Symmetry

42 pages, 565 KiB

Open AccessArticle

From QCD Phenomenology to Nuclear Physics Phenomenology: The Chiral Confining Model

by Guy Chanfray, Magda Ericson, Hubert Hansen, Jérôme Margueron and Marco Martini

Symmetry 2025, 17(2), 313; https://doi.org/10.3390/sym17020313 - 19 Feb 2025

Viewed by 430

We present a theoretical framework that allows one to make an explicit connection between the phenomenology of QCD, namely the properties of the gluon correlator and Wilson loops, and a particular relativistic model for the description of nuclear matter and neutron stars: the [...] Read more.

We present a theoretical framework that allows one to make an explicit connection between the phenomenology of QCD, namely the properties of the gluon correlator and Wilson loops, and a particular relativistic model for the description of nuclear matter and neutron stars: the chiral confining model. Starting with the field correlator method, which explicitly and simultaneously incorporates confinement and chiral symmetry breaking, we describe how to obtain the response of the composite nucleon to the nuclear scalar field, as well as the relative role of confinement and chiral symmetry breaking in in-medium nucleon mass evolution, thereby generating the three-body forces needed for the saturation mechanism. Full article

(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)

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15 pages, 328 KiB

Open AccessArticle

Null Hybrid Curves and Some Characterizations of Null Hybrid Bertrand Curves

by Jeta Alo

Symmetry 2025, 17(2), 312; https://doi.org/10.3390/sym17020312 - 19 Feb 2025

Viewed by 333

Abstract

In this paper, we investigate null curves in

R_{2}^{4}

, the four-dimensional Minkowski space of index 2, utilizing the concept of hybrid numbers. Hybrid and spatial hybrid-valued functions of a single variable describe a curve in

R_{2}^{4}

. We [...] Read more.

In this paper, we investigate null curves in

R_{2}^{4}

, the four-dimensional Minkowski space of index 2, utilizing the concept of hybrid numbers. Hybrid and spatial hybrid-valued functions of a single variable describe a curve in

R_{2}^{4}

. We first derive Frenet formulas for a null curve in

R_{2}^{3}

, the three-dimensional Minkowski space of index 2, by means of spatial hybrid numbers. Next, we apply the Frenet formulas for the associated null spatial hybrid curve corresponding to a null hybrid curve in order to derive the Frenet formulas for this curve in

R_{2}^{4}

. This approach is simpler and more efficient than the classical differential geometry methods and enables us to determine a null curve in

R_{2}^{3}

corresponding to the null curve in

R_{2}^{4}

. Additionally, we provide an example of a null hybrid curve, demonstrate the construction of its Frenet frame, and calculate the curvatures of the curve. Finally, we introduce null hybrid Bertrand curves, and by using their symmetry properties, we provide some characterizations of these curves. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 4th Edition)

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15 pages, 646 KiB

Open AccessArticle

An Optimal Investment Decision Problem Under the HARA Utility Framework

by Aiyin Wang, Xiao Ji, Lu Zhang, Guodong Li and Wenjie Li

Symmetry 2025, 17(2), 311; https://doi.org/10.3390/sym17020311 - 19 Feb 2025

Viewed by 338

Abstract

This paper is dedicated to studying the optimal investment proportions of three types of assets with symmetry, namely, risky assets, risk-free assets, and wealth management products, when the stochastic expenditure process follows a jump-diffusion model. The stochastic expenditure process is treated as an [...] Read more.

This paper is dedicated to studying the optimal investment proportions of three types of assets with symmetry, namely, risky assets, risk-free assets, and wealth management products, when the stochastic expenditure process follows a jump-diffusion model. The stochastic expenditure process is treated as an exogenous cash flow and is assumed to follow a stochastic differential process with jumps. Under the Cox–Ingersoll–Ross interest rate term structure, it is presumed that the prices of multiple risky assets evolve according to a multi-dimensional geometric Brownian motion. By employing stochastic control theory, the Hamilton–Jacobi–Bellman (HJB) equation for the household portfolio problem is formulated. Considering various risk-preference functions, particularly the Hyperbolic Absolute Risk Aversion (HARA) function, and given the algebraic form of the objective function through the terminal-value maximization condition, an explicit solution for the optimal investment strategy is derived. The findings indicate that when household investment behavior is characterized by random expenditures and symmetry, as the risk-free interest rate rises, the optimal proportion of investment in wealth-management products also increases, whereas the proportion of investment in risky assets continually declines. As the expected future expenditure increases, households will decrease their acquisition of risky assets, and the proportion of risky-asset purchases is sensitive to changes in the expectation of unexpected expenditures. Full article

(This article belongs to the Section Mathematics)

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16 pages, 284 KiB

Open AccessArticle

Coefficient Estimates in a Class of Close-to-Convex Functions

by Lucyna Trojnar-Spelina

Symmetry 2025, 17(2), 310; https://doi.org/10.3390/sym17020310 - 19 Feb 2025

Viewed by 324

Abstract

In this paper, we consider analytic functions with the formalization

f (0) = f^{'} (0) - 1 = 0

, which satisfy [...] Read more.

In this paper, we consider analytic functions with the formalization

f (0) = f^{'} (0) - 1 = 0

, which satisfy

Re {(1 - α z^{2}) f^{'} (z)} > 0, z \in Δ = {z \in C : | z | < 1},

where

α \in [- 1, 1]

. The set of such functions is a subclass of the class of close-to-convex functions. In this paper, we present sharp bounds of

| a_{n} |

, where

a_{n}

is the

n -

th Taylor’s coefficients for functions in this class. In addition, we consider several symmetric coefficient problems when the second coefficient

a_{2}

is established. In particular, we provide bounds of

| a_{n + 1} - a_{n} |

and of

| 2 n a_{2 n} - (2 n - 1) a_{2 n - 1} |

for the considered class under this additional assumption. Full article

(This article belongs to the Section Mathematics)

19 pages, 9554 KiB

Open AccessArticle

A Lightweight PCB Defect Detection Algorithm Based on Improved YOLOv8-PCB

by Jianan Wang, Xin Xie, Guoying Liu and Liang Wu

Symmetry 2025, 17(2), 309; https://doi.org/10.3390/sym17020309 - 19 Feb 2025

Cited by 1 | Viewed by 1207

Abstract

Tackling the widespread problems of inaccuracies, slow detection speed, and poor adaptability in small object defect detection on PCB circuits, this study suggests a lightweight printed circuit board surface defect identification algorithm, building upon an improved YOLOv8-PCB. This algorithm first introduces the C2f_SHSA [...] Read more.

