Symmetry

23 pages, 437 KiB

Open AccessArticle

Explicit form for the Most General Lorentz Transformation Revisited

by Howard E. Haber

Symmetry 2024, 16(9), 1155; https://doi.org/10.3390/sym16091155 - 4 Sep 2024

Explicit formulae for the

4 \times 4

Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation [...] Read more.

Explicit formulae for the

4 \times 4

Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a

4 \times 4

real matrix A, where A is a product of the diagonal matrix

diag (+ 1, - 1, - 1, - 1)

and an arbitrary

4 \times 4

real antisymmetric matrix. The formula for

exp A

depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product

η^{†} {\bar{σ}}^{μ} χ

transforms as a Lorentz four-vector, where

χ

and

η

are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation

Λ

reduces to the computation of the trace of a product of

2 \times 2

matrices. Both computations are shown to yield equivalent expressions for

Λ

. Full article

(This article belongs to the Section Physics)

16 pages, 274 KiB

Open AccessArticle

Exploring Properties and Applications of Laguerre Special Polynomials Involving the Δ_h Form

by Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Fakhredine Gassem and Anas Altaleb

Symmetry 2024, 16(9), 1154; https://doi.org/10.3390/sym16091154 - 4 Sep 2024

Abstract

The primary objective of this research is to introduce and investigate novel polynomial variants termed

Δ_{h}

Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights [...] Read more.

The primary objective of this research is to introduce and investigate novel polynomial variants termed

Δ_{h}

Laguerre polynomials. This unique polynomial type integrates the monomiality principle alongside operational rules. Through this innovative approach, the study delves into uncharted territory, unveiling fresh insights that build upon prior research endeavours. Notably, the

Δ_{h}

Laguerre polynomials exhibit significant utility in the realm of quantum mechanics, particularly in the modelling of entropy within quantum systems. The research meticulously unveils explicit formulas and elucidates the fundamental properties of these polynomials, thereby forging connections with established polynomial categories. By shedding light on the distinct characteristics and functionalities of the

Δ_{h}

Laguerre polynomials, this study contributes significantly to their comprehension and application across diverse mathematical and scientific domains. Full article

(This article belongs to the Special Issue Special Functions, Integral Transforms and Polynomial Sequences in Real World with Symmetry)

33 pages, 1702 KiB

Open AccessArticle

Five-Element Cycle Optimization Algorithm Based on an Integrated Mutation Operator for the Traveling Thief Problem

by Yue Xiang, Jingjing Guo, Zhengyan Mao, Chao Jiang and Mandan Liu

Symmetry 2024, 16(9), 1153; https://doi.org/10.3390/sym16091153 - 4 Sep 2024

Abstract

This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, [...] Read more.

This paper presents a novel algorithm named Five-element Cycle Integrated Mutation Optimization (FECOIMO) for solving the Traveling Thief Problem (TTP). The algorithm introduces a five-element cycle structure that integrates various mutation operations to enhance both global exploration and local exploitation capabilities. In experiments, FECOIMO was extensively tested on 39 TTP instances of varying scales and compared with five common metaheuristic algorithms: Enhanced Simulated Annealing (ESA), Improved Grey Wolf Optimization Algorithm (IGWO), Improved Whale Optimization Algorithm (IWOA), Genetic Algorithm (GA), and Profit-Guided Coordination Heuristic (PGCH). The experimental results demonstrate that FECOIMO outperforms the other algorithms across all instances, particularly excelling in large-scale instances. The results of the Friedman test show that FECOIMO significantly outperforms other algorithms in terms of average solution, maximum solution, and solution standard deviation. Additionally, although FECOIMO has a longer execution time, its complexity is comparable to that of other algorithms, and the additional computational overhead in solving complex optimization problems translates into better solutions. Therefore, FECOIMO has proven its effectiveness and robustness in handling complex combinatorial optimization problems. Full article

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11 pages, 344 KiB

Open AccessArticle

Predictor Laplace Fractional Power Series Method for Finding Multiple Solutions of Fractional Boundary Value Problems

by Abedel-Karrem Alomari, Wael Mahmoud Mohammad Salameh, Mohammad Alaroud and Nedal Tahat

Symmetry 2024, 16(9), 1152; https://doi.org/10.3390/sym16091152 - 4 Sep 2024

Abstract

This research focuses on finding multiple solutions (MSs) to nonlinear fractional boundary value problems (BVPs) through a new development, namely the predictor Laplace fractional power series method. This method predicts the missing initial values by applying boundary or force conditions. This research provides [...] Read more.

