Search Results (751)

Many machine-learning tasks involve structured data whose geometry, local feature distributions, and global organization interact in ways that are not well captured by existing methods based on vectorization, graph metrics, or homological signatures. We introduce Fiber Bundle Learning (FBL), a topological framework that represents each data sample as a discrete fiber bundle and extracts a classification signature combining persistent homology, local feature geometry, and gluing structure. FBL builds a base space from the coarse geometry of each object, models local feature patches as fibers, and estimates transition maps between neighboring fibers to construct a discrete connection. From this representation, FBL computes a set of invariants: persistent homology of the base, fibers, and total space; holonomy obtained by transporting fiber states along cycles; curvature-like quantities measuring transition inconsistency; and discrete analogues of characteristic classes. These components are assembled into a fixed-length feature vector that can be used with any standard classifier. We show that FBL yields a signature with three desirable theoretical properties: stability under perturbations of geometry and local features, invariance under isometries and global fiber reparameterizations, and robustness to sampling noise. Our synthetic experiments show that FBL distinguishes twisted from untwisted bundles with identical homology, a distinction classical topological methods fail to capture. Additional tests quantify the system’s resistance to noise, its invariance to geometric transformations, and the contribution of each signature component. Taken together, our results indicate that representing data through fiber bundle structure may provide an effective tool for classifying complex, multi-level objects. Full article

Network function virtualization (NFV) enables cost reduction and optimized service deployment. By means of virtualization, network functions which used to be executed on specialized hardware are being replaced with software called Virtual Network Functions (VNFs) that can run on commodity hardware. These VNFs are applied to data flows passing through network nodes with VNFs hosted on them. To fully realize the benefits of NFV, each flow must be fully processed on VNF nodes. Given the budget constraints, only a finite number of nodes can be selected to host VNFs, and these nodes also have limited capacity to process the flows passing through them. In this paper, we consider the problem of VNF node placement and capacity allocation in a network graph $G=(V,E)$, i.e., selecting the best subset of VNF nodes and optimally distributing their bandwidth to maximize the total volume of fully processed traffic flows F. We propose a simpler algorithm for solving this problem than the previously proposed version, representing it as an integer linear programming problem with an approximation ratio of ${\displaystyle \frac{1}{2}}(1-1/e)$, and time complexity $O(|V{|}^{2.5}·|F{|}^{2.5}·L)$, where L is the number of bits of input data. Full article

Virtual reality (VR)-based rehabilitation is an established modality for upper extremity motor recovery; however, existing systems frequently rely on fixed, random, or therapist-tuned target placement that disregards patient-specific motor capacity and population-level priors. This study proposes a cross-patient collaborative swarm intelligence framework that derives zone-based patient profiles from real VR trajectories and augments them with a similarity-weighted cohort prior distilled from clinically similar patients’ successful trajectory clouds and zone-transition graphs. A hybrid Ant Colony Optimization (ACO)–Particle Swarm Optimization (PSO) algorithm optimizes 12 targets per session across a 27-zone ($3\times 3\times 3$) workspace using a five-component fitness function encompassing reachability, zone balance, movement efficiency, heatmap-guided challenge coverage, and swarm-flow consistency. The framework was evaluated retrospectively on a single-center cohort of 36 post-stroke patients and 6373 sessions under a leakage-safe simulation protocol with 70/30 chronological splits; outcomes are model-based proxy success rates derived from each patient’s profile rather than directly observed task success. The hybrid strategy achieved a mean simulated success rate of 85.5% ± 5.5%, a 36.4% relative improvement over random placement (Wilcoxon $p<{10}^{-7}$, Cohen’s $d=4.91$); the leakage-safe split yielded 80.1% on the held-out segment versus 61.1% for random, with no statistically significant train–test gap ($p=0.470$). Ablation confirmed both PSO and ACO are individually necessary ($\mathsf{\Delta }\ge 2.7$ pp, $p<0.001$). Total session-start computation is 78 ms on standard CPU hardware. These findings constitute a proof-of-concept that collaborative personalized swarm optimization can substantially outperform heuristic target placement under in silico evaluation; clinical efficacy in terms of standardized motor outcome measures remains to be established in a prospective randomized controlled trial, and the findings should be replicated across centers, task modes, and a larger cohort before generalization. Full article

