Convolutional neural networks (CNN) have attracted much attention as a commonly used method for hyperspectral image (HSI) classification in recent years, however, CNNs can only be applied to Euclidean data and have limitations in dealing with relationships due to the limitations of local feature extraction. However, each pixel of a hyperspectral image contains a set of spectral bands that are correlated and interact with each other, and the methods used to process Euclidean data cannot effectively obtain these correlations. In contrast, the graph convolutional network (GCN) can be used in non-Euclidean data, but usually leads to oversmoothing and ignoring local detail features due to the need for superpixel segmentation processing to reduce computational effort. To overcome the above problems, we constructed a network a fusion network based on GCN and CNN, which contains two branches: a graph convolutional network based on superpixel segmentation and a convolutional network with added attention mechanism. The graph convolu-tional branch can extract the structural features and capture the relationships between the nodes, and the convolutional branch can extract the detailed features in the local fine region. Owing to the fact that the features extracted from the two branches are different, the classification performance can be improved by fusing the complementary features extracted from the two branches. To vali-date the proposed algorithm, experiments were conducted on three widely used datasets, namely Indian Pines, Pavia University, and Salinas, and the overall accuracy of 98.78% was obtained in the Indian Pines dataset, and the overall accuracy of 98.99% and 98.69% was obtained in the other two datasets. The results showed that the proposed fusion network can obtain richer features and achieve high classification accuracy.

To address the challenge of recognizing ship states accurately amidst the complexities of marine environments, this study proposes a novel ship state recognition approach leveraging a graph convolutional neural network (GCNN). Initially, the method extracts canonical and efficient ship motion trajectories from AIS data. Subsequently, a state recognition network tailored for ship motion trajectories is devised and implemented employing graph convolution. Notably, the accuracy of this model is enhanced through the introduction of novel weights and optimization of the Adj parameter. Experimental evaluations conducted on a ship state dataset demonstrate significant performance improvements. Specifically, the proposed recognition network achieves a recognition accuracy of 98.3% for regulated ship trajectories, marking an impressive 8.4% enhancement over traditional convolutional neural networks. This advancement holds promise for enhancing ship state recognition accuracy across diverse maritime applications including maritime supervision, navigation safety, and ship management.

The root system plays an irreplaceable role in plant growth. Its improvement can increase crop productivity. However, such system is still mysterious for us. The underlying mechanism has not been fully uncovered. The investigation on proteins related to the root system is an important means to complete this task. In the previous time, lack of root-related proteins makes it impossible to adopt machine learning methods for designing efficient models for the discovery of novel root-related proteins. Recently, a public database on root-related proteins was set up and machine learning methods can be applied in this field. In this study, we proposed a machine learning based model, named Graph-Root, for identification of root-related proteins. The features derived from protein sequences and one network were extracted, where the former features were processed by graph convolutional neural network and multi-head attention, and the later features abstracted the linkage between proteins. These features were fed into the fully connected layer to make prediction. The 5-fold cross-validation and independent tests suggested its good performance. It also outperformed the only one previous model, SVM-Root. Furthermore, the importance of each feature type and component in the proposed model was investigated.

Graph neural networks and graph convolutional networks are effective at representing complex relationships. We attempt to apply them to sports analytics by reviewing existing applications in sports. These methodologies leverage the inherent graph structure of sports data, capturing interactions among players, teams, and game events. By systematically examining various studies, we highlight how GNNs and GCNs can enhance performance prediction, player evaluation, and tactical analysis in sports. Our review emphasizes the unique advantages these models offer over traditional analytical approaches, particularly in their ability to account for the dynamic and interconnected nature of sports activities. We conclude by identifying potential areas for future research and application, suggesting that the integration of advanced graph-based techniques could significantly advance the field of sports analytics.

This paper explores the use of GNN architectures, including Graph Convolutional Networks (GCNs), Graph Attention Networks (GATs), and GraphSAGE, in modeling blockchain data. A specific focus is given to their applications in cryptocurrency transaction networks, where GNNs can detect fraudulent activities and track illicit fund flows by learning from transaction patterns and network structure. Additionally, future directions for GNN research in blockchain are discussed, including scalability challenges, privacy-preserving models, and multi-chain graph analysis. Through these advancements, GNNs offer significant potential for enhancing the security, transparency, and efficiency of blockchain and cryptocurrency ecosystems. This paper also shows an example of fraud detection for Ethereum cryptocurrencies.

Financial fraud refers to the act of obtaining financial benefits through dishonest means. Such acts not only disrupt the order of the financial market, but also harm social and economic development, and breed other illegal and criminal acts. With the proliferation of the internet and online payment methods, many fraudulent activities and money laundering have shifted from offline to online, posing a significant challenge for regulators. In this work, we proposed a novel detection model by utilizing the graph neural network. Specifically, the general model structure includes the combination of Graph Convolutional Network (GCN) and Graph Attention Network (GAT), which can effectively capture the complex relationships and features in the financial transaction network. By building a multilayer graph neural network, the model can perform deep learning on the implicit patterns between nodes, thereby improving the accuracy of fraud detection. Experimental analysis results show that the performance of the proposed method on multiple public datasets is better than that of traditional methods, showing its potential in practical application.

Drug development is a lengthy process with a high failure rate. Increasingly, machine learning is utilized to facilitate the drug development processes. These models aim to enhance our understanding of drug characteristics, including their activity in biological contexts. However, a major challenge in drug response (DR) prediction is model interpretability as it aids in the validation of findings. This is important in biomedicine, where models need to be understandable in comparison with established knowledge of drug interactions with proteins. drGAT, a graph deep learning model, leverages a heterogeneous graph composed of relationships between proteins, cell lines, and drugs. drGAT is designed with two objectives: DR prediction as a binary sensitivity prediction and elucidation of drug mechanism from attention coefficients. drGAT has demonstrated superior performance over existing models, achieving 78\% accuracy (and precision), and 76\% F1 score for 269 DNA-damaging compounds of the NCI60 drug response dataset. To assess the model's interpretability, we conducted a review of drug-gene co-occurrences in Pubmed abstracts in comparison to the top 5 genes with the highest attention coefficients for each drug. We also examined whether known relationships were retained in the model by inspecting the neighborhoods of topoisomerase-related drugs. For example, our model retained TOP1 as a highly weighted predictive feature for irinotecan and topotecan, in addition to other genes that could potentially be regulators of the drugs. Our method can be used to accurately predict sensitivity to drugs and may be useful in the identification of biomarkers relating to the treatment of cancer patients.

The popularity and development of social media has made it more and more convenient to spread rumors, and it has become especially important to detect rumor information from massive amounts of information. Most of the traditional rumor detection methods use content characteristics or propagation structure to mine rumor characteristics, ignoring the fusion characteristics of content and structure and their interaction characteristics. Therefore, a novel rumor detection method based on heterogeneous convolutional networks is proposed. Firstly, this paper constructs a heterogeneous map of joint rumor content and propagation structure to explore the interaction between content and propagation structure during rumor propagation and obtain rumor representation. On that basis, this paper uses the deep residual graph convolutional neural network to construct the content and structure interaction information of the current network propagation model. Finally, this paper uses the two datasets of Twitter15 and Twitter16 to verify the proposed method. Experimental results show that the proposed method has higher detection accuracy than the traditional rumor detection method.

Paraphrase generation is an important yet challenging task in NLP. Neural network-based approaches have achieved remarkable success in sequence-to-sequence(seq2seq) learning. Previous paraphrase generation work generally ignores syntactic information regardless of its availability, with the assumption that neural nets could learn such linguistic knowledge implicitly. In this work we make an endeavor to probe into the efficacy of explicit syntactic information for the task of paraphrase generation. Syntactic information can appear in the form of dependency trees which could be easily acquired from off-the-shelf syntactic parsers. Such tree structures could be conveniently encoded via graph convolutional networks(GCNs) to obtain more meaningful sentence representations, which could improve generated paraphrases. Through extensive experiments on four paraphrase datasets with different sizes and genres, we demonstrate the utility of syntactic information in neural paraphrase generation under the framework of seq2seq modeling. Specifically, our GCN-enhanced models consistently outperform their syntax-agnostic counterparts in multiple evaluation metrics.

Link prediction is to complete the missing links in the network or to predict the generation of new links according to the current network structure information, which is very important for mining and analyzing the evolution of the network such for construction and analysis of logical architecture in 6G network. Link prediction algorithms based on node similarity need predefined similarity functions, which is highly hypothetical and only applies to specific network structures without generality. To solve this problem, this paper proposes a link prediction algorithm based on the subgraph of the target node pair. In order to automatically learn the graph structure characteristics, the algorithm firstly extracts the h-hop subgraph of the target node pair, and then predicts whether the target node pair will be linked according to the subgraph. Experiments on seven real data sets show that the link prediction algorithm based on target node pair subgraph is suitable for various network structures and superior to other link prediction algorithms.

Simulated Annealing (SA), Tabu Search (TS), and Variable Neighborhood Search (VNS) are well-established single-solution-based metaheuristics known for their efficiency. In this paper, we explore the application of these techniques to enhance the performance of graph network models, specifically Graph Neural Networks (GNNs) and Graph Convolutional Networks (GCNs). By leveraging these metaheuristics, we aim to optimize key aspects of graph-based learning, such as hyperparameter tuning, architecture design, feature selection, and graph structure learning. Our approach demonstrates how these metaheuristics can improve the generalization, efficiency, and robustness of GNNs/GCNs, facilitating their use in large-scale graph-based tasks. The proposed framework illustrates the potential of combining advanced optimization techniques with state-of-the-art graph machine learning models.

The task of human action recognition (HAR) based on skeleton data is a challenging yet crucial technique owing to its wide-ranging applications in numerous domains, including patient monitoring, security surveillance, and observation of human-machine interactions. While numerous algorithms have been proposed in an attempt to distinguish between a myriad of activities, most practical applications necessitate highly accurate detection of specific activity types. This study proposes a novel and highly accurate spatiotemporal graph autoencoder network for HAR based on skeleton data. Furthermore, an extensive investigation was conducted employing diverse modalities. To this end, a spatiotemporal graph autoencoder was constructed to automatically learn both spatial and temporal patterns from human skeleton datasets. The powerful graph convolutional network, designated as GA-GCN, developed in this study, notably outperforms the majority of existing state-of-the-art methods when evaluated on two common datasets, namely NTU RGB+D and NTU RGB+D 120. On the first dataset, the proposed approach achieved accuracies of 92.3\% and 96.8\% for the cross-subject and cross-view evaluations, respectively. On the more challenging NTU RGB+D 120 dataset, GA-GCN attained accuracies of 88.8\% and 90.4\% for the cross-subject and cross-set evaluations, respectively.

