Symmetry

36 pages, 2925 KiB

Open AccessArticle

Is Dark Matter a Misinterpretation of a Perspective Effect?

by Gianni Pascoli and Louis Pernas

Symmetry 2024, 16(7), 937; https://doi.org/10.3390/sym16070937 - 22 Jul 2024

Viewed by 324

Very recently, a straightforward method was proposed to understand galaxies and galactic clusters without using the very elusive dark matter concept. This method is called the

κ

-model. The main idea is to maintain the form of the usual physical laws, especially Newton’s [...] Read more.

Very recently, a straightforward method was proposed to understand galaxies and galactic clusters without using the very elusive dark matter concept. This method is called the

κ

-model. The main idea is to maintain the form of the usual physical laws, especially Newton’s laws of motion when gravity is weak, but only by applying a local scaling procedure for the related lengths, distances, and velocities. This local scaling appears as a correspondence principle in the

κ

-model. In this model, the fundamental physical constants remain universal, i.e., they are independent of a point in space and of time. The

κ

-model is Newtonian in its essence, but there is a relativistic extension that can easily be built. The aim of the present paper is to detail the mathematical formalism supporting it. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Dark Matter)

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14 pages, 279 KiB

Open AccessArticle

An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets

by Estrella Alonso, Mariló López and Javier Rodrigo

Symmetry 2024, 16(7), 936; https://doi.org/10.3390/sym16070936 - 22 Jul 2024

Viewed by 956

Abstract

In this paper, we provide improvements in the additive constant of the current best asymptotic upper bound for the maximum number of halving lines for planar sets of n points, where n is an even number. We also improve this current best upper [...] Read more.

In this paper, we provide improvements in the additive constant of the current best asymptotic upper bound for the maximum number of halving lines for planar sets of n points, where n is an even number. We also improve this current best upper bound for small values of n, namely,

106 \leq n \leq 336

. To obtain this enhancements, we provide lower bounds for the sum of the squares of the degrees of the vertices of a graph related to the halving lines. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Partial Differential Equations and Rogue Waves)

13 pages, 1334 KiB

Open AccessArticle

Graph-Based Traffic Forecasting with the Dynamics of Road Symmetry and Capacity Performance

by Ye Yuan, Yuan Peng, Ruicai Meng and Yongliang Sun

Symmetry 2024, 16(7), 935; https://doi.org/10.3390/sym16070935 - 22 Jul 2024

Viewed by 451

Abstract

Symmetry in traffic patterns is a fundamental aspect of intelligent transportation systems, aiming to precisely predict traffic flow in real time despite the complex interplay of spatial and temporal factors. This paper presents a novel method of traffic forecasting that incorporates parameters related [...] Read more.

Symmetry in traffic patterns is a fundamental aspect of intelligent transportation systems, aiming to precisely predict traffic flow in real time despite the complex interplay of spatial and temporal factors. This paper presents a novel method of traffic forecasting that incorporates parameters related to road symmetry into a Graph Convolution Network model. Our model is crafted to dynamically adjust to real-time changes in road conditions, including the presence of symmetric and asymmetric road layouts, which substantially influence traffic flow. We have developed a GCN model that not only accounts for standard traffic flow metrics but also integrates a matrix representing road symmetry. The model undergoes training and validation on the METR-LA dataset, showcasing a significant enhancement in prediction accuracy. In the comparative analysis of state-of-the-art methods, our model demonstrated a significant enhancement in performance, achieving 30.68% improvement in Mean Squared Error (MSE) and a 24.28% improvement in Mean Absolute Error (MAE) over the best-performing method. The implications of our research are profound for urban planners, traffic management systems, and navigation service providers, as it offers a more dependable tool for forecasting traffic conditions, aiding in road design, and refining route planning strategies based on the symmetry of road networks. Full article

(This article belongs to the Section Engineering and Materials)

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23 pages, 4933 KiB

Open AccessArticle

Advanced Multimodal Sentiment Analysis with Enhanced Contextual Fusion and Robustness (AMSA-ECFR): Symmetry in Feature Integration and Data Alignment

by Qing Chen, Shenghong Dong and Pengming Wang

Symmetry 2024, 16(7), 934; https://doi.org/10.3390/sym16070934 - 22 Jul 2024

Viewed by 985

Abstract

Multimodal sentiment analysis, a significant challenge in artificial intelligence, necessitates the integration of various data modalities for accurate human emotion interpretation. This study introduces the Advanced Multimodal Sentiment Analysis with Enhanced Contextual Fusion and Robustness (AMSA-ECFR) framework, addressing the critical challenge of data [...] Read more.

