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
Short-Term Electrical Load Forecasting Using an Enhanced Extreme Learning Machine Based on the Improved Dwarf Mongoose Optimization Algorithm
Symmetry 2024, 16(5), 628; https://doi.org/10.3390/sym16050628 (registering DOI) - 18 May 2024
Abstract
Accurate short-term electrical load forecasting is crucial for the stable operation of power systems. Given the nonlinear, periodic, and rapidly changing characteristics of short-term power load forecasts, this paper introduces a novel forecasting method employing an Extreme Learning Machine (ELM) enhanced by an
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Accurate short-term electrical load forecasting is crucial for the stable operation of power systems. Given the nonlinear, periodic, and rapidly changing characteristics of short-term power load forecasts, this paper introduces a novel forecasting method employing an Extreme Learning Machine (ELM) enhanced by an improved Dwarf Mongoose Optimization Algorithm (Local escape Dwarf Mongoose Optimization Algorithm, LDMOA). This method addresses the significant prediction errors of conventional ELM models and enhances prediction accuracy. The enhancements to the Dwarf Mongoose Optimization Algorithm include three key modifications: initially, a dynamic backward learning strategy is integrated at the early stages of the algorithm to augment its global search capabilities. Subsequently, a cosine algorithm is employed to locate new food sources, thereby expanding the search scope and avoiding local optima. Lastly, a “madness factor” is added when identifying new sleeping burrows to further widen the search area and effectively circumvent local optima. Comparative analyses using benchmark functions demonstrate the improved algorithm’s superior convergence and stability. In this study, the LDMOA algorithm optimizes the weights and thresholds of the ELM to establish the LDMOA-ELM prediction model. Experimental forecasts utilizing data from China’s 2016 “The Electrician Mathematical Contest in Modeling” demonstrate that the LDMOA-ELM model significantly outperforms the original ELM model in terms of prediction error and accuracy.
Full article
(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)
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Open AccessArticle
Best Proximity Point Results via Simulation Function with Application to Fuzzy Fractional Differential Equations
by
Ghada Ali, Nawab Hussain and Abdelhamid Moussaoui
Symmetry 2024, 16(5), 627; https://doi.org/10.3390/sym16050627 - 17 May 2024
Abstract
In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for
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In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations.
Full article
(This article belongs to the Special Issue Symmetry in Metric Spaces and Topology)
Open AccessArticle
Sedenion Algebra Model as an Extension of the Standard Model and Its Link to SU(5)
by
Qiang Tang and Jau Tang
Symmetry 2024, 16(5), 626; https://doi.org/10.3390/sym16050626 - 17 May 2024
Abstract
In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an
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In the Standard Model, ad hoc hypotheses assume the existence of three generations of point-like leptons and quarks, which possess a point-like structure and follow the Dirac equation involving four anti-commutative matrices. In this work, we consider the sedenion hypercomplex algebra as an extension of the Standard Model and show its close link to SU(5), which is the underlying symmetry group for the grand unification theory (GUT). We first consider the direct-product quaternion model and the eight-element octonion algebra model. We show that neither the associative quaternion model nor the non-associative octonion model could generate three fermion generations. Instead, we show that the sedenion model, which contains three octonion sub-algebras, leads naturally to precisely three fermion generations. Moreover, we demonstrate the use of basis sedenion operators to construct twenty-four 5 × 5 generalized lambda matrices representing SU(5) generators, in analogy to the use of octonion basis operators to generate Gell-Mann’s eight 3 × 3 lambda-matrix generators for SU(3). Thus, we provide a link between the sedenion algebra and Georgi and Glashow’s SU(5) GUT model that unifies the electroweak and strong interactions for the Standard Model’s elementary particles, which obey SU(3)SU(2)U(1) symmetry.
Full article
(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)
Open AccessArticle
Inference for Compound Exponential XLindley Model with Applications to Lifetime Data
by
Fatimah M. Alghamdi, Mohammed Amine Meraou, Hassan M. Aljohani, Amani Alrumayh, Fathy H. Ryad, Sara Mohamed Ahmed Alsheikh and Meshayil M. Alsolmi
Symmetry 2024, 16(5), 625; https://doi.org/10.3390/sym16050625 - 17 May 2024
Abstract
The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric,
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The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.
