Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences. Symmetry is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics); Q1 (Physics and Astronomy); Q1 (Computer Science)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.2 days after submission; acceptance to publication is undertaken in 3.5 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about Symmetry.
Impact Factor:
2.7 (2022);
5-Year Impact Factor:
2.7 (2022)
Latest Articles
DAE-GAN: Underwater Image Super-Resolution Based on Symmetric Degradation Attention Enhanced Generative Adversarial Network
Symmetry 2024, 16(5), 588; https://doi.org/10.3390/sym16050588 (registering DOI) - 9 May 2024
Abstract
Underwater images often exhibit detail blurring and color distortion due to light scattering, impurities, and other influences, obscuring essential textures and details. This presents a challenge for existing super-resolution techniques in identifying and extracting effective features, making high-quality reconstruction difficult. This research aims
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Underwater images often exhibit detail blurring and color distortion due to light scattering, impurities, and other influences, obscuring essential textures and details. This presents a challenge for existing super-resolution techniques in identifying and extracting effective features, making high-quality reconstruction difficult. This research aims to innovate underwater image super-resolution technology to tackle this challenge. Initially, an underwater image degradation model was created by integrating random subsampling, Gaussian blur, mixed noise, and suspended particle simulation to generate a highly realistic synthetic dataset, thereby training the network to adapt to various degradation factors. Subsequently, to enhance the network’s capability to extract key features, improvements were made based on the symmetrically structured blind super-resolution generative adversarial network (BSRGAN) model architecture. An attention mechanism based on energy functions was introduced within the generator to assess the importance of each pixel, and a weighted fusion strategy of adversarial loss, reconstruction loss, and perceptual loss was utilized to improve the quality of image reconstruction. Experimental results demonstrated that the proposed method achieved significant improvements in peak signal-to-noise ratio (PSNR) and underwater image quality measure (UIQM) by 0.85 dB and 0.19, respectively, significantly enhancing the visual perception quality and indicating its feasibility in super-resolution applications.
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(This article belongs to the Section Engineering and Materials)
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Enhancing Knowledge Graph Embedding with Hierarchical Self-Attention and Graph Neural Network Techniques for Drug-Drug Interaction Prediction in Virtual Reality Environments
by
Lizhen Jiang and Sensen Zhang
Symmetry 2024, 16(5), 587; https://doi.org/10.3390/sym16050587 (registering DOI) - 9 May 2024
Abstract
In biomedicine, the critical task is to decode Drug–Drug Interactions (DDIs) from complex biomedical texts. The scientific community employs Knowledge Graph Embedding (KGE) methods, enhanced with advanced neural network technologies, including capsule networks. However, existing methodologies primarily focus on the structural details of
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In biomedicine, the critical task is to decode Drug–Drug Interactions (DDIs) from complex biomedical texts. The scientific community employs Knowledge Graph Embedding (KGE) methods, enhanced with advanced neural network technologies, including capsule networks. However, existing methodologies primarily focus on the structural details of individual entities or relations within Biomedical Knowledge Graphs (BioKGs), overlooking the overall structural context of BioKGs, molecular structures, positional features of drug pairs, and their critical Relational Mapping Properties. To tackle the challenges identified, this study presents HSTrHouse an innovative hierarchical self-attention BioKGs embedding framework. This architecture integrates self-attention mechanisms with advanced neural network technologies, including Convolutional Neural Network (CNN) and Graph Neural Network (GNN), for enhanced computational modeling in biomedical contexts. The model bifurcates the BioKGs into entity and relation layers for structural analysis. It employs self-attention across these layers, utilizing PubMedBERT and CNN for position feature extraction, and a GNN for drug pair molecular structure analysis. Then, we connect the position and molecular structure features to integrate them into the self-attention calculation of entity and relation. After that, the output of the self-attention layer is combined with the connected vectors of the position feature and molecular structure feature to obtain the final representation vector, and finally, to model the Relational Mapping Properties (RMPs), the representation vector is embedded into the complex vector space using Householder projections to obtain the BioKGs model. The paper validates HSTrHouse’s efficacy by comparing it with advanced models on three standard BioKGs for DDIs research.