Multimodal sentiment analysis, a significant challenge in artificial intelligence, necessitates the integration of various data modalities for accurate human emotion interpretation. This study introduces the Advanced Multimodal Sentiment Analysis with Enhanced Contextual Fusion and Robustness (AMSA-ECFR) framework, addressing the critical challenge of data sparsity in multimodal sentiment analysis. The main components of the proposed approach include a Transformer-based model employing BERT for deep semantic analysis of textual data, coupled with a Long Short-Term Memory (LSTM) network for encoding temporal acoustic features. Innovations in AMSA-ECFR encompass advanced feature encoding for temporal dynamics and an adaptive attention-based model for efficient cross-modal integration, achieving symmetry in the fusion and alignment of asynchronous multimodal data streams. Additionally, the framework employs generative models for intelligent approximation of missing features. It ensures robust alignment of high-level features with multimodal data context, effectively tackling issues of incomplete or noisy inputs. In simulation studies, the AMSA-ECFR model demonstrated superior performance against existing approaches. The symmetrical approach to feature integration and data alignment contributed significantly to the model’s robustness and precision. In simulations, the AMSA-ECFR model demonstrated a 10% higher accuracy and a 15% lower mean absolute error than the current best multimodal sentiment analysis frameworks. Full article

(This article belongs to the Special Issue Advances in Computer Vision, Pattern Recognition, Machine Learning and Symmetry)

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16 pages, 303 KiB

Open AccessArticle

Oscillatory Features of Fourth-Order Emden–Fowler Differential Equations with Sublinear Neutral Terms

by Fahd Masood, Wedad Albalawi, Osama Moaaz and Hamdy El-Metwally

Symmetry 2024, 16(7), 933; https://doi.org/10.3390/sym16070933 - 22 Jul 2024

Viewed by 762

Abstract

This article examines the oscillatory characteristics of a fourth-order Emden–Fowler differential equation, specifically when it includes a sublinear neutral term. Our methodology centers on establishing multiple theorems that introduce innovative conditions to guarantee that there are no positive solutions to the examined equation. [...] Read more.

This article examines the oscillatory characteristics of a fourth-order Emden–Fowler differential equation, specifically when it includes a sublinear neutral term. Our methodology centers on establishing multiple theorems that introduce innovative conditions to guarantee that there are no positive solutions to the examined equation. Due to the symmetry between non-oscillatory solutions, we obtain oscillation conditions by excluding only positive solutions. We employ the Riccati technique in various ways to achieve this objective. The criteria presented in this study complement and generalize many findings published in the literature. We support the efficiency of our findings by applying them to an example. Full article

(This article belongs to the Special Issue The Qualitative Theory of Functional Differential Equations and their Applications)

32 pages, 371 KiB

Open AccessArticle

An Algorithmic Evaluation of a Family of Logarithmic Integrals and Associated Euler Sums

by Junesang Choi and Necdet Batır

Symmetry 2024, 16(7), 932; https://doi.org/10.3390/sym16070932 - 21 Jul 2024

Viewed by 896

Abstract

Numerous logarithmic integrals have been extensively documented in the literature. This paper presents an algorithmic evaluation of a specific class of these integrals. Our systematic approach, rooted in logarithmic principles, enables us to extend our findings to other cases within this family of [...] Read more.

Numerous logarithmic integrals have been extensively documented in the literature. This paper presents an algorithmic evaluation of a specific class of these integrals. Our systematic approach, rooted in logarithmic principles, enables us to extend our findings to other cases within this family of integrals. Furthermore, we explore special cases derived from our main results, thereby enhancing the applicability and significance of our work for a wider audience of researchers. Full article

(This article belongs to the Section Mathematics)

21 pages, 401 KiB

Open AccessArticle

Neutral Emden–Fowler Differential Equation of Second Order: Oscillation Criteria of Coles Type

by Amany Nabih, Asma Al-Jaser and Osama Moaaz

Symmetry 2024, 16(7), 931; https://doi.org/10.3390/sym16070931 - 21 Jul 2024

Viewed by 428

Abstract

In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation

{(a (v) η (x (v)) z^{'} (v))}^{'}

+

q (v) F (x (g (v)))

= 0, where [...] Read more.

In this work, we study the asymptotic and oscillatory behavior of solutions to the second-order general neutral Emden–Fowler differential equation

{(a (v) η (x (v)) z^{'} (v))}^{'}

+

q (v) F (x (g (v)))

= 0, where

v \geq v_{0}

and the corresponding function z = x + p

(x \circ h)

. Besides the importance of equations of the neutral type, studying the qualitative behavior of solutions to these equations is rich in analytical points and interesting issues. We begin by finding the monotonic features of positive solutions. The new properties contribute to obtaining new and improved relationships between x and z for use in studying oscillatory behavior. We present new conditions that exclude the existence of positive solutions to the examined equation, and then we establish oscillation criteria through the symmetry property between non-oscillatory solutions. We use the generalized Riccati substitution method, which enables us to apply the results to a larger area than the special cases of the considered equation. The new results essentially improve and extend previous results in the literature. We support this claim by applying the results to an example and comparing them with previous findings. Moreover, the reduction of our results to Euler’s differential equation introduces the well-known sharp oscillation criterion. Full article

(This article belongs to the Section Mathematics)

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10 pages, 1215 KiB

Open AccessArticle

Exploring Ring Structures: Multiset Dimension Analysis in Compressed Zero-Divisor Graphs

by Nasir Ali, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran Qureshi, Suhad Ali Osman Abdallah, Albandary Almahri, Jihad Asad and Ali Akgül

Symmetry 2024, 16(7), 930; https://doi.org/10.3390/sym16070930 - 20 Jul 2024

Viewed by 374

Abstract

This paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDGs) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring

R

and the associated compressed zero-divisor graph. An undirected graph consisting of [...] Read more.

