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29 pages, 3861 KB  
Article
Mitigating Crossfire Attacks via Topology Spoofing Based on ENRNN-MTD
by Dexian Chang, Xiaobing Zhang, Jiajia Sun and Chen Fang
Appl. Sci. 2025, 15(21), 11432; https://doi.org/10.3390/app152111432 (registering DOI) - 25 Oct 2025
Abstract
Crossfire attacks disrupt network services by targeting critical links of server groups, causing traffic congestion and server failures that prevent legitimate users from accessing services. To counter this threat, this study proposes a novel topology spoofing defense mechanism based on a sequence-based Graph [...] Read more.
Crossfire attacks disrupt network services by targeting critical links of server groups, causing traffic congestion and server failures that prevent legitimate users from accessing services. To counter this threat, this study proposes a novel topology spoofing defense mechanism based on a sequence-based Graph Neural Network–Moving Target Defense (ENRNN-MTD). During the reconnaissance phase, the method employs a GNN to generate multiple random and diverse virtual topologies, which are mapped to various external hosts. This obscures the real internal network structure and complicates the attacker’s ability to accurately identify it. In the attack phase, an IP random-hopping mechanism using a chaotic sequence is introduced to conceal node information and increase the cost of launching attacks, thereby enhancing the protection of critical services. Experimental results demonstrate that, compared to existing defense mechanisms, the proposed approach exhibits significant advantages in terms of deception topology randomness, defensive effectiveness, and system load management. Full article
(This article belongs to the Special Issue IoT Technology and Information Security)
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20 pages, 5128 KB  
Article
Bioinformatics Approach to mTOR Signaling Pathway-Associated Genes and Cancer Etiopathogenesis
by Kursat Ozdilli, Gozde Oztan, Demet Kıvanç, Ruştu Oğuz, Fatma Oguz and Hayriye Senturk Ciftci
Genes 2025, 16(11), 1253; https://doi.org/10.3390/genes16111253 (registering DOI) - 24 Oct 2025
Viewed by 131
Abstract
Background/Objectives: The mTOR serine/threonine kinase coordinates protein translation, cell growth, and metabolism, and its dysregulation promotes tumorigenesis. We present a reproducible, pan-cancer, network-aware framework that integrates curated resources with genomics to move beyond pathway curation, yielding falsifiable hypotheses and prioritized candidates for [...] Read more.
Background/Objectives: The mTOR serine/threonine kinase coordinates protein translation, cell growth, and metabolism, and its dysregulation promotes tumorigenesis. We present a reproducible, pan-cancer, network-aware framework that integrates curated resources with genomics to move beyond pathway curation, yielding falsifiable hypotheses and prioritized candidates for mTOR axis biomarker validation. Materials and Methods: We assembled MTOR-related genes and interactions from GeneCards, KEGG, STRING, UniProt, and PathCards and harmonized identifiers. We formulated a concise working model linking genotype → pathway architecture (mTORC1/2) → expression-level rewiring → phenotype. Three analyses operationalized this model: (i) pan-cancer alteration mapping to separate widely shared drivers from tumor-specific nodes; (ii) expression-based activity scoring to quantify translational/nutrient-sensing modules; and (iii) topology-aware network propagation (personalized PageRank/Random Walk with Restart on a high-confidence STRING graph) to nominate functionally proximal neighbors. Reproducibility was supported by degree-normalized diffusion, predefined statistical thresholds, and sensitivity analyses. Results: Gene ontology analysis demonstrated significant enrichment for mTOR-related processes (TOR/TORC1 signaling and cellular responses to amino acids). Database synthesis corroborated disease associations involving MTOR and its partners (e.g., TSC2, RICTOR, RPTOR, MLST8, AKT1 across selected carcinomas). Across cohorts, our framework distinguishes broadly shared upstream drivers (PTEN, PIK3CA) from lineage-enriched nodes (e.g., RICTOR-linked components) and prioritizes non-mutated, network-proximal candidates that align with mTOR activity signatures. Conclusions: This study delivers a transparent, pan-cancer framework that unifies curated biology, genomics, and network topology to produce testable predictions about the mTOR axis. By distinguishing shared drivers from tumor-specific nodes and elevating non-mutated, topology-inferred candidates, the approach refines biomarker discovery and suggests architecture-aware therapeutic strategies. The analysis is reproducible and extensible, supporting prospective validation of prioritized candidates and the design of correlative studies that align pathway activity with clinical response. Full article
(This article belongs to the Section Human Genomics and Genetic Diseases)
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24 pages, 6909 KB  
Article
LA-GATs: A Multi-Feature Constrained and Spatially Adaptive Graph Attention Network for Building Clustering
by Xincheng Yang, Xukang Xie and Dingming Liu
ISPRS Int. J. Geo-Inf. 2025, 14(11), 415; https://doi.org/10.3390/ijgi14110415 - 23 Oct 2025
Viewed by 167
Abstract
Building clustering is a key challenge in cartographic generalization, where the goal is to group spatially related buildings into semantically coherent clusters while preserving the true distribution patterns of urban structures. Existing methods often rely on either spatial distance or building feature similarity [...] Read more.