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(This article belongs to the Section Computer)
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Open AccessArticle
An Improved Dung Beetle Optimization Algorithm for High-Dimension Optimization and Its Engineering Applications
by
Xu Wang, Hongwei Kang, Yong Shen, Xingping Sun and Qingyi Chen
Symmetry 2024, 16(5), 586; https://doi.org/10.3390/sym16050586 (registering DOI) - 9 May 2024
Abstract
One of the limitations of the dung beetle optimization (DBO) is its susceptibility to local optima and its relatively low search accuracy. Several strategies have been utilized to improve the diversity, search precision, and outcomes of the DBO. However, the equilibrium between exploration
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One of the limitations of the dung beetle optimization (DBO) is its susceptibility to local optima and its relatively low search accuracy. Several strategies have been utilized to improve the diversity, search precision, and outcomes of the DBO. However, the equilibrium between exploration and exploitation has not been achieved optimally. This paper presents a novel algorithm called the ODBO, which incorporates cat map and an opposition-based learning strategy, which is based on symmetry theory. In addition, in order to enhance the performance of the dung ball rolling phase, this paper combines the global search strategy of the osprey optimization algorithm with the position update strategy of the DBO. Additionally, we enhance the population’s diversity during the foraging phase of the DBO by incorporating vertical and horizontal crossover of individuals. This introduction of asymmetry in the crossover operation increases the exploration capability of the algorithm, allowing it to effectively escape local optima and facilitate global search.
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(This article belongs to the Section Computer)
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Open AccessArticle
Nonstandard Nearly Exact Analysis of the FitzHugh–Nagumo Model
by
Shahid, Mujahid Abbas and Eddy Kwessi
Symmetry 2024, 16(5), 585; https://doi.org/10.3390/sym16050585 (registering DOI) - 9 May 2024
Abstract
The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literature, many approaches have been proposed to study its dynamics.
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The FitzHugh–Nagumo model has been used empirically to model certain types of neuronal activities. It is also a non-linear dynamical system applicable to chemical kinetics, population dynamics, epidemiology and pattern formation. In the literature, many approaches have been proposed to study its dynamics. In this paper, initially, we have employed cutting-edge tools from discrete dynamics for discretization and fixed points. It has been proven that an exact discrete scheme exists for this paradigm. This project also considers the phase space and integral surfaces of these evolutionary equations. In addition, it carries out a thorough symmetry analysis of this reaction diffusion system to find equivalent systems. Moreover, steady-state solutions are obtained using ansatzes for traveling wave solutions. The existence of infinite traveling wave solutions has also been proven. Yet again, this investigation establishes the potential of symmetry methods to unravel non-linearity. Finally, singular perturbation theory has been employed to obtain analytical approximations and to study stability in different parameter regimes.
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(This article belongs to the Special Issue Nonlinear Symmetric Systems and Chaotic Systems in Engineering)
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Non-Hermitian Quantum Rényi Entropy Dynamics in Anyonic-PT Symmetric Systems
by
Zhihang Liu and Chao Zheng
Symmetry 2024, 16(5), 584; https://doi.org/10.3390/sym16050584 - 9 May 2024
Abstract
We reveal the continuous change of information dynamics patterns in anyonic-PT symmetric systems that originates from the continuity of anyonic-PT symmetry. We find there are three information dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable
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We reveal the continuous change of information dynamics patterns in anyonic-PT symmetric systems that originates from the continuity of anyonic-PT symmetry. We find there are three information dynamics patterns for anyonic-PT symmetric systems: damped oscillations with an overall decrease (increase) and asymptotically stable damped oscillations, which are three-fold degenerate and are distorted using the Hermitian quantum Rényi entropy or distinguishability. It is the normalization of the non-unitary evolved density matrix that causes the degeneracy and distortion. We give a justification for non-Hermitian quantum Rényi entropy being negative. By exploring the mathematics and physical meaning of the negative entropy in open quantum systems, we connect negative non-Hermitian quantum Rényi entropy and negative quantum conditional entropy, paving the way to rigorously investigate negative entropy in open quantum systems.