This paper explores the concept of multiset dimensions (Mdim) of compressed zero-divisor graphs (CZDGs) associated with rings. The authors investigate the interplay between the ring-theoretic properties of a ring

R

and the associated compressed zero-divisor graph. An undirected graph consisting of a vertex set

Z (R_{E}) \ {[0]} = R_{E} \ {[0], [1]}

, where

R_{E} = {[x] : x \in R}

and

[x] = {y \in R : a n n (x) = a n n (y)}

is called a compressed zero-divisor graph, denoted by

Γ_{E} (R)

. An edge is formed between two vertices

[x]

and

[y]

of

Z (R_{E})

if and only if

[x] [y] = [x y] = [0],

that is, iff

x y = 0

. For a ring

R

, graph

G

is said to be realizable as

Γ_{E} (R)

if

G

is isomorphic to

Γ_{E} (R)

. We classify the rings based on Mdim of their associated CZDGs and obtain the bounds for the Mdim of the compressed zero-divisor graphs. We also study the Mdim of realizable graphs of rings. Moreover, some examples are provided to support our results. Notably, we discuss the interconnection between Mdim, girth, and diameter of CZDGs, elucidating their symmetrical significance. Full article

(This article belongs to the Special Issue Symmetry and Graph Theory)

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18 pages, 697 KiB

Open AccessArticle

Improving Influenza Epidemiological Models under Caputo Fractional-Order Calculus

by Nahaa E. Alsubaie, Fathelrhman EL Guma, Kaouther Boulehmi, Naseam Al-kuleab and Mohamed A. Abdoon

Symmetry 2024, 16(7), 929; https://doi.org/10.3390/sym16070929 - 20 Jul 2024

Viewed by 493

Abstract

The Caputo fractional-order differential operator is used in epidemiological models, but its accuracy benefits are typically ignored. We validated the suggested fractional epidemiological seasonal influenza model of the SVEIHR type to demonstrate the Caputo operator’s relevance. We analysed the model using fractional calculus, [...] Read more.

The Caputo fractional-order differential operator is used in epidemiological models, but its accuracy benefits are typically ignored. We validated the suggested fractional epidemiological seasonal influenza model of the SVEIHR type to demonstrate the Caputo operator’s relevance. We analysed the model using fractional calculus, revealing its basic properties and enhancing our understanding of disease progression. Furthermore, the positivity, bounds, and symmetry of the numerical scheme were examined. Adjusting the Caputo fractional-order parameter

α

= 0.99 provided the best fit for epidemiological data on infection rates. We compared the suggested model with the Caputo fractional-order system and the integer-order equivalent model. The fractional-order model had lower absolute mean errors, suggesting that it could better represent sickness transmission and development. The results underline the relevance of using the Caputo fractional-order operator to improve epidemiological models’ precision and forecasting. Integrating fractional calculus within the framework of symmetry helps us build more reliable models that improve public health interventions and policies. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Models)

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19 pages, 420 KiB

Open AccessArticle

k-Nearest Neighbors Estimator for Functional Asymmetry Shortfall Regression

by Mohammed B. Alamari, Fatimah A. Almulhim, Zoulikha Kaid and Ali Laksaci

Symmetry 2024, 16(7), 928; https://doi.org/10.3390/sym16070928 - 19 Jul 2024

Viewed by 477

Abstract

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. [...] Read more.

This paper deals with the problem of financial risk management using a new expected shortfall regression. The latter is based on the expectile model for financial risk-threshold. Unlike the VaR model, the expectile threshold is constructed by an asymmetric least square loss function. We construct an estimator of this new model using the k-nearest neighbors (kNN) smoothing approach. The mathematical properties of the constructed estimator are stated through the establishment of the pointwise complete convergence. Additionally, we prove that the constructed estimator is uniformly consistent over the nearest neighbors (UCNN). Such asymptotic results constitute a good mathematical support of the proposed financial risk process. Thus, we examine the easy implantation of this process through an artificial and real data. Our empirical analysis confirms the superiority of the kNN-approach over the kernel method as well as the superiority of the expectile over the quantile in financial risk analysis. Full article

(This article belongs to the Section Mathematics)

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50 pages, 5398 KiB

Open AccessArticle

Novel Hybrid Crayfish Optimization Algorithm and Self-Adaptive Differential Evolution for Solving Complex Optimization Problems

by Hussam N. Fakhouri, Abdelraouf Ishtaiwi, Sharif Naser Makhadmeh, Mohammed Azmi Al-Betar and Mohannad Alkhalaileh

Symmetry 2024, 16(7), 927; https://doi.org/10.3390/sym16070927 - 19 Jul 2024

Viewed by 919

Abstract

This study presents the Hybrid COASaDE Optimizer, a novel combination of the Crayfish Optimization Algorithm (COA) and Self-adaptive Differential Evolution (SaDE), designed to address complex optimization challenges and solve engineering design problems. The hybrid approach leverages COA’s efficient exploration mechanisms, inspired by crayfish [...] Read more.