Aiming at the problem that the existing human skeleton behavior recognition methods are insensitive to human local movements and have inaccurate recognition in distinguishing similar behaviors, a multi-scale spatio-temporal graph convolution method incorporating multi-granularity features is proposed for human behavior recognition.Firstly, a skeleton fine-grained division strategy is proposed, which initializes the skeleton data into data streams of different granularities.Using a normalized Gaussian function, an adaptive cross scale feature fusion layer is designed for feature fusion between different granularities, and fine-grained features guide the model to focus on discriminative feature expressions between similar behaviors. Secondly, a sparse multi-scale adjacency matrix is introduced to solve the bias weighting problem that amplifies the multi-scale spatial domain modeling process under multi granularity conditions. Finally, an end-to-end graph convolutional neural network is constructed to improve the feature expression ability of spatio-temporal receptive field information and enhance the robustness of recognition between similar behaviors. The feasibility of the proposed algorithm was verified on the public behavior recognition dataset MSR Action 3D, with a recognition rate of 95.67%, which is superior to most existing behavior recognition methods.

A growing area in neurosciences is focused on the modeling and analysis the complex system of connections in neural systems, i.e. the connectome. Here we focus on the representation of connectomes by using graph theory formalisms. The human brain connectomes are usually derived from neuroimages; the analyzed brains are co-registered in the image domain and brought to a common anatomical space. An atlas is then applied in order to define anatomically meaningful regions that will serve as the nodes of the network - this process is referred to as parcellation. Recently, it has been proposed to perform atlas-free random brain parcellation into nodes and align brains in the network space instead of the anatomical image space to define network nodes of individual brain networks. In the network domain, the question of comparison of the structure of networks arises. Such question is tackled by modeling the comparison of brain network as a network alignment (NA) problem. In this paper, we first defined the NA problem formally, then we applied three existing state of the art of multiple alignment algorithms (MNA) on diffusion MRI-derived brain networks and we compared the performances. The results confirm that MNA algorithms may be applied in cases of atlas-free parcellation for a fully network-driven comparison of connectomes.

In the field of recommender systems, difficult negative samples that are easily misclassified by classifiers have higher learning value. In order to solve the problem that the existing graph convolutional network lacks the exploration of negative sampling strategy, a multivariate sampling based on graph convolution collaborative filtering recommendation model was proposed. Firstly, part of the information in the positive sample was injected into the negative sample, and the high quality difficult negative sample was selected by the inner product method. Then, contrastive learning is used to maximize the similarity between the difficult negative samples and the positive samples, so that the difficult negative samples are as close to the positive samples as possible in the feature space. Ultimately, a multi-task approach was employed to concurrently enhance both the recommendation supervision task and the contrastive learning task. To validate the effectiveness of our approach, we conducted comparative evaluations utilizing three publicly accessible datasets. The experimental outcomes indicate that our proposed model surpasses the baseline model in terms of performance.

In this paper, we explore the theoretical foundation of Graph Neural Network (GNN) model and apply it to various traditional supply chain logistics problem. In particular, we study the Route Optimization Problem, Demand Forecasting Problem, Risk Assessment and Anomaly Detection, Supplier Section and Procurement Optimization, Inventory Optimization Problem, and Green Supply Chain Problem. The study helps us the expand the use the GNN and gives daily supply chain management a boost.

With the rapid development of wireless communication networks, using AI to predict complex city-scale network traffic has become a significant research challenge. This paper, based on a Graph Convolutional Network (GCN) architecture, proposes a novel wireless network traffic prediction algorithm focused on predicting city-level communication traffic data at an hourly granularity. The algorithm enhances prediction accuracy through two key innovations: first, we introduce a hierarchical attention architecture that combines dynamic and static attention mechanisms. The static attention mechanism, based on wireless channel models, captures fixed spatial relationships between base stations, such as inter-station distances and stable connections. The dynamic attention mechanism, on the other hand, dynamically adjusts to account for time-varying traffic patterns, such as rush hours and holiday effects, enabling the model to adapt to temporal variations in network traffic. These two attention mechanisms are seamlessly integrated within the model through feature concatenation and interactive learning, allowing the model to capture both spatial and temporal characteristics of network traffic simultaneously. Secondly, we innovatively introduce a strategy for adjusting the aggregation iterations of the Graph Convolutional Network (GCN) based on the Laplacian matrix. By leveraging the spectral information provided by the Laplacian matrix, we dynamically determine the depth of the graph convolutional network, thereby avoiding issues of over-smoothing or underfitting and ensuring stable performance in complex network structures. Experimental results demonstrate that the proposed algorithm significantly outperforms existing methods across multiple dataset, particularly in predicting network traffic data with intricate spatiotemporal characteristics.

There is a considerable amount of research in online social networks, most of which focuses on the structural analysis of social graphs. The interpersonal relationships of social networks, especially friend circle, can solve the cold start and sparsity problems, and through the relationship between social networks can effectively recommend users' favorite items (items), such as music , videos, brands/products, preferred tags, location, services, etc. User relationships in social networks are diverse and there are many different perspectives on different social networks. Associations among users can form multi-layered composite networks, and multi-layered social networks present new challenges and opportunities. Different relationships can influence users' preferences to different degrees, which in turn affects their behavior. Therefore, fusing multiple social networks is an effective way to improve recommendation. Although some studies have started to address multiple social network recommendations, simple linear superposition cannot reflect the coupling and nonlinear association between multiple social networks. In this paper, we propose a graph neural network recommendation model under social relationships based on this background. We first propose to compute the 2nd order collaborative signals and their intensities directly from the neighboring matrix for updating the node embedding of the graph convolution layer. Secondly by embedding historical evaluations, various social networks constituting different dimensions, the attention integration of user preferences by different social networks is achieved, and its effectiveness and scalability are demonstrated in theoretical derivation and experimental validation. The theoretical derivation and experimental validation demonstrate its effectiveness and scalability.

This paper investigates the integration of Graph Neural Networks (GNNs) and incremental learning for blockchain applications, with a focus on fraud detection, anomaly detection, and smart contract verification. By leveraging graph structure exploitation, GNNs can propagate information across nodes, reducing label dependency. Incremental learning enhances the model's adaptability to evolving blockchain networks, allowing continual learning without full retraining. Together, these technologies provide a scalable, efficient solution for improving security, performance, and adaptability in decentralized financial systems and smart contract environments.

Selecting road networks in cartographic generalization has consistently posed formidable challenges, driving research towards the application of intelligent models. Despite previous efforts, the accuracy and connectivity preservation in these studies, particularly when dealing with road types of similar sample sizes, still warrant improvement. To address these shortcomings, we introduce a Heterogeneous Graph Attention Network (HAN) for road selection, where feature masking method is initially utilized to assess the significance of road features. Concentrating on the most relevant features, two meta-paths are introduced within the HAN framework: one for aggregating features of the same road type within the first-order neighborhood, emphasizing local connectivity, and another extending this aggregation to the second-order neighborhood, capturing a broader spatial context. For a comprehensive evaluation, we introduce a set of metrics considering both quantitative and qualitative aspects of the road network. Compared to traditional neural networks, our HAN model demonstrates superior accuracy and F1-score, particularly for road types with comparable samples. Additionally, it enhances the overall connectivity of the selected network. In summary, our HAN-based method provides an advanced solution for road network selection, surpassing previous approaches in terms of accuracy and connectivity preservation.

With the improvement of software copyright protection awareness, code obfuscation technology plays a crucial role in protecting key code segments. As the obfuscation technology becomes more and more complex and diverse, it has spawned a large number of malware variants, which make it easy to evade the detection of anti-virus software. Malicious code detection mainly depends on binary code similarity analysis. However, the existing software analysis technologies are difficult to deal with the growing complex obfuscation technologies. To solve this problem, this paper proposes a new obfuscation-resilient program analysis method, which is based on the data flow transformation relationship of the intermediate representation and the graph network model. In our approach, we first construct the data transformation graph based on LLVM IR. Then, we design a novel intermediate language representation model based on graph networks, named DFSGraph, to learn the data flow semantics from DTG. DFSGraph can detect the similarity of obfuscated code by extracting the semantic information of program data flow without deobfuscation. Extensive experiments prove that our approach is more accurate than existing deobfuscation tools when searching for similar functions from obfuscated code.

Animal models of diseases in particular, the mice, are considered to be the cornerstone for translational research in immunology. The aim of the present study is to model the geometry and analyze the network structure of murine lymphatic system (LS). The algorithm for building the graph model of the LS makes use of anatomical data. To identify the edge directions of the graph model, a mass balance approach to lymph dynamics based on Hagen-Poiseuille equation is applied. It is the first study in which a geometric model of the murine LS has been developed and characterized in terms of its structural organization and the lymph transfer function. Our study meets the demand for quantitative mechanistic approaches in the growing field of immunoengineering to utilize or exploit the lymphatic system for immunotherapy.

Here we present a fast and highly scalable community structure preserving network module detection that recursively integrates graph sparsification and clustering. Our algorithm, called SparseClust, participated in the most recent DREAM community challenge on disease module identification, an open competition to comprehensively assess module identification methods across a wide range of biological networks.

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel graph neural network model designed to efficiently address complex matching problems at scale. HybridGNN combines the capabilities of Graph Attention Networks (GAT), GATv2, and Graph SAGE (SAGEConv) layers, integrating techniques like mixed precision training, gradient accumulation, and Jumping Knowledge networks to enhance computational efficiency and performance. Additionally, the incorporation of Graph Isomorphism Networks (GIN) enhances the model's ability to discriminate between structurally different graphs. A time complexity analysis shows that HybridGNN achieves efficient computation across different layers. When evaluated on an email communication dataset, HybridGNN outperformed traditional algorithms such as Hopcroft-Karp, particularly on large and complex graphs. These results demonstrate that HybridGNN offers a powerful and efficient approach for solving maximum matching problems in bipartite graphs, with potential applications in various fields requiring analysis of large-scale and complex graph data.

With the deepening of the diversification and openness of financial system, financial vulnerability, as an endogenous attribute of financial system, becomes an important measurement of financial security. Based on network analysis, we introduce network curvature indicator improved by Copula entropy as an innovative metric of financial vulnerability. Compared with previous network curvature analysis method, CE-based curvature proposed in this paper can measure market vulnerability and systematic risk with significant advantages.

