Symmetry

19 pages, 714 KB

Open AccessArticle

The Determination Risk Level of Manufacturing Process Based on IF-TOPSIS and IF-Fuzzy Logic Rules

by Ranka Sudžum, Snežana Nestić, Aleksandar Aleksić, Nikola Komatina, Dragan Marinković and Slaviša Moljević

Symmetry 2025, 17(9), 1535; https://doi.org/10.3390/sym17091535 (registering DOI) - 14 Sep 2025

Abstract

In a dynamic and uncertain environment, maintaining a high level of business process (BP) reliability represents a key long-term objective for organizations. The manufacturing process, as the most critical business process in manufacturing enterprises, is emphasized due to its potential to cause significant [...] Read more.

In a dynamic and uncertain environment, maintaining a high level of business process (BP) reliability represents a key long-term objective for organizations. The manufacturing process, as the most critical business process in manufacturing enterprises, is emphasized due to its potential to cause significant disruptions across other BPs if it fails. This paper proposes a two-stage model. In the first stage, failures leading to lean waste are evaluated and ranked using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) combined with interval-valued intuitionistic fuzzy numbers (IVIFNs), referred to as IF-TOPSIS. The model is grounded in the Failure Mode and Effect Analysis (FMEA) framework. In the second stage, a modified fuzzy logic system with IVIFN-based rules is applied to determine the risk level of the manufacturing process. This approach is based on the property of symmetry in the decision-making process, ensuring that criteria are treated in a balanced manner and inference rules are applied consistently. A case study based on real-life data demonstrates that the obtained results identify measures that can enhance business strategy and reduce failure rates. Thus, the model is validated and shown to contribute to lean waste reduction. It can be concluded that the proposed methodology provides clear and practical guidance to enterprise management, as well as to all sectors and individuals involved in ensuring a reliable manufacturing process, for defining failure priorities and implementing preventive measures. Full article

(This article belongs to the Special Issue Computing with Words with Symmetry)

27 pages, 354 KB

Open AccessArticle

New Families of Certain Special Polynomials: A Kaniadakis Calculus Viewpoint

by Ugur Duran, Mehmet Acikgoz and Serkan Araci

Symmetry 2025, 17(9), 1534; https://doi.org/10.3390/sym17091534 (registering DOI) - 14 Sep 2025

Abstract

In this paper, we introduce a new family of Stirling polynomials of the second kind, Bell polynomials, bivariate Bell polynomials, Bernoulli polynomials of higher order, and Euler polynomials of higher order arising from the Kaniadakis calculus viewpoint. We refer to each of them [...] Read more.

In this paper, we introduce a new family of Stirling polynomials of the second kind, Bell polynomials, bivariate Bell polynomials, Bernoulli polynomials of higher order, and Euler polynomials of higher order arising from the Kaniadakis calculus viewpoint. We refer to each of them as

κ

-polynomials. Through the defined concepts of Kaniadakis calculus, we derive explicit formulas, summation formulas, and addition formulas for the polynomials discussed in the present paper. We also present the Volkenborn integral and the fermionic p-adic integral representations in terms of the

κ

-Stirling polynomials of the second kind, bivariate

κ

-Bell polynomials,

κ

-Bernoulli polynomials of higher order, and

κ

-Euler polynomials of higher order. We establish some formulae, including old and new polynomials. Finally, we investigate determinantal representations for the

κ

-Euler polynomials and the

κ

-Bernoulli polynomials. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials: 3rd Edition)

16 pages, 1133 KB

Open AccessArticle

An Analytical Solution for the Uncertain Damped Wave Equation

by Huimin Zhang, Zhenhui Zhang and Shaoling Zhou

Symmetry 2025, 17(9), 1533; https://doi.org/10.3390/sym17091533 (registering DOI) - 14 Sep 2025

Abstract

Damped wave equations, as an important class of partial differential equations, have wide applications in fields such as acoustics, signal processing, and fluid mechanics. However, wave propagation is often affected by noise interference, including medium randomness, random external forces and so on. Therefore, [...] Read more.

Damped wave equations, as an important class of partial differential equations, have wide applications in fields such as acoustics, signal processing, and fluid mechanics. However, wave propagation is often affected by noise interference, including medium randomness, random external forces and so on. Therefore, an uncertain term needs to be added to the damped wave equation to enhance the model’s fidelity to real-world scenarios. Based on uncertainty theory, this paper introduces the Liu process to the damped wave equation to characterize uncertainties, thereby establishing a new type of equation—the uncertain damped wave equation. In order to solve this equation, the method of separation of variables is employed to derive the analytical solution. The uniqueness of the solution is proved under given initial and boundary conditions. Finally, several examples are provided to illustrate the analytical solutions. Full article

(This article belongs to the Special Issue Symmetry Applications in Uncertain Differential Equations)

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20 pages, 447 KB

Open AccessArticle

Coefficient Estimates and Symmetry Analysis for Certain Families of Bi-Univalent Functions Defined by the 𝒒-Bernoulli Polynomial

by Abbas Kareem Wanas, Qasim Ali Shakir and Adriana Catas

Symmetry 2025, 17(9), 1532; https://doi.org/10.3390/sym17091532 (registering DOI) - 13 Sep 2025

Abstract

In the present work, we define certain families,

M_{Σ} (μ, Υ, ℷ, q; x)

and

N_{Σ} (μ, Υ, ℷ, q; x)

, of normalized holomorphic and bi-univalent functions associated with Bazilevič [...] Read more.

In the present work, we define certain families,

M_{Σ} (μ, Υ, ℷ, q; x)

and

N_{Σ} (μ, Υ, ℷ, q; x)

, of normalized holomorphic and bi-univalent functions associated with Bazilevič functions and

ℷ

-pseudo functions involving the

q

-Bernoulli polynomial, which is defined by the symmetric nature of quantum calculus in the open unit disk

U

. We determine the upper bounds for the initial symmetry Taylor–Maclaurin coefficients and the Fekete–Szegö-type inequalities of functions in the families we have introduced here. In addition, we indicate certain special cases and consequences for our results. Full article

(This article belongs to the Special Issue Applications of Special Functions in Complex Analysis and Their Symmetries)

19 pages, 2187 KB

Open AccessArticle

Balancing Feature Symmetry: IFEM-YOLOv13 for Robust Underwater Object Detection Under Degradation

by Zhen Feng and Fanghua Liu

Symmetry 2025, 17(9), 1531; https://doi.org/10.3390/sym17091531 (registering DOI) - 13 Sep 2025

Abstract

This paper proposes IFEM-YOLOv13, a high-precision underwater target detection method designed to address challenges such as image degradation, low contrast, and small target obscurity caused by light attenuation, scattering, and biofouling. Its core innovation is an end-to-end degradation-aware system featuring: (1) an Intelligent [...] Read more.