This research focuses on finding multiple solutions (MSs) to nonlinear fractional boundary value problems (BVPs) through a new development, namely the predictor Laplace fractional power series method. This method predicts the missing initial values by applying boundary or force conditions. This research provides a set of theorems necessary for deriving the recurrence relations to find the series terms. Several examples demonstrate the efficacy, convergence, and accuracy of the algorithm. Under Caputo’s definition of the fractional derivative with symmetric order, the obtained results are visualized numerically and graphically. The behavior of the generated solutions indicates that altering the fractional derivative parameters within their domain symmetrically changes these solutions, ultimately aligning them with the standard derivative. The results are compared with the homotopy analysis method and are presented in various figures and tables. Full article

(This article belongs to the Section Mathematics)

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28 pages, 605 KiB

Open AccessArticle

A Convolutional Neural Network with Hyperparameter Tuning for Packet Payload-Based Network Intrusion Detection

by Ammar Boulaiche, Sofiane Haddad and Ali Lemouari

Symmetry 2024, 16(9), 1151; https://doi.org/10.3390/sym16091151 - 4 Sep 2024

Abstract

In the last few years, the use of convolutional neural networks (CNNs) in intrusion detection domains has attracted more and more attention. However, their results in this domain have not lived up to expectations compared to the results obtained in other domains, such [...] Read more.

In the last few years, the use of convolutional neural networks (CNNs) in intrusion detection domains has attracted more and more attention. However, their results in this domain have not lived up to expectations compared to the results obtained in other domains, such as image classification and video analysis. This is mainly due to the datasets used, which contain preprocessed features that are not compatible with convolutional neural networks, as they do not allow a full exploit of all the information embedded in the original network traffic. With the aim of overcoming these issues, we propose in this paper a new efficient convolutional neural network model for network intrusion detection based on raw traffic data (pcap files) rather than preprocessed data stored in CSV files. The novelty of this paper lies in the proposal of a new method for adapting the raw network traffic data to the most suitable format for CNN models, which allows us to fully exploit the strengths of CNNs in terms of pattern recognition and spatial analysis, leading to more accurate and effective results. Additionally, to further improve its detection performance, the structure and hyperparameters of our proposed CNN-based model are automatically adjusted using the self-adaptive differential evolution (SADE) metaheuristic, in which symmetry plays an essential role in balancing the different phases of the algorithm, so that each phase can contribute in an equal and efficient way to finding optimal solutions. This helps to make the overall performance more robust and efficient when solving optimization problems. The experimental results on three datasets, KDD-99, UNSW-NB15, and CIC-IDS2017, show a strong symmetry between the frequency values implemented in the images built for each network traffic and the different attack classes. This was confirmed by a good predictive accuracy that goes well beyond similar competing models in the literature. Full article

(This article belongs to the Section Computer)

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15 pages, 1867 KiB

Open AccessArticle

Enzymatic Deracemization of Fluorinated Arylcarboxylic Acids: Chiral Enzymatic Analysis and Absolute Stereochemistry Using Chiral HPLC

by Oleg I. Kolodiazhnyi, Anastasiia O. Kolodiazhna, Oleh Faiziiev and Yuliia Gurova

Symmetry 2024, 16(9), 1150; https://doi.org/10.3390/sym16091150 - 4 Sep 2024

Abstract

The hydrolase-catalyzed kinetic resolution of fluorinated racemates of 3-arylcarboxylic acids is described. Hydrolysis of ethyl esters of fluorinated acids by esterases and hydrolases in all cases resulted in the formation of hydrolyzed (S)-carboxylic acids and unreacted (R)-esters in high [...] Read more.

The hydrolase-catalyzed kinetic resolution of fluorinated racemates of 3-arylcarboxylic acids is described. Hydrolysis of ethyl esters of fluorinated acids by esterases and hydrolases in all cases resulted in the formation of hydrolyzed (S)-carboxylic acids and unreacted (R)-esters in high yields and high enantiomeric purity. The influence of separation conditions on the efficiency and enantioselectivity of biocatalytic conversion was also studied. The reactions were carried out under normal conditions (stirring with a magnetic stirrer at room temperature) and microwave irradiation in the presence of hydrolases. Amano PS showed excellent selectivity and good yields in the hydrolysis of fluorinated aromatic compounds. The absolute configuration of the resulting compounds was based on biokinetic studies and the use of chiral HPLC. A molecular modeling of the kinetic resolution of carboxylic acid esters was carried out. Full article

(This article belongs to the Collection Feature Papers in Chemistry)

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28 pages, 2065 KiB

Open AccessArticle

Symmetry-Based Urban Rail Transit Network Planning Using Two-Stage Robust Optimization

by Zhaoguo Huang and Changxi Ma

Symmetry 2024, 16(9), 1149; https://doi.org/10.3390/sym16091149 - 4 Sep 2024

Abstract

To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its [...] Read more.

To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model. Full article

(This article belongs to the Section Mathematics)

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12 pages, 882 KiB

Open AccessArticle

Object Skill Advantage in Infants with a Hand Preference

by Emily C. Marcinowski, George F. Michel and Eliza L. Nelson

Symmetry 2024, 16(9), 1148; https://doi.org/10.3390/sym16091148 - 4 Sep 2024

Abstract

How infants engage with objects changes dramatically over the first year of life. While some infants exhibit a consistent hand preference for acquiring objects during this period, others have no identifiable preference. The goal of this study was to test whether lateralization confers [...] Read more.