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(This article belongs to the Topic Quantum Information and Quantum Computing, 2nd Volume)
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Open AccessArticle
Global Models of Collapsing Scalar Field: Endstate
by
Dario Corona and Roberto Giambò
Symmetry 2024, 16(5), 583; https://doi.org/10.3390/sym16050583 - 9 May 2024
Abstract
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data
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The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analyzed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed by Einstein’s equations, considering variations in parameters that influence naked singularity formation. We illustrate how these results apply to a family of scalar field models, concluding with a discussion on the concept of genericity in singularity studies.
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(This article belongs to the Special Issue Recent Advance in Mathematical Physics II)
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Symmetric Collaborative Fault-Tolerant Control of Multi-Intelligence under Long-Range Transmission in Air–Ground Integrated Wireless High-Mobility Self-Organizing Networks
by
Zhifang Wang, Mingzhe Shao, Wenke Xu, Xuewei Huang, Yang Bai, Quanzhen Huang and Jianguo Yu
Symmetry 2024, 16(5), 582; https://doi.org/10.3390/sym16050582 - 8 May 2024
Abstract
With the continuous development and progress of wireless self-organizing network communication technology, how to carry out long-distance cooperative control of multiple intelligences under the framework of an air–ground integrated wireless high-mobility self-organizing network has become a hot and difficult topic that needs to
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With the continuous development and progress of wireless self-organizing network communication technology, how to carry out long-distance cooperative control of multiple intelligences under the framework of an air–ground integrated wireless high-mobility self-organizing network has become a hot and difficult topic that needs to be solved urgently. This paper takes the air–ground integrated wireless high-mobility self-organizing network system as the basic framework and focuses on solving the long-distance cooperative fault-tolerant control of multi-intelligent bodies and the topological stability of a wireless mobile self-organizing network. To solve the above problems, a direct neural network with a robust adaptive fault-tolerant controller is designed in this paper. By constructing a symmetric population neural network model and combining it with the Lyapunov stabilization criterion, the system feedback matrix K has the ability of autonomous adaptive learning, and symmetrically distorts, rotates, or scales the training data to instantly adjust the system’s fault-tolerant corrections and adaptive adjusting factors to resist the unknown disturbances and faults, to achieve the goals of multi-intelligent body stable control and the stable operation of a wireless high-mobility self-organizing network topology. Simulation results show that with the feedback adjustment of the multi-system under the designed controller, the multi-system as a whole has good fault-tolerant performance and autonomous learning approximation performance, and the tracking error asymptotically converges to zero. The experimental results show that the multi-flight subsystems fly stably, the air–ground integrated wireless high-mobility self-organizing network topology has good stability performance, and the maximum relative improvement of the topology stability performance is 50%.
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(This article belongs to the Special Issue Symmetry/Asymmetry in Wireless Communication and Sensor Networks II)
Open AccessArticle
Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation
by
Ma’mon Abu Hammad, Rami Alkhateeb, Nabil Laiche, Adel Ouannas and Shameseddin Alshorm
Symmetry 2024, 16(5), 581; https://doi.org/10.3390/sym16050581 - 8 May 2024
Abstract
This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive
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This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements.
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(This article belongs to the Special Issue Advance in Functional Equations, Second Edition)
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On Uniformly Starlike Functions with Respect to Symmetrical Points Involving the Mittag-Leffler Function and the Lambert Series
by
Jamal Salah
Symmetry 2024, 16(5), 580; https://doi.org/10.3390/sym16050580 - 8 May 2024
Abstract
The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions ΤJ(αi). Further, we obtain coefficient estimates, convex linear combinations,
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The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions ΤJ(αi). Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions f∈ΤJ(αi). In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass.
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(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
Open AccessReview
Non-Local Cosmology: From Theory to Observations
by
Francesco Bajardi and Salvatore Capozziello
Symmetry 2024, 16(5), 579; https://doi.org/10.3390/sym16050579 - 8 May 2024
Abstract
We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function
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We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function , where R denotes the Ricci curvature scalar and the operator introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.