Building clustering is a key challenge in cartographic generalization, where the goal is to group spatially related buildings into semantically coherent clusters while preserving the true distribution patterns of urban structures. Existing methods often rely on either spatial distance or building feature similarity alone, leading to clusters that sacrifice either accuracy or spatial continuity. Moreover, most deep learning-based approaches, including graph attention networks (GATs), fail to explicitly incorporate spatial distance constraints and typically restrict message passing to first-order neighborhoods, limiting their ability to capture long-range structural dependencies. To address these issues, this paper proposes LA-GATs, a multi-feature constrained and spatially adaptive building clustering network. First, a Delaunay triangulation is constructed based on nearest-neighbor distances to represent spatial topology, and a heterogeneous feature matrix is built by integrating architectural spatial features, including compactness, orientation, color, and height. Then, a spatial distance-constrained attention mechanism is designed, where attention weights are adjusted using a distance decay function to enhance local spatial correlation. A second-order neighborhood aggregation strategy is further introduced to extend message propagation and mitigate the impact of triangulation errors. Finally, spectral clustering is performed on the learned similarity matrix. Comprehensive experimental validation on real-world datasets from Xi’an and Beijing, showing that LA-GATs outperforms existing clustering methods in both compactness, silhouette coefficient and adjusted rand index, with up to about 21% improvement in residential clustering accuracy. Full article
22 pages, 10534 KB  
Article
M3ASD: Integrating Multi-Atlas and Multi-Center Data via Multi-View Low-Rank Graph Structure Learning for Autism Spectrum Disorder Diagnosis
by Shuo Yang, Zuohao Yin, Yue Ma, Meiling Wang, Shuo Huang and Li Zhang
Brain Sci. 2025, 15(11), 1136; https://doi.org/10.3390/brainsci15111136 - 23 Oct 2025
Viewed by 251
Abstract
Background: Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental condition for which accurate and automated diagnosis is crucial to enable timely intervention. Resting-state functional magnetic resonance imaging (rs-fMRI) serves as one of the key modalities for diagnosing ASD and elucidating its underlying [...] Read more.
Background: Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental condition for which accurate and automated diagnosis is crucial to enable timely intervention. Resting-state functional magnetic resonance imaging (rs-fMRI) serves as one of the key modalities for diagnosing ASD and elucidating its underlying mechanisms. Numerous existing studies using rs-fMRI data have achieved accurate diagnostic performance. However, these methods often rely on a single brain atlas for constructing brain networks and overlook the data heterogeneity caused by variations in imaging devices, acquisition parameters, and processing pipelines across multiple centers. Methods: To address these limitations, this paper proposes a multi-view, low-rank subspace graph structure learning method to integrate multi-atlas and multi-center data for automated ASD diagnosis, termed M3ASD. The proposed framework first constructs functional connectivity matrices from multi-center neuroimaging data using multiple brain atlases. Edge weight filtering is then applied to build multiple brain networks with diverse topological properties, forming several complementary views. Samples from different classes are separately projected into low-rank subspaces within each view to mitigate data heterogeneity. Multi-view consistency regularization is further incorporated to extract more consistent and discriminative features from the low-rank subspaces across views. Results: Experimental results on the ABIDE-I dataset demonstrate that our model achieves an accuracy of 83.21%, outperforming most existing methods and confirming its effectiveness. Conclusions: The proposed method was validated using the publicly available Autism Brain Imaging Data Exchange (ABIDE) dataset. Experimental results demonstrate that the M3ASD method not only improves ASD diagnostic accuracy but also identifies common functional brain connections across atlases, thereby enhancing the interpretability of the method. Full article
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19 pages, 1018 KB  
Article
Fractality and Percolation Sensitivity in Software Vulnerability Networks: A Study of CWE–CVE–CPE Relations
by Iulian Tiță, Mihai Cătălin Cujbă and Nicolae Țăpuș
Appl. Sci. 2025, 15(21), 11336; https://doi.org/10.3390/app152111336 - 22 Oct 2025
Viewed by 128
Abstract
Public CVE feeds add tens of thousands of entries each year, overwhelming patch-management capacity. We model the CWE–CVE–CPE triad and, for each CWE, build count-weighted product co-exposure graphs by projecting CVE–CPE links. Because native graphs are highly fragmented, we estimate graph-distance box-counting dimensions [...] Read more.