This paper proposes IFEM-YOLOv13, a high-precision underwater target detection method designed to address challenges such as image degradation, low contrast, and small target obscurity caused by light attenuation, scattering, and biofouling. Its core innovation is an end-to-end degradation-aware system featuring: (1) an Intelligent Feature Enhancement Module (IFEM) that employs learnable sharpening and pixel-level filtering for adaptive optical compensation, incorporating principles of symmetry in its multi-branch enhancement to balance color and structural recovery; (2) a degradation-aware Focal Loss incorporating dynamic gradient remapping and class balancing to mitigate sample imbalance through symmetry-preserving optimization; and (3) a cross-layer feature association mechanism for multi-scale contextual modeling that respects the inherent scale symmetry of natural objects. Evaluated on the J-EDI dataset, IFEM-YOLOv13 achieves 98.6% mAP@0.5 and 82.1% mAP@0.5:0.95, outperforming the baseline YOLOv13 by 0.7% and 3.0%, respectively. With only 2.5 M parameters and operating at 217 FPS, it surpasses methods including Faster R-CNN, YOLO variants, and RE-DETR. These results demonstrate its robust real-time detection capability for diverse underwater targets such as plastic debris, biofouled objects, and artificial structures, while effectively handling the symmetry-breaking distortions introduced by the underwater environment. Full article

(This article belongs to the Section Engineering and Materials)

26 pages, 12632 KB

Open AccessArticle

Application of an Improved Double Q-Learning Algorithm in Ground Mobile Robots

by Jinchao Zhao, Ya Zhang, Nan Wu, Xinye Han, Luoyin Ning, Xiaowei Ren, Lingling Fang, Jiaxuan Wang, Xu Ren, Yu Zhang and Jinghao Feng

Symmetry 2025, 17(9), 1530; https://doi.org/10.3390/sym17091530 - 12 Sep 2025

Abstract

Since efficient path planning technology is the key to the safe and autonomous navigation of autonomous ground robots, and in the complex and asymmetrically distributed land environment, the existing path planning and obstacle avoidance technologies seem somewhat inadequate. Since efficient path planning technology [...] Read more.

Since efficient path planning technology is the key to the safe and autonomous navigation of autonomous ground robots, and in the complex and asymmetrically distributed land environment, the existing path planning and obstacle avoidance technologies seem somewhat inadequate. Since efficient path planning technology is key to the safe and autonomous navigation of autonomous ground robots, an advanced double Q-learning algorithm based on self-supervised prediction and curiosity-driven exploration is proposed. The algorithm reduces the risk of overestimation and bootstrapping by adjusting the calculation method of the target Q value and optimizing the network structure. In addition, a priority experience replay is introduced to set the priority for the data in the experience pool, thereby increasing the probability that better data is extracted. Experience pool data with fewer training times can be used more effectively. Adding the curiosity network to the original neural network, each state is given an overall reward when performing diverse actions. This method enhances the exploration of unmanned ground mobile robots and can independently select the shortest path to the endpoint. In complex environments, compared with the Sparrow Search Algorithm, Dung Beetle Optimization Algorithm, and Particle Swarm Optimization Algorithm, the results of the proposed algorithm are reduced by 18.07%, 7.91%, and 5.56%, respectively. Therefore, it could better cope with the challenges brought by complex environments and solve the problem that the algorithm cannot converge in complex environments. Full article

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26 pages, 3019 KB

Open AccessArticle

Energy Analysis, Soliton Dynamics, Chaos, and Sensitivity Analysis for a Forced Damped Gardner Model

by Syed T. R. Rizvi, Atef F. Hashem, Aiman Shahbaz, Zunaira Iqbal, Ijaz Ali, A. S. Al-Moisheer and Aly R. Seadawy

Symmetry 2025, 17(9), 1529; https://doi.org/10.3390/sym17091529 - 12 Sep 2025

Abstract

In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equation, enabling the derivation of a wide class [...] Read more.

In this study, the complete discrimination system for the polynomial method (CDSPM) is employed to analyze the integrable Gardner Equation (IGE). Through a traveling wave transformation, the model is reduced to a nonlinear ordinary differential equation, enabling the derivation of a wide class of exact solutions, including trigonometric, hyperbolic, rational, and Jacobi elliptic functions. For example, a bright soliton solution is obtained for parameters

A = 1.3

,

β = - 0.1

, and

γ = 0.8

. Qualitative analysis reveals diverse phase portraits, indicating the presence of saddle points, centers, and cuspidal points depending on parameter values. Chaos and quasi-periodic dynamics are investigated via Poincaré maps and time-series analysis, where chaotic patterns emerge for values like

ν_{1} = 1.45

,

ν_{2} = 2.18

,

Ξ_{0} = 4

, and

λ = 2 π

. Sensitivity analysis confirms the model’s sensitivity to initial conditions

χ = 2.2, 2.4, 2.6

, reflecting real-world unpredictability. Additionally, the energy balance method (EBM) is applied to approximate periodic solutions by conserving kinetic and potential energies. These results highlight the IGE’s ability to capture complex nonlinear behaviors relevant to fluid dynamics, plasma waves, and nonlinear optics. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)

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12 pages, 2724 KB

Open AccessArticle

Tin Phthalocyanine Nanoprobes with Symmetric Macrocyclic Structures: Nonlinear Dynamics of Pulse Trains with Tunable ps/ns Subpulse Widths and Enhanced Optical Limiting for MEMS Microdevices

by Quan Miao, Erping Sun and Yan Xu

Symmetry 2025, 17(9), 1528; https://doi.org/10.3390/sym17091528 - 12 Sep 2025

Abstract

Tin phthalocyanine (SnPc) nanoprobes with strong reverse saturable absorption (RSA) are extremely needed for photoacoustic (PA) molecular imaging. The optical properties and dynamics of SnPc nanoprobes by pulse trains were studied. During the propagating of pulse trains in SnPc, the electronic structure of [...] Read more.

