Search Results (1,818)

Topological graph theory provides a quantitative approach to understanding the structural complexities of sulfonamide compounds, which are prominent for their therapeutic importance in cancer treatment. A new computational scheme to predict the physicochemical and biological functions of sulfonamide derivatives, based on connection numbers and connection-based topological indices as alternatives to the theoretically overt degree-based index, is proposed. A set of structurally diverse sulfonamide compounds as chemical graphs is considered, and the relevant graph descriptors are computed using different connection numbers. Due to the complexity of the calculations involved in connectivity and other such indices, algorithms were developed in Python 3.12.12 to automate the extraction and calculation of these indices. QSPR analysis, with the help of supervised machine learning models like linear regression, among others, and various statistical techniques, was employed to obtain insight into the relationships existing between the structural properties and the molecular properties measured, such as melting point, molecular weight, etc. These results demonstrate the great predictive capability of connection-based indices in assessing pharmacologic efficacy or molecular behavior. The holistic setting thus links topological modeling to data-driven prediction and provides a window into the rational design and optimization of sulfonamide-based cancer therapeutics. Full article

Assessing and optimizing regional ecological networks is critical for mitigating fragmentation-driven ecological risks and informing evidence-based territorial spatial planning in China. In this study, we developed a comprehensive evaluation framework integrating ecosystem services, ecological sensitivity, and landscape connectivity to identify ecological sources in Anyang City, China. We then extracted ecological corridors and nodes using circuit theory and constructed the city’s ecological network. Notably, we applied complex network theory combined with topological robustness analysis for optimization to enhance network stability. The analysis identified 43 ecological sources (820.72 km²; 11.16% of the region), predominantly distributed in western Anyang. A total of 82 corridors (460.35 km), 62 pinch points, and 120 barrier points were mapped—primarily in the west, revealing critical connectivity deficits. Network optimization through the addition of 10 strategic corridors significantly enhanced structural balance and functionality, with average degree, closeness centrality, clustering coefficient, eigenvector centrality, and graph density increasing by 5.55–12.19%, and their standard deviations decreasing by an average of 19.32%. Global efficiency (+8.74%), the largest connected component ratio (+0.73%), and node/edge recovery robustness (+17.44%/+18.08%) also improved markedly, confirming greater connectivity and resilience. Our methodology comprehensively integrates ecosystem functional services, disturbance resistance, and spatial structural stability, providing a practical reference for the construction and optimization of regional ecological networks in mountainous–plain transition zones of China. Full article

Rapid search for evasive targets using multiple Unmanned Aerial Vehicles (UAVs) presents significant challenges, as it requires real-time target-motion prediction, multi-agent coordination, and adherence to kinematic constraints. Existing cooperative search methods often assume non-adversarial target behavior or model target motion independently of UAV actions, which reduces their effectiveness against targets that actively evade based on UAV positions. To address these limitations, this study introduces the Cooperative Rapid Search Algorithm for Evasive Targets (CRS-AET). The proposed framework utilizes graph-theoretic modeling to represent spatial-temporal relationships among UAVs, targets, and environmental grids. A directional gradient-based motion prediction (DG-Prediction) method first estimates probable movement areas of dynamic targets within the graph-structured environment. An improved multi-round auction algorithm with graph-based utility propagation (IMRAA) then optimizes UAV resource allocation. Finally, Dubins-Constrained Trajectory Optimization (DC-RTO) is integrated within a distributed model predictive control (DMPC) scheme to ensure kinematic feasibility. Simulation results across three representative scenarios indicate that CRS-AET enables faster target detection, enhanced area coverage, and more efficient coordination than baseline methods. Hardware-in-the-loop (HIL) experiments further confirm the robustness and practical applicability of the framework in realistic operational environments. Full article

Hybrid renewable energy systems (HRESs), mixing conventional and renewable power sources and occasionally storage units, have become the norm regarding electricity generation. Robust long-term planning of such systems requires stakeholders to test different layouts and system configurations, while their operational management relies on forecasting surpluses and deficits to achieve optimal decision making. However, both tasks, which in fact constitute a flow allocation problem across power networks, are subject to multiple peculiarities, arising from the nonlinear dynamics of the underlying processes, subject to numerous technical and operational constraints. Interestingly, a mutual problem emerges in water resource systems, also comprising network-type storage, abstraction and conveyance components. In this vein, triggered from well-established simulation approaches from the water domain, we introduce a generic (i.e., topology-free) and time-agnostic framework, the key methodological elements of which are: (a) the graph-based representation of the power fluxes; (b) the effective handling of energy uses and constraints through virtual nodes and edges; (c) the implementation of priorities via proper assignment of virtual costs across all graph components; and (d) the configuration of the overall problem as a network linear programming context, which allows the use of exceptionally fast solvers. Specific adjustments are required to address highly complex issues within HRESs, particularly the representation of conventional thermal and pumped-storage hydropower units, as well as the power losses across transmission lines. The modeling approach is stress-tested by means of configuring a hypothetical HRES in a non-interconnected Aegean island, i.e., Sifnos, Greece. Full article