With the rapid development of Internet of Things (IoT)-based near-earth remote sensing technology, the problem of network intrusion for near-earth remote sensing systems has become more complex and large-scale. Therefore, it is essential to seek an intelligent, automated, and robust network intrusion detection method. In recent years, network intrusion detection methods based on graph neural networks (GNNs) have been proposed. However, there are still some practical issues with these methods. For example, they have not taken into consideration the characteristics of near-earth remote sensing systems, the state of the nodes, and the temporal features. Therefore, this article analyzes the characteristics of existing near-earth remote sensing systems and proposes a spatio-temporal graph attention network (N-STGAT) that considers the state of nodes. The proposed network applies spatiotemporal graph neural networks to the network intrusion detection of near-earth remote sensing systems and validates the effectiveness of the proposed method on the latest flow-based dataset.

In underwater clustering and benchmark networks, nodes need to reduce the rate and energy consumption of acoustic communication while ensuring synchronization accuracy. In large-scale networks, the improvement of the efficiency of existing network time synchronization often relies on optimization of topological structures, and the improvement in efficiency within local areas is limited. This paper proposes a method to synchronize underwater time using the probability graph model. The method utilizes the positional and motion status information of sensor networks to construct a factor graph model for distributed network synchronization. By simplifying the marginal probability density function of the system clock difference, it can quickly calculate the clock difference parameters of nodes, thereby effectively improving the synchronization efficiency. Experimental results show that the method can complete global time synchronization within a cycle while achieving a clock difference correction accuracy higher than seconds, significantly optimizing the synchronization period and efficiency, and reducing the energy consumption of acoustic communication.

This paper investigates the application of Graph Neural Networks (GNNs) in solving the facility location decision problem. By adapting the learning objectives and structure of GNNs, this research bridges the gap between traditional optimization approaches and modern machine learning techniques. The proposed method demonstrates improved decision-making capabilities, providing promising results for facility location optimization. Additionally, potential future research directions are outlined, highlighting areas where GNNs can further enhance decision-making processes in complex supply chain networks. Hybrid GNN and Mixed Integer Programming solutions have been proposed.

Mechanical equipment is composed of several parts, the interaction between the parts exists throughout whole life cycle leads to the widespread phenomenon of fault coupling and the diagnosis of independent faults cannot meet the requirements of the health management of mechanical equipment under actual working conditions. In this paper, the topological structure of graph neural network is used to describe the correlation of coupling faults and multiple fault types are regarded as network nodes respectively. The fault features are fused and extracted by graph convolution to achieve the classification of coupling faults. In this paper, dynamic vertexes are defined in data topology and the parameters of DIGNN classification model are optimized by changing the fault type of dynamic vertexes during training stage. The data is loaded into dynamic vertexes for classification and analysis during testing stage. The one-dimensional vibration data is converted into two-dimensional time-frequency domain data by wavelet transform making the input features of the model interpretable to reduce the uncertainty of model training. The data topology is then fed into DIGNN for fault classification, and GCN's node aggregation gives interpretability to each layer of network data processing. The method proposed in this paper can realize accurate diagnosis of independent faults on the data set, and can effectively judge the coupling mode of coupling faults, which is suitable for coupling fault analysis of mechanical equipment.

Drug repositioning (also called drug repurposing) is a strategy for identifying new therapeutic targets for existing drugs. This approach is of great importance in pharmacology as it is a faster and cheaper way to develop new medical treatments. In this paper, we present, to our knowledge, the first application of multiplex-heterogeneous network embedding to drug repositioning. Network embedding learns the vector representations of nodes, opening the whole machine learning toolbox for a wide variety of applications including link prediction, node labelling or clustering. So far, the application of network embedding for drug repositioning focused on heterogeneous networks. Our approach for drug repositioning is based on multiplex-heterogeneous network embedding. Such method allows the richness and complexity of multiplex and heterogeneous networks to be projected in the same vector space. In other words, multiplex-heterogeneous networks aggregate different multi-omics data in the same network representation. We validate the approach on a task of link prediction and on a case study for SARS-CoV2 drug repositioning. Experimental results show that our approach is highly robust and effective for finding new drug-target associations.

：Non-Euclidean data, such as social networks, and citation relationships between documents, has node information and structural information. Graph Convolutional Network(GCN) can automatically learn node features and association information between nodes. The core ideology of the graph convolutional network is to aggregate node information by using edge information, thereby generating a new node feature. In the process of updating node features, there are two core influencing factors. One is the number of neighboring nodes of the central node, the other is the contribution of the neighboring nodes to the central node. Due to the previous GCN methods not simultaneously considering the numbers and different contributions of neighboring nodes to the central node, we design the Adaptive Attention Mechanism(AAM). To further enhance the representational capability of the model, we utilize Multi-Head Graph Convolution(MHGC). Finally, we adopt cross-entropy(CE) loss function to describe the difference between the predicted results of node categories and the ground truth (GT). Combined with backpropagation, this ultimately achieves accurate node classification. Based on AAM, MHGC and CE, we contrive the novel Graph Adaptive Attention Network (GAAN). Experiments show that the classification accuracy has achieved outstanding performances on Cora, Citeseer and Pubmed datasets.

Background: Patients undergoing brain tumor resection experience neurological and cognitive (i.e., neurocognitive) changes reflected in altered performance on neuropsychological tests. These changes can be difficult to explain or predict. Brain connectivity, measured with neuroimaging, offers one potential model for examining these changes. In this study, we evaluated whether longitudinal changes in brain connectivity correlated with changes in neurocognitive abilities in patients before and after brain tumor resection. Methods: Patients underwent functional and diffusion MR scanning and neuropsychological evaluation before tumor resection followed by repeat scanning and evaluation two weeks post-resection. Using this functional and diffusion imaging data, we measured changes in the topology of the functional and structural networks. From the neuropsychological testing scores, we derived a composite score that described a patient’s overall level of neurocognitive functioning. We then used a multiple linear regression model to test whether structural and functional connectivity measures were correlated with changes in composite scores. Results: Multiple linear regression on 21 subjects showed that connectivity changes were highly correlated with changes in neuropsychological evaluation scores (R² adjusted = 0.79, p<0.001). Changes in functional local efficiency (p<0.001) and global efficiency (p<0.05) were inversely correlated with changes in composite score, while changes in modularity (p<0.01) as well as the patient’s age (p<0.05) were directly correlated with changes in composite score. Conclusion: Short interval changes in brain connectivity markers were strongly correlated with changes in the composite neuropsychological test scores in brain tumor resection patients. Our findings support the need for further exploration of brain connectivity as a biomarker relevant to brain tumor patients.

Tackling the intricacies of network dismantling in complex systems poses significant challenges. This task has relevance across various practical domains, yet traditional approaches focus primarily on singular metrics, such as the number of nodes in the Giant Connected Component (GCC) or average pairwise connectivity. In contrast, we propose a unique metric that concurrently targets nodes with the highest degree and reduces the GCC size. Given the NP-hard nature of optimizing this metric, we introduce MaxShot, an innovative end-to-end solution that leverages graph representation learning and reinforcement learning. Through comprehensive evaluations on both synthetic and real-world datasets, our method consistently outperforms leading benchmarks in accuracy and efficiency. These results highlight MaxShot’s potential as a superior approach to address the network dismantling problem effectively.

The basic challenges of this work are twofold: demonstrating the dependence between the functional and topological qualities of partition networks and finding the simplest—with respect to algorithmic complexity—network elements. The study of these problems is based on finding the solution to an appropriate antagonistic vertex game. The results of the numerical simulations of antagonistic partition games demonstrate that the winner’s graphs are “almost always” dense and hyperenergetic compared to the loser’s graphs. These observations reveal that successful evolutionary mechanisms can be realized, in principle, by the simplest objects (such as viruses).

This study examines the causal relationships between interest rates in the Korean financial market using a vector error correction model (VECM) and a Bayesian network. The Bayesian network, a novel approach in this context, identifies two distinct transmission channels: one led by call rates (reflecting monetary policy) and another by 10-year Treasury bond yields (reflecting fiscal policy). While the call rate channel aligns with traditional views, affecting bank lending rates, corporate bond spreads, and commercial paper rates, the 10-year Treasury yield channel highlights a separate fiscal policy transmission mechanism, influencing commercial paper rates indirectly through 30-year Treasury yields and directly impacting merchant bank lending rates. This finding suggests that fiscal intervention could potentially interfere with monetary policy, emphasizing the need for coordinated macroeconomic policy measures. The study also emphasizes the role of 10-year Treasury bonds as a benchmark in the Korean bond market, reflecting medium- to long-term economic outlooks and serving as the underlying asset for various derivatives.

Although Lov\'{a}sz introduced the graph exponential $G^K$ in 1967, this product has received little attention. This paper focuses on the number of components in $G^K$ when exponent $K$ is a complete graph $K_n$. For a connected bipartite $G$, when $K$ is $K_2$, $G^{K_2}$ has three components; and when $K$ is $K_n$ with $n>2$, $G^{K_n}$ produces $\lceil\frac{n+1}{2}\rceil$ components. A connected $G$ with an odd cycle produces one component in $G^{K_n}$.

Course recommendation is an important service of Intelligent tutoring systems (ITS), the rapid development of large-scale online courses has generated a substantial amount of learning process data for online learning platforms, providing valuable support for understanding learners' interests and preferences. However, despite made considerable achievements, there are still unresolved challenges:(1) Current research neglects the sequential relationship between the course learners learn. (2) It does not take advantage of the differences in learners' interest in different courses during the knowledge dissemination process. To overcome these challenges, we propose an innovative solution called PGDB (Preference-aware graph diffusion network and BiLSTM) for course recommendation. Specifically, we analyze learners' preferences for courses and relational paths using a relation-aware multi-head attention network, learn the semantic diversity of different contexts, effectively distinguish the difference of learners' interest in different courses in the process of knowledge transmission. In addition, the temporal preference modeling module employs a bi-directional long short-term memory network to mine learners' interest evolution patterns, generating learner-dependent representations, efficient use of the sequential relationship between the courses taken by learners. Experimental results on real datasets demonstrate that the proposed model greatly exceeds the performance of the most recent baseline models, thereby validating the model's effectiveness.