How infants engage with objects changes dramatically over the first year of life. While some infants exhibit a consistent hand preference for acquiring objects during this period, others have no identifiable preference. The goal of this study was to test whether lateralization confers an advantage in the development of early object management skills. We examined whether lateralized infants show different rates of growth in how they interact with multiple objects as compared to infants without a hand preference. In a longitudinal study consisting of seven monthly visits from 6 to 12 months, 303 infants were assessed for their hand preference and object management skill (i.e., holding up to three objects). Group-Based Trajectory Modeling (GBTM) identified the following three hand preference trajectory groups: Left, Right, and No Preference (NP). A Hierarchical Generalized Linear Model (HGLM) with the NP infants as the reference group for statistical comparisons revealed that while all the infants showed similar trends in their object management skills over time, the lateralized infants had an advantage over the non-lateralized infants. The infants in the Right and Left groups transitioned from holding one to two objects more quickly relative to the NP infants. Further research is needed to determine if this early object skill advantage cascades to a more complex handling of multiple objects. Full article

(This article belongs to the Section Life Sciences)

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23 pages, 6132 KiB

Open AccessArticle

Local-Energy-Conservation-Based Decomposition Method for Wall Friction and Heat Flux

by Mingzhi Tang, Wenfeng Zhou, Yanchao Hu, Gang Wang and Yanguang Yang

Symmetry 2024, 16(9), 1147; https://doi.org/10.3390/sym16091147 - 4 Sep 2024

Abstract

A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this [...] Read more.

A novel decomposition method that adheres to both local time translation symmetry and spatial rotational symmetry is proposed in this study, thereby extending the limitations of existing methods, which are typically restricted to quasi-two-dimensional configurations. Grounded in the FIK and RD identities, this method provides a clear physical and reliable interpretation suitable for arbitrary-curvature profiles. Utilizing this method, an analysis of the aerothermodynamic characteristics of the bistable states of curved compression ramp flows was conducted. The results reveal that the generation of undisturbed and peak

C_{f}

is dominated by viscous dissipation. Specifically, flow separation happens when all of the energy input from the work exerted by the adverse pressure gradient (APG) is insufficient to be entirely converted into local viscous dissipation and kinetic energy. Furthermore, the propensity for flow separation at higher wall temperatures is firstly elucidated quantitatively from the perspective of the work by the APG. The peak heat flux is predominantly triggered by the work of viscous stress, with the secondary contribution from energy transport playing a more significant role in the generation of the peak heat flux of the separation state than that of the attachment state. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

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19 pages, 717 KiB

Open AccessArticle

Imperative Genetic Programming

by Iztok Fajfar, Žiga Rojec, Árpád Bűrmen, Matevž Kunaver, Tadej Tuma, Sašo Tomažič and Janez Puhan

Symmetry 2024, 16(9), 1146; https://doi.org/10.3390/sym16091146 - 3 Sep 2024

Viewed by 119

Abstract

Genetic programming (GP) has a long-standing tradition in the evolution of computer programs, predominantly utilizing tree and linear paradigms, each with distinct advantages and limitations. Despite the rapid growth of the GP field, there have been disproportionately few attempts to evolve ’real’ Turing-like [...] Read more.

Genetic programming (GP) has a long-standing tradition in the evolution of computer programs, predominantly utilizing tree and linear paradigms, each with distinct advantages and limitations. Despite the rapid growth of the GP field, there have been disproportionately few attempts to evolve ’real’ Turing-like imperative programs (as contrasted with functional programming) from the ground up. Existing research focuses mainly on specific special cases where the structure of the solution is partly known. This paper explores the potential of integrating tree and linear GP paradigms to develop an encoding scheme that universally supports genetic operators without constraints and consistently generates syntactically correct Python programs from scratch. By blending the symmetrical structure of tree-based representations with the inherent asymmetry of linear sequences, we created a versatile environment for program evolution. Our approach was rigorously tested on 35 problems characterized by varying Halstead complexity metrics, to delineate the approach’s boundaries. While expected brute-force program solutions were observed, our method yielded more sophisticated strategies, such as optimizing a program by restricting the division trials to the values up to the square root of the number when counting its proper divisors. Despite the recent groundbreaking advancements in large language models, we assert that the GP field warrants continued research. GP embodies a fundamentally different computational paradigm, crucial for advancing our understanding of natural evolutionary processes. Full article

(This article belongs to the Special Issue Evolutionary Computation, Metaheuristics, Nature-Inspired Algorithms, and Symmetry)

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21 pages, 382 KiB

Open AccessArticle

Power Series Expansions of Real Powers of Inverse Cosine and Sine Functions, Closed-Form Formulas of Partial Bell Polynomials at Specific Arguments, and Series Representations of Real Powers of Circular Constant

by Feng Qi

Symmetry 2024, 16(9), 1145; https://doi.org/10.3390/sym16091145 - 3 Sep 2024

Viewed by 242

Abstract

In this paper, by means of the Faà di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine functions, and [...] Read more.

In this paper, by means of the Faà di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine functions, and by virtue of two combinatorial identities containing the Stirling numbers of the first kind, the author establishes power series expansions for real powers of the inverse cosine (sine) functions and the inverse hyperbolic cosine (sine) functions. By comparing different series expansions for the square of the inverse cosine function and for the positive integer power of the inverse sine function, the author not only finds infinite series representations of the circular constant

π

and its real powers, but also derives several combinatorial identities involving central binomial coefficients and the Stirling numbers of the first kind. Full article

(This article belongs to the Section Mathematics)

12 pages, 950 KiB

Open AccessArticle

Analysis of a Bifurcation and Stability of Equilibrium Points for Jeffrey Fluid Flow through a Non-Uniform Channel

by Mary G. Thoubaan, Dheia G. Salih Al-Khafajy, Abbas Kareem Wanas, Daniel Breaz and Luminiţa-Ioana Cotîrlă

Symmetry 2024, 16(9), 1144; https://doi.org/10.3390/sym16091144 - 3 Sep 2024

Viewed by 185

Abstract

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider [...] Read more.

