Symmetry

19 pages, 1408 KiB

Open AccessArticle

Finite Population Variance Estimation Using Monte Carlo Simulation and Real Life Application

by Umer Daraz, Jinbiao Wu, Della Agustiana and Walid Emam

Symmetry 2025, 17(1), 84; https://doi.org/10.3390/sym17010084 - 7 Jan 2025

In this paper, we introduce a new, improved family of estimators aimed at improving the accuracy of finite population variance estimation. The proposed class of estimators is enhanced in terms of overall estimating performance and robustness by using the maximum and minimum values [...] Read more.

In this paper, we introduce a new, improved family of estimators aimed at improving the accuracy of finite population variance estimation. The proposed class of estimators is enhanced in terms of overall estimating performance and robustness by using the maximum and minimum values as supplementary information to improve precision and reliability. The bias and mean square error are theoretically obtained to the first order of approximation. We carried out a simulation study to evaluate the performance of the proposed estimators and validate the theoretical results. The findings show that the proposed estimators have higher percent relative efficiencies than the existing estimators across all of the simulated scenarios. Additionally, three independent symmetric and asymmetric datasets are analyzed to further confirm the better efficiency of proposed estimators compared with traditional estimators. Full article

(This article belongs to the Section Mathematics)

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22 pages, 342 KiB

Open AccessArticle

Hyers–Ulam and Hyers–Ulam–Rassias Stability for a Class of Fractional Evolution Differential Equations with Neutral Time Delay

by Kholoud N. Alharbi

Symmetry 2025, 17(1), 83; https://doi.org/10.3390/sym17010083 - 7 Jan 2025

Abstract

In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann–Liouville and Caputo fractional derivatives with orders

0 < α < 1

and [...] Read more.

In this paper, we demonstrate that neutral fractional evolution equations with finite delay possess a stable mild solution. Our model incorporates a mixed fractional derivative that combines the Riemann–Liouville and Caputo fractional derivatives with orders

0 < α < 1

and

1 < β < 2

. We identify the infinitesimal generator of the cosine family and analyze the stability of the mild solution using both Hyers–Ulam–Rassias and Hyers–Ulam stability methodologies, ensuring robust and reliable results for fractional dynamic systems with delay. In order to guarantee that the features of invariance under transformations, such as rotations or reflections, result in the presence of fixed points that remain unchanging and represent the consistency and balance of the underlying system, fixed-point theorems employ the symmetry idea. Lastly, the results obtained are applied to a fractional order nonlinear wave equation with finite delay with respect to time. Full article

(This article belongs to the Special Issue Nonlinear Differential and Integral Equations and Their Infinite Systems)

42 pages, 14236 KiB

Open AccessReview

Asymmetric Transformations of Levulinic Acid to γ-Valerolactone and 5-Methylpyrrolidin-2-one Derivatives: Chiral Compounds with Biological Potential

by Elżbieta Łastawiecka and Katarzyna Szwaczko

Symmetry 2025, 17(1), 82; https://doi.org/10.3390/sym17010082 - 7 Jan 2025

Abstract

Levulinic acid is a key platform molecule derived from biomass and readily available from natural sources, making it an attractive starting material for the synthesis of high-value chiral compounds. Among them, γ-valerolactone and 5-methylpyrrolidin-2-one derivatives are notable for their widespread occurrence and [...] Read more.

Levulinic acid is a key platform molecule derived from biomass and readily available from natural sources, making it an attractive starting material for the synthesis of high-value chiral compounds. Among them, γ-valerolactone and 5-methylpyrrolidin-2-one derivatives are notable for their widespread occurrence and biological importance. This review paper highlights the importance of γ-valerolactone and 5-methylpyrrolidin-2-one derivatives as frameworks found in biologically active compounds and pharmaceuticals. It focuses on the asymmetric synthesis of these chiral building blocks from levulinic acid, highlighting recent advances in catalytic transformations that allow for efficient and selective transformations. The potential applications of these chiral molecules in medicine and industry underscore the importance of developing sustainable and scalable processes for their production. This review also examines future directions in the field, given the growing demand for green chemistry approaches and the increasing importance of chiral molecules in drug development. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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20 pages, 305 KiB

Open AccessArticle

Derivation of Tensor Algebra as a Fundamental Operation—The Fermi Derivative in a General Metric Affine Space

by Michael Tsamparlis

Symmetry 2025, 17(1), 81; https://doi.org/10.3390/sym17010081 - 7 Jan 2025

Abstract

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which [...] Read more.