Public CVE feeds add tens of thousands of entries each year, overwhelming patch-management capacity. We model the CWE–CVE–CPE triad and, for each CWE, build count-weighted product co-exposure graphs by projecting CVE–CPE links. Because native graphs are highly fragmented, we estimate graph-distance box-counting dimensions component-wise on the fragmented graphs using greedy box covering on unweighted shortest paths, then assess significance on the largest component of reconnected graphs. Significance is evaluated against degree-preserving nulls, reporting null percentiles, a z-score–based p-value, and complementary KS checks. We further characterise meso-scale organisation via normalized rich-club coefficients and k-core structure. Additionally, we quantify percolation sensitivity on the reconnected graphs by contrasting targeted removals with random failures for budgets of 1%, 5%, 10%, and 20%. This quantification involves tracking changes in largest-component size, average shortest-path length on the LCC, and global efficiency, and an amplification factor at 10%. Our corpus covers the MITRE CWE Top 25; we report high-level summaries for all 25 and perform the deepest null-model and sensitivity analyses on a subset of 12 CWEs selected on the basis of CVE volume. This links self-similar topology on native fragments with rich-club/core organisation and disruption sensitivity on reconnections, yielding actionable, vendor/software-type-aware mitigation cues. Structural indices are used descriptively to surface topological hotspots within CWE-conditioned product networks and are interpreted alongside, not in place of, EPSS/KEV/CVSS severity metrics. Full article
(This article belongs to the Special Issue Novel Approaches for Cybersecurity and Cyber Defense)
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22 pages, 8095 KB  
Article
Characterizing the Evolution of Multi-Scale Communities in Urban Road Networks
by Yifan Wang, Yi Li, Xingwa Song, Shilong Wang and Ning Wang
Sustainability 2025, 17(20), 9355; https://doi.org/10.3390/su17209355 - 21 Oct 2025
Viewed by 271
Abstract
The growing abundance of traffic data offers new opportunities to uncover dynamic traffic patterns in urban road networks, providing valuable insights for promoting sustainable mobility. By leveraging these data, road segments can be grouped into communities to capture the spatiotemporal correlations driving the [...] Read more.
The growing abundance of traffic data offers new opportunities to uncover dynamic traffic patterns in urban road networks, providing valuable insights for promoting sustainable mobility. By leveraging these data, road segments can be grouped into communities to capture the spatiotemporal correlations driving the dynamic evolution of traffic states. However, existing distance-based methods lack the capacity to facilitate multi-scale analysis of urban traffic patterns and are limited in capturing the heterogeneity of road regions. To address this gap, in this study, we introduce a traffic-data-driven approach to detect road segment communities and extract multi-scale traffic patterns. Here, traffic data are mapped onto a dual graph of urban road networks, with node correlations weighted using Dynamic Time Warping (DTW). A hierarchical community detection algorithm is then applied to identify multi-scale communities, revealing the spatiotemporal structure of urban traffic dynamics. The robustness and effectiveness of the proposed method were tested on the road network of Chengdu. The results show that the method successfully integrates the topological structure with traffic data, capturing multi-scale spatial autocorrelation communities. By characterizing the evolution of traffic patterns, our method has potential applications in traffic prediction, traffic control, and urban planning applications, contributing to sustainable urban transportation through congestion mitigation and efficiency enhancement. Full article
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26 pages, 32866 KB  
Article
Low-Altitude Multi-Object Tracking via Graph Neural Networks with Cross-Attention and Reliable Neighbor Guidance
by Hanxiang Qian, Xiaoyong Sun, Runze Guo, Shaojing Su, Bing Ding and Xiaojun Guo
Remote Sens. 2025, 17(20), 3502; https://doi.org/10.3390/rs17203502 - 21 Oct 2025
Viewed by 353
Abstract
In low-altitude multi-object tracking (MOT), challenges such as frequent inter-object occlusion and complex non-linear motion disrupt the appearance of individual targets and the continuity of their trajectories, leading to frequent tracking failures. We posit that the relatively stable spatio-temporal relationships within object groups [...] Read more.