Tackling the widespread problems of inaccuracies, slow detection speed, and poor adaptability in small object defect detection on PCB circuits, this study suggests a lightweight printed circuit board surface defect identification algorithm, building upon an improved YOLOv8-PCB. This algorithm first introduces the C2f_SHSA attention mechanism in the backbone network, which unites the merits of channel attention and spatial attention, facilitating an efficient fusion of local and global features in a lightweight manner, thereby enhancing the model’s identification preciseness for small defects. Subsequently, in the neck network, the C2f_IdentityFormer structure, which combines the C2f structure with the IdentityFormer structure, supplants the initial C2f structure. This enhancement improves the model’s sensitivity to subtle features and further optimizes the effect of feature fusion. Eventually, the PIoU is presented to enhance the model’s adaptability to small, complex PCB defects with varying sizes and shapes, while also accelerating the mode’s convergence speed. Experimental outcomes reveal that the improved YOLOv8-PCB algorithm displays remarkable performance in the PCB dataset, with a Recall rate of 94.0%, a mean Average Precision (mAP) of 96.1%, and an F1 score of 94.35%. Moreover, the model’s weight size is only 5.2 MB. Compared to the YOLOv8n baseline model, the Recall rate has a 3.6% improvement, the mAP is raised by 1.8%, and the F1 score is enhanced by 1.9%, while the model’s weight is reduced by 17.46%. The enhancements in performance metrics confirm that the improved algorithm not only fulfills the requirements for efficient and real-time detection in PCB surface defect identification tasks but is also better suited for deployment and operation on edge devices. Full article

(This article belongs to the Section Computer)

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19 pages, 735 KiB

Open AccessArticle

Pythagorean Fuzzy TOPSIS Method of Excessive Hesitation

by Xiuli Du, Rui Zhou, Kun Lu and Weilong Cheng

Symmetry 2025, 17(2), 308; https://doi.org/10.3390/sym17020308 - 18 Feb 2025

Viewed by 390

Abstract

In cases where the comprehensive hesitation degree among experts in decision-making is excessively high, the calculation of the comprehensive evaluation index using the TOPSIS method may lead to asymmetric bias. To address this issue, a formula for the comprehensive evaluation index considering excessive [...] Read more.

In cases where the comprehensive hesitation degree among experts in decision-making is excessively high, the calculation of the comprehensive evaluation index using the TOPSIS method may lead to asymmetric bias. To address this issue, a formula for the comprehensive evaluation index considering excessive hesitation is proposed, followed by the introduction of a Pythagorean fuzzy TOPSIS method that accounts for high hesitation. Initially, the Pythagorean fuzzy number is utilized to calculate the comprehensive hesitancy of the evaluation matrix by experts. Subsequently, when excessive hesitancy is detected, a ranking correction coefficient is proposed to adjust the comprehensive evaluation index, which helps to prevent misjudgment of the optimal solution and ensures the symmetry of optimal decision-making, thereby yielding a more accurate and reasonable ranking of alternatives. Finally, experimental examples demonstrate the feasibility and effectiveness of the proposed method. Full article

(This article belongs to the Section Mathematics)

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27 pages, 4905 KiB

Open AccessArticle

Robust Discriminative Non-Negative and Symmetric Low-Rank Projection Learning for Feature Extraction

by Wentao Zhang and Xiuhong Chen

Symmetry 2025, 17(2), 307; https://doi.org/10.3390/sym17020307 - 18 Feb 2025

Viewed by 446

Abstract

Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient [...] Read more.

Feature extraction plays a vital role in pattern recognition and computer vision. In recent years, low-rank representation (LRR) has been widely used in feature extraction, due to its robustness against noise. However, existing methods often overlook the impact of a well-constructed low-rank coefficient matrix on projection learning. This paper introduces a novel feature extraction method, i.e., robust discriminative non-negative and symmetric low-rank projection learning (RDNSLRP), where a coefficient matrix with better properties, such as low-rank, non-negativity, symmetry and block-diagonal structure, is utilized as a graph matrix for learning the projection matrix. Additionally, a discriminant term is introduced to increase inter-class divergence while decreasing intra-class divergence, thereby extracting more discriminative features. An iterative algorithm for solving the proposed model was designed by using the augmented Lagrange multiplier method, and its convergence and computational complexity were analyzed. Our experimental results on multiple data sets demonstrate the effectiveness and superior image-recognition performance of the proposed method, particularly on data sets with complex intrinsic structures. Furthermore, by investigating the effects of noise corruption and feature dimension, the robustness against noise and the discrimination of the proposed model were further verified. Full article

(This article belongs to the Special Issue Advances in Machine Learning and Symmetry/Asymmetry)

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24 pages, 2354 KiB

Open AccessArticle

Research on Evaluation Methods of Complex Product Design Based on Hybrid Kansei Engineering Modeling

by Tianlu Zhu, Cengjuan Wu, Zhizheng Zhang, Yajun Li and Tianyu Wu

Symmetry 2025, 17(2), 306; https://doi.org/10.3390/sym17020306 - 18 Feb 2025

Viewed by 689

Abstract

The field of complex product design evaluation can attract high ambiguity due to difficulties in establishing indicators and the subjectivity of expert evaluation scoring. Indeed, traditional Kansei Engineering (KE) relies on user requirements and feedback for design evaluation, which may not fully and [...] Read more.

