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In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs are reported. Examples are provided to illustrate the applications of this product in some growing graphs and complex networks. [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]

Language phrases are an effective way to express uncertain pieces of information, and easily conforms to the language habits of decision makers to describe the evaluation of things. The consistency judgment of a linguistic judgment matrices is the key to analytic hierarchy process (AHP). If a linguistic judgment matrix has a satisfactory consistency, then the rank of the decision schemes can be determined. In this study, the comparison relation between the decision schemes is first represented by a directed graph. The preference relation matrix of the linguistic judgment matrix is the adjacency matrix of the directed graph. We can use the $ n - 1 $ st power of the preference relation to judge the linguistic judgment matrix whether has a satisfactory consistency. The method is utilized if there is one and only one element in the $ n - 1 $ st power of the preference relation, and the element 1 is not on the main diagonal. Then the linguistic judgment matrix has a satisfactory consistency. If there are illogical judgments, the decision schemes that form a 3-loop can be identified and expressed through the second-order sub-matrix of the preference relation matrix. The feasibility of this theory can be verified through examples. The corresponding schemes for illogical judgments are represented in spatial coordinate system.

We extend the notion of balance from the realm of signed and gain graphs to conjugate skew gain graphs which are skew gain graphs where the labels on the oriented edges get conjugated when we reverse the orientation. We characterize the balance in a conjugate skew gain graph in several ways especially by dealing with its adjacency matrix and the g -Laplacian matrix. We also deal with the concept of anti-balance in conjugate skew gain graphs. [ABSTRACT FROM AUTHOR]

This paper presents a collaborative filtering algorithm based on reinforcement learning theory. Then, the personalized bank financial recommendation system for users is constructed in the massive data environment. Tags mimic different types of user interest points to build a representative personalized data set. The collaborative screening of bank financial products is realized using the simulation results and users' historical access records. The ranking calculation of related financial products is added to the general bank financial product recommendation system. This method can more accurately express the query results for a specific user. It is found that the collaborative filtering algorithm based on enhanced learning theory can improve the efficiency of collaborative screening of bank financial products. The best results can be obtained by combining the two organically. This paper proposes that the recommendation algorithm of reinforcement learning bank financial products based on user preference and collaborative filtering is feasible. [ABSTRACT FROM AUTHOR]

In addressing the challenges of trajectory prediction in multi-ship interaction scenarios and aiming to improve the accuracy of multi-ship trajectory prediction, this paper proposes a multi-ship trajectory prediction model, GL-STGCNN. The GL-STGCNN model employs a ship interaction adjacency matrix extraction module to obtain a more reasonable ship interaction adjacency matrix. Additionally, after obtaining the distribution of predicted trajectories using the model, a model predictive control trajectory correction method is introduced to enhance the accuracy and reasonability of the predicted trajectories. Through quantitative analysis of different datasets, it was observed that GL-STGCNN outperforms previous prediction models with a 31.8% improvement in the average displacement error metric and a 16.8% improvement in the final displacement error metric. Furthermore, trajectory correction through model predictive control shows a performance boost of 44.5% based on the initial predicted trajectory distribution. While GL-STGCNN excels in multi-ship interaction trajectory prediction by reasonably modeling ship interaction adjacency matrices and employing trajectory correction, its performance may vary in different datasets and ship motion patterns. Future work could focus on adapting the model's ship interaction adjacency matrix modeling to diverse environmental scenarios for enhanced performance. [ABSTRACT FROM AUTHOR]

Aspect-level sentiment analysis is used to predict the sentiment polarity of a specific aspect in a sentence. However, most current research cannot fully utilize semantic information, and the models lack robustness. Therefore, this article proposes a model for aspect-level sentiment analysis based on a combination of adversarial training and dependency syntax analysis. First, BERT is used to transform word vectors and construct adjacency matrices with dependency syntactic relationships to better extract semantic dependency relationships and features between sentence components. A multi-head attention mechanism is used to fuse the features of the two parts, simultaneously perform adversarial training on the BERT embedding layer to enhance model robustness, and, finally, to predict emotional polarity. The model was tested on the SemEval 2014 Task 4 dataset. The experimental results showed that, compared with the baseline model, the model achieved significant performance improvement after incorporating adversarial training and dependency syntax relationships. [ABSTRACT FROM AUTHOR]