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(This article belongs to the Special Issue Selected Papers on Nonlinear Dynamics)
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Engineering Drawing Applied to the Study of the Design of a Two-Cylinder Entablature Steam Engine with Parallel Motion Crosshead
by
José Ignacio Rojas-Sola and Juan Carlos Barranco-Molina
Symmetry 2024, 16(5), 578; https://doi.org/10.3390/sym16050578 - 8 May 2024
Abstract
This article presents an investigation into a historical invention consisting of a stationary steam engine designed by Henry Muncaster: a two-cylinder entablature steam engine with parallel motion crosshead. The present interdisciplinary research, based on the theoretical and methodological concepts of engineering drawing and
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This article presents an investigation into a historical invention consisting of a stationary steam engine designed by Henry Muncaster: a two-cylinder entablature steam engine with parallel motion crosshead. The present interdisciplinary research, based on the theoretical and methodological concepts of engineering drawing and computer-aided design, has allowed us to understand the operation of this invention from the 3D CAD model of the invention obtained thanks to the original drawings published in the magazine Model Engineer in 1957 and reproduced in 2017, since there is no descriptive information related to the invention. However, there have been drawbacks in the geometric modeling process since the dimensions of some components did not exist and in other cases they were erroneous. For this reason, dimensional, geometric and movement constraints (degrees of freedom) had to be applied so that said 3D CAD model would be coherent and functional, and an interference analysis also had to be performed. Finally, the existing symmetry in the arrangement of the cylinders and the crosshead has been discovered, it being essential to guarantee that the forces and movements are uniform on both sides of the steam engine, and allowing the work to be carried out in a more balanced manner by reducing vibrations and improving the overall efficiency of the invention.
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(This article belongs to the Special Issue Graphic Representation and Symmetry Applied to the Technical Historical Heritage)
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Frequency Analysis of Asymmetric Circular Organic Solar Cells Embedded in an Elastic Medium under Hygrothermal Conditions
by
Muneer Alali, Mohammad A. Abazid and Mohammed Sobhy
Symmetry 2024, 16(5), 577; https://doi.org/10.3390/sym16050577 - 7 May 2024
Abstract
This research represents the first theoretical investigation about the vibration behavior of circular organic solar cells. Therefore, the vibration response of asymmetric circular organic solar cells that represent a perfect renewable energy source is demonstrated. For this purpose, the differential quadrature method (DQM)
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This research represents the first theoretical investigation about the vibration behavior of circular organic solar cells. Therefore, the vibration response of asymmetric circular organic solar cells that represent a perfect renewable energy source is demonstrated. For this purpose, the differential quadrature method (DQM) is employed. The organic solar cell is modeled as a laminated plate consisting of five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. This cell is rested on a Winkler–Pasternak elastic foundation and assumed to be exposed to various types of hygrothermal loadings. There are three different kinds of temperature and moisture variations that are taken into account: uniform, linear, and nonlinear distribution throughout the cell’s thickness. The displacement field is presented based on a new inverse hyperbolic shear deformation theory considering only two unknowns. The motion equations including hygrothermal effect and plate–foundation interaction are established within the framework of Hamilton’s principle. The DQM is utilized to solve these equations. In order to ensure the accuracy of the proposed theory, the present results are compared with those reported by other higher-order theories. A comprehensive parametric illustration is conducted on the impacts of different parameters involving the geometrical configuration, elastic foundation parameters, temperature, and moisture concentration on the deduced eigenfrequency of the circular organic solar cells.
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(This article belongs to the Section Mathematics)
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Open AccessEditorial
Editorial for Special Issue “Various Approaches for Generalized Integral Transforms”
by
Hwajoon Kim
Symmetry 2024, 16(5), 576; https://doi.org/10.3390/sym16050576 - 7 May 2024
Abstract
The Laplace transform can be interpreted as a method of converting a function from the time domain to the complex domain [...]
