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31 pages, 288617 KB  
Article
Spatial Mismatch and Synergy Between Structural Importance and Carbon Sequestration for Sustainable Management of Green Highway Networks: An Integrated Complex Network Analysis
by Zhiwen Wang, Jinru Hu, Yongfeng Zhao, Xudong Lu and Qi Shi
Sustainability 2026, 18(11), 5328; https://doi.org/10.3390/su18115328 (registering DOI) - 25 May 2026
Abstract
Green highway networks function as critical linear carbon sinks for sustainable transportation systems, yet the link between their network topological structure and sequestration efficiency remains poorly understood. This research establishes an integrated framework to explore the spatial synergy and mismatch between green highway [...] Read more.
Green highway networks function as critical linear carbon sinks for sustainable transportation systems, yet the link between their network topological structure and sequestration efficiency remains poorly understood. This research establishes an integrated framework to explore the spatial synergy and mismatch between green highway network structure and carbon sequestration in Shandong Province. We constructed a spatially explicit “node-edge” network at a road corridor scale (250-m buffer) and quantified seasonal Net Primary Productivity (NPP) using the CASA model. Results demonstrate: (1) The green highway network exhibits a highly heterogeneous, heavy-tailed structure with low clustering coefficients (<0.01), characterized by high connectivity efficiency but limited structural redundancy; (2) The network’s NPP shows pronounced spatiotemporal dynamics, peaking in summer (mean: 364.7 gC · m2· season1) and reaching its nadir in winter (mean: 52.2 gC · m2· season1); (3) Statistically significant spatial synergies (p<0.01,Z>4.00) exist between green highway topology and NPP, with weighted closeness (I=0.29) and weighted degree (I=0.21) showing the highest effect sizes; (4) LISA analysis identified specific spatial mismatches, such as “High-Low” clusters (high structural importance but low carbon efficiency) in northern inland regions, which represent priority targets for ecological retrofitting. These outcomes quantify that network topology effectively reflects ecological performance, offering a “topology-guided” strategy to promote climate change mitigation and enhance the long-term sustainability of regional transportation infrastructure. Full article
(This article belongs to the Special Issue Sustainable Transportation Systems Design and Management)
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22 pages, 37722 KB  
Article
Graph-Based Clustering of Urban Water Consumption Profiles via Adaptive Attention and Multi-Relational Topologies
by Jonnatan Arias-Garcia, David Cárdenas-Peña, Álvaro Angel Orozco-Gutiérrez, Hernán Felipe Garcia-Arias and Jhoniers Gilberto Guerrero-Erazo
Water 2026, 18(11), 1272; https://doi.org/10.3390/w18111272 - 24 May 2026
Abstract
Conventional clustering techniques for urban water consumption profiling treat each household as an independent entity, thereby disregarding the spatial, socioeconomic, and infrastructural contexts that jointly govern demand behavior. This structural limitation prevents the extraction of contextually coherent consumption profiles—a critical shortcoming for utility [...] Read more.
Conventional clustering techniques for urban water consumption profiling treat each household as an independent entity, thereby disregarding the spatial, socioeconomic, and infrastructural contexts that jointly govern demand behavior. This structural limitation prevents the extraction of contextually coherent consumption profiles—a critical shortcoming for utility managers who must design spatially targeted conservation interventions. To overcome this, we propose Simple GLAC, a novel graph clustering framework that leverages graph neural networks with an adaptive attention mechanism to dynamically model these complex interdependencies. The model’s end-to-end training jointly optimizes a latent representation for cluster cohesion, separation, and spatial homogeneity, where each household’s multi-month consumption record serves as the node feature vector encoding temporal consumption patterns. Evaluated on a large-scale real-world dataset of 4590 residential households across four distinct graph topologies, Simple GLAC consistently achieves superior multi-metric performance over both traditional and graph-based benchmarks, yielding interpretable and operationally actionable consumption profiles aligned with the spatial, administrative, socioeconomic, and infrastructural dimensions of urban water governance in the studied context. This work provides a data-driven tool for utility managers to deploy targeted water conservation strategies, with findings grounded in a Colombian mid-sized city and generalization to broader urban settings identified as a priority direction for future work. Full article
(This article belongs to the Special Issue Advancing Water Resource Management with Smart Technologies)
27 pages, 4671 KB  
Article
Unmanned Aerial Vehicle Cluster Communication–Navigation Integrated Cooperative Positioning Algorithm Based on China Satellite Network
by Chengkai Tang, Songnian Zhang, Zesheng Dan, Yangyang Liu and Lingling Zhang
Drones 2026, 10(6), 403; https://doi.org/10.3390/drones10060403 - 23 May 2026
Abstract
Unmanned Aerial Vehicle (UAV) clusters have broad applications in agricultural detection, traffic control, and disaster rescue, where navigation and positioning serve as the core technology. However, satellite navigation fails to meet the requirements of region-wide navigation due to the urban canyon effect. Although [...] Read more.
