Symmetry

15 pages, 340 KB

Open AccessArticle

Nonlinear Almost Relational Contractions via a Triplet of Test Functions and Applications to Second-Order Ordinary Differential Equations

by Doaa Filali and Faizan Ahmad Khan

Symmetry 2025, 17(11), 1798; https://doi.org/10.3390/sym17111798 (registering DOI) - 24 Oct 2025

Abstract

After the introduction of the relation-theoretic contraction principle, the branch of metric fixed-point theory has attracted much attention in this direction, and various fixed-point results have been proven in the framework of relational metric space via different approaches. The aim of this article [...] Read more.

After the introduction of the relation-theoretic contraction principle, the branch of metric fixed-point theory has attracted much attention in this direction, and various fixed-point results have been proven in the framework of relational metric space via different approaches. The aim of this article is to establish some fixed-point outcomes in the framework of relational metric space verifying a generalized nonlinear contraction utilizing three test functions

Φ

,

Ψ

and

Θ

satisfying the appropriate characteristics. The findings obtained herein expand, sharpen, improve, modify and unify a few well-known findings. To demonstrate the utility of our outcomes, several examples are furnished. We utilized our outcomes to investigate a unique solution of second-order ordinary differential equations prescribed with specific boundary conditions. Full article

(This article belongs to the Special Issue Nonlinear Analysis and Applications, Geometry of Banach Spaces and Symmetry II)

14 pages, 271 KB

Open AccessArticle

On Finitely Generated Neutrosophic Modules with Finite Value Distribution

by Amr Elrawy and Ali Yahya Hummdi

Symmetry 2025, 17(11), 1797; https://doi.org/10.3390/sym17111797 (registering DOI) - 24 Oct 2025

Abstract

This paper presents the novel framework of neutrosophic modules, an algebraic structure that arises by superimposing neutrosophic sets on classical module theory. The core of this study lies in the investigation of the structural symmetry between the axioms of a module and the [...] Read more.

This paper presents the novel framework of neutrosophic modules, an algebraic structure that arises by superimposing neutrosophic sets on classical module theory. The core of this study lies in the investigation of the structural symmetry between the axioms of a module and the trivalent nature of the neutrosophic set. We define a new class of modules based on the neutrosophic set. In addition, this study establishes and examines the categorical structure corresponding to neutrosophic

R

-modules. Furthermore, it presents the procedures by which finitely generated variants of these modules can be formulated and studied. Partial characterizations are given for a particular type in which the distribution of neutrosophic values remains within a finite set. Full article

(This article belongs to the Section Mathematics)

20 pages, 1982 KB

Open AccessArticle

Bias Term for Outlier Detection and Robust Regression

by Felix Ndudim and Thanasak Mouktonglang

Symmetry 2025, 17(11), 1796; https://doi.org/10.3390/sym17111796 (registering DOI) - 24 Oct 2025

Abstract

Noisy data and outliers are among the main challenges in machine learning, as their presence in training data can significantly reduce model performance and generalization. Detecting and handling these anomalous samples is particularly difficult because it is hard to distinguish them from normal [...] Read more.

Noisy data and outliers are among the main challenges in machine learning, as their presence in training data can significantly reduce model performance and generalization. Detecting and handling these anomalous samples is particularly difficult because it is hard to distinguish them from normal data. In this study, we propose a novel bias-based method (BT-SVR) to detect outliers and noisy inputs. The method uses a bias term derived from pairwise relationships among data points, which captures structural information about input distances. Outliers and noisy samples typically produce near-zero bias responses, allowing them to be identified effectively. A root-mean-square (RMS) scoring mechanism is then applied to quantify the anomaly strength of each sample, enabling the impact of outliers to be underweighted before training. Experiments demonstrate that BT-SVR improves the performance of Support Vector Regression (SVR) and enhances its robustness against noisy and anomalous data. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis III)

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23 pages, 882 KB

Open AccessArticle

A Gauss Hypergeometric-Type Model for Heavy-Tailed Survival Times in Biomedical Research

by Jiju Gillariose, Mahmoud M. Abdelwahab, Joshin Joseph and Mustafa M. Hasaballah

Symmetry 2025, 17(11), 1795; https://doi.org/10.3390/sym17111795 - 24 Oct 2025

Abstract

In this study, we introduced and analyzed the Slash–Log–Logistic (SlaLL) distribution, a novel statistical model developed by applying the slash methodology to log–logistic and beta distributions. The SlaLL distribution is particularly suited for modeling datasets characterized by heavy tails and extreme [...] Read more.

