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Accurate forecasting of taxi demand has facilitated the rational allocation of urban public transport resources, reduced congestion in urban transport networks, and shortened passenger waiting time. However, virtual station discovery and modelling of the demand when forecasting through graph convolutional neural networks remains challenging. In this study, the virtual station discovery problem was addressed by using a two-stage clustering approach, which considers the geographical and load characteristics of taxi demand. Furthermore, a fusion model combining non-negative matrix decomposition and a graph convolutional neural network was proposed in order to extract the features of the nodes for dimension reduction and adaptive adjacency matrix computation. By the construction of a local processing structure, further extraction of the local characteristics of the demand was achieved. The experimental results show that the method in this study outperforms state-of-the-art methods in terms of the root mean square error and average absolute value error. Therefore, the model proposed in this study is able to achieve accurate forecasting of taxi demand. [ABSTRACT FROM AUTHOR]

In this article, we discuss the spectral properties of the general extended adjacency matrix for chain graphs. In particular, we discuss the eigenvalues of the general extended adjacency matrix of the chain graphs and obtain its general extended adjacency inertia. We obtain bounds for the largest and the smallest general extended adjacency eigenvalues and characterize the extremal graphs. We also obtain a lower bound for the spread of the general extended adjacency matrix. We characterize chain graphs with all the general extended adjacency eigenvalues being simple and chain graphs that are non-singular under the general extended adjacency matrix. Further, we determine the explicit formula for the determinant and the trace of the square of the general extended adjacency matrix of chain graphs. Finally, we discuss the energy of the general extended adjacency matrix and obtain some bounds for it. We characterize the extremal chain graphs attaining these bounds. [ABSTRACT FROM AUTHOR]

In the paper, we introduce the signless Laplacian A B C -matrix Q ̃ (G) = D ¯ (G) + A ̃ (G) , where D ¯ (G) is the diagonal matrix of A B C -degrees and A ̃ (G) is the A B C -matrix of G. The eigenvalues of the matrix Q ̃ (G) are the signless Laplacian A B C -eigenvalues of G. We give some basic properties of the matrix Q ̃ (G) , which includes relating independence number and clique number with signless Laplacian A B C -eigenvalues. For bipartite graphs, we show that the signless Laplacian A B C -spectrum and the Laplacian A B C -spectrum are the same. We characterize the graphs with exactly two distinct signless Laplacian A B C -eigenvalues. Also, we consider the problem of the characterization of the graphs with exactly three distinct signless Laplacian A B C -eigenvalues and solve it for bipartite graphs and, in some cases, for non-bipartite graphs. We also introduce the concept of the trace norm of the matrix Q ̃ (G) − t r (Q ̃ (G)) n I , called the signless Laplacian A B C -energy of G. We obtain some upper and lower bounds for signless Laplacian A B C -energy and characterize the extremal graphs attaining it. Further, for graphs of order at most 6, we compare the signless Laplacian energy and the A B C -energy with the signless Laplacian A B C -energy and found that the latter behaves well, as there is a single pair of graphs with the same signless Laplacian A B C -energy unlike the 26 pairs of graphs with same signless Laplacian energy and eight pairs of graphs with the same A B C -energy. [ABSTRACT FROM AUTHOR]

Let G be a graph with the adjacency matrix A (G) , and let D (G) be the diagonal matrix of the degrees of G. Nikiforov first defined the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G) , 0 ≤ α ≤ 1 , which shed new light on A (G) and Q (G) = D (G) + A (G) , and yielded some surprises. The α − adjacency energy E A α (G) of G is a new invariant that is calculated from the eigenvalues of A α (G) . In this work, by combining matrix theory and the graph structure properties, we provide some upper and lower bounds for E A α (G) in terms of graph parameters (the order n, the edge size m, etc.) and characterize the corresponding extremal graphs. In addition, we obtain some relations between E A α (G) and other energies such as the energy E (G) . Some results can be applied to appropriately estimate the α -adjacency energy using some given graph parameters rather than by performing some tedious calculations. [ABSTRACT FROM AUTHOR]

For a simple finite graph G, the generalized adjacency matrix is defined as A α (G) = α D (G) + (1 − α) A (G) , α ∈ [ 0 , 1 ] , where A (G) and D (G) are respectively the adjacency matrix and diagonal matrix of the vertex degrees. The A α -spread of a graph G is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the A α (G) . In this paper, we answer the question posed in (Lin, Z.; Miao, L.; Guo, S. Bounds on the A α -spread of a graph. Electron. J. Linear Algebra2020, 36, 214–227). Furthermore, we show that the path graph, P n , has the smallest S (A α) among all trees of order n. We establish a relationship between S (A α) and S (A). We obtain several bounds for S (A α) . [ABSTRACT FROM AUTHOR]

The demand for accurate and reliable unsupervised image segmentation methods is high. Regardless of whether we are faced with a problem for which we do not have a usable training dataset, or whether it is not possible to obtain one, we still need to be able to extract the desired information from images. In such cases, we are usually gently pushed towards the best possible clustering method, as it is often more robust than simple traditional image processing methods. We investigate the usefulness of combining two clustering methods for unsupervised image segmentation. We use the mixture models to extract the color and spatial image features based on the obtained output segments. Then we construct a similarity matrix (adjacency matrix) based on these features to perform spectral clustering. In between, we propose a label noise correction using Markov random fields. We investigate the usefulness of our method on many hand-crafted images of different objects with different shapes, colorization, and noise. Compared to other clustering methods, our proposal performs better, with 10% higher accuracy. Compared to state-of-the-art supervised image segmentation methods based on deep convolutional neural networks, our proposal proves to be competitive. [ABSTRACT FROM AUTHOR]