This study presents the Hybrid COASaDE Optimizer, a novel combination of the Crayfish Optimization Algorithm (COA) and Self-adaptive Differential Evolution (SaDE), designed to address complex optimization challenges and solve engineering design problems. The hybrid approach leverages COA’s efficient exploration mechanisms, inspired by crayfish behaviour, with the symmetry of SaDE’s adaptive exploitation capabilities, characterized by its dynamic parameter adjustment. The balance between these two phases represents a symmetrical relationship wherein both components contribute equally and complementary to the algorithm’s overall performance. This symmetry in design enables the Hybrid COASaDE to maintain consistent and robust performance across a diverse range of optimization problems. Experimental evaluations were conducted using CEC2022 and CEC2017 benchmark functions, demonstrating COASaDE’s superior performance compared to state-of-the-art optimization algorithms. The results and statistical analyses confirm the robustness and efficiency of the Hybrid COASaDE in finding optimal solutions. Furthermore, the applicability of the Hybrid COASaDE was validated through several engineering design problems, where COASaDE outperformed other optimizers in achieving the optimal solution. Full article

(This article belongs to the Section Computer)

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28 pages, 995 KiB

Open AccessArticle

Symmetry Classification of Antiferromagnets with Four Types of Multipoles

by Satoru Hayami

Symmetry 2024, 16(7), 926; https://doi.org/10.3390/sym16070926 - 19 Jul 2024

Viewed by 518

Abstract

A plethora of antiferromagnetic structures have been so far found in condensed matter physics, where the antiferromagnetic phase transition is characterized by symmetry lowering under the magnetic point group. Depending on the types of symmetry lowering, various cross-correlation phenomena, such as the anomalous [...] Read more.

A plethora of antiferromagnetic structures have been so far found in condensed matter physics, where the antiferromagnetic phase transition is characterized by symmetry lowering under the magnetic point group. Depending on the types of symmetry lowering, various cross-correlation phenomena, such as the anomalous Hall effect, magneto-electric effect, and magneto-piezoelectric effect, emerge below the critical temperature. We revisit a close relationship between the symmetry of the antiferromagnetic structures and cross-correlations based on the augmented multipoles consisting of electric, magnetic, magnetic toroidal, and electric toroidal multipoles with different spatial inversion and time-reversal parities. The symmetry classification will be useful for further exploration of functional antiferromagnetic materials. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2024)

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20 pages, 18126 KiB

Open AccessArticle

Spherical Superpixel Segmentation with Context Identity and Contour Intensity

by Nannan Liao, Baolong Guo, Fangliang He, Wenxing Li, Cheng Li and Hui Liu

Symmetry 2024, 16(7), 925; https://doi.org/10.3390/sym16070925 - 19 Jul 2024

Viewed by 364

Abstract

Superpixel segmentation is a popular preprocessing tool in the field of image processing. Nevertheless, conventional planar superpixel generation algorithms are inadequately suited for segmenting symmetrical spherical images due to the distinctive geometric differences. In this paper, we present a novel superpixel algorithm termed [...] Read more.

Superpixel segmentation is a popular preprocessing tool in the field of image processing. Nevertheless, conventional planar superpixel generation algorithms are inadequately suited for segmenting symmetrical spherical images due to the distinctive geometric differences. In this paper, we present a novel superpixel algorithm termed context identity and contour intensity (CICI) that is specifically tailored for spherical scene segmentation. By defining a neighborhood range and regional context identity, we propose a symmetrical spherical seed-sampling method to optimize both the quantity and distribution of seeds, achieving evenly distributed seeds across the panoramic surface. Additionally, we integrate the contour prior to superpixel correlation measurements, which could significantly enhance boundary adherence across different scales. By implementing the two-fold optimizations on the non-iterative clustering framework, we achieve synergistic CICI to generate higher-quality superpixels. Extensive experiments on the public dataset confirm that our work outperforms the baselines and achieves comparable results with state-of-the-art superpixel algorithms in terms of several quantitative metrics. Full article

(This article belongs to the Special Issue Symmetry Applied in Computer Vision, Automation, and Robotics)

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16 pages, 681 KiB

Open AccessArticle

Ideals in Bipolar Quantum Linear Algebra

by Kittipong Laipaporn and Prathomjit Khachorncharoenkul

Symmetry 2024, 16(7), 924; https://doi.org/10.3390/sym16070924 - 19 Jul 2024

Cited by 1 | Viewed by 633

Abstract

Since bipolar quantum linear algebra (BQLA), under two operations–-addition and multiplication—demonstrates the properties of semirings, and since ideals play an important role in abstract algebra, our results are compelling for the ideals of a semiring. In this article, we investigate the characteristics of [...] Read more.

Since bipolar quantum linear algebra (BQLA), under two operations–-addition and multiplication—demonstrates the properties of semirings, and since ideals play an important role in abstract algebra, our results are compelling for the ideals of a semiring. In this article, we investigate the characteristics of ideals, principal ideals, prime ideals, maximal ideals, and the smallest ideal containing any nonempty subset. By applying elementary real analysis, particularly the infimum, our main result is stated as follows: for any closed set I in BQLA, I is a nontrivial proper ideal if and only if there exists

c \in (0, 1]

such that

I = \{(- x, y) \in R^{2} | c x \leq y \leq \frac{x}{c} and x, y \geq 0\}

. This shows that its shape has to be symmetric with the graph

y = - x

. Full article

(This article belongs to the Section Mathematics)

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13 pages, 2079 KiB

Open AccessArticle

A Genetic Algorithm for Three-Dimensional Discrete Tomography

by Elena Toscano and Cesare Valenti

Symmetry 2024, 16(7), 923; https://doi.org/10.3390/sym16070923 - 19 Jul 2024

Viewed by 341

Abstract

Discrete tomography is a specific case of computerized tomography that deals with the reconstruction of objects made of a few density values on a discrete lattice of points (integer valued coordinates). In the general case of computerized tomography, several hundreds of projections are [...] Read more.