In this study, we introduced and analyzed the Slash–Log–Logistic (SlaLL) distribution, a novel statistical model developed by applying the slash methodology to log–logistic and beta distributions. The SlaLL distribution is particularly suited for modeling datasets characterized by heavy tails and extreme values, frequently encountered in survival time analyses. We derived the mathematical representation of the distribution involving Gauss hypergeometric and beta functions, explicitly established the probability density function, cumulative distribution function, hazard rate function, and reliability function, and provided clear definitions of its moments. Through comprehensive simulation studies, the accuracy and robustness of maximum likelihood and Bayesian methods for parameter estimation were validated. Comparative empirical analyses demonstrated the SlaLL distribution’s superior fitting performance over well-known slash-based models, emphasizing its practical utility in accurately capturing the complexities of real-world survival time data. Full article

(This article belongs to the Section Mathematics)

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24 pages, 384 KB

Open AccessArticle

h-Almost Conformal η-Ricci–Bourguignon Solitons and Spacetime Symmetry in Barotropic Fluids Within f(

R, T

) Gravity

by Sunil Kumar Yadav, Sameh Shenawy, Hanan Alohali and Carlo Mantica

Symmetry 2025, 17(11), 1794; https://doi.org/10.3390/sym17111794 - 23 Oct 2025

Abstract

We investigate the geometric and physical properties of the h-almost conformal

η

-Ricci–Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of

f (R, T)

gravity. We derive this barotropic equation of [...] Read more.

We investigate the geometric and physical properties of the h-almost conformal

η

-Ricci–Bourguignon soliton and its gradient form by employing a barotropic equation of state within the framework of

f (R, T)

gravity. We derive this barotropic equation of state under the assumption that the matter content of

f (R, T)

gravity is modeled by a barotropic perfect fluid. We also examine the way in which these soliton structures both reveal and limit the underlying symmetries of the spacetime geometry. Furthermore, we obtain modified Poisson and Liouville equations associated with these solitons in such a gravitational setting. Additionally, we explore certain harmonic aspects of the h-almost conformal

η

-Ricci–Bourguignon soliton on a spacetime filled with a barotropic perfect fluid, considering a harmonic potential function

Ψ

. Finally, we present physical interpretations of the conformal pressure

\tilde{p}

in the context of the h-almost conformal

η

-Ricci–Bourguignon soliton within

f (R, T)

gravity. Full article

(This article belongs to the Section Physics)

14 pages, 1036 KB

Open AccessArticle

Biomedical Knowledge Graph Embedding with Hierarchical Capsule Network and Rotational Symmetry for Drug-Drug Interaction Prediction

by Sensen Zhang, Xia Li, Yang Liu, Peng Bi and Tiangui Hu

Symmetry 2025, 17(11), 1793; https://doi.org/10.3390/sym17111793 - 23 Oct 2025

Abstract

The forecasting of Drug-Drug Interactions (DDIs) is essential in pharmacology and clinical practice to prevent adverse drug reactions. Existing approaches, often based on neural networks and knowledge graph embedding, face limitations in modeling correlations among drug features and in handling complex BioKG relations, [...] Read more.

The forecasting of Drug-Drug Interactions (DDIs) is essential in pharmacology and clinical practice to prevent adverse drug reactions. Existing approaches, often based on neural networks and knowledge graph embedding, face limitations in modeling correlations among drug features and in handling complex BioKG relations, such as one-to-many, hierarchical, and composite interactions. To address these issues, we propose Rot4Cap, a novel framework that embeds drug entity pairs and BioKG relationships into a four-dimensional vector space, enabling effective modeling of diverse mapping properties and hierarchical structures. In addition, our method integrates molecular structures and drug descriptions with BioKG entities, and it employs capsule network–based attention routing to capture feature correlations. Experiments on three benchmark BioKG datasets demonstrate that Rot4Cap outperforms state-of-the-art baselines, highlighting its effectiveness and robustness. Full article

(This article belongs to the Section Computer)

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12 pages, 500 KB

Open AccessArticle

A New Mathematical Model for Eye Vision Disability Dynamics: Investigation of Visual Acuity, Lens Power, Pupil Diameter, and Environmental Factors

by Ibrahim Al-Dayel

Symmetry 2025, 17(11), 1792; https://doi.org/10.3390/sym17111792 - 23 Oct 2025

Abstract

This study presents a mathematical model to understand the dynamics of eye vision disability, incorporating key physiological and environmental variables such as visual acuity, lens power, pupil diameter, and environmental influence. The novel model developed in this work consists of four state variables [...] Read more.

