Distribution Of Nodes Research Articles

HGBER: Heterogeneous Graph Neural Network With Bidirectional Encoding Representation.

Heterogeneous graphs with multiple types of nodes and link relationships are ubiquitous in many real-world applications. Heterogeneous graph neural networks (HGNNs) as an efficient technique have shown superior capacity of dealing with heterogeneous graphs. Existing HGNNs usually define multiple meta-paths in a heterogeneous graph to capture the composite relations and guide neighbor selection. However, these models only consider the simple relationships (i.e., concatenation or linear superposition) between different meta-paths, ignoring more general or complex relationships. In this article, we propose a novel unsupervised framework termed Heterogeneous Graph neural network with bidirectional encoding representation (HGBER) to learn comprehensive node representations. Specifically, the contrastive forward encoding is firstly performed to extract node representations on a set of meta-specific graphs corresponding to meta-paths. We then introduce the reversed encoding for the degradation process from the final node representations to each single meta-specific node representations. Moreover, to learn structure-preserving node representations, we further utilize a self-training module to discover the optimal node distribution through iterative optimization. Extensive experiments on five open public datasets show that the proposed HGBER model outperforms the state-of-the-art HGNNs baselines by 0.8%-8.4% in terms of accuracy on most datasets in various downstream tasks.

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Identification of Traditional Culture Communication in Social Media Based on Information Dissemination Tree

In the era of social media platforms like Douyin, preserving the essence of traditional Chinese culture while adapting it to contemporary trends is crucial for its continued relevance and vitality. This paper delves into the practical implications of leveraging social media for cultural communication, emphasizing communication strategies tailored to platforms like Douyin. It introduces two novel algorithms for generating Douyin information dissemination trees: one based on retweeting relationships and another optimized for rapid dissemination. Comparative experiments assess the performance of these algorithms and analyze the node distribution within dissemination trees, aiming to enhance the dissemination power of traditional culture and foster its inheritance and innovation.

Bayesian varying‐effects vector autoregressive models for inference of brain connectivity networks and covariate effects in pediatric traumatic brain injury

AbstractIn this article, we develop an analytical approach for estimating brain connectivity networks that accounts for subject heterogeneity. More specifically, we consider a novel extension of a multi‐subject Bayesian vector autoregressive model that estimates group‐specific directed brain connectivity networks and accounts for the effects of covariates on the network edges. We adopt a flexible approach, allowing for (possibly) nonlinear effects of the covariates on edge strength via a novel Bayesian nonparametric prior that employs a weighted mixture of Gaussian processes. For posterior inference, we achieve computational scalability by implementing a variational Bayes scheme. Our approach enables simultaneous estimation of group‐specific networks and selection of relevant covariate effects. We show improved performance over competing two‐stage approaches on simulated data. We apply our method on resting‐state functional magnetic resonance imaging data from children with a history of traumatic brain injury (TBI) and healthy controls to estimate the effects of age and sex on the group‐level connectivities. Our results highlight differences in the distribution of parent nodes. They also suggest alteration in the relation of age, with peak edge strength in children with TBI, and differences in effective connectivity strength between males and females.

A robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for nonlinear solid mechanics

In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points in the problem domain, permitting irregular node distributions. (2) Nodes are placed also beyond the domain boundary, allowing the convenient implementation of boundary conditions of both Dirichlet and Neumann types. (3) It uses strain energy in an integral form as a part of the loss function, ensuring solution stability. (4) A well-developed gradient descendant algorithm in machine learning is employed to find the optimal solution, enabling robustness and ease in handling material and geometrical nonlinearities. (5) The proposed RPIM-NNS is compatible with parallel computing schemes. The performance of this method is tested using nonlinear problems including Cook's membrane and 3D twisting rubber problems, demonstrating its remarkable stability and robustness. This work, which seamlessly integrates the neural network solvers with mechanics governing equations and computational mechanics techniques, offers an excellent alternative for nonlinear solid mechanics problems. MATLAB codes are made available at https://github.com/JinshuaiBai/RPIM_NNS for free downloading.

