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Folk art education is an important way to inherit and develop traditional culture. In this paper, the cascade propagation of typical decentralized Internet-social networks is modeled as a propagation dynamic graph model, and an enhanced graph-aware neural network is proposed through the analysis of the learning process of neural graph networks. A further recurrent graph-aware neural network is proposed for the characteristics of information dissemination in the decentralized Internet, and the transmission and development of traditional culture in folk art education are analyzed based on this network model. In folk art education, the most common type of traditional culture dissemination is ink painting, accounting for 20.32%, which is 6.91%, 12.35%, and 14.86% higher than other types, respectively. From 2014 to 2021, the percentage of Internet-based communication media increased from 12.47% to 24.78%, an increase of 12.31 percentage points. The analysis based on the decentralized Internet can accurately extract the characteristics of traditional culture integrated into folk art education, which helps to inherit further and promote the excellent traditional culture.

Coastal acoustic tomography (CAT) is a remote sensing technique that utilizes acoustic methodologies to measure the dynamic characteristics of the ocean in expansive marine domains. This approach leverages the speed of sound propagation to derive vital ocean parameters such as temperature and salinity by inversely estimating the acoustic ray speed during its traversal through the aquatic medium. Concurrently, analyzing the speed of different acoustic waves in their round-trip propagation enables the inverse estimation of dynamic hydrographic features, including flow velocity and directional attributes. An accurate forecasting of inversion answers in CAT rapidly contributes to a comprehensive analysis of the evolving ocean environment and its inherent characteristics. Graph neural network (GNN) is a new network architecture with strong spatial modeling and extraordinary generalization. We proposed a novel method: employing GraphSAGE to predict inversion answers in OAT, using experimental datasets collected at the Huangcai Reservoir for prediction. The results show an average error 0.01% for sound speed prediction and 0.29% for temperature predictions along each station pairwise. This adequately fulfills the real-time and exigent requirements for practical deployment.

The K -core of a graph is the unique maximum subgraph within which each vertex connects to K or more other vertices. The optimal K -core attack problem asks to delete the minimum number of vertices from the K -core to induce its complete collapse. A hierarchical cycle-tree packing model is introduced here for this challenging combinatorial optimization problem. We convert the temporally long-range correlated K -core pruning dynamics into locally tree-like static patterns and analyze this model through the replica-symmetric cavity method of statistical physics. A set of coarse-grained belief propagation equations are derived to predict single vertex marginal probabilities efficiently. The associated hierarchical cycle-tree guided attack (hCTGA) algorithm is able to construct nearly optimal attack solutions for regular random graphs and Erdös-Rényi random graphs. Our cycle-tree packing model may also be helpful for constructing optimal initial conditions for other irreversible dynamical processes on sparse random graphs.

We present a numerical analysis on injection-induced crack propagation and coalescence in brittle rock. The DEM network coupling model in PFC is modified to capture the evolution of fracture geometry. An improved fluid flow model for fractured porous media is proposed and coupled with a bond-based DEM model to simulate the interactions among cracks induced by injecting fluid in two nearby flaws at identical injection rates. The material parameters are calibrated based on the macro-properties of Lac du Bonnet granite and KGD solution. A grain-based model, which generates larger grains from assembles of particles bonded together, is calibrated to identify the microscopic mechanical and hydraulic parameters of Lac du Bonnet granite such that the DEM model yields a ratio between the compressive and tensile strength consistent with experiments. The simulations of fluid injection reveal that the initial flaw direction plays a crucial role in crack interaction and coalescence pattern. When two initial flaws are aligned, cracks generally propagate faster. Some geometrical measures from graph theory are used to analyze the geometry and connectivity of the crack network. The results reveal that initial flaws in the same direction may lead to a well-connected crack network with higher global efficiency.

Accurate and timely traffic flow prediction plays a crucial role in improving road utilization, reducing congestion, and optimizing public transportation management. However, modern urban traffic faces challenges such as complex road network structures and the variation in traffic flow across different temporal and spatial scales. These issues lead to complex spatiotemporal correlations and heterogeneity, resulting in low prediction accuracy and poor real-time performance of existing models. In this work, we propose a novel traffic flow prediction model called TMDCN (Temporal Attention and Multi-Graph Adjacency Fusion Using DynamicChebNet), which integrates temporal attention and multi-graph adjacency matrix fusion. First, to address the difficulty of capturing dependencies across multiple time scales, we construct a Temporal Feature Extraction Block that combines attention mechanisms with multi-scale convolutional layers, enhancing the model’s ability to handle complex traffic pattern changes and capture flow variations and temporal dependencies. Next, we leverage multi-graph adjacency matrix fusion and dynamic Chebyshev graph convolutional networks to capture the spatial dependencies of the traffic network. Experiments on the PeMS04 and PeMS08 datasets show that, compared to conventional methods, the proposed method reduces the Mean Absolute Error (MAE) of traffic flow prediction one hour ahead to 18.33 and 13.72, respectively. The source code for this paper is available at https://github.com/tyut-zjb/TMDCN .

Industrial symbiosis network (ISN) is crucial to improving resource utilization efficiency and promoting sustainable development. In order to mitigate the damage caused to symbiotic systems by risk propagation, this paper constructs a directed weighted multilayer hypernetwork model that considers bounded rational decision and risk propagation coupling (UAPAHU−SIS), providing a new method for risk management in industrial symbiosis networks. This paper constructs a weighted hypernetwork model to simulate the interaction of risk information in a symbiotic network and uses a time-varying adaptive propagation mechanism to describe the changes in bounded rational decisions made by enterprises during the risk information interaction process. A directed weighted network is developed to simulate the evolution process of an industrial symbiosis network, with the network topology representing the risk propagation path. The study also considers the roles of mass media and crowd effects and innovatively introduces the assumption of decision incubation periods. The proposed coupled dynamic model is theoretically analyzed and numerically simulated by using the Microscopic Markov Chain Approach (MMCA). The findings indicate that enhancing the enterprises’ risk response willingness and risk perception ability, improving the risk recovery ability, and cooperating with timely and accurate media reports can effectively inhibit the risk propagation on ISN.