Tin phthalocyanine (SnPc) nanoprobes with strong reverse saturable absorption (RSA) are extremely needed for photoacoustic (PA) molecular imaging. The optical properties and dynamics of SnPc nanoprobes by pulse trains were studied. During the propagating of pulse trains in SnPc, the electronic structure of SnPc is simplified to the five-state energy model. The pulse train contains 25 subpulses with space 13 ns, and the widths of subpulses were set as

3.5

ps, 35 ps, 350 ps,

3.5

ns, 10 ns, 20 ns, 35 ns and 100 ns, respectively. In this work, we solved two-dimensional paraxial field coupled with rate equations employing the Crank–Nicholson numerical method. The results reveal the unique optical properties and outstanding optical limiting (OL) effects of SnPc nanoprobes, indicating huge application potential as optical limiters, sensors and switches. Full article

(This article belongs to the Section Physics)

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18 pages, 437 KB

Open AccessArticle

Functional Identities in Superalgebras: Theoretical Insights and Computational Verification

by Ali Yahya Hummdi and Mohammad Shane Alam

Symmetry 2025, 17(9), 1527; https://doi.org/10.3390/sym17091527 - 12 Sep 2025

Abstract

This paper investigates functional identities in superalgebras, building on Wang’s foundational work. We study d-superfree subsets and k-supercommuting maps in prime superalgebras, both with and without superinvolution, introducing new results on symmetric and skew elements. Using SageMath, we computationally verify key [...] Read more.

This paper investigates functional identities in superalgebras, building on Wang’s foundational work. We study d-superfree subsets and k-supercommuting maps in prime superalgebras, both with and without superinvolution, introducing new results on symmetric and skew elements. Using SageMath, we computationally verify key properties in the finite-dimensional superalgebra

M_{2} (Q)

, including supercommutators, superinvolutions, and k-supercommuting maps, thereby providing concrete illustrations of the abstract theory. These computations underscore the practical applicability of functional identities in finite-dimensional settings and offer fresh insights into superalgebra structures. Full article

(This article belongs to the Section Mathematics)

28 pages, 395 KB

Open AccessArticle

A Study of Symmetric q-Dunkl-Classical Orthogonal q-Polynomials Through a Second Structure Relation

by Jihad Souissi and Khalid Ali Alanezy

Symmetry 2025, 17(9), 1526; https://doi.org/10.3390/sym17091526 - 12 Sep 2025

Abstract

This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the

q^{2}

-analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of [...] Read more.

This paper establishes a new characterization of symmetric q-Dunkl-classical orthogonal polynomials through a second structure relation. These symmetric polynomials generalize the

q^{2}

-analogues of Hermite and Gegenbauer polynomials. Our main result provides a finite expansion of each polynomial in terms of its q-Dunkl derivatives, offering a new effective classification method. We derive explicit structure relations for the

q^{2}

-analogue of generalized Hermite and the

q^{2}

-analogue of generalized Gegenbauer polynomials. Full article

(This article belongs to the Special Issue Advances in Mathematical Models and Partial Differential Equations: 2nd Edition)

20 pages, 4425 KB

Open AccessArticle

Multi-Method Sensitivity Analysis of Influencing Factors on the Lateral Displacement of Retaining Piles in Asymmetric Excavations in Soft Soil Areas

by Feng Cheng, Maosha Li and Qingwang Li

Symmetry 2025, 17(9), 1525; https://doi.org/10.3390/sym17091525 - 12 Sep 2025

Viewed by 16

Abstract

Asymmetric structures are widespread in deep excavation engineering and place heightened demands on the deformation control and safety of retaining systems. This study focuses on an asymmetric deep foundation pit project in a soft soil area, using PLAXIS 3D to model the entire [...] Read more.

Asymmetric structures are widespread in deep excavation engineering and place heightened demands on the deformation control and safety of retaining systems. This study focuses on an asymmetric deep foundation pit project in a soft soil area, using PLAXIS 3D to model the entire excavation process, with model accuracy confirmed by measured values. The study systematically explores the impact of multiple factors—including surcharge loading, external groundwater level, soil internal friction angle and cohesion, and the elastic modulus and embedment ratio of the retaining structure—on the lateral displacement of retaining piles. Orthogonal experimental design is utilized to calculate lateral displacements for various factor combinations, with sensitivity analyzed using the range method and verified by grey relational analysis. The results demonstrate that all factors influence the maximum lateral displacement of retaining piles to varying degrees. Both the orthogonal tests and range analysis consistently identify the influence ranking as soil internal friction angle > soil cohesion > retaining structure elastic modulus > embedment ratio > external groundwater level > surcharge loading. The grey relational analysis yields identical rankings. These results offer theoretical support and practical guidance for the design and monitoring of retaining structures in asymmetric deep excavations within soft soil environments. Full article

(This article belongs to the Section Engineering and Materials)

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9 pages, 742 KB

Open AccessArticle

Experimental Search for Neutron–Antineutron Oscillation with the Use of Ultra-Cold Neutrons Revisited

by Tatsushi Shima

Symmetry 2025, 17(9), 1524; https://doi.org/10.3390/sym17091524 - 12 Sep 2025

Viewed by 30

Abstract

Neutron–antineutron oscillation (nnbar-osc) is a baryon number-violating process and a sensitive probe for physics beyond the standard model. Ultra-cold neutrons (UCNs) are attractive for nnbar-osc searches because of their long storage time, but earlier analyses indicated that phase shifts on wall reflection differ [...] Read more.

Neutron–antineutron oscillation (nnbar-osc) is a baryon number-violating process and a sensitive probe for physics beyond the standard model. Ultra-cold neutrons (UCNs) are attractive for nnbar-osc searches because of their long storage time, but earlier analyses indicated that phase shifts on wall reflection differ for neutrons and antineutrons, leading to severe decoherence and a loss of sensitivity. Herein, we revisit this problem by numerically solving the time-dependent Schrödinger equation for the two-component n/nbar wave function, explicitly including wall interactions. We show that decoherence can be strongly suppressed by selecting a wall material whose neutron and antineutron optical potentials are nearly equal. Using coherent scattering length data and estimates for antineutrons, we identify a Ni–Al alloy composition that matches the potentials within a few percent while providing a high absolute value, enabling long UCN storage. With such a bottle and an improved UCN source, the sensitivity could reach an oscillation period

τ_{n n b a r}

of the order 10¹⁰ s, covering most of the range predicted with certain grand unified models. This approach revives the feasibility of high-sensitivity nnbar-osc searches using stored UCNs and offers a clear path to probe baryon number violation far beyond existing limits. Full article

(This article belongs to the Section Physics)

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24 pages, 2730 KB

Open AccessArticle

Generating Software Architectural Model from Source Code Using Module Clustering

by Bahman Arasteh, Seyed Salar Sefati, Huseyin Kusetogullari and Farzad Kiani

Symmetry 2025, 17(9), 1523; https://doi.org/10.3390/sym17091523 - 12 Sep 2025

Viewed by 17

Abstract

Software maintenance is one of the most expensive phases in software development, especially when complex source code is the only available artifact. Clustering software modules and generating a structured architectural model can significantly reduce the effort and cost of maintenance. This study aims [...] Read more.