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters. Full article

(This article belongs to the Special Issue Recent Advances in Mathematical Aspect in Engineering—Second Edition)

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17 pages, 9660 KiB

Open AccessArticle

The Impact of the Nonlinear Integral Positive Position Feedback (NIPPF) Controller on the Forced and Self-Excited Nonlinear Beam Flutter Phenomenon

by Khalid Alluhydan, Yasser A. Amer, Ashraf Taha EL-Sayed and Marwa Abdelaziz EL-Sayed

Symmetry 2024, 16(9), 1143; https://doi.org/10.3390/sym16091143 - 3 Sep 2024

Viewed by 205

Abstract

This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the [...] Read more.

This article presents a novel approach to impact regulation of nonlinear vibrational responses in a beam flutter system subjected to harmonic excitation. This study introduces the use of a Nonlinear Integral Positive Position Feedback (NIPPF) controller for this purpose. This technique models the system as a three-degree-of-freedom nonlinear system representing the beam flutter, coupled with a first-order and a second-order filter representing the NIPPF controller. By applying perturbation analysis to the linearized system model, the authors obtain analytical solutions for the autonomous system with the controller. This study aims to reduce vibration amplitudes in a nonlinear dynamic system, specifically when 1:1 internal resonance occurs. The Routh–Hurwitz criterion is utilized to evaluate the system’s stability. Furthermore, the frequency–response curves (FRCs) exhibit symmetry across a range of parameter values. The findings highlight that the effectiveness of vibration suppression is directly related to the product of the NIPPF control signal after comparing with different controllers. Numerical simulations, conducted using the fourth-order Runge–Kutta method, validate the analytical solutions and demonstrate the system’s amplitude response. The strong correlation between the analytical and numerical results highlights the accuracy and dependability of the proposed method. Full article

(This article belongs to the Section Mathematics)

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20 pages, 382 KiB

Open AccessArticle

Spectral Properties of Dual Unit Gain Graphs

by Chunfeng Cui, Yong Lu, Liqun Qi and Ligong Wang

Symmetry 2024, 16(9), 1142; https://doi.org/10.3390/sym16091142 - 3 Sep 2024

Viewed by 145

Abstract

In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer [...] Read more.

In this paper, we study dual quaternion, dual complex unit gain graphs, and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications in robotics and computer graphics. Dual complex numbers have found application in brain science recently. We establish the interlacing theorem for dual unit gain graphs, and show that the spectral radius of a dual unit gain graph is always not greater than the spectral radius of the underlying graph, and these two radii are equal if, and only if, the dual gain graph is balanced. By using dual cosine functions, we establish the closed form of the eigenvalues of adjacency and Laplacian matrices of dual complex and quaternion unit gain cycles. We then show the coefficient theorem holds for dual unit gain graphs. Similar results hold for the spectral radius of the Laplacian matrix of the dual unit gain graph too. Full article

(This article belongs to the Special Issue Exploring Symmetry in Dual Quaternion Matrices and Matrix Equations)

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15 pages, 1711 KiB

Open AccessArticle

On the Interpretation of Cosmic Acceleration

by Enrique Gaztanaga

Symmetry 2024, 16(9), 1141; https://doi.org/10.3390/sym16091141 - 3 Sep 2024

Viewed by 149

Abstract

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually [...] Read more.

In relativity, the Newtonian concepts of velocity and acceleration are observer-dependent quantities that vary with the chosen frame of reference. It is well established that in the comoving frame, cosmic expansion is currently accelerating; however, in the rest frame, this expansion is actually decelerating. In this paper, we explore the implications of this distinction. The traditional measure of cosmic acceleration, denoted by q, is derived from the comoving frame and describes the acceleration of the scale factor a for a 3D space-like homogeneous sphere. We introduce a new parameter

q_{E}

representing the acceleration experienced between observers within the light cone. By comparing

q_{E}

to the traditional q using observational data from Type Ia supernovae (SN) and the radial clustering of galaxies and quasars (BAO)—including the latest results from DESI2024—our analysis demonstrates that

q_{E}

aligns more closely with these data. The core argument of the paper is that

Λ

—regardless of its origin—creates an event horizon that divides the manifold into two causally disconnected regions analogous to conditions inside a black hole’s interior, thereby allowing for a rest-frame perspective

q_{E}

in which cosmic expansion appears to be decelerating and the horizon acts like a friction term. Such a horizon suggests that the universe cannot maintain homogeneity outside. The observed cosmological constant

Λ

can then be interpreted not as a driver of new dark energy or a modification of gravity but as a boundary term exerting an attractive force, akin to a rubber band, resisting further expansion and preventing event horizon crossings. This interpretation calls for a reconsideration of current cosmological models and the assumptions underlying them. Full article

(This article belongs to the Section Physics)

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16 pages, 1476 KiB

Open AccessArticle

Stability Analysis of Stable Circular Orbit in Multi-Static Black Hole Spacetime

by Zefang Fan, Yu Wang and Xianggao Wang

Symmetry 2024, 16(9), 1140; https://doi.org/10.3390/sym16091140 - 3 Sep 2024

Viewed by 168

Abstract

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black [...] Read more.