PM2.5 and near-surface O₃ compound pollution is a major challenge for further air quality improvement in the Yangtze River Delta (YRD). Despite research on the chemical coupling mechanisms and concentration co-variation between PM2.5 and O₃, the directional linkages of compound pollution events among cities and the network mechanisms underlying their formation remain unclear. Here, we identified PM2.5–O₃ compound pollution events for 41 YRD cities from 2015 to 2024 using city-year-specific P80 dual-threshold criteria. We then constructed annual directed synchronization networks based on event-leading relationships and used temporal exponential random graph models to identify the formation mechanisms of significant leading ties. PM2.5–O₃ compound pollution events in the YRD generally decreased during 2015–2024, with characteristics shifting from high frequency, persistence, and strong intercity linkage in the early stage to lower frequency, weaker intensity, and continued episodic fluctuations. Directed event networks exhibited a clear stage-dependent evolution: network density, total edge weight, reciprocity, and local closure were relatively high during 2015–2018, networks became markedly sparse during 2020–2022, and a partial rebound occurred after 2023. Spatial backbone analysis indicated reorganization of the dominant linkage structure, shifting from the Shanghai–southern Jiangsu–northern Zhejiang coastal core toward the northern Jiangsu, Anhui, and interprovincial corridors. Key node analysis further revealed a clear functional differentiation among cities, with some cities acting as potential leading sources, some as receiving nodes, and several non-traditional core cities serving as cross-regional bridges. Significant leading ties were jointly shaped by reciprocity, local closures, temporal memory, economic development, industrial structure, and digital governance. Therefore, as well as a problem of co-occurrence, PM2.5–O₃ compound pollution in the YRD is a cross-city event-network process characterized by directionality, stage-dependent evolution, and differentiated urban roles. This study provides empirical evidence for dynamic joint prevention and control based on event linkages, urban roles, and cross-city coordination. Full article

Accurate effluent-quality prediction is essential for improving nitrogen and phosphorus removal performance and reducing energy consumption in wastewater treatment plants (WWTPs). However, the strong coupling, high noise, and time-lag effects in wastewater treatment processes pose significant challenges to existing prediction models. In this study, we propose a GAT-CNN-LSTM(GCL) model for the prediction of effluent total nitrogen (TN) and total phosphorus (TP). The GCL model first uses a graph attention network (GAT) to adaptively learn inter-variable relationships, and then applies a convolutional neural network (CNN) and long short-term memory (LSTM) network to extract local and long-term temporal features. The GCL model is trained and evaluated using real operational data from a municipal WWTP in northern China. Based on the best run of each model, GCL improves the $R^2$ by 13.7% and 6.4% over LSTM and Transformer for TN prediction, while reducing MAPE by 39.4% and 30.4%, respectively. For TP prediction, the corresponding improvements in $R^2$ are 70.7% and 59.1%, with MAPE reductions of 37.1% and 36.0%. Ablation experiments further demonstrate the complementary contributions of the three modules, showing that graph-based feature fusion enhances subsequent temporal modeling. The temporal variation in neighbor attention weights and one-at-a-time (OAT) sensitivity analysis provide interpretability consistent with A²/O process mechanisms. These findings provide a preliminary validation based on a limited dataset from a single WWTP, and broader applicability under more diverse operating conditions warrants further investigation. Full article

Causal graphs are powerful instruments for structuring information and analyzing the extent to which an observed effect can be attributed to a given cause. In this work, we demonstrate how edge-weighted causal graphs can be used to quantify whether a sentence acts as a direct or indirect cause. We introduce methods to identify the causal path with the highest total strength between two concepts and, given a specific context, to determine the pair of concepts with the strongest causal connection. In addition, we propose centrality measures that incorporate causality scores and graph weights, enabling the ranking of sentences by causal importance and identifying the most relevant ones. Full article