This study presents a mathematical model to understand the dynamics of eye vision disability, incorporating key physiological and environmental variables such as visual acuity, lens power, pupil diameter, and environmental influence. The novel model developed in this work consists of four state variables that describe their interactions, aiming to simulate changes in visual acuity and the progression of vision disability under different circumstances. Various mathematical aspects including positivity and equilibrium points along with local and global stability are demonstrated. In addition, the sensitivity analysis is also presented to examine the impact of variations in parameters on the model’s outcomes, highlighting the factors that significantly influence visual acuity and pupil adjustments. Furthermore, the phase portraits explore the dynamic interactions between variables, revealing different insights into the stability of the system and adaptive responses. These results provide a thorough understanding of factors influencing eye vision, offering new insights into vision disability dynamics through an integrated, non-autonomous model and practical applications in developing corrective strategies. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications Ⅱ)

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33 pages, 2812 KB

Open AccessArticle

A Symmetry-Aware Predictive Framework for Olympic Cold-Start Problems and Rare Events Based on Multi-Granularity Transfer Learning and Extreme Value Analysis

by Yanan Wang, Yi Fei and Qiuyan Zhang

Symmetry 2025, 17(11), 1791; https://doi.org/10.3390/sym17111791 - 23 Oct 2025

Abstract

This paper addresses the cold-start problem and rare event prediction challenges in Olympic medal forecasting by proposing a predictive framework that integrates multi-granularity transfer learning with extreme value theory. The framework comprises two main components, a Multi-Granularity Transfer Learning Core (MG-TLC) and a [...] Read more.

This paper addresses the cold-start problem and rare event prediction challenges in Olympic medal forecasting by proposing a predictive framework that integrates multi-granularity transfer learning with extreme value theory. The framework comprises two main components, a Multi-Granularity Transfer Learning Core (MG-TLC) and a Rare Event Analysis Module (RE-AM), which address multi-level prediction for data-scarce countries and first medal prediction tasks. The MG-TLC incorporates two key components: Dynamic Feature Space Reconstruction (DFSR) and the Hierarchical Adaptive Transfer Strategy (HATS). The RE-AM combines a Bayesian hierarchical extreme value model (BHEV) with piecewise survival analysis (PSA). Experiments based on comprehensive, licensed Olympic data from 1896–2024, where the framework was trained on data up to 2016, validated on the 2020 Games, and tested by forecasting the 2024 Games, demonstrate that the proposed framework significantly outperforms existing methods, reducing MAE by 25.7% for data-scarce countries and achieving an AUC of 0.833 for first medal prediction, 14.3% higher than baseline methods. This research establishes a foundation for predicting the 2028 Los Angeles Olympics and provides new approaches for cold-start and rare event prediction, with potential applicability to similar challenges in other data-scarce domains such as economics or public health. From a symmetry viewpoint, our framework is designed to preserve task-relevant invariances—permutation invariance in set-based country aggregation and scale robustness to macro-covariate units—via distributional alignment between data-rich and data-scarce domains and Olympic-cycle indexing. We treat departures from these symmetries (e.g., host advantage or event-program changes) as structured asymmetries and capture them with a rare event module that combines extreme value and survival modeling. Full article

(This article belongs to the Special Issue Applications Based on Symmetry in Machine Learning and Data Mining)

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25 pages, 5642 KB

Open AccessArticle

A Trusted Transaction Method for Remote Sensing Image Data Based on a Homomorphic Encryption Watermark and Blockchain

by Minxuan Wang, Lei Zhang, Na Ren and Changqing Zhu

Symmetry 2025, 17(11), 1790; https://doi.org/10.3390/sym17111790 - 23 Oct 2025

Abstract

Existing methods for the secure transaction and circulation of remote sensing image data primarily focus on post-event investigation, lacking a reliable mechanism for secure distribution and fair trading of data. To address this issue, this study proposes a trusted transaction method that integrates [...] Read more.