The field of complex product design evaluation can attract high ambiguity due to difficulties in establishing indicators and the subjectivity of expert evaluation scoring. Indeed, traditional Kansei Engineering (KE) relies on user requirements and feedback for design evaluation, which may not fully and effectively validate the design evaluation results, let alone determine whether they apply to complex products with more evaluation index systems. To overcome these drawbacks, this study proposes an evaluation method based on Hybrid Kansei Engineering (HKE) modeling for complex product design evaluation. HKE modeling consists of two parts, namely Forward Kansei Engineering (FKE) and Backward Kansei Engineering (BKE). In this study, four electric forklift designs are used as an example. The FKE system adopts the multi-attribute decision evaluation method; obtains the evaluation indexes of the forklift product imagery and then establishes the perceptual word collection; constructs the evaluation index system of the forklift via the Analytic Hierarchy Process (AHP); calculates the weights of the evaluation indexes of each level and their rankings; and calculates the final rankings of the four electric forklift design solutions by adopting the Fuzzy Comprehensive Evaluation (FCE) method. The BKE system adopts eye tracking (ET) to extract the attention time, visual attention hotspot, and other eye movement index data, and the Gray Relation Analysis (GRA) method was used to validate the model to derive the ranking, which verifies the effectiveness and scientific validity of the evaluation method. The results of this study show that the two-way evaluation of HKE modeling can effectively avoid subjective factors in product design, improve the scientific nature of the design, and guarantee the logical rigor of the perceptual design procedure. Full article

(This article belongs to the Section Engineering and Materials)

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9 pages, 240 KiB

Open AccessArticle

Roots of Binary Shuffle Squares

by Dominika Datko and Bartłomiej Pawlik

Symmetry 2025, 17(2), 305; https://doi.org/10.3390/sym17020305 - 17 Feb 2025

Viewed by 384

Abstract

A square is a word of the form

X X

, where X is any finite non-empty word. For example, couscous is a square. A shuffle square is a finite word that can be formed by self-shuffling a word; for instance, the Spanish [...] Read more.

A square is a word of the form

X X

, where X is any finite non-empty word. For example, couscous is a square. A shuffle square is a finite word that can be formed by self-shuffling a word; for instance, the Spanish word acaece is a shuffle square but not a square. We discuss both known and novel enumerative problems related to shuffle squares, with a focus on the number of distinct roots of binary shuffle squares. We introduce the term explicit shuffle squares, propose several conjectures, and present some preliminary results towards their resolution. Our discussion is supported by computational experiments. In particular, we determine the exact number of distinct roots of binary shuffle squares with a length of up to 24. On the other hand, we show that every non-constant binary word of length n generates at least n different shuffle squares. Full article

(This article belongs to the Special Issue Symmetry in Numerical Analysis and Applied Mathematics)

20 pages, 3535 KiB

Open AccessArticle

L_2,1-Norm Regularized Double Non-Negative Matrix Factorization for Hyperspectral Change Detection

by Xing-Hui Zhu, Meng-Ting Li, Yang-Jun Deng, Xu Luo, Lu-Ming Shen and Chen-Feng Long

Symmetry 2025, 17(2), 304; https://doi.org/10.3390/sym17020304 - 17 Feb 2025

Viewed by 503

Abstract

Hyperspectral image (HSI) change detection (CD) is an important technology for identifying surface changes using multi-temporal HSIs. Nevertheless, the high dimensionality of HSIs presents significant challenges for CD tasks, including issues such as lack of robustness and high computational costs in existing methods. [...] Read more.

Hyperspectral image (HSI) change detection (CD) is an important technology for identifying surface changes using multi-temporal HSIs. Nevertheless, the high dimensionality of HSIs presents significant challenges for CD tasks, including issues such as lack of robustness and high computational costs in existing methods. To address those issues, this paper proposes an unsupervised simple and effective HSI CD model termed

L_{2, 1}

-norm regularized double non-negative matrix factorization (

L_{2, 1}

-DNMF). Specifically, the proposed model employs a symmetric double non-negative matrix factorization (NMF) framework to jointly analyze multitemporal HSIs, capturing their common and invariant structural information to construct a shared feature basis. Meanwhile, two non-negative feature weight matrices are learned to generate a differential image matrix that directly reflects the change regions. To enhance robustness against noise, an

L_{2, 1}

-norm constraint is imposed on the difference image matrix, ensuring that unchanged areas exhibit near-zero values while changed areas present nonzero values. Finally, comprehensive experiments performed on three benchmark hyperspectral datasets validated the efficacy of the proposed method, which is superior to some state-of-the-art ones regarding detection performance and computational cost. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Image Processing and Optimization)

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34 pages, 5593 KiB

Open AccessArticle

Toward a Quantum Computing Formulation of the Electron Nuclear Dynamics Method via Fukutome Unitary Representation

by Juan C. Dominguez, Ismael de Farias and Jorge A. Morales

Symmetry 2025, 17(2), 303; https://doi.org/10.3390/sym17020303 - 17 Feb 2025

Cited by 1 | Viewed by 671

Abstract

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with [...] Read more.

We present the first step toward the quantum computing (QC) formulation of the electron nuclear dynamics (END) method within the variational quantum simulator (VQS) scheme: END/QC/VQS. END is a time-dependent, variational, on-the-flight, and non-adiabatic method to simulate chemical reactions. END represents nuclei with frozen Gaussian wave packets and electrons with a single-determinantal state in the Thouless non-unitary representation. Within the hybrid quantum/classical VQS, END/QC/VQS currently evaluates the metric matrix M and gradient vector V of the symplectic END/QC equations on the QC software development kit QISKIT, and calculates basis function integrals and time evolution on a classical computer. To adapt END to QC, we substitute the Thouless non-unitary representation with Fukutome unitary representation. We derive the first END/QC/VQS version for pure electronic dynamics in multielectron chemical models consisting of two-electron units with fixed nuclei. Therein, Fukutome unitary matrices factorize into triads of one-qubit rotational matrices, which leads to a QC encoding of one electron per qubit. We design QC circuits to evaluate M and V in one-electron diatomic molecules. In log2-log2 plots, errors and deviations of those evaluations decrease linearly with the number of shots and with slopes = −1/2. We illustrate an END/QC/VQS simulation with the pure electronic dynamics of H₂⁺ We discuss the present results and future END/QC/QVS extensions. Full article

(This article belongs to the Special Issue Symmetry Aspects in Quantum Computing)

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26 pages, 1678 KiB

Open AccessArticle

Study of Change-Point Detection and Applications Based on Several Statistical Methods

by Fenglin Tian, Yue Qi, Yong Wang and Boping Tian

Symmetry 2025, 17(2), 302; https://doi.org/10.3390/sym17020302 - 17 Feb 2025

Viewed by 520

Abstract

In the current global context of economic integration, unexpected events have an important influence in the financial field. In 2020, the “COVID-19” outbreak triggered financial turmoil throughout the whole country and even in the global market. In the wake of this era, how [...] Read more.

