Symmetry

21 pages, 3715 KB

Open AccessArticle

SPIRIT: Symmetry-Prior Informed Diffusion for Thangka Segmentation

by Yukai Xian, Yurui Lee, Liang Yan, Te Shen, Ping Lan, Qijun Zhao and Yi Zhang

Symmetry 2025, 17(10), 1643; https://doi.org/10.3390/sym17101643 - 3 Oct 2025

Thangka paintings, as intricate forms of Tibetan Buddhist art, present unique challenges for image segmentation due to their densely arranged symbolic elements, complex color patterns, and strong structural symmetry. To address these difficulties, we propose SPIRIT, a structure-aware and prompt-guided diffusion segmentation framework [...] Read more.

Thangka paintings, as intricate forms of Tibetan Buddhist art, present unique challenges for image segmentation due to their densely arranged symbolic elements, complex color patterns, and strong structural symmetry. To address these difficulties, we propose SPIRIT, a structure-aware and prompt-guided diffusion segmentation framework tailored for Thangka images. Our method incorporates a support-query-encoding scheme to exploit limited labeled samples and introduces semantic guided attention fusion to integrate symbolic knowledge into the denoising process. Moreover, we design a symmetry-aware refinement module to explicitly preserve bilateral and radial symmetries, enhancing both accuracy and interpretability. Experimental results on our curated Thangka dataset and the artistic ArtBench benchmark demonstrate that our approach achieves 88.3% mIoU on Thangka and 86.1% mIoU on ArtBench, outperforming the strongest baseline by 6.1% and 5.6% mIoU, respectively. These results confirm that SPIRIT not only captures fine-grained details, but also excels in segmenting structurally complex regions of artistic imagery. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Image Processing and Computer Vision)

17 pages, 330 KB

Open AccessArticle

On ps-Supplement Submodules

by İrfan Soydan, Ergül Türkmen and Hashem Bordbar

Symmetry 2025, 17(10), 1642; https://doi.org/10.3390/sym17101642 - 3 Oct 2025

Abstract

In this work, we introduce $p s$ -supplement submodules as a kind of supplements. Specifically, a submodule V of a module M is referred to as a $p s$ -supplement if there exists another submodule

U \subseteq M

such that [...] Read more.

In this work, we introduce $p s$ -supplement submodules as a kind of supplements. Specifically, a submodule V of a module M is referred to as a $p s$ -supplement if there exists another submodule

U \subseteq M

such that

M = U + V

and the intersection

U \cap V

is projective semisimple. We demonstrate that, over an arbitrary ring, the collection

PS

of short exact sequences of the form

0 ⟶ M \overset{ψ}{⟶} N \overset{ϕ}{⟶} K ⟶ 0,

where

Im (ψ)

is a

p s

-supplement in N, constitutes a proper class. In addition, we explore several homological aspects of this class, including the symmetry of the relations between the modules. Finally, we provide that a ring R is a left SI-ring with essential socle if and only if every left R-module is

p s

-supplemented. Full article

(This article belongs to the Section Mathematics)

18 pages, 347 KB

Open AccessArticle

On One Laura Mayer’s Theorem

by Bektur Baizhanov, Nargiza Tazabekova and Tatyana Zambarnaya

Symmetry 2025, 17(10), 1641; https://doi.org/10.3390/sym17101641 - 3 Oct 2025

Abstract

The article’s primary focus is on the study of the number of countable non-isomorphic models of linearly ordered theories. The orthogonality of 1-types and their convex closures is employed to analyse a class of theories with a specific type of monotonic non-orthogonality, which [...] Read more.

The article’s primary focus is on the study of the number of countable non-isomorphic models of linearly ordered theories. The orthogonality of 1-types and their convex closures is employed to analyse a class of theories with a specific type of monotonic non-orthogonality, which includes weakly o-minimal theories. For such theories, a theorem analogous to L. Mayer’s result on the independence of any pairwise independent family of 1-types in o-minimal theories is proven. The article provides conditions for the infinity and maximality of the countable spectrum of weakly o-minimal theories. Full article

(This article belongs to the Section Mathematics)

15 pages, 1199 KB

Open AccessArticle

Wearable Activity Monitors to Quantify Gait During Stroke Rehabilitation: Data from a Pilot Randomised Controlled Trial Examining Auditory Rhythmical Cueing

by Christopher Buckley, Lisa Shaw, Patricia McCue, Philip Brown, Silvia Del Din, Richard Francis, Heather Hunter, Allen Lambert, Lynn Rochester and Sarah A. Moore

Symmetry 2025, 17(10), 1640; https://doi.org/10.3390/sym17101640 - 3 Oct 2025

Abstract

Hemiparesis is a disabling consequence of stroke, causing abnormal gait patterns with biomechanical asymmetries. Gait mechanics for stroke survivors appear resistant to conventional rehabilitation. Auditory rhythmical cueing (ARC) represents an emerging intervention option. To determine effective gait interventions, objective measures of gait collected [...] Read more.