The aim of this work is to demonstrate that all linear derivatives of the tensor algebra over a smooth manifold M can be viewed as specific cases of a broader concept—the operation of derivation. This approach reveals the universal role of differentiation, which simplifies and generalizes the study of tensor derivatives, making it a powerful tool in Differential Geometry and related fields. To perform this, the generic derivative is introduced, which is defined in terms of the quantities

Q_{k}^{(i)} (X)

. Subsequently, the transformation law of these quantities is determined by the requirement that the generic derivative of a tensor is a tensor. The quantities

Q_{k}^{(i)} (X)

and their transformation law define a specific geometric object on M, and consequently, a geometric structure on M. Using the generic derivative, one defines the tensor fields of torsion and curvature and computes them for all linear derivatives in terms of the quantities

Q_{k}^{(i)} (X)

. The general model is applied to the cases of Lie derivative, covariant derivative, and Fermi derivative. It is shown that the Lie derivative has non-zero torsion and zero curvature due to the Jacobi identity. For the covariant derivative, the standard results follow without any further calculations. Concerning the Fermi derivative, this is defined in a new way, i.e., as a higher-order derivative defined in terms of two derivatives: a given derivative and the Lie derivative. Being linear derivative, it has torsion and curvature tensor. These fields are computed in a general affine space from the corresponding general expressions of the generic derivative. Applications of the above considerations are discussed in a number of cases. Concerning the Lie derivative, it is been shown that the Poisson bracket is in fact a Lie derivative. Concerning the Fermi derivative, two applications are considered: (a) the explicit computation of the Fermi derivative in a general affine space and (b) the consideration of Freedman–Robertson–Walker spacetime endowed with a scalar torsion field, which satisfies the Cosmological Principle and the computation of Fermi derivative of the spatial directions defining a spatial frame along the cosmological fluid of comoving observers. It is found that torsion, even in this highly symmetric case, induces a kinematic rotation of the space axes, questioning the interpretation of torsion as a spin. Finally it is shown that the Lie derivative of the dynamical equations of an autonomous conservative dynamical system is equivalent to the standard Lie symmetry method. Full article

(This article belongs to the Special Issue Advances in Nonlinear Systems and Symmetry/Asymmetry)

29 pages, 934 KiB

Open AccessArticle

Empowering WBANs: Enhanced Energy Efficiency Through Cluster-Based Routing and Swarm Optimization

by Sureshkumar S, Santhosh Babu A. V, Joseph James S and Priya R

Symmetry 2025, 17(1), 80; https://doi.org/10.3390/sym17010080 - 7 Jan 2025

Abstract

Wireless body area networks (WBANs) have great potential to supply society with vital technical services, but the low power of network nodes severely hampers their development. To solve this problem, Energy-Efficient, a low-power cluster-based routing system intended for precise biological data gathering in [...] Read more.

Wireless body area networks (WBANs) have great potential to supply society with vital technical services, but the low power of network nodes severely hampers their development. To solve this problem, Energy-Efficient, a low-power cluster-based routing system intended for precise biological data gathering in WBANs, is presented in this study. This approach comprises three main stages: data aggregation, cluster head (CH) selection, and cluster creation. The suggested approach balances biosensor energy and optimizes energy usage by utilizing the modified snake swarm optimization algorithm (MSSOA) for routing and the adaptive binary bird swarm optimization algorithm (ABBSOA) for cluster formation and CH selection. The suggested technique outperforms the most recent WBAN routing protocols, including MT-MAC, ALOC, DHCO, and M-GWO, by using a power-balancing routing tree and considering biosensor distance and remaining energy. The experimental results demonstrate that the proposed ABBSOA-MSSOA model achieves a jitter protocol value of 0.3 ms at 100 nodes, a buffer occupancy ratio of 2.5%, a cluster lifetime of 600 s, a cluster building time of 12.2 s, an energy consumption of 42 mJ, a communication overhead of 8.3%, a packet delivery ratio of 98.2%, and an average end-to-end delay of 25 ms compared to other existing methods. Full article