Hyperspectral small target detection (HSTD) is a promising pixel-level detection task. However, due to the low contrast and imbalance number between the target and background spatially and high dimensions spectrally, it is a challenging one. To address these issues, this work proposes a representation learning-based graph and generative network for hyperspectral small target detection. The model builds a fusion network through frequency representation for HSTD, where the novel architecture incorporates irregular topological data and the spatial-spectral feature to improve its representation ability. Firstly, a graph convolutional network (GCN) module better models the non-local topological relationship between samples to represent the hyperspectral scene’s underlying data structure. The mini-batch-training pattern of the GCN decreases the high computational cost of building an adjacency matrix for high-dimensional data sets. In parallel, the generative model enhances the differentiation reconstruction and the deep feature representation ability with respect to the target spectral signature. Finally, a fusion module compensates for the extracted different types of HS features and integrates their complementary merits for hyperspectral data interpretation while increasing detection and background suppression capabilities. Experiments on different hyperspectral data sets demonstrate the advantages of the proposed architecture.

In this paper, we review metaheuristic optimization techniques for machine learning with Graph Neural Networks (GNNs), focusing on two major categories: single-solution-based and population-based metaheuristics. We provide an in-depth analysis of Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), highlighting their effectiveness in optimizing GNN hyperparameters. By exploring the strengths and weaknesses of these methods, we aim to provide insights into their application and performance in enhancing the efficiency and accuracy of GNN models. We will also review the similarities of supervised learning and metaheuristic solutions.

Considering that emotional events diversify as one ages, this study formulates the Salient Episodic Memory Aggregation Hypothesis, which claims that aging induces homogenization of episodic memory and consequently increases the salience of emotional episodes. To test this hypothesis, the study focused on sadness episodic memory and conducted a web-based survey and a combined analysis consisting of natural language processing, machine learning, and network graph analysis. A sample of 2,954 adults aged between their 20s and over 70s participated in this study. They were asked to describe a sad event they had experienced and assess the psychological properties of the recalled episodes. After isolating and lemmatizing episodic words using natural language processing, vocabulary frequency was counted for each generation, and network graph analysis based on machine learning was performed to compare the structures of sadness episodes between generations. As a result, there were mainly two types of episodic words for which frequencies either declined or increased with age. The network structures of episodic words for the older generations possessed higher proximity (shortest path length) to higher concentrations of episodic words. These findings support the current hypothesis, indicating that the nature of sadness episodes differ between generations, and that older people have more aggregated episodic memory structures.

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.

We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

A signed graph is an undirected graph such that all of its edges are labeled positive or negative. Let D be an embedding of a signed graph G in the Euclidean line. If in D for all of the vertices their positive neighbors are closer than the negative neighbors, then D is called a valid drawing of G. In this paper we show that signed trees, unicyclic graphs, and ladder graphs have a valid drawing in the Euclidean line.

Introduced in 1967 by Lov\'{a}sz, graph exponentiation has received little attention over the past several decades. Since graph exponentiation produces large graphs and any graph can be constructed utilizing its adjacency matrix, we provide a four step linear construction algorithm that generates the adjacency matrix for the graph exponential.

The commonly-used large-scale knowledge bases have been facing challenges in open domain question answering tasks which are caused by the loose knowledge association and weak structural logic of triplet-based knowledge. To find a way out of this dilemma, this work proposes a novel metaknowledge enhanced approach for open domain question answering. We design an automatic approach to extract metaknowledge and build metaknowledge network from Wiki documents. For the purpose of representing the directional weighted graph with hierarchical and semantic features, we present an original graph encoder GE4MK to model the metaknowledge network. Then a metaknowledge enhanced graph reasoning model MEGr-Net is proposed for question answering, which aggregates both relational and neighboring interactions comparing with R-GCN and GAT. Experiments have proved the improvement of metaknowledge over main-stream triplet-based knowledge. We have found that the graph reasoning models and pre-trained language models also have influences on the metaknowledge enhanced question answering approaches.

Everyday place descriptions provide a rich source of knowledge about places and their relative locations. This research proposes a place graph model for modeling this spatial, non-spatial, and contextual knowledge from place descriptions. The model extends a prior place graph, and overcomes a number of limitations. The model is implemented using the Neo4j graph database, and a management system has also been developed that allows operations including querying, mapping, and visualizing the stored knowledge in an extended place graph. Then three experimental tasks, namely georeferencing, reasoning, and querying, are selected to demonstrate the superiority of the extended model.

Ligand-based virtual screening (LBVS) is a promising approach for rapid and low-cost screening of potentially bioactive molecules in the early stage of drug discovery. Compared with traditional similarity-based machine learning methods, deep learning frameworks for LBVS can more effectively extract high-order molecule structure representations from molecular fingerprints or structures. However, the 3D conformation of a molecule largely influences its bioactivity and physical properties, and has rarely been considered in previous deep learning-based LBVS methods. Moreover, the relative bioactivity benchmark dataset is still lacking. To address these issues, we introduce a novel end-to-end deep learning architecture trained from molecular conformers for LBVS. We first extracted molecule conformers from multiple public molecular bioactivity data and consolidated them into a large-scale bioactivity benchmark dataset, which totally includes millions of endpoints and molecules corresponding to 954 targets. Then, we devised a deep learning-based LBVS called EquiVS to learn molecule representations from conformers for bioactivity prediction. Specifically, graph convolutional network (GCN) and equivariant graph neural network (EGNN) are sequentially stacked to learn high-order molecule-level and conformer-level representations, followed by attention-based deep multiple-instance learning (MIL) to aggregate these representations and then predict the potential bioactivity for the query molecule on a given target. We conducted various experiments to validate the data quality of our benchmark dataset, and confirmed EquiVS achieved better performance compared with 10 traditional machine learning or deep learning-based LBVS methods. Further ablation studies demonstrate the significant contribution of molecular conformation for bioactivity prediction, as well as the reasonability and non-redundancy of deep learning architecture in EquiVS. Finally, a model interpretation case study on CDK2 shows the potential of EquiVS in optimal conformer discovery. The overall study shows that our proposed benchmark dataset and EquiVS method have promising prospects in virtual screening applications.

The Randić index of a graph G is the sum of (dG(u)dG(v))−1/2 over all edges uv of G, where dG(u) denotes the degree of vertex u in G. In this paper, we investigate a few graph transformations that decrease Randić index of graph. By applying those transformations, we determine the minimum Randić index on tricyclic graphs, and characterize the corresponding extremal graphs.

Incorporating knowledge graphs as auxiliary information to enhance recommendation systems can improve the representations learning of users and items. Recommendation methods based on knowledge graph can introduce user-item interaction learning into the item graph, focusing only on learning the node vector representations within a single graph; alternatively, they can treat user-item interactions and item graphs as two separate graphs and learn from each graph individually. Learning from two graphs has natural advantages in exploring original information and interaction information, but faces two main challenges: 1) in complex graph connection scenarios, how to adequately mine the self-information of each graph, and 2) how to merge interaction information from the two graphs while ensuring that user-item interaction information predominates. Existing methods do not thoroughly explore the simultaneous mining of self-information from both graphs and effective interaction information, leading to the loss of valuable insights. Considering the success of contrastive learning in mining self-information and auxiliary information, this paper proposes a dual-graph contrastive learning recommendation method based on knowledge graphs (KGDC) to explore a more accurate representations of users and items in recommendation systems based on external knowledge graphs. In the learning process within the self-graph, KGDC has strengthened and represented the information of different connecting edges in both graphs, and extracted the existing information more fully. In interactive information learning, KGDC reinforces the interaction relationship between users and items in the external knowledge graph, realizing the leading role of the main task. We have conducted a series of experiments on three standard datasets, and the results show that the proposed method can achieve better results.

The graph model enables a broad range of analysis, thus graph processing is an invaluable tool in data analytics. At the heart of every graph processing system lies a concurrent graph data structure that stores the graph. Such a data structure needs to be highly efficient for both graph algorithms and queries. Due to the continuous evolution, the sparsity, and the scale-free nature of real-world graphs, graph processing systems face the challenge of providing an appropriate graph data structure that enables both fast analytical workloads and low-memory fast graph mutations. Existing graph structures offer a hard tradeoff between read-only performance, update friendliness, and memory consumption upon updates. In this paper, we introduce CSR++, a new graph data structure that removes these tradeoffs and enables both fast read-only analytics and quick and memory-friendly mutations. CSR++ combines ideas from CSR, the fastest read-only data structure, and adjacency lists to achieve the best of both worlds. We compare CSR++ to CSR, adjacency lists from the Boost Graph Library, as well as state-of-the-art update-friendly graph structures: LLAMA, STINGER, GraphOne, and Teseo. In our evaluation, which is based on popular graph processing algorithms executed over real-world graphs, we show that CSR++ remains close to CSR in read-only concurrent performance (within 10% on average), while significantly outperforming CSR (by an order of magnitude) and LLAMA (by almost 2×) with frequent updates. We also show that both CSR++’s update throughput and analytics performance exceed that of several state-of-the-art graph structures, while maintaining low memory consumption when the workload includes updates.

This paper describes a polynomial time algorithm for solving graph isomorphism and automorphism. We introduce a new tree data structure called Walk Length Tree. We show that such tree can be both constructed and compared with another in polynomial time. We prove that graph isomorphism and automorphism can be solved in polynomial time using Walk Length Trees.

Molecular descriptors are essential in mathematical chemistry for studying quantitative structure-property relationships (QSPR), and topological indices are a valuable source of information about molecular properties such as size, cyclicity, branching degree, and symmetry. Graph theory has played a crucial role in the development of topological indices and dominating parameters for molecular descriptors. The molecule graph, under graph isomorphism conditions, represents an invariant number, and the graph theory approach considers dominating sets, which are subsets of the vertex set where every vertex outside the set is adjacent to at least one vertex inside the set. The dominating sigma index, a topological index that incorporates the mathematical principles of domination topological indices and the sigma index, is applicable to some families of graphs, such as book graphs, windmill graphs, and some graph operations, which have exact values for this new index. To evaluate the effectiveness of the domination sigma index in QSPR studies, a comparative analysis was conducted to establish an appropriate domination index that correlates with the physicochemical properties of octane and its isomers. Linear and non-linear models were developed using the QSPR approach to predict the properties of interest, and the results showed that both the domination forgotten and domination first Zagreb indices exhibited satisfactory performance in comparison testing. Further research into QSAR/QSPR domination indices is required to build more robust models for predicting the physicochemical properties of organic compounds while maintaining the importance of symmetry.

Euler's theorem about the relationship between the numbers of individual elements of planar graphs (vertices, edges, faces) is also satisfied when the graph has zero vertices. The problem of the existence or not of such graphs has so far been the subject of very few studies. Plus, research that didn't prove anything. The paper presents an interpretation of this kind of graphs as mathematical formations lying on piecewise smooth surfaces. The lines of intersection of two or more smooth surfaces (faces of a graph) form edges without a vertex of the graph. The elementary properties of such graphs are discussed, the method of counting non-isomorphic 0-vertex graphs and their importance in physics and chemistry are given.