Software maintenance is one of the most expensive phases in software development, especially when complex source code is the only available artifact. Clustering software modules and generating a structured architectural model can significantly reduce the effort and cost of maintenance. This study aims to achieve high-quality modularization by maximizing intra-cluster cohesion, minimizing inter-cluster coupling, and optimizing overall modular quality. Since finding optimal clustering is an NP-complete problem, many existing methods suffer from poor modular structures, instability, and inconsistent results. To overcome these limitations, this paper proposes a module clustering method using a discrete bedbug optimizer. In software architecture, symmetry refers to the balanced and structured arrangement of modules. In the proposed method, module clustering aims to identify and group related modules based on structural and behavioral similarities, reflecting symmetrical properties in the source code. Conversely, asymmetries, such as modules with irregular dependencies, can indicate architectural flaws. The method was evaluated on ten widely used real-world software datasets. The experimental results show that the proposed algorithm consistently delivers superior modularization quality, with an average score of 2.806 and a well-balanced trade-off between cohesion and coupling. Overall, this research presents an effective solution for software module clustering and provides better architecture recovery and more maintainable systems. Full article

(This article belongs to the Section Computer)

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18 pages, 785 KB

Open AccessArticle

Efficient Lattice-Based Digital Signatures for Embedded IoT Systems

by Maksim Iavich, Nursulu Kapalova and Kairat Sakan

Symmetry 2025, 17(9), 1522; https://doi.org/10.3390/sym17091522 - 12 Sep 2025

Viewed by 29

Abstract

This paper offers a lattice-based digital signature construction, optimized for the provision of post-quantum security in resource-constrained environments, such as Internet of Things (IoT) devices. The offered scheme is built upon structured hardness assumptions, defined over polynomial rings that exhibit inherent algebraic symmetry. [...] Read more.

This paper offers a lattice-based digital signature construction, optimized for the provision of post-quantum security in resource-constrained environments, such as Internet of Things (IoT) devices. The offered scheme is built upon structured hardness assumptions, defined over polynomial rings that exhibit inherent algebraic symmetry. By exploiting the cyclic properties of these ring structures and implementing efficient Number Theoretic Transforms (NTTs), the construction achieves compact signatures that are under 3 KB and a runtime feasibility that uses less than 10 KB of RAM. The signature generation process incorporates balanced rejection sampling and carefully designed polynomial encodings that preserve structural regularity and computational efficiency. The security of the offered scheme is proven. The benchmark results generated from using the ARM Cortex-M4 platform demonstrate its practical usability. This study highlights how symmetric algebraic frameworks based on lattice-based cryptography can be leveraged to achieve both theoretical security and real-world performance in the post-quantum era. Full article

(This article belongs to the Section Computer)

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42 pages, 11490 KB

Open AccessReview

Experimental Review of the Quarkonium Physics at the LHC

by Yiyang Zhao, Jinfeng Liu, Xing Cheng, Chi Wang and Zhen Hu

Symmetry 2025, 17(9), 1521; https://doi.org/10.3390/sym17091521 - 12 Sep 2025

Viewed by 84

Abstract

We review recent heavy quarkonium measurements in

p p

,

p P b

, and

PbPb

collisions at the LHC by the ALICE, ATLAS, CMS, and LHCb collaborations using Run-2 and early Run-3 data. Production studies include present differential cross-sections and polarization measurements [...] Read more.

We review recent heavy quarkonium measurements in

p p

,

p P b

, and

PbPb

collisions at the LHC by the ALICE, ATLAS, CMS, and LHCb collaborations using Run-2 and early Run-3 data. Production studies include present differential cross-sections and polarization measurements of charmonium and bottomonium, providing precise tests of QCD theoretical calculations and unveiling symmetry relations among spin and orbital configurations. Notably, a

t \bar{t}

quasi-bound-state has been observed at the LHC recently. Suppression analyses quantify the sequential melting of bottomonium states in

PbPb

collisions, serving as a probe of the deconfined quark–gluon plasma. Cold nuclear matter effects are constrained through comparisons of quarkonium yields in pPb and

p p

collisions. Furthermore, multi-quarkonium investigations observe di- and tri-quarkonium production processes and resonances, exploring multi-parton interactions and the symmetry structure underlying exotic hadron states. Full article

(This article belongs to the Special Issue Symmetry in Hadron Physics)

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25 pages, 7964 KB

Open AccessArticle

DSCSRN: Physically Guided Symmetry-Aware Spatial-Spectral Collaborative Network for Single-Image Hyperspectral Super-Resolution

by Xueli Chang, Jintong Liu, Guotao Wen, Xiaoyu Huang and Meng Yan

Symmetry 2025, 17(9), 1520; https://doi.org/10.3390/sym17091520 - 12 Sep 2025

Viewed by 55

Abstract

Hyperspectral images (HSIs), with their rich spectral information, are widely used in remote sensing; yet the inherent trade-off between spectral and spatial resolution in imaging systems often limits spatial details. Single-image hyperspectral super-resolution (HSI-SR) seeks to recover high-resolution HSIs from a single low-resolution [...] Read more.