(This article belongs to the Section Engineering and Materials)

19 pages, 2223 KiB

Open AccessArticle

Mysterious Anomalies in Earth’s Atmosphere and Strongly Interacting Dark Matter

by Ariel Zhitnitsky and Marios Maroudas

Symmetry 2025, 17(1), 79; https://doi.org/10.3390/sym17010079 - 6 Jan 2025

Abstract

It has been recently argued that numerous enigmatic observations remain challenging to explain within the framework of conventional physics. These anomalies include unexpected correlations between temperature variations in the stratosphere, the total electron content of the Earth’s atmosphere, and earthquake activity on one [...] Read more.

It has been recently argued that numerous enigmatic observations remain challenging to explain within the framework of conventional physics. These anomalies include unexpected correlations between temperature variations in the stratosphere, the total electron content of the Earth’s atmosphere, and earthquake activity on one hand and the positions of planets on the other. Decades of collected data provide statistically significant evidence for these observed correlations. These works suggest that these correlations arise from strongly interacting “streaming invisible matter” which gets gravitationally focused by the solar system bodies including the Earth’s inner mass distribution. Here, we propose that some of these, as well as other anomalies, may be explained by rare yet energetic events involving the so-called axion quark nuggets (AQNs) impacting the Earth. In other words, we identify the “streaming invisible matter” conjectured in that works with AQNs, offering a concrete microscopic mechanism to elucidate the observed correlations. It is important to note that the AQN model was originally developed to address the observed similarity between the dark matter and visible matter densities in the Universe, i.e.,

Ω_{DM} \sim Ω_{visible}

, and not to explain the anomalies discussed here. Nonetheless, we support our proposal by demonstrating that the intensity and spectral characteristics of AQN-induced events are consistent with the aforementioned puzzling observations. Full article

(This article belongs to the Special Issue The Dark Universe: The Harbinger of a Major Discovery)

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29 pages, 654 KiB

Open AccessArticle

Equivalence of History and Generator ϵ-Machines

by Nicholas F. Travers and James P. Crutchfield

Symmetry 2025, 17(1), 78; https://doi.org/10.3390/sym17010078 - 6 Jan 2025

Abstract

ϵ

-Machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization though, [...] Read more.

ϵ

-Machines are minimal, unifilar presentations of stationary stochastic processes. They were originally defined in the history machine sense as hidden Markov models whose states are the equivalence classes of infinite pasts with the same probability distribution over futures. In analyzing synchronization though, an alternative generator definition was given as follows: unifilar, edge-emitting hidden Markov models with probabilistically distinct states. The key difference is that history

ϵ

-machines are defined by a process, whereas generator

ϵ

-machines define a process. We show here that these two definitions are equivalent in the finite-state case. Full article

(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)

19 pages, 2595 KiB

Open AccessArticle

The Limits of Riemann Solutions for Chaplygin Gas Magnetohydrodynamics Euler Equations with Active Terms

by Kangning Yu, Wenxia Xu, Jibin Yang, Shuo Li and Guodong Li

Symmetry 2025, 17(1), 77; https://doi.org/10.3390/sym17010077 - 6 Jan 2025

Abstract

Chaplygin gas magnetohydrodynamics Euler equations with active terms are often used to study physical phenomena in the universe, which is of great significance for exploring unknown fields. This article mainly studies the limited behavior of Riemann solutions of Chaplygin gas magnetohydrodynamics Euler equations [...] Read more.

