [...] Read more.
In this manuscript, we examine the dynamical behavior of the coherence in open quantum systems using the l1 norm. We consider a two-qubit system that evolves in the framework of Kossakowski-type quantum dynamical semigroups (KTQDSs) of completely positive maps (CPMs). We find that the quantum coherence can be asymptotically maintained with respect to the values of the system parameters. Moreover, we show that the quantum coherence can resist the effect of the environment and preserve even in the regime of long times. The obtained results also show that the initially separable states can provide a finite value of the coherence during the time evolution. Because of such properties, several states in this type of environments are good candidates for incorporating quantum information and optics (QIO) schemes. Finally, we compare the dynamical behavior of the coherence with the entire quantum correlation. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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Article
A New Generalization of the Student’s t Distribution with an Application in Quantile Regression
Symmetry 2021, 13(12), 2444; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122444 - 17 Dec 2021
Viewed by 412
Abstract
In this work, we present a new generalization of the student’s t distribution. The new distribution is obtained by the quotient of two independent random variables. This quotient consists of a standard Normal distribution divided by the power of a chi square distribution [...] Read more.
In this work, we present a new generalization of the student’s t distribution. The new distribution is obtained by the quotient of two independent random variables. This quotient consists of a standard Normal distribution divided by the power of a chi square distribution divided by its degrees of freedom. Thus, the new symmetric distribution has heavier tails than the student’s t distribution and extensions of the slash distribution. We develop a procedure to use quantile regression where the response variable or the residuals have high kurtosis. We give the density function expressed by an integral, we obtain some important properties and some useful procedures for making inference, such as moment and maximum likelihood estimators. By way of illustration, we carry out two applications using real data, in the first we provide maximum likelihood estimates for the parameters of the generalized student’s t distribution, student’s t, the extended slash distribution, the modified slash distribution, the slash distribution generalized student’s t test, and the double slash distribution, in the second we perform quantile regression to fit a model where the response variable presents a high kurtosis. Full article
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Article
A Novel Model for Distributed Denial of Service Attack Analysis and Interactivity
Symmetry 2021, 13(12), 2443; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122443 - 17 Dec 2021
Viewed by 352
Abstract
A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots [...] Read more.
A Distributed Denial of Service (DDoS) attack is a type of cybercrime that renders a target service unavailable by overwhelming it with traffic from several sources (attack nodes). In this paper, we focus on DDoS attacks on a computer network by spreading bots throughout the network. A mathematical differential equation model is proposed to represent the dynamism of nodes at different compartments of the model. The model considers two levels of security, with the assumption that the recovered nodes do not return to the same security level. In previous models, the recovered nodes are returned to be suspect on the same security level, which is an unrealistic assumption. Moreover, it is assumed that the attacker can use the infected target nodes to attack again. With such epidemic-like assumptions of infection, different cases are presented and discussed, and the stability of the model is analyzed as well; reversing the symmetry transformation of attacking nodes population is also proven. The proposed model has many parameters in order to precisely describe the infection movement and propagation. Numerical simulation methods are used to solve the developed system of equations using MATLAB, with the intention of finding the best counteraction to control DDoS spread throughout a network. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Hybrid Sliding Mode Control of Full-Car Semi-Active Suspension Systems
Symmetry 2021, 13(12), 2442; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122442 - 17 Dec 2021
Viewed by 453
Abstract
With the advance in technology in driving vehicles, there is currently more emphasis on developing advanced control systems for better road handling stability and ride comfort. However, one of the challenging problems in the design and implementation of intelligent suspension systems is that [...] Read more.
With the advance in technology in driving vehicles, there is currently more emphasis on developing advanced control systems for better road handling stability and ride comfort. However, one of the challenging problems in the design and implementation of intelligent suspension systems is that there is currently no solution supporting the export of generic suspension models and control components for integration into embedded Electronic Control Units (ECUs). This significantly limits the usage of embedded suspension components in automotive production code software as it requires very high efforts in implementation, manual testing, and fulfilling coding requirements. This paper introduces a new dynamic model of full-car suspension system with semi-active suspension behavior and provides a hybrid sliding mode approach for control of full-car suspension dynamics such that the road handling stability and ride comfort characteristics are ensured. The semi-active suspension model and the hybrid sliding mode controller are implemented as Functional Mock-Up Units (FMUs) conforming to the Functional Mock-Up Interface for embedded systems (eFMI) and are calibrated with a set experimental tests using a 1/5 Soben-car test bench. The methods and prototype implementation proposed in this paper allow both model and controller re-usability and provide a generic way of integrating models and control software into embedded ECUs. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
On the Crossing Numbers of the Join Products of Six Graphs of Order Six with Paths and Cycles
Symmetry 2021, 13(12), 2441; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122441 - 17 Dec 2021
Viewed by 291
Abstract
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on [...] Read more.