Discrete tomography is a specific case of computerized tomography that deals with the reconstruction of objects made of a few density values on a discrete lattice of points (integer valued coordinates). In the general case of computerized tomography, several hundreds of projections are required to obtain a single high-resolution slice of the object; in the case of discrete tomography, projections of an object made by just one homogeneous material are sums along very few angles of the pixel values, which can be thought to be 0’s or 1’s without loss of generality. Genetic algorithms are global optimization techniques with an underlying random approach and, therefore, their convergence to a solution is provided in a probabilistic sense. We present here a genetic algorithm able to straightforwardly reconstruct binary objects in the three-dimensional space. To the best of our knowledge, our methodology is the first to require no model of the shape (e.g., periodicity, convexity or symmetry) to reconstruct. Experiments were carried out to test our new approach in terms of computational time and correctness of the solutions. Over the years, discrete tomography has been studied for many interesting applications to computer vision, non-destructive reverse engineering and industrial quality control, electron microscopy, X-rays crystallography, biplane angiography, data coding and compression. Full article

(This article belongs to the Special Issue Feature Papers in Mathematics Section)

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12 pages, 2159 KiB

Open AccessArticle

The Application of Multilinear Regression Model for Quantitative Analysis on the Basis of Excitation-Emission Matrix Spectra and the Release of a Free Graphical User Interface

by Xinkang Li, Zirui Chen, Lijun Tang, Jingjing Guo and Baoqiong Li

Symmetry 2024, 16(7), 922; https://doi.org/10.3390/sym16070922 - 18 Jul 2024

Viewed by 464

Abstract

Multivariate regression is a fundamental supervised chemometric method for developing the relationship between the independent variables and quantitative response, and it has been widely applied for data analysis in many research fields. In this study, we propose an effective method for the quantitative [...] Read more.

Multivariate regression is a fundamental supervised chemometric method for developing the relationship between the independent variables and quantitative response, and it has been widely applied for data analysis in many research fields. In this study, we propose an effective method for the quantitative determination of target compounds in traditional Chinese medicine, specifically Mongolia, using excitation-emission matrix (EEM) spectra with partial overlap. The accuracy and reliability of the established model have been validated, demonstrating that the proposed method can realize the accurate quantitative analysis purpose. In order to facilitate the calculation easier, the authors have developed a friendly graphical user interface (GUI). The GUI offers the procedures for data imputation, model establishment, model optimization and results presentation. Full article

(This article belongs to the Section Mathematics)

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21 pages, 712 KiB

Open AccessArticle

OPT-FRAC-CHN: Optimal Fractional Continuous Hopfield Network

by Karim El Moutaouakil, Zakaria Bouhanch, Abdellah Ahourag, Ahmed Aberqi and Touria Karite

Symmetry 2024, 16(7), 921; https://doi.org/10.3390/sym16070921 - 18 Jul 2024

Viewed by 447

Abstract

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution [...] Read more.

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article

(This article belongs to the Special Issue Challenges and New Trends in Optimization and Control Theory in the Era of AI: Analysis, Modelling, and Symmetrical Mathematical Methods)

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16 pages, 2591 KiB

Open AccessArticle

Symmetry-Enhanced LSTM-Based Recurrent Neural Network for Oscillation Minimization of Overhead Crane Systems during Material Transportation

by Xu Cui, Kavimbi Chipusu, Muhammad Awais Ashraf, Mudassar Riaz, Jianbing Xiahou and Jianlong Huang

Symmetry 2024, 16(7), 920; https://doi.org/10.3390/sym16070920 - 18 Jul 2024

Viewed by 440

Abstract

This paper introduces a novel methodology for mitigating undesired oscillations in overhead crane systems used in material handling operations in the industry by leveraging Long Short-Term Memory (LSTM)-based Recurrent Neural Networks (RNNs). Oscillations during material transportation, particularly at the end location, pose safety [...] Read more.

This paper introduces a novel methodology for mitigating undesired oscillations in overhead crane systems used in material handling operations in the industry by leveraging Long Short-Term Memory (LSTM)-based Recurrent Neural Networks (RNNs). Oscillations during material transportation, particularly at the end location, pose safety risks and prolong carrying times. The methodology involves collecting sensor data from an overhead crane system, preprocessing the data, training an LSTM-based RNN model that incorporates symmetrical features, and integrating the model into a control algorithm. The control algorithm utilizes swing angle predictions from the symmetry-enhanced LSTM-based RNN model to dynamically adjust crane motion in real time, minimizing oscillations. Symmetry in this framework refers to the balanced and consistent handling of oscillatory data, ensuring that the model can generalize better across different scenarios and load conditions. The LSTM-based RNN model accurately predicts swing angles, enabling proactive control actions to be taken. Experimental validation demonstrates the effectiveness of the proposed approach, achieving an accuracy of approximately 98.6% in swing angle prediction. This innovative approach holds promise for transforming material transportation processes in industrial settings, enhancing operational safety, and optimizing efficiency. Full article

(This article belongs to the Special Issue Unraveling the Black Box: Unleashing the Power of Explainable Deep Learning in Advanced Engineering Sciences)

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15 pages, 662 KiB

Open AccessArticle

Comparing the Numerical Solution of Fractional Glucose–Insulin Systems Using Generalized Euler Method in Sense of Caputo, Caputo–Fabrizio and Atangana–Baleanu

by Muflih Alhazmi

Symmetry 2024, 16(7), 919; https://doi.org/10.3390/sym16070919 - 18 Jul 2024

Viewed by 842

Abstract

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated with changes in beta-cell kinetics. We [...] Read more.