Analysis of the dynamic response for Kirchhoff plates by the element-free Galerkin method

Dynamic response analysis involves examining structural behavior under dynamic loading conditions. Transient dynamic analysis emerges as a method employed to assess the responses of deformable bodies. Due to the depth analysis of transient responses for thin plates, the associated error analysis work becomes particularly important. In this work, we conduct stability and convergence analysis of the element-free Galerkin (EFG) method for the dynamic response of Kirchhoff plate model. We start by discretizing the thin plate dynamics using the EFG method for the spatial domain and the central difference scheme for the temporal domain. Stability and convergence analysis for transient responses, including deflection and moment responses, are derived similarly to those in two-dimensional transient structural dynamic analysis. The key to the analysis is transforming the governing equations and clamped boundary conditions into a weak formulation with penalty terms using the penalty method. The main results demonstrate a significant correlation between the error estimate and both nodal spacing and time step size. Additionally, the continuity of the approximation functions and the selection of penalty factors significantly affect numerical accuracy. To validate the theoretical results, we conduct numerical experiments involving clamped square and L-shaped plates with uniform and nonuniform node distributions, as well as a perforated plate model. Furthermore, we investigate the impact of node influence domains and penalty factors on numerical accuracy, facilitating parameter selection for practical engineering applications.

Inter-structure and intra-semantics graph contrastive learning for disease prediction

Ever-evolving healthcare applications have witnessed a surge in the utilization of electronic health records (EHR) for predicting future patient diagnoses. While Graph Neural Networks have demonstrated that promise in modeling disease-patient relationships, challenges arise from the sparsity and imbalance of patient and diagnostic data. Moreover, the existing models face difficulties in learning the unique disease combination features of patients. To address these challenges, we proposed a novel disease. prediction architecture based on Contrastive Learning (CL) from interstructural and intrasemantic perspectives, rather than traditional CL methods. We generated an initial global static disease graph to directly represent the relationships. among all diseases and a local dynamic disease graph to capture the indirect latent disease relationships among different patients. Multiple CL tasks were designed to learn sparse and imbalanced potentials. Relationships Between Diseases. Interstructure graph CL was first proposed to sample a graph enhancement, based on the distribution of nodes in the global disease graph. To further explore the deep embedding space of the disease, an intra-view graph CL was introduced by injecting noise at the semantic level for robust graph comparison. Experimental validation on two real EHR datasets demonstrates the superior performance of the approach by comparing it with state-of-the-art models.

An immersed boundary fast meshfree integration methodology with consistent weight learning

An immersed boundary fast integration methodology featured by a consistent weight learning is proposed to accelerate Galerkin meshfree computation. In the proposed approach, the problem domain is embedded in a rectangular spatial domain discretized by regular distributions of meshfree nodes and integration sampling points with virtual integration cells. A trimming operation of the rectangular spatial domain by the physical problem boundary with nodal discretization yields the discrete model for meshfree computation, where the integration sampling points are grouped into the interior sampling points and the near boundary sampling points which form a training set. For the interior sampling points, a natural alignment between the influence domains of meshfree shape functions and virtual integration cells can be easily realized through employing integer support sizes, which ensures a satisfactory accuracy for the basis degree correspondent normal order Gauss integration. The background cells for the domain integration are completely avoided, which greatly simplifies the preprocessing for numerical integration. Meanwhile, a machine learning module is devised to optimize the weights of near boundary integration sampling points. The key step to construct this machine learning module for weight optimization is the selection of the variational integration consistency condition as the loss function, which guarantees the convergence of Galerkin meshfree formulation. The accuracy and efficiency of the proposed weight learning immersed boundary fast integration methodology is thoroughly validated through numerical results.