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on six vertices with paths and cycles on n vertices. The idea of configurations is generalized for the first time onto the family of subgraphs whose edges cross the edges of the considered graph at most once, and their lower bounds of necessary numbers of crossings are presented in the common symmetric table. Some proofs of the join products with cycles are done with the help of several well-known auxiliary statements, the idea of which is extended by a suitable classification of subgraphs that do not cross the edges of the examined graphs. Full article
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Article
Numerical Study on Effects of Geometric Parameters on the Release Characteristics of Straight Sudden Expansion Gas Extinguishing Nozzles
Symmetry 2021, 13(12), 2440; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122440 - 17 Dec 2021
Viewed by 323
Abstract
In order to guide the optimization design of the nozzle of the aircraft-fixed gas fire extinguishing system, we studied the influence of nozzle geometric parameters including outlet–inlet area ratio, length–diameter aspect ratio, and wall roughness on the distribution of pressure and velocity in [...] Read more.
In order to guide the optimization design of the nozzle of the aircraft-fixed gas fire extinguishing system, we studied the influence of nozzle geometric parameters including outlet–inlet area ratio, length–diameter aspect ratio, and wall roughness on the distribution of pressure and velocity in the nozzle on the basis of CFD simulations. Although the structure of the nozzle is axisymmetric, the spatial distribution of the pressure and velocity during the flow and release of gas extinguishing agent is not completely symmetric. It was found that both of the outlet–inlet area ratio (δ) and the length–diameter aspect ratio (ξ) had a significant impact on the distribution characteristics of the pressure and axial velocity in the nozzle. With the increase of δ, the average pressure at the outlet cross-section of the nozzle decreased monotonically, while the average axial velocity at the outlet increased approximately linearly. When ξ2, the uniformity of the pressure and velocity distribution at the nozzle outlet was significantly improved. Moreover, with the increase of ξ, the average pressure and the average axial velocity of the outlet both showed a non-monotonic change trend, and the optimal value of ξ should be about 3.0. Compared with δ and ξ, the influence of the nozzle wall roughness (εN) on the flow and release characteristics of the extinguishing agent was weak. With the increase of εN, the average pressure of the nozzle outlet increased slightly, while the average axial velocity at the nozzle outlet decreased slightly. Full article
(This article belongs to the Special Issue Asymmetry in Fire Dynamics and Modelling)
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Review
A Review of Interpretable ML in Healthcare: Taxonomy, Applications, Challenges, and Future Directions
Symmetry 2021, 13(12), 2439; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122439 - 17 Dec 2021
Viewed by 404
Abstract
We have witnessed the impact of ML in disease diagnosis, image recognition and classification, and many more related fields. Healthcare is a sensitive field related to people’s lives in which decisions need to be carefully taken based on solid evidence. However, most ML [...] Read more.
We have witnessed the impact of ML in disease diagnosis, image recognition and classification, and many more related fields. Healthcare is a sensitive field related to people’s lives in which decisions need to be carefully taken based on solid evidence. However, most ML models are complex, i.e., black-box, meaning they do not provide insights into how the problems are solved or why such decisions are proposed. This lack of interpretability is the main reason why some ML models are not widely used yet in real environments such as healthcare. Therefore, it would be beneficial if ML models could provide explanations allowing physicians to make data-driven decisions that lead to higher quality service. Recently, several efforts have been made in proposing interpretable machine learning models to become more convenient and applicable in real environments. This paper aims to provide a comprehensive survey and symmetry phenomena of IML models and their applications in healthcare. The fundamental characteristics, theoretical underpinnings needed to develop IML, and taxonomy for IML are presented. Several examples of how they are applied in healthcare are investigated to encourage and facilitate the use of IML models in healthcare. Furthermore, current limitations, challenges, and future directions that might impact applying ML in healthcare are addressed. Full article
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Article
Applying GMEI-GAN to Generate Meaningful Encrypted Images in Reversible Data Hiding Techniques
Symmetry 2021, 13(12), 2438; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122438 - 16 Dec 2021
Viewed by 336
Abstract
With the rapid development of information technology, the transmission of information has become convenient. In order to prevent the leakage of information, information security should be valued. Therefore, the data hiding technique has become a popular solution. The reversible data hiding technique (RDH) [...] Read more.