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(This article belongs to the Special Issue Various Approaches for Generalized Integral Transforms)
Open AccessArticle
Domain Transformation of Distortion Costs for Efficient JPEG Steganography with Symmetric Embedding
by
Yuanfeng Pan and Jiangqun Ni
Symmetry 2024, 16(5), 575; https://doi.org/10.3390/sym16050575 - 7 May 2024
Abstract
Nowadays, most image steganographic schemes embed secret messages by minimizing a well-designed distortion cost function for the corresponding domain, i.e., the spatial domain for spatial image steganography or the JPEG (Joint Photographic Experts Group) domain for JPEG image steganography. In this paper, we
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Nowadays, most image steganographic schemes embed secret messages by minimizing a well-designed distortion cost function for the corresponding domain, i.e., the spatial domain for spatial image steganography or the JPEG (Joint Photographic Experts Group) domain for JPEG image steganography. In this paper, we break the boundary between these two types of schemes by establishing a theoretical link between the distortion costs in the spatial domain and those in the JPEG domain and thus propose a scheme for domain transformations of distortion costs for efficient JPEG steganography with symmetric embedding, which can directly convert the spatial distortion cost into its JPEG counterpart. Specifically, by formulating the distortion cost function for JPEG images in the decompressed spatial domain, a closed-form expression for a distortion cost cross-domain transformation is derived theoretically, which precisely characterizes the conversion from the distortion costs obtained by existing spatial steganographic schemes to those applied in JPEG steganography. Experimental results demonstrate that the proposed method outperforms other advanced JPEG steganographic schemes, e.g., JUNIWARD (JPEG steganography with Universal Wavelet Relative Distortion), JMiPOD (JPEG steganography by Minimizing the Power of the Optimal Detector), and DCDT (Distortion Cost Domain Transformation), in resisting the detection of various advanced steganalyzers.
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(This article belongs to the Section Computer)
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Novel Distance Measures of q-Rung Orthopair Fuzzy Sets and Their Applications
by
Donglai Wang, Yige Yuan, Zhe Liu, Sijia Zhu and Zhifang Sun
Symmetry 2024, 16(5), 574; https://doi.org/10.3390/sym16050574 - 7 May 2024
Abstract
The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of the parameter q allows for
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The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of the parameter q allows for the q-rung orthopair fuzzy sets to capture a broader range of uncertainty of information. In this paper, we present two novel distance measures for q-ROFSs inspired by the Jensen–Shannon divergence, called and , and we analyze some properties they satisfy, such as non-degeneracy, symmetry, boundedness, and triangular inequality. Then, the normalized distance measures, called and , are proposed and we verify their rationality through numerical experiments. Finally, we apply the proposed distance measures to practical scenarios, including pattern recognition and multicriteria decision-making, and the results demonstrate the effectiveness of the proposed distance measures.
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(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
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A Nonlinear Programming Approach to Solving Interval-Valued Intuitionistic Hesitant Noncooperative Fuzzy Matrix Games
by
Shuvasree Karmakar and Mijanur Rahaman Seikh
Symmetry 2024, 16(5), 573; https://doi.org/10.3390/sym16050573 - 7 May 2024
Abstract
Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered
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Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models.
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(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)
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Towards Modelling Mechanical Shaking Using Potential Energy Surfaces: A Toy Model Analysis
by
Sergei D. Odintsov and Vasilis K. Oikonomou
Symmetry 2024, 16(5), 572; https://doi.org/10.3390/sym16050572 - 7 May 2024
Abstract
In this work, we formalize the effect of mechanical shaking by using various forms of an externally exerted force, which may be constant or may be position-dependent, and we examine the changes in the potential energy surfaces that quantify the chemical reaction. We
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In this work, we formalize the effect of mechanical shaking by using various forms of an externally exerted force, which may be constant or may be position-dependent, and we examine the changes in the potential energy surfaces that quantify the chemical reaction. We use a simple toy model to model the potential energy surfaces of a chemical reaction, and we study the effect of a constant or position-dependent externally exerted force for various forms of the force. As we demonstrate, the effect of the force can be quite dramatic on the potential energy surfaces, which acquire new stationary points and new Newton trajectories that are distinct from the original ones that were obtained in the absence of mechanochemical effects. We also introduce a new approach to mechanochemical interactions, using a dynamical systems approach for the Newton trajectories. As we show, the dynamical system attractor properties of the trajectories in the phase space are identical to the stationary points of the potential energy surfaces, but the phase space contains much more information regarding the possible evolution of the chemical reaction—information that is quantified by the existence of unstable or saddle fixed points in the phase space. We also discuss how an experimental method for a suitable symmetric liquid solution substance might formalize the effect of shaking via various forms of external force, even in the form of an extended coordinate-dependent force matrix. This approach may experimentally quantify the Epstein effect of shaking in chemical solutions via mechanochemistry methods.