We introduce a generalized adjacency matrix in order to distinguish cospectral graphs. Our reasoning is motivated by the work of Johnson and Newman and properties of p-adic numbers. Using a polynomial time algorithm, we comment on computer experiments with which we can distinguish cospectral (non-isomorphic) graphs. [ABSTRACT FROM AUTHOR]

Entity alignment is an important task in knowledge fusion, which aims to link entities that have the same real-world identity in two knowledge graphs. However, in the process of constructing a knowledge graph, some noise may inevitably be introduced, which must affect the results of the entity alignment tasks. The triple confidence calculation can quantify the correctness of the triples to reduce the impact of the noise on entity alignment. Therefore, we designed a method to calculate the confidence of the triples and applied it to the knowledge representation learning phase of entity alignment. The method calculates the triple confidence based on the pairing rates of the three angles between the entities and relations. Specifically, the method uses the pairing rates of the three angles as features, which are then fed into a feedforward neural network for training to obtain the triple confidence. Moreover, we introduced the triple confidence into the knowledge representation learning methods to improve their performance in entity alignment. For the graph neural network-based method GCN, we considered entity confidence when calculating the adjacency matrix, and for the translation-based method TransE, we proposed a strategy to dynamically adjust the margin value in the loss function based on confidence. These two methods were then applied to the entity alignment, and the experimental results demonstrate that compared with the knowledge representation learning methods without integrating confidence, the confidence-based knowledge representation learning methods achieved excellent performance in the entity alignment task. [ABSTRACT FROM AUTHOR]

This work surveys the use of directed weighted graphs in conducting comparative static analyses. The paper discusses the implementation of a computer-aided process for building spreadsheet-based graph models for inter- and intra-regional financial flows. The graph-theoretic techniques are programmed to enable the interactive visualization and analysis of financial data using Wolfram technologies (i.e., Mathematica software v. 11.3 or later, Wolfram player v. 12 or later). The paper describes the workflow for several interactive visualizations applicable to financial networks. The author provides four programs, written in the Wolfram language, that customize input–output financial models by combining the Manipulate command with built-in Mathematica functions and functions of the IGraph package (IGraph/M). The study is a tutorial article for the generation of a suite of visual schemes that provide patterns, practices, and roadmaps of the financial markets across the globe. [ABSTRACT FROM AUTHOR]

Applying machine learning algorithms to graph-structured data has garnered significant attention in recent years due to the prevalence of inherent graph structures in real-life datasets. However, the direct application of traditional deep learning algorithms, such as Convolutional Neural Networks (CNNs), is limited as they are designed for regular Euclidean data like 2D grids and 1D sequences. In contrast, graph-structured data are in a non-Euclidean form. Graph Neural Networks (GNNs) are specifically designed to handle non-Euclidean data and make predictions based on connectivity rather than spatial structure. Real-life graph data can be broadly categorized into two types: spatially-invariant graphs, where the link structure between nodes is independent of their spatial positions, and spatially-variant graphs, where node positions provide additional information about the graph's properties. However, there is limited understanding of the effect of spatial variance on the performance of Graph Neural Networks. In this study, we aim to address this issue by comparing the performance of GNNs and CNNs on spatially-variant and spatially-invariant graph data. In the case of spatially-variant graphs, when represented as adjacency matrices, they can exhibit Euclidean-like spatial structure. Based on this distinction, we hypothesize that CNNs may outperform GNNs when working with spatially-variant graphs, while GNNs may excel on spatially-invariant graphs. To test this hypothesis, we compared the performance of CNNs and GNNs under two scenarios: (i) graphs in the training and test sets had the same connectivity pattern and spatial structure, and (ii) graphs in the training and test sets had the same connectivity pattern but different spatial structures. Our results confirmed that the presence of spatial structure in a graph allows for the effective use of CNNs, which may even outperform GNNs. Thus, our study contributes to the understanding of the effect of spatial graph structure on the performance of machine learning methods and allows for the selection of an appropriate algorithm based on the spatial properties of the real-life graph dataset. [ABSTRACT FROM AUTHOR]

Community structure is a significant characteristic of complex networks, and community detection has valuable applications in network structure analysis. Non-negative matrix factorization (NMF) is a key set of algorithms used to solve the community detection issue. Nevertheless, the localization of feature vectors in the adjacency matrix, which represents the characteristics of complex network structures, frequently leads to the failure of NMF-based approaches when the data matrix has a low density. This paper presents a novel algorithm for detecting sparse network communities using non-negative matrix factorization (NMF). The algorithm utilizes local feature vectors to represent the original network topological features and learns regularization matrices. The resulting feature matrices effectively reveal the global structure of the data matrix, demonstrating enhanced feature expression capabilities. The regularized data matrix resolves the issue of localized feature vectors caused by sparsity or noise, in contrast to the adjacency matrix. The approach has superior accuracy in detecting community structures compared to standard NMF-based community detection algorithms, as evidenced by experimental findings on both simulated and real-world networks. [ABSTRACT FROM AUTHOR]

For a simple graph with vertex set { v 1 , v 2 , ... , v n } with degree sequence d v i of vertex v i , i = 1 , 2 , ... , n , the inverse sum indeg matrix ( I S I -matrix) A I S I (G) = (a i j) n × n of G is defined by a i j = d v i d v j d v i + d v j , if v i is adjacent to v j , and zero, otherwise. The multiset of eigenvalues of A I S I (G) is the I S I -spectrum of G and the sum of their absolute values is the I S I -energy of G . In this paper, we modify the two results of (Li, Ye and Broersma, 2022), give the correct characterization of the extremal graphs and thereby obtain better bounds than the already known results. Moreover, we also discuss the QSPR analysis and carry the statistical modelling (linear, logarithmic and quadratic) of the physicochemical properties of anticancer drugs with the I S I -index (energy). [ABSTRACT FROM AUTHOR]