Hyperspectral images (HSIs), with their rich spectral information, are widely used in remote sensing; yet the inherent trade-off between spectral and spatial resolution in imaging systems often limits spatial details. Single-image hyperspectral super-resolution (HSI-SR) seeks to recover high-resolution HSIs from a single low-resolution input, but the high dimensionality and spectral redundancy of HSIs make this task challenging. In HSIs, spectral signatures and spatial textures often exhibit intrinsic symmetries, and preserving these symmetries provides additional physical constraints that enhance reconstruction fidelity and robustness. To address these challenges, we propose the Dynamic Spectral Collaborative Super-Resolution Network (DSCSRN), an end-to-end framework that integrates physical modeling with deep learning and explicitly embeds spatial–spectral symmetry priors into the network architecture. DSCSRN processes low-resolution HSIs with a Cascaded Residual Spectral Decomposition Network (CRSDN) to compress redundant channels while preserving spatial structures, generating accurate abundance maps. These maps are refined by two Synergistic Progressive Feature Refinement Modules (SPFRMs), which progressively enhance spatial textures and spectral details via a multi-scale dual-domain collaborative attention mechanism. The Dynamic Endmember Adjustment Module (DEAM) then adaptively updates spectral endmembers according to scene context, overcoming the limitations of fixed-endmember assumptions. Grounded in the Linear Mixture Model (LMM), this unmixing–recovery–reconstruction pipeline restores subtle spectral variations alongside improved spatial resolution. Experiments on the Chikusei, Pavia Center, and CAVE datasets show that DSCSRN outperforms state-of-the-art methods in both perceptual quality and quantitative performance, achieving an average PSNR of 43.42 and a SAM of 1.75 (×4 scale) on Chikusei. The integration of symmetry principles offers a unifying perspective aligned with the intrinsic structure of HSIs, producing reconstructions that are both accurate and structurally consistent. Full article

(This article belongs to the Section Computer)

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16 pages, 4343 KB

Open AccessArticle

A YOLO-Based Multi-Scale and Small Object Detection Framework for Low-Altitude UAVs in Cluttered Scenes

by Zhi Yang, Rijun Wang, Wenjin Chen, Keer Du, Zhigong Huang and Yu Huang

Symmetry 2025, 17(9), 1519; https://doi.org/10.3390/sym17091519 - 12 Sep 2025

Viewed by 79

Abstract

Low-altitude UAVs pose increasing security concerns due to their small sizes, high mobility, and low observability. Detecting such targets in cluttered environments remains challenging due to strong background interference and significant scale variations. To address these issues, we propose an efficient and accurate [...] Read more.

Low-altitude UAVs pose increasing security concerns due to their small sizes, high mobility, and low observability. Detecting such targets in cluttered environments remains challenging due to strong background interference and significant scale variations. To address these issues, we propose an efficient and accurate multi-scale detection framework based on YOLO11, specifically tailored for small UAVs in cluttered scenes. The framework incorporates three core modules: C3K2-FB to enhance feature extraction and suppress background noise, MS_FPN for edge-aware multi-scale feature fusion, and RFCBAM to jointly leverage spatial and channel attention for improved focus on discriminative regions. Extensive experiments on the DeTFly dataset show that our method achieves 94.4% mAP@0.5 and 60.9% mAP@0.5:0.95, outperforming state-of-the-art models including YOLO11n, YOLOv10n, and RT-DETR-L in both accuracy and robustness. These results validate the effectiveness of the proposed framework for real-world UAV detection tasks involving small-scale targets in cluttered environments. Full article

(This article belongs to the Section Engineering and Materials)

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29 pages, 5370 KB

Open AccessArticle

Quadratic Control Model for Shuttle Dispatching in Automated Overhead Rail Systems

by Thuy Duy Truong, Xuan Tuan Nguyen and Tuong Quan Vo

Symmetry 2025, 17(9), 1518; https://doi.org/10.3390/sym17091518 - 11 Sep 2025

Viewed by 169

Abstract

Automated Overhead Rail Systems (AORs) have a key role in warehouse and in-house industry, as well as in the modern hospital, where efficient shuttle dispatching directly impacts throughput and reliability. This paper presents a quadratic control model formulated in symmetric quadratic matrix form [...] Read more.

Automated Overhead Rail Systems (AORs) have a key role in warehouse and in-house industry, as well as in the modern hospital, where efficient shuttle dispatching directly impacts throughput and reliability. This paper presents a quadratic control model formulated in symmetric quadratic matrix form to capture balanced interactions between shuttles, tasks, and priorities. A Genetic Algorithm (GA) is employed to solve the optimization problem, with operators adapted to exploit quadratic symmetry, for faster convergence and stable performance. Simulation results on a microcontroller-based testbed demonstrated that the proposed model achieved shorter dispatching times, reduced waiting costs, and more symmetrically distributed workloads compared with conventional heuristic approaches. The study shows that symmetry is not only a modeling feature, but also a design principle, supporting future extensions such as emergency handling and multi-priority dispatching. Full article

(This article belongs to the Section Engineering and Materials)

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20 pages, 1654 KB

Open AccessArticle

Complexity Hierarchies in Euclidean Stars

by Luis Herrera, Alicia Di Prisco and Justo Ospino

Symmetry 2025, 17(9), 1517; https://doi.org/10.3390/sym17091517 - 11 Sep 2025

Viewed by 144

Abstract

We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, non-dissipative and dissipative systems. Solutions range from the simplest one, in order of [...] Read more.

We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, non-dissipative and dissipative systems. Solutions range from the simplest one, in order of increasing complexity. Some specific models are found and analyzed in detail. Full article

(This article belongs to the Special Issue Gravitational Physics and Symmetry)

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31 pages, 8133 KB

Open AccessArticle

Effects of Symmetric Wing Sweep Angle Variations on the Performance and Stability of Variable-Sweep Wing Aircraft

by Omer Tasci and Ugur Ozdemir

Symmetry 2025, 17(9), 1516; https://doi.org/10.3390/sym17091516 - 11 Sep 2025

Viewed by 166

Abstract

Research on morphing aircraft that can change geometry to achieve the desired performance and stability under different flight conditions has been ongoing for many years. This study provides a conceptual-level, preliminary analysis of the impact of symmetrically changing the wing sweep angle on [...] Read more.

