Search Results (129)

Personalized recommendation for online learning courses stands as a critical research topic in educational technology, where algorithmic performance directly impacts learning efficiency and user experience. To address the limitations of existing studies in multimodal heterogeneous data fusion and high-order relationship modeling, this research proposes a Heterogeneous Hypergraph and Attention-based Online Course Recommendation (HHAOCR) algorithm. By constructing a heterogeneous hypergraph structure encompassing three entity types (students, instructors, and courses), we innovatively designed hypergraph convolution operators to achieve bidirectional vertex-hyperedge information aggregation, integrated with a dynamic attention mechanism to quantify important differences among entities. The method establishes computational frameworks for hyperedge-vertex coefficient matrices and inter-hyperedge attention scores, effectively capturing high-order nonlinear correlations within multimodal heterogeneous data, while employing temporal attention units to track the evolution of user preferences. Experimental results on the MOOCCube dataset demonstrate that the proposed algorithm achieves significant improvements in NDCG@15 and F1-Score@15 metrics compared to TP-GNN (enhanced by 0.0699 and 0.0907) and IRS-GCNet (enhanced by 0.0808 and 0.0999). This work provides a scalable solution for multisource heterogeneous data fusion and precise recommendation for online education platforms. Full article

Drones are widely used in urban air pollution monitoring. Although studies have focused on single-drone applications, collaborative applications for air pollution detection are relatively underexplored. This paper presents a 3D cube-based adaptive cooperative search algorithm that allows two drones to collaborate to explore air pollution. The search space is divided into cubic regions, and each drone explores the upper or lower halves of the cubes and collects data from their vertices. The vertex with the highest measurement is selected by comparing the collected data, and an adjacent cube-shaped search area is generated for exploration. The search continues iteratively until any vertex measurement reaches a predefined threshold. An improved algorithm is also proposed to address the divergence and oscillation that occur during the search. In simulations, the proposed method consumed 21 times less CPU time and required 23 times less search distance compared to linear search. Additionally, the cooperative search method using multiple drones was more efficient than single-drone exploration in terms of the same parameters. Specifically, compared to single-drone exploration, the collaborative drone search reduced CPU time by a factor of 2.6 and search distance by approximately a factor of 2. In experiments in real-world scenarios, multiple drones equipped with the proposed algorithm successfully detected cubes containing air pollution above the threshold level. The findings serve as an important reference for research on drone-assisted target exploration, including air pollution detection. Full article

Recently, the exponential arithmetic–geometric index ($EAG$) was introduced. The exponential arithmetic–geometric index ($EAG$) of a graph G is defined as $EAG\left(G\right)={\displaystyle \sum _{v_i{v}_j\in E\left(G\right)}}{e}^{{\displaystyle \frac{d_i+d_j}{2\sqrt{d_i{d}_j}}}}$, where $d_i$ represents the degree of the vertex $v_i$ in G. The characterization of extreme structures in relation to graph invariants from the class of unicyclic graphs is an important problem in discrete mathematics. Cruz et al., 2022 proposed a unified method for finding extremal unicyclic graphs for exponential degree-based graph invariants. However, in the case of $EAG$, this method is insufficient for generating the maximal unicyclic graph. Consequently, the same article presented an open problem for the investigation of the maximal unicyclic graph with respect to this invariant. This article completely characterizes the maximal unicyclic graph in relation to $EAG$. Full article

In this paper, we study the fault-tolerant metric dimension in graph theory, an important measure against failures in unique vertex identification. The metric dimension of a graph is the smallest number of vertices required to uniquely identify every other vertex based on their distances from these chosen vertices. Building on existing work, we explore fault tolerance by considering the minimal number of vertices needed to ensure that all other vertices remain uniquely identifiable even if a specified number of these vertices fails. We compute the fault-tolerant metric dimension of various chemical graphs, namely fullerenes, benzene, and polyphenyl graphs. Full article

Ensuring vehicle security and preventing unauthorized driving are critical in modern transportation. Traditional driver identification methods, such as biometric authentication, require additional hardware and may not adapt well to changing driving behaviors. This study proposes a real-time driver identification system leveraging a Machine Learning Operations (MLOps)-based platform that continuously re-trains a deep learning model using vehicle Controller Area Network (CAN) data. The system collects CAN data, converts them into Markov Transition Field (MTF) images, and classifies drivers using a ResNet-18 model deployed on the Google Cloud Platform (GCP). An automated pipeline utilizing Pub/Sub, GCP Composer, and Vertex AI ensures continuous model updates based on newly uploaded driving data. Our experimental results demonstrate that models trained only on recent data significantly outperform those incorporating historical data, highlighting the necessity of frequent retraining. The intruder detection system effectively identifies unregistered drivers, further enhancing vehicle security. By automating model retraining and deployment, this system provides an adaptive solution that accommodates evolving driving behaviors, reducing reliance on static models. These findings emphasize the importance of real-time data adaptation in driver authentication systems, contributing to enhanced vehicle security and safety. Full article