Existing Knowledge Graph (KG) models for commonsense question answering present two challenges: (i) existing methods retrieved entities related to questions from the knowledge graph, which may extract noise and irrelevant nodes, and (ii) lack of interaction representation between questions and graph entities. However, current methods mainly focus on retrieving relevant entities with some noisy and irrelevant nodes. In this paper, we propose a novel Retrieval-augmented Knowledge Graph (RAKG) model, which solves the above issues through two key innovations. First, we leverage the density matrix to make the model reason along the corrected knowledge path and extract an enhanced knowledge graph subgraph. Second, we fuse representations of questions and graph entities through a bidirectional attention strategy, in which two representations fuse and update by Graph Convolutional Network (GCN). To evaluate the performance of our method, we conduct experiments on two widely-used benchmark datasets CommonsenseQA and OpenBookQA. The case study gives insight into findings that the augmented subgraph provides reasoning along the corrected knowledge path for question answering.

In this article, there's an effort to make sense about the new versions of matroid. I believe that there's new idea on the background of. matroid. Two styles of matroid is defined in the background of fixed graphs and after that the attributes of these new notion on the graph and its parameters have been studied. The focus of this article is on the version of matroid which has the basis on the cycles as if there's gentle discussion on the results which are based on the set of independent vertices as matroid-x. The relation amid fundamental parameters and specific set like independent set and minimal set in the terminology of graph theory have been considered. Matroid is the word to use in the study on the parameters of graph theory as if set theory and its terminology are also recorded. The terms of word in various terminology have been relatively used. There are open ways to use hypergraphs or some serious relations amid these two types.

In considering knowledge graphs in a diverse range of domains of interest, graph neural networks have demonstrated significant improvements in node classification and prediction when applied to graph representation with learning node embedding to effectively represent hierarchical properties of graphs. DiffPool is a deep-learning approach using a differentiable graph pooling technique that generates hierarchical representations of graphs. In operation DiffPool is a differentiable graph pooling technique that generates hierarchical representations of graphs. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep graph neural network with nodes mapped sets of clusters. However, control of the learning process is difficult given the complexity and large number of parameters on an `end-to-end’ model. To address this difficulty we propose an novel approach termed FPool which is predicated on the basic approach adopted in DiffPool (where pooling is applied directly to node representations). Methods designed to enhance data classification have been developed and evaluated using a number popular and publicly available sensor data sets. Experimental results for FPool demonstrate improved classification and prediction performance when compared to alternative methods. Moreover, FPool shows an important reduction in the training time over the basic DiffPool framework.

Metabolic pathways provide key information to achieve a better understanding of life and all its processes; this is useful information for the improvement of medicine, agronomy, pharmacy, and other similar areas. The main analysis tool used to study these pathways is based on the idea of pathway comparison, using graph data structures. Metabolic pathway comparison has been defined as a computationally complex task \cite{ay2011submap,abaka2013campways}. In previous work from 2017, two different approaches that simplify the problem of comparing pathways represented as graphs were introduced. The first algorithm consists of the transformation of a two-dimensional graph structure, representing a metabolic pathway, to a one-dimensional structure and thus aligning the corresponding data using a reduced 1 dimension string. The second algorithm consists of performing a paired analysis between reactions in pathways and thus eliminating all similarities, finally, showing these differences to the user. The suggestion is to use the information provided by these algorithms as a previous analysis to a deeper, more expensive, comparison tool use. Here we provide an extension of this work with more data and deeper analysis. These methods have shown to be an effective way to treat the problem of metabolic pathway comparison as listed in the discussion and results section. Our results show evidence of a quick, simple and effective way to resolve the described problem.

Abnormal connections in brain networks of healthy people always bring the problems of cognitive impairments and degeneration of specific brain circuits, which may finally result in Alzheimer’s disease (AD). Exploring the development of the brain from normal controls (NC) to AD is an essential part of human research. Although connections changes have been found in the development, the connection mechanism that drives these changes remain incompletely understood. The purpose of this study is to explore the connection changes in brain networks in the process from NC to AD, and uncover the underlying connection mechanism that shapes the topologies of AD brain networks. In particular, we propose a model named MINM from the perspective of topology-based mutual information to achieve our aim. MINM concerns the question of estimating the connection probability between two cortical regions with the consideration of both the mutual information of their observed network topologies and their Euclidean distance in anatomical space. In addition, MINM considers establishing and deleting connections, simultaneously, during the networks modeling from the stage of NC to AD. Experiment results show that MINM is sufficient to capture an impressive range of topological properties of real brain networks such as characteristic path length, network efficiency, and transitivity, and it also provides an excellent fit to the real brain networks in degree distribution compared to experiential models. Thus, we anticipate that MINM may explain the connection mechanism for the formation of the brain network organization in AD patients.

Re-shaping of thermodynamics with the graph theory and Ramsey theory is suggested. Maps built of thermodynamic states are addressed. Thermodynamic states may be attainable and non-attainable by the thermodynamic process in the system of constant mass. We address the following question how large should be a graph describing connections between discrete thermodynamic states to guarantee the appearance of thermodynamic cycles? The Ramsey theory supplies the answer to this question. Direct graphs emerging from the chains of irreversible thermodynamic processes are considered. In any complete directed graph, representing the thermodynamic states of the system the Hamiltonian path is found. Transitive thermodynamic tournaments are addressed. The entire transitive thermodynamic tournament built of irreversible processes does not contain a cycle of length 3, or in other words, the transitive thermodynamic tournament is acyclic and contains no directed thermodynamic cycles.

The realization of the third-generation artificial intelligence (AI) requires the evolution from perceptual intelligence to cognitive intelligence, where knowledge graphs may not meet the practical needs anymore. Based on the dual channel theory, cognitive graphs are established and developed through coordinating the implicit extraction module and the explicit reasoning module as well as integrating knowledge graphs, cognitive reasoning and logical expressions, which have achieved successes in multi-hop question answering. It is desired for cognitive graphs to be widely used in advanced AI applications such as large-scale knowledge representations and intelligent responses, promoting the development of Al dramatically. This review discusses cognitive graphs systematically and elaborately, including basic concepts, generations, theories and technologies. Moreover, we try to predict the development of cognitive intelligence in the short-term future and further enlighten more researches and studies.

With recent advancements in network technology and spread of Internet, use of social network services and Internet of Things devices has flourished, leading to a continuous generation of large volumes of graph stream data, where changes, such as additions or deletions of vertices and edges occur over time. Additionally, owing to the need for efficient use of storage space and security requirements, graph stream data compression has become essential in various applications. Even though various studies on graph compression methods have been conducted, most of them do not fully reflect the dynamic characteristics of graph streams and complexity of large graphs. In this paper, we propose a compression scheme using provenance data to efficiently process and analyze large graph stream data. It obtains provenance data by analyzing graph stream data and builds a pattern dictionary based on this to perform dictionary-based compression. By improving the existing dictionary-based graph compression methods, it enables more efficient dictionary management through tracking pattern changes and evaluating their importance using provenance. Furthermore, it considers the relationships among sub-patterns using an FP-tree and performs pattern dictionary management that updates pattern scores based on time. Our experiments show that the proposed scheme outperforms existing graph compression methods in key performance metrics, such as compression rate and processing time.

Application of the Ramsey Theory to the set of the points placed in the plane is discussed. Consider a set of N points located in the same plane. The straight lines connecting these points are yikx=αikx+βik i,k=1...N. Listed below values of slopes αik are possible: αik&gt;0; αik=0; αik is not defined; αik&lt;0. Following coloring procedure is introduced: we connect the pairs of points for which αik&gt;0, αik=0 or αik is not defined, with the red links, and the pairs of points for which αik&lt;0 place with green links. The suggested coloring procedure enables building of the complete bi-colored graph for any set containing N points located in the same plane. We apply the Ramsey theorem to the complete graph emerging from the suggested coloring. For the set containing N=6 points at least one monochromatic triangle will necessarily appear in the graph. The values of the slopes αik depend on the chosen coordinate system. The rotation of coordinate axes changes the coloring of the graph; however, at least one monochromatic triangle will be present for N=6. The introduced coloring procedure diminishes the order of the symmetry group of the regular hexagon, irrespectively to the orientation of the coordinate axes. We hypothesized that this will be true for arbitrary regular n-polygon, independently on the orientation of coordinate axes. The inverse bi-color Ramsey graphs arise, when we replace red links appearing in the source graph with red ones, and vice versa. The total number of triangles in the “direct” and “inverse” Ramsey graphs is the same. We considered the particular case of the set of points for which αik&gt;0 or αik&lt;0 is true in the given coordinates. In this particular case, the rotation of the Cartesian coordinate axes to the angle θ=π2 yields the inverse complete graph. Generalization of this coloring for an arbitrary number and arbitrary location of the source points is introduced.

It has recently been shown that, contrary to the wide belief that a shift-enabled condition (necessary for any shift-invariant filter to be representable by a graph shift matrix) can be ignored because any non-shift-enabled matrix can be converted to a shift-enabled matrix, such a conversion in general may not hold for a directed graph with non-symmetric shift matrix. This paper extends this prior work, focusing on undirected graphs where the shift matrix is generally symmetric. We show that while, in this case, the shift matrix can be converted to satisfy the original shift-enabled condition, the converted matrix is not associated with the original graph, that is, it does not capture anymore the structure of the graph signal. We show via a counterexample, that a non-shift-enabled matrix cannot be converted to a shift-enabled one and still maintain the topological structure of the underlying graph, which is necessary to facilitate localized signal processing.

Traffic congestion and frequent traffic accidents have become main problems affecting urban traffic. Effective location prediction of vehicle trajectory can help alleviate traffic congestion, reduce the occurrence of traffic accidents, and optimize the urban traffic system. Vehicle trajectory is closely related to the surrounding Points of Interest (POI). POI can be considered as the spatial feature and can be fused with trajectory points to improve prediction accuracy. A Local Dynamic Graph Spatiotemporal- Long Short-Term Memory (LDGST-LSTM) is proposed in this paper to extract and fuse the POI knowledge and realize next location prediction. POI semantic information is learned by constructing the traffic knowledge graph, and spatial and temporal features are extracted by combining Graph Attention Network (GAT) and temporal attention mechanism. Moreover, the weights of POI that influence location prediction are visualized to improve the interpretability of the proposed model. The effectiveness of LDGST-LSTM is verified on two datasets, including Chengdu taxi trajectory data in October 2018 and August 2014. The accuracy and robustness of the proposed model are significantly improved compared with the benchmark models.