In the current global context of economic integration, unexpected events have an important influence in the financial field. In 2020, the “COVID-19” outbreak triggered financial turmoil throughout the whole country and even in the global market. In the wake of this era, how to sum up past developments and predict future development through change-point detection is particularly important. In this paper, four methods for detecting change-points are presented: the likelihood ratio method, least squares method, CUSUM method, and local comparison method. Considering that Bernstein polynomials have worked well in density function approximation, the multi-dimensional Bernstein polynomials are presented. The study applies multiple change-point detection methods to determine the most suitable degree of freedom

m_{j}

for multi-dimensional Bernstein models, after which various rewriting expressions can be obtained. Next, “COVID-19” data and money supply data are used for change-point detection with good results. Then, we focus on conducting change-point testing on the S&P 500 index and SSE 50 index, indicating strong symmetry when major crisis events occur. All analyses indicate that change-point detection plays an important role in identifying major crisis events and financial shocks. Full article

(This article belongs to the Section Mathematics)

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29 pages, 3567 KiB

Open AccessArticle

Kinematic Fuzzy Logic-Based Controller for Trajectory Tracking of Wheeled Mobile Robots in Virtual Environments

by José G. Pérez-Juárez, José R. García-Martínez, Alejandro Medina Santiago, Edson E. Cruz-Miguel, Luis F. Olmedo-García, Omar A. Barra-Vázquez and Miguel A. Rojas-Hernández

Symmetry 2025, 17(2), 301; https://doi.org/10.3390/sym17020301 - 17 Feb 2025

Cited by 1 | Viewed by 770

Abstract

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller [...] Read more.

Mobile robots represent one of the most relevant areas of study within robotics due to their potential for designing and developing new nonlinear control structures that can be implemented in simulations and applications in specific environments. In this work, a fuzzy steering controller with a symmetric distribution of fuzzy numbers is proposed and designed for implementation in the kinematic model of a non-holonomic mobile robot. The symmetry in the distribution of triangular fuzzy numbers contributes to a balanced response to disturbances and minimizes systematic errors in direction estimation. Additionally, it improves the system’s adaptability to various reference paths, ensuring accurate tracking and optimized performance in robot navigation. Furthermore, this fuzzy logic-based controller emulates the behavior of a classic PID controller by offering a robust and flexible alternative to traditional methods. A virtual environment was also developed using the UNITY platform to evaluate the performance of the fuzzy controller. The results were evaluated by considering the average tracking error, maximum error, steady-state error, settling time, and total distance traveled, emphasizing the trajectory error. The circular trajectory showed high accuracy with an average error of 0.0089 m, while the cross trajectory presented 0.01814 m, reflecting slight deviations in the turns. The point-to-point trajectory registered a more significant error of 0.9531 m due to abrupt transitions, although with effective corrections in a steady state. The simulation results validate the robustness of the proposed fuzzy controller, providing quantitative insights into its precision and efficiency in a virtual environment, and demonstrating the effectiveness of the proposal. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Fuzzy Control)

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3 pages, 126 KiB

Open AccessEditorial

Symmetry in Civil Transportation Engineering

by Yao Bai and Renliang Shan

Symmetry 2025, 17(2), 300; https://doi.org/10.3390/sym17020300 - 17 Feb 2025

Viewed by 528

Abstract

Symmetrical structures, such as tunnels, diaphragm walls, and blasting charge structures, are becoming increasingly prevalent in civil transportation engineering [...] Full article

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

18 pages, 3447 KiB

Open AccessArticle

A Geometric Berry Phase Angle Induced in Im-3m H₃S at 200 GPa by Ultra-Fast Laser Pulses

by Genwei Hong, Xinjie Zhou, Huan He, Tianlv Xu, Herbert Früchtl, Tanja van Mourik, Yaxin Zhai, Steven R. Kirk and Samantha Jenkins

Symmetry 2025, 17(2), 299; https://doi.org/10.3390/sym17020299 - 16 Feb 2025

Viewed by 624

Abstract

We investigated Im-3m H₃S at 200 GPa, a pressure regime where crystalline H₃S is widely considered to be a superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics [...] Read more.

We investigated Im-3m H₃S at 200 GPa, a pressure regime where crystalline H₃S is widely considered to be a superconductor. Simulated circularly polarized 10 femtosecond (fs) laser pulses were applied and we quantified the effects on the electron dynamics both during the application of the ultra-fast laser pulse and 5.0 fs after the pulse was switched off. In addition, the carrier-envelope phase (CEP) angle ϕ, which quantifies the relationship between the time-varying direction of electric (E)-field and the amplitude envelope, is employed to control the time evolution of the wavefunction ψ(r). This is undertaken for the first application of Next Generation Quantum Theory of Atoms in Molecules (NG-QTAIM) to the solid state. Ultra-fast phenomena related to superconductivity are discovered in the form of a geometric Berry phase angle associated with the H--H bonding in addition to very high values of the chirality–helicity function that correspond to values normally found in chiral molecules. Future applications are discussed, including chiral spin selective phenomena in addition to high-temperature superconductivity and organic superconductors where phonons do not play a significant role. Full article

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

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23 pages, 19012 KiB

Open AccessArticle

Modeling and Research on Multi-Speed Heterogeneous Crowd Evacuation with Asymmetric Competitiveness

by Yuanchun Ding and Binwen Liu

Symmetry 2025, 17(2), 298; https://doi.org/10.3390/sym17020298 - 16 Feb 2025

Viewed by 576

Abstract

In order to investigate the influence of factors such as pheromones and avoidance behavior on the evacuation of heterogeneous crowds, a multi-speed cellular automata evacuation model based on asymmetric competitiveness is proposed for the evacuation of the complex groups in a single-exit room. [...] Read more.