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated with changes in beta-cell kinetics. We discuss the solution to the problem with respect to its existence, uniqueness, non-negativity, and boundedness. Using three different fractional derivative operators, the proposed model is examined. To approximate fractional-order systems, we use an efficient numerical Euler method in Caputo, Caputo–Fabrizio, and Atangana–Baleanu sense. Several asymptomatic behaviors are observed in the proposed models based on these three operators. These behaviors do not appear in integer-order derivative models. These behaviors are essential for understanding fractional-order systems dynamics. Our results provide insight into fractional-order systems dynamics. These operators analyze local and global stability and Hyers–Ulam stability. Furthermore, the numerical solutions for the proposed model are simulated using the three methods. Full article

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25 pages, 8256 KiB

Open AccessArticle

Small-Signal Modeling and Frequency Support Capacity Analysis of Power Load Considering Voltage Variation Effect

by Tao Zhou, Yuxin Zheng, Cheng Wang, Lei Chen, Bo Liu and Zhong Chen

Symmetry 2024, 16(7), 918; https://doi.org/10.3390/sym16070918 - 18 Jul 2024

Viewed by 692

Abstract

The frequency support capacity of power loads is essential for maintaining active power symmetry and balance between the generation and demand sides of power systems. As the proportion of renewable energy sources and power electronic equipment increases, the inertia on the power generation [...] Read more.

The frequency support capacity of power loads is essential for maintaining active power symmetry and balance between the generation and demand sides of power systems. As the proportion of renewable energy sources and power electronic equipment increases, the inertia on the power generation side decreases, highlighting the growing importance of frequency support on the load side. As it is generally believed that the active power balance of power systems determines the frequency stability, few studies have considered the effect of voltage variation on the frequency response dynamics. It is important to note that the node voltage keeps fluctuating throughout the frequency dynamic process, which affects the active power of loads and should not be neglected. Based on the aforementioned rationales, this paper endeavors to investigate the modeling of power load frequency response and analyze its support capability considering the voltage variation effect. This paper initially establishes the small-signal model of dynamic load under frequency dynamics, derives the transfer function relating active power to system frequency deviation, and subsequently develops its frequency response model. Subsequently, commencing with the ZIP model of static load, the power fluctuation of load nodes is derived from the influence of preceding nodes, and the frequency response model of the static load is formulated and its frequency support capacity is scrutinized. Based on this foundation, a comprehensive aggregation model of the complex load is constructed, and its frequency support capability is assessed using actual data. Finally, the proposed model and analysis results are validated through simulation, confirming their correctness and effectiveness. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry Studies in Modern Power Systems)

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16 pages, 532 KiB

Open AccessReview

Current Status of the Standard Model Prediction for the B_s → μ⁺μ⁻ Branching Ratio

by Mateusz Czaja and Mikołaj Misiak

Symmetry 2024, 16(7), 917; https://doi.org/10.3390/sym16070917 - 18 Jul 2024

Viewed by 779

Abstract

The rare decay

B_{s} \to μ^{+} μ^{-}

provides an important constraint on possible deviations from the Standard Model in b-s-ℓ-ℓ interactions. The present weighted average of its branching ratio measurements amounts to [...] Read more.

The rare decay

B_{s} \to μ^{+} μ^{-}

provides an important constraint on possible deviations from the Standard Model in b-s-ℓ-ℓ interactions. The present weighted average of its branching ratio measurements amounts to

(3.34 \pm 0.27) \times 10^{- 9}

, which remains in good agreement with the theoretical prediction of

(3.64 \pm 0.12) \times 10^{- 9}

within the Standard Model. In the present paper, we review calculations that have contributed to this prediction and discuss the associated uncertainties. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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1 pages, 131 KiB

Open AccessRetraction

RETRACTED: Sun et al. Application of Symmetry Law in Numerical Modeling of Hydraulic Fracturing by Finite Element Method. Symmetry 2020, 12, 1122

by Shanhui Sun, Meihua Zhou, Wei Lu and Afshin Davarpanah

Symmetry 2024, 16(7), 916; https://doi.org/10.3390/sym16070916 - 18 Jul 2024

Viewed by 336

Abstract

The journal retracts the article titled “Application of Symmetry Law in Numerical Modeling of Hydraulic Fracturing by Finite Element Method” [...] Full article

14 pages, 7567 KiB

Open AccessArticle

Transforming Controlled Duffing Oscillator to Optimization Schemes Using New Symmetry-Shifted

G (t) -

Polynomials

by Fatima Hussain and Suha Shihab

Symmetry 2024, 16(7), 915; https://doi.org/10.3390/sym16070915 - 17 Jul 2024

Viewed by 398

Abstract

This work introduces and studies the important properties of a special class of new symmetry-shifted

G (t) -

olynomials (NSSG). Such polynomials have a symmetry property over the interval [−2, 0], with

G_{n}^{[- 2, 0]} (0) =

[...] Read more.