With the rapid development of information technology, the transmission of information has become convenient. In order to prevent the leakage of information, information security should be valued. Therefore, the data hiding technique has become a popular solution. The reversible data hiding technique (RDH) in particular uses symmetric encoding and decoding algorithms to embed the data into the cover carrier. Not only can the secret data be transmitted without being detected and retrieved completely, but the cover carrier also can be recovered without distortion. Moreover, the encryption technique can protect the carrier and the hidden data. However, the encrypted carrier is a form of ciphertext, which has a strong probability to attract the attention of potential attackers. Thus, this paper uses the generative adversarial networks (GAN) to generate meaningful encrypted images for RDH. A four-stage network architecture is designed for the experiment, including the hiding network, the encryption/decryption network, the extractor, and the recovery network. In the hiding network, the secret data are embedded into the cover image through residual learning. In the encryption/decryption network, the cover image is encrypted into a meaningful image, called the marked image, through GMEI-GAN, and then the marked image is restored to the decrypted image via the same architecture. In the extractor, 100% of the secret data are extracted through the residual learning framework, same as the hiding network. Lastly, in the recovery network, the cover image is reconstructed with the decrypted image and the retrieved secret data through the convolutional neural network. The experimental results show that using the PSNR/SSIM as the criteria, the stego image reaches 45.09 dB/0.9936 and the marked image achieves 38.57 dB/0.9654. The proposed method not only increases the embedding capacity but also maintains high image quality in the stego images and marked images. Full article
(This article belongs to the Section Computer and Engineering Science and Symmetry/Asymmetry)
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Article
SimBetaReg Web-Tool: The Easiest Way to Implement the Beta and Simplex Regression Models
Symmetry 2021, 13(12), 2437; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122437 - 16 Dec 2021
Viewed by 424
Abstract
When the response variable is defined on the (0,1) interval, the beta and simplex regression models are commonly used by researchers. However, there is no software support for these models to make their implementation easy for researchers. In this study, we developed a [...] Read more.
When the response variable is defined on the (0,1) interval, the beta and simplex regression models are commonly used by researchers. However, there is no software support for these models to make their implementation easy for researchers. In this study, we developed a web-tool, named SimBetaReg, to help researchers who are not familiar with programming to implement the beta and simplex regression models. The developed application is free and works independently from the operating systems. Additionally, we model the incidence ratios of COVID-19 with educational and civic engagement indicators of the OECD countries using the SimBetaReg web-tool. Empirical findings show that when the educational attainment, years in education, and voter turnout increase, the incidence ratios of the countries decrease. Full article
(This article belongs to the Special Issue Probability, Statistics and Applied Mathematics)
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Article
Research on Optimization of Urban Public Transport Network Based on Complex Network Theory
Symmetry 2021, 13(12), 2436; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122436 - 16 Dec 2021
Viewed by 400
Abstract
The urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the [...] Read more.
The urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the operation of the public transportation system. This paper uses complex network theory and the symmetry of the up and down bus routes and stations to establish an urban public transit network model and calculates the probability of passengers choosing different routes in the public transit network according to passenger travel impedance. Based on passenger travel impedance, travel path probability and passenger travel demand, the links are weighed, and the network efficiency calculation method is improved. Finally, the public transit network optimization model was established with network efficiency as the objective function and solved by the ant colony algorithm. In order to verify the effectiveness of the model and the solution method, this paper selects areas in Nanguan District of Changchun City for example analysis. The result shows that the efficiency of the optimized network is 8.5% higher than that of the original network, which proves the feasibility of the optimized model and solution method. Full article
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Article
Continuity and Analyticity for the Generalized Benjamin–Ono Equation
Symmetry 2021, 13(12), 2435; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122435 - 16 Dec 2021
Viewed by 380
Abstract
This work mainly focuses on the continuity and analyticity for the generalized Benjamin–Ono (g-BO) equation. From the local well-posedness results for g-BO equation, we know that its solutions depend continuously on their initial data. In the present paper, we further show that such [...] Read more.