Unmanned Aerial Vehicle (UAV) clusters have broad applications in agricultural detection, traffic control, and disaster rescue, where navigation and positioning serve as the core technology. However, satellite navigation fails to meet the requirements of region-wide navigation due to the urban canyon effect. Although the China Satellite Network (CSN) boasts advantages such as high landing power and low latency, it can only achieve single-link communication. Consequently, exploring how to realize cooperative positioning via UAV clusters has become an urgent research need. In this paper, an Unmanned Aerial Vehicle Cluster Communication–Navigation Integrated Cooperative Positioning (UCNCP) algorithm is proposed. This algorithm combines the communication and navigation characteristics of the CSN, establishes a single pseudorange measurement model and cluster geometric topology, and constructs an architecture for cooperative positioning based on UAV cluster pseudorange measurements and inter-UAV ranging data, thereby achieving reliable navigation and positioning of UAV clusters. Comparative experiments between the proposed method and other low-orbit satellite positioning methods demonstrate that the UCNCP algorithm exhibits higher positioning stability. When abrupt changes occur in navigation information, it can effectively mitigate the impact of abrupt change errors on positioning accuracy, improving the positioning stability of UAV clusters by more than 30%. Full article
(This article belongs to the Section Drone Communications)
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32 pages, 806 KB  
Article
A Three-Stage Approach for the Multi-Depot VRP with Priority Requests
by Yehya Bouchbout, Brahim Farou, Bálint Molnár, Ala-Eddine Benrazek, Khawla Bouafia and Hamid Seridi
Appl. Sci. 2026, 16(11), 5188; https://doi.org/10.3390/app16115188 - 22 May 2026
Viewed by 100
Abstract
Field-service operations for utility companies require routing technicians across multiple depots while guaranteeing same-day response to critical infrastructure customers, a constraint that standard multi-depot routing methods cannot structurally enforce. We introduce the MDVRP with Priority Requests (MDVRP-PR), formalised as a lexicographic optimisation problem [...] Read more.
Field-service operations for utility companies require routing technicians across multiple depots while guaranteeing same-day response to critical infrastructure customers, a constraint that standard multi-depot routing methods cannot structurally enforce. We introduce the MDVRP with Priority Requests (MDVRP-PR), formalised as a lexicographic optimisation problem that guarantees service to priority customers before maximising coverage and minimising route duration. A three-stage pipeline is proposed: hybrid DBSCAN-Hierarchical clustering for topology-aware depot assignment, an Enhanced Max-Min Ant System (MMAS) with priority-driven construction, lexicographic solution selection, and repair, and a Boundary Relocate post-optimisation stage with global cross-depot recovery. The approach is evaluated on a real-world applied case study from Algérie Télécom (Guelma, Algeria), comprising a single four-depot field-service instance scaled to three sizes (55, 90, and 150 customers) and assessed over 2135 controlled runs. On this case study, the proposed clustering method outperforms the MDVRP-adapted Sweep baseline by 22.9 percentage points on the largest instance (n = 150; Friedman p < 0.001). The priority mechanisms sustain 100% feasibility across all configurations, compared to complete collapse without them (0/10 seeds at 40% priority), at a route-time overhead below 5%. Relative to the company’s current manual practice, the framework improves customer coverage by 16.1 percentage points within 28 s, confirming its practical utility for daily deployment in this capacity-constrained, priority-sensitive routing context. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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50 pages, 3820 KB  
Article
Emergency Logistics Distribution Center Location Model Based on ISG-IAGNES Clustering and Symmetrical IDFS Spatial Decision Tree Algorithm
by Xiao Zhou, Wenbing Liu, Jun Wang and Fan Jiang
Symmetry 2026, 18(5), 868; https://doi.org/10.3390/sym18050868 - 20 May 2026
Viewed by 78
Abstract
Taking emergency logistics scenarios under urban public emergencies as the research background, this paper analyzes the current research status and existing problems of distribution center location methods. It constructs an emergency logistics distribution center location model based on ISG-IAGNES clustering and a symmetrical [...] Read more.