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(This article belongs to the Section Mathematics)
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Open AccessArticle
An Effective Method for the Evaluation of the Enantiomeric Purity of 1,2-Diacyl-sn-glycero-3-phosphocholine-Based Lipids by NMR Analysis
by
Antonia Di Mola, Lorenzo de Ferra, Mauro Anibaldi, Guglielmo Monaco and Antonio Massa
Symmetry 2024, 16(5), 624; https://doi.org/10.3390/sym16050624 - 17 May 2024
Abstract
In this article, we report a very efficient method for the determination of the enantiopurity of 1,2-diacyl-sn-glycero-3-phosphocholine by 1H NMR analysis using a readily available chiral derivatizing boronic acid (CDA), (R)-(2-(((1-phenylethyl)amino)methyl)phenyl)boronic acid. After the removal of the acyl
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In this article, we report a very efficient method for the determination of the enantiopurity of 1,2-diacyl-sn-glycero-3-phosphocholine by 1H NMR analysis using a readily available chiral derivatizing boronic acid (CDA), (R)-(2-(((1-phenylethyl)amino)methyl)phenyl)boronic acid. After the removal of the acyl groups of 1,2-diacyl-sn-glycero-3-phosphocholine via methanolysis and washing fatty acid byproducts with CHCl3, the obtained sn-glycero-3-phosphocholine (GPC) with the free diol moiety is derivatized by the chiral boronic acid and analyzed by 1H NMR analysis. The choline methyl resonance of each diastereomer is observed at distinctive chemical shifts in the 1H NMR spectrum. Integration of the respective resonances allows direct determination of the enantiomeric purity. The procedure was tested successfully using 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) with different enantiomeric purities and with commercially available 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC).
Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Medicinal Chemistry)
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Open AccessArticle
An Improved BGE-Adam Optimization Algorithm Based on Entropy Weighting and Adaptive Gradient Strategy
by
Yichuan Shao, Jiantao Wang, Haijing Sun, Hao Yu, Lei Xing, Qian Zhao and Le Zhang
Symmetry 2024, 16(5), 623; https://doi.org/10.3390/sym16050623 - 17 May 2024
Abstract
This paper introduces an enhanced variant of the Adam optimizer—the BGE-Adam optimization algorithm—that integrates three innovative technologies to augment the adaptability, convergence, and robustness of the original algorithm under various training conditions. Firstly, the BGE-Adam algorithm incorporates a dynamic parameter adjustment mechanism
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This paper introduces an enhanced variant of the Adam optimizer—the BGE-Adam optimization algorithm—that integrates three innovative technologies to augment the adaptability, convergence, and robustness of the original algorithm under various training conditions. Firstly, the BGE-Adam algorithm incorporates a dynamic parameter adjustment mechanism that utilizes the rate of gradient variations to dynamically adjust the exponential decay rates of the first and second moment estimates ( and ), the adjustment of and is symmetrical, which means that the rules that the algorithm considers when adjusting and are the same. This design helps to maintain the consistency and balance of the algorithm, allowing the optimization algorithm to adaptively capture the trending movements of gradients. Secondly, it estimates the direction of future gradients by a simple gradient prediction model, combining historic gradient information with the current gradient. Lastly, entropy weighting is integrated into the gradient update step. This strategy enhances the model’s exploratory nature by introducing a certain amount of noise, thereby improving its adaptability to complex loss surfaces. Experimental results on classical datasets, MNIST and CIFAR10, and gastrointestinal disease medical datasets demonstrate that the BGE-Adam algorithm has improved convergence and generalization capabilities. In particular, on the specific medical image gastrointestinal disease test dataset, the BGE-Adam optimization algorithm achieved an accuracy of 69.36%, a significant improvement over the 67.66% accuracy attained using the standard Adam algorithm; on the CIFAR10 test dataset, the accuracy of the BGE-Adam algorithm reached 71.4%, which is higher than the 70.65% accuracy of the Adam optimization algorithm; and on the MNIST dataset, the BGE-Adam algorithm’s accuracy was 99.34%, surpassing the Adam optimization algorithm’s accuracy of 99.23%. The BGE-Adam optimization algorithm exhibits better convergence and robustness. This research not only demonstrates the effectiveness of the combination of these three technologies but also provides new perspectives for the future development of deep learning optimization algorithms.