Hemiparesis is a disabling consequence of stroke, causing abnormal gait patterns with biomechanical asymmetries. Gait mechanics for stroke survivors appear resistant to conventional rehabilitation. Auditory rhythmical cueing (ARC) represents an emerging intervention option. To determine effective gait interventions, objective measures of gait collected from real-world environments may be required in addition to standard clinical outcomes to aid understanding of gait mechanics. This study reports on the ability of wearable activity monitors to quantify an ARC intervention for fifty-nine stroke survivors randomised into an ARC gait and balance training programme or an equivalent training programme without ARC. Gait assessments were undertaken at baseline and at 6 weeks for 4-metre walks and continuously for 7 days following each home assessment using a wearable activity monitor. The success rates of data collection using the wearable activity monitors ranged from 64 to 95%. Forty-eight Digital Mobility Outcomes representing a broad range of gait mechanics were calculated. Visualisation of all DMOs using radar plots indicated changes from baseline in both groups, with individual data indicating large variability in response to the intervention and control programme. Including wearable activity monitors to evaluate gait interventions for stroke survivors provides additional value to traditional methods and aids understanding of individual responses; as such, they should be used for future intervention-based research. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Human Movement and Sensors Applied in Bioengineering)

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17 pages, 2223 KB

Open AccessArticle

Dynamic Evolution Analysis of Incentive Strategies and Symmetry Enhancement in the Personal-Data Valorization Industry Chain

by Jun Ma, Junhao Yu and Yingying Cheng

Symmetry 2025, 17(10), 1639; https://doi.org/10.3390/sym17101639 - 3 Oct 2025

Abstract

The value of personal data can only be unlocked through efficient circulation. This study explores a multi-party collaborative mechanism for personal-data trading, aiming to improve data quality and market vitality via incentive-compatible institutional design, thereby supporting the high-quality development of the digital economy. [...] Read more.

The value of personal data can only be unlocked through efficient circulation. This study explores a multi-party collaborative mechanism for personal-data trading, aiming to improve data quality and market vitality via incentive-compatible institutional design, thereby supporting the high-quality development of the digital economy. Symmetry enhancement refers to the use of strategies and mechanisms to narrow the information gap among data controllers, operators, and demanders, enabling all parties to facilitate personal-data transactions on relatively equal footing. Drawing on evolutionary-game theory, we construct a tripartite dynamic-game model that incorporates data controllers, data operators, and data demanders. We analyze how initial willingness, payoff structures, breach costs, and risk factors (e.g., data leakage) shape each party’s strategic choices (cooperate vs. defect) and their evolutionary trajectories, in search of stable equilibrium conditions and core incentive mechanisms for a healthy market. We find that (1) the initial willingness to cooperate among participants is the foundation of a virtuous cycle; (2) the net revenue of data products significantly influences operators’ and demanders’ propensity to cooperate; and (3) the severity of breach penalties and the potential losses from data leakage jointly affect the strategies of all three parties, serving as key levers for maintaining market trust and compliance. Accordingly, we recommend strengthening contract enforcement and trust-building; refining the legal and regulatory framework for data rights confirmation, circulation, trading, and security; and promoting stable supply–demand cooperation and market education to enhance awareness of data value and compliance, thereby stimulating individuals’ willingness to authorize the use of their data and maximizing its value. Full article

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26 pages, 12409 KB

Open AccessArticle

Digital Twin Integration for Active Learning in Robotic Manipulator Control Within Engineering 4.0

by Fernando J. Pantusin, Jessica S. Ortiz, Christian P. Carvajal, Víctor H. Andaluz, Lenin G. Yar, Flavio Roberti and Daniel Gandolfo

Symmetry 2025, 17(10), 1638; https://doi.org/10.3390/sym17101638 - 3 Oct 2025

Abstract

Robotic systems play an increasingly significant role in both education and industry; however, access to physical robots remains a challenge due to high costs and operational risks. This work presents a training platform based on Digital Twins, aimed at active learning in the [...] Read more.