Taking emergency logistics scenarios under urban public emergencies as the research background, this paper analyzes the current research status and existing problems of distribution center location methods. It constructs an emergency logistics distribution center location model based on ISG-IAGNES clustering and a symmetrical IDFS spatial decision tree algorithm. Firstly, the ISG spatial model is constructed to divide urban geographic space into cellular units and then topologically generate the cellular space. Secondly, the IAGNES algorithm is established to achieve cellular space clustering, realizing the dimensionality reduction operation of the urban emergency space. Thirdly, the symmetrical characteristic of the pathway is taken as the core condition to construct the DFS algorithm to build the graph global searching model, and then the logistics distribution center location model based on the symmetrical IDFS spatial decision tree algorithm is constructed. The experiment proves that the optimization rate of the distribution center selected by the proposed algorithm in terms of route distance cost and time cost is 9.82% compared to the centroid method and analytic hierarchy process, 14.41% compared to the Dijkstra algorithm, and 17.21% compared to the Prim algorithm. It proves that the proposed algorithm has advantages over traditional algorithms in reducing the distance cost and time cost of logistics routes. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Data Mining and Machine Learning)
38 pages, 7610 KB  
Article
Sustainable Urban Mobility Challenges: Multi-Dimensional Topological Fracture Typology of Pedestrian Travel Networks in 15-Minute Neighborhoods, a Case Study of Hefei
by Chunxiang Dong, Mengru Zhou, Hanbin Wei, Chunfeng Yang and Yi Yao
Buildings 2026, 16(10), 1952; https://doi.org/10.3390/buildings16101952 - 14 May 2026
Viewed by 154
Abstract
The 15-min neighborhood paradigm has reshaped the evaluation system of urban pedestrian mobility, shifting pedestrian network assessment from single facility supply to holistic topological structural analysis. Structural fracture of pedestrian systems has thus become a prominent challenge restricting high-quality sustainable urban travel and [...] Read more.
The 15-min neighborhood paradigm has reshaped the evaluation system of urban pedestrian mobility, shifting pedestrian network assessment from single facility supply to holistic topological structural analysis. Structural fracture of pedestrian systems has thus become a prominent challenge restricting high-quality sustainable urban travel and neighborhood renewal. Existing studies mainly focus on macroscopic accessibility and geometric connectivity, lacking systematic multi-dimensional quantitative measurement and refined typological identification of network topological fractures. Taking 52 typical 15-min neighborhoods in Baohe District, Hefei as research samples, this paper constructs a four-dimensional topological fracture evaluation system, and conducts empirical analysis through correlation analysis, K-means++ clustering and micro topological feature mining. The results show that functional fracture and hierarchical fracture are weakly correlated and relatively independent (ρ = 0.068). Four distinct topological fracture types are classified, among which the Cognitive Disorientation type accounts for the largest proportion of 37.3%. Microscopic topological verification further reveals the formation mechanisms and spatial differentiation laws of various fracture patterns. This study provides a scientific typological basis and targeted topological intervention strategies for sustainable governance, classified regulation and optimized upgrading of urban pedestrian travel networks. Full article
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24 pages, 3391 KB  
Article
Adaptive Boundary-Aware Fact-Checker Placement for Misinformation Suppression in Social Networks
by Mostafa Taghizade Firouzjaee, Ghazal Naderi, Ross Gore and Neda Moghim
Appl. Sci. 2026, 16(10), 4740; https://doi.org/10.3390/app16104740 - 11 May 2026
Viewed by 267
Abstract
The spread of fake news on online social networks is driven by imitation-based user behavior and network topology, often leading to persistent misinformation clusters and echo chambers. In this study, we develop a spatial evolutionary game-theoretic framework in which agents update their latent [...] Read more.