Large-scale agricultural remote sensing monitoring is challenged by pronounced spatial heterogeneity arising from fragmented terrain, complex climatic backgrounds, and diverse cropping structures. However, existing agricultural zoning schemes generally lack an integrated consideration of remote sensing imaging mechanisms and key variable conditions such as atmospheric interference and crop phenology, limiting their direct utility in guiding region-specific sensor selection and classification algorithm calibration. To address this limitation, this study integrates multi-source earth observation data and agricultural statistical information to construct an Agricultural Remote-sensing Classification Difficulty Index (ARCDI) from multiple dimensions, including image availability, cropping structure, cropland fragmentation, and topographic environment. On this basis, a graph theory-based spatially constrained Skater clustering algorithm is introduced to establish a two-tier “cropland–major cereal crops” zoning framework oriented toward remote sensing applications. The results indicate that the proposed framework delineates five distinct first-tier cropland classification difficulty zones across China. This zoning scheme effectively quantifies the regional heterogeneities in monitoring challenges. Building upon this first-tier zoning, the framework is further refined into 50 second-tier major cereal crop classification difficulty zones, including 13 winter wheat zones, 21 maize zones, and 16 rice zones. Statistical tests and spatial analyses demonstrate that the proposed zoning scheme significantly outperforms conventional clustering approaches in balancing within-zone homogeneity and spatial continuity. This advantage is quantitatively reflected by consistently lower residual spatial autocorrelation (residual Moran’s I ≈ 0.10–0.11) and an approximately 20% reduction in within-zone variance compared with other spatially constrained methods. Extensive field-sample validation provides preliminary evidence of an inverse relationship between crop-type classification difficulty and accuracy. These results confirm the framework’s reliability in identifying regional difficulty and its decision-support value for selecting remote sensing strategies. Overall, this study systematically elucidates the spatial differentiation patterns of remote sensing classification difficulty for cropland and major cereal crops across China. The proposed framework provides robust scientific support for data selection, algorithm optimization, and differentiated strategy formulation in national-scale agricultural monitoring, thereby facilitating the operationalization of regional agricultural remote sensing applications. Full article

This paper establishes a graph-theoretic framework for idealization semigroups arising from Bruck–Reilly extensions. Building on a recent study by Wazzan and Ozalan, we introduce five graph families—${\Gamma }_E$, ${\Gamma }_0$, ${\Gamma }_{\mathrm{Cay}}$, ${\Gamma }_{\mathcal{K}}$, and $\Gamma \left(G_k\right)$—each encoding a distinct algebraic facet of $S{B}_i(\bowtie )B$. We prove explicit correspondences linking combinatorial invariants to algebraic structure: diameter captures generating efficiency and semilattice height; girth signals short relations; chromatic number bounds idempotent cardinalities and $\mathcal{D}$-class counts; clique number measures maximal commuting subsets; and Laplacian spectra encode ideal size and Schützenberger groups. Our central result demonstrates that Green’s relations are combinatorially recoverable from graph pairs. For commutative $S{B}_i(\bowtie )B$, $({\Gamma }_E,{\Gamma }_{\mathcal{K}})$ uniquely determines $\mathcal{J}$-order, $\mathcal{D}$-classes, and $\mathcal{H}$-classes via neighborhood inclusions, bipartite components, and automorphism orbits, yielding the first algorithmic reconstruction of ideal-theoretic structure from graph data. The framework is implemented in SageMath as a reproducible open-source toolkit validated on concrete examples. This work synthesizes algebraic graph theory, semigroup theory, and computational mathematics into a unified algebraic-combinatorial dictionary, providing both new analytical tools and a methodological template for studying algebraic constructions via graph invariants. Full article