The accurate assessment of node influence is of vital significance for enhancing system stability. Given the structural redundancy problem triggered by the network topology deviation when an empirical network is copied, as well as the dynamic characteristics of the empirical network itself, it is difficult for traditional static assessment methods to effectively capture the dynamic evolution of node influence. Therefore, we propose a heuristic-based spatiotemporal feature node influence assessment model (HEIST). First, the zero-model method is applied to optimize the network-copying process and reduce the noise interference caused by network structure redundancy. Second, the copied network is divided into subnets, and feature modeling is performed to enhance the node influence differentiation. Third, node influence is quantified based on the spatiotemporal depth-perception module, which has a built-in local and global two-layer structure. At the local level, a graph convolutional neural network (GCN) is used to improve the spatial perception of node influence; it fuses the feature changes of the nodes in the subnetwork variation, combining this method with a long- and short-term memory network (LSTM) to enhance its ability to capture the depth evolution of node influence and improve the robustness of the assessment. Finally, a heuristic assessment algorithm is used to jointly optimize the influence strength of the nodes at different stages and quantify the node influence via a nonlinear optimization function. The experiments show that the Kendall coefficients exceed 90% in multiple datasets, proving that the model has good generalization performance in empirical networks.

Purpose – The purpose of this paper is to theoretically study the problem of the peristaltic flow of Jeffrey fluid in a non-uniform rectangular duct under the effects of Hall and ion slip. An incompressible and magnetohydrodynamics fluid is also taken into account. The governing equations are modelled under the constraints of low Reynolds number and long wave length. Recent development in biomedical engineering has enabled the use of the periastic flow in modern drug delivery systems with great utility. Design/methodology/approach – Numerical integration is used to analyse the novel features of volumetric flow rate, average volume flow rate, instantaneous flux and the pressure gradient. The impact of physical parameters is depicted with the help of graphs. The trapping phenomenon is presented through stream lines. Findings – The results of Newtonian fluid model can be obtained by taking out the effects of Jeffrey parameter from this model. No-slip case is a special case of the present work. The results obtained for the flow of Jeffrey fluid reveal many interesting behaviours that warrant further study on the non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear-thinning reduces the wall shear stress. Originality/value – The results of this paper are new and original.

Current methods for public opinion propagation prediction struggle to jointly model temporal dynamics, structural complexity, and dynamic node influence in evolving social networks. To overcome these limitations, this paper proposes a public opinion dissemination prediction model based on the integration of dynamic time-weighted Rényi entropy (DTWRE) and graph neural networks. By incorporating a time-weighted mechanism, the model devises two tiers of Rényi entropy metrics—local node entropy and global time-step entropy—to effectively quantify the uncertainty and complexity of network topology at different time points. Simultaneously, by integrating DTWRE features with high-dimensional node embeddings generated by Node2Vec and utilizing GraphSAGE to construct a spatiotemporal fusion modeling framework, the model achieves precise prediction of link formation and key node identification in public opinion dissemination. The model was validated on multiple public opinion datasets, and the results indicate that, compared to baseline methods, it exhibits significant advantages in several evaluation metrics such as AUC, thereby fully demonstrating the effectiveness of the dynamic time-weighted mechanism in capturing the temporal evolution of public opinion dissemination and the dynamic changes in network structure.

In this work, a thermodynamically consistent three-dimensional (3D) small strain-based theory to describe the deformation and fracture in quasi-brittle and brittle elastic solids is presented. The description of fracture at a material point resembles the microplane fracture approach developed by Bažant et al. (J Eng Mech 126(9):944–953, 2000, J Eng Mech 122(3): 245–254, 1996), but the present theory has the following novel features: (a) a probabilistic description of fracture propagation is used, developing evolution equations for the probability of a microcrack occurring at a given location and (b) a kinematical approach to modeling crack opening and closing. The new 3-D constitutive theory, in which elements were recently proposed by Srinivasa et al. (Mech Adv Mater Struct 80(27–30):2099–2108, 2020), has been computationally implemented within a Graph-based Finite-Element Analysis (GraFEA) framework developed by Reddy and colleagues (Khodabakhshi et al. in Meccanica 51:3129–3147, 2016, Acta Mech 230:3593–3612, 2019), and it has also been implemented into the dynamics-based Abaqus/Explicit (Reference manuals. Simulia-Dassault Systémes, 2020) finite element program through a vectorized user–material subroutine interface. Our computational approach for fracture modeling is intra-element-based, which is central to the GraFEA approach rather than inter-element fracture, as is done in cohesive zone-based numerical methods, together with selective non-locality where the non-locality is only for probability evolution motivated by population dynamic models that allows us to perform efficient implementation of the code without special elements or other numerical artifacts. Several homogeneous deformation cases for fracture in cementitious and brittle elastic materials were modeled, and the response obtained from the constitutive theory and its finite element implementation are qualitatively similar to that obtained in the literature. In particular, we show that our computational procedure is able to model crack closure in solids in a robust, relatively simple and elegant manner instead of relying on a previously developed method of decomposing the stored energy into “positive” and “negative” portions (Amor et al. in J Mech Phys Solids 57(8):1209–1229, 2009, Miehe et al. in Int J Numer Meth Eng 83:1273–1311, 2010).