Robotic systems play an increasingly significant role in both education and industry; however, access to physical robots remains a challenge due to high costs and operational risks. This work presents a training platform based on Digital Twins, aimed at active learning in the control of robotic manipulators, with a focus on the UFACTORY 850 arm. The proposed approach integrates mathematical modeling, interactive simulation, and experimental validation, enabling the implementation and testing of control strategies in three virtual scenarios that replicate real-world conditions: a laboratory, a service environment, and an industrial production line. The system relies on kinematic and dynamic models of the manipulator, using maneuverability velocities as input signals, and employs ROS as middleware to link the Unity 2022.2.14 graphics engine with the control algorithms developed in MATLAB R2022a. Experimental results demonstrate the accuracy of the implemented models and the effectiveness of the control algorithms, validating the usefulness of Digital Twins as a pedagogical tool to support safe, accessible, and innovative learning in robotic engineering. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Control Systems and Robotics)

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26 pages, 1520 KB

Open AccessArticle

Terminal Forensics in Mobile Botnet Command and Control Detection Using a Novel Complex Picture Fuzzy CODAS Algorithm

by Geng Niu, Fei Zhang and Muyuan Guo

Symmetry 2025, 17(10), 1637; https://doi.org/10.3390/sym17101637 - 3 Oct 2025

Abstract

Terminal forensics in large mobile networks is a vital activity for identifying compromised devices and analyzing malicious actions. In contrast, the study described here begins with the domain of terminal forensics as the primary focus, rather than the threat itself. This paper proposes [...] Read more.

Terminal forensics in large mobile networks is a vital activity for identifying compromised devices and analyzing malicious actions. In contrast, the study described here begins with the domain of terminal forensics as the primary focus, rather than the threat itself. This paper proposes a new multi-criteria decision-making (MCDM) model that integrates complex picture fuzzy sets (CPFS) with the combinative distance-based assessment (CODAS), referred to throughout as complex picture fuzzy CODAS (CPF-CODAS). The aim is to assist in forensic analysis for detecting mobile botnet command and control (C&C) systems. The CPF-CODAS model accounts for the uncertainty, hesitation, and complex numerical values involved in expert decision-making, using degrees of membership as positive, neutral, and negative values. An illustrative forensic case study is constructed where three mobile devices are evaluated by three cybersecurity professionals based on six key parameters related to botnet activity. The results demonstrate that the model can effectively distinguish suspicious devices and support the use of the CPF-CODAS approach in terminal forensics of mobile networks. The robustness, symmetry, and advantages of this model over existing MCDM methods are confirmed through sensitivity and comparison analyses. In conclusion, this paper introduces a novel probabilistic decision-support tool that digital forensic specialists can incorporate into their workflow to proactively identify and prevent actions of mobile botnet C&C servers. Full article

(This article belongs to the Section Mathematics)

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9 pages, 1739 KB

Open AccessArticle

Quantum Behavior of 10D Planck Unit: Stationary Electron, Compton Photon and Gravitational Field

by Yan Zhou, Junyan Zhang, Ernst Meyer, Xingkai Zhang and Hongyu Liang

Symmetry 2025, 17(10), 1636; https://doi.org/10.3390/sym17101636 - 2 Oct 2025

Abstract

This work focuses on the origin of electrons, Compton photons and a gravitational field. Based on the discovered 10D Planck units, the physical behavior of these units was further studied in isolated systems. Investigation shows that a 10D Planck unit in the in [...] Read more.

This work focuses on the origin of electrons, Compton photons and a gravitational field. Based on the discovered 10D Planck units, the physical behavior of these units was further studied in isolated systems. Investigation shows that a 10D Planck unit in the in situ state has the same properties as a stationary electron, while its non-in situ state shares the same physics with a Compton photon. Results indicate that photons’ potential exists between any two Compton photons, with their strength being determined by the distance between the two photons. Finally, the potential field was proved to be the gravitational field of a proton. Full article

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

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23 pages, 3987 KB

Open AccessArticle

From Symmetry to Semantics: Improving Heritage Point Cloud Classification with a Geometry-Aware, Uniclass-Informed Taxonomy for Random Forest Implementation in Automated HBIM Modelling

by Aleksander Gil and Yusuf Arayici

Symmetry 2025, 17(10), 1635; https://doi.org/10.3390/sym17101635 - 2 Oct 2025

Abstract

Heritage Building Information Modelling (HBIM) requires the accurate classification of diverse building elements from 3D point clouds. This study presents a novel classification approach integrating a bespoke Uniclass-derived taxonomy with a hierarchical Random Forest model. It was applied to the 17th-century Queen’s House [...] Read more.