Water distribution networks (WDNs), which are responsible for delivering water of adequate quantity and quality, are vulnerable to threats such as leaks, pipe breaks, and contaminant intrusions. Hence, it is important to identify critical network elements to develop more assertive maintenance strategies for water systems. This paper aims to perform a risk assessment on leaks and pipe breaks to support the identification of critical elements in water supply systems. To this end, complex network theory (CNT) is applied as an alternative to conventional approaches that rely on multiple hydraulic simulations. Metrics such as robustness, redundancy, centrality, and connectivity are used to analyze graphs representing WDNs. Failures are modeled using hydraulic simulations to evaluate their impact on parameters such as pressure and flow. CNT metrics are then applied, including shortest path calculations between water sources and demand vertices to assess pipe importance, and vertex centrality metrics to evaluate node influence on the network. The results of the hydraulic simulations are compared with the outcomes of CNT-based analyses. Multi-criteria analysis is then employed to determine the asset maintenance priority, considering multiple failures and the associated impacts on the system. The results highlight a novel approach that shifts the focus from hydraulic state-based assessments to topology-driven analysis, reducing the influence of uncertainties inherent in water distribution network models. Full article

The dune density is an important parameter for representing the characteristics of desert geomorphology, providing a precise depiction of the undulating topography of the desert. Owing to the limitations of estimation methods and data availability, accurately quantifying dune density has posed a significant challenge; in response to this issue, we propose an innovative model to estimate dune density using a dune vertex search combined with four-directional orographic spectral decomposition. This study reveals several key insights: (1) Taklimakan Desert distributes approximately 5.31 × 10⁷ dunes, with a linear regression fit R² of 0.79 between the estimated and observed values. The average absolute error and root mean square error are calculated as 25.61 n/km² and 30.48 n/km², respectively. (2) The distribution of dune density across the eastern, northeastern, southern, and western parts of the Taklimakan Desert is relatively lower, while there is higher dune density in the central and northern areas. (3) The observation data constructed using the improved YOLOv8s algorithm and remote sensing imagery effectively validate the estimation results of dune density. The new algorithm demonstrates a high level of accuracy in estimating sand dune density, thereby providing crucial parameters for sub-grid orographic parameterization in desert regions. Additionally, its application potential in dust modeling appears promising. Full article

Vertex models have become essential tools for understanding tissue morphogenesis by simulating the mechanical and geometric properties of cells in various biological systems. These models represent cells as polygons or polyhedra, capturing cellular interactions such as adhesion, tension, and force generation. This review explores the ongoing evolution of computational vertex models, highlighting their application to complex tissue dynamics, including organoid development, wound healing, and cancer metastasis. We examine different energy formulations used in vertex models, which account for mechanical forces such as surface tension, volume conservation, and intercellular adhesion. Additionally, this review discusses the challenges of expanding traditional 2D models to 3D structures, which require the inclusion of factors like mechanical polarisation and topological transitions. We also introduce recent advancements in modelling techniques that allow for more flexible and dynamic cell shapes, addressing limitations in earlier frameworks. Mechanochemical feedback and its role in tissue behaviour are explored, along with cutting-edge approaches like self-propelled Voronoi models. Finally, the review highlights the importance of parameter inference in these models, particularly through Bayesian methods, to improve accuracy and predictive power. By integrating these new insights, vertex models continue to provide powerful frameworks for exploring the complexities of tissue morphogenesis. Full article

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structures. In this paper, we propose a new index, the weighted asymmetry index, a graph-theoretic metric quantifying the asymmetry in a network using the distances of the vertices connected by an edge. This index measures how uneven the distances from each vertex to the rest of the graph are when considering the contribution of each edge. We show how the index can capture the intrinsic asymmetries in diverse networks and is an important tool for applications in network analysis, optimization problems, social networks, chemical graph theory, and modeling complex systems. We first identify its extreme values and describe the corresponding extremal trees. We also give explicit formulas for the weighted asymmetry index for path, star, complete bipartite, complete tripartite, generalized star, and wheel graphs. At the end, we propose some open problems. Full article

A vertex-degree-based topological index $\phi$ associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by $m\left(G,k\right)$. Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index $\phi$. This number was denoted by $m_k\left(G,\phi \right)$ and called the k-matchings of G with respect to the topological index $\phi$. It turns out that $m_1\left(G,\phi \right)=\phi \left(G\right),$ and so for $k\ge 2,$ the k-matching numbers $m_k\left(G,\phi \right)$ can be viewed as kth order topological indices which involve both the topological index $\phi$ and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices ${\mathcal{SC}}_{\mathit{\alpha }}$, over the set ${\mathcal{T}}_n$ of trees with n vertices, when $\alpha$ is a real number in the interval $\left[-1,0\right).$ Full article