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(This article belongs to the Section Computer)
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Open AccessArticle
A Blockchain-Based Privacy Preserving Intellectual Property Authentication Method
by
Shaoqi Yuan, Wenzhong Yang, Xiaodan Tian and Wenjie Tang
Symmetry 2024, 16(5), 622; https://doi.org/10.3390/sym16050622 - 17 May 2024
Abstract
With the continuous advancement of information technology, a growing number of works, including articles, paintings, and music, are being digitized. Digital content can be swiftly shared and disseminated via the Internet. However, it is also vulnerable to malicious plagiarism, which can seriously infringe
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With the continuous advancement of information technology, a growing number of works, including articles, paintings, and music, are being digitized. Digital content can be swiftly shared and disseminated via the Internet. However, it is also vulnerable to malicious plagiarism, which can seriously infringe upon the rights of creators and dampen their enthusiasm. To protect creators’ rights and interests, a sophisticated method is necessary to authenticate digital intellectual property rights. Traditional authentication methods rely on centralized, trustworthy organizations that are susceptible to single points of failure. Additionally, these methods are prone to network attacks that can lead to data loss, tampering, or leakage. Moreover, the circulation of copyright information often lacks transparency and traceability in traditional systems, which leads to information asymmetry and prevents creators from controlling the use and protection of their personal information during the authentication process. Blockchain technology, with its decentralized, tamper-proof, and traceable attributes, addresses these issues perfectly. In blockchain technology, each node is a peer, ensuring the symmetry of information. However, the transparent feature of blockchains can lead to the leakage of user privacy data. Therefore, this study designs and implements an Ethereum blockchain-based intellectual property authentication scheme with privacy protection. Firstly, we propose a method that combines elliptic curve cryptography (ECC) encryption with digital signatures to achieve selective encryption of user personal information. Subsequently, an authentication algorithm based on Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (zk-SNARK) is adopted to complete the authentication of intellectual property ownership while encrypting personal privacy data. Finally, we adopt the InterPlanetary File System (IPFS) to store large files, solving the problem of blockchain storage space limitations.
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(This article belongs to the Section Computer)
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Open AccessEditorial
Symmetry and Symmetry-Breaking in Fluid Dynamics
by
Andrzej Herczyński and Roberto Zenit
Symmetry 2024, 16(5), 621; https://doi.org/10.3390/sym16050621 - 17 May 2024
Abstract
It may seem that the heading of this Special Issue of Symmetry—though narrower than the famous all-inclusive title of an essay by Jean-Paul Sartre, Being and Nothingness—encompasses most, if not all, fluid phenomena [...]
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(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)
Open AccessArticle
Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory
by
Saira Javed
Symmetry 2024, 16(5), 620; https://doi.org/10.3390/sym16050620 - 16 May 2024
Abstract
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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were
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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and associated eigenvector of spline coefficients. The frequency of shells was analysed by varying the geometric parameters such as length of shell, cone angle, node number in circumference direction and number of layers, as well as three thickness variations such as linear, sinusoidal and exponential. It was also evident that by varying geometrical parameters, the mechanical parameters such as stress, moment and shear resultants were affected. Research results concluded that for three different thickness variations, as the number of layers of conical shells increases, the frequency values decrease. Moreover, by varying length ratios and cone angles, shells with variable thickness had lower frequency values compared to shells of constant thickness. The numerical results obtained were verified through the already existing literature. It is evident that the present results are very close to the already existing literature.
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Open AccessArticle
Effect of Salt Solution Tracer Dosage on the Transport and Mixing of Tracer in a Water Model of Asymmetrical Gas-Stirred Ladle with a Moderate Gas Flowrate
by
Linbo Li, Chao Chen, Xin Tao, Hongyu Qi, Tao Liu, Qiji Yan, Feng Deng, Arslan Allayev, Wanming Lin and Jia Wang
Symmetry 2024, 16(5), 619; https://doi.org/10.3390/sym16050619 - 16 May 2024
Abstract
In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow
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In previous research simulating steelmaking ladles using cold water models, the dosage/volume of the salt tracer solution is one of the factors that has been overlooked by researchers to a certain extent. Previous studies have demonstrated that salt tracers may influence the flow and measured mixing time of fluids in water models. Based on a water model scaled down from an industrial 130-ton ladle by a ratio of 1:3, this study investigates the impact of salt tracer dosage on the transport and mixing of tracers in the water model of gas-stirred ladle with a moderate gas flow rate. A preliminary uncertainty analysis of the experimental mixing time is performed, and the standard deviations were found to be less than 15%. It was observed in the experiments that the transport paths of tracers in the ladle can be classified into two trends. A common trend is that the injected salt solution tracer is asymmetrically transported towards the left sidewall of the ladle by the main circulation. In another trend, the injected salt solution tracer is transported both by the main circulation to the left side wall and by downward flow towards the gas column. The downward flow may be accelerated and become a major flow pattern when the tracer volume increases. For the dimensionless concentration curve, the sinusoidal type, which represents a rapid mixing, is observed at the top surface monitoring points, while the parabolic type is observed at the bottom monitoring points. An exception is the monitoring point at the right-side bottom (close to the asymmetric gas nozzle area), where both sinusoidal-type and parabolic-type curves are observed. Regarding the effect of tracer volume on the curve and mixing time, the curves at the top surface monitoring points are less influenced but curves at the bottom monitoring points are noticeably influenced by the tracer volume. A trend of decreasing and then increasing as the tracer volume increases was found at the top surface monitoring points, while the mixing times at the bottom monitoring points decrease with the increase in the tracer volume.