Heritage Building Information Modelling (HBIM) requires the accurate classification of diverse building elements from 3D point clouds. This study presents a novel classification approach integrating a bespoke Uniclass-derived taxonomy with a hierarchical Random Forest model. It was applied to the 17th-century Queen’s House in Greenwich, a building rich in classical architectural elements whose geometric properties are often defined by principles of symmetry. The bespoke classification was implemented across three levels (50 mm, 20 mm, 5 mm point cloud resolutions) and evaluated against the prior experiment that used Uniclass classification. Results showed a substantial improvement in classification precision and overall accuracy at all levels. The Level 1 classifier’s accuracy increased by 15% of points (relative ~50% improvement) with the bespoke classification taxonomy, reducing the misclassifications and error propagation in subsequent levels. This research demonstrates that tailoring the Uniclass building classification for heritage-specific geometry significantly enhances machine learning performance, which, to date, has not been published in the academic domain. The findings underscore the importance of adaptive taxonomies and suggest pathways for integrating multi-scale features and advanced learning methods to support automated HBIM workflows. Full article

(This article belongs to the Section Computer)

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24 pages, 9336 KB

Open AccessArticle

Temporal-Aware and Intent Contrastive Learning for Sequential Recommendation

by Yuan Zhang, Yaqin Fan, Tiantian Sheng and Aoshuang Wang

Symmetry 2025, 17(10), 1634; https://doi.org/10.3390/sym17101634 - 2 Oct 2025

Abstract

In recent years, research in sequential recommendation has primarily refined user intent by constructing sequence-level contrastive learning tasks through data augmentation or by extracting preference information from the latent space of user behavior sequences. However, existing methods suffer from two critical limitations. Firstly, [...] Read more.

In recent years, research in sequential recommendation has primarily refined user intent by constructing sequence-level contrastive learning tasks through data augmentation or by extracting preference information from the latent space of user behavior sequences. However, existing methods suffer from two critical limitations. Firstly, they fail to account for how random data augmentation may introduce unreasonable item associations in contrastive learning samples, thereby perturbing sequential semantic relationships. Secondly, the neglect of temporal dependencies may prevent models from effectively distinguishing between incidental behaviors and stable intentions, ultimately impairing the learning of user intent representations. To address these limitations, we propose TCLRec, a novel temporal-aware and intent contrastive learning framework for sequential recommendation, incorporating symmetry into its architecture. During the data augmentation phase, the model employs a symmetrical contrastive learning architecture and incorporates semantic enhancement operators to integrate user preferences. By introducing user rating information into both branches of the contrastive learning framework, this approach effectively enhances the semantic relevance between positive sample pairs. Furthermore, in the intent contrastive learning phase, TCLRec adaptively attenuates noise information in the frequency domain through learnable filters, while in the pre-training phase of sequence-level contrastive learning, it introduces a temporal-aware network that utilizes additional self-supervised signals to assist the model in capturing both long-term dependencies and short-term interests from user behavior sequences. The model employs a multi-task training strategy that alternately performs intent contrastive learning and sequential recommendation tasks to jointly optimize user intent representations. Comprehensive experiments conducted on the Beauty, Sports, and LastFM datasets demonstrate the soundness and effectiveness of TCLRec, where the incorporation of symmetry enhances the model’s capability to represent user intentions. Full article

(This article belongs to the Section Computer)

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17 pages, 828 KB

Open AccessArticle

Quantum Coherence and Mixedness in Hydrogen Atoms: Probing Hyperfine Structure Dynamics Under Dephasing Constraints

by Kamal Berrada and Smail Bougouffa

Symmetry 2025, 17(10), 1633; https://doi.org/10.3390/sym17101633 - 2 Oct 2025

Abstract

We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical [...] Read more.