In order to investigate the influence of factors such as pheromones and avoidance behavior on the evacuation of heterogeneous crowds, a multi-speed cellular automata evacuation model based on asymmetric competitiveness is proposed for the evacuation of the complex groups in a single-exit room. By optimizing the crowd density and pedestrian speed equations, multi-speed heterogeneous crowds can be obtained in the model. In order to achieve the description of a multi-dimensional asymmetric competitiveness heterogeneous population, the evacuation competitiveness is considered in the pedestrians with different speed, age, gender, etc., and by considering the avoidance character existing among pedestrians, the avoidance behavior is also discussed in this model. It is well known that the information received by different pedestrians is different. In order to consider the asymmetry of information, the pheromones are introduced into the evacuation model to discuss the effect of information differences on evacuation. The evacuation results show that the asymmetry of information has a facilitating effect on the evacuation speed of pedestrians, and the best evacuation effect is obtained when the radius of the pheromone is about 3 m. Moreover, evacuation time is weakly correlated with pedestrians’ gender but strongly correlated with pedestrians’ age. The avoidance behavior plays a positive role in evacuation, and the evacuation time reaches the minimum value when the avoidance probability is about 0.5. The slope of the reduction in evacuation time is greatest when the avoidance threshold is 0.4 to 0.8. The findings can support evacuation capacity assessment, emergency planning, and decision making. Full article

(This article belongs to the Section Mathematics)

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24 pages, 5661 KiB

Open AccessFeature PaperArticle

Symmetry-Inspired Prediction of Nitrous Oxide Emissions in Wastewater Treatment Using Deep Learning and Explainable Analysis

by Zhengze Huang, Yuqi Bai and Hengyu Liu

Symmetry 2025, 17(2), 297; https://doi.org/10.3390/sym17020297 - 16 Feb 2025

Viewed by 593

Abstract

Nitrous oxide produced during wastewater treatment is a major greenhouse gas, and accurate prediction and control of N₂O emissions are crucial for achieving carbon neutrality. In this study, aiming to address the complex issues of N₂O emission prediction in [...] Read more.

Nitrous oxide produced during wastewater treatment is a major greenhouse gas, and accurate prediction and control of N₂O emissions are crucial for achieving carbon neutrality. In this study, aiming to address the complex issues of N₂O emission prediction in wastewater treatment, large-scale multidimensional data from the Altenrhein wastewater treatment plant was used to build a sample database. The role of symmetry in model architecture and data analysis was discussed, and six intelligent prediction models for N₂O emissions were proposed based on deep learning technology. The results showed that the PLO-CNN-BiLSTM-Attention model achieved the best performance, with an R² of 0.99 on the test set. Engineering validation using 48 subsequent datasets confirmed the model’s strong generalization ability and robustness. Feature importance analysis based on SHAP revealed that water temperature was the most critical factor influencing N₂O emissions, while dissolved oxygen concentration and inlet flow rate also had impacts but showed a certain symmetrical change between summer and winter. This study provides efficient and reliable technical support for monitoring and predicting N₂O emissions in urban wastewater treatment plants and offers a scientific basis for developing strategies to reduce greenhouse gas emissions. Full article

(This article belongs to the Section Computer)

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16 pages, 4920 KiB

Open AccessArticle

Molecular Dynamics Simulations of CeO₂ Nano-Fuel: Thermodynamic and Kinetic Properties

by Rui Zhang, Jianbo Zhou, Yingjie Zhao, Zhen He, Wenxiong Xi and Weidong Zhao

Symmetry 2025, 17(2), 296; https://doi.org/10.3390/sym17020296 - 16 Feb 2025

Viewed by 613

Abstract

This study explores the thermodynamic and kinetic properties of CeO₂ nano-fuels, with a particular focus on the influence of nanoparticle additives on the diffusion and thermal conductivity of C14-based fuel systems. Using molecular dynamics simulations and the COMPASS force field, we model [...] Read more.

This study explores the thermodynamic and kinetic properties of CeO₂ nano-fuels, with a particular focus on the influence of nanoparticle additives on the diffusion and thermal conductivity of C14-based fuel systems. Using molecular dynamics simulations and the COMPASS force field, we model the interactions between C14 molecules and CeO₂ nanoparticles, varying nanoparticle size and concentration. Our results reveal that the inclusion of CeO₂ nanoparticles leads to significant enhancements in both thermal conductivity (increasing by 9.8–23.6%) and diffusion coefficients (increasing by approximately 140%) within the 20 °C to 100 °C temperature range. These improvements are attributed to the interactions between nanoparticles and fuel molecules, which facilitate more efficient energy and mass transport. Notably, nanoparticles with smaller sizes (0.2 nm and 0.5 nm) exhibit more pronounced effects on both the thermodynamic and kinetic properties than larger nanoparticle analogs (20 nm and 50 nm). The study also highlights the temperature-dependent nature of these properties, demonstrating that nanoparticle additives enhance the fuel’s thermal stability and diffusion behavior, particularly at elevated temperatures. This work provides valuable insights into the optimization of nano-fuel systems, with potential applications in enhancing the performance and efficiency of diesel combustion and heat transfer processes. Full article

(This article belongs to the Special Issue Symmetry Studies in Heat and Mass Transfer)

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13 pages, 262 KiB

Open AccessArticle

Initial Value Problem for Mixed Differential Equations of Variable Order with Finite Delay

by Souad Guedim, Amar Benkerrouche, Kanokwan Sitthithakerngkiet, Mohammed Said Souid and Abdelkader Amara

Symmetry 2025, 17(2), 295; https://doi.org/10.3390/sym17020295 - 15 Feb 2025

Viewed by 432

Abstract

This study presents a fresh perspective on the existence, uniqueness, and stability of solutions for initial value problems involving variable-order differential equations with finite delay. Departing from conventional techniques that utilize generalized intervals and piecewise constant functions, we introduce a novel fractional operator [...] Read more.