Data exploration, usually the first step in data analysis, is a useful method to tackle challenges caused by big geoscience data. It conducts quick analysis of data, investigates the patterns, and generates/refines research questions to guide advanced statistics and machine learning algorithms. The background of this work is the open mineral data provided by several sources, and the focus is different types of associations in mineral properties and occurrences. Researchers in mineralogy have been applying different techniques for exploring such associations. Although the explored associations can lead to new scientific insights that contribute to crystallography, mineralogy, and geochemistry, the exploration process is often daunting due to the wide range and complexity of factors involved. In this study, our purpose is implementing a visualization tool based on the adjacency matrix for a variety of datasets and testing its utility for quick exploration of association patterns in mineral data. Algorithms, software packages, and use cases have been developed to process a variety of mineral data. The results demonstrate the efficiency of adjacency matrix in real-world usage. All the developed works of this study are open source and open access.

In today's world, various approaches and parameters exist for designing a plan and determining its spatial, placement. Hence, various modes for identifying crucial locations can be explored when an architectural plan is designed in different dimensions. While designing all these modes takes considerable time, there are numerous potential applications for artificial intelligence (AI) in this domain. This study aims to compute and use an adjacency matrix to generate architectural residential plans. Additionally, it develops a plan generation algorithm in Rhinoceros software, utilizing the Grasshopper plugin to create a dataset of architectural plans. In the following step, the data was entered into a neural network to identify the architectural plan's type, furniture, icons, and use of spaces, which was achieved using YOLOv4, EfficientDet, YOLOv5, DetectoRS, and RetinaNet. The algorithm's execution, testing, and training were conducted using Darknet and PyTorch. The research dataset comprises 12,000 plans, with 70% employed in the training phase and 30% in the testing phase. The network was appropriately trained practically and precisely in relation to an average precision (AP) resulting of 91.50%. After detecting the types of space use, the main research algorithm has been designed and coded, which includes determining the adjacency matrix of architectural plan spaces in seven stages. All research processes were conducted in Python, including dataset preparation, network object detection, and adjacency matrix algorithm design. Finally, the adjacency matrix is given to the input of the proposed plan generator network, which consequently, based on the resulting adjacency, obtains different placement modes for spaces and furniture.

This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]

In today's world, various approaches and parameters exist for designing a plan and determining its spatial, placement. Hence, various modes for identifying crucial locations can be explored when an architectural plan is designed in different dimensions. While designing all these modes takes considerable time, there are numerous potential applications for artificial intelligence (AI) in this domain. This study aims to compute and use an adjacency matrix to generate architectural residential plans. Additionally, it develops a plan generation algorithm in Rhinoceros software, utilizing the Grasshopper plugin to create a dataset of architectural plans. In the following step, the data was entered into a neural network to identify the architectural plan's type, furniture, icons, and use of spaces, which was achieved using YOLOv4, EfficientDet, YOLOv5, DetectoRS, and RetinaNet. The algorithm's execution, testing, and training were conducted using Darknet and PyTorch. The research dataset comprises 12,000 plans, with 70% employed in the training phase and 30% in the testing phase. The network was appropriately trained practically and precisely in relation to an average precision (AP) resulting of 91.50%. After detecting the types of space use, the main research algorithm has been designed and coded, which includes determining the adjacency matrix of architectural plan spaces in seven stages. All research processes were conducted in Python, including dataset preparation, network object detection, and adjacency matrix algorithm design. Finally, the adjacency matrix is given to the input of the proposed plan generator network, which consequently, based on the resulting adjacency, obtains different placement modes for spaces and furniture. [ABSTRACT FROM AUTHOR]

Emotion is one of the most important higher cognitive functions of the human brain and plays an important role in transaction processing and decisions. In traditional emotion recognition studies, the frequency band features in EEG signals have been shown to have a high correlation with emotion production. However, traditional emotion recognition methods cannot satisfactorily solve the problem of individual differences in subjects and data heterogeneity in EEG, and subject-independent emotion recognition based on EEG signals has attracted extensive attention from researchers. In this paper, we propose a subject-independent emotion recognition model based on adaptive extraction of layer structure based on frequency bands (BFE-Net), which is adaptive in extracting EEG map features through the multi-graphic layer construction module to obtain a frequency band-based multi-graphic layer emotion representation. To evaluate the performance of the model in subject-independent emotion recognition studies, extensive experiments are conducted on two public datasets including SEED and SEED-IV. The experimental results show that in most experimental settings, our model has a more advanced performance than the existing studies of the same type. In addition, the visualization of brain connectivity patterns reveals that some of the findings are consistent with previous neuroscientific validations, further validating the model in subject-independent emotion recognition studies. [ABSTRACT FROM AUTHOR]