Existing methods for the secure transaction and circulation of remote sensing image data primarily focus on post-event investigation, lacking a reliable mechanism for secure distribution and fair trading of data. To address this issue, this study proposes a trusted transaction method that integrates a watermark based on Paillier homomorphic encryption, blockchain, and smart contract. This method leverages the homomorphic property of the Paillier cryptosystem to imperceptibly embed the ciphertext of the watermark generated from transaction information into encrypted remote sensing image data. The data buyer at the receiving end decrypts the key pair using the private key, thereby decrypting the data to obtain the watermarked plaintext. Simultaneously, transaction records are immutably stored on trusted blockchain nodes via smart contracts. Throughout the entire transaction process, data encryption/decryption and watermark embedding/extraction are symmetric. The experimental results demonstrate that the watermark can be effectively extracted after encryption, thereby supporting transaction verification and traceability. Furthermore, the three smart contracts designed in this study all exhibit strong execution performance. In particular, the smart contract employed for verification demonstrated an average execution latency of only 0.19 s per instance. Through enforcing the retrieval of parameters and storage credentials from the blockchain, the proposed method effectively constrains malicious behavior from both parties, offering a novel technical approach to facilitate consensus and mutual trust. Full article

(This article belongs to the Section Computer)

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27 pages, 341 KB

Open AccessArticle

Four-Dimensional Spaces of Complex Numbers and Unitary States of Two-Qubit Quantum Systems

by Mars B. Gabbassov, Tolybay Z. Kuanov, Turganbay K. Yermagambetov and Berik I. Tuleuov

Symmetry 2025, 17(11), 1789; https://doi.org/10.3390/sym17111789 - 22 Oct 2025

Abstract

The pure states of two-qubit quantum systems are described by a four-dimensional vector of complex numbers, and unitary operators transferring a two-qubit quantum system from one state to another have the form of a

4 \times 4

matrix with complex elements. This fact [...] Read more.

The pure states of two-qubit quantum systems are described by a four-dimensional vector of complex numbers, and unitary operators transferring a two-qubit quantum system from one state to another have the form of a

4 \times 4

matrix with complex elements. This fact brings to mind the idea of studying the spaces of four-dimensional numbers with complex components. Moreover, the results obtained by the authors for four-dimensional numbers with real components inspire some optimism. In this paper we construct four-dimensional spaces of complex numbers by analogy with four-dimensional spaces of real numbers. Each four-dimensional number is mapped to a matrix formed from its components and it is proved that the constructed mapping is a bijection and a homomorphism. In the space of four-dimensional numbers of the eight basis elements, half are real and half are imaginary. The presence of such symmetry distinguishes these spaces from the space of quaternions, in which one basis element is real and the rest are imaginary. The symmetry of the basis numbers makes these spaces a natural generalization of one-dimensional and two-dimensional (complex) algebra. The conditions under which the corresponding matrices are gates for two-qubit quantum systems are defined. The notion of a unitary state of a two-qubit quantum system is introduced, to which various gates from commutative groups of gates correspond. It is shown that any gate of a unitary state transforms a unitary state into a unitary state and a non-unitary state into a non-unitary state. Almost all gates used in the construction of quantum circuits, in particular H, SWAP, CX, CY, and CZ, have the same properties. The problem of searching for a gate that transfers a quantum system from one unitary state to another unitary state has been solved. Thus, with the help of four-dimensional spaces of complex numbers it was possible to construct whole classes of two-qubit gates, which opens new possibilities for the construction of quantum algorithms. The results obtained have important theoretical and practical implications for quantum computing. Full article

(This article belongs to the Section Physics)

25 pages, 1741 KB

Open AccessArticle

Event-Aware Multimodal Time-Series Forecasting via Symmetry-Preserving Graph-Based Cross-Regional Transfer Learning

by Shu Cao and Can Zhou

Symmetry 2025, 17(11), 1788; https://doi.org/10.3390/sym17111788 - 22 Oct 2025

Abstract

Forecasting real-world time series in domains with strong event sensitivity and regional variability poses unique challenges, as predictive models must account for sudden disruptions, heterogeneous contextual factors, and structural differences across locations. In tackling these challenges, we draw on the concept of symmetry [...] Read more.