This study presents a fresh perspective on the existence, uniqueness, and stability of solutions for initial value problems involving variable-order differential equations with finite delay. Departing from conventional techniques that utilize generalized intervals and piecewise constant functions, we introduce a novel fractional operator tailored for this specific problem. Our methodology integrates sophisticated mathematical analysis, including the Schauder fixed-point theorem and Banach’s contraction principle, with an examination of the Ulam–Hyers stability of the problem. The strength of our approach is in its simplicity, requiring fewer restrictive assumptions. We conclude with a practical application to illustrate our findings. These results are valuable for understanding complex dynamical systems with time delays, offering applications in diverse fields such as engineering, economics, and medicine, and enhancing numerical methods for solving delay equations. Full article

(This article belongs to the Section Mathematics)

25 pages, 7932 KiB

Open AccessArticle

An Efficient Traceable and Revocable Access Control Scheme for Smart Grids

by Ye Lu, Hao Wang and Xiaomei Jin

Symmetry 2025, 17(2), 294; https://doi.org/10.3390/sym17020294 - 14 Feb 2025

Viewed by 478

Abstract

In smart grids, power monitoring equipment produces large volumes of data that are exchanged between microgrids and the main grid. This data exchange can potentially expose users’ private information, including their living habits and economic status. Therefore, implementing secure and effective data access [...] Read more.

In smart grids, power monitoring equipment produces large volumes of data that are exchanged between microgrids and the main grid. This data exchange can potentially expose users’ private information, including their living habits and economic status. Therefore, implementing secure and effective data access control mechanisms is crucial. Ciphertext-Policy Attribute-Based Encryption (CP-ABE) is a widely used encryption scheme in distributed systems, offering fine-grained access control. However, in CP-ABE systems, malicious users might leak decryption keys to third parties, creating a significant security threat. Thus, there is an urgent need for tracing mechanisms to identify and track these malicious users. Moreover, tracing and user revocation are complementary processes. Although using a binary tree for user revocation is efficient, it limits the number of users. This paper suggests an access control scheme that combines CP-ABE with blockchain to overcome these limitations, leveraging blockchain’s tamper-resistant features. This scheme enables user revocation, tracing, partial policy hiding, and ciphertext searchability, and it has been proven secure. Simulation results show that our approach reduces time overhead by 24% to 68%, compared to other solutions. While some solutions are similar in efficiency to ours, our approach offers more comprehensive functionality and better meets the security requirements of smart grids. Full article

(This article belongs to the Section Computer)

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66 pages, 24939 KiB

Open AccessReview

Dynamic Point-to-Helical and Point-to-Axial Chirality Transmission and Induction of Optical Activity in Multichromophoric Systems: Basic Principles and Relevant Applications in Chirality Sensing

by Tomasz Mądry, Jadwiga Gajewy and Marcin Kwit

Symmetry 2025, 17(2), 293; https://doi.org/10.3390/sym17020293 - 14 Feb 2025

Viewed by 971

Abstract

The analysis of natural and artificial chiral compounds is vital wherever the nuances in the three-dimensional structure are decisive for the possibility of their further use, e.g., as pharmaceuticals or catalysts. The qualitative determination of the structure of a chiral entity requires either [...] Read more.

The analysis of natural and artificial chiral compounds is vital wherever the nuances in the three-dimensional structure are decisive for the possibility of their further use, e.g., as pharmaceuticals or catalysts. The qualitative determination of the structure of a chiral entity requires either an anomalous scattering of X-ray radiation or chiroptical techniques, of which electronic circular dichroism (ECD) is one of the most useful. Chiroptical sensing that uses stereodynamic probes remains one of the remedies for the problem of the lack of a suitable chromophore in the molecules of the chiral compound. A covalent or non-covalent binding of an ECD-silent chiral molecule (the inducer) to the UV-active chromophoric system (chiroptical probe) led to obtaining complex ECD active at a given spectral region. The transfer of structural information from a permanently chiral inducer molecule to the structurally labile chromophoric system of the probe results in adjusting the latter’s structure to the chiral environment. This contribution focuses on some fundamental aspects of chirality sensing using conformationally labile probes. It discusses the mechanism of action of arbitrarily chosen stereodynamic chirality sensors, with particular emphasis on probes based on di- and triarylmethyl derivatives and biphenyl and its congeners. Full article

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

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18 pages, 320 KiB

Open AccessArticle

Symmetric Spaces of Qubits and Gaussian Modes

by Antonio de Jesús Castillo Moctezuma, José Luis Lucio and Alan Josué Sierra-Torres

Symmetry 2025, 17(2), 292; https://doi.org/10.3390/sym17020292 - 14 Feb 2025

Viewed by 505

Abstract

The understanding of the properties of multipartite systems is a long-standing challenge in quantum theory that signals the need for new ideas and alternative frameworks that can shed light on the intricacies of quantum behavior. In this work, we argue that symmetric spaces [...] Read more.

The understanding of the properties of multipartite systems is a long-standing challenge in quantum theory that signals the need for new ideas and alternative frameworks that can shed light on the intricacies of quantum behavior. In this work, we argue that symmetric spaces provide a common language to describe two-qubit and two-mode Gaussian systems. Our approach relies on the use of equivalence classes that are defined by a subgroup of the maximal symmetry group of the system and involves an involution which enables the Cartan decomposition of the group elements. We work out the symmetric spaces of two qubits and two modes to identify classes which include an equal degree of mixing states, product states, and X states, among others. For three qubits and three modes, we point out how the framework can be generalized and report partial results about the physical interpretations of the symmetric spaces. Full article

(This article belongs to the Section Physics)

19 pages, 955 KiB

Open AccessArticle

Resolving the Open Problem by Proving a Conjecture on the Inverse Mostar Index for c-Cyclic Graphs

by Liju Alex and Kinkar Chandra Das

Symmetry 2025, 17(2), 291; https://doi.org/10.3390/sym17020291 - 14 Feb 2025

Viewed by 409

Abstract

Inverse topological index problems involve determining whether a graph exists with a given integer as its topological index. One such index, the Mostar index,

M o (G)

, is defined as [...] Read more.