This work mainly focuses on the continuity and analyticity for the generalized Benjamin–Ono (g-BO) equation. From the local well-posedness results for g-BO equation, we know that its solutions depend continuously on their initial data. In the present paper, we further show that such dependence is not uniformly continuous in Sobolev spaces Hs(R) with s>3/2. We also provide more information about the stability of the data-solution map, i.e., the solution map for g-BO equation is Hölder continuous in Hr-topology for all 0r<s with exponent α depending on s and r. Finally, applying the generalized Ovsyannikov type theorem and the basic properties of Sobolev–Gevrey spaces, we prove the Gevrey regularity and analyticity for the g-BO equation. In addition, by the symmetry of the spatial variable, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients
Symmetry 2021, 13(12), 2434; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122434 - 16 Dec 2021
Viewed by 374
Abstract
In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some [...] Read more.
In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some specific cases are obtained. By virtue of the fractional conservation theorem, the conservation laws are constructed. Full article
Article
The FUor Star V2493 Cyg (HBC 722)—Eleven Years at Maximum Brightness
Symmetry 2021, 13(12), 2433; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122433 - 16 Dec 2021
Viewed by 379
Abstract
At the time of stellar evolution, young stellar objects go through processes of increased activity and instability. Star formation takes place in several stages during which the star accumulates enough mass to initiate thermonuclear reactions in the nucleus. A significant percentage of the [...] Read more.
At the time of stellar evolution, young stellar objects go through processes of increased activity and instability. Star formation takes place in several stages during which the star accumulates enough mass to initiate thermonuclear reactions in the nucleus. A significant percentage of the mass of Sun-like stars accumulates during periods of increased accretion known as FUor outbursts. Since we know only about two dozen stars of this type, the study of each new object is very important for our knowledge. In this paper, we present data from photometric monitoring on a FUor object V2493 Cyg discovered in 2010. Our data were obtained in the optical region with BVRI Johnson–Cousins set of filters during the period from November 2016 to February 2021. The results of our observations show that during this period no significant changes in the brightness of the star were registered. We only detect variations with a small amplitude around the maximum brightness value. Thus, since 2013 V2493 Cyg remains at its maximum brightness, without a decrease in brightness. Such photometric behavior is not typical of other stars from FUor type. Usually, the light curves of FUors are asymmetrical, with a very rapid rise and gradual decline of the brightness. V2493 Cyg remains unique in this respect with a very rapid rise in brightness and prolonged retention in maximum light. Our period analysis made for the interval February 2013–February 2021 reveals a well-defined period of 914 ± 10 days. Such periodicity can be explained by dust structures remaining from star formation in orbit around the star. Full article
(This article belongs to the Special Issue Observational Studies of Star Formation)
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Article
Authenticated Encryption Based on Chaotic Neural Networks and Duplex Construction
Symmetry 2021, 13(12), 2432; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122432 - 16 Dec 2021
Viewed by 483
Abstract
In this paper, we propose, implement and analyze an Authenticated Encryption with Associated Data Scheme (AEADS) based on the Modified Duplex Construction (MDC) that contains a chaotic compression function (CCF) based on our chaotic neural network revised (CNNR). Unlike the standard duplex construction [...] Read more.
In this paper, we propose, implement and analyze an Authenticated Encryption with Associated Data Scheme (AEADS) based on the Modified Duplex Construction (MDC) that contains a chaotic compression function (CCF) based on our chaotic neural network revised (CNNR). Unlike the standard duplex construction (SDC), in the MDC there are two phases: the initialization phase and the duplexing phase, each contain a CNNR formed by a neural network with single layer, and followed by a set of non-linear functions. The MDC is implemented with two variants of width, i.e., 512 and 1024 bits. We tested our proposed scheme against the different cryptanalytic attacks. In fact, we evaluated the key and the message sensitivity, the collision resistance analysis and the diffusion effect. Additionally, we tested our proposed AEADS using the different statistical tests such as NIST, Histogram, chi-square, entropy, and correlation analysis. The experimental results obtained on the security performance of the proposed AEADS system are notable and the proposed system can then be used to protect data and authenticate their sources. Full article
(This article belongs to the Special Issue Chaotic Systems and Nonlinear Dynamics)
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Article
Some New Reverse Hilbert’s Inequalities on Time Scales
Symmetry 2021, 13(12), 2431; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122431 - 15 Dec 2021
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Abstract
This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for [...] Read more.
This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type. Full article
Article
A New Integrated FUCOM–CODAS Framework with Fermatean Fuzzy Information for Multi-Criteria Group Decision-Making
Symmetry 2021, 13(12), 2430; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122430 - 15 Dec 2021
Viewed by 362
Abstract
Smartphones have become an inevitable part of every facet of modern society. The selection of a particular smartphone brand from multiple options that are available is a complex and dynamic decision-making problem, involving multiple conflicting criteria that are associated with imprecise asymmetric information [...] Read more.