Forecasting real-world time series in domains with strong event sensitivity and regional variability poses unique challenges, as predictive models must account for sudden disruptions, heterogeneous contextual factors, and structural differences across locations. In tackling these challenges, we draw on the concept of symmetry that refers to the balance and invariance patterns across temporal, multimodal, and structural dimensions, which help reveal consistent relationships and recurring patterns within complex systems. This study is based on two multimodal datasets covering 12 tourist regions and more than 3 years of records, ensuring robustness and practical relevance of the results. In many applications, such as monitoring economic indicators, assessing operational performance, or predicting demand patterns, short-term fluctuations are often triggered by discrete events, policy changes, or external incidents, which conventional statistical and deep learning approaches struggle to model effectively. To address these limitations, we propose an event-aware multimodal time-series forecasting framework with graph-based regional transfer built upon an enhanced PatchTST backbone. The framework unifies multimodal feature extraction, event-sensitive temporal reasoning, and graph-based structural adaptation. Unlike Informer, Autoformer, FEDformer, or PatchTST, our model explicitly addresses naive multimodal fusion, event-agnostic modeling, and weak cross-regional transfer by introducing an event-aware Multimodal Encoder, a Temporal Event Reasoner, and a Multiscale Graph Module. Experiments on diverse multi-region multimodal datasets demonstrate that our method achieves substantial improvements over eight state-of-the-art baselines in forecasting accuracy, event response modeling, and transfer efficiency. Specifically, our model achieves a 15.06% improvement in the event recovery index, a 15.1% reduction in MAE, and a 19.7% decrease in event response error compared to PatchTST, highlighting its empirical impact on tourism event economics forecasting. Full article

(This article belongs to the Special Issue Symmetry in Data Sciences and Machine Learning for Multidisciplinary Research)

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24 pages, 38382 KB

Open AccessArticle

Skeleton Information-Driven Reinforcement Learning Framework for Robust and Natural Motion of Quadruped Robots

by Huiyang Cao, Hongfa Lei, Yangjun Liu, Zheng Chen, Shuai Shi, Bingquan Li, Weichao Xu and Zhi-Xin Yang

Symmetry 2025, 17(11), 1787; https://doi.org/10.3390/sym17111787 - 22 Oct 2025

Abstract

Legged robots have great potential in complex environments, but achieving robust and natural locomotion remains difficult due to challenges in generating smooth gaits and resisting disturbances. This article presents a novel reinforcement learning framework that integrates a skeleton-aware graph neural network (GNN), a [...] Read more.

Legged robots have great potential in complex environments, but achieving robust and natural locomotion remains difficult due to challenges in generating smooth gaits and resisting disturbances. This article presents a novel reinforcement learning framework that integrates a skeleton-aware graph neural network (GNN), a single-stage teacher–student architecture, a system-response model, and a Wasserstein Adversarial Motion Priors (wAMP) module. The skeleton-aware GNN enriches observations by encoding key node information and link properties, providing structured body information and better spatial awareness on irregular terrains. Unlike conventional two-stage approaches, this method jointly trains teacher and student policies to accelerate learning and improve sim-to-real transfer using hybrid advantage estimation (HAE). The system-response model further enhances robustness by predicting future observations from historical states via contrastive learning, enabling the policy to anticipate terrain variations and external disturbances. Finally, wAMP provides a more stable adversarial imitation method for fitting expert datasets of both flat ground and stair locomotion. Experiments on quadruped robots demonstrate that the proposed approach achieves more natural gaits and stronger robustness than existing baselines. Full article

(This article belongs to the Special Issue Latest Advancements in Symmetry and Asymmetry in Robotics and Mechatronics: Highlighting Emerging Trends and Their Intersections with Artificial Intelligence (AI), Machine Learning, Nonlinear Systems, and Control)

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16 pages, 18210 KB

Open AccessArticle

Basic Study of Blood Coagulation by Microplasma

by Marius Gabriel Blajan, Anca Daniela Stoica, Cristian Sevcencu, Septimiu Cassian Tripon, Vasile Surducan and Kazuo Shimizu

Symmetry 2025, 17(11), 1786; https://doi.org/10.3390/sym17111786 - 22 Oct 2025

Abstract

Plasma medicine is a field of research that focuses on the sterilization of bacteria, wounds and cancer treatment, tissue regeneration and other biomedical applications using plasma. Dielectric barrier discharge microplasma was used for biomedical applications such as sterilization of bacteria and skin treatment [...] Read more.