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(This article belongs to the Special Issue Symmetry and Its Applications in Experimental Fluid Mechanics)
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The Dynamical and Kinetic Equations of Four-Five-Six-Wave Resonance for Ocean Surface Gravity Waves in Water with a Finite Depth
by
Guobin Lin
Symmetry 2024, 16(5), 618; https://doi.org/10.3390/sym16050618 - 16 May 2024
Abstract
Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions , the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant
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Based on the Hamilton canonical equations for ocean surface waves with four-five-six-wave resonance conditions , the determinate dynamical equation of four-five-six-wave resonances for ocean surface gravity waves in water with a finite depth is established, thus leading to the elimination of the nonresonant second-, third-, fourth-, and fifth-order nonlinear terms though a suitable canonical transformation. The four kernels of the equation and the 18 coefficients of the transformation are expressed in explicit form in terms of the expansion coefficients of the gravity wave Hamiltonian in integral-power series in normal variables. The possibilities of the existence of integrals of motion for the wave momentum and the wave action are discussed, particularly the special integrals for the latter. For ocean surface capillary–gravity waves on a fluid with a finite depth, the sixth-order expansion coefficients of the Hamiltonian in integral-power series in normal variables are concretely provided, thus naturally including the classical fifth-order kinetic energy expansion coefficients given by Krasitskii.
Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
Open AccessArticle
High-Order Extended Kalman Filter for State Estimation of Nonlinear Systems
by
Linwang Ding and Chenglin Wen
Symmetry 2024, 16(5), 617; https://doi.org/10.3390/sym16050617 - 16 May 2024
Abstract
In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to
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In general, the extended Kalman filter (EKF) has a wide range of applications, aiming to minimize symmetric loss function (mean square error) and improve the accuracy and efficiency of state estimation. As the nonlinear model complexity increases, rounding errors gradually amplify, leading to performance degradation. After multiple iterations, divergence may occur. The traditional extended Kalman filter cannot accurately estimate the nonlinear model, and these errors still have an impact on the accuracy. To improve the filtering performance of the extended Kalman filter (EKF), this paper proposes a new extended Kalman filter (REKF) method that utilizes the statistical properties of the rounding error to enhance the estimation accuracy. After establishing the state model and measurement model, the residual term is used to replace the higher-order term in the Taylor expansion, and the least squares method is applied to identify the residual term step by step. Then, the iterative process of updating the extended Kalman filter is carried out. Within the Kalman filter framework, a higher-order rounding error-based extended Kalman filter (REKF) is designed for the joint estimation of rounding error and random variables, and the solution method for the rounding error is considered for the multilevel approximation of the original function. Through numerical simulations on a general nonlinear model, the higher-order rounding error-based extended Kalman filter (REKF) achieves better estimation results than the extended Kalman filter (EKF) and improves the filtering accuracy by utilizing the higher-order rounding error information, which also proves the effectiveness of the proposed method.