The spread of fake news on online social networks is driven by imitation-based user behavior and network topology, often leading to persistent misinformation clusters and echo chambers. In this study, we develop a spatial evolutionary game-theoretic framework in which agents update their latent opinions through payoff-biased imitation, while external fact-checkers act as non-imitative intervention nodes. Building on this formulation, we propose an adaptive, boundary-aware intervention mechanism that dynamically regulates both the density and spatial allocation of fact-checkers according to real-time system conditions. Competing information clusters are identified through local neighborhood composition, enabling boundary nodes, i.e., interfaces between fake-news and non-fake-news regions, to be detected and targeted where strategic shifts are most likely to occur. Importantly, fact-checking is modeled as an external intervention that may induce a probabilistic lasting correction on agents’ latent opinions after removal, capturing more realistic post-intervention behavior. Unlike static strategies that assume fixed fact-checker distributions, the proposed approach continuously reallocates interventions toward structurally critical regions, while adaptively adjusting resource intensity based on misinformation prevalence. Extensive simulations on small-world, scale-free, and random networks show that the adaptive model consistently outperforms static baselines, reducing the final fake-news prevalence by over 90%, accelerating suppression, and improving overall system efficiency. Statistical tests confirm the significance of these improvements (p<0.001), while sensitivity analyses demonstrate robustness across parameter settings and intervention assumptions. Full article
(This article belongs to the Special Issue New Trends in Decision Support Systems and Their Applications)
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20 pages, 1745 KB  
Article
Analysis of Opinion Evolution Based on Hegselmann–Krause Model with Historical Opinion
by Yuqi Zhou and Junyao Sun
Entropy 2026, 28(5), 541; https://doi.org/10.3390/e28050541 - 10 May 2026
Viewed by 171
Abstract
In realistic social networks, individuals are influenced not only by current interactions, but also by recent historical opinions, prior experience, and external guidance. However, historical dependence and its decaying effect remain insufficiently studied in bounded-confidence opinion dynamics. To address this issue, this paper [...] Read more.
In realistic social networks, individuals are influenced not only by current interactions, but also by recent historical opinions, prior experience, and external guidance. However, historical dependence and its decaying effect remain insufficiently studied in bounded-confidence opinion dynamics. To address this issue, this paper proposes an extended Hegselmann–Krause (HK) model in which each individual updates its opinion according to four information sources: the current opinion, historical opinions, neighbors’ opinions, and a target opinion. The historical-opinion term is modeled as a weighted average of recent historical opinions, and its influence is regulated by an attenuation rate to capture memory decay over time. Simulation experiments are conducted to examine the effects of confidence thresholds, attenuation rates, weighting coefficients, and network topology on opinion evolution. The results show that low confidence thresholds tend to generate fragmented clusters, moderate thresholds facilitate opinion integration, and excessively high thresholds may lead to rapid homogenization. The attenuation rate regulates the balance between historical dependence and adaptability to new information, while different weighting configurations produce distinct evolution patterns. In addition, comparisons across ER random, WS small-world, and BA scale-free networks show that network topology significantly affects convergence speed and final opinion distributions. Finally, simulations on a real-world review-network topology derived from the Epinions dataset illustrate the applicability of the proposed model in an e-commerce-related setting. These findings extend the HK framework from a memory-aware perspective. Full article
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20 pages, 1933 KB  
Article
Leak Location in Water Distribution Networks Using Deep Learning Techniques: A Synthetic Application
by Oscar Iván Pérez-Sandoval, Cristian Eduardo Boyain y Goytia-Luna, Cruz Octavio Robles Rovelo, Erick Dante Mattos-Villarroel, Jose Ricardo Gómez-Rodríguez and Pedro Alvarado-Medellin
Water 2026, 18(10), 1129; https://doi.org/10.3390/w18101129 - 9 May 2026
Viewed by 540
Abstract
Leak localization and maintenance in water distribution networks (WDNs) are essential for reducing water losses and operating costs; however, they usually require extensive monitoring and large datasets. This work proposes a methodology that combines topological sectorization of a hydraulic node network and deep [...] Read more.