Chaplygin gas magnetohydrodynamics Euler equations with active terms are often used to study physical phenomena in the universe, which is of great significance for exploring unknown fields. This article mainly studies the limited behavior of Riemann solutions of Chaplygin gas magnetohydrodynamics Euler equations with active terms using methods such as the characteristic line method and the Lax–Friedrichs method. In cases where only the magnetic field disappears, it was found, using the characteristic line method, that the solution converges to Chaplygin gas magnetohydrodynamics Euler equations with active terms. Additionally, we have identified the cause of the generation of

δ

shock waves. When pressure and magnetic induction disappear simultaneously, the reasons for the generation of

δ

shock waves and vacuum solutions are found. In the Discussion section, the Lax–Friedrichs method was used for numerical experiments to simulate the occurrence of phenomena such as mass concentration and vacuum. The innovation of this article lies in the construction of the Riemann problem for Chaplygin gas MHD Euler equations with active terms, as well as the study of the scenario where the magnetic field and pressure gradually weaken and approach zero. Finally, numerical experiments are used to verify the theoretical results. Compared with previous work, this article not only focuses on theoretical derivation, but also applies numerical simulation, especially simulating the characteristic lines of physical planes. This achievement provides a powerful tool for studying more complex Riemann problems. Full article

(This article belongs to the Section Mathematics)

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23 pages, 355 KiB

Open AccessArticle

On the Symmetric Form of the Three Primes Theorem Weighted by Δ(x)

by Zhen Guo

Symmetry 2025, 17(1), 76; https://doi.org/10.3390/sym17010076 - 6 Jan 2025

Abstract

Let x be a large real number,

d (n)

be the Dirichlet divisor function and

Δ (x) = \sum_{n ⩽ x} d (n) - x log x - (2 γ - 1) x

. [...] Read more.

Let x be a large real number,

d (n)

be the Dirichlet divisor function and

Δ (x) = \sum_{n ⩽ x} d (n) - x log x - (2 γ - 1) x

. In this paper, we consider a weighted form of the three primes theorem:

S (N; k_{1}, k_{2}, k_{3}) : = \sum_{p_{1} + p_{2} + p_{3} = N} Δ^{k_{1}} (p_{1}) Δ^{k_{2}} (p_{2}) Δ^{k_{3}} (p_{3}),

where

p_{1}, p_{2}, p_{3}

run over primes,

k_{1}, k_{2}, k_{3} \in {1, 2, \dots, 9}

, and N is an large odd integer. For the case

k_{i} \in {2, 3, \dots, 9}

(i = 1, 2, 3)

, the others two

k_{j} \in {2, 3, 4}

with

j \neq i

, an asymptotic formula for

S (N; k_{1}, k_{2}, k_{3})

has been derived, along with a non-trivial upper bound estimate for

S (N; k_{1}, k_{2}, k_{3})

when

min (k_{1}, k_{2}, k_{3}) = 1

. Full article

(This article belongs to the Section Mathematics)

21 pages, 6342 KiB

Open AccessArticle

Prediction of Structural Vibration Induced by Subway Operations Using Hybrid Method Based on Improved LSTM and Spectral Analysis

by Xiaolin Liu, Guoyuan Xu and Xijun Ye

Symmetry 2025, 17(1), 75; https://doi.org/10.3390/sym17010075 - 5 Jan 2025

Abstract

With the rapid expansion of urban subway networks, vibrations induced by subway operations have become an increasingly significant concern for nearby structures. To assess the influence of subway-induced vibrations on nearby structures, it is essential to predict the vibration effects accurately prior to [...] Read more.

With the rapid expansion of urban subway networks, vibrations induced by subway operations have become an increasingly significant concern for nearby structures. To assess the influence of subway-induced vibrations on nearby structures, it is essential to predict the vibration effects accurately prior to the construction of the subway system. By combining an improved Long Short-Term Memory (LSTM) model with a spectral analysis, this paper proposes a hybrid method to enhance the accuracy and efficiency of predicting structural vibrations induced by subway operations. The improved LSTM model is composed of BiLSTM, an attention mechanism, and the DBO algorithm. The symmetry inherent in the vibration propagation paths and the structural layouts of subway systems is leveraged to improve the feature extraction and modeling accuracy. Additionally, the hybrid method utilizes the symmetric properties of vibration signals in the spectral domain to enhance prediction robustness and efficiency. Then, the hybrid method is utilized to rapidly achieve highly accurate vibration responses induced by subway operations. The verification results demonstrate the following: (1) The improved LSTM model enhances the ability to recognize patterns in time-series vibration data, leading to improved model convergence and generalization. The improved LSTM mode has a significant improvement in prediction accuracy compared to the standard LSTM network. For numerical simulation and real-world measured signals, values of R² increased by 3% and 49.37%. (2) The proposed hybrid method significantly reduces computational time while ensuring results consistent with those obtained from the time-history analysis method. Applying the proposed hybrid method for data augmentation enhances the accuracy of the spectral analysis. The hybrid method achieves an improvement of 7% for the prediction accuracy. Full article