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(This article belongs to the Section Engineering and Materials)
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Open AccessArticle
A Transformer and LSTM-Based Approach for Blind Well Lithology Prediction
by
Danyan Xie, Zeyang Liu, Fuhao Wang and Zhenyu Song
Symmetry 2024, 16(5), 616; https://doi.org/10.3390/sym16050616 - 16 May 2024
Abstract
Petrographic prediction is crucial in identifying target areas and understanding reservoir lithology in oil and gas exploration. Traditional logging methods often rely on manual interpretation and experiential judgment, which can introduce subjectivity and constraints due to data quality and geological variability. To enhance
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Petrographic prediction is crucial in identifying target areas and understanding reservoir lithology in oil and gas exploration. Traditional logging methods often rely on manual interpretation and experiential judgment, which can introduce subjectivity and constraints due to data quality and geological variability. To enhance the precision and efficacy of lithology prediction, this study employed a Savitzky–Golay filter with a symmetric window for anomaly data processing, coupled with a residual temporal convolutional network (ResTCN) model tasked with completing missing logging data segments. A comparative analysis against the support vector regression and random forest regression model revealed that the ResTCN achieves the smallest MAE, at 0.030, and the highest coefficient of determination, at 0.716, which are indicative of its proximity to the ground truth. These methodologies significantly enhance the quality of the training data. Subsequently, a Transformer–long short-term memory (T-LS) model was applied to identify and classify the lithology of unexplored wells. The input layer of the Transformer model follows an embedding-like principle for data preprocessing, while the encoding block encompasses multi-head attention, Add & Norm, and feedforward components, integrating the multi-head attention mechanism. The output layer interfaces with the LSTM layer through dropout. A performance evaluation of the T-LS model against established rocky prediction techniques such as logistic regression, k-nearest neighbor, and random forest demonstrated its superior identification and classification capabilities. Specifically, the T-LS model achieved a precision of 0.88 and a recall of 0.89 across nine distinct lithology features. A Shapley analysis of the T-LS model underscored the utility of amalgamating multiple logging data sources for lithology classification predictions. This advancement partially addresses the challenges associated with imprecise predictions and limited generalization abilities inherent in traditional machine learning and deep learning models applied to lithology identification, and it also helps to optimize oil and gas exploration and development strategies and improve the efficiency of resource extraction.
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(This article belongs to the Special Issue Advances in Computer Vision, Pattern Recognition, Machine Learning and Symmetry)
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Open AccessArticle
A Systematic Formulation into Neutrosophic Z Methodologies for Symmetrical and Asymmetrical Transportation Problem Challenges
by
Muhammad Kamran, Manal Elzain Mohamed Abdalla, Muhammad Nadeem, Anns Uzair, Muhammad Farman, Lakhdar Ragoub and Ismail Naci Cangul
Symmetry 2024, 16(5), 615; https://doi.org/10.3390/sym16050615 - 15 May 2024
Abstract
This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the
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This study formulates a multi-objective, multi-item solid transportation issue with parameters that are neutrosophic Z-number fuzzy variables such as transportation costs, supplies, and demands. This work covers two scenarios where uncertainty in the problem can arise: the fuzzy solid transportation problem and the interval solid transportation problem. The first scenario arises when we represent data problems as intervals instead of exact values, while the second scenario arises when the information is not entirely clear. We address both models when the uncertainty alone impacts the constraint set. In order to find a solution for the interval case, we generate an additional problem. Since this auxiliary problem is typical of solid transportation, we can resolve it using the effective techniques currently in use. In the fuzzy scenario, a parametric method is used to discover a fuzzy solution to the earlier issue. Parametric analysis identifies that the best parameterized approaches to complementary problems are characterized by the application of parametric analysis. We present a suggested algorithm for determining the stability set. Finally, we provide a numerical example and sensitivity analysis for the transportation problem, which is both symmetrical and asymmetrical.
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(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)
Open AccessArticle
Belief Reliability Modeling Method for Wind Farms Considering Two-Directional Rotor Equivalent Wind Speed
by
Shuyu Li, Rui Kang, Meilin Wen and Tianpei Zu
Symmetry 2024, 16(5), 614; https://doi.org/10.3390/sym16050614 - 15 May 2024
Abstract
Compared to conventional energy sources, wind power is a clean energy source with high intermittence and uncertainty. As a system that converts wind energy into electricity, wind farms inevitably face severe reliability issues. In this paper, based on reliability theory, a new reliability
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Compared to conventional energy sources, wind power is a clean energy source with high intermittence and uncertainty. As a system that converts wind energy into electricity, wind farms inevitably face severe reliability issues. In this paper, based on reliability theory, a new reliability modeling method for wind farms is proposed. Firstly, a belief reliability model for wind farms is constructed. Then, a power generation model based on two-directional rotor equivalent wind speed is established to represent the wind farm performance in the belief reliability model. Finally, several numerical studies are conducted to verify the power generation model under different wind speeds and directions, to demonstrate the belief reliability model with different levels of uncertainty, and to compare the belief reliability considering two-directional rotor equivalent wind speed with other methods.