We herein study the circular orbit stability of a static black hole system composed of multiple Reissner–Nordstrom (RN) black holes. By comparing the circular orbits of two static black holes, three static black holes (TBHs), four static black holes and five static black holes at different spacetime, we find that the continuity of their stable circular orbits changes, i.e., the peaks of the effective potentials are transformed from single-peaked to bi-peaked, and that the distance a between the black holes is the main reason for this change. This characteristic is completely different from the continuity of the stable circular orbit interval of any kind of single black hole in the past. After calculation, we obtain several critical values that lead to the change in circular orbit stability. The three fundamental frequencies (orbital frequency, radial local frequency, and vertical local frequency) are derived and compared for two different spacetimes of double and three black holes. We also analyse the effect of the black hole distance a on the three fundamental frequencies of circular orbits. Full article

(This article belongs to the Section Physics)

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25 pages, 577 KiB

Open AccessArticle

Invariant Sets, Global Dynamics, and the Neimark–Sacker Bifurcation in the Evolutionary Ricker Model

by Rafael Luís and Brian Ryals

Symmetry 2024, 16(9), 1139; https://doi.org/10.3390/sym16091139 - 2 Sep 2024

Viewed by 265

Abstract

In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce [...] Read more.

In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce the number of parameters as well as bring symmetry to the isoclines of the mapping. With this new model, we demonstrate the existence of a forward invariant and globally attracting set where all the dynamics occur. In this set, the model possesses two symmetric fixed points: the origin, which is always a saddle fixed point, and an interior fixed point that may be globally asymptotically stable. Moreover, we observe the presence of a supercritical Neimark–Sacker bifurcation, a phenomenon that is not present in the original non-evolutionary model. Full article

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

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15 pages, 861 KiB

Open AccessArticle

A Unified Hardware Design for Multiplication, Division, and Square Roots Using Binary Logarithms

by Dat Ngo, Siyeon Han and Bongsoon Kang

Symmetry 2024, 16(9), 1138; https://doi.org/10.3390/sym16091138 - 2 Sep 2024

Viewed by 309

Abstract

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, [...] Read more.

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, subtraction, and shifts, enabling a unified hardware implementation—a marked departure from conventional methods that handle these operations separately. The proposed design, involving logarithm and antilogarithm calculations, exhibits an algebraically symmetrical pattern that further optimizes the processing flow. Additionally, this study introduces innovative log-domain correction terms specifically designed to minimize computation errors—a critical improvement over existing methods that often struggle with precision. Compared to standard hardware implementations, the proposed design significantly reduces hardware resource utilization and power consumption while maintaining high operational frequency. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)

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19 pages, 1172 KiB

Open AccessArticle

Existence and Uniqueness of Solution Represented as Fractional Power Series for the Fractional Advection–Dispersion Equation

by Alexandru-Nicolae Dimache, Ghiocel Groza, Marilena Jianu and Iulian Iancu

Symmetry 2024, 16(9), 1137; https://doi.org/10.3390/sym16091137 - 2 Sep 2024

Viewed by 258

Abstract

The fractional advection–dispersion equation is used in groundwater hydrology for modeling the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. This model is used for the prediction of the transport of nonreactive dissolved contaminants in groundwater. [...] Read more.

The fractional advection–dispersion equation is used in groundwater hydrology for modeling the movements of contaminants/solute particles along with flowing groundwater at the seepage velocity in porous media. This model is used for the prediction of the transport of nonreactive dissolved contaminants in groundwater. This paper establishes the existence and the uniqueness of solutions represented as fractional bi-variate power series of some initial-value problems and boundary-value problems for the fractional advection–dispersion equation. Moreover, a method to approximate the solutions using fractional polynomials in two variables and to evaluate the errors in a suitable rectangle is designed. Illustrative examples showing the applicability of the theoretical results are presented. Full article

(This article belongs to the Section Mathematics)

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20 pages, 5472 KiB

Open AccessArticle

The Relationship between Cardiomyocyte Action Potentials and Ion Concentrations: Machine Learning Prediction Modeling and Analysis of Spontaneous Spiral Wave Generation Mechanisms

by Jing Bai, Chunfu Zhang, Yanchun Liang, Adriano Tavares, Lidong Wang, Xue Gu and Ziyao Meng

Symmetry 2024, 16(9), 1136; https://doi.org/10.3390/sym16091136 - 2 Sep 2024

Viewed by 249

Abstract

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely [...] Read more.