This work introduces and studies the important properties of a special class of new symmetry-shifted

G (t) -

olynomials (NSSG). Such polynomials have a symmetry property over the interval [−2, 0], with

G_{n}^{[- 2, 0]} (0) =

{{(- 1)}^{n} G}_{n}^{[- 2, 0]} (- 2)

. An explicit formulation of an NSSG operational matrixwas constructed, which served as a powerful tool for obtaining the desired numerical solutions. Then, a modified direct computational algorithm was suggested for solving the controlled Duffing oscillator problem. The idea behind the proposed algorithm is based on using symmetry basis functions, which are important and have real-world applications in physics and engineering. The original controlled Duffing oscillator problem was transformed into a nonlinear quadratic programming problem. Finally, numerical experiments are presented to validate our theoretical results. The numerical results emphasize that the modified proposed approach reaches the desired value of the performance index, with a few computations and with the minimum order of the NSSG basis function when compared with the other existing method, which is an important factor to consider when choosing the appropriate method in other mathematical and engineering applications. Full article

(This article belongs to the Section Mathematics)

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24 pages, 345 KiB

Open AccessArticle

Gauge Symmetry of Magnetic and Electric Two-Potentials with Magnetic Monopoles

by Rodrigo R. Cuzinatto, Pedro J. Pompeia and Marc de Montigny

Symmetry 2024, 16(7), 914; https://doi.org/10.3390/sym16070914 - 17 Jul 2024

Viewed by 742

Abstract

We generalize the U(1) gauge transformations of electrodynamics by means of an analytical extension of their parameter space and observe that this leads naturally to two gauge potentials, one electric, one magnetic, which permit the writing of local Lagrangians describing elementary particles with [...] Read more.

We generalize the U(1) gauge transformations of electrodynamics by means of an analytical extension of their parameter space and observe that this leads naturally to two gauge potentials, one electric, one magnetic, which permit the writing of local Lagrangians describing elementary particles with electric and magnetic charges. Gauge invariance requires a conformal transformation of the metric tensor. We apply this approach, which borrows from Utiyama’s methodology, to a model with a massless scalar field and a model with a massless spinor field. We observed that for spinor models non-symmetrized Lagrangians can enable the existence of magnetic monopoles, but this is not possible with symmetrized Lagrangian. Such restrictions do not occur for spinless fields, but the model does not allow spin-one fields interacting with monopoles. Full article

(This article belongs to the Special Issue Application of Symmetry in Equations)

21 pages, 15278 KiB

Open AccessArticle

Dynamic Analysis and Optimization of the Coupling System of Vibrating Flip-Flow Screen and Material Group

by Sanpeng Gong, Chenhao Wang, Jialiang Guo, Ziqi Qiao, Guofeng Zhao, Junkai Fan, Ningning Xu and Xinwen Wang

Symmetry 2024, 16(7), 913; https://doi.org/10.3390/sym16070913 - 17 Jul 2024

Viewed by 752

Abstract

Vibrating flip-flow screens (VFFSs) provide an effective solution for deeply screening moist and fine-grained minerals, and an accurate dynamic model of VFFSs is critical for its dynamic analysis and optimization, thereby improving the vibration stability and symmetry of VFFSs. In this paper, uniaxial [...] Read more.

Vibrating flip-flow screens (VFFSs) provide an effective solution for deeply screening moist and fine-grained minerals, and an accurate dynamic model of VFFSs is critical for its dynamic analysis and optimization, thereby improving the vibration stability and symmetry of VFFSs. In this paper, uniaxial tension, uniaxial compression, plane tension, and shear stress relaxation experiments were conducted on screen panel samples to illustrate that the third-order Ogden model and the generalized Maxwell model can accurately describe the hyperelasticity and viscoelasticity of screen panels. Then, the coupling method of finite element and discrete element was adopted to establish the simulation model of the screen panel and material group coupling system, and the dynamics of the coupling system under different loading conditions were explored. Finally, the dynamic model of the coupling system of VFFSs mass, screen panel, and material group was proposed, and the non-dominated sorting genetic algorithm II was applied to optimize the system’s dynamic response. The results reveal that the use of optimized shear springs can reduce the relative amplitude change rate of the main and floating screen frame by 44.30% while maintaining the periodic motion of the VFFSs under operation conditions, greatly enhancing the stability of the VFFSs system. Full article

(This article belongs to the Section Engineering and Materials)

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14 pages, 859 KiB

Open AccessArticle

Analyzing the Approximate Error and Applicable Condition of the Fractional Reduced Differential Transform Method

by Jianbing Hu

Symmetry 2024, 16(7), 912; https://doi.org/10.3390/sym16070912 - 17 Jul 2024

Viewed by 687

Abstract

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The obtained result is the approximation of the real value. Currently, there are few reports on the approximate error and applicable condition. In this paper, we study [...] Read more.