(This article belongs to the Section Engineering and Materials)

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12 pages, 3415 KiB

Open AccessArticle

Dynamics and Stability Analysis for Rope-Driven Bridge Pier Damage Detection Robot

by Xiaoyu Zhang, Junjie Xie, Yanlin Wang, Hui Dou, Yuan He and Keke Zhou

Symmetry 2025, 17(1), 74; https://doi.org/10.3390/sym17010074 - 5 Jan 2025

Abstract

In order to solve the limitations of the existing bridge pier damage detection equipment, a rope-driven bridge pier damage detection robot (RDBPDR) is proposed. Firstly, the composition of the RDBPDR system was introduced. Secondly, the kinematical and dynamical model of the RDBPDR was [...] Read more.

In order to solve the limitations of the existing bridge pier damage detection equipment, a rope-driven bridge pier damage detection robot (RDBPDR) is proposed. Firstly, the composition of the RDBPDR system was introduced. Secondly, the kinematical and dynamical model of the RDBPDR was established, and the optimization model of rope tension was given. Based on the dynamic model, the evaluation method and index of the stability of the RDBPDR were given. Finally, the distribution of the stability evaluation index of the RDBPDR in the workspace was clarified with an example calculation and analysis. The results show that the stability of the RDBPR gradually decreases from the geometric center to the boundary area in the horizontal section. With the increase in the height of the damage detection platform, the stability of the RDBPDR gradually increases in the vertical direction, but this change is not significant. It provides a basis for detection task planning, overall structure configuration, and prototype testing in the future. Full article

(This article belongs to the Special Issue Symmetry in Robot Design and Application)

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22 pages, 1579 KiB

Open AccessArticle

Spillover Effects of Currency Interactions Across Economic Cycles: A Quantile-VAR Analysis

by Zhuqin Liang and Mohd Tahir Ismail

Symmetry 2025, 17(1), 73; https://doi.org/10.3390/sym17010073 - 4 Jan 2025

Abstract

This study employs Markov-Switching Regression (MS-Regression) to model four macroeconomic indicators—US GDP, CPI, interest rate, and unemployment rate—to identify economic crisis cycles, while all indicators provide some level of insight into these cycles, the unemployment rate offers the closest alignment with the actual [...] Read more.

This study employs Markov-Switching Regression (MS-Regression) to model four macroeconomic indicators—US GDP, CPI, interest rate, and unemployment rate—to identify economic crisis cycles, while all indicators provide some level of insight into these cycles, the unemployment rate offers the closest alignment with the actual patterns of economic cycles. Based on the regime identification derived from the unemployment rate, we delineate the time series for expansion and recession periods. Subsequently, we apply the Quantile Vector Autoregression (Quantile-VAR) model to analyze three sets of time series: the entire dataset, the expansion period, and the recession period. Our findings reveal that, under normal conditions, the US dollar exerts the greatest influence on and is most influenced by other currencies, whereas the Australian dollar has the least impact on others. In the extreme lower and upper tails, the mutual influence among the currencies of different countries intensifies, concurrently diminishing the relative influence of the US dollar. Notably, the spillover effects under extreme lower and upper tail conditions are not consistent, as the occurrence of extreme values does not coincide, suggesting an asymmetry in the spillover effects at these quantiles. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Multivariate Statistics and Data Science, Second Edition)

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23 pages, 13359 KiB

Open AccessArticle

The Design of the Flight Corridor for the Terminal Area Energy Management Phase of Gliding Hypersonic Unmanned Aerial Vehicles

by Jingang Wang, Yichong Shao, Cheng Chen and Zian Wang

Symmetry 2025, 17(1), 72; https://doi.org/10.3390/sym17010072 - 4 Jan 2025

Abstract

This paper introduces an innovative approach to optimizing flight corridors under complex constraints, particularly focusing on the Terminal Area Energy Management (TAEM) phases of reusable vehicles, where nominal trajectories may be inadequate due to initial condition and aerodynamic deviations. Leveraging the elegant principles [...] Read more.