Inverse topological index problems involve determining whether a graph exists with a given integer as its topological index. One such index, the Mostar index,

M o (G)

, is defined as

M o (G) = \sum_{u v \in E (G)} | n_{u} (e | G) - n_{v} (e | G) |,

where

n_{u} (e | G)

and

n_{v} (e | G)

represent the number of vertices closer to vertex u than v and closer to v than u, respectively, for an edge

e = u v

. The inverse Mostar index problem has gained significant attention recently. In their work, Alizadeh et al. [Solving the Mostar index inverse problem, J. Math. Chem. 62 (5) (2024) 1079–1093] proposed the following open problem: “Which nonnegative integers can be realized as Mostar indices of c-cyclic graphs, for a given positive integer c?”. Subsequently, one of the present authors [On the inverse Mostar index problem for molecular graphs, Trans. Comb. 14 (1) (2024) 65–77] conjectured that, except for finitely many positive integers, all other positive integers can be realized as the Mostar index of a c-cyclic graph, where

c \geq 3

. In this paper, we address the inverse Mostar index problem for c-cyclic graphs. Specifically, we construct infinitely many families of symmetric c-cyclic structures, thereby demonstrating a solution to the inverse Mostar index problem using an infinite family of such symmetric structures. By providing a comprehensive proof of the conjecture, we fully resolve this longstanding open problem. Full article

(This article belongs to the Special Issue Symmetry and Graph Theory, 2nd Edition)

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20 pages, 37686 KiB

Open AccessArticle

Multi-Source Training-Free Controllable Style Transfer via Diffusion Models

by Cuihong Yu, Cheng Han and Chao Zhang

Symmetry 2025, 17(2), 290; https://doi.org/10.3390/sym17020290 - 13 Feb 2025

Cited by 1 | Viewed by 1453

Abstract

Diffusion models, as representative models in the field of artificial intelligence, have made significant progress in text-to-image synthesis. However, studies of style transfer using diffusion models typically require a large amount of text to describe semantic content or specific painting attributes, and the [...] Read more.

Diffusion models, as representative models in the field of artificial intelligence, have made significant progress in text-to-image synthesis. However, studies of style transfer using diffusion models typically require a large amount of text to describe semantic content or specific painting attributes, and the style and layout of semantic content in synthesized images are frequently uncertain. To accomplish high-quality fixed content style transfer, this paper adopts text-free guidance and proposes a multi-source, training-free and controllable style transfer method by using single image or video as content input and single or multiple style images as style guidance. To be specific, the proposed method firstly fuses the inversion noise of a content image with that of a single or multiple style images as the initial noise of stylized image sampling process. Then, the proposed method extracts the self-attention mechanism’s query, key, and value vectors from the DDIM inversion process of content and style images and injects them into the stylized image sampling process to improve the color, texture and semantics of stylized images. By setting the hyperparameters involved in the proposed method, the style transfer effect of symmetric style proportion and asymmetric style distribution can be achieved. By comparing with state-of-the-art baselines, the proposed method demonstrates high fidelity and excellent stylized performance, and can be applied to numerous image or video style transfer tasks. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Artificial Intelligence and Machine Learning-Based Image Processing)

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21 pages, 7863 KiB

Open AccessArticle

Enhancement of Thermomechanical Protocol for Automotive Brake Using the Symmetry of the Disc: Numerical Validation and Material Selection

by Mohammed Berrada Gouzi, Ali Hajjia, Ahmed El Khalfi, Bilal Harras, Sorin Vlase and Maria Luminita Scutaru

Symmetry 2025, 17(2), 289; https://doi.org/10.3390/sym17020289 - 13 Feb 2025

Viewed by 584

Abstract

In the context of the automotive industry, this paper proposes an enhancement of the numerical simulation using FEM and performing material choosing with the Ashby method for automotive brake discs, using the symmetric shape of the disc. Automotive braking involves the dissipation of [...] Read more.

In the context of the automotive industry, this paper proposes an enhancement of the numerical simulation using FEM and performing material choosing with the Ashby method for automotive brake discs, using the symmetric shape of the disc. Automotive braking involves the dissipation of kinetic energy through heat generation due to friction, a physical phenomenon that alters the mechanical properties of brake discs. This prompts automotive development engineers to investigate new materials capable of absorbing heat while maintaining their mechanical properties. A thermomechanical study of a ventilated front brake disc has successfully demonstrated a good performance of cast iron because the equivalent stress is significantly lower than the elastic limit, with a margin of approximately 73 MPa. Compared to validated results extracted from the state of the art, the adopted methodology gives more realistic results with minimum CPU requirements, where the total time of calculation is around 40 min. More than that, the results are suitable to be used for studying durability and other properties like mechanical impact and fatigue. Full article

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

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15 pages, 298 KiB

Open AccessArticle

Symmetry Properties and Their Application to Hilfer Fractional Systems

by Beata Sikora

Symmetry 2025, 17(2), 288; https://doi.org/10.3390/sym17020288 - 13 Feb 2025

Viewed by 413

Abstract

The paper investigates semilinear Hilfer fractional systems. A symmetric fractional derivative and its properties are discussed. A symmetrized model for these systems is proposed and examined. A bounded nonlinear function

f

is applied, depending on the time as well as on the state. [...] Read more.

The paper investigates semilinear Hilfer fractional systems. A symmetric fractional derivative and its properties are discussed. A symmetrized model for these systems is proposed and examined. A bounded nonlinear function

f

is applied, depending on the time as well as on the state. The Laplace transformation is used to derive the solution formula for the systems under consideration. The primary contribution of the paper is the formulation and proof of controllability criteria for symmetrized Hilfer systems. To deepen the understanding of the dynamics of such systems, the concept of reflection symmetries is introduced with a detailed analysis of their essential features, including projection functions and a reflection operator. Furthermore, a decomposition of the symmetric Hilfer fractional derivative is presented, utilizing the projection function and reflection operator. This decomposition not only provides a controllability condition for symmetrized Hilfer systems but also clarifies the relationship between the system’s trajectory across subintervals. Two illustrative examples are presented to demonstrate the computational and practical significance of the theoretical results. Full article

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

17 pages, 5463 KiB

Open AccessArticle

Asymmetric Finite-Range Persistence in Time Series Generated by the Modified Discrete Langevin Model

by Zbigniew Czechowski

Symmetry 2025, 17(2), 287; https://doi.org/10.3390/sym17020287 - 13 Feb 2025

Viewed by 474

Abstract

The concept of asymmetric persistence in time series was proposed and an appropriate stochastic Langevin-type model was presented. The influence of this particular form of memory on the behavior of the generated time series was examined. It has been shown that asymmetry causes [...] Read more.