The changes in cardiomyocyte action potentials are related to variations in intra- and extracellular ion concentrations. Abnormal ion concentrations can lead to irregular action potentials, subsequently affecting wave propagation in myocardial tissue and potentially resulting in the formation of spiral waves. Therefore, timely monitoring of ion concentration changes is essential. This study presents a novel machine learning classification model that predicts ion concentration changes based on action potential variation data. We conducted simulations using a single-cell model, generating a dataset of 850 action potential variations corresponding to different ion concentration changes. The model demonstrated excellent predictive performance, achieving an accuracy of 0.988 on the test set. Additionally, the causes of spontaneous spiral wave generation in the heart are insufficiently studied. This study presents a new mechanism whereby changes in extracellular potassium ion concentration leads to the spontaneous generation of spiral waves. By constructing composite myocardial tissue containing both myocardial and fibroblast cells, we observed that variations in extracellular potassium ion concentration can either trigger or inhibit cardiomyocyte excitation. We developed three tissue structures, and by appropriately adjusting the extracellular potassium ion concentration, we observed the spontaneous generation of single spiral waves, symmetrical spiral wave pairs, and asymmetrical double spiral waves. Full article

(This article belongs to the Section Computer)

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20 pages, 12496 KiB

Open AccessArticle

Structural and Spectral Properties of Chordal Ring, Multi-Ring, and Mixed Graphs

by M. A. Reyes, C. Dalfó and M. A. Fiol

Symmetry 2024, 16(9), 1135; https://doi.org/10.3390/sym16091135 - 2 Sep 2024

Viewed by 266

Abstract

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), [...] Read more.

The chordal ring (CR) graphs are a well-known family of graphs used to model some interconnection networks for computer systems in which all nodes are in a cycle. Generalizing the CR graphs, in this paper, we introduce the families of chordal multi-ring (CMR), chordal ring mixed (CRM), and chordal multi-ring mixed (CMRM) graphs. In the case of mixed graphs, we can have edges (without direction) and arcs (with direction). The chordal ring and chordal ring mixed graphs are bipartite and 3-regular. They consist of a number r (for

r \geq 1

) of (undirected or directed) cycles with some edges (the chords) joining them. In particular, for CMR, when

r = 1

, that is, with only one undirected cycle, we obtain the known families of chordal ring graphs. Here, we used plane tessellations to represent our chordal multi-ring graphs. This allowed us to obtain their maximum number of vertices for every given diameter. Additionally, we computationally obtained their minimum diameter for any value of the number of vertices. Moreover, when seen as a lift graph (also called voltage graph) of a base graph on Abelian groups, we obtained closed formulas for the spectrum, that is, the eigenvalue multi-set of its adjacency matrix. Full article

(This article belongs to the Special Issue Symmetry in Combinatorial Structures)

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17 pages, 301 KiB

Open AccessArticle

Sharp Results for a New Class of Analytic Functions Associated with the q-Differential Operator and the Symmetric Balloon-Shaped Domain

by Adeel Ahmad, Jianhua Gong, Akhter Rasheed, Saqib Hussain, Asad Ali and Zeinebou Cheikh

Symmetry 2024, 16(9), 1134; https://doi.org/10.3390/sym16091134 - 2 Sep 2024

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Abstract

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order [...] Read more.

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order Hankel determinants, the Zalcman conjecture, and its generalized conjecture for this newly defined class of q-starlike functions with respect to symmetric points. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

17 pages, 281 KiB

Open AccessArticle

Three-Dimensional Lorentz-Invariant Velocities

by James M. Hill

Symmetry 2024, 16(9), 1133; https://doi.org/10.3390/sym16091133 - 2 Sep 2024

Viewed by 248

Abstract

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are [...] Read more.

Lorentz invariance underlies special relativity, and the energy formula and relative velocity formula are well known to be invariant under a Lorentz transformation. Here, we determine the functional forms in terms of four arbitrary functions for those three dimensional velocity fields that are automatically invariant under the most general fully three-dimensional Lorentz transformation. For general three-dimensional motion, using rectangular Cartesian coordinates

(x, y, z)

, we determine the first-order partial differential equations for the three velocity components

u (x, y, z, t)

,

v (x, y, z, t)

and

w (x, y, z, t)

in the

x -

,

y -

and

z -

directions respectively. These partial differential equations and the associated partial differential relations connecting energy and momentum are fully compatible with the Lorentz-invariant energy–momentum relations and appear not to have been given previously in the literature. We determine the spatial and temporal dependence of the functional forms for those three-dimensional velocity fields that are automatically invariant under three-dimensional Lorentz transformations. An interesting special case gives rise to families of particle paths for which the magnitude of the velocity is the speed of light. This is indicative of the abundant possibilities existing in the “fast lane”. Full article

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

11 pages, 1079 KiB

Open AccessArticle

The Optimal Experimental Design for Exponentiated Frech’et Lifetime Products

by Shu-Fei Wu

Symmetry 2024, 16(9), 1132; https://doi.org/10.3390/sym16091132 - 2 Sep 2024

Viewed by 245

Abstract

In many manufacturing industries, the lifetime performance index

C_{L}

is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to [...] Read more.

In many manufacturing industries, the lifetime performance index

C_{L}

is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech’et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines Fourth Edition)

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10 pages, 256 KiB

Open AccessArticle

Discrete Z₄ Symmetry in Quantum Gravity

by Grigory E. Volovik

Symmetry 2024, 16(9), 1131; https://doi.org/10.3390/sym16091131 - 1 Sep 2024

Viewed by 189

Abstract

We consider the discrete

Z_{4}

symmetry

\hat{i}

, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, [...] Read more.