The $\delta$-complement $G_{\delta }$ of a graph G, introduced by Pai et al., is a variant of the ordinary complement that toggles edges only between vertices of equal degree. Tangjai et al. recently established Nordhaus–Gaddum-type bounds for the ordinary domination number on G and $G_{\delta }$, raising the natural question of analogous bounds for stronger domination invariants. We prove a sharp Nordhaus–Gaddum-type bound on the Roman domination number of the form ${\gamma }_R\left(G\right)+{\gamma }_R\left(G_{\delta }\right)\le n+3k-2s_1-s_2$, where n is the order of G, k is the number of distinct vertex degrees, and $s_1,s_2$ count degree classes of size 1 and 2, respectively. The bound strictly refines the trivial estimate $2(n+k)$ and is attained on an explicit infinite family of graphs of the form $m{K}_2$. For the total domination number, we pose the corresponding conjecture ${\gamma }_t\left(G\right)+{\gamma }_t\left(G_{\delta }\right)\le n+2k$ whenever G and $G_{\delta }$ have no isolated vertices. We are able to settle this bound only in part: we prove it unconditionally on the subclass of graphs whose every degree-class subgraph and its complement are free of isolated vertices, and we verify it computationally for all orders $3\le n\le 8$, but a proof in full generality remains open, so the bound is stated as a conjecture. The Roman bound is likewise checked by exhaustive enumeration of all $\mathrm{13,595}$ non-isomorphic simple graphs of orders $3\le n\le 8$, with zero violations and all 26 sharp instances identified. Full article

Industrial-park integrated electricity–heat–hydrogen energy systems (IEHESs) face a challenging rolling dispatch problem because strong multi-energy coupling, intertemporal storage dynamics, and forecast uncertainty make it difficult to achieve economy, low-carbon operation, and hard-constraint feasibility simultaneously. To address this issue, this paper proposes a graph spatiotemporal world-model-driven rolling model predictive control (MPC) framework, termed GraphWorldModel_MPC, for low-carbon economic dispatch of industrial-park IEHESs. First, a unified graph-based representation is constructed to characterize the topology-aware coupling relationships among the electricity, heat, and hydrogen subsystems. Second, a graph spatiotemporal world model is developed to learn multi-step state transitions, while constraint-aligned physics-consistency terms are incorporated to align the predicted trajectories with multi-energy balance, storage-boundary evolution, and ramping semantics. In addition, the learned dynamics are embedded into a hard-constrained economic MPC framework, and a quantile-based safety-tightening mechanism is adopted to mitigate residual prediction uncertainty and enhance closed-loop feasibility. Case studies on an industrial-park IEHES show that the proposed method achieves an average 24-step normalized root mean square error (NRMSE) of 4.28% and reduces the monthly total operating cost by 6.07%, 3.83%, and 10.79% compared with conventional economic MPC (EMPC), distributionally robust adaptive MPC (DRAMPC), and GRU-MPC, respectively. It also reduces equivalent carbon emissions by 6.89%, 4.52%, and 9.50% relative to these benchmarks, while maintaining zero dispatch violations in the tested monthly horizon. Full article

A neighbor sum distinguishing (NSD) total coloring of a graph G is a mapping $\varphi :T\left(G\right)=V\left(G\right)\cup E\left(G\right)\to \{1,2,\cdots ,k\}$ such that any two adjacent or incident elements in $T\left(G\right)$ receive different colors, and the sum of the colors of all incident edges of u and the color of u is different from the sum of the colors of all incident edges of v and the color of v for each edge $uv$. The NSD total chromatic number of G, denoted by ${\chi }_{\mathrm{\Sigma }}^t\left(G\right)$, is the smallest integer k such that G has an NSD total coloring. For any graph G, there is a conjecture that the NSD total chromatic number ${\chi }_{\mathrm{\Sigma }}^t\left(G\right)\le \Delta \left(G\right)+3$, where $\Delta \left(G\right)$ denotes the maximum degree of G. The neighbor sum distinguishing total choice number of G, denoted by ${\mathrm{ch}}_{\mathrm{\Sigma }}^t\left(G\right)$, is the smallest integer k such that, after assigning each $z\in T\left(G\right)$ a set $L\left(z\right)$ of k real numbers, G has an NSD total coloring $\varphi$ satisfying $\varphi \left(z\right)\in L\left(z\right)$ for each $z\in T\left(G\right)$. Obviously, ${\chi }_{\mathrm{\Sigma }}^t\left(G\right)\le$${\mathrm{ch}}_{\mathrm{\Sigma }}^t\left(G\right)$. In this paper, we prove that ${\mathrm{ch}}_{\mathrm{\Sigma }}^t\left(G\right)\le \Delta \left(G\right)+3$ for any IC-planar graph G without 4-cycles and $\Delta \left(G\right)\ge 7$ by applying the Combinatorial Nullstellensatz, which improves upon the previous results. Full article