This study examined the role of e-modules and learning applications in enhancing scientific literacy among Grade 11 Life Sciences learners in a South African secondary school. Grounded in constructivist and connectivist learning theories, the research responded to persistent challenges in learners’ conceptual understanding, scientific reasoning, and application of scientific knowledge. A mixed-methods case study design was employed, combining quantitative pre- and post-test data with qualitative classroom observations and semi-structured learner interviews. Thirty learners participated in a technology-enhanced instructional intervention using curriculum-aligned e-modules delivered through Binogi and Google Classroom. Quantitative findings revealed a statistically significant improvement in scientific literacy following the intervention. Learners’ mean scores increased from 39.20% (pre-test) to 63.07% (post-test), representing a gain of 23.87 percentage points. A paired-samples t-test confirmed that this improvement was extremely significant (t (29) = 11.58, p < 0.0001), with a very large effect size (Cohen’s d = 2.11). Qualitative findings indicated that learners experienced enhanced engagement, improved conceptual clarity, and greater motivation when using digital learning tools, particularly through visualisations, animations, and self-paced learning. However, persistent difficulties with graph interpretation were also identified. The study concludes that the intentional integration of e-modules and learning applications can substantially enhance scientific literacy in Life Sciences by supporting conceptual understanding, reasoning, and learner engagement. These findings highlight the importance of pedagogically guided digital integration and teacher professional development to strengthen science learning outcomes. Full article

Urban road networks (URNs) underpin critical urban functions ranging from public service provision to emergency response. However, URN resilience is commonly assessed using aggregate performance metrics or critical-element identification, which offers limited insight into how disruption reshapes spatial accessibility. This limitation is increasingly salient under stock-based urban development, where opportunities for large-scale physical network reconfiguration and segment-level engineering interventions are constrained, and resilience enhancement increasingly depends on facility-based adaptation. To address this gap, drawing on graph theory and percolation theory, this study proposes a disconnection-pattern-based (DPB) analytical approach for mapping spatial configurations of URN vulnerability. Two generic disconnection patterns derived from topological limits of network redundancy are conceptualized: Local Island Disconnection (LID) and Global Structural Fragmentation (GSF). Corresponding quantitative mapping methods are developed and applied to cities with contrasting URN morphologies. Results show that spatial configurations of connectivity vulnerability can be systematically mapped across heterogeneous URNs, yielding spatially explicit information critical to resilience-oriented facility siting. By treating vulnerability as a spatial configuration rather than a single-state metric, the proposed approach extends URN resilience assessment toward facility-planning strategies that adapt to existing road-network risk configurations under stock-based development. Full article

The diagnosis of attention-deficit/hyperactivity disorder (ADHD) has long relied on subjective scales, lacking objective neuroimaging biomarkers. Static functional connectivity (sFC) and dynamic functional connectivity (dFC), as commonly used metrics in resting-state functional magnetic resonance imaging (rs-fMRI) analysis, provide important perspectives for related research. However, existing unimodal approaches struggle to effectively integrate the spatiotemporal characteristics of functional connectivity. To address this, this paper proposes the multimodal fusion framework D-SFANet, which synergistically models the static and dynamic features of brain functional connectivity through an attention mechanism: in the static path, it integrates a multi-scale convolutional network with phenotypic information extraction to extract hierarchical topological features; in the dynamic path, it combines graph theory with a bidirectional long short-term memory network (BiLSTM) to capture key state transition patterns in brain networks. Experimental validation demonstrates that D-SFANet achieves significantly higher classification accuracy than existing mainstream methods, robustly validating the effectiveness of its spatiotemporal fusion strategy. Full article

This study analyzes network coherence in two-layer and three-layer networks with positive and negative inter-layer correlation patterns. Using algebraic graph theory, we construct the Laplacian matrices for different correlated graph structures and compute their Laplacian spectra. The impact of correlation patterns on network coherence is investigated for two-layer and three-layer structures, and numerical evaluations are performed. The results show that negative-correlation patterns yield better network coherence than positive ones. This work provides fundamental insights into the structural robustness of layered networks and offers theoretical guidance for the design of robust networked systems. Full article

We address a gap in Machine Learning–human alignment research by proposing that methods from Explainable AI (XAI) can be repurposed to quantitatively model human learning. To achieve alignment between human experts and Machine Learning (ML) models, we must first be able to explain the problem-solving strategies of human experts with the same rigor we apply to ML models. To demonstrate this approach, we model expertise in the complex domain of particle accelerator operations. Analyzing 14 years of operational text logs, we construct weighted graphs where nodes represent operational subtasks and edges capture their strategic relationships. We then examine these strategic models across four granularity levels. Our analysis reveals statistically significant changes with expertise at three of four graph levels. Remarkably, despite numerous possible ways to partition subtasks, operators across all expertise levels demonstrate a striking consistency in high-level strategy, partitioning the task into the same three functional communities. This suggests a shared “divide and conquer” cognitive framework. Expertise develops within this stable framework, as experts exhibit greater cognitive flexibility (forming more cross-community connections) and build more refined internal models. The primary contribution of this work is a methodology for creating a quantitative, interpretable baseline of expert human performance. This provides a “ground truth” for future research in alignment between humans and ML models, enabling a new approach to verification: the ML model’s representation of the task can be quantitatively compared against the human expert benchmark to measure their alignment. This paves the way for building safer, more interpretable partnerships between humans and ML models. Full article