This paper defines the weighted super adjacency matrix based on the existing super adjacency matrix. This paper, for the first time, combines the trade network, competitive network, and complementary network to construct the trade multilayer network, and innovatively defines the interlayer connections. Based on this, we build trade multilayer networks for three major agricultural products in the western region along the "Belt and Road". The paper then proposes analytical methods, including a classification algorithm for local network relations and a comparative analysis of trade development priorities based on the local network relations. The former is used to identify and categorize key trading countries and potential trading countries for western agricultural products along the "Belt and Road". The latter is used to examine the western regions' order of priority in developing trade relations with the classified countries. According to the findings, category I agricultural trade has 37 key trading countries among the "Belt and Road" countries. Their local network relationships are classified into six groups, and their trade development priorities are classified into four levels. There are 49 key trading countries in category II agricultural trade. Their local network relations can be classified into three groups, and their trade development priorities can be classified into two levels. There are 62 key trading countries in category IV agricultural trade. Their local network relationships are classified into six groups, and their trade development priorities are classified into four levels. Furthermore, only Chile is a potential trading partner in category I agricultural trade. Finally, this paper offers policy recommendations for the development of agricultural trade along the "Belt and Road" in the western region. [ABSTRACT FROM AUTHOR]

Traffic flow forecasting is challenging for us to analyze intricate spatial–temporal dependencies and obtain incomplete information of spatial–temporal connection. Existing frameworks mostly construct spatial and temporal modeling based on a fixed graph structure and given time series. However, a fixed adjacency matrix is limited to learn effective spatial–temporal correlations of the network because it represents incomplete information for missing genuine relation. To solve the difficulty, we design a novel spatial–temporal adaptive fusion graph network (STFAGN) for traffic prediction. First, our model combines fusion convolution layers with a novel adaptive dependency matrix by end-to-end training to capture the hidden spatial-temporal dependency on the data to complete incomplete information. Second, STFAGN could, in parallel, acquire hidden spatial–temporal dependencies by a fusion operation and temporal trend by fast-DTW. Meanwhile, we use ReZero connection as a simple change of deep residual networks to facilitate deep signal propagation and faster converge. Lastly, we conduct comparative experiments on two public traffic network datasets, whose results demonstrate the superiority of our algorithm compared to state-of-the-art baseline types. Ablation experiments also prove the rationality of the framework of STFAGN. [ABSTRACT FROM AUTHOR]

Graph convolutional networks (GCNs) provide an advantage in node classification tasks for graph-related data structures. In this paper, we propose a GCN model for enhancing the performance of node classification tasks. We design a GCN layer by updating the aggregation function using an updated value of the weight coefficient. The adjacency matrix of the input graph and the identity matrix are used to calculate the aggregation function. To validate the proposed model, we performed extensive experimental studies with seven publicly available datasets. The proposed GCN layer achieves comparable results with the state-of-the-art methods. With one single layer, the proposed approach can achieve superior results. [ABSTRACT FROM AUTHOR]

In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. Let G1,nc and G2,ncbe the classes of the connected graphs of order n whose complements are bicyclic with exactly two and three cycles, respectively. In this paper, we characterize the unique minimizing graph among all the graphs which belong to Gnc= G1,nc [ G2,nc, a class of the connected graphs of order n whose complements are bicyclic. [ABSTRACT FROM AUTHOR]

Using the notions of clique partitions and edge clique covers of graphs, we consider the corresponding incidence structures. This connection furnishes lower bounds on the negative eigenvalues and their multiplicities associated with the adjacency matrix, bounds on the incidence energy, and on the signless Laplacian energy for graphs. For the more general and well-studied set S (G) of all real symmetric matrices associated with a graph G, we apply an extended version of an incidence matrix tied to an edge clique cover to establish several classes of graphs that allow two distinct eigenvalues. [ABSTRACT FROM AUTHOR]

The analysis of network structure is essential to many scientific areas ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO-based approach that only needs number-of-nodes qubits and is represented by a QUBO matrix as sparse as the input graph's adjacency matrix. The substantial improvement in the sparsity of the QUBO matrix, which is typically very dense in related work, is achieved through the novel concept of separation nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which, upon its removal from the graph, yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept by achieving an up to 95% optimal solution quality on three established real-world benchmark datasets. This work hence displays a promising approach to NISQ-ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large-scale, real-world problem instances. [ABSTRACT FROM AUTHOR]

Relation extraction tasks aim to predict potential relations between entities in a target sentence. As entity mentions have ambiguity in sentences, some important contextual information can guide the semantic representation of entity mentions to improve the accuracy of relation extraction. However, most existing relation extraction models ignore the semantic guidance of contextual information to entity mentions and treat entity mentions in and the textual context of a sentence equally. This results in low-accuracy relation extractions. To address this problem, we propose a contextual semantic-guided entity-centric graph convolutional network (CEGCN) model that enables entity mentions to obtain semantic-guided contextual information for more accurate relational representations. This model develops a self-attention enhanced neural network to concentrate on the importance and relevance of different words to obtain semantic-guided contextual information. Then, we employ a dependency tree with entities as global nodes and add virtual edges to construct an entity-centric logical adjacency matrix (ELAM). This matrix can enable entities to aggregate the semantic-guided contextual information with a one-layer GCN calculation. The experimental results on the TACRED and SemEval-2010 Task 8 datasets show that our model can efficiently use semantic-guided contextual information to enrich semantic entity representations and outperform previous models. [ABSTRACT FROM AUTHOR]

Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A (G) and D (G) and defined the A α -matrix for every real α ∈ [ 0 , 1 ] as: A α (G) = α D (G) + (1 − α) A (G). In this paper, using a different demonstration technique, we present a way to compare the Estrada index of the A α -matrix with the Estrada index of the adjacency matrix of the graph G. Furthermore, lower bounds for the Estrada index are established. [ABSTRACT FROM AUTHOR]

Graph embedding plays an important role in the analysis and study of typical non-Euclidean data, such as graphs. Graph embedding aims to transform complex graph structures into vector representations for further machine learning or data mining tasks. It helps capture relationships and similarities between nodes, providing better representations for various tasks on graphs. Different orders of neighbors have different impacts on the generation of node embedding vectors. Therefore, this paper proposes a multi-order adjacency view encoder to fuse the feature information of neighbors at different orders. We generate different node views for different orders of neighbor information, consider different orders of neighbor information through different views, and then use attention mechanisms to integrate node embeddings from different views. Finally, we evaluate the effectiveness of our model through downstream tasks on the graph. Experimental results demonstrate that our model achieves improvements in attributed graph clustering and link prediction tasks compared to existing methods, indicating that the generated embedding representations have higher expressiveness. [ABSTRACT FROM AUTHOR]

The energy of a graph G as a chemical concept leading to HMO theory was introduced by Hückel in 1931 and developed into a mathematical interpretation many years later when Gutman in 1978 gave his famous definition of the graph energy as the sum of the absolute values of the eigenvalues of the adjacency matrix of G. One of the general requirements for any topological index is that similar molecules have close TI values, which is called smoothness. To explore this property, we consider two variants of structure sensitivity and abruptness as introduced by Furtula et al. in 2013 and 2019, for hydrocarbons with up to 20 carbon atoms. Finally, we investigate the relationships between graph energies of acyclic hydrocarbons compared to their cyclic versions. [ABSTRACT FROM AUTHOR]

Nowadays, graph representation learning methods, in particular graph neural network methods, have attracted great attention and performed well in many downstream tasks. However, most graph neural network methods have a single perspective since they start from the edges (or adjacency matrix) of graphs, ignoring the mesoscopic structure (high-order local structure). In this paper, we introduce HS-GCN (High-order Node Similarity Graph Convolutional Network), which can mine the potential structural features of graphs from different perspectives by combining multiple high-order node similarity methods. We analyze HS-GCN theoretically and show that it is a generalization of the convolution-based graph neural network methods from different normalization perspectives. A series of experiments have shown that by combining high-order node similarities, our method can capture and utilize the high-order structural information of the graph more effectively, resulting in better results. [ABSTRACT FROM AUTHOR]

In recent years, graph convolutional neural networks (GCNs) have become a popular research topic due to their outstanding performance in various complex network data mining tasks. However, current research on graph neural networks lacks understanding of the high-order structural features of networks, focusing mostly on node features and first-order neighbor features. This article proposes two new models, MGAT and MGATv2, by introducing high-order structure motifs that frequently appear in networks and combining them with graph attention mechanisms. By introducing a mixed information matrix based on motifs, the generation process of graph attention coefficients is improved, allowing the model to capture higher-order structural features. Compared with the latest research on various graph neural networks, both MGAT and MGATv2 achieve good results in node classification tasks. Furthermore, through various experimental studies on real datasets, we demonstrate that the introduction of network structural motifs can effectively enhance the expressive power of graph neural networks, indicating that both high-order structural features and attribute features are important components of network feature learning. [ABSTRACT FROM AUTHOR]

The domain of Aspect Level Sentiment Classification, in which the sentiment toward a given aspect is analyzed, attracts much attention in NLP. Recently, the state-of-the-art Aspect Level Sentiment Classification methods are devised by using the Graph Convolutional Networks to deal with both the semantics and the syntax of the sentence. Generally, the parsing of syntactic structure inevitably incorporates irrelevant information toward the aspect. Besides, the syntactic and semantic alignment and uniformity that contribute to the sentiment delivery is currently neglected during processing. In this work, a Triplet Contrastive Learning Network is developed to coordinate the syntactic information and the semantic information. To start with, the aspect-oriented sub-tree is constructed to replace the syntactic adjacency matrix. Further, a sentence-level contrastive learning scheme is proposed to highlight the features of sentiment words. Based on The Triple Contrastive Learning, the syntactic information and the semantic information are thoroughly interacted and coordinated whilst the global semantics and syntax can be exploited. Extensive experiments are performed on three benchmark datasets and achieve accuracies (BERT-based) of 87.40, 82.80, 77.55 on Rest14, Lap14, and Twitter datasets, which demonstrate that our approach achieves state-of-the-art results in Aspect Level Sentiment Classification task. [ABSTRACT FROM AUTHOR]

The Estrada index of a graph G is defined as E E (G) = ∑ i = 1 n e λ i , where λ 1 , λ 2 , ... , λ n are the eigenvalues of the adjacency matrix of G. A unicyclic graph is a connected graph with a unique cycle. Let U (n , d) be the set of all unicyclic graphs with n vertices and diameter d. In this paper, we give some transformations which can be used to compare the Estrada indices of two graphs. Using these transformations, we determine the graphs with the maximum Estrada indices among U (n , d) . We characterize two candidate graphs with the maximum Estrada index if d is odd and three candidate graphs with the maximum Estrada index if d is even. [ABSTRACT FROM AUTHOR]