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(This article belongs to the Special Issue Advances and Applications of Uncertainty Theory in Reliability and Systems Engineering)
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On Neutrosophic Fuzzy Metric Space and Its Topological Properties
by
Samriddhi Ghosh, Sonam, Ramakant Bhardwaj and Satyendra Narayan
Symmetry 2024, 16(5), 613; https://doi.org/10.3390/sym16050613 - 15 May 2024
Abstract
The present research introduces a novel concept termed “neutrosophic fuzzy metric space”, which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric
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The present research introduces a novel concept termed “neutrosophic fuzzy metric space”, which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric space has been conducted. Additionally, counterparts of well-known theorems such as the Uniform Convergence Theorem and the Baire Category Theorem have been established for this generalized metric space. Through rigorous analysis, a detailed understanding of its fundamental characteristics has been attained, illuminating its potential applications and theoretical significance.
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(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)
Open AccessArticle
Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment
by
Chunwei Wang, Shujing Wang, Jiaen Xu and Shaohua Li
Symmetry 2024, 16(5), 612; https://doi.org/10.3390/sym16050612 - 15 May 2024
Abstract
In order to deal with complex risk scenarios involving claims, uncertainty, and investments, we consider the ruin problems in a compound Poisson risk model with liquid reserves and proportional investments and study the expected discounted penalty function under threshold dividend strategies. Firstly, the
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In order to deal with complex risk scenarios involving claims, uncertainty, and investments, we consider the ruin problems in a compound Poisson risk model with liquid reserves and proportional investments and study the expected discounted penalty function under threshold dividend strategies. Firstly, the integral differential equation of the expected discounted penalty function is derived. Secondly, since the closed-form solution of the equation cannot be obtained, a sinc method is used to obtain the numerical approximation solution of the equation. Finally, the feasibility and superiority of the sinc method are illustrated by error analysis. In addition, based on a symmetric jump risk market, we discuss the influence of some parameters on the ruin probability with some examples. This study can help actuaries develop more robust risk management strategies and ensure the long-term stability and profitability of insurance companies. It provides a theoretical basis for actuaries to carry out risk management.
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(This article belongs to the Section Mathematics)
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A New Modification of the Weibull Distribution: Model, Theory, and Analyzing Engineering Data Sets
by
Huda M. Alshanbari, Zubair Ahmad, Abd Al-Aziz Hosni El-Bagoury, Omalsad Hamood Odhah and Gadde Srinivasa Rao
Symmetry 2024, 16(5), 611; https://doi.org/10.3390/sym16050611 - 15 May 2024
Abstract
Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the
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Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al2O3).
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(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)
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Open AccessArticle
On the Maximum Likelihood Estimators’ Uniqueness and Existence for Two Unitary Distributions: Analytically and Graphically, with Application
by
Gadir Alomair, Yunus Akdoğan, Hassan S. Bakouch and Tenzile Erbayram
Symmetry 2024, 16(5), 610; https://doi.org/10.3390/sym16050610 - 14 May 2024
Abstract
Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator.
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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.
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(This article belongs to the Section Mathematics)
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Open AccessArticle
Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation
by
Ikram Medjahdi, Fatima Zohra Lachachi, María Ángeles Castro and Francisco Rodríguez
Symmetry 2024, 16(5), 609; https://doi.org/10.3390/sym16050609 - 14 May 2024
Abstract
The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay
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The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay was incorporated into this model to account for the lag between water infiltration into the soil and the following water uptake by plants. In this work, we consider a more ecologically realistic distributed delay to relate plant growth and soil water availability and analyse the effects of different delay types on the dynamics of both mean-field and spatial Klausmeier–Gray–Scott models. We consider distributed delays based on Gamma kernels and use the so-called linear chain trick to analyse the stability of the uniformly vegetated equilibrium. It is shown that the presence of delays can lead to the loss of stability in the constant equilibrium and to a reduction of the parameter region where steady-state vegetation patterns can arise through symmetry-breaking by diffusion-driven instability. However, these effects depend on the type of delay, and they are absent for distributed delays with weak kernels when vegetation mortality is low.
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(This article belongs to the Special Issue Mathematical Modeling in Biology and Life Sciences)
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