Research on morphing aircraft that can change geometry to achieve the desired performance and stability under different flight conditions has been ongoing for many years. This study provides a conceptual-level, preliminary analysis of the impact of symmetrically changing the wing sweep angle on aircraft performance and stability. The T-37B-like aircraft is selected as a base to compare the results with T-37B’s known data. The T-37B-like aircraft is modeled in both Digital DATCOM and Open VSP software. Changes in aircraft performance and stability are demonstrated for changes in the wing sweep angle between −10° and 40°. When 0° and 40° wing sweep configurations are compared, it is observed that the 40° wing sweep configuration performs better in terms of climb and range, but worse in terms of takeoff distance, glide, approach, and radius of turn. In terms of static stability, it has a positive effect on longitudinal stability. While it does not significantly affect lateral stability overall, it contributes positively to stability around the roll axis. Changing the symmetrical wing sweep angle is expected to improve certain performance and stability parameters while degrading others. A symmetrical variable-sweep wing offers advantages by adjusting to the optimal sweep angle for each flight phase. Thus, benefits can be fully utilized, and drawbacks minimized. However, it entails design, mechanical, weight, and financial costs. Therefore, whether the performance and stability benefits outweigh these costs must be evaluated on an aircraft-specific basis. Full article

(This article belongs to the Section Engineering and Materials)

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13 pages, 855 KB

Open AccessArticle

A Novel Meta-ELM with Orthogonal Constraints for Regression Problems

by Licheng Cui and Huawei Zhai

Symmetry 2025, 17(9), 1515; https://doi.org/10.3390/sym17091515 - 11 Sep 2025

Viewed by 122

Abstract

ELM is an innovative learning algorithm that minimizes output error by only finding optimal output weights. Meta-learning is composed of base ELMs and exhibits good generalization. To improve its performance further by introducing orthogonal constraints into the base ELMs and “top” ELM, we [...] Read more.

ELM is an innovative learning algorithm that minimizes output error by only finding optimal output weights. Meta-learning is composed of base ELMs and exhibits good generalization. To improve its performance further by introducing orthogonal constraints into the base ELMs and “top” ELM, we propose a novel Meta-ELM with orthogonal constraints (Meta-QEC-ELM). Because of the particularity of the Meta-ELM, its orthogonal constraint problem is the quadratic equality constraint problem—that is, a one-column Procrustes problem—and it can preserve much more information from feature space to output subspace. The experimental results show that the Meta-QEC-ELM is both effective and feasible. Full article

(This article belongs to the Section Computer)

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15 pages, 278 KB

Open AccessArticle

Sharp Curvature Inequalities for Submanifolds in Conformal Sasakian Space Forms Equipped with Quarter-Symmetric Metric Connection

by Md Aquib, Mohd Aslam, Pooja Bansal and Ibrahim Al-Dayel

Symmetry 2025, 17(9), 1514; https://doi.org/10.3390/sym17091514 - 11 Sep 2025

Viewed by 115

Abstract

This study focuses on submanifolds embedded in a conformal Sasakian space form (CSSF) equipped with a quarter-symmetric metric connection (QSMC). Utilizing the framework of generalized normalized

δ

-Casorati curvature (GNDCC) alongside scalar curvature, we derive sharp optimal inequalities that characterize the intrinsic and [...] Read more.

This study focuses on submanifolds embedded in a conformal Sasakian space form (CSSF) equipped with a quarter-symmetric metric connection (QSMC). Utilizing the framework of generalized normalized

δ

-Casorati curvature (GNDCC) alongside scalar curvature, we derive sharp optimal inequalities that characterize the intrinsic and extrinsic geometry of the submanifolds. Additionally, we examine the geometric behavior of these submanifolds under conformal deformations of the ambient manifold. To substantiate the theoretical developments, we construct an explicit example of a conformal Sasakian manifold that is not Sasakian, thereby confirming the validity and applicability of the derived results. Full article

(This article belongs to the Section Mathematics)

33 pages, 2380 KB

Open AccessReview

A Comprehensive Review of Symmetrical Multilateral Well (MLW) Applications in Cyclic Solvent Injection (CSI): Advancements, Challenges, and Future Prospects

by Shengyi Wu, Farshid Torabi and Ali Cheperli

Symmetry 2025, 17(9), 1513; https://doi.org/10.3390/sym17091513 - 11 Sep 2025

Viewed by 174

Abstract

This paper presents a comprehensive review and theoretical analysis of integrating Cyclic Solvent Injection (CSI) with multilateral well (MLW) technologies to enhance heavy oil recovery. Given that many MLW configurations inherently exhibit symmetrical geometries, CSI–MLW integration offers structural advantages for fluid distribution. CSI [...] Read more.

This paper presents a comprehensive review and theoretical analysis of integrating Cyclic Solvent Injection (CSI) with multilateral well (MLW) technologies to enhance heavy oil recovery. Given that many MLW configurations inherently exhibit symmetrical geometries, CSI–MLW integration offers structural advantages for fluid distribution. CSI offers a non-thermal mechanism for oil production through viscosity reduction, oil swelling, and foamy oil behaviour, but its application is often limited by poor sweep efficiency and non-uniform solvent distribution in conventional single-well configurations. In contrast, MLW configurations are effective in increasing reservoir contact and improving flow control but lack solvent-based enhancement mechanisms. In particular, symmetrical MLW configurations, such as dual-opposing laterals and evenly spaced fishbone laterals, can facilitate balanced solvent distribution and pressure profiles, thereby improving sweep efficiency and mitigating early breakthrough. By synthesizing experimental findings and theoretical insights from the existing literature, laboratory studies have reported that post-CHOPS CSI using a 28% C₃H₈–72% CO₂ mixture can recover about 50% of the original oil in place after six cycles, while continuous-propagation CSI (CPCSI) has achieved up to ~85% OOIP in 1D physical models. These representative values illustrate the performance spectrum observed across different CSI operational modes, underscoring the importance of operational parameters in governing recovery outcomes. Building on this foundation, this paper synthesizes key operational parameters, including solvent composition, pressure decline rate, and well configuration, that influence CSI performance. While previous studies have extensively reviewed CSI and MLW as separate technologies, systematic analyses of their integration remain limited. This review addresses that gap by providing a structured synthesis of CSI–MLW interactions, supported by representative quantitative evidence from the literature. The potential synergy between CSI and MLW is highlighted as a promising direction to overcome current limitations. By leveraging geometric symmetry in well architecture, the integrated CSI–MLW approach offers unique opportunities for optimizing solvent utilization, enhancing recovery efficiency, and guiding future experimental and field-scale developments. Such symmetry-oriented designs are also central to the experimental framework proposed in this study, in which potential methods, such as the microfluidic visualization of different MLW configurations, spanning small-scale visualization studies, bench-scale experiments on fluid and chemical interactions, and mock field setups with pipe networks, are proposed as future avenues to further explore and validate this integrated strategy. Full article

(This article belongs to the Special Issue Advances in Fluid Dynamics and Energy Systems: Applications of Symmetry and Asymmetry)

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34 pages, 3701 KB

Open AccessArticle

Symmetry-Aware Short-Term Load Forecasting in Distribution Networks: A Synergistic Enhanced KMA-MVMD-Crossformer Framework

by Jingfeng Zhao, Kunhua Liu, Qi You, Lan Bai, Shuolin Zhang, Huiping Guo and Haowen Liu

Symmetry 2025, 17(9), 1512; https://doi.org/10.3390/sym17091512 - 11 Sep 2025

Viewed by 150

Abstract

Accurate and efficient short-term load forecasting is crucial for the secure and stable operation and scheduling of power grids. Addressing the inability of traditional Transformer-based prediction models to capture symmetric correlations between different feature sequences and their susceptibility to multi-scale feature influences, this [...] Read more.