For α ∈ [ 0 , 1 ] , let A α (G σ) = α D (G) + (1 − α) A (G σ) , where G is a simple undirected graph, D (G) is the diagonal matrix of its vertex degrees and A (G σ) is the adjacency matrix of the signed graph G σ whose underlying graph is G. In this paper, basic properties of A α (G σ) are obtained, its positive semidefiniteness is studied and some bounds on its eigenvalues are derived—in particular, lower and upper bounds on its largest eigenvalue are obtained. [ABSTRACT FROM AUTHOR]

Let G be a graph, for any real 0 ≤ α ≤ 1 , Nikiforov defines the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G) , where A (G) and D (G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G. This paper presents some extremal results about the spectral radius ρ α (G) of the matrix A α (G) . In particular, we give a lower bound on the spectral radius ρ α (G) in terms of order and independence number. In addition, we obtain an upper bound for the spectral radius ρ α (G) in terms of order and minimal degree. Furthermore, for n > l > 0 and 1 ≤ p ≤ ⌊ n − l 2 ⌋ , let G p ≅ K l ∨ (K p ∪ K n − p − l) be the graph obtained from the graphs K l and K p ∪ K n − p − l and edges connecting each vertex of K l with every vertex of K p ∪ K n − p − l. We prove that ρ α (G p + 1) < ρ α (G p) for 1 ≤ p ≤ ⌊ n − l 2 ⌋ − 1 . [ABSTRACT FROM AUTHOR]

The ontology knowledge base (KB) can be divided into two parts: TBox and ABox, where the former models schema-level knowledge within the domain, and the latter is a set of statements of assertions or facts about instances. ABox reasoning is a process of discovering implicit knowledge in ABox based on the existing KB, which is of great value in KB applications. ABox reasoning is influenced by both the complexity of TBox and scale of ABox. The traditional logic-based ontology reasoning methods are usually designed to be provably sound and complete but suffer from long algorithm runtimes and do not scale well for ontology KB represented by OWL DL (Description Logic). In some application scenarios, the soundness and completeness of reasoning results are not the key constraints, and it is acceptable to sacrifice them in exchange for the improvement of reasoning efficiency to some extent. Based on this view, an approximate reasoning method for large-scale ABox in OWL DL KBs was proposed, which is named the ChunfyReasoner (CFR). The CFR introduces neural-symbolic learning into ABox reasoning and integrates the advantages of symbolic systems and neural networks (NNs). By training the NN model, the CFR approximately compiles the logic deduction process of ontology reasoning, which can greatly improve the reasoning speed while ensuring higher reasoning quality. In this paper, we state the basic idea, framework, and construction process of the CFR in detail, and we conduct experiments on two open-source ontologies built on OWL DL. The experimental results verify the effectiveness of our method and show that the CFR can support the applications of large-scale ABox reasoning of OWL DL KBs. [ABSTRACT FROM AUTHOR]

Let G be a graph on n vertices and m edges, with maximum degree Δ (G) and minimum degree δ (G). Let A be the adjacency matrix of G, and let λ 1 ≥ λ 2 ≥ ... ≥ λ n be the eigenvalues of G. The energy of G, denoted by E (G) , is defined as the sum of the absolute values of the eigenvalues of G, that is E (G) = | λ 1 | + ... + | λ n | . The energy of G is known to be at least twice the minimum degree of G, E (G) ≥ 2 δ (G). Akbari and Hosseinzadeh conjectured that the energy of a graph G whose adjacency matrix is nonsingular is in fact greater than or equal to the sum of the maximum and the minimum degrees of G, i.e., E (G) ≥ Δ (G) + δ (G). In this paper, we present a proof of this conjecture for hyperenergetic graphs, and we prove an inequality that appears to support the conjectured inequality. Additionally, we derive various lower and upper bounds for E (G) . The results rely on elementary inequalities and their application. [ABSTRACT FROM AUTHOR]

Traffic flow prediction is essential to the intelligent transportation system (ITS). However, due to the complex spatial-temporal dependence of traffic flow data, it is insufficient in the extraction of local and global spatial-temporal correlations for the previous process on road network and traffic flow modeling. This paper proposes an attention and wavelet-based spatial-temporal graph neural network for traffic flow and speed prediction (STAGWNN). It integrated attention and graph wavelet neural networks to capture local and global spatial information. Meanwhile, we stacked a gated temporal convolutional network (gated TCN) with a temporal attention mechanism to extract the time series information. The experiment was carried out on real public transportation datasets: PEMS-BAY and PEMSD7(M). The comparison results showed that our proposed model outperformed baseline networks on these datasets, which indicated that STAGWNN could better capture the spatial-temporal correlation information. [ABSTRACT FROM AUTHOR]

Manifold learning-based approaches have emerged as prominent techniques for dimensionality reduction. Among these methods, t-Distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) stand out as two of the most widely used and effective approaches. While both methods share similar underlying procedures, empirical observations indicate two distinctive properties: global data structure preservation and computational efficiency. However, the underlying mathematical principles behind these distinctions remain elusive. To address this gap, this study presents a comparative analysis of the subprocesses involved in these methods, aiming to elucidate the mathematical mechanisms underlying the observed distinctions. By meticulously examining the equation formulations, the mathematical mechanisms contributing to global data structure preservation and computational efficiency are elucidated. To validate the theoretical analysis, data are collected through a laboratory experiment, and an open-source dataset is utilized for validation across different datasets. The consistent alignment of results obtained from both balanced and unbalanced datasets robustly confirms the study's findings. The insights gained from this study provide a deeper understanding of the mathematical underpinnings of t-SNE and UMAP, enabling more informed and effective use of these dimensionality reduction techniques in various applications, such as anomaly detection, natural language processing, and bioinformatics. [ABSTRACT FROM AUTHOR]

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric ( M C ) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities. [ABSTRACT FROM AUTHOR]