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(This article belongs to the Special Issue Symmetry: Recent Developments in Engineering Science and Applications)
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Open AccessArticle
Cross-Water–Air Optical Wireless Communication Using Orthogonal Time–Frequency Space Modulation
by
Dianbin Lian, Yan Gao and Jie Lian
Symmetry 2024, 16(5), 571; https://doi.org/10.3390/sym16050571 - 7 May 2024
Abstract
This paper examines the communication difficulties encountered in cross-media wireless optical transmission through simulated research on the utilization of orthogonal time and frequency space (OTFS) modulation technology. Our analysis and comparison demonstrate that OTFS significantly improves the reliability and throughput of data transmission
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This paper examines the communication difficulties encountered in cross-media wireless optical transmission through simulated research on the utilization of orthogonal time and frequency space (OTFS) modulation technology. Our analysis and comparison demonstrate that OTFS significantly improves the reliability and throughput of data transmission in intricate multipath channel settings. In contrast to conventional orthogonal frequency division multiplexing (OFDM) technology, OTFS displays better resilience and transmission effectiveness. We foresee additional enhancements and progress in OTFS technology to present a sturdier and more efficient resolution for wireless communication, thereby providing valuable perspectives and encouragement for associated research initiatives. Our results underscore the capability of OTFS technology to transform wireless communication systems in demanding multipath channel conditions.
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(This article belongs to the Special Issue Symmetry and Its Application in Wireless Communication)
Open AccessArticle
Brauer Analysis of Some Cayley and Nilpotent Graphs and Its Application in Quantum Entanglement Theory
by
Agustín Moreno Cañadas, Ismael Gutierrez and Odette M. Mendez
Symmetry 2024, 16(5), 570; https://doi.org/10.3390/sym16050570 - 6 May 2024
Abstract
Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph algebras and Brauer configuration
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Cayley and nilpotent graphs arise from the interaction between graph theory and algebra and are used to visualize the structures of some algebraic objects as groups and commutative rings. On the other hand, Green and Schroll introduced Brauer graph algebras and Brauer configuration algebras to investigate the algebras of tame and wild representation types. An appropriated system of multisets (called a Brauer configuration) induces these algebras via a suitable bounded quiver (or bounded directed graph), and the combinatorial properties of such multisets describe corresponding indecomposable projective modules, the dimensions of the algebras and their centers. Undirected graphs are examples of Brauer configuration messages, and the description of the related data for their induced Brauer configuration algebras is said to be the Brauer analysis of the graph. This paper gives closed formulas for the dimensions of Brauer configuration algebras (and their centers) induced by Cayley and nilpotent graphs defined by some finite groups and finite commutative rings. These procedures allow us to give examples of Hamiltonian digraph constructions based on Cayley graphs. As an application, some quantum entangled states (e.g., Greenberger–Horne–Zeilinger and Dicke states) are described and analyzed as suitable Brauer messages.
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(This article belongs to the Special Issue Symmetry in Graph Algorithms and Graph Theory III)
Open AccessArticle
Number of Volatility Regimes in the Muscat Securities Market Index in Oman Using Markov-Switching GARCH Models
by
Brahim Benaid, Iman Al Hasani and Mhamed Eddahbi
Symmetry 2024, 16(5), 569; https://doi.org/10.3390/sym16050569 - 6 May 2024
Abstract
The predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive performance of specific GARCH models, particularly the Markov-Switching GARCH (MS-GARCH). The primary objective is to determine the optimal
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The predominant approach for studying volatility is through various GARCH specifications, which are widely utilized in model-based analyses. This study focuses on assessing the predictive performance of specific GARCH models, particularly the Markov-Switching GARCH (MS-GARCH). The primary objective is to determine the optimal number of regimes within the MS-GARCH framework that effectively captures the conditional variance of the Muscat Securities Market Index (MSMI). To achieve this, we employ the Akaike Information Criterion (AIC) to compare different MS-GARCH models, estimated via Maximum Likelihood Estimation (MLE). Our findings indicate that the chosen models consistently exhibit at least two regimes across various GARCH specifications. Furthermore, a validation using the Value at Risk (VaR) confirms the accuracy of volatility forecasts generated by the selected models.
Full article
(This article belongs to the Special Issue Mathematical Theories, Models and Methods in Applied Sciences: Deterministic, Stochastic and Symmetry Perspectives)
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