Quantitative study on the acupoint effects based on complex network analysis: with the examples of the textbook networks formed by Chinese Acupuncture and Moxibustion Therapy and Practical Acupuncture and Moxibustion

By extracting the acupoint names and their main indications from cases in Chinese Acupuncture and Moxibustion Therapy and Practical Acupuncture and Moxibustion, the acupoints and their main indications are represented in a reduced dimension, establishing an "acupoint-indication" linkage. Using complex network detection results (node degree values), the specificity of acupoints was assessed. The small-world characteristics of the "acupoint-indication" network are utilized to analyze the consistency of acupoint selection in acupuncture prescriptions and strategies to avoid redundant acupoints. The results show that the "acupoint-indication" network formed by both texts exhibited an approximate "long-tail" distribution, with a large number of node degree values concentrated between 0 and 4 000, while a few nodes have degree values exceeding 10 000. There are significant differences in the number and distribution of nodes with degree values> 10 000 between the two texts. Chinese Acupuncture and Moxibustion Therapy includes 11 acupoints with multiple edges across the body, whereas Practical Acupuncture and Moxibustion contains only 2 such acupoints, located in the lower limbs. Clinically, some acupoints have a broad therapeutic effect and appear in numerous prescriptions. The division of acupoints based on node degree values can coarsely evaluate the body region specificity of acupoints' regulatory effects. The "acupoint-indication" network of Chinese Acupuncture and Moxibustion Therapy has a higher number of edges than that of Practical Acupuncture and Moxibustion, which might be related to the different historical contexts of the two texts. In the future, diagnostic and therapeutic patterns with historical continuity can be utilized to optimize acupuncture prescriptions.

Deep graph clustering by integrating community structure with neighborhood information

Deep graph clustering approaches employ deep graph neural networks to encode node embeddings and subsequently partition nodes based on these representations. Recent one-step methods have demonstrated progress; however, they often encounter issues during the representation learning phase. A primary challenge is that the encoding networks fail to capture the high-order structural information of the graph for effective clustering. We believe that combining the two distributions comprehensively characterizes the real node distribution in terms of neighborhood proximity and community aggregation to achieve better clustering. Additionally, the prevalent representation learning paradigms based on adjacency matrix reconstruction are computationally intensive and increase optimization challenges. This paper presents a novel deep graph clustering model, termed Deep Integration of Community structure and Neighborhood information (DICN). The model incorporates a graph self-attention mechanism to aggregate neighborhood-level node information, and utilizes a probabilistic generative model for edge community detection to captain community-level node information. These two-level embeddings are employed to compute explicit node membership distributions for the clustering loss. This ensures that the clustering objective effectively integrates both low-order and high-order node characteristics. The comprehensive learning process of DICN optimizes not only the node embeddings but also the clustering results by integrating the two-level losses from representation learning and the clustering loss with a weak guidance loss for clustering. Experiments on some benchmark datasets illustrate that DICN model has superior performance over existing state-of-the-art methods.

Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity

Enhancing RBF-FD Efficiency for Highly Non-Uniform Node Distributions via Adaptivity

Remote and controlled quantum teleportation network of the polarization squeezed state

Quantum teleportation is a building block in quantum computation and quantum communication. The continuous-variable polarization squeezed state is a key resource in quantum networks, offering advantages for long-distance distribution and direct interfacing of quantum nodes. Although polarization squeezed state has been generated and distributed between remote users, it is a long-standing goal to implement controlled quantum teleportation of the polarization squeezed state with multiple remote users. Here, we propose a feasible scheme to teleport a polarization squeezed state among multiple remote users under control. The polarization state is transferred between different remote quantum networks, and the controlled quantum teleportation of the polarization state can be implemented in one quantum network involving multiple remote users. The results show that such a controlled quantum teleportation can be realized with 36 users through about 6-km free-space or fiber quantum channels, where the fidelity of 0.352 is achieved beyond the classical limit of 0.349 with an input squeezing variance of 0.25. This scheme provides a direct reference for the experimental implementation of remote and controlled quantum teleportation of polarization states, thus enabling more teleportation-based quantum network protocols.