We investigate the quantum dynamics of coherence in the hyperfine structure of hydrogen atoms subjected to dephasing noise, modeled using the Lindblad master equation. The effective Hamiltonian describes the spin–spin interaction between the electron and proton, with dephasing introduced via Lindblad operators. Analytical solutions for the time-dependent density matrix are derived for various initial states, including separable, partially entangled, and maximally entangled configurations. Quantum coherence is quantified through the

l_{1}

-norm measures, while purity is evaluated to assess mixedness. Results demonstrate that coherence exhibits oscillatory decay modulated by the dephasing rate, with antiparallel spin states showing greater resilience against noise compared to parallel configurations. These findings highlight the interplay between coherent hyperfine dynamics and environmental dephasing, offering insights into preserving quantum resources in atomic systems for applications in quantum information science. Full article

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

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35 pages, 1088 KB

Open AccessArticle

A Survey of Maximum Entropy-Based Inverse Reinforcement Learning: Methods and Applications

by Li Song, Qinghui Guo, Irfan Ali Channa and Zeyu Wang

Symmetry 2025, 17(10), 1632; https://doi.org/10.3390/sym17101632 - 2 Oct 2025

Abstract

In recent years, inverse reinforcement learning algorithms have garnered substantial attention and demonstrated remarkable success across various control domains, including autonomous driving, intelligent gaming, robotic manipulation, and automated industrial systems. Nevertheless, existing methodologies face two persistent challenges: (1) finite or non-optimal expert demonstration [...] Read more.

In recent years, inverse reinforcement learning algorithms have garnered substantial attention and demonstrated remarkable success across various control domains, including autonomous driving, intelligent gaming, robotic manipulation, and automated industrial systems. Nevertheless, existing methodologies face two persistent challenges: (1) finite or non-optimal expert demonstration and (2) ambiguity in which different reward functions lead to same expert strategies. To improve and enhance the expert demonstration data and to eliminate the ambiguity caused by the symmetry of rewards, there has been a growing interest in research on developing inverse reinforcement learning based on the maximum entropy method. The unique advantage of these algorithms lies in learning rewards from expert presentations by maximizing policy entropy, matching expert expectations, and then optimizing the policy. This paper first provides a comprehensive review of the historical development of maximum entropy-based inverse reinforcement learning (ME-IRL) methodologies. Subsequently, it systematically presents the benchmark experiments and recent application breakthroughs achieved through ME-IRL. The concluding section analyzes the persistent technical challenges, proposes promising solutions, and outlines the emerging research frontiers in this rapidly evolving field. Full article

(This article belongs to the Section Mathematics)

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14 pages, 4629 KB

Open AccessArticle

Zak-Phase Dislocations in Trimer Lattices

by Tileubek Uakhitov, Abdybek Urmanov, Serik E. Kumekov and Anton S. Desyatnikov

Symmetry 2025, 17(10), 1631; https://doi.org/10.3390/sym17101631 - 2 Oct 2025

Abstract

Wave propagation in periodic media is governed by energy–momentum relations and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that, in the off-diagonal trimer lattices, Zak phase carries quantized screw-type dislocations winding around degeneracies in parameter space. [...] Read more.

Wave propagation in periodic media is governed by energy–momentum relations and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that, in the off-diagonal trimer lattices, Zak phase carries quantized screw-type dislocations winding around degeneracies in parameter space. If the lattice evolves in time periodically, as in adiabatic Thouless pumps, the corresponding closed trajectory in parameter space is characterized by a Chern number equal to the negative total winding number of Zak phase dislocations enclosed by the trajectory. We discuss the correspondence between bulk Chern numbers and the edge states in a finite system evolving along various pumping cycles. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Topological Phases)

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21 pages, 524 KB

Open AccessArticle

Emergence and Localization of Exceptional Points in an Exactly Solvable Toy Model

by Miloslav Znojil

Symmetry 2025, 17(10), 1630; https://doi.org/10.3390/sym17101630 - 2 Oct 2025

Abstract

In contrast to classical physics, there are not too many mathematical tools facilitating the study of singularities in quantum systems. One of the exceptions is Kato’s notion of exceptional points (EPs). Their emergence and localization are analyzed here via a family of schematic [...] Read more.

In contrast to classical physics, there are not too many mathematical tools facilitating the study of singularities in quantum systems. One of the exceptions is Kato’s notion of exceptional points (EPs). Their emergence and localization are analyzed here via a family of schematic toy models. Full article

(This article belongs to the Section Physics)

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23 pages, 1548 KB

Open AccessArticle

Customizable Length Constrained Image-Text Summarization via Knapsack Optimization

by Xuan Liu, Xiangyu Qu, Yu Weng, Yutong Gao, Zheng Liu and Xianggan Liu

Symmetry 2025, 17(10), 1629; https://doi.org/10.3390/sym17101629 - 2 Oct 2025

Abstract

With the proliferation of multimedia data, controllable summarization generation has become a key focus in Artificial Intelligence Content Generation. However, many traditional methods lack precise control over output length, often resulting in summaries that are either too verbose or too brief, thus failing [...] Read more.