Smartphones have become an inevitable part of every facet of modern society. The selection of a particular smartphone brand from multiple options that are available is a complex and dynamic decision-making problem, involving multiple conflicting criteria that are associated with imprecise asymmetric information imposed by the uncertainty of the consumers. In this paper, we propose a novel hybrid full consistency method (FUCOM) and a combinative distance based assessment (CODAS) based on the multi-criteria group decision-making (MAGDM) framework in the Fermatean fuzzy (FF) domain for smartphone brand selection. We derive the criteria using the UTAUT2 (unified theory of acceptance and ese of technology) model. A group of 15 decision makers (DMs) participated in our study. We compare 14 leading smartphone brands in India and find that the brands having superior features of a good quality and selling a brand image at a affordable price outperform other smartphones. To check the validity of our framework, we compare the results using extant multi-criteria decision-making (MCDM) models. We observe our model provides a consistent solution. Furthermore, we carry out a sensitivity analysis for ascertaining the robustness and stability of the results generated by our model. The results of the sensitivity analysis show that our proposed framework delivers a stable and robust solution. Full article
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Article
A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables
Symmetry 2021, 13(12), 2429; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122429 - 15 Dec 2021
Viewed by 313
Abstract
As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key [...] Read more.
As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry. Full article
(This article belongs to the Special Issue Uncertainty Theory: Symmetry and Applications)
Article
Numerical Solutions of the Mathematical Models on the Digestive System and COVID-19 Pandemic by Hermite Wavelet Technique
Symmetry 2021, 13(12), 2428; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122428 - 15 Dec 2021
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Abstract
This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system [...] Read more.
This article developed a functional integration matrix via the Hermite wavelets and proposed a novel technique called the Hermite wavelet collocation method (HWM). Here, we studied two models: the coupled system of an ordinary differential equation (ODE) is modeled on the digestive system by considering different parameters such as sleep factor, tension, food rate, death rate, and medicine. Here, we discussed how these parameters influence the digestive system and showed them through figures and tables. Another fractional model is used on the COVID-19 pandemic. This model is defined by a system of fractional-ODEs including five variables, called S (susceptible), E (exposed), I (infected), Q (quarantined), and R (recovered). The proposed wavelet technique investigates these two models. Here, we express the modeled equation in terms of the Hermite wavelets along with the collocation scheme. Then, using the properties of wavelets, we convert the modeled equation into a system of algebraic equations. We use the Newton–Raphson method to solve these nonlinear algebraic equations. The obtained results are compared with numerical solutions and the Runge–Kutta method (R–K method), which is expressed through tables and graphs. The HWM computational time (consumes less time) is better than that of the R–K method. Full article
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Article
The Multi-Compartment SI(RD) Model with Regime Switching: An Application to COVID-19 Pandemic
Symmetry 2021, 13(12), 2427; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122427 - 15 Dec 2021
Viewed by 356
Abstract
We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading [...] Read more.
We study—with existence and unicity results—a variant of the SIR model for an infectious disease incorporating both the possibility of a death outcome—in a short period of time—and a regime switch that can account for the mitigation measures used to control the spreading of the infections, such as a total lockdown. This model is parametrised by three parameters: the basic reproduction number, the mortality rate of the infected, and the duration of the disease. We discuss a particular example of application to Portuguese COVID-19 data in two short periods just after the start of the epidemic in 4 March 2020, with the first two cases dated that day. We propose a simple and effective method for the estimation of the main parameters of the disease, namely, the basic reproduction number and the mortality rate of the infected. We correct these estimated values to take into account the asymptomatic non-diagnosed members of the population. We compare the outcome of the model in the cases of the existence, or not, of a regime switch, and under three different scenarios, with a remarkable agreement between model and data deaths in the case of our basis scenario. In a final short remark, we deal with the existence of symmetries for the proposed model. Full article
(This article belongs to the Special Issue Probability, Statistics and Applied Mathematics)
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Article
Rotational Cryptanalysis of MORUS
Symmetry 2021, 13(12), 2426; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122426 - 15 Dec 2021
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Abstract
MORUS is one of the finalists of the CAESAR competition. This is an ARX construction that required investigation against rotational cryptanalysis. We investigated the power of rotational cryptanalysis against MORUS. We show that all the operations in the state update function of MORUS [...] Read more.