Accurate and efficient short-term load forecasting is crucial for the secure and stable operation and scheduling of power grids. Addressing the inability of traditional Transformer-based prediction models to capture symmetric correlations between different feature sequences and their susceptibility to multi-scale feature influences, this paper proposes a short-term power distribution network load forecasting model based on an enhanced Komodo Mlipir Algorithm (KMA)—Multivariate Variational Mode Decomposition (MVMD)-Crossformer. Initially, the KMA is enhanced with chaotic mapping and temporal variation inertia weighting, which strengthens the symmetric exploration of the solution space. This enhanced KMA is integrated into the parameter optimization of the MVMD algorithm, facilitating the decomposition of distribution network load sequences into multiple Intrinsic Mode Function (IMF) components with symmetric periodic characteristics across different time scales. Subsequently, the Multi-variable Rapid Maximum Information Coefficient (MVRapidMIC) algorithm is employed to extract features with strong symmetric correlations to the load from weather and date characteristics, reducing redundancy while preserving key symmetric associations. Finally, a power distribution network short-term load forecasting model based on the Crossformer is constructed. Through the symmetric Dimension Segmentation (DSW) embedding layer and the Two-Stage Attention (TSA) mechanism layer with bidirectional symmetric correlation capture, the model effectively captures symmetric dependencies between different feature sequences, leading to the final load prediction outcome. Experimental results on the real power distribution network dataset show that: the Root Mean Square Error (RMSE) of the proposed model is as low as 14.7597 MW, the Mean Absolute Error (MAE) is 13.9728 MW, the Mean Absolute Percentage Error (MAPE) reaches 4.89%, and the coefficient of determination (R²) is as high as 0.9942. Full article

(This article belongs to the Section Engineering and Materials)

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26 pages, 1401 KB

Open AccessArticle

Lagrangian Field Approach to Einstein–Maxwell Equation for Brain Toroidal Topology

by Manuel Rivas and Manuel Reina

Symmetry 2025, 17(9), 1511; https://doi.org/10.3390/sym17091511 - 11 Sep 2025

Viewed by 187

Abstract

The population activity of grid cells from a single module is topologically constrained to a toroidal manifold. Our work proposes an improved version of Gardner’s earlier model, which can account for both geometric properties and force field dynamics. Employing methods from Differential Geometry, [...] Read more.

The population activity of grid cells from a single module is topologically constrained to a toroidal manifold. Our work proposes an improved version of Gardner’s earlier model, which can account for both geometric properties and force field dynamics. Employing methods from Differential Geometry, we have derived Lagrangian densities that—under very general assumptions and avoiding dimensionful constants—provide a rationale for the trajectories associated with the synaptic spacetime as a global solution to the Einstein–Maxwell field equations. Then, we investigate the helical solutions to show that the synaptic toroidal topological space, as a locally flat Minkowski spacetime, with a Lorentzian metric is geodesically complete and, therefore, exhibits maximal stability. Finally, we consider a Lorentzian metric with curved spacetimes that give rise to Lorentzian tori admitting curvature spacetime singularities. Full article

(This article belongs to the Section Physics)

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18 pages, 319 KB

Open AccessArticle

Integrable Multispecies Totally Asymmetric Stochastic Interacting Particle Systems with Homogeneous Rates

by Eunghyun Lee and Temirlan Raimbekov

Symmetry 2025, 17(9), 1510; https://doi.org/10.3390/sym17091510 - 11 Sep 2025

Viewed by 176

Abstract

We study one-dimensional stochastic particle systems with exclusion interaction—each site can be occupied by at most one particle—and homogeneous jumping rates. Earlier work of Alimohammadi and Ahmadi classified 28 Yang–Baxter integrable two-particle interaction rules for two-species models with homogeneous rates. In this work, [...] Read more.

We study one-dimensional stochastic particle systems with exclusion interaction—each site can be occupied by at most one particle—and homogeneous jumping rates. Earlier work of Alimohammadi and Ahmadi classified 28 Yang–Baxter integrable two-particle interaction rules for two-species models with homogeneous rates. In this work, we show that 7 of these 28 cases can be naturally extended to integrable models with an arbitrary number of species

N \geq 2

. A key novelty of our approach is the discovery of new integrable families with one or two continuous parameters that generalize these seven cases, significantly broadening the known class of multispecies integrable exclusion processes. Furthermore, for 8 of the remaining 21 cases, we propose an alternative extension scheme that also yields integrable N-species models, thereby opening new directions for constructing and classifying integrable particle systems. Full article

(This article belongs to the Special Issue From Symmetry to Fluctuations: Topics and Advances in Statistical Mechanics and Probability Theory)

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15 pages, 3086 KB

Open AccessArticle

Uncovering New Wave Profiles in Boussinesq-Type KdV Systems Through Symbolic and Semi-Analytical Methods

by Mehmet Şenol, Nadiyah Hussain Alharthi, Bahadır Kopçasız, Hatice Ceyda Türk and Rubayyi T. Alqahtani

Symmetry 2025, 17(9), 1509; https://doi.org/10.3390/sym17091509 - 11 Sep 2025

Viewed by 143

Abstract

We study here the Boussinesq-type Korteweg–de Vries (KdV) equation, a nonlinear partial differential equation, for describing the wave propagation of long, nonlinear, and dispersive waves in shallow water and other physical scenarios. In order to obtain novel families of wave solutions, we apply [...] Read more.