We consider the discrete

Z_{4}

symmetry

\hat{i}

, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation,

\hat{i}

, the emerging tetrads are multiplied by the imaginary unit,

\hat{i} e_{μ}^{a} = - i e_{μ}^{a}

. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid ³He-B. The order parameter in ³He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The

\hat{i}

-symmetry operation changes the phase of the complex order parameter by

π / 2

, which corresponds to the

Z_{4}

discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this

Z_{4}

symmetry, in which the

\hat{i}

-operation changes sign of the scalar curvature,

\hat{i} R = - R

, and thus the Einstein–Hilbert action violates the

\hat{i}

-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling

K = 1 / 16 π G

plays the role of the order parameter, which changes sign under

\hat{i}

-transformation. Full article

(This article belongs to the Section Physics)

21 pages, 8464 KiB

Open AccessArticle

Geometric Parameter Effects on Bandgap Characteristics of Periodic Pile Barriers in Passive Vibration Isolation

by Jinglei Liu, Xiuxin Li, Jinyuan Cao, Zhengchun Duan, Qingzhi Ye and Guishuai Feng

Symmetry 2024, 16(9), 1130; https://doi.org/10.3390/sym16091130 - 1 Sep 2024

Viewed by 279

Abstract

To investigate the impact of the geometric parameters of periodic pile barriers on bandgap characteristics in passive vibration isolation, a two-dimensional, three-component unit cell was developed using the finite element method (FEM). This study analyzed the bandgap properties of periodic pile barriers and [...] Read more.

To investigate the impact of the geometric parameters of periodic pile barriers on bandgap characteristics in passive vibration isolation, a two-dimensional, three-component unit cell was developed using the finite element method (FEM). This study analyzed the bandgap properties of periodic pile barriers and validated the effectiveness of the FEM through model testing. The FEM was then methodically applied to evaluate the effects of pipe pile thickness, periodic constant, arrangement pattern, and cross-sectional shape on the bandgap characteristics, culminating in the proposition of a novel H-shaped cross-section for the piles. The results demonstrated that the FEM-calculated bandgap frequency range, featuring steel piles arranged in a square pattern, closely aligned with the attenuation zone in the model tests. The lower band frequency (LBF) was primarily influenced by the pipe pile’s inner radius, while the upper band frequency (UBF) was predominantly affected by its outer radius. As the periodic constant increased, the LBF, UBF, and the width of band gap (WBG) all decreased. Conversely, changing the arrangement pattern from square to hexagonal led to increases in UBF and WBG, while the LBF diminished. Notably, the WBG of the H-section steel piles, possessing the same cross-sectional area, was 1.31 times greater than that of the steel pipe piles, indicating an enhanced vibration isolation performance. Additionally, the impact of transverse and vertical characteristic dimensions of the H-shaped pile on the band gap distribution was assessed, revealing that the transverse characteristic dimensions exerted a more significant influence than the vertical dimensions. Full article

(This article belongs to the Section Engineering and Materials)

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16 pages, 7496 KiB

Open AccessArticle

Trajectory Planning Design for Parallel Parking of Autonomous Ground Vehicles with Improved Safe Travel Corridor

by Xianjian Jin, Yinchen Tao and Nonsly Valerienne Opinat Ikiela

Symmetry 2024, 16(9), 1129; https://doi.org/10.3390/sym16091129 - 1 Sep 2024

Viewed by 310

Abstract

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles—that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most [...] Read more.

In this paper, the concept of symmetry is utilized to design the trajectory planning for parallel parking of autonomous ground vehicles—that is, the construction and the solution of the optimization-based trajectory planning approach are symmetrical. Parking is the main factor that troubles most drivers for their daily driving travel, and it can even lead to traffic congestion in severe cases. With the rise of new intelligent and autonomous vehicles, automatic parking seems to have become a trend. Traditional geometric planning methods are less adaptable to parking scenarios, while the parking paths planned by graph search methods may only achieve local optimality. Additionally, significant computational time is often required by numerical optimization methods to find a parking path when a good initial solution is not available. This paper presents a hierarchical trajectory planning approach for high-quality parallel parking of autonomous ground vehicles. The approach begins with a graph search layer to roughly generate an initial solution, which is refined by a numerical optimization layer to produce a high-quality parallel parking trajectory. Considering the high dimensionality and difficulty of finding an optimal solution for the path planning optimization problem, this paper proposes an improved safe travel corridor (I-STC) with the construction of collision constraints isolated from surrounding environmental obstacles. By constructing collision constraints of the I-STC based on the initial solution, the proposed method avoids the complexities and non-differentiability of traditional obstacle avoidance constraints, and simplifies the problem modeling the subsequent numerical optimization process. The simulation results demonstrate that the I-STC is capable of generating parallel parking trajectories with both comfort and safety. Full article

(This article belongs to the Section Engineering and Materials)

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23 pages, 4721 KiB

Open AccessArticle

The Influence of the Assembly Line Configuration and Reliability Parameter Symmetry on the Key Performance Indicators

by Adrian Kampa and Iwona Paprocka

Symmetry 2024, 16(9), 1128; https://doi.org/10.3390/sym16091128 - 31 Aug 2024

Viewed by 415

Abstract

In the context of the demand for mass customization of products, a trade-off between highly efficient automated systems and flexible manual operators is sought. The linear arrangement of workstations made it possible to divide the process into many simple operations, which increases production [...] Read more.