Plasma medicine is a field of research that focuses on the sterilization of bacteria, wounds and cancer treatment, tissue regeneration and other biomedical applications using plasma. Dielectric barrier discharge microplasma was used for biomedical applications such as sterilization of bacteria and skin treatment for transdermal drug delivery. In this study, we investigated the feasibility of using microplasma for improving blood coagulation parameters. Blood samples collected from one dog and one cat were treated with microplasma, and the blood coagulation effect of this treatment was compared with the effect achieved by treating the blood with air flow only. The microplasma electrodes were energized using a negative pulse voltage power supply and environmental air was used as discharge gas. The microplasma treatment produced clear coagulation effects that increased proportionally with treatment time, discharge voltage and frequency. In contrast, the treatment with air flow only had no coagulation effects after the same treatment time as for the microplasma treatment. The observed blood coagulation effects induced by microplasma treatment could be attributed to the reactive oxygen and nitrogen species generated by microplasma. The blood sample subjected to microplasma treatment had a slight temperature increase (≈4 °C) confirming the nonthermal operation. In conclusion, this study shows promising results that suggest the potential of using microplasma treatment as a tool for improving blood coagulation parameters. Furthermore, microplasma’s suitability for portability and integration indicates the potential for developing a compact microplasma device tailored for use by first responders in cases of bleeding. Full article

(This article belongs to the Special Issue Advances in Plasma Physics with Symmetry/Asymmetry)

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26 pages, 1271 KB

Open AccessArticle

Predicting the Forest Fire Duration Enriched with Meteorological Data Using Feature Construction Techniques

by Constantina Kopitsa, Ioannis G. Tsoulos, Andreas Miltiadous and Vasileios Charilogis

Symmetry 2025, 17(11), 1785; https://doi.org/10.3390/sym17111785 - 22 Oct 2025

Abstract

The spread of contemporary artificial intelligence technologies, particularly machine learning, has significantly enhanced the capacity to predict asymmetrical natural disasters. Wildfires constitute a prominent example, as machine learning can be employed to forecast not only their spatial extent but also their environmental and [...] Read more.

The spread of contemporary artificial intelligence technologies, particularly machine learning, has significantly enhanced the capacity to predict asymmetrical natural disasters. Wildfires constitute a prominent example, as machine learning can be employed to forecast not only their spatial extent but also their environmental and socio-economic impacts, propagation dynamics, symmetrical or asymmetrical patterns, and even their duration. Such predictive capabilities are of critical importance for effective wildfire management, as they inform the strategic allocation of material resources, and the optimal deployment of human personnel in the field. Beyond that, examination of symmetrical or asymmetrical patterns in fires helps us to understand the causes and dynamics of their spread. The necessity of leveraging machine learning tools has become imperative in our era, as climate change has disrupted traditional wildfire management models due to prolonged droughts, rising temperatures, asymmetrical patterns, and the increasing frequency of extreme weather events. For this reason, our research seeks to fully exploit the potential of Principal Component Analysis (PCA), Minimum Redundancy Maximum Relevance (MRMR), and Grammatical Evolution, both for constructing Artificial Features and for generating Neural Network Architectures. For this purpose, we utilized the highly detailed and publicly available symmetrical datasets provided by the Hellenic Fire Service for the years 2014–2021, which we further enriched with meteorological data, corresponding to the prevailing conditions at both the onset and the suppression of each wildfire event. The research concluded that the Feature Construction technique, using Grammatical Evolution, combines both symmetrical and asymmetrical conditions, and that weather phenomena may provide and outperform other methods in terms of stability and accuracy. Therefore, the asymmetric phenomenon in our research is defined as the unpredictable outcome of climate change (meteorological data) which prolongs the duration of forest fires over time. Specifically, in the model accuracy of wildfire duration using Feature Construction, the mean error was 8.25%, indicating an overall accuracy of 91.75%. Full article

(This article belongs to the Special Issue Symmetry in Stochastic Models for Machine Learning Applications: Theoretical Insights and Applications)

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19 pages, 2186 KB

Open AccessArticle

A Range Query Method with Data Fusion in Two-Layer Wire-Less Sensor Networks

by Shouxue Chen, Yun Deng and Xiaohui Cheng

Symmetry 2025, 17(11), 1784; https://doi.org/10.3390/sym17111784 - 22 Oct 2025

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Abstract

Wireless sensor networks play a crucial role in IoT applications. Traditional range query methods have limitations in multi-sensor data fusion and energy efficiency. This paper proposes a new range query method for two-layer wireless sensor networks. The method supports data fusion operations directly [...] Read more.