Leak localization and maintenance in water distribution networks (WDNs) are essential for reducing water losses and operating costs; however, they usually require extensive monitoring and large datasets. This work proposes a methodology that combines topological sectorization of a hydraulic node network and deep learning techniques to improve leak location by selecting representative nodes to reduce the spatial dimensionality of the WDNs. The network is partitioned using a Spectral Clustering algorithm to identify key nodes based on a weighted criterion that considers pressure variability, flow rate, and proximity to the centroid. Subsequently, a Bidirectional Long Short-Term Memory (Bi-LSTM) neural network classifies the cluster and sub-cluster where a leak occurs, using pressure and flow time series simulated in EPANET. This methodology was validated on the L-Town network, achieving an accuracy of 99.94% for cluster classification and 99.82% for sub-clusters, with a validation loss of 0.024%. During validation with 117 unseen leakage scenarios, the model reached an overall effectiveness of 85%. Moreover, Spectral Clustering outperformed K-Means in preserving physical connectivity. These results confirm the efficiency of the proposed methodology and highlight its potential for application in other hydraulic networks. Full article
(This article belongs to the Section Urban Water Management)
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19 pages, 1687 KB  
Article
Inflammatory Proteomic Heterogeneity Beyond Glycemia Status in Severe Obesity
by Melissa M. Milito, Mattia Chiesa, Alice Mallia, Giulia G. Papaianni, Julia T. Regalado, Claudio Tiribelli, Deborah Bonazza, Natalia Rosso, Silvia Palmisano, Cristina Banfi and Pablo J. Giraudi
Int. J. Mol. Sci. 2026, 27(9), 4152; https://doi.org/10.3390/ijms27094152 - 6 May 2026
Viewed by 309
Abstract
Chronic low-grade inflammation is a key feature of obesity-associated dysglycemia, yet substantial heterogeneity exists in inflammatory responses among individuals with normoglycemia, prediabetes, and type 2 diabetes mellitus (T2DM). Whether circulating inflammatory protein profiles define distinct patient phenotypes beyond conventional glycemic classification remains incompletely [...] Read more.
Chronic low-grade inflammation is a key feature of obesity-associated dysglycemia, yet substantial heterogeneity exists in inflammatory responses among individuals with normoglycemia, prediabetes, and type 2 diabetes mellitus (T2DM). Whether circulating inflammatory protein profiles define distinct patient phenotypes beyond conventional glycemic classification remains incompletely understood. In this cross-sectional analysis of 142 individuals with severe obesity, plasma inflammatory proteins were quantified using Olink proximity extension assay technology. Subjects were stratified by glycemic status (noDM, normoglycemia; PreDM, prediabetes and T2DM) while maintaining comparable distributions of metabolic dysfunction-associated steatotic liver disease. Differential expression analyses were performed across glycemic groups, and unsupervised topological data analysis (TDA) was applied to identify inflammatory protein-based patient subgroups. Several inflammatory proteins were significantly upregulated in T2DM and PreDM compared with noDM, with interleukin-8 (IL-8), Fms-relatedlike tyrosine kinase 3 ligand (Flt3L), and CUB domain containing protein (CDCP1) showing the largest significant differences. NPX distributions of these proteins exhibited gradual increases across glycemic stages with substantial inter-individual variability. TDA identified seven clusters defined by distinct inflammatory protein signatures. One cluster was enriched for individuals with T2DM and characterized by coordinated upregulation of IL-8, Flt3L, CDCP1, and additional immune- and cytokine-related proteins, whereas other clusters displayed alternative inflammatory profiles that were not explained by glycemic status alone. Inflammatory proteomic profiling in severe obesity reveals both glycemia-associated protein changes and distinct inflammatory phenotypes that transcend conventional clinical classification. Integration of differential expression analysis with TDA highlights heterogeneity in inflammatory states, supporting a hypothesis-generating framework for future studies aimed at validating these proteomic patterns and clarifying their longitudinal relevance in obesity-related dysglycemia. Full article
(This article belongs to the Special Issue Molecular Aspects of Diabetes and Its Complications)
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26 pages, 2255 KB  
Article
Distribution Network Planning Considering Harmonics Based on a Parallel Genetic Algorithm Using Message Passing Interface
by Vincent Roberge and Mohammed Tarbouchi
Algorithms 2026, 19(5), 365; https://doi.org/10.3390/a19050365 - 5 May 2026
Viewed by 211
Abstract
This paper presents a parallel genetic algorithm (GA) for the planning of power distribution networks considering harmonics. Power distribution systems are generally operated in a radial configuration, supplemented by tie switches that enable network reconfiguration during unexpected outages or planned maintenance. They can [...] Read more.