Distributed angle‐only orbit determination algorithm for non‐cooperative spacecraft based on factor graph

AbstractBayesian filtering provides an effective approach for the orbit determination of a non‐cooperative target using angle measurements from multiple CubeSats. However, existing methods face challenges such as low reliability and limited estimation accuracy. Two distributed filtering algorithms based on factor graphs employed in the sub‐parent and distributed cluster spacecraft architectures are proposed. Two appropriate factor graphs representing different cluster spacecraft structures are designed and implement distributed Bayesian filtering within these models. The Gaussian messages transmitted between nodes and the probability distributions of variable nodes are calculated using the derived non‐linear Gaussian belief propagation algorithm. Gaussian messages propagate from the deputy spacecraft to the chief spacecraft in the sub‐parent spacecraft architecture, demonstrating that the estimation accuracy converges to the centralised extended Kalman filter (EKF). Simulation results indicate that the algorithm enhances system robustness in observation node failures without compromising accuracy. In the distributed spacecraft architecture, neighbouring spacecraft iteratively exchanges Gaussian messages. The accuracy of the algorithm can rapidly approach the centralised EKF, benefiting from the efficient and unbiased transmission of observational information. Compared to existing distributed consensus filtering algorithms, the proposed algorithm improves estimation accuracy and reduces the number of iterations needed to achieve consensus.

Collaborative Operation Optimization Scheduling Strategy of Electric Vehicle and Steel Plant Considering V2G

With the shortage of fossil fuels and the increasingly serious problem of environmental pollution, low-carbon industrial production technology has become an effective way to reduce industrial carbon emissions. Electrified steel plants based on electronic arc furnaces (EAF) can reduce most carbon emissions compared with traditional steel production methods, but the production steps have fixed electricity consumption behavior, and impact loads are easily generated in the production process, which has an impact on the stability of the power system. EV has the characteristics of a mobile energy storage unit. When a large number of EVs are connected to the power grid, they can be regarded as distributed energy storage units with scheduling flexibility. Through the orderly scheduling of EVs, the spatial–temporal transfer of EV charging and discharging load can be realized. Therefore, the EV situated in the steel plant’s distribution network node has the capacity to be utilized by providing peak shaving and valley filling services for the steel production load. This study proposes an operation optimization scheduling method for EVs and steel plants. Taking the lowest overall operating cost as the objective, an optimal scheduling model considering EVs operation, steel plant, and distributed generator is established. Based on the IEEE-33 node distribution network model considering distributed generators, the proposed model is simulated and analyzed, and the effectiveness of the EV steel plant operation optimization scheduling strategy is investigated.

Highly accurate wavelet solution for the two-dimensional Bratu's problem

A modified wavelet interpolation Galerkin method (WIGM) with improved flexibility of nodal distribution is formulated and utilized to solve the Bratu's problem. Such a method treats the nonlinear term as an independent function and directly approximates it through the proposed wavelet interpolation, resulting in a low-cost discretization of the Bratu's equation with exponential nonlinearity. An efficient implementation of Newton's method to find the lower and upper branches of solution as well as the turning point is then presented. Numerical results demonstrate that the present WIGM can accurately estimate both two solution branches and turning point for the Bratu's problem. Compared with many other existing methods, the proposed WIGM also offers marked superiority in terms of accuracy when using the same node distribution. Moreover, a convergent solution to the resulting nonlinear discrete system obtained by the WIGM can be observed in a few iterations even when the initial guess significantly deviates from the exact solution. Finally, a highly accurate approximation of both two-branched solutions and the turning point for the two-dimensional Bratu's problem is obtained by the proposed WIGM.

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.

On individual leaf depths of trees

We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work of Panholzer and Prodinger, we apply this method to study the depth distributions of individual nodes or leaves in rooted binary trees, plane trees, noncrossing trees, and increasing trees; the height distributions of individual vertices and individual steps in Dyck paths; and the number of diagonals separating two fixed sides of a convex polygon in a triangulation or dissection. We obtain both exact and asymptotic results, which sometimes refine known formulas or provide combinatorial proofs of results from the probability literature.

Improving analytic approximations of TSP tour lengths with adjustment factors

Optimizing Traveling Salesman Problem (TSP) tours requires substantial computational effort, leading researchers to develop approximations relating tour length to the number of visited points, n. Existing models, such as the √nA predictor, effectively approximate tour lengths for large-capacity vehicles but sacrifice accuracy for small n values relevant for most practical applications. Consequently, this study addresses this gap by proposing models with uniform node distributions, which incorporate realistic factors, such as central vs. random starting points and various service zone shapes. These factors are then integrated into a single equation, enhancing applicability. Furthermore, the exponent of n is statistically estimated to be significantly different from 0.5, challenging previous studies. Our proposed model estimates TSP tour lengths more accurately, particularly for small n values, and maintains accuracy for large n values, with errors below 3.11% for up to 600 points. This model offers a more precise and versatile alternative to current models.