Wireless sensor networks play a crucial role in IoT applications. Traditional range query methods have limitations in multi-sensor data fusion and energy efficiency. This paper proposes a new range query method for two-layer wireless sensor networks. The method supports data fusion operations directly on storage nodes. Communication costs between sink nodes and storage nodes are significantly reduced. Reverse Z-O coding optimizes the encoding process by focusing only on the most valuable data. This approach shortens both encoding time and length. Data security is ensured using the Paillier homomorphic encryption algorithm. A comparison chain for the most valuable data is generated using Reverse Z-O coding and HMAC. Storage nodes can perform multi-sensor data fusion under encryption. Experiments were conducted on Raspberry Pi 2B+ and NVIDIA TX2 platforms. Performance was evaluated in terms of fusion efficiency, query dimensions, and data volume. The results demonstrate secure and efficient multi-sensor data fusion with lower energy consumption. The method outperforms existing approaches in reducing communication and computational costs. Full article

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

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27 pages, 4517 KB

Open AccessArticle

Bridging 3D Confinement and 2D Correlations in Counterion Layers at Charged Interfaces: An Extended Percus Relation from First Principles

by Hiroshi Frusawa

Symmetry 2025, 17(11), 1783; https://doi.org/10.3390/sym17111783 - 22 Oct 2025

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Abstract

We develop a first-principles theory that bridges three-dimensional (3D) confinement and two-dimensional (2D) in-plane correlations in counterion layers at oppositely charged interfaces. The system is controlled by two independent coupling constants. While a 3D parameter (

γ

) for perpendicular localization varies with [...] Read more.

We develop a first-principles theory that bridges three-dimensional (3D) confinement and two-dimensional (2D) in-plane correlations in counterion layers at oppositely charged interfaces. The system is controlled by two independent coupling constants. While a 3D parameter (

γ

) for perpendicular localization varies with the strength and direction of the applied electric field, a 2D parameter (

Γ

) for lateral correlations depends solely on system-specific conditions. This independence allows for strongly coupled yet noncrystalline liquid states. Our theoretical framework is based on a hybrid of density functional and statistical field theory, thereby yielding an extended Percus relation that, unlike its conventional counterpart for uniform 2D liquids, is valid for the spatially inhomogeneous density profiles. This extension is critical, as it establishes a direct connection between the 3D confinement and the resulting 2D in-plane structure. Numerical investigations of this relation reveal key in-plane structural features in the strong 3D coupling limit (

γ \to \infty

): a geometric length scale, the minimal inter-particle separation (

d_{\min}

), governs both the first peak of the radial distribution function and the wavelength (

λ

) of its oscillatory tail. These findings clarify that in-plane order in these strongly coupled counterion liquids is determined by a geometric constraint rather than any crystalline symmetry. Full article

(This article belongs to the Section Physics)

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30 pages, 4237 KB

Open AccessReview

A Review of Hydrodynamic Cavitation Passive and Active Control Methods in Marine Engineering Applications

by Ebrahim Kadivar and Pankaj Kumar

Symmetry 2025, 17(11), 1782; https://doi.org/10.3390/sym17111782 - 22 Oct 2025

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Abstract

Hydrodynamic cavitation usually occurs in marine and ocean engineering and hydraulic systems and may lead to destructive effects such as an enhanced drag force, noise, vibration, surface damage, and reduced efficiency. Previous studies employed several passive and active control strategies to manage unstable [...] Read more.