This paper presents a parallel genetic algorithm (GA) for the planning of power distribution networks considering harmonics. Power distribution systems are generally operated in a radial configuration, supplemented by tie switches that enable network reconfiguration during unexpected outages or planned maintenance. They can also include distributed generators (DGs), capacitor banks (CBs), and soft open points (SOPs) to lower distribution losses and improve the voltage profile. Some of the loads and DG units may be nonlinear, generating harmonic currents in the system, polluting the power, and increasing losses. This paper makes use of a parallel GA to find an optimized configuration, optimized location, and sizing of DGs, CBs, and SOPs to lower real power distribution losses while considering harmonics and the physical constraints of the network. The proposed algorithm uses a solution encoding based on the minimum spanning tree to guarantee the radial topology of candidate solutions. It uses the backward–forward power flow method to compute the fundamental voltages and a decoupled harmonic power flow for the harmonic components. The algorithm is parallelized on a small computer cluster using the Message Passing Interface (MPI) to reduce its execution time. The proposed solver is validated on distribution systems ranging from 16 to 880 buses. The results show that simultaneously optimizing the topology, the DGs, the CBs, and the SOPs results in reducing power losses by 37% to 93%, improving the overall efficiency of the distribution system. The parallelization using MPI allows for a 90.9× speedup on a 96-core cluster. Full article
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35 pages, 20666 KB  
Article
Freight Big Data-Based Dual-Scale Study of Economic Spatial Organization and Planning Responses in Hubei Province
by Haijuan Zhao, Xuejun Liu, Yan Long, Jingmei Shao, Jiaqi Chen, Zixuan Chen and Guoen Wang
Land 2026, 15(5), 752; https://doi.org/10.3390/land15050752 - 28 Apr 2026
Viewed by 239
Abstract
Using truck GPS trajectory data, this study measures the intensity of economic spatial linkages in Hubei Province at both administrative and cross-administrative scales and examines the hierarchical structure and spatial pattern of its urban economic network. By comparing the results with existing regional [...] Read more.
Using truck GPS trajectory data, this study measures the intensity of economic spatial linkages in Hubei Province at both administrative and cross-administrative scales and examines the hierarchical structure and spatial pattern of its urban economic network. By comparing the results with existing regional plans, the study provides empirical support for regional coordination and spatial planning. Network centrality analysis, linkage intensity measurement, and community detection algorithms are integrated to construct a topological model of the urban economic network from three dimensions: urban node hierarchy, inter-city linkage intensity, and urban cluster structure. To overcome administrative boundary constraints, a 5 km × 5 km grid-based approach is applied to identify functionally connected urban economic communities. The results indicate that Hubei Province’s urban economic network exhibits a highly dominant core accompanied by multiple secondary supporting centers. While the Wuhan Metropolitan Area demonstrates high economic activity, internal horizontal linkages remain relatively weak, and the roles of Yichang and Xiangyang as regional sub-centers require further strengthening. Grid-based analysis further reveals pronounced cross-administrative economic linkages. Accordingly, this study suggests strengthening support for regional sub-centers and promoting better alignment between administrative space and functional space within the spatial planning system, with enhanced cross-regional coordination. Full article
(This article belongs to the Special Issue Big Data-Driven Urban Spatial Perception)
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21 pages, 2870 KB  
Article
Optimizing Social Media Campaigns Through Engagement Topology and Behavioral Clustering
by Tichaona Chikore, Moster Zhangazha and Farai Nyabadza
Mathematics 2026, 14(9), 1466; https://doi.org/10.3390/math14091466 - 27 Apr 2026
Viewed by 424
Abstract
Social media engagement drives both individual behavior and content dissemination, yet traditional analytics often reduce interactions to simple counts, obscuring the complex structures underlying user activity. In the highly competitive digital landscape, understanding how users interact with content is crucial for businesses aiming [...] Read more.