Reconstructing a genome from collections of short DNA fragments is a fundamental problem in modern sequencing. Although genome assembly algorithms are widely used in practice, the mathematical conditions that allow exact reconstruction are not always clear. This study develops a graph-theoretic framework for genome reconstruction using De Bruijn graphs and Eulerian paths in an idealized, error-free setting. Each k-mer is represented as a directed edge connecting its $(k-1)$-length prefix and suffix. The resulting overlap graph is constructed using a balanced search tree and traversed with a stack-based Eulerian algorithm. Numerical experiments over a broad range of genome lengths and fragment lengths reveal a sharp transition in reconstruction accuracy. This transition is explained by a probabilistic model for prefix collisions in the directed graph. The theoretical predictions agree with simulation results and provide conditions on the fragment length required for reliable reconstruction. These results show that the difficulty of genome assembly is governed primarily by the combinatorial structure of the underlying graph rather than by algorithmic heuristics. Full article

This paper investigates the fully distributed observer-based dynamic double-event-triggered bipartite consensus tracking problem of fractional-order multi-agent systems (FOMASs) with input saturation under a directed graph. First, to address this complex challenge, a pull-based dynamic double-event-triggered mechanism (DDETM) with different event-triggered conditions and capable of operating independently is designed, which can effectively reduce communication costs and controller updates concurrently. Then, the low-gain feedback technique is used to solve the input saturation problem faced by FOMASs under a directed graph. Based on the estimated state information, a fully distributed control protocol with pull-based DDETM is proposed to ensure the achievement of bipartite consensus tracking for FOMASs. A noteworthy feature of this control protocol is its ability to achieve system stability without the need for global information. Correspondingly, the sufficient conditions for achieving bipartite consensus is obtained with the help of low gain feedback technology and Lyapunov stability theory. Moreover, the Zeno behavior is precluded. Finally, a simulation example is presented to illustrate the theoretical results. Full article

Recently, piecewise differential operators have been introduced to capture crossover dynamics in physical systems. In the evolution of corruption, the underlying dynamics can shift across different regimes. These crossovers occur due to policy changes, economic shocks, or shifts in social behavior. To demonstrate the crossover dynamics of a corruption mathematical system, we use a piecewise operator. The piecewise operator is divided into three pieces: a classic or integer order operator, a fractional operator, and a stochastic operator. For the fractional order case, we use the constant proportional Caputo (CPC) operator, which is a straightforward linear combination of the Riemann–Liouville (RL) integral and the Caputo derivative. Theoretical analysis such as existence and uniqueness of solutions for the fractional case under CPC derivative, is elucidated via notions of fixed point theory, specifically the implication of Perov’s fixed point result and for the stochastic model using Ito calculus. Numerical results are presented for the proposed model. Graphical analysis of the corruption model is performed using PW operators across three distinct intervals to portray the crossover dynamics of the considered system. Also, the influence of various parameters on the crossover dynamics of the corruption model is illustrated via numerical simulations. Sensitivity of parameters is demonstrated via some statistical experiments, such as scatter plots and Pearson correlation coefficients, quantifying the relationship between key parameters of the system. The validity of the result is verified by comparing the system dynamics with real data dynamics via 2D graphs. Full article

Deep learning models typically rely on large-scale datasets with accurate annotations, yet real-world applications inevitably suffer from label noise, which severely degrades generalization—particularly for lightweight neural networks with limited capacity. Existing learning with noisy labels methods are mainly designed for over-parameterized models and are often unsuitable for resource-constrained deployment. To address this challenge, we propose a robust framework that integrates a Micro Hybrid Attention Module (MHAM) with knowledge distillation (KD) for lightweight architectures such as MobileNetV3. MHAM employs a decoupled channel–spatial attention design to enhance discriminative feature extraction while suppressing noise-sensitive background responses. From a graph–signal perspective, MHAM can be interpreted as a spectral smoothing operator that improves optimization stability. In addition, knowledge distillation with soft teacher supervision mitigates overfitting to corrupted hard labels and reduces prediction uncertainty. Extensive experiments demonstrate the effectiveness of the proposed method. On FER2013, a real-world noisy facial expression recognition benchmark, our approach achieves 68.5% accuracy with only 0.52M parameters, while reducing optimization variance by 24%. On CIFAR-10 with 40% symmetric label noise, it improves accuracy from 54.85% to 60.10%. On CIFAR-10N with multiple types of real-world human annotation noise, the proposed method consistently achieves 63.9–71.9% accuracy under different noise protocols. These results show that the proposed framework provides an efficient and robust solution for noisy label learning in lightweight facial expression and object classification on edge devices. Full article