Drug repositioning is a less expensive and time-consuming method than the traditional method of drug discovery. It is a strategy for identifying new uses for approved or investigational drugs that are outside the scope of the original medical indication. A key strategy in repositioning approved or investigational drugs is determining the binding affinity of these drugs to target proteins. The large increase in available experimental data has helped deep learning methods to demonstrate superior performance compared to conventional prediction and other traditional computational methods in precise binding affinity prediction. However, these methods are complex and time-consuming, presenting a significant barrier to their development and practical application. In this context, quantum computing (QC) and quantum machine learning (QML) theoretically offer promising solutions to effectively address these challenges. In this work, we introduce a hybrid quantum–classical framework to predict binding affinity. Our approach involves, initially, the implementation of an efficient classical model using convolutional neural networks (CNNs) for feature extraction and three fully connected layers for prediction. Subsequently, retaining the classical module for feature extraction, we implement various quantum and classical modules for binding affinity prediction, which accept the concatenated features as input. Quantum predicted modules are implemented with Variational Quantum Regressions (VQRs), while classical predicted modules are implemented with various fully connected layers. Our findings clearly show that hybrid quantum–classical models accelerate the training process in terms of epochs and achieve faster stabilization. Also, these models demonstrate quantum superiority in terms of complexity, accuracy, and generalization, thereby indicating a promising direction for QML. [ABSTRACT FROM AUTHOR]

In this paper, three sorts of network indices for the weighted three-layered graph are studied through the methods of graph spectra theory combined with analysis methods. The concept of union of graphs are applied to design two sorts of weighted layered multi-fan composed graphs, and the accurate mathematical expressions of the network indices are obtained through the derivations of Laplacian spectra; furthermore, the asymptotic properties are also derived. We find that when the cardinalities of the vertices on a sector-edge-link tend to infinity, the indices of FONC and EMFPT are irrelevant with the number of copies of the fan-substructure based on the considered graph framework. [ABSTRACT FROM AUTHOR]

With the implementation of conceptual labeling on online learning resources, knowledge-concept recommendations have been introduced to pinpoint concepts that learners may wish to delve into more deeply. As the core subject of learning, learners' preferences in knowledge concepts should be given greater attention. Research indicates that learners' preferences for knowledge concepts are influenced by the characteristics of their group structure. There is a high degree of homogeneity within a group, and notable distinctions exist between the internal and external configurations of a group. To strengthen the group-structure characteristics of learners' behaviors, a multi-task strategy for knowledge-concept recommendations is proposed; this strategy is called Knowledge-Concept Recommendations with Heterogeneous Graph-Contrastive Learning. Specifically, due to the difficulty of accessing authentic social networks, learners and their structural neighbors are considered positive contrastive pairs to construct self-supervision signals on the predefined meta-path from heterogeneous information networks as auxiliary tasks, which capture the higher-order neighbors of learners by presenting different perspectives. Then, the Information Noise-Contrastive Estimation loss is regarded as the main training objective to increase the differentiation of learners from different professional backgrounds. Extensive experiments are constructed on MOOCCube, and we find that our proposed method outperforms the other state-of-the-art concept-recommendation methods, achieving 6.66 % with H R @ 5 , 8.85 % with N D C G @ 5 , and 8.68 % with M R R . [ABSTRACT FROM AUTHOR]

The use of graph theory for solving labyrinths and mazes is well known, understanding the possible paths as the connections between the nodes that represent the corners or bifurcations. This work presents a new idea: minimizing the length of the optimal path formulated as a topology optimization problem. The maze is mapped with finite elements, and then, through the eigenvalues of the Laplacian matrix of the graph, a constraint is imposed over the connectivity between the input and the output. Several 2D examples are provided to support this approach, allowing for unequivocally finding the shortest path in mazes with multiple connections between entrance and exit, resulting in an nonheuristic algorithm. [ABSTRACT FROM AUTHOR]

To address the limitations of existing graph contrastive learning methods, which fail to adaptively integrate feature and topological information and struggle to efficiently capture multi-hop information, we propose an adaptive multi-view parallel graph contrastive learning framework (AMPGCL). It is an unsupervised graph representation learning method designed to generate task-agnostic node embeddings. AMPGCL constructs and encodes feature and topological views to mine feature and global topological information. To encode global topological information, we introduce an H-Transformer to decouple multi-hop neighbor aggregations, capturing global topology from node subgraphs. AMPGCL learns embedding consistency among feature, topology, and original graph encodings through a multi-view contrastive loss, generating semantically rich embeddings while avoiding information redundancy. Experiments on nine real datasets demonstrate that AMPGCL consistently outperforms thirteen state-of-the-art graph representation learning models in classification accuracy, whether in homophilous or non-homophilous graphs. [ABSTRACT FROM AUTHOR]

Deep Hashing is widely used for large-scale image-retrieval tasks to speed up the retrieval process. Current deep hashing methods are mainly based on the Convolutional Neural Network (CNN) or Vision Transformer (VIT). They only use the local or global features for low-dimensional mapping and only use the similarity loss function to optimize the correlation between pairwise or triplet images. Therefore, the effectiveness of deep hashing methods is limited. In this paper, we propose a dual-stream correlation-enhanced deep hashing framework (DSCEH), which uses the local and global features of the image for low-dimensional mapping and optimizes the correlation of images from the model architecture. DSCEH consists of two main steps: model training and deep-hash-based retrieval. During the training phase, a dual-network structure comprising CNN and VIT is employed for feature extraction. Subsequently, feature fusion is achieved through a concatenation operation, followed by similarity evaluation based on the class token acquired from VIT to establish edge relationships. The Graph Convolutional Network is then utilized to enhance correlation optimization between images, resulting in the generation of high-quality hash codes. This stage facilitates the development of an optimized hash model for image retrieval. In the retrieval stage, all images within the database and the to-be-retrieved images are initially mapped to hash codes using the aforementioned hash model. The retrieval results are subsequently determined based on the Hamming distance between the hash codes. We conduct experiments on three datasets: CIFAR-10, MSCOCO, and NUSWIDE. Experimental results show the superior performance of DSCEH, which helps with fast and accurate image retrieval. [ABSTRACT FROM AUTHOR]