In low-altitude multi-object tracking (MOT), challenges such as frequent inter-object occlusion and complex non-linear motion disrupt the appearance of individual targets and the continuity of their trajectories, leading to frequent tracking failures. We posit that the relatively stable spatio-temporal relationships within object groups (e.g., pedestrians and vehicles) offer powerful contextual cues to resolve such ambiguities. We present NOWA-MOT (Neighbors Know Who We Are), a novel tracking-by-detection framework designed to systematically exploit this principle through a multi-stage association process. We make three primary contributions. First, we introduce a Low-Confidence Occlusion Recovery (LOR) module that dynamically adjusts detection scores by integrating IoU, a novel Recovery IoU (RIoU) metric, and location similarity to surrounding objects, enabling occluded targets to participate in high-priority matching. Second, for initial data association, we propose a Graph Cross-Attention (GCA) mechanism. In this module, separate graphs are constructed for detections and trajectories, and a cross-attention architecture is employed to propagate rich contextual information between them, yielding highly discriminative feature representations for robust matching. Third, to resolve the remaining ambiguities, we design a cascaded Matched Neighbor Guidance (MNG) module, which uniquely leverages the reliably matched pairs from the first stage as contextual anchors. Through MNG, star-shaped topological features are built for unmatched objects relative to their stable neighbors, enabling accurate association even when intrinsic features are weak. Our comprehensive experimental evaluation on the VisDrone2019 and UAVDT datasets confirms the superiority of our approach, achieving state-of-the-art HOTA scores of 51.34% and 62.69%, respectively, and drastically reducing identity switches compared to previous methods. Full article
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29 pages, 13306 KB  
Article
Building Outline Extraction via Topology-Aware Loop Parsing and Parallel Constraint from Airborne LiDAR
by Ke Liu, Hongchao Ma, Li Li, Shixin Huang, Liang Zhang, Xiaoli Liang and Zhan Cai
Remote Sens. 2025, 17(20), 3498; https://doi.org/10.3390/rs17203498 - 21 Oct 2025
Viewed by 253
Abstract
Building outlines are important vector data for various applications, but due to the uneven point density and complex building structures, extracting satisfactory building outlines from airborne light detection and ranging point cloud data poses significant challenges. Thus, a building outline extraction method based [...] Read more.
Building outlines are important vector data for various applications, but due to the uneven point density and complex building structures, extracting satisfactory building outlines from airborne light detection and ranging point cloud data poses significant challenges. Thus, a building outline extraction method based on topology-aware loop parsing and parallel constraint is proposed. First, constrained Delaunay triangulation (DT) is used to organize scattered projected building points, and initial boundary points and edges are extracted based on the constrained DT. Subsequently, accurate semantic boundary points are obtained by parsing the topology-aware loops searched from an undirected graph. Building dominant directions are estimated through angle normalization, merging, and perpendicular pairing. Finally, outlines are regularized using the parallel constraint-based method, which simultaneously considers the fitness between the dominant direction and boundary points, and the length of line segments. Experiments on five datasets, including three datasets provided by ISPRS and two datasets with high-density point clouds and complex building structures, verify that the proposed method can extract sequential and semantic boundary points, with over 97.88% correctness. Additionally, the regularized outlines are attractive, and most line segments are parallel or perpendicular. The RMSE, PoLiS, and RCC metrics are better than 0.94 m, 0.84 m, and 0.69 m, respectively. The extracted building outlines can be used for building three-dimensional (3D) reconstruction. Full article
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19 pages, 674 KB  
Article
Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators
by Alexander Yeung, Peter DelMastro, Arjun Karuvally, Hava Siegelmann, Edward Rietman and Hananel Hazan
Analytics 2025, 4(4), 28; https://doi.org/10.3390/analytics4040028 - 20 Oct 2025
Viewed by 213
Abstract
Reservoir computing is an approach to machine learning that leverages the dynamics of a complex system alongside a simple, often linear, machine learning model for a designated task. While many efforts have previously focused their attention on integrating neurons, which produce an output [...] Read more.