Learning path optimization is crucial in intelligent educational systems, with the core challenge of efficient multi-objective sequential decision-making under complex prerequisite constraints. To address the poor generalization of existing methods relying on fixed operator scheduling or handcrafted heuristics, this paper proposes a hyper-heuristic framework based on Dueling Deep Q-Network (Dueling DQN-HH), formulating operator selection as a sequential decision-making process for dynamic adaptive scheduling of low-level operators. The framework adopts priority-based encoding to unify learning path representation (decoupling the hyper-heuristic layer from the problem domain) and designs a composite reward mechanism integrating reward shaping, exploration incentives, and computational cost awareness to balance solution quality and efficiency. Additionally, it employs a dueling network architecture with prioritized experience replay to enhance policy learning stability. Experimental results show the proposed method outperforms representative baseline algorithms in solution quality, convergence stability, and computational efficiency. The framework demonstrates superior performance across multiple objectives, particularly in minimizing the total learning time (F_time), as validated on two heterogeneous datasets: MOOCCube (Computer Science) and PsyDataset (Psychology). Further ablation studies and operator evolution analyses verify its adaptive scheduling capability under different objectives and knowledge graph structures, demonstrating strong objective independence and cross-dataset generalization. Full article

Spatial transcriptomics (ST) has emerged as an essential technology for interpreting the molecular profiles underlying pathological tissue morphology. Most existing ST analyses are limited to 2D sections, which ignore the complex structural and molecular heterogeneity of biological tissues in 3D space and may cause diagnostic oversights. Since acquiring complete 3D ST volumes is resource-intensive, recent 3D imputation paradigms provide a cost-effective alternative by integrating 3D whole-slide images (WSIs) with sparse 2D ST references (e.g., a single slide). Despite this methodological advancement, effectively modeling complex cross-layer spatial dependencies remains challenging. Current mainstream solutions predominantly adopt standard Transformers for cross-scale feature aggregation, which may bring computational overhead and higher overfitting risk while having limited explicit mechanisms for hierarchical anatomical guidance. To address these limitations, we propose a Hierarchical MambaOut-based Spatial Imputation Graph Network (HM-ASIGN) for anatomy-aware 3D spatial transcriptomics imputation. Our architecture leverages MambaOut’s dynamic gated 1D convolutions as a parameter-efficient alternative to dense global self-attention. This design captures the depth-wise evolution of pathological features while reducing over-parameterization. Inspired by the macro-to-micro diagnostic reasoning of clinical pathologists, HM-ASIGN introduces a multi-scale recursive guidance mechanism. It constructs a top-down information flow by extracting global anatomical priors at macroscopic scales and injecting them as contextual anchors into regional and spot-level features in a cascaded manner. This helps ensure that fine-grained molecular predictions are properly constrained by global morphological structures. Evaluation experiments on multiple public breast cancer datasets demonstrate that HM-ASIGN achieves competitive reference-level performance against existing baselines, reaching a Pearson Correlation Coefficient (PCC) of 0.772. Specifically, when evaluated against the foundational ASIGN framework, it improves predictive accuracy while reducing the total parameter count by approximately 33.3% and improving inference throughput. Our results suggest that HM-ASIGN provides a computationally efficient approach for 3D spatial molecular mapping. Full article

Background/Objectives: This cross-sectional study aimed to estimate the Locally Estimated Scatterplot Smoothing (LOESS)-smoothed percentiles for growth trajectories and evaluate age-related tendencies across groups using visual cross-sectional graphs. Methods: A total of 1147 patient records were analyzed, including 648 females and 469 males aged 5–20 years, with a mean age of 11.9 (SD ± 3.8) years. Twenty-seven cephalometric variables were organized into six measurement domains: cranial base, maxillary complex, mandibular complex, occlusal plane, vertical relationship, and sagittal relationship. Percentile curves were generated using LOESS regression across an age range of 5–20 years. Results: The LOESS-smoothed curves showed age-related trends across age groups. An upward trend in the curves was observed for the anterior and posterior cranial bases between 5 and 12 years of age, a plateau indicating reduced age-related change across groups during mid-adolescence. Maxillary measurements showed a similar pattern, with a clear upward tendency during childhood and reduced age-related change after approximately 12 years. Mandibular length and projection showed increasing trends during childhood, followed by a plateau or reduced slope across later age groups. The occlusal plane and vertical dimensions showed consistent patterns that approached a plateau around 12 years, indicating minimal age-related differences between groups. Changes in the ANB angle and Wits appraisal reflected a progressive forward tendency of the mandible across childhood age groups, followed by reduced age-related change during adolescence. Conclusions: These findings suggest that many craniofacial measurements show an upward trend during childhood followed by a plateau or reduced age-related change across age groups between approximately 12 and 14 years. The percentile-based growth curves presented here offer a practical reference for clinicians to evaluate craniofacial growth trajectories as population-level approximations derived from cross-sectional data in the pediatric population. Full article

Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach to protect against attacks, but energy, connectivity, and capacity constraints should be considered while picking monitor nodes. In this paper, we tackle the Minimum-Weighted Connected Capacitated Vertex Cover (MWCCVC) problem, which minimizes monitoring costs, ensures backbone connectivity, and adheres to per-node capacity constraints. Unlike prior works that consider weighted vertex cover, connectivity constraints, or capacitated variants separately, the proposed MWCCVC model jointly integrates all three dimensions within a single vertex cover-based monitoring framework. We first provide a Branch-and-Bound (B&B) solver with linear programming relaxation bounds and constraint-based pruning strategies that produces optimum solutions. Three constructive greedy heuristics (GD, GR, GW) and two hybrid genetic algorithms (HGA, HGA-v2) that combine parameterized greedy decoders with evolutionary search are proposed; all methods guarantee full edge coverage, induced-subgraph connectivity, and max-flow-validated capacity feasibility. Tests on 130 small, 160 medium, and 19 large benchmark instances show that HGA matches B&B optima on every small instance, beats the time-limited B&B by 6.6% on medium instances, where the percentage is computed based on the relative difference in average total weight with respect to B&B, and stays the best on large graphs with up to 1000 nodes. The HGA-v2 tries to balance the quality and speed, with only a 3.1% difference at $10\times$ faster execution. Full article

Distributed hybrid flow-shop scheduling problems (DHFSPs) are widely encountered in manufacturing systems. Their complexity increases significantly when multiple overhead cranes are used for material handling. This paper investigates a distributed hybrid flow-shop scheduling problem with multiple overhead crane transportation (DHFSP-MCT), aiming to simultaneously minimize makespan and total energy consumption (including machining and transport). A hierarchical reinforcement learning-based bi-population collaborative metaheuristic algorithm (HRL-BCMA) is proposed. In HRL-BCMA, an iterated greedy strategy is first adopted to generate an initial population. Then, a two-level reinforcement learning framework is designed: a high-level agent decides when to release jobs to the shop floor, while a low-level agent based on a graph isomorphism network selects improvement operators. Furthermore, a bi-population co-evolutionary framework and a knowledge-informed strategy are introduced to enhance solution quality and diversity. Experimental evaluations on both randomly generated instances and a real-world-inspired aluminum manufacturing case show that HRL-BCMA reduces makespan by 8.6% and total energy consumption by 12.3% on average compared to the best existing algorithm (CBMA) while achieving superior Pareto front coverage. These results demonstrate the effectiveness of the proposed method for green scheduling problems with crane transport constraints. Full article

In this article, we study the homotopy aspects of intersection graphs of topological semigroups. We begin by defining the top intersection graph $T{G}_{\mathbb{X}}$ and investigating how the algebraic and topological properties of a topological semigroup are reflected in the global structure of this graph. In particular, we characterize when $T{G}_{\mathbb{X}}$ is totally disconnected, bipartite, or planar in terms of the order and factorization of the underlying semigroup. We then introduce the notions of $HTG$-semigroups, graphical homomorphisms, and graphical homotopy relations, thereby developing a graphical homotopy framework. Within this setting, we study $Gr$-homotopy equivalences, $Gr$-contractible spaces, and retraction phenomena, including $DGr$-retracts and homotopy extension properties. Finally, we introduce graphical total semigroups and equip the set of $Gr$-path homotopy classes $\left[{\mathbb{X}}_{pe}\right]$ with a natural $\Delta$-uniform topology. We show that this topology is compatible with the induced semigroup operation, yielding a topological semigroup structure. Overall, this work provides a unified algebraic, topological, and graph-theoretic perspective, and opens the door to further applications of homotopy theory in the study of intersection graphs of topological semigroups. Full article