Social media engagement drives both individual behavior and content dissemination, yet traditional analytics often reduce interactions to simple counts, obscuring the complex structures underlying user activity. In the highly competitive digital landscape, understanding how users interact with content is crucial for businesses aiming to optimize social media campaigns and maximize return on investment (ROI). Traditional engagement metrics, such as likes and shares, fail to capture the underlying structure and dynamics of user behavior. This study investigates the latent patterns of engagement by combining topological data analysis (TDA) with behavioral clustering across 100,000 posts on multiple platforms. Using persistent homology and k-nearest neighbour graphs, we reveal a primary bifurcation between Active (validation-focused) and Passive (consumption/propagation) users, nested four-strain substructures, and over 650 significant H1 loops indicating recurring feedback cycles. Active users exhibit strong cluster cohesion and high engagement rates, while Passive users contribute broadly to content diffusion with slightly higher loop counts, highlighting distinct functional roles in social media dynamics. These findings provide a principled framework for targeting content, reinforcing feedback loops, and leveraging hub posts to amplify engagement. By linking topological structure to behavioral patterns, this work advances both the theoretical understanding of digital interaction and the practical design of more effective social media campaigns. Full article
(This article belongs to the Special Issue Advanced Research in Complex Networks and Social Dynamics)
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27 pages, 3059 KB  
Article
A Study on the Vulnerability of Multilayer Subway Networks Based on the SPM and DQN
by Chen Yang, Lei Zhang, Liang You, Wenjie Tian, Chuhan Ma and Bowu Wei
Appl. Sci. 2026, 16(9), 4259; https://doi.org/10.3390/app16094259 - 27 Apr 2026
Viewed by 211
Abstract
To address the escalating vulnerability of metro systems under multiple perturbations—including extreme rainfall, equipment failures, and passenger surges—this study tackles several limitations in existing research: the predominant focus on single-layer topology, the neglect of cross-layer coupling effects between physical facilities and functional systems, [...] Read more.
To address the escalating vulnerability of metro systems under multiple perturbations—including extreme rainfall, equipment failures, and passenger surges—this study tackles several limitations in existing research: the predominant focus on single-layer topology, the neglect of cross-layer coupling effects between physical facilities and functional systems, the lack of dynamic global information in critical node identification, and the insufficient consideration of network clustering characteristics in cascading failure analysis. Drawing on complex systems theory, this study constructs a physical–functional bilayer coupled network model, proposes three improved Deep Q-Network algorithms for identifying cross-layer critical nodes, and introduces a cluster-augmented sandpile model to simulate the differentiated propagation of cascading failures. An empirical case study of the Zhengzhou Metro network demonstrates that the constructed bilayer network exhibits scale-free properties, that the improved DQN algorithms significantly outperform classical benchmarks—including degree centrality, betweenness centrality, closeness centrality, and the greedy algorithm—in sequential disruption efficiency, and that the safety tolerance coefficient and limit coefficient exert substantial regulatory effects on network vulnerability. The methodological framework developed herein—integrating bilayer coupled modeling, deep reinforcement learning-based critical node identification, and cluster-augmented sandpile cascading failure analysis—provides a transferable technical pathway for vulnerability assessment of multilayer coupled networks, with its applicability validated through the Zhengzhou case. Full article
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24 pages, 6532 KB  
Article
Deep Basis Non-Negative Matrix Factorization with Multi-Centroid Contrastive Learning
by Guoqing Luo, Yuan Wan, Hubo Tan and Zaichun Sun
Mathematics 2026, 14(9), 1452; https://doi.org/10.3390/math14091452 - 26 Apr 2026
Viewed by 208
Abstract
Non-negative Matrix Factorization (NMF) is a fundamental technique in unsupervised learning for data representation and clustering tasks. Although deep NMF methods have been developed to uncover hierarchical latent features, many existing approaches primarily rely on coefficient-matrix-based decomposition or single-centroid representations. This often limits [...] Read more.
Non-negative Matrix Factorization (NMF) is a fundamental technique in unsupervised learning for data representation and clustering tasks. Although deep NMF methods have been developed to uncover hierarchical latent features, many existing approaches primarily rely on coefficient-matrix-based decomposition or single-centroid representations. This often limits the integration of intra-class structural features during deep decomposition, resulting in ambiguous and incomplete local feature representations. Moreover, these frameworks often exhibit feature blurring and inadequate discriminability across hierarchical levels. This paper introduces a novel Deep Basis Non-negative Matrix Factorization with Multi-Centroid Contrastive Learning (DBMCNMF) algorithm that addresses these limitations through innovative architectural design. The proposed method integrates multi-centroid representation learning with contrastive regularization constraints within a deep basis matrix factorization framework. The algorithm uses Gaussian similarity measures to establish attractive and repulsive regularization terms that preserve manifold topology while promoting discriminative clustering. DBMCNMF uses multiple centroids instead of single-centroid methods to comprehensively cover complex data distributions and capture local geometric structures that are typically inaccessible to conventional methods. The proposed model is evaluated on several benchmark image datasets. The results indicate that DBMCNMF consistently outperforms traditional single-centroid methods by achieving higher clustering accuracy and preserving the underlying manifold structure more effectively. Full article
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