Reservoir computing is an approach to machine learning that leverages the dynamics of a complex system alongside a simple, often linear, machine learning model for a designated task. While many efforts have previously focused their attention on integrating neurons, which produce an output in response to large, sustained inputs, we focus on using differentiating neurons, which produce an output in response to large changes in input. Here, we introduce a small-world graph built from rings of differentiating neurons as a Reservoir Computing substrate. We find the coupling strength and network topology that enable these small-world networks to function as an effective reservoir. The dynamics of differentiating neurons naturally give rise to oscillatory dynamics when arranged in rings, where we study their computational use in the Reservoir Computing setting. We demonstrate the efficacy of these networks in the MNIST digit recognition task, achieving comparable performance of 90.65% to existing Reservoir Computing approaches. Beyond accuracy, we conduct systematic analysis of our reservoir’s internal dynamics using three complementary complexity measures that quantify neuronal activity balance, input dependence, and effective dimensionality. Our analysis reveals that optimal performance emerges when the reservoir operates with intermediate levels of neural entropy and input sensitivity, consistent with the edge-of-chaos hypothesis, where the system balances stability and responsiveness. The findings suggest that differentiating neurons can be a potential alternative to integrating neurons and can provide a sustainable future alternative for power-hungry AI applications. Full article
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35 pages, 2576 KB  
Article
A Study on Risk Factors Associated with Gestational Diabetes Mellitus
by Isabel Salas Lorenzo, Jair J. Pineda-Pineda, Ernesto Parra Inza, Saylé Sigarreta Ricardo and Sergio José Torralbas Fitz
Diabetology 2025, 6(10), 119; https://doi.org/10.3390/diabetology6100119 - 17 Oct 2025
Viewed by 436
Abstract
Background/Objectives: Gestational Diabetes Mellitus (GDM) is a global health issue with immediate and long-term maternal–fetal complications. Current diagnostic approaches, such as the Oral Glucose Tolerance Test (OGTT), have limitations in accessibility, sensitivity, and timing. This study aimed to identify key nodes and structural [...] Read more.
Background/Objectives: Gestational Diabetes Mellitus (GDM) is a global health issue with immediate and long-term maternal–fetal complications. Current diagnostic approaches, such as the Oral Glucose Tolerance Test (OGTT), have limitations in accessibility, sensitivity, and timing. This study aimed to identify key nodes and structural interactions associated with GDM using graph theory and network analysis to improve early predictive strategies. Methods: A literature review inspired by PRISMA guidelines (2004–2025) identified 44 clinically relevant factors. A directed graph was constructed using Python (version 3.10.12), and centrality metrics (closeness, betweenness, eigenvector), k-core decomposition, and a Minimum Dominating Set (MDS) were computed. The MDS, derived using an integer linear programming model, was used to determine the smallest subset of nodes with systemic dominance across the network. Results: The MDS included 20 nodes, with seven showing a high out-degree (≥4), notably Apo A1, vitamin D, vitamin D deficiency, and sedentary lifestyle. Vitamin D exhibited 15 outgoing edges, connecting directly to protective factors like HDL and inversely to risk factors such as smoking and obesity. Sedentary behavior also showed high structural influence. Closeness centrality highlighted triglycerides, insulin resistance, uric acid, fasting plasma glucose, and HDL as nodes with strong predictive potential, based on their high closeness and multiple incoming connections. Conclusions: Vitamin D and sedentary behavior emerged as structurally dominant nodes in the GDM network. Alongside metabolically relevant nodes with high closeness centrality, these findings support the utility of graph-based network analysis for early detection and targeted clinical interventions in maternal health. Full article
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14 pages, 1050 KB  
Article
Construction and Application of Knowledge Graph for Power Grid New Equipment Start-Up
by Wei Tang, Yue Zhang, Xun Mao, Hetong Jia, Kai Lv, Lianfei Shan, Yongtian Qiao and Tao Jiang
Energies 2025, 18(20), 5471; https://doi.org/10.3390/en18205471 - 17 Oct 2025
Viewed by 229
Abstract
To address the lack of effective risk-identification methods during the commissioning of new power grid equipment, we propose a knowledge graph construction approach for both scheme generation and risk identification. First, a gated attention mechanism fuses textual semantics with knowledge embeddings to enhance [...] Read more.