Let A(G) be the adjacency matrix of a simple connected undirected graph G. A graph G of order n is said to be non-singular (respectively singular) if A(G) is non-singular (respectively singular). The spectrum of a graph G is the set of all its eigenvalues denoted by spec(G). The antireciprocal (respectively reciprocal) eigenvalue property for a graph G can be defined as "Let G be a non-singular graph G if the negative reciprocal (respectively positive reciprocal) of each eigenvalue is likewise an eigenvalue of G, then G has anti-reciprocal (respectively reciprocal) eigenvalue property." Furthermore, a graph G is said to have strong anti-reciprocal eigenvalue property (resp. strong reciprocal eigenvalue property) if the eigenvalues and their negative (resp. positive) reciprocals are of same multiplicities. In this article, graphs satisfying anti-reciprocal eigenvalue (or property (-R)) and strong anti-reciprocal eigenvalue property (or property (-SR)) are discussed. [ABSTRACT FROM AUTHOR]

For the adjacency matrix A(G) and diagonal matrix of the vertex degrees D(G) of a simple graph G, the A(G) matrix is the convex combinations of D(G) and A(G), and is defined as A(G) = D(G)+(1)A(G), for 0 n be the eigenvalues of A(G) (which we call -adjacency eigenvalues of the graph G). The generalized adjacency energy also called -adjacency energy of the graph G is defined as EA (G) = is the average vertex degree, m is the size and n is the order of G. The -adjacency energy of a graph G merges the theory of energy (adjacency energy) and the signless Laplacian energy, as EA0 (G) = E (G) and 2E A 12 (G) = QE(G), where E (G) is the energy and QE(G) is the signless Laplacian energy of G. In this paper, we obtain some new upper and lower bounds for the generalized adjacency energy of a graph, in terms of different graph parameters like the vertex covering number, the Zagreb index, the number of edges, the number of vertices, etc. We characterize the extremal graphs attained these bounds. [ABSTRACT FROM AUTHOR]

With the rapid advancement of deep learning, 3D human pose estimation has largely freed itself from reliance on manually annotated methods. The effective utilization of joint features has become significant. Utilizing 2D human joint information to predict 3D human skeletons is of paramount importance. Effectively leveraging 2D joint data can improve the accuracy of 3D human skeleton prediction. In this paper, we propose the SCGFormer model to reduce the error in predicting human skeletal poses in three-dimensional space. The network architecture of SCGFormer encompasses Transformer and two distinct types of graph convolution, organized into two interconnected modules: SGraAttention and AcChebGconv. SGraAttention extracts global feature information from each 2D human joint, thereby augmenting local feature learning by integrating prior knowledge of human joint relationships. Simultaneously, AcChebGconv broadens the receptive field for graph structure information and constructs implicit joint relationships to aggregate more valuable adjacent features. SCGraFormer is tested on widely recognized benchmark datasets such as Human3.6M and MPI-INF-3DHP and achieves excellent results. In particular, on Human3.6M, our method achieves the best results in 9 actions (out of a total of 15 actions), with an overall average error reduction of about 1.5 points compared to state-of-the-art methods, demonstrating the excellent performance of SCGFormer. [ABSTRACT FROM AUTHOR]

The concept of a swarm of drones assumes the presence of a wireless ad hoc network, in which drones are network nodes and exchanging information with each other. This article is devoted to studying the behavior of an ad hoc network in a transient mode and assessing the characteristics of updating local adjacency matrices (LAM), which allow network nodes to autonomously form packet transmission routes. Using a simulation model, a comparison was made of two multiple access methods to a common data transmission channel in the process of updating matrices: cyclic and random (slotted ALOHA). The simulation results made it possible to determine areas of their effective application: slotted ALOHA is advisable to use with relatively high probabilities of packet distortion (of the order of 0.1 and higher), a numerous nodes (more than 40), and low network connectivity, and cyclic access (CA) is effective at a low level of distortion. It is shown that the completion of the process of updating adjacency matrices (AM) can be judged by such indicators of the exchange of routing information as the achievement of a certain threshold of the number of transmissions and a decrease in the level of network traffic.

In this note we show that for each positive integer a⩾2 there exist infinitely many trees whose spectral radius is equal to 2a. Such trees are obtained by replacing the central edge of the double star S(a,2a−2) with suitable bidegreed caterpillars.