By constructing a complex network model grounded in time series analysis, this study delves into the intricate relationships between the stock markets of 18 countries worldwide. Utilizing 31 distinct time series distance functions to formulate the network, we employ Hamming distance to quantify the resemblance between networks derived from different distance functions. By modulating the network density through distance percentiles ( p = 0.1 , 0.3, 0.5), we demonstrate the similarity of various distance functions across multiple density levels. Our findings reveal that certain distance functions exhibit high degrees of similarity across varying network densities, suggesting their potential for mutual substitution in network construction. Furthermore, the centroid network identified via hierarchical cluster analysis highlights the similarities between the stock markets of different nations, mirroring the intricate interconnections within the global financial landscape. The insights gained from this study offer crucial perspectives for comprehending the intricate network structure of global financial time series data, paving the way for further analysis and prediction of global financial market dynamics. [ABSTRACT FROM AUTHOR]

The power graph P (Z n) of Z n for a finite cyclic group Z n is a simple undirected connected graph such that two distinct nodes x and y in Z n are adjacent in P (Z n) if and only if x ≠ y and x i = y or y i = x for some non-negative integer i . In this article, we find the Laplacian eigenvalues of P (Z n) and show that P (Z n) is Laplacian integral (integer algebraic connectivity) if and only if n is either the product of two distinct primes or a prime power. That answers a conjecture by Panda, Graphs and Combinatorics, (2019). [ABSTRACT FROM AUTHOR]

Growing neural gas (GNG) has been widely used in topological mapping, clustering and unsupervised tasks. It starts from two random nodes and grows until it forms a topological network covering all data. The time required for growth depends on the total amount of data and the current network nodes. To accelerate growth, we introduce a novel distributed batch processing method to extract the rough distribution called Distributed Batch Learning Growing Neural Gas (DBL-GNG). First, instead of using a for loop in standard GNG, we adopt a batch learning approach to accelerate learning. To do this, we replace most of the standard equations with matrix calculations. Next, instead of starting with two random nodes, we start with multiple nodes in different distribution areas. Furthermore, we also propose to add multiple nodes to the network instead of adding them one by one. Finally, we introduce an edge cutting method to reduce unimportant links between nodes to obtain a better cluster network. We demonstrate DBL-GNG on multiple benchmark datasets. From the results, DBL-GNG performs faster than other GNG methods by at least 10 times. We also demonstrate the scalability of DBL-GNG by implementing a multi-scale batch learning process in it, named MS-DBL-GNG, which successfully obtains fast convergence results. In addition, we also demonstrate the dynamic data adaptation of DBL-GNG to 3D point cloud data. It is capable of processing and mapping topological nodes on point cloud objects in real time. [ABSTRACT FROM AUTHOR]

This study designed an adaptive neural network (NN) control method for a category of multi-robotic systems with parametric uncertainties. In practical engineering applications, systems commonly face design challenges due to uncertainties in their parameters. Especially when a system's parameters are completely unknown, the unpredictability caused by parametric uncertainties may increase control complexity, and even cause system instability. To address these problems, an adaptive NN compensation mechanism is proposed. Moreover, using backstepping and barrier Lyapunov functions (BLFs), guarantee that state constraints can be ensured. With the aid of the transform function, systems' convergence speeds were greatly improved. Under the implemented control strategy, the prescribed time control of multi-robotic systems with parametric uncertainties under the prescribed performance was achieved. Finally, the efficacy of the proposed control strategy was verified through the application of several cases. [ABSTRACT FROM AUTHOR]

Operation Sequencing (OS) is one of the most critical tasks in a CAPP system. This process could be modelled as a combinatorial problem where finding a suitable solution within a reasonable time interval is difficult. This work implements a novel Discrete Differential Evolution Algorithm (DDEA) to solve the OS problem, focusing on parts of up to 76 machining operations; the relationships among operations are represented as a directed graph; the contributions of the DDEA are as follows: (1) operates with a discrete representation in the space of feasible solutions; (2) employs mutation and crossover operators to update solutions and to reduce machining and setup costs, (3) possess a local search strategy to achieve better solutions, and (4) integrates a statistical method based on quantiles to measure the quality and likelihood for an achieving a solution. To demonstrate the efficiency and robustness of the DDEA, five prismatic parts with different numbers of machining operations as benchmarks to address the OS problem were selected. The results generated the same OS for parts with a few machining operations (up to 23 machining operations). Conversely, for parts with more machining operations, the DDEA needs more runs to achieve the best solution. [ABSTRACT FROM AUTHOR]

In recent years, convolutional neural networks (CNNs) have emerged as highly efficient architectures for image and audio classification tasks, gaining widespread adoption in state-of-the-art methodologies. While CNNs excel in machine learning scenarios where the data representation exhibits a grid structure, they face challenges in generalizing to other data types. For instance, they struggle with data structured on 3D meshes (e.g., measurements from a network of meteorological stations) or data represented by graph structures (e.g., molecular graphs). To address such challenges, the scientific literature proposes novel graph-based convolutional network architectures, extending the classical convolution concept to data structures defined by graphs. In this paper, we use such a deep learning architecture to examine graphs defined using the ICD-10 codes appearing in the medical data of patients who suffered hemorrhagic stroke in Hungary in the period 2006–2012. The purpose of the analysis is to predict the risk of stroke by examining a patient's ICD graph. Finally, we also compare the effectiveness of this method with classical machine learning classification methods. The results demonstrate that the graph-based method can predict the risk of stroke with an accuracy of over 73%, which is more than 10% higher than the classical methods. [ABSTRACT FROM AUTHOR]