The continuous retained-mandrel rolling process is a promising method for titanium tube production with high efficiency and a short process. The importance of mandrel as a deformation tool supporting the inner wall is crucial. This paper thoroughly examines the influence of mandrel velocity on the deformation characteristics at the groove vertex using three approaches: numerical simulation, shear-deformation observation experiments, and microstructure analysis. The following conclusions are drawn: Decreasing the mandrel velocity enhances the penetration of shear deformation into the inner wall of the titanium tube, improves thickness uniformity, and shifts the deformation mechanism near the inner wall from twinning to dislocation slip. As a result, the volume fraction of recrystallization increases from 18.4% to 42.3%. However, the mean shear strain increases first and then decreases to a certain value as the mandrel speed decreases, which is attributed to the combined influence of the cross-shear zone and the rolling force. Full article

In materials science, the open nanotube derived from an octagonal grid is one of the most important and extensively researched compounds. Finding strategies for representing a variety of chemical compounds so that different compounds can have different representations is necessary for the investigation of chemical structures. In this work, the double edge-based resolving partition is discussed and the exchange property applied. Let $Q_1$ and $Q_2$ be two edge-resolving partition sets and $Q_1\ne Q_2$, such that $Q_1\cap Q_2\ne 0$. This shows that this structure has exchange property for edge partition. The exchange property in edge partitions is a novel work. It is introduced in this paper. The application of this work is to transform projects or objects to better places. The resolvability of these compounds is studied to gain an understanding of the chemical composition of the compounds. We perform this by using the terms vertex and edge-based distance and edge-resolving sets of graphs. Full article

The incidence of edges on vertices is a cornerstone of graph theory, with profound implications for various graph properties and applications. Understanding degree distributions and their implications is crucial for analyzing and modeling real-world networks. This study investigates the impact of vertex degree distribution on the energy landscape of graphs in network theory. By analyzing how vertex connectivity influences graph energy, the research enhances the understanding of network structure and dynamics. It establishes important properties and sharp bounds related to degree spectra and degree energy. Furthermore, the study determines the degree spectra and degree energy for several key families of graphs, providing valuable insights with potential applications across various fields. Full article

Turbulence is the most important, ubiquitous, and difficult problem of classical physics. Feynman viewed it as essentially unsolved, without a rigorous mathematical basis to describe the statistical dynamics of this most complex of fluid motion. However, the paradigm shift came in 1959, with the formulation of the Eulerian direct interaction approximation (DIA) closure by Kraichnan. It was based on renormalized perturbation theory, like quantum electrodynamics, and is a bare vertex theory that is manifestly realizable. Here, we review some of the subsequent exciting achievements in closure theory and subgrid modelling. We also document in some detail the progress that has been made in extending statistical dynamical turbulence theory to the real world of interactions with mean flows, waves and inhomogeneities such as topography. This includes numerically efficient inhomogeneous closures, like the realizable quasi-diagonal direct interaction approximation (QDIA), and even more efficient Markovian Inhomogeneous Closures (MICs). Recent developments include the formulation and testing of an eddy-damped Markovian anisotropic closure (EDMAC) that is realizable in interactions with transient waves but is as efficient as the eddy-damped quasi-normal Markovian (EDQNM). As well, a similarly efficient closure, the realizable eddy-damped Markovian inhomogeneous closure (EDMIC) has been developed. Moreover, we present subgrid models that cater for the complex interactions that occur in geophysical flows. Recent progress includes the determination of complete sets of subgrid terms for skilful large-eddy simulations of baroclinic inhomogeneous turbulent atmospheric and oceanic flows interacting with Rossby waves and topography. The success of these inhomogeneous closures has also led to further applications in data assimilation and ensemble prediction and generalization to quantum fields. Full article

Identifying patients with left ventricular ejection fraction (EF), either reduced [EF < 40% (rEF)], mid-range [EF 40–50% (mEF)], or preserved [EF > 50% (pEF)], is considered of primary clinical importance. An end-to-end video classification using AutoML in Google Vertex AI was applied to echocardiographic recordings. Datasets balanced by majority undersampling, each corresponding to one out of three possible classifications, were obtained from the Standford EchoNet-Dynamic repository. A train–test split of 75/25 was applied. A binary video classification of rEF vs. not rEF demonstrated good performance (test dataset: ROC AUC score 0.939, accuracy 0.863, sensitivity 0.894, specificity 0.831, positive predicting value 0.842). A second binary classification of not pEF vs. pEF was slightly less performing (test dataset: ROC AUC score 0.917, accuracy 0.829, sensitivity 0.761, specificity 0.891, positive predicting value 0.888). A ternary classification was also explored, and lower performance was observed, mainly for the mEF class. A non-AutoML PyTorch implementation in open access confirmed the feasibility of our approach. With this proof of concept, end-to-end video classification based on transfer learning to categorize EF merits consideration for further evaluation in prospective clinical studies. Full article