MORUS is one of the finalists of the CAESAR competition. This is an ARX construction that required investigation against rotational cryptanalysis. We investigated the power of rotational cryptanalysis against MORUS. We show that all the operations in the state update function of MORUS maintain the rotational pairs when the rotation distance is set to a multiple of the sub-word size. Our investigation also confirms that the rotational pairs can be used as distinguishers for the full version of MORUS if the constants used in MORUS are rotational-invariant. However, the actual constants used in MORUS are not rotational-invariant. The introduction of such constants in the state update function breaks the symmetry of the rotational pairs. Experimental results show that rotational pairs can be used as distinguishers for only one step of the initialization phase of MORUS. For more than one step, there are not enough known differences in the rotational pairs of MORUS to provide an effective distinguisher. This is due to the XOR-ing of the constants that are not rotational-invariant. Therefore, it is unlikely for an adversary to construct a distinguisher for the full version of MORUS by observing the rotational pairs. Full article
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Article
Key Concepts of Systemological Approach to CPS Adaptive Information Security Monitoring
Symmetry 2021, 13(12), 2425; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122425 - 15 Dec 2021
Viewed by 349
Abstract
Modern cyber-physical systems (CPS) use digital control of physical processes. This allows attackers to conduct various cyberattacks on these systems. According to the current trends, an information security monitoring system (ISMS) becomes part of a security management system of CPS. It provides information [...] Read more.
Modern cyber-physical systems (CPS) use digital control of physical processes. This allows attackers to conduct various cyberattacks on these systems. According to the current trends, an information security monitoring system (ISMS) becomes part of a security management system of CPS. It provides information to make a decision and generate a response. A large number of new methods are aimed at CPS security, including security assessment, intrusion detection, and ensuring sustainability. However, as a cyber-physical system operates over time, its structure and requirements may change. The datasets available for the protection object (CPS) and the security requirements have become dynamic. This dynamic effect causes asymmetry between the monitoring data collection and processing subsystem and the presented security tasks. The problem herein is the choice of the most appropriate set of methods in order to solve the security problems of a particular CPS configuration from a particular bank of the available methods. To solve this problem, the authors present a method for the management of an adaptive information security monitoring system. The method consists of solving a multicriteria discrete optimization problem under Pareto-optimality conditions when the available data, methods or external requirements change. The experimental study was performed on an example of smart home intrusion detection. In the study, the introduction of a constraint (a change in requirements) led to the revision of the monitoring scheme and a different recommendation of the monitoring method. As a result, the information security monitoring system gains the property of adaptability to changes in tasks and the available data. An important result from the study is the fact that the monitoring scheme obtained using the proposed management method has a proven optimality under the given conditions. Therefore, the asymmetry between the information security monitoring data collection and processing subsystem and the set of security requirements in cyber-physical systems can be overcome. Full article
(This article belongs to the Topic Multi-Criteria Decision Making)
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Article
Investigation on the Prediction of Cardiovascular Events Based on Multi-Scale Time Irreversibility Analysis
Symmetry 2021, 13(12), 2424; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122424 - 15 Dec 2021
Viewed by 362
Abstract
Investigation of the risk factors associated with cardiovascular disease (CVD) plays an important part in the prevention and treatment of CVD. This study investigated whether alteration in the multi-scale time irreversibility of sleeping heart rate variability (HRV) was a risk factor for cardiovascular [...] Read more.
Investigation of the risk factors associated with cardiovascular disease (CVD) plays an important part in the prevention and treatment of CVD. This study investigated whether alteration in the multi-scale time irreversibility of sleeping heart rate variability (HRV) was a risk factor for cardiovascular events. The D-value, based on analysis of multi-scale increments in HRV series, was used as the measurement of time irreversibility. Eighty-four subjects from an open-access database (i.e., the Sleep Heart Health Study) were included in this study. None of them had any CVD history at baseline; 42 subjects had cardiovascular events within 1 year after baseline polysomnography and were classed as the CVD group, and the other 42 subjects in the non-CVD group were age matched with those in the CVD group and had no cardiovascular events during the 15-year follow-up period. We compared D-values of sleeping HRV between the CVD and non-CVD groups and found that the D-values of the CVD group were significantly lower than those of the non-CVD group on all 10 scales, even after adjusting for gender and body mass index. Moreover, we investigated the performance of a machine learning model to classify CVD and non-CVD subjects. The model, which was fed with a feature space based on the D-values on 10 scales and trained by a random forest algorithm, achieved an accuracy of 80.8% and a positive prediction rate of 86.7%. These results suggest that the decreased time irreversibility of sleeping HRV is an independent predictor of cardiovascular events that could be used to assist the intelligent prediction of cardiovascular events. Full article
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