Fluviomorphic trajectories for dryland ephemeral stream channels following extreme flash floods

AbstractEphemeral alluvial streams pose globally significant flood hazards to human habitation in drylands, but sparse data for these regions limit understanding of the character and impacts of extreme flooding. In this study, we document decadal changes in dryland ephemeral channel patterns at two sites in the lower Colorado River Basin (southwestern United States) that were ravaged by extraordinary flash floods in the 1970s: Bronco Creek, Arizona (1971), and Eldorado Canyon, Nevada (1974). We refer to these two floods as ‘fluviomorphic erasure events’, because they produced blank slates for the channels that were gradually moulded by more frequent but much smaller flood events. We studied georectified aerial photos that span ~60 years at each site to show that both study sites recovered to their pre‐flood condition after ~25 years. We employ channel network metrics: stream‐link area (SLA), geometric braiding index and junction‐node density. Each metric decreased during the short‐duration extreme flood erasure events. Subsequently, a fluviomorphic trajectory at a decadal tempo returned the channels to pre‐flood values. The SLA decreased at rates of 3.6%–4.1% per year in the decade following the floods. The extreme flood events decreased the pre‐flood geometric braiding index at the two sites by 56%–68%, and it took 15–24 years for this index to recover to pre‐flood values. In contrast, it took 30–35 years for the channels to recover to a uniform pre‐flood channel form, as indicated by the spatial distribution of bars and junction nodes. Our results document baseline examples of ephemeral stream channel evolution trajectories, as future climatic change will likely accelerate increases in the magnitudes and frequencies of extreme floods and geomorphic erasure events.

Advanced human immunodeficiency virus (HIV) does not affect ability to utilize lymphadenopathy in assessment of drug reaction with eosinophilia and systemic symptoms syndrome in HIV and tuberculosis: Prospective comparative study

RegiSCAR validation criteria for drug reaction with eosinophilia and systemic symptoms (DRESS) includes lymphadenopathy, a frequent feature of both tuberculosis (TB) and human immunodeficiency virus (HIV). TB is the most common HIV-associated coinfection. Advanced HIV is associated with lymph node (LN) fibrosis. It is not clear if this negatively affects case validation in HIV-associated DRESS. To answer this question, we designed a prospective descriptive study to assess lymphadenopathy in various combinations of comorbid HIV, TB, and DRESS. We sought to describe the prevalence of DRESS-associated lymphadenopathy and characterize LN quality, size, and distribution in a high HIV-TB burden setting over time. We prospectively and systematically examined LN in 25 consecutive acute DRESS cases hospitalized at a South African tertiary-care center and 10 hospitalized non-DRESS HIV-TB coinfected controls. Fourteen (56%) of 25 patients were HIV infected, with a median (interquartile range) CD4 count of 254 (66-478) cells/mm³, and 7 of 14 were coinfected with TB. Using RegiSCAR criteria, 12 (46%) of 25 were definite DRESS cases, 8(31%) of 25 probable, and 5 (23%) of 25 possible. Possible cases were excluded in the analysis. Fifteen (75%) of 20 subjects had LN in ≥2 anatomic sites, including all 7 patients with HIV-TB coinfection. In contrast, 1 (20%) of 5 hospitalized non-DRESS HIV-TB coinfected controls had LN. Cervical LN, in 15 (88%) of 17, was most common, followed by axillary (76%) and inguinal (59%). Cervical LN ranged between 1 and 2 cm in size. Among the 8 (32%) of 25 subjects with follow-up data, LN had regressed in all within 6 weeks of stopping the offending drug and initiating TB treatment. There was no correlation with CD4 cell count and LN. Lymphadenopathy is a common feature of acute DRESS, even among HIV-TB-coinfected patients with advanced immunosuppression.