In bioinformatics research, traditional machine learning methods have demonstrated efficacy in addressing Euclidean data. However, real-world data often encompasses non-Euclidean forms, such as graph data, which contain intricate structural patterns or high-order relationships that elude conventional machine-learning approaches. Representation learning seeks to derive valuable data representations from enhancing predictive or analytic tasks, capturing vital patterns and structures. This method has proven particularly beneficial in bioinformatics and biomedicine, as it effectively handles high-dimensional, sparse data, detects complex biological patterns, and optimizes predictive performance. In recent years, graph representation learning has become a popular research direction. It embeds graphs into a low-dimensional space while preserving the structural and attribute information of the graph, enabling better feature extraction for downstream tasks. This study extensively reviews representation learning advancements, particularly in the research of representation methods since the emergence of COVID-19. We begin with an analysis and classification of neural network-based language model representation learning techniques as well as graph representation learning methods. Subsequently, we explore their methodological innovations in the context of COVID-19, with a focus on the domains of drugs, public health, and healthcare. Furthermore, we discuss the challenges and opportunities associated with graph representation learning. This comprehensive review presents invaluable insights for researchers as it documents the development of COVID-19 and offers experiential lessons to preempt future infectious diseases. Moreover, this study guides future bioinformatics and biomedicine research methodologies.

Graph unlearning has emerged as a crucial technique in privacy-preserving applications, particularly in scenarios where sensitive data must be erased from graph-based systems. This paper explores the fundamental concepts, challenges, and methodologies associated with graph unlearning, including its application to domains such as social networks, financial transaction systems, and healthcare networks. By delving into various algorithms, including local and global unlearning methods, we analyze the trade-offs between accuracy, privacy, and computational efficiency. The paper further investigates the security risks associated with graph unlearning, including adversarial and inference attacks, and proposes mitigation strategies to safeguard unlearning processes. We also examine the unique challenges posed by federated learning systems, where unlearning requires coordination across decentralized clients. Finally, the paper evaluates graph unlearning techniques using performance metrics such as time complexity, accuracy, and privacy guarantees, supported by real-world examples from diverse applications. The findings emphasize the importance of developing robust, scalable, and secure unlearning mechanisms to ensure data privacy and compliance with regulations. Evaluation and metrics for Graph Unlearning will also be discussed in this paper.

Generally, when cognitive radio users are in Underlay mode, through the analysis of the electromagnetic spectrum in time, frequency, space, and field of multiple dimensional data accounts for judging the inherent correlation of the radio spectrum used/idle state, this is the realization of cognitive radio users (secondary users, SUs) efficient access to the foundation of the limited spectrum resources. Therefore, how to efficiently use of spectrum status of each SU implementation of reception multidimensional combination forecasting is the core of this paper addressing the problem. In this paper, we propose a deep-learning hybrid model called TensorGCN-LSTM based on the tensor data structure. The model treats SUs deployed at different spatial locations under the same frequency and the spectrum status of SUs themselves under different frequencies in the task area as nodes and constructs two types of graph structures. Graph convolutional operations are used to sequentially extract corresponding spatial-domain and frequency-domain features from the two types of graph structures. Then, the long short-term memory (LSTM) model is used to fuse the spatial, frequency, and temporal features of the cognitive radio environment data. Finally, the prediction task of the spectrum distribution situation is accomplished through fully connected layers. Specifically, the model constructs a tensor graph based on the spatial similarity of SUs' locations and the frequency correlation between different frequency signals received by SUs, which describes the electromagnetic wave's dependency relationship in spatial and frequency domains. LSTM is used to capture the electromagnetic wave's dependency relationship in the temporal domain. To evaluate the effectiveness of the model, we conducted ablation experiments on LSTM, GCN, GC-LSTM, and TensorGCN-LSTM models using simulated data. The experimental results show that our model achieved better prediction performance in RMSE, and the correlation coefficient R2 of 0.8753 also confirmed the feasibility of the model.

Shannon entropy quantifying bi-colored Ramsey complete graphs is introduced. Complete graphs in which vertices are connected with two types of links, labeled as α-links and β-links are considered. Shannon-entropy is introduced according to the classical Shannon formula considering the fractions of monochromatic convex α-colored polygons with n α-sides or edges, and the fraction of monochromatic β-colored convex polygons with m β-sides in the given complete graph. Introduced Shannon entropy is insensitive to the exact shape of the graph, but it is sensitive to the distribution of monochromatic polygons in a given graph. The introduced Shannon Entropies Sα and Sβ are interpreted as follows: Sα is interpreted as an average uncertainty to find the green α-polygon in the given graph, Sβ is, in turn, an average uncertainty to find the red β-polygon in the same graph. The re-shaping of the Ramsey theorem in terms of the Shannon Entropy is suggested. Various measures quantifying the Shannon Entropy of the entire complete bi-colored graphs are suggested. Physical interpretations of the suggested Shannon Entropies are discussed.

Constructing new graph from the graph's parameters and related notions in the way that, the study on the new graph and old graph in their parameters could be facilitated. As graph, new graph has some characteristics and results which are related to the structure of this graph. For this purpose, regular graph is considered so the internal relation and external relation on this new graph are studied. The kind of having same number of edges when this number is originated by common number of graphs like maximum degree, minimum degree, domination number, coloring number and clique number, is founded in the word of having regular graph

We studied generalization of a method for extending configurational studies to variables that are not exclusively geographical, in order to allow investigation of generic relationships in the built environment. We observed a number of limitations of the classical approach of configurational studies and we considered how a complex analytical method could be implemented in the study of non-topological variables, such as land use, noise pollution and financial or property rents. In order to do this we established a system of relationships based on a labeled primary graph. Categorization of the labels of the links was performed on a generic variable, specifically, the predominant use of roads. The graph was then contracted using an optimization algorithm, which we describe. The algorithm allows the network to be reduced to a more streamlined system that can better analyze the relationships between the different categories. Application of the method showed that it is faster to identify weaknesses in urban networks, and then take measures to resolve them. The case study concerns the pedestrianization of the Colosseum area in Rome.

Graph query languages such as Cypher are widely adopted to match and retrieve data in a graph representation, due to their ability of retrieving and transforming information. Despite the most natural way to match and transform information is through rewriting rules, those are scarcely or partially adopted in graph query languages. Their inability of doing so has a major impact on the subsequent way the information is structured, as it might then appear more natural to provide major constraint over the data representation so to consequently constraint the way the information should be represented. On the other hand, recent works are starting to move towards an opposite direction, as the provision of a truly general semistructured model (GSM) allows to both represent all the available data formats (Network-Based, Relational, and Semistructured) as well as support an holistic query language expressing all major queries in such languages. In this paper, we show that the usage of GSM enables the definition of a general rewriting mechanism which can be expressed in current graph query languages only at the cost of adhering the query to the specificity of the underlying data representation. We formalise the proposed query language in terms graph rewriting mechanisms described as a set of production rules $L\to R$ while providing restriction to the characterization of L, while extending it to support structural graph nesting operations, useful to aggregate similar information around an entry-point of interest. We discuss how GSM, by fully supporting index-based data representation, allows for a better physical model implementation leveraging the benefits of columnar database storages. Preliminary benchmarks shows the scalability of this proposed implementation in comparison with state-of-the-art implementations.

This work considers the task of representation learning on the attributed relational graph (ARG). Both the nodes and edges in an ARG are associated with attributes/features allowing ARGs to encode rich structural information widely observed in real applications. Existing graph neural networks offer limited ability to capture complex interactions within local structural contexts, which hinders them from taking advantage of the expression power of ARGs. We propose Motif Convolution Module (MCM), a new motif-based graph representation learning technique to better utilize local structural information. The ability to handle continuous edge and node features is one of MCM’s advantages over existing motif-based models. MCM builds a motif vocabulary in an unsupervised way and deploys a novel motif convolution operation to extract the local structural context of individual nodes, which is then used to learn higher-level node representations via multilayer perceptron and/or message passing in graph neural networks. When compared with other graph learning approaches to classifying synthetic graphs, our approach is substantially better in capturing structural context. We also demonstrate the performance and explainability advantages of our approach by applying it to several molecular benchmarks.

The COVID-19 pandemic has resulted in a wide range of spatial interventions to slow down the spread of the virus. The spatial limitations of narrow public circulation spaces within informal settlements, which house over one billion people around the world, make it impossible for pedestrians to practice physical distancing (or social distancing). In this paper, we propose a flexible mathematical method, named the Cluster Lane Method, for turning a planar circulation network of any size or complexity into a network of unidirectional lanes, making physical distancing possible in narrow circulation spaces by limiting face-to-face interactions. New notions and theorems about oriented graphs in graph theory are introduced. The paper ends with a discussion of the potential implementation of this cost-efficient, low-tech, sustainable solution, and with the introduction of a novel unidirectional tactile paving for the visually impaired.

Link prediction is a fundamental problem in graphs. Currently, SubGraph Representation Learning (SGRL) methods provide state-of-the-art solutions for link prediction by transforming the task into a graph classification problem. However, existing SGRL solutions suffer from high computational costs and lack scalability. In this paper, we propose a novel SGRL framework called Augmented Feature Diffusion on Sparsely Sampled Subgraph (AFD3S). The AFD3S first uses a conditional variational autoencoder to augment the local features of the input graph, effectively improving the expressive ability of downstream Graph Neural Networks. Then, based on a random walk strategy, sparsely sampled subgraphs are obtained from the target node pairs, reducing computational and storage overhead. Graph diffusion is then performed on the sampled subgraph to achieve specific weighting. Finally, the diffusion matrix of the subgraph and its augmented feature matrix are used for feature diffusion to obtain operator-level node representations as inputs for the SGRL-based link prediction. Feature diffusion effectively simulates the message-passing process, simplifying subgraph representation learning, thus accelerating the training and inference speed of subgraph learning. Our proposed AFD3S achieves optimal prediction performance on several benchmark datasets, with significantly reduced storage and computational costs.

Multimodal knowledge graph completion necessitates the integration of information from multiple modalities (such as images and text) into the structural representation of entities to improve link prediction. However, most existing studies have overlooked the interaction between different modalities. To address this issue, this paper proposed a Transformer-based knowledge graph link prediction model (MM-Transformer) that fuses multimodal features. Different modal encoders are employed to extract structural, visual and textual features, and hybrid key-value calculations are performed on features from different modalities based on the Transformer architecture. The similarities of textual tags to structural tags and visual tags are calculated and aggregated respectively, and multimodal entity representations are modeled and optimized to reduce the heterogeneity of the representations. Experimental results demonstrate that, compared to the current multimodal state-of-the-art methods, the proposed method achieves significant performance improvements in knowledge graph link prediction tasks. This proves that the proposed method effectively addresses the problem of multimodal feature fusion in knowledge graph link prediction tasks.