We study here the Boussinesq-type Korteweg–de Vries (KdV) equation, a nonlinear partial differential equation, for describing the wave propagation of long, nonlinear, and dispersive waves in shallow water and other physical scenarios. In order to obtain novel families of wave solutions, we apply two efficient analytical techniques: the Modified Extended tanh (ME-tanh) method and the Modified Residual Power Series Method (mRPSM). These methods are used for the very first time in this equation to produce both exact and high-order approximate solutions with rich wave behaviors including soliton formation and energy localization. The ME-tanh method produces a rich class of closed-form soliton solutions via systematic simplification of the PDE into simple ordinary differential forms that are readily solved, while the mRPSM produces fast-convergent approximate solutions via a power series representation by iteration. The accuracy and validity of the results are validated using symbolic computation programs such as Maple and Mathematica. The study not only enriches the current solution set of the Boussinesq-type KdV equation but also demonstrates the efficiency of hybrid analytical techniques in uncovering sophisticated wave patterns in multimensional spaces. Our findings find application in coastal hydrodynamics, nonlinear optics, geophysics, and the theory of elasticity, where accurate modeling of wave evolution is significant. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)

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22 pages, 6249 KB

Open AccessReview

Computational Fluid Dynamics and Potential Flow Modelling Techniques for Floating Photovoltaic Systems: A Systematic Review

by Aditya Nair, Luofeng Huang and Patrick G. Verdin

Symmetry 2025, 17(9), 1508; https://doi.org/10.3390/sym17091508 - 10 Sep 2025

Viewed by 208

Abstract

Land availability constraints limit the installation of conventional ground-mounted solar installations. As a result, Floating Photovoltaic (FPV) systems are gaining popularity as an alternative to renewable energy generation. FPV consist of individual solar panels that are commonly symmetrical and modular. However, the hydrodynamic [...] Read more.

Land availability constraints limit the installation of conventional ground-mounted solar installations. As a result, Floating Photovoltaic (FPV) systems are gaining popularity as an alternative to renewable energy generation. FPV consist of individual solar panels that are commonly symmetrical and modular. However, the hydrodynamic behaviour of FPVs in water surface waves is understudied to ensure their stability and optimal performance under varying environmental conditions. This literature review examines various modelling techniques applied in studying FPV hydrodynamics. Specifically, the application of Computational Fluid Dynamics (CFD) solvers and potential flow theory solvers is investigated for their effectiveness in capturing the behaviour of FPVs and mooring dynamics under the impact of wind and waves. The review highlights the advantages and limitations of each approach. Findings suggest that a combined CFD-potential flow approach offers a perfect balance between accuracy and computational efficiency, offering valuable insights into the performance of FPVs. However, extensive research is notably absent in hydrodynamic modelling for large-scale FPVs. This lack of research represents a significant gap in our current study on multiscale FPV systems. Full article

(This article belongs to the Special Issue Symmetry in Marine Hydrodynamics: Applications to Ocean Engineering)

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18 pages, 601 KB

Open AccessArticle

Back-Reaction of Super-Hubble Fluctuations, Late Time Tracking, and Recent Observational Results

by Marco A. Alvarez, Leila L. Graef and Robert Brandenberger

Symmetry 2025, 17(9), 1507; https://doi.org/10.3390/sym17091507 - 10 Sep 2025

Viewed by 191

Abstract

Previous studies have suggested that the back-reaction of super-Hubble cosmological fluctuations on a symmetric background space-time, with respect to being homogeneous and isotropic, could behave like a dynamical relaxation of the cosmological constant. Moreover, this mechanism appears to be self-regulatory, potentially leading to [...] Read more.

Previous studies have suggested that the back-reaction of super-Hubble cosmological fluctuations on a symmetric background space-time, with respect to being homogeneous and isotropic, could behave like a dynamical relaxation of the cosmological constant. Moreover, this mechanism appears to be self-regulatory, potentially leading to oscillatory behavior in the effective DE. Such an effect would occur in any cosmological model with super-Hubble matter fluctuations, including the standard

Λ

CDM model. Apart from that, recent DESI data, which indicate that DE may be dynamical, have renewed interest in exploring scenarios leading to such an oscillatory behavior. In this study, we propose a parameterization to account for the impact of super-Hubble fluctuations on the background energy density of the Universe. We model the total effective cosmological constant as the sum of a constant and an oscillating contribution. We performed a preliminary comparison of the background dynamics of this model with recent radial BAO data from DESI. We also discuss the status of the

H_{0}

tension problem in this model. Full article

(This article belongs to the Special Issue Symmetry and Cosmology)

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27 pages, 13123 KB

Open AccessArticle

Symmetric Boundary-Enhanced U-Net with Mamba Architecture for Glomerular Segmentation in Renal Pathological Images

by Shengnan Zhang, Xinming Cui, Guangkun Ma and Ronghui Tian

Symmetry 2025, 17(9), 1506; https://doi.org/10.3390/sym17091506 - 10 Sep 2025

Viewed by 207

Abstract

Accurate glomerular segmentation in renal pathological images is a key challenge for chronic kidney disease diagnosis and assessment. Due to the high visual similarity between pathological glomeruli and surrounding tissues in color, texture, and morphology, significant “camouflage phenomena” exist, leading to boundary identification [...] Read more.

Accurate glomerular segmentation in renal pathological images is a key challenge for chronic kidney disease diagnosis and assessment. Due to the high visual similarity between pathological glomeruli and surrounding tissues in color, texture, and morphology, significant “camouflage phenomena” exist, leading to boundary identification difficulties. To address this problem, we propose BM-UNet, a novel segmentation framework that embeds boundary guidance mechanisms into a Mamba architecture with a symmetric encoder–decoder design. The framework enhances feature transmission through explicit boundary detection, incorporating four core modules designed for key challenges in pathological image segmentation. The Multi-scale Adaptive Fusion (MAF) module processes irregular tissue morphology, the Hybrid Boundary Detection (HBD) module handles boundary feature extraction, the Boundary-guided Attention (BGA) module achieves boundary-aware feature refinement, and the Mamba-based Fused Decoder Block (MFDB) completes boundary-preserving reconstruction. By introducing explicit boundary supervision mechanisms, the framework achieves significant segmentation accuracy improvements while maintaining linear computational complexity. Validation on the KPIs2024 glomerular dataset and HuBMAP renal tissue samples demonstrates that BM-UNet achieves a 92.4–95.3% mean Intersection over Union across different CKD pathological conditions, with a 4.57% improvement over the Mamba baseline and a processing speed of 113.7 FPS. Full article

(This article belongs to the Section Computer)

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