This paper introduces an innovative approach to optimizing flight corridors under complex constraints, particularly focusing on the Terminal Area Energy Management (TAEM) phases of reusable vehicles, where nominal trajectories may be inadequate due to initial condition and aerodynamic deviations. Leveraging the elegant principles of symmetry, the proposed optimal flight corridor design method, based on the Lagrange multiplier technique, offers a harmonious balance between trajectory accuracy and adaptability. By describing the TAEM flight corridor through a range–altitude profile and utilizing iterative optimization to uphold physical constraints such as dynamic pressure, overload, and roll angle, this method ensures symmetrical alignment of the design parameters. Through a comprehensive analysis of aerodynamic and initial position uncertainties, this method showcases exceptional symmetry in adapting to trajectory design uncertainties. The simulation results demonstrate the resilient nature of the designed flight corridor, capable of seamlessly accommodating initial state deviations and aerodynamic uncertainties. This symmetrical optimization of flight corridors not only enhances trajectory planning and control capabilities during the terminal energy management phase, but also showcases a paradigm shift towards precision and balance in aerospace engineering. Our simulation findings underscore the efficiency of this approach by reducing the flight corridor range by 50% compared to the nominal state while maintaining robustness across deviation conditions, embodying the symmetrical resilience needed for optimal trajectory design. Full article

(This article belongs to the Section Computer)

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12 pages, 7432 KiB

Open AccessArticle

Effect of TiS₂ on Hydrogen Absorption and Desorption Performance of Mechanically Ball-Milled Mg₉₅Ce₅ Alloy

by Haitao Lv, Liangrui Wang, Xiulong Ou and Zhiming Li

Symmetry 2025, 17(1), 71; https://doi.org/10.3390/sym17010071 - 4 Jan 2025

Abstract

Magnesium-based materials have been considered to be potential hydrogen storage materials due to their high hydrogen storage capacity and abundance in natural resources. In order to improve the hydrogen storage performance of magnesium-based materials, a Mg₉₅Ce₅ alloy was prepared by [...] Read more.

Magnesium-based materials have been considered to be potential hydrogen storage materials due to their high hydrogen storage capacity and abundance in natural resources. In order to improve the hydrogen storage performance of magnesium-based materials, a Mg₉₅Ce₅ alloy was prepared by using the vacuum induction melting method. Moreover, TiS₂ was used as a catalyst, and a series of Mg₉₅Ce₅ + x wt% TiS₂ (x = 0, 3, 5 and 10) composites with different TiS₂ contents were prepared by the mechanical ball-milling method. The addition of TiS₂ as a catalyst broke the inherent symmetry of the Mg₉₅Ce₅ alloy at both the atomic and defect levels, potentially improving hydrogen storage by modifying hydrogen diffusion pathways and interaction sites. The structural analysis results indicate that the Mg₉₅Ce₅ alloy is composed of Mg and CeMg₁₂ phases. After the hydrogenation process, the Mg and CeMg₁₂ phases in the Mg₉₅Ce₅–TiS₂ composites transformed into CeH_2.73 and MgH₂. In addition, CeS₂ and TiH_1.5 could be detected in the hydrogenated samples, indicating that the TiS₂ decomposed and changed into CeS₂ and TiH_1.5 during the hydrogenation reaction. Adding TiS₂ to Mg₉₅Ce₅ alloy could significantly improve the hydrogen absorption and desorption kinetic properties, and the dehydrogenation peak temperature of the composites was reduced from 389.5 °C to 329.7 °C when the TiS₂ content increased from 0 to 10 wt%. However, the addition of TiS₂ inevitably reduced the reversable hydrogen storage capacity of the composites. The hydrogen absorption and desorption thermodynamic measurement results indicate that the TiS₂ catalyst has almost no influence on the enthalpy and entropy changes of the composites during the hydrogenation process. Full article

(This article belongs to the Section Engineering and Materials)