The concept of asymmetric persistence in time series was proposed and an appropriate stochastic Langevin-type model was presented. The influence of this particular form of memory on the behavior of the generated time series was examined. It has been shown that asymmetry causes a significant distortion of the effect of drift forces and has a weaker impact on stochastic diffusion forces. Due to this, the current known methods for reconstructing the Langevin-type model fail. The results of this work may help in deriving a new reconstruction method. Full article

(This article belongs to the Section Physics)

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13 pages, 3483 KiB

Open AccessArticle

Deep Learning-Based Exposure Asymmetry Multispectral Reconstruction from Digital RGB Images

by Jinxing Liang, Xin Hu, Wensen Zhou, Kaida Xiao and Zhaojing Wang

Symmetry 2025, 17(2), 286; https://doi.org/10.3390/sym17020286 - 13 Feb 2025

Viewed by 649

Abstract

Multispectral reconstruction is an important way to acquire spectral images with a high spatial resolution as snapshots. Current deep learning-based multispectral reconstruction models perform well under symmetric conditions, where the exposure of training and testing images is consistent. However, further research has shown [...] Read more.

Multispectral reconstruction is an important way to acquire spectral images with a high spatial resolution as snapshots. Current deep learning-based multispectral reconstruction models perform well under symmetric conditions, where the exposure of training and testing images is consistent. However, further research has shown that these models are sensitive to exposure changes. When the exposure symmetry is not maintained and testing images are input into the multispectral reconstruction model under different exposure conditions, the reconstructed multispectral images tend to deviate from the real ground truth to varying degrees. This limitation restricts the robustness and applicability of the model in practical scenarios. To address this challenge, we propose an exposure estimation multispectral reconstruction model of EFMST++ with data augmentation and optimized deep learning architecture, where Retinex decomposition and a wavelet transform are introduced into the proposed model. Based on the currently available dataset in this field, a comprehensive comparison is made between the proposed and existing models. The results show that after the current multispectral reconstruction models are retrained using the augmented datasets, the average MRAE and RMSE of the current most advanced model of MST++ are reduced from 0.570 and 0.064 to 0.236 and 0.040, respectively. The proposed method further reduces the average MRAE and RMSE to 0.229 and 0.037, with the average PSNR increasing from 27.94 to 31.43. The proposed model supports the use of multispectral reconstruction in open environments. Full article

(This article belongs to the Section Computer)

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20 pages, 1332 KiB

Open AccessArticle

Time-Irreversible Quantum-Classical Dynamics of Molecular Models in the Brain

by Alessandro Sergi, Antonino Messina, Rosalba Saija, Gabriella Martino, Maria Teresa Caccamo, Min-Fang Kuo and Michael A. Nitsche

Symmetry 2025, 17(2), 285; https://doi.org/10.3390/sym17020285 - 13 Feb 2025

Cited by 1 | Viewed by 695

Abstract

This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other approaches, briefly sketched in the text, have advocated the need to deal [...] Read more.

This manuscript aims to illustrate a quantum-classical dissipative theory (suited to be converted to effective algorithms for numerical simulations) within the long-term project of studying molecular processes in the brain. Other approaches, briefly sketched in the text, have advocated the need to deal with both quantum and classical dynamic variables when studying the brain. At variance with these other frameworks, the manuscript’s formalism allows us to explicitly treat the classical dynamical variables. The theory must be dissipative not because of formal requirements but because brain processes appear to be dissipative at the molecular, physiological, and high functional levels. We discuss theoretically that using Brownian dynamics or the Nosè-Hoover-Chain thermostat to perform computer simulations provides an effective way to introduce an arrow of time for open quantum systems in a classical environment. In the future, We plan to study classical models of neurons and astrocytes, as well as their networks, coupled to quantum dynamical variables describing, e.g., nuclear and electron spins, HOMO and LUMO orbitals of phenyl and indole rings, ion channels, and tunneling protons. Full article

(This article belongs to the Section Physics)

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24 pages, 1188 KiB

Open AccessArticle

A Probabilistic Approach to Overestimation by an Imperfect Inspector Subject to Random Defective Rates

by Kyo-Chan Koo

Symmetry 2025, 17(2), 284; https://doi.org/10.3390/sym17020284 - 12 Feb 2025

Viewed by 566

Abstract

This study investigates overestimations in defect inspections performed by imperfect inspectors, particularly in scenarios involving random defective rates. Mathematical models are developed under two key assumptions: (1) inspection errors are either constant or uniformly distributed and (2) defective rates follow a random uniform [...] Read more.

This study investigates overestimations in defect inspections performed by imperfect inspectors, particularly in scenarios involving random defective rates. Mathematical models are developed under two key assumptions: (1) inspection errors are either constant or uniformly distributed and (2) defective rates follow a random uniform distribution. Four analytical models are used to evaluate the probability of overestimation (PO) and identify critical defect rate thresholds (CFBs). The findings reveal that the PO approaches 100% as defect rates approach zero, irrespective of inspection error characteristics. Sensitivity analysis demonstrates model robustness under varying error distributions and parameter changes. Addressing practical concerns, this research highlights the need to revise inspection schemes to mitigate biases, especially in industries with stringent quality control standards, such as electronics and pharmaceuticals. Recommendations include integrating probabilistic error models and adopting dynamic calibration systems to improve inspection accuracy. By providing a theoretical foundation for tackling overestimation, this study has significant implications for improving fairness and efficiency in global supply chains. Full article

(This article belongs to the Section Mathematics)

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Symmetry, Volume 17, Issue 2 (February 2025) – 166 articles

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