To address the lack of effective risk-identification methods during the commissioning of new power grid equipment, we propose a knowledge graph construction approach for both scheme generation and risk identification. First, a gated attention mechanism fuses textual semantics with knowledge embeddings to enhance feature representation. Then, by introducing a global memory matrix with a decay-factor update mechanism, long-range dependencies across paragraphs are captured, yielding a domain-knowledge-augmentation universal information-extraction framework (DKA-UIE). Using the DKA-UIE, we learn high-dimensional mappings of commissioning-scheme entities and their labels, linking them according to equipment topology and risk-identification logic to build a commissioning knowledge graph for new equipment. Finally, we present an application that utilizes this knowledge graph for the automated generation of commissioning plans and risk identification. Experimental results show that our model achieves an average precision of 99.19%, recall of 99.47%, and an F1-score of 99.33%, outperforming existing methods. The resulting knowledge graph effectively supports both commissioning-plan generation and risk identification for new grid equipment. Full article
(This article belongs to the Special Issue Digital Modeling, Operation and Control of Sustainable Energy Systems)
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16 pages, 3660 KB  
Article
A Network Scanning Organization Discovery Method Based on Graph Convolutional Neural Network
by Pengfei Xue, Luhan Dong, Chenyang Wang, Cheng Huang and Jie Wang
Information 2025, 16(10), 899; https://doi.org/10.3390/info16100899 - 15 Oct 2025
Viewed by 196
Abstract
With the quick development of network technology, the number of active IoT devices is growing rapidly. Numerous network scanning organizations have emerged to scan and detect network assets around the clock. This greatly facilitates illegal cyberattacks and adversely affects cybersecurity. Therefore, it is [...] Read more.
With the quick development of network technology, the number of active IoT devices is growing rapidly. Numerous network scanning organizations have emerged to scan and detect network assets around the clock. This greatly facilitates illegal cyberattacks and adversely affects cybersecurity. Therefore, it is important to discover and identify network scanning organizations on the Internet. Motivated by this, we propose a network scanning organization discovery method based on a graph convolutional neural network, which can effectively cluster out network scanning organizations. First, we constructed a network scanning attribute graph to represent the topological relationship between network scanning behaviors and targets. Then, we extract the deep feature relationships in the attribute graph via graph convolutional neural network and perform clustering to get network scanning organizations. Finally, the effectiveness of the method proposed in this paper is experimentally verified with an accuracy of 83.41% for the identification of network scanning organizations. Full article
(This article belongs to the Special Issue Cyber Security in IoT)
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17 pages, 291 KB  
Article
On Topological Structures and Mapping Theorems in Intuitionistic Fuzzy 2-Normed Spaces
by Sahar Almashaan
Symmetry 2025, 17(10), 1733; https://doi.org/10.3390/sym17101733 - 14 Oct 2025
Viewed by 149
Abstract
In intuitionistic fuzzy 2-normed spaces, there are numerous symmetries in the topological structures and mapping theorems. In this work, we present the concept of an intuitionistic fuzzy 2-normed space(IF2NS) and demonstrate its structural properties using illustrative examples. This approach unifies and broadens [...] Read more.