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28 pages, 1127 KiB

Open AccessArticle

Prioritized Decision Support System for Cybersecurity Selection Based on Extended Symmetrical Linear Diophantine Fuzzy Hamacher Aggregation Operators

by Muhammad Zeeshan Hanif and Naveed Yaqoob

Symmetry 2025, 17(1), 70; https://doi.org/10.3390/sym17010070 - 3 Jan 2025

Abstract

The symmetrical linear Diophantine fuzzy Hamacher aggregation operators play a fundamental role in many decision-making applications. The selection of a cyber security system is of paramount importance for maintaining digital assets. It necessitates a comprehensive review of threat landscapes, vulnerability assessments, and the [...] Read more.

The symmetrical linear Diophantine fuzzy Hamacher aggregation operators play a fundamental role in many decision-making applications. The selection of a cyber security system is of paramount importance for maintaining digital assets. It necessitates a comprehensive review of threat landscapes, vulnerability assessments, and the specific needs of the organization in order to ensure the implementation of effective security measures. Smart grid (SG) technology uses modern communication and monitoring technologies to enhance the management and regulation of electricity production and transmission. However, greater dependence on technology and connection creates new vulnerabilities, exposing SG communication networks to large-scale attacks. Unlike previous surveys, which often give broad overviews of SG design, our research goes a step further, giving a full architectural layout that includes major SG components and communication linkages. This in-depth review improves comprehension of possible cyber threats and allows SGs to analyze cyber risks more systematically. To determine the best cybersecurity strategies, this study introduces a multi-criteria group decision-making (MCGDM) approach using the linear Diophantine fuzzy Hamacher prioritized aggregation operator (LDFHPAO). In real-world applications, aggregation operators (AOs) are essential for information fusion. This research presents innovative prioritized AOs designed to address MCGDM problems in uncertain environments. We developed the LDF Hamacher prioritized weighted average (LDFHPWA) and LDF Hamacher prioritized weighted geometric (LDFHPWG) operators, which address the shortcomings of traditional operators and provide a more robust modeling approach for MCGDM challenges. This study also outlines key characteristics of these new prioritized AOs. An MCGDM approach incorporating these operators is proposed and demonstrated to be effective through an example that compares and selects the optimal cybersecurity. Full article

(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)

22 pages, 1021 KiB

Open AccessArticle

Sharp Front Approach Solutions to Some Doubly Degenerate Reaction-Diffusion Models

by Jordan Hristov

Symmetry 2025, 17(1), 69; https://doi.org/10.3390/sym17010069 - 3 Jan 2025

Abstract

Approximate analytical solutions to doubly degenerate reaction-diffusion models pertinent to population dynamics and chemical kinetics have been developed. The double integral-balance method applied to preliminary transformed models and by a direct integration approach has provided physically reasonable results. The model equation scaling has [...] Read more.

Approximate analytical solutions to doubly degenerate reaction-diffusion models pertinent to population dynamics and chemical kinetics have been developed. The double integral-balance method applied to preliminary transformed models and by a direct integration approach has provided physically reasonable results. The model equation scaling has revealed the time and length scales, as well as the characteristic velocity of the process and the Fourier number as the controlling dimensionless group. Full article

(This article belongs to the Section Mathematics)

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36 pages, 448 KiB

Open AccessArticle

A Robust-Fitted-Mesh-Based Finite Difference Approach for Solving a System of Singularly Perturbed Convection–Diffusion Delay Differential Equations with Two Parameters

by Jenolin Arthur, George E. Chatzarakis, S. L. Panetsos and Joseph Paramasivam Mathiyazhagan

Symmetry 2025, 17(1), 68; https://doi.org/10.3390/sym17010068 - 3 Jan 2025

Abstract

This paper presents a robust fitted mesh finite difference method for solving a dynamical system of two parameter convection–reaction–diffusion delay differential equations defined on the interval

[0, 2]

. The method incorporates a piecewise uniform Shishkin mesh to accurately resolve [...] Read more.