Hydrodynamic cavitation usually occurs in marine and ocean engineering and hydraulic systems and may lead to destructive effects such as an enhanced drag force, noise, vibration, surface damage, and reduced efficiency. Previous studies employed several passive and active control strategies to manage unstable cavitation and its adverse effects. This study reviews various passive and active control strategies for managing diverse cavitation stages, such as partial, cloud, and tip vortex. Regarding the passive methods, different control factors, including the sweep angle of the foil, roughness, bio-inspired riblets, V-shaped grooves, J grooves, obstacles, surface roughness, blunt trailing edge, slits, various vortex generators, and triangular slots, are discussed. Regarding the active methods, various injection methods including air, water, polymer, and synthetic jet and piezoelectric actuators are reviewed. It can be concluded that unstable cavitation can be controlled by both the active and passive approaches independently. However, in the severe conditions of cavitation and higher angles of attack, the passive control methods can only alleviate some re-entrant jets propagating in the downward direction, and proper control of the cavity structure cannot be achieved. In addition, active control methods mostly require supplementary energy and, consequently, lead to higher expenses. Combined passive active control technologies are suggested by the author, using the strengths of both methods to suppress cavitation and control the cavitation instability for a broad range of cavitating flows efficiently in future works. Full article

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

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33 pages, 1373 KB

Open AccessArticle

Multi-Objective Approach for Wide-Area Damping Control Design

by Murilo E. C. Bento

Symmetry 2025, 17(11), 1781; https://doi.org/10.3390/sym17111781 - 22 Oct 2025

Viewed by 39

Abstract

Poorly damped low-frequency oscillation modes can destabilize power systems in the event of contingencies. Advances in the widespread use of phasor measurement units (PMUs) in power systems have led to the development of wide-area damping controllers (WADCs) capable of ensuring good damping ratios [...] Read more.

Poorly damped low-frequency oscillation modes can destabilize power systems in the event of contingencies. Advances in the widespread use of phasor measurement units (PMUs) in power systems have led to the development of wide-area damping controllers (WADCs) capable of ensuring good damping ratios for these oscillation modes. However, cyberattacks or communication failures affect PMU data and can cause WADC malfunctions. Poor WADC operation can even destabilize the power system. Therefore, this paper proposes the design of a WADC robust to communication failures through a multi-objective optimization model requiring high damping ratios for the closed-loop system and the existence of a symmetric and positive defined matrix to guarantee the stability of the system. Bio-inspired algorithms can solve this proposed multi-objective optimization model, and the stellar oscillation optimizer proved to be a bio-inspired algorithm with an excellent ability to reach an optimal solution. Case studies show that defining the limiting values of the WADC time constants and the existence of this symmetric, positive-definite matrix are beneficial for good system dynamic performance. Full article

(This article belongs to the Special Issue Symmetry in Optimal Control and Applications)

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28 pages, 5176 KB

Open AccessArticle

Bearing Fault Diagnosis Using PSO-VMD and a Hybrid Transformer-CNN-BiGRU Model

by Hualin Dai, Daoxuan Yang, Liying Zhang and Guorui Liu

Symmetry 2025, 17(11), 1780; https://doi.org/10.3390/sym17111780 - 22 Oct 2025

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Abstract

Reliable bearing fault diagnosis is essential for the steady running of mechanical systems. However, existing diagnostic models still face significant limitations in feature extraction, primarily due to the non-stationary and nonlinear characteristics of vibration signals, which lead to a decline in diagnostic performance. [...] Read more.

Reliable bearing fault diagnosis is essential for the steady running of mechanical systems. However, existing diagnostic models still face significant limitations in feature extraction, primarily due to the non-stationary and nonlinear characteristics of vibration signals, which lead to a decline in diagnostic performance. To address this issue, this paper proposes a novel diagnostic framework that combines Particle Swarm Optimization-based Variational Mode Decomposition (PSO-VMD) for feature extraction with a deeply integrated Transformer-Convolutional Neural Network-Bidirectional Gated Recurrent Unit (TCB) model for fault classification. Bearing fault diagnosis is crucial for the stable operation of mechanical equipment, yet existing models often suffer from limited feature extraction and low detection accuracy. To address this, PSO-VMD is employed to extract informative, band-limited features from vibration signals, yielding a highly correlated feature set; a composite model TCB, combining a Transformer, a CNN, and a bidirectional GRU (BiGRU), is then used for fault classification. To prevent window-level leakage, the dataset is split before windowing and normalization, and all baselines are aligned under identical preprocessing and training settings. On the CWRU benchmark, the model attains 98.9% accuracy, 98.8% precision, 99.4% recall, 99.1% F1, and macro-F1 = 0.9766 over five runs. The approach offers a favorable accuracy –latency trade-off and yields interpretable, band-limited modes, supporting reproducible deployment in practice. Full article

(This article belongs to the Section Engineering and Materials)

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Symmetry, Volume 17, Issue 11 (November 2025) – 19 articles

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