Symmetry, as a key concept in geometry and the foundational principle of mathematical concepts, is a fundamental part of geometry and nature, creating patterns that help us conceptually organize our world. It is often linked with aesthetic beauty and can be observed in both natural phenomena and human-made objects, such as artworks and manufactured products, across the globe. The automorphism group of a graph is a mathematical structure that captures all the symmetries of the graph. symmetry refers to the property of a graph, indicating that it can be transformed without changing its structure, while the automorphism group is the collection of all permutations of the vertices that preserve the graph's adjacency relationships. In graph theory, the concepts of symmetry group and automorphism group play fundamental roles in understanding the symmetries and structural properties of graphs. This paper aims to explore the relationship between symmetry groups and automorphism groups, shedding light on their interconnected nature and their significance in graph theory. We delve into the definitions and properties of both symmetry groups and automorphism groups, highlighting their similarities and distinctions. Furthermore, we discuss their applications in various fields, including computer science, chemistry, and network analysis. Through this exploration, we aim to provide a comprehensive understanding of the relationship between symmetry groups and automorphism groups, deepening our comprehension of the symmetries and structures inherent in graphs.

In recent years, graph neural networks (GNNs) have become a promising method for analyzing data structured in graph format. By considering connections between entities in a graph, GNNs are able to extract valuable insights. One notable variation of GNN is the graph attention network (GAT), which employs the attention mechanism and has demonstrated promising performance in various applications. However, its ability to incorporate feature information from nodes beyond the immediate neighborhood is limited, leading to degraded performance on heterophilic data. To address this limitation, this thesis proposes a novel attention-based model, namely the Directional Graph Attention Network (DGAT). This model combines the feature-based attention with the global directional information extracted from the graph topology, as inspired by the Directional Graph Network (DGN). A new class of Laplacian matrices is proposed and an existing theoretical result on DGN is extended. This extension bridges a gap in the literature. The experimental results presented in the thesis, based on nine real-world benchmarks and ten synthetic data sets, demonstrate the superiority of the proposed DGAT model compared to the GAT baseline model. Particularly on heterophilic data sets, DGAT showed a notable average increase of approximately 35% in node classification tasks across all heterophilic real-world data sets. In addition, DGAT outperforms GAT by an average margin of around 51% in all ten synthetic data sets with various levels of heterophily

Ensuring the integrity of scientific literature is essential for advancing knowledge and research. However, the credibility and trustworthiness of scholarly publications are compromised by manipulated citations. Traditional methods, such as manual inspection and basic statistical analyses, have limitations in detecting intricate patterns and subtle manipulations of citations. In recent years, network-based approaches have emerged as promising techniques for identifying and understanding citation manipulation. This study introduces a novel method to identify potential citation manipulation in academic papers using perturbations of a deep embedding model. The key idea is to reconstruct meaningful connections represented by citations within a network by exploring slightly longer alternative paths. These indirect pathways enable the recovery of original and reliable citations while estimating their trustworthiness. The investigation takes a comprehensive approach to link prediction, leveraging the consistent behavior of prominent connections when exposed to network perturbations. Through numerical experiments, the method demonstrates a high capability to identify reliable citations as the core of the analyzed data and to raise suspicions about unreliable references that may have been manipulated.

In the last decade several projects have been developed for the digitization and semantization of cultural heritage data. They were developed to preserve and maintain this heritage, but bringing it closer to all types of users and allowing access to this information to other sectors such as tourism, education, etc. In these developments, web technologies are combined, along with the use of knowledge graphs and interactive visualisation tools. Although remarkably interesting projects have been developed, in those projects, the data visualization tools are usually focused on the project context. This makes it difficult to reuse these jobs. Additionally, there are peculiarities of cultural heritage data considered with little depth, such as uncertainty, spatial and temporal granularity, as well as other aspects, such as relationships between data. In this article, these problems are described and based on other works such as VUMO or VISO, the design of an ontology that formalizes how to visualise this information is proposed, considering these problems. In addition, the development of a platform that allows the visualisation of this information through a web application and its evaluation of its use in projects such as SILKNOW, or Arxiu Valencià del Disseny is exposed

Formation in soccer is among the most important tactical choices for a successful match.Herein, the simulations of 420000 match-plays have been performed varying the formation, the number of opponents that are actively pressing the team, the speed of the opponents in attempting a pass interception. Dribbling has been neglected. The match-play ends either with a successful series of passes from a central back to the line of the strikers or with the opponents that steal the ball. In this work, I demonstrate that 3-4-3 formation, which is among the most employed formations, relates to the highest probability of success.

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.

Since the outbreak of 2019 novel coronavirus (2019-nCoV) at the hardest-hit city of Wuhan, the fast-moving spread has killed over three hundred people and infected more than ten thousands in China¹. There are more than one hundred cases outside of China, affecting a dozen of countries globally². The genome sequence of 2019-nCoV has been reported and fast diagnostic kits, effective treatment as well as preventive vaccines are rapidly being developed³. Initial fast-growing confirmed cases triggered lock-down of Wuhan as well as nearby cities in Hubei Province. Mathematical models have been proposed by scientists around the world to project the numbers of infected cases in the coming days ^4,5. However, major factors such as transportation and cultural customs have not been weighed enough. Our model is not set out for precise prediction of the number of infected cases, rather, it is meant for a glance of the dynamics under a public epidemic emergency situation and of different contributing factors. We hope that our model and simulation would provide more insights and perspective information to public health authorities around the globe for better informed prevention and containment solution.

Plants produce a diverse portfolio of sesquiterpenes that are important in their response to herbivores and the interaction with other plants. Their biosynthesis from farnesyl diphosphate depends on the sesquiterpene synthases. Here, we investigate to what extent metabolic pathways can be reconstructed just from knowledge of the final product and the reaction mechanisms catalyzed by sesquiterpene synthases. We use the software package MedØlDatschgerl (MØD) to generate chemical networks and elucidate pathways contained in them. As examples, we successfully consider the reachability of the important plant sesquiterpenes β-caryophyllene, α-humulene, and β-farnesene. We also introduce a graph database to integrate simulation results with experimental biological evidence for selected predicted sesquiterpenes biosynthesis.

Combinatoric measures of entropy capture the complexity of a graph, but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of alternative vertex level measures of entropy that do not suffer from this pathological computational complexity. It can be demonstrated that they are still effective at quantifying graph complexity. It is intriguing to consider whether there is a fundamental link between local and global entropy measures. In this paper, we investigate the existence of correlation between vertex level and global measures of entropy, for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate close correlation for this subset of graphs and outline how this may arise theoretically.

This paper presents a new method : HIVEC to learn latent vector representations of graphs in a manner that captures the semantic dependencies of sub-structures. The representations can then be used in machine learning algorithms for tasks such as graph classification, clustering etcetera. The method proposed is unsupervised and uses the information of co-occurrence of sub-structures. It introduces a notion of hierarchical embeddings that allows us to avoid repetitive learning of sub-structures for every new graph. As an alternative to deep learning methods, the edit distance similarity between sub-structures is also used to learn vector representations. We compare the performance of these methods against previous work.

We introduce the Concept-Model-Graph-View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision-making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.

With the sharp increase in the number of vehicles, the issue of parking difficulties has emerged as an urgent challenge that many cities need to address promptly. In the task of predicting large-scale urban parking data, existing research often lacks effective deep learning models and strategies. To tackle this challenge, this paper proposes an innovative framework for predicting large-scale urban parking graphs leveraging real-time service capabilities, aimed at improving the accuracy and efficiency of parking predictions. Specifically, we introduce a graph attention mechanism that assesses the real-time service capabilities of parking lots to construct a dynamic parking graph that accurately reflects real preferences in parking behavior. To effectively handle large-scale parking data, this study combines graph coarsening techniques with temporal convolutional autoencoders to achieve unified dimension reduction of the complex urban parking graph structure and features. Subsequently, we use a spatio-temporal graph convolutional model to make predictions based on the coarsened graph, and a pre-trained autoencoder-decoder module restores the predicted results to their original data dimensions, completing the task. Our methodology has been rigorously tested on a real dataset from parking lots in Shenzhen. The experimental results indicate that compared to traditional parking prediction models, our framework achieves improvements of 46.8% and 30.5% in accuracy and efficiency, respectively. Remarkably, with the expansion of the graph’s scale, our framework’s advantages become even more apparent, showcasing its substantial potential for solving complex urban parking dilemmas in practical scenarios.

The P versus NP problem is a cornerstone of theoretical computer science, asking whether problems that are easy to check are also easy to solve. "Easy" here means solvable in polynomial time, where the computation time grows proportionally to the input size. While this problem's origins can be traced to John Nash's 1955 letter, its formalization is credited to Stephen Cook and Leonid Levin. Despite decades of research, a definitive answer remains elusive. Central to this question is the concept of NP-completeness. If even one NP-complete problem could be solved efficiently, it would imply that all problems in NP could be solved efficiently, proving P equals NP. This research proposes that SAT, a notoriously difficult NP-complete problem, can be solved efficiently, thereby potentially establishing the equivalence of P and NP. This work is an expansion and refinement of the article "Note for the P versus NP problem", published in IPI Letters.

The evaluation of machine unlearning has become increasingly significant as machine learning systems face growing demands for privacy, security, and regulatory compliance. This paper focuses on categorizing and analyzing evaluation metrics for machine unlearning, essential for assessing the success of unlearning processes. We divide the metrics into three key dimensions: unlearning effectiveness, unlearning efficiency, and model utility. Unlearning effectiveness examines the degree to which data is removed from the model, utilizing methods such as data removal completeness, privacy leakage detection, and perturbation analysis to ensure thorough data erasure. Unlearning efficiency considers metrics like time to unlearn, computational cost, and scalability, which are crucial for maintaining system performance in real-time environments. Model utility metrics, including accuracy retention, robustness, and fairness, ensure that unlearning does not compromise the model’s predictive capabilities. Through this categorization, we present a comprehensive framework for evaluating machine unlearning, providing a foundation for developing unlearning techniques that balance privacy, performance, and regulatory needs across diverse industries, particularly finance.