In the context of the demand for mass customization of products, a trade-off between highly efficient automated systems and flexible manual operators is sought. The linear arrangement of workstations made it possible to divide the process into many simple operations, which increases production efficiency, but also results in an increase in the number of workstations and a significant extension of the line. A human operator is usually treated as a quasi-mechanical object, and a human error is considered, similarly, as a failure of a technical component. However, human behavior is more complex and difficult to predict. A mathematical model of a new production organization is presented, including dividing the traditional production line into shorter sections or replacing the serial assembly line with a U-line with cells. Moreover, the reliability of operator and technical means are distinguished. Work-in-progress inventories are located between line sections to improve system stability. The stability of the assembly line is examined based on the system configuration and probabilistic estimates of human failure. The influence of the symmetry of reliability parameters of people on key performance indicators (KPI (headcount), KPI (surface) and KPI (Overall Equipment Effectiveness) is examined. KPI (solution robustness) and KPI (quality robustness) are also presented in order to evaluate the impact of a disruption on the assembly line performance. New rules for assigning tasks to stations are proposed, taking into account the risk of disruptions in the execution of tasks. For comparison of assembly problems, heuristic methods with newly developed criteria are used. The results show the impact of symmetry/asymmetry on assembly line performance and an asymmetric distribution of manual assembly times that is significantly skewed to the right due to human errors. On the assembly line, the effects of these errors are cumulative and lead to longer assembly times and lower KPIs. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)

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14 pages, 1813 KiB

Open AccessArticle

Research on Classification Maintenance Strategy for More Electric Aircraft Actuation Systems Based on Importance Measure

by Xiaoyu Cui, Xuanhao Li, Zhiyao Zhao, Jiabin Yu and Di Liu

Symmetry 2024, 16(9), 1127; https://doi.org/10.3390/sym16091127 - 31 Aug 2024

Viewed by 325

Abstract

In this paper, a practical maintenance algorithm is proposed to improve the reliability of actuation systems and their components, specifically addressing the consistency degradation caused by faults in the symmetric actuation system components of more electric aircraft (MEA). By integrating important measures with [...] Read more.

In this paper, a practical maintenance algorithm is proposed to improve the reliability of actuation systems and their components, specifically addressing the consistency degradation caused by faults in the symmetric actuation system components of more electric aircraft (MEA). By integrating important measures with traditional genetic algorithms, the accuracy of the algorithm is improved. Prior to maintenance, a reasonable classification of components is built to mitigate the adverse effects of extreme fault conditions on the algorithm. This approach improves both the effectiveness and efficiency of the algorithm, rendering the overall maintenance strategy better suited for real-world needs. Finally, comparative simulations confirm the algorithm’s superior performance in reliability improvement, demonstrating its substantial contribution to the field of MEA maintenance and reliability. Full article

(This article belongs to the Special Issue Symmetry in Reliability Engineering)

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19 pages, 1122 KiB

Open AccessArticle

Comparative Analysis of Influenza Modeling Using Novel Fractional Operators with Real Data

by Mohamed A. Abdoon and Abdulrahman B. M. Alzahrani

Symmetry 2024, 16(9), 1126; https://doi.org/10.3390/sym16091126 - 30 Aug 2024

Viewed by 336

Abstract

In this work, the efficacy of fractional models under Atangana–Baleanu–Caputo, Caputo–Fabrizio, and Caputo is compared to the performance of integer-order models in the forecasting of weekly influenza cases using data from the Kingdom of Saudi Arabia. The suggested fractional influenza model was effectively [...] Read more.

In this work, the efficacy of fractional models under Atangana–Baleanu–Caputo, Caputo–Fabrizio, and Caputo is compared to the performance of integer-order models in the forecasting of weekly influenza cases using data from the Kingdom of Saudi Arabia. The suggested fractional influenza model was effectively verified using fractional calculus. Our investigation uncovered the topic’s essential properties and deepened our understanding of disease progression. Furthermore, we analyzed the numerical scheme’s positivity, limitations, and symmetry. The fractional-order models demonstrated superior accuracy, producing smaller root mean square error (RMSE) and mean absolute error (MAE) than the classical model. The novelty of this work lies in introducing the Atangana–Baleanu–Caputo fractional model to influenza forecasting to incorporate memory of an epidemic, which leads to higher accuracy than traditional models. These models effectively captured the peak and drop of influenza cases. Based on these findings, it can be concluded that fractional-order models perform better than typical integer-order models when predicting influenza dynamics. These insights should illuminate the importance of fractional calculus in addressing epidemic threats. Full article

(This article belongs to the Special Issue Mathematical Modeling of the Infectious Diseases and Their Controls)

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Symmetry, Volume 16, Issue 9 (September 2024) – 61 articles

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