This paper presents a robust fitted mesh finite difference method for solving a dynamical system of two parameter convection–reaction–diffusion delay differential equations defined on the interval

[0, 2]

. The method incorporates a piecewise uniform Shishkin mesh to accurately resolve the solution behavior caused by small perturbation parameters and delay terms. The proposed numerical scheme is proven to be parameter-robust and achieves almost first-order convergence. Numerical illustrations are provided to showcase the method’s effectiveness, highlighting its capability to address boundary and interior layers with improved accuracy. The results, supported by symmetrical considerations in the figures, enhance the precision and serve as validation for the theoretical results. Full article

(This article belongs to the Section Mathematics)

23 pages, 4257 KiB

Open AccessArticle

Dynamic Task Allocation for Collaborative Data Collection: A Vehicle–Drone Approach

by Geng Wu, Jing Lu, Dai Hou, Lei Zheng, Di Han, Haohua Meng, Fei Long, Lijun Luo and Kai Peng

Symmetry 2025, 17(1), 67; https://doi.org/10.3390/sym17010067 - 2 Jan 2025

Abstract

In recent years, unmanned aerial vehicles (UAVs, also known as drones) have gained widespread application in fields such as data collection and inspection, owing to their lightweight design and high mobility. However, due to limitations in battery life, UAVs are often unable to [...] Read more.

In recent years, unmanned aerial vehicles (UAVs, also known as drones) have gained widespread application in fields such as data collection and inspection, owing to their lightweight design and high mobility. However, due to limitations in battery life, UAVs are often unable to independently complete large-scale data collection tasks. To address this limitation, vehicle–drone collaborative data collection has emerged as an effective solution. Existing research, however, primarily focuses on collaborative work in static task scenarios, overlooking the complexities of dynamic environments. In dynamic scenarios, tasks may arrive during the execution of both the vehicle and UAV, and each drone has different positions and remaining endurance, creating an asymmetric state. This introduces new challenges for path planning. To tackle this challenge, we propose a 0–1 integer programming model aimed at minimizing the total task completion time. Additionally, we introduce an efficient dynamic solving algorithm, referred to as Greedy and Adaptive Memory Process-based Dynamic Algorithm (GAMPDA). This algorithm first generates an initial global data collection plan based on the initial task nodes and dynamically adjusts the current data collection scheme using a greedy approach as new task nodes arrive during execution. Through comparative experiments, it was demonstrated that GAMPDA outperforms SCAN and LKH in terms of time cost, vehicle travel distance, and drone flight distance and approaches the ideal results. GAMPDA significantly enhances task completion efficiency in dynamic scenarios, providing an effective solution for collaborative data collection tasks in such environments. Full article

(This article belongs to the Section Computer)

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14 pages, 5970 KiB

Open AccessArticle

Universal Image Vaccine Against Steganography

by Shiyu Wei, Zichi Wang and Xinpeng Zhang

Symmetry 2025, 17(1), 66; https://doi.org/10.3390/sym17010066 - 2 Jan 2025

Abstract

In the past decade, the diversification of steganographic techniques has posed significant threats to information security, necessitating effective countermeasures. Current defenses, mainly reliant on steganalysis, struggle with detection accuracy. While “image vaccines” have been proposed, they often target specific methodologies. This paper introduces [...] Read more.

In the past decade, the diversification of steganographic techniques has posed significant threats to information security, necessitating effective countermeasures. Current defenses, mainly reliant on steganalysis, struggle with detection accuracy. While “image vaccines” have been proposed, they often target specific methodologies. This paper introduces a universal steganographic vaccine to enhance steganalysis accuracy. Our symmetric approach integrates with existing methods to protect images before online dissemination using the Contrast Limited Adaptive Histogram Equalization (CLAHE) algorithm. Experimental results show significant accuracy improvements across traditional and deep learning-based steganalysis, especially at medium-to-high payloads. Specifically, for payloads of 0.1–0.5 bpp, the original detection error rate was reduced from 0.3429 to 0.2346, achieving an overall average reduction of 31.57% for traditional algorithms, while the detection success rate of deep learning-based algorithms can reach 100%. Overall, integrating CLAHE as a universal vaccine significantly advances steganalysis. Full article

(This article belongs to the Special Issue Security, Communication and Privacy in Internet of Things: Symmetry and Advances — Volume II)

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