In online social networks, users can vote on different trust levels for each other to indicate how much they trust their friends. Researchers have improved their ability to predict social trust relationships through a variety of methods, one of which is the graph neural network (GNN) method, but they have also brought the vulnerability of the GNN method into the social trust network model. We propose a data-poisoning attack method for GNN-based social trust models based on the characteristics of social trust networks. We used a two-sample test for power-law distributions of discrete data to avoid changes in the dataset being detected and used an enhanced surrogate model to generate poisoned samples. We further tested the effectiveness of our approach on three real-world datasets and compared it with two other methods. The experimental results using three datasets show that our method can effectively avoid detection. We also used three metrics to illustrate the effectiveness of our attack, and the experimental results show that our attack stayed ahead of the other two methods in all three datasets. In terms of one of our metrics, our attack method decreased the accuracies of the attacked models by 12.6%, 22.8%, and 13.8%. [ABSTRACT FROM AUTHOR]

Breast cancer is the first cancer incidence and the second cancer mortality in women. Therefore, for the life and health of breast cancer patients, the research and development of breast cancer drugs should be accelerated. In drug development, the search for compounds with good bioactivity, pharmacokinetics, and safety, including Absorption, Distribution, Metabolism, Excretion, and Toxicity (ADMET), has always been a time-consuming and labor-intensive process. In this paper, the relationship between the molecular descriptor and ADMET properties of compounds is studied. Aiming at the problem of composite ADMET attribute classification, a Stacking Algorithm based on Graph Convolutional Network (SA-GCN) was proposed. Firstly, feature selection was performed in the data of molecular descriptors. Then the SA-GCN is developed by integrating the advantages of ten classical classification algorithms. Finally, various performance indicators were used to conduct comparative experiments. Experiments show that the SA-GCN is superior to other classifiers in the classification performance of ADMET, and the classification accuracy is 97.6391%, 98.1450%, 94.4351%, 96.4587%, and 97.9764% compared to other classifiers. Therefore, this method can be well applied to the classification of ADMET properties of compounds and then could provide some help to screen out compounds with good biological activities. [ABSTRACT FROM AUTHOR]

Urban crowd flow prediction is an important task for transportation systems and public safety. While graph convolutional networks (GCNs) have been widely adopted for this task, existing GCN-based methods still face challenges. Firstly, they employ fixed receptive fields, failing to account for urban region heterogeneity where different functional zones interact distinctly with their surroundings. Secondly, they lack mechanisms to adaptively adjust spatial receptive fields based on temporal dynamics, which limits prediction performance. To address these limitations, we propose an Adaptive Receptive Field Graph Convolutional Network (ARFGCN) for urban crowd flow prediction. ARFGCN allows each region to independently determine its receptive field size, adaptively adjusted and learned in an end-to-end manner during training, enhancing model prediction performance. It comprises a time-aware adaptive receptive field (TARF) gating mechanism, a stacked 3DGCN, and a prediction layer. The TARF aims to leverage gating in neural networks to adapt receptive fields based on temporal dynamics, enabling the predictive network to adapt to urban regional heterogeneity. The TARF can be easily integrated into the stacked 3DGCN, enhancing the prediction. Experimental results demonstrate ARFGCN's effectiveness compared to other methods. [ABSTRACT FROM AUTHOR]

Predicting breakthrough papers holds great significance; however, prior studies encountered challenges in this task, indicating a need for substantial improvement. We propose that the failure to capture the dynamic structural-evolutionary features of citation networks is one of the major reasons. To overcome this limitation, this paper introduces a new method for constructing citation cascades of focus papers, allowing the creation of a time-series-like set of citation cascades. Then, through a thorough review, three types of structural indicators in these citation networks that could reflect breakthroughs are identified, including certain basic topological metrics, PageRank values, and the von Neumann graph entropy. Based on the time-series-like set of citation cascades, the dynamic trajectories of these indicators are calculated and employed as predictors. Using the Nobel Prize-winning papers as a landmark dataset, our prediction method yields approximately a 7% improvement in the ROC-AUC score compared to static-based prior methods. Additionally, our method advances in achieving earlier predictions than other previous methods. The main contribution of this paper is proposing a novel method for creating citation cascades in chronological order and confirming the significance of predicting breakthroughs from a dynamic structural perspective. [ABSTRACT FROM AUTHOR]

Localizing the brain regions affected by tasks is crucial to understanding the mechanisms of brain function. However, traditional statistical analysis does not accurately identify the brain regions of interest due to factors such as sample size, task design, and statistical effects. Here, we propose a hypergraph-based multitask feature selection framework, referred to as HMTFS, which we apply to a functional magnetic resonance imaging (fMRI) dataset to extract task-related brain regions. HMTFS is characterized by its ability to construct a hypergraph through correlations between subjects, treating each subject as a node to preserve high-order information of time-varying signals. Additionally, it manages feature selection across different time windows in fMRI data as multiple tasks, facilitating time-constrained group sparse learning with a smoothness constraint. We utilize a large fMRI dataset from the Human Connectome Project (HCP) to validate the performance of HMTFS in feature selection. Experimental results demonstrate that brain regions selected by HMTFS can provide higher accuracy for downstream classification tasks compared to other competing feature selection methods and align with findings from previous neuroscience studies. [ABSTRACT FROM AUTHOR]