In intuitionistic fuzzy 2-normed spaces, there are numerous symmetries in the topological structures and mapping theorems. In this work, we present the concept of an intuitionistic fuzzy 2-normed space(IF2NS) and demonstrate its structural properties using illustrative examples. This approach unifies and broadens the scope of both classical 2-normed spaces and intuitionistic fuzzy normed spaces when specific conditions are met. We introduce the idea of fuzzy open balls and explore the convergence of sequences with respect to the topology derived from the intuitionistic fuzzy 2-norm. In addition, we define left and right N-Cauchy sequences relative to the topologies τN and τN1 and analyze their convergence characteristics. Special attention is given to the inherent symmetry of the 2-norm, where the magnitude of a pair of vectors remains invariant under exchange of arguments, and to the balanced interaction between membership and non-membership functions in the intuitionistic fuzzy setting. This intrinsic symmetry is further reflected in the proofs of the open mapping and closed graph theorems, which naturally preserve the symmetric structure of the underlying space The paper culminates with the formulation and proof of the open mapping theorem that can be considered for its symmetric properties and the closed graph theorem in the context of IF2NS, thereby generalizing essential theorems of functional analysis to this fuzzy setting. Full article
(This article belongs to the Section Mathematics)
26 pages, 1118 KB  
Article
Nested Ensemble Learning with Topological Data Analysis for Graph Classification and Regression
by Innocent Abaa and Umar Islambekov
Int. J. Topol. 2025, 2(4), 17; https://doi.org/10.3390/ijt2040017 - 14 Oct 2025
Viewed by 232
Abstract
We propose a nested ensemble learning framework that utilizes Topological Data Analysis (TDA) to extract and integrate topological features from graph data, with the goal of improving performance on classification and regression tasks. Our approach computes persistence diagrams (PDs) using lower-star filtrations induced [...] Read more.
We propose a nested ensemble learning framework that utilizes Topological Data Analysis (TDA) to extract and integrate topological features from graph data, with the goal of improving performance on classification and regression tasks. Our approach computes persistence diagrams (PDs) using lower-star filtrations induced by three filter functions: closeness, betweenness, and degree 2 centrality. To overcome the limitation of relying on a single filter, these PDs are integrated through a data-driven, three-level architecture. At Level-0, diverse base models are independently trained on the topological features extracted for each filter function. At Level-1, a meta-learner combines the predictions of these base models for each filter to form filter-specific ensembles. Finally, at Level-2, a meta-learner integrates the outputs of these filter-specific ensembles to produce the final prediction. We evaluate our method on both simulated and real-world graph datasets. Experimental results demonstrate that our framework consistently outperforms base models and standard stacking methods, achieving higher classification accuracy and lower regression error. It also surpasses existing state-of-the-art approaches, ranking among the top three models across all benchmarks. Full article
(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)
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17 pages, 1278 KB  
Article
KG-FLoc: Knowledge Graph-Enhanced Fault Localization in Secondary Circuits via Relation-Aware Graph Neural Networks
by Xiaofan Song, Chen Chen, Xiangyang Yan, Jingbo Song, Huanruo Qi, Wenjie Xue and Shunran Wang
Electronics 2025, 14(20), 4006; https://doi.org/10.3390/electronics14204006 - 13 Oct 2025
Viewed by 312
Abstract
This paper introduces KG-FLoc, a knowledge graph-enhanced framework for secondary circuit fault localization in intelligent substations. The proposed KG-FLoc innovatively formalizes secondary components (e.g., circuit breakers, disconnectors) as graph nodes and their multi-dimensional relationships (e.g., electrical connections, control logic) as edges, constructing the [...] Read more.
This paper introduces KG-FLoc, a knowledge graph-enhanced framework for secondary circuit fault localization in intelligent substations. The proposed KG-FLoc innovatively formalizes secondary components (e.g., circuit breakers, disconnectors) as graph nodes and their multi-dimensional relationships (e.g., electrical connections, control logic) as edges, constructing the first comprehensive knowledge graph (KG) to structurally and operationally model secondary circuits. By reframing fault localization as a knowledge graph link prediction task, KG-FLoc identifies missing or abnormal connections (edges) as fault indicators. To address dynamic topologies and sparse fault samples, KG-FLoc integrates two core innovations: (1) a relation-aware gated unit (RGU) that dynamically regulates information flow through adaptive gating mechanisms, and (2) a hierarchical graph isomorphism network (GIN) architecture for multi-scale feature extraction. Evaluated on real-world datasets from 110 kV/220 kV substations, KG-FLoc achieves 97.2% accuracy in single-fault scenarios and 93.9% accuracy in triple-fault scenarios, surpassing SVM, RF, MLP, and standard GNN baselines by 12.4–31.6%. Beyond enhancing substation reliability, KG-FLoc establishes a knowledge-aware paradigm for fault diagnosis in industrial systems, enabling precise reasoning over complex interdependencies. Full article
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