With the proliferation of multimedia data, controllable summarization generation has become a key focus in Artificial Intelligence Content Generation. However, many traditional methods lack precise control over output length, often resulting in summaries that are either too verbose or too brief, thus failing to meet diverse user needs. In this paper, we propose a length-customizable approach for multimodal image-text summarization. Our method integrates combinatorial optimization with deep learning to address the length-control challenge. Specifically, we formulate the summarization task as a knapsack optimization problem, enhanced by a greedy algorithm to strictly adhere to user-defined length constraints. Additionally, we introduce a multimodal attention mechanism to ensure balanced and coherent integration of textual and visual information. To further enhance semantic alignment, we employ a cross-modal matching strategy for image selection based on pre-trained vision-language models. Experimental evaluations on the MSMO dataset and validate against baselines like LEAD-3, Seq2Seq, Attention, and Transformer that our method achieves a ROUGE-1 score of 40.52, ROUGE-2 of 16.07, and ROUGE-L of 35.15, outperforming existing length-controllable baselines. Moreover, our approach attains the lowest length variance, confirming its precise adherence to target summary lengths. These results validate the effectiveness of our method in generating high-quality, length-constrained multimodal summaries. Full article

(This article belongs to the Section Computer)

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16 pages, 319 KB

Open AccessArticle

Fuzzy Graphic Binary Matroid Approach to Power Grid Communication Network Analysis

by Jing Li, Buvaneswari Rangasamy, Saranya Shanmugavel and Aysha Khan

Symmetry 2025, 17(10), 1628; https://doi.org/10.3390/sym17101628 - 2 Oct 2025

Abstract

Matroid is a mathematical structure that extends the concept of independence. The fuzzy graphic binary matroid serves as a generalization of linear dependence, and its properties are examined. Power grid networks, which manage the generation, transmission, and distribution of electrical energy from power [...] Read more.

Matroid is a mathematical structure that extends the concept of independence. The fuzzy graphic binary matroid serves as a generalization of linear dependence, and its properties are examined. Power grid networks, which manage the generation, transmission, and distribution of electrical energy from power plants to consumers, are inherently a complex system. A key objective in analyzing these networks is to ensure a reliable and uninterrupted supply of electricity. However, several critical issues must be addressed, including uncertainty in communication links, detection of redundant or sensitive circuits, evaluation of network resilience under partial failures, and optimization of reliability in interconnected network systems. To support this goal, the concept of a fuzzy graphic binary matroid is applied in the analysis of power grid communication network, offering a framework that not only incorporates fuzziness and binary conditions but also enables systematic identification of weak circuits, redundancy planning, and reliability enhancement. This approach provides a more realistic representation of operational conditions, ensuring better fault tolerance and improved efficiency of the grid. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)

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27 pages, 16191 KB

Open AccessArticle

Far Transfer Effects of Multi-Task Gamified Cognitive Training on Simulated Flight: Short-Term Theta and Alpha Signal Changes and Asymmetry Changes

by Peng Ding, Chen Li, Zhengxuan Zhou, Yang Xiang, Shaodi Wang, Xiaofei Song and Yingwei Li

Symmetry 2025, 17(10), 1627; https://doi.org/10.3390/sym17101627 - 1 Oct 2025

Abstract

Cognitive deficiencies are significant factors affecting aviation piloting capabilities. However, due to the limited stability resulting from the insufficient appeal of traditional attention or memory cognitive training, multi-task gamified cognitive training (MTGCT) may be more beneficial in generating far transfer effects in task [...] Read more.