The P versus NP problem is a fundamental question in computer science. It asks whether problems whose solutions can be quickly verified can also be quickly solved. Here, "quickly" refers to computational time that grows proportionally to the size of the input (polynomial time). While the problem's roots trace back to a 1955 letter from John Nash, its formalization is attributed to Stephen Cook and Leonid Levin. Despite extensive research, a definitive answer remains elusive. Closely tied to this is the concept of NP-completeness. If a single NP-complete problem could be solved efficiently, it would imply that all problems in NP can be solved efficiently, proving that P equals NP. This work posits that MONOTONE ONE-IN-THREE 3SAT, a notoriously difficult NP-complete problem, can be solved efficiently, thereby establishing the equivalence of P and NP.

The objective of person re-identification (ReID) tasks is to match a specific individual across different times, locations, or camera viewpoints. The prevalent issue of occlusion in real-world scenarios affects image information, rendering the affected features unreliable. The difficulty and core challenge lie in how to effectively discern and extract visual features from human images under various complex conditions, including cluttered backgrounds, diverse postures, and the presence of occlusions. Some works have employed pose estimation or human keypoint detection to construct graph-structured information to counteract the effects of occlusions. However, this approach introduces new noise due to issues such as the invisibility of keypoints. Our proposed module, in contrast, does not require the use of additional feature extractors. Our module employs multi-scale graph attention for the reweighting of feature importance. This allows features to concentrate on areas genuinely pertinent to the re-identification task, thereby enhancing the model's robustness against occlusions. To address these problems, a model that employs multi-scale graph attention to re-weight the importance of features is proposed in this study, significantly enhancing the model’s robustness against occlusions. Our experimental results demonstrate that, compared to baseline models, the method proposed herein achieves a notable improvement in mAP on occluded data sets, with increases of 0.5%, 31.5%, and 12.3% in mAP scores.

The amide group (R-C(=O)-NH-R') is crucial in the functionality of biologically relevant compounds, such as peptides, proteins, and active pharmaceutical ingredients. Its significance in drug design and development is underlined by its presence in several top-selling drugs, where it contributes to the formation of hydrogen bonds. This research examines how heteroatoms in a six- or five-membered pyridine, thiophene or furan ring spacer between two carboxamide groups influence the hydrogen-bonding for advancements in supramolecular chemistry and drug development. The solvent-free crystal structures of 3,5-pyridinedicarboxamide (PDC), 2,5-thiophenedicarboxamide (TDC) and 2,5-furandicarboxamide (FDC-subl, crystallized by sublimation) and the monohydrate structure of FDC-solv (crystallized from methanol) were described by the Etter graph-set notation in level 1 units with the shortest rings and chains as calculated by Mercury. The nearly planar dicarboxamide molecules all have an angular or V-shaped orientation of the two amide groups. The carbon atoms of the amide groups form an angle of 124° in PDC, 129° in TDC and 117° in FDC with the ring centroid. The orientations of the two amide groups with respect to each other are C=O anti NH2 in PDC, syn-CO and syn-NH2 in TDC and FDC. In TDC the CO groups are on the side of the sulfur heteroatom. In FDC the NH2 groups lie on the side of the furan O atom which enables a chelating-type R21(10) ring H-bonding interaction with with the O=C group of a nearby symmetry-related molecule. Only in the structure of PDC the heteroatom acts as an H-bond acceptor as part of a C11(6) chain. In TDC and FDC the heteroatoms do not interact with the amide -NH2 groups. In all structures except for FDC-subl complementary head-to-tail R22(8) rings are formed together with C11(6) and C11(8) chains in PDC, with three different C11(4) chains in TDC with two of them straight and one 21-helical, and with C11(8), C22(10) and C22(16) chains, two finite D11(2) patterns and R21(10) rings in FDC-solv. From sublimation the FDC-subl crystals contain two symmetry independent molecules in the asymmetric unit combining through two C11(4), two C11(8) chains, four different finite D11(2) patterns and two R21(10) rings.

Identifying influential actors within social networks is pivotal for optimizing information flow and mitigating the spread of both rumors and diseases. Several methods have emerged to pinpoint these influential entities in networks that are represented as graphs. In these graphs, nodes corre-spond to individuals and edges indicate their connections. This study focuses on centrality measures, prized for their straightforwardness and effectiveness. We categorize structural central-ity into two: local, considering a node's immediate vicinity, and global, accounting for overarching path structures. Some techniques blend both centralities to highlight nodes influential at both mi-cro and macro levels. Our paper presents a novel centrality measure, accentuating node degree and incorporating the network's broader features, especially paths of different lengths. Through Spearman and Pearson's correlations tested on seven standard datasets, our method proves its merit against traditional centrality measures. Additionally, we employ the SIR model, portraying disease spread, to further validate our approach. The ultimate influential node is gauged by its capacity to infect the most nodes during the SIR model's progression. Our results indicate a nota-ble correlative efficacy across various real-world networks relative to other centrality metrics.

The study introduces a novel method to identify potential citation manipulation in academic papers using perturbations of a deep embedding model, incorporating Graph Masked Autoencoders. This approach integrates textual information with graph connectivity evidence, resulting in a more sophisticated model of citation distribution. By training a deep network using partial data and reconstructing masked connections, the method leverages the inherent characteristics of central connections under network perturbations. Quantitative evaluations demonstrate its remarkable ability to pinpoint trustworthy citations in the analyzed data and raise concerns about potentially unreliable references due to potential manipulation.

This paper presents the Advanced Syntactic-Graph Convolutional Model (ASGCM), a pioneering approach in Aspect-Based Sentiment Analysis (ABSA) that integrates syntactic dependency features within a graph convolution framework. ASGCM stands out for its novel use of dependency edge encoding and tag-based graph convolutions, providing a fine-grained analysis of sentiments associated with specific aspects in text. This model meticulously captures the intricacies of syntactic structures, thereby offering enhanced precision in sentiment analysis. Notably, ASGCM incorporates a dual-layer graph convolution system: one layer processes syntactic dependencies (edges), while the other interprets semantic roles (tags), ensuring a comprehensive understanding of both structural and contextual elements in text. We rigorously tested ASGCM on multiple datasets, including both English and Chinese languages, and our findings reveal a significant improvement in sentiment classification accuracy compared to existing models. The versatility of ASGCM makes it a robust tool for diverse linguistic environments, setting a new standard for ABSA methodologies.

Consensus algorithms are the core technology of blockchain and a focus in the current distributed system research. The consensus algorithms are widely used in distributed systems, it has solved the decentralization problem. The traditional consensus algorithm needs the process of node legitimacy checking, identity authentication, and primary node view change, so the time cost of reaching an agreement between nodes is still exponential. In response to the problem, a lightweight consensus algorithm based on graph (LCAG) is proposed for the Internet of Things (IoT) in this paper, which is proposes an access control table, and reaches an agreement among nodes by calculating the probability of nodes in the control table, and reduces the time overhead of the reaching an agreement in distributed systems. We have carried out simulation experiments for the new algorithm, and the experiments show that: the new algorithm needs less time overhead than the classical Byzantine algorithm need, as well as Byzantine Generals problem (BGP), practical Byzantine fault-tolerant algorithm (PBFT) and directed acyclic graph (DAG) algorithm, and so on. The new algorithm can be applied to the devices of IoT, which have limited computing power.

It is difficult to effectively operate a dual-arm robot using only the information written in a cooking recipe. To cope with this problem, this paper proposes a graph based approach on bimanual cooking motion planning from a cooking recipe. In our approach, we first decompose the cooking recipe into graph elements. Then, we try to connect the graph elements taking into account the attributes of the input/output nodes. If two graph elements cannot be connected each other, we search for a graph element that can be inserted between them from the database of graph elements. Since the constructed graph includes the whole sequence of the robot’s motions to perform the cooking task, we can generate a task sequence of a dual-arm manipulator simultaneously performing two different tasks by using two arms. Through experimental study, we show that it is possible to generate robot motions from a cooking recipe and perform the cooking motions while simultaneously moving the left and right arms.

With the development of data science, more and more machine learning technologies have been designed to solve complicated and challenging real-world tasks containing a large volume of data. And many significant real-world datasets contain data in the form of networks or graphs. Graph Neural Networks is one of the powerful machine learning tools, which could provide a perfect solution to processing a large amount of non-Euclidean data. And because most bio information data in bioinformatics is in the non-Euclidean domain, Graph Neural Networks could then directly be applied to solve problems in bioinformatics. Much research has been done in the field of GNN, and there are also some surveys related to GNN and its applications. However, there has been little research focusing on GNN in bioinformatics, and we think in the future we could better utilize GNN in the field of biology, so we would like to write a literature review to help take a comprehensive look at GNN and their applications in the field of bioinformatics. In this paper, we would first introduce SOTA models in Graph Neural Networks, and second, introduce their applications in bio information. And then we would provide future directions of Graph Neural Networks in bioinformatics.

Forest fire identification is important for forest resource protection. Effective monitoring of forest fires requires the deployment of multiple monitors with different viewpoints, while most traditional recognition models can only recognize images from a single source. By ignoring the information from images with different viewpoints, these models produce high rates of missed and false alarms. In this paper, we propose a graph neural network model based on the similarity of dynamic features of multi-view images to improve the accuracy of forest fire recognition. The input features of the nodes on the graph are converted into relational features of different gallery pairs by establishing pairs (nodes) representing different viewpoint images and gallery images. The new feature library relationship is used to update the image gallery with dynamic features in order to achieve the estimation of similarity between images and improve the image recognition rate of the model. In addition, to reduce the complexity of image pre-processing process and extract key features in images effectively, this paper also proposes a dynamic feature extraction method for fire regions based on image segment ability. By setting the threshold value of HSV color space, the fire region is segmented from the image, and the dynamic features of successive frames of the fire region are extracted. The experimental results show that, compared with the baseline method Resnet, this paper's method is more effective in identifying forest fires, and its recognition accuracy is improved by 2%. And the scheme of this paper can adapt to different forest fire scenes, with better generalization ability and anti-interference ability.

Recent years have seen the growing adoption of non-relational data models for representing diverse, incomplete data. Among these, the RDF graph-based data model has seen ever-broadening adoption, particularly on the Web. This adoption has prompted the standardization of the SPARQL query language for RDF, as well as the development of a variety of local and distributed engines for processing queries over RDF graphs. These engines implement a diverse range of specialized techniques for storage, indexing, and query processing. A number of benchmarks, based on both synthetic and real-world data, have also emerged to allow for contrasting the performance of different query engines, often at large scale. This survey paper draws together these developments, providing a comprehensive review of the techniques, engines and benchmarks for querying RDF knowledge graphs.