The fractional reduced differential transform method is a finite iterative method based on infinite fractional expansions. The obtained result is the approximation of the real value. Currently, there are few reports on the approximate error and applicable condition. In this paper, we study the factors related to the approximate errors according to the fractional expansions. Our research shows that the approximate errors relate not only to fractional order but also to time t, and that they increase rapidly with time t. This method can only be applied within a certain time range, and the time range is relevant to fractional order and fractional expansions. We can ascertain this time range according to the absolute error and the relative error. Many obtained achievements may be incorrect if the applicable conditions are not satisfied. Some examples presented in this paper verify our analysis. Full article

(This article belongs to the Section Mathematics)

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15 pages, 8166 KiB

Open AccessArticle

Synthesis, X-ray Diffraction and Computational Druglikeness Evaluation of New Pyrrolo[1,2-a][1,10]Phenanthrolines Bearing a 9-Cyano Group

by Mihaela Cristea, Marcel Mirel Popa, Sergiu Shova, Maria Gdaniec, Amalia Stefaniu, Constantin Draghici, Mihai Raduca, Nicoleta Doriana Banu and Florea Dumitrascu

Symmetry 2024, 16(7), 911; https://doi.org/10.3390/sym16070911 - 17 Jul 2024

Viewed by 406

Abstract

New 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines 5a–d, obtained by a 1,3-dipolar cycloaddition reaction between the corresponding N-ylides of 1,10-phenanthrolinium bromides 2a–d, generated in situ and acrylonitrile as a dipolarophile, were investigated by single-crystal X-ray diffraction and computational studies to assess their [...] Read more.

New 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines 5a–d, obtained by a 1,3-dipolar cycloaddition reaction between the corresponding N-ylides of 1,10-phenanthrolinium bromides 2a–d, generated in situ and acrylonitrile as a dipolarophile, were investigated by single-crystal X-ray diffraction and computational studies to assess their druglikeness and evaluate their structure-activity properties. The non-covalent interactions present within the supramolecular landscape of the new 9-cyano-pyrrolo[1,2-a][1,10]phenanthrolines were correlated with the SAR investigations with the aim of estimating the propensity for bioactivity in these compounds. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry of Molecules Related to Biological Activity)

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9 pages, 614 KiB

Open AccessArticle

Manifestation of Superfluidity in Atom-Number-Imbalanced Two-Component Bose–Einstein Condensates

by Saeed Majed Al-Marzoug, Bakhtiyor Baizakov, Usama Al Khawaja and Hocine Bahlouli

Symmetry 2024, 16(7), 910; https://doi.org/10.3390/sym16070910 - 17 Jul 2024

Viewed by 346

Abstract

Superfluid and dissipative regimes in the dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate (BEC) with unequal atom numbers in the two components have been explored. The system supports localized waves of the symbiotic type owing to the same-species repulsion and cross-species attraction. The [...] Read more.

Superfluid and dissipative regimes in the dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate (BEC) with unequal atom numbers in the two components have been explored. The system supports localized waves of the symbiotic type owing to the same-species repulsion and cross-species attraction. The minority BEC component moves through the majority component and creates excitations. To quantify the emerging excitations, we introduce a time-dependent function called disturbance. Through numerical simulations of the coupled Gross–Pitaevskii equations with periodic boundary conditions, we have identified a critical velocity of the localized wave, above which a transition from the superfluid to dissipative regime occurs, as evidenced by a sharp increase in the disturbance function. The factors responsible for the discrepancy between the actual critical velocity and the speed of sound, expected from theoretical arguments, have been discussed. Full article

(This article belongs to the Special Issue Nonlinear Science and Numerical Simulation with Symmetry)

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12 pages, 1342 KiB

Open AccessArticle

Symmetry and Analysis of Fluid Queueing Systems Driven by Non-Truncated Erlangian Service Queues

by Mahdy Shebl El-Paoumy and Taha Radwan

Symmetry 2024, 16(7), 909; https://doi.org/10.3390/sym16070909 - 16 Jul 2024

Viewed by 397

Abstract

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of [...] Read more.

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. Full article

(This article belongs to the Section Mathematics)

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19 pages, 1853 KiB

Open AccessArticle

A Symmetrical Analysis of Decision Making: Introducing the Gaussian Negative Binomial Mixture with a Latent Class Choice Model

by Irsa Sajjad, Ibrahim Ali Nafisah, Mohammed M. A. Almazah, Osama Abdulaziz Alamri and Javid Gani Dar

Symmetry 2024, 16(7), 908; https://doi.org/10.3390/sym16070908 - 16 Jul 2024

Viewed by 446

Abstract

This research presents a model called the ‘Gaussian negative binomial mixture with a latent class choice model’, which serves as a robust and efficient tool for analyzing decisions across different areas. Our innovative model combines elements of mixture models, negative binomial distributions, and [...] Read more.

This research presents a model called the ‘Gaussian negative binomial mixture with a latent class choice model’, which serves as a robust and efficient tool for analyzing decisions across different areas. Our innovative model combines elements of mixture models, negative binomial distributions, and latent class choice modeling to create an approach that captures the complexities of decision-making processes. We explain how the model is formulated and estimated, showcasing its effectiveness in analyzing and predicting choices in scenarios. Through the use of a dataset, we demonstrate the performance of this method, marking a significant advancement in choice modeling. Our results highlight the applications of this model and point towards promising directions for future research, especially in exploring symmetrical patterns and structures, within decision-making processes. Full article

(This article belongs to the Special Issue Symmetric or Asymmetric Distributions and Its Applications)

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Symmetry, Volume 16, Issue 7 (July 2024) – 159 articles

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