Cognitive deficiencies are significant factors affecting aviation piloting capabilities. However, due to the limited stability resulting from the insufficient appeal of traditional attention or memory cognitive training, multi-task gamified cognitive training (MTGCT) may be more beneficial in generating far transfer effects in task performance. This study explores the enhancement effects of simulated flight operation capabilities based on visuo-spatial attention and working memory MTGCT. Additionally, we explore the neurophysiological impacts through changes in EEG power spectral density (PSD) characteristics and brain asymmetry, and whether these impacts exhibit a certain retention effect. This study designed a 28-day simulated flight operation capability enhancement experiment. In addition, the behavioral performance and EEG signal changes in 28 college students (divided into control and training groups) were analyzed. The results indicated that MTGCT significantly enhanced simulated flight operational capabilities, and the neural framework formed by physiological changes remains effective for at least two weeks. The physiological changes included a decrease in the

θ

band PSD and an increase in the

α

band PSD in the frontal and parietal lobes due to optimized cognitive resource allocation, as well as the frontal

θ

band leftward asymmetry and the frontoparietal

α

band rightward asymmetry due to the formation of neural activity patterns. These findings support, to some extent, the feasibility and effectiveness of using MTGCT as a periodic training method to enhance the operational and cognitive abilities of aviation personnel. Full article

(This article belongs to the Special Issue Advances in Symmetry/Asymmetry and Biomedical Engineering)

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15 pages, 275 KB

Open AccessArticle

Hyers–Ulam–Rassias Stability of Reciprocal-Type Functional Equations: Comparative Study of Direct and Fixed Point Methods

by Heejeong Koh

Symmetry 2025, 17(10), 1626; https://doi.org/10.3390/sym17101626 - 1 Oct 2025

Abstract

In this paper, we investigate the Hyers–Ulam–Rassias stability of reciprocal functional equations in non-Archimedean fuzzy normed spaces by using both the direct method and the fixed point alternative. In addition, we study a modified reciprocal type functional equation within the same framework using [...] Read more.

In this paper, we investigate the Hyers–Ulam–Rassias stability of reciprocal functional equations in non-Archimedean fuzzy normed spaces by using both the direct method and the fixed point alternative. In addition, we study a modified reciprocal type functional equation within the same framework using Brzdȩk’s fixed point method. A brief remark is provided on the incidental role of symmetry in the structure of such functional equations. Finally, a comparative analysis highlights the distinctive features, strengths, and limitations of each approach. Full article

(This article belongs to the Special Issue Functional Equations and Inequalities: Topics and Applications)

23 pages, 14097 KB

Open AccessArticle

Comparative Analysis of Local Flow Fields of Typical Inner Jet Holes-Type Reverse Circulation Drill Bit for Pneumatic Hollow-Through DTH Hammer Based on CFD Simulation

by Jiwei Wen, Jiang Chen and Fengtao Zhang

Symmetry 2025, 17(10), 1625; https://doi.org/10.3390/sym17101625 - 1 Oct 2025

Abstract

The reverse circulation drill bit is the key component for the efficient and smooth implementation of the pneumatic hollow-through down-the-hole (DTH) hammer reverse circulation continuous coring (sampling) technology. To obtain the structural form of a reverse circulation drill bit with better reverse circulation [...] Read more.

The reverse circulation drill bit is the key component for the efficient and smooth implementation of the pneumatic hollow-through down-the-hole (DTH) hammer reverse circulation continuous coring (sampling) technology. To obtain the structural form of a reverse circulation drill bit with better reverse circulation performance, revealing its local flow fields by computational fluid dynamics (CFD) simulation is an effective approach. Taking the inner jet holes-type reverse circulation drill bit as the research object, three kinds of symmetrical and asymmetrical structures of inner jet holes were proposed. The CFD simulation results show that increasing the air volume supply and the number of inner jet holes leads to an increase in the velocity of air flow jet within the inner jet holes, an increase in the negative pressure formed in the central through channel below the inner jet holes, an enhancement of the reverse circulation performance and suction capacity formed by the reverse circulation drill bit, and an acceleration of the upward flow velocity of the rock cores (samples) located at the bottom of the borehole. Additionally, the reverse circulation performance formed by the reverse circulation drill bit with staggered arranged inner jet holes is superior to that of the reverse circulation drill bit with uniformly distributed inner jet holes. Under the same simulation conditions, the static pressure (i.e., negative pressure) and the upward flow velocity formed by the JB6 model are 2.34 kPa and 30.778 m/s higher than those formed by the JB3-3 model, while these two values formed by the JC6 model are 0.197 kPa and 3.689 m/s higher than those formed by the JB6 model, respectively. In conclusion, an asymmetric structural design would be more reasonable for the design of the inner jet holes-type reverse circulation drill bit. Full article

(This article belongs to the Topic Energy Power, Mechanical Engineering and Their Applications)

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