Video motion recognition plays a crucial role in advanced sports analysis. With video motion recognition, sports analytics has become more data-driven and result-oriented, significantly enhancing the professionalism and efficiency in the sports domain. Over the years, the accuracy of skelecton-based motion recognition algorithms using Recurrent Neural Networks (RNNs) and Convolutional Neural Networks (ConvNets) has plateaued on relevant datasets, struggling to achieve further breakthroughs. This is partly because RNNs lack sufficient capability to model spatial structural features, and while ConvNets can alleviate difficulties in modeling spatial structures, the conversion of skelecton sequences into RGB pseudo-images inherently leads to some information loss. Moreover, ConvNets are not particularly adept at modeling temporal features. Since the associations between articulations in bodily skelectons are better represented using a graph structure, Graph Convolution Network (GCN)-based skelecton motion recognition methods have gained more attention. Recent advancements in Shift Graph Convolutional Network (S-GCN) have enhanced the expressiveness of spatial graphs while improving the versatility of spatial and temporal graph receptive fields. To further enhance this versatility, we propose the Dynamic Motion-Aware Shift Graph Convolutional Network (DMA-SGCN) for video motion recognition. Specifically, we introduce a data-aware driven method to represent associations between articulations. By analyzing the attributes of different motions and combining them with the natural associations of the bodily skelecton, we compute articulation affinities through representation learning. This approach not only improves the accuracy in defining articulation associations but also enhances the awareness of related articulation associations during motion behaviours. Furthermore, we dynamically use the adjacency matrix of skeletal data to guide the feature transfer between articulations. This topological method allows for more effective shift transformations based on articulation associations, addressing the issue of rigid receptive fields in previous GCNs for motion recognition. Contrast and ablation experiments on the largest 3D motion recognition dataset demonstrate that starting from the skeletal data and the motions themselves enables more accurate excavation of dynamic associations of skeletal articulations in the individual motion recognition.

AbstractThe aim of this paper is to study the determinant and inverse of the adjacency matrices of weighted and directed versions of Boolean graphs. Our approach is recursive. We describe the adjacency matrix of a weighted Boolean graph in terms of the adjacency matrix of a smaller-sized weighted Boolean graph. This allows us to compute the determinant and inverse of the adjacency matrix of a weighted Boolean graph recursively. In particular, we show that the determinant of a directed Boolean graph is 1. Further, using a classical theorem of Cayley which expresses the determinant of any skew-symmetric matrix as a square of its Pfaffian, we show that for any directed Boolean graph, the characteristic polynomial has all its even degree coefficients strictly positive with the odd ones being zero.

This study employs deep learning techniques to present a compelling approach for modeling brain connectivity in EEG motor imagery classification through graph embedding. The compelling aspect of this study lies in its combination of graph embedding, deep learning, and different brain connectivity types, which not only enhances classification accuracy but also enriches the understanding of brain function. The approach yields high accuracy, providing valuable insights into brain connections and has potential applications in understanding neurological conditions. The proposed models consist of two distinct graph-based convolutional neural networks, each leveraging different types of brain connectivities to enhance classification performance and gain a deeper understanding of brain connections. The first model, Adjacency-based Convolutional Neural Network Model (Adj-CNNM), utilizes a graph representation based on structural brain connectivity to embed spatial information, distinguishing it from prior spatial filtering approaches dependent on subjects and tasks. Extensive tests on a benchmark dataset-IV-2a demonstrate that an accuracy of 72.77% is achieved by the Adj-CNNM, surpassing baseline and state-of-the-art methods. The second model, Phase Locking Value Convolutional Neural Network Model (PLV-CNNM), incorporates functional connectivity to overcome structural connectivity limitations and identifies connections between distinct brain regions. The PLV-CNNM achieves an overall accuracy of 75.10% across the 1-51 Hz frequency range. In the preferred 8-30 Hz frequency band, known for motor imagery data classification (includingα, μ, and β waves), individual accuracies of 91.9%, 90.2%, and 85.8% are attained for α, μ, and β, respectively. Moreover, the model performs admirably with 84.3% accuracy when considering the entire 8-30 Hz band. Notably, the PLV-CNNM reveals robust connections between different brain regions during motor imagery tasks, including the frontal and central cortex and the central and parietal cortex. These findings provide valuable insights into brain connectivity patterns, enriching the comprehension of brain function. Additionally, the study offers a comprehensive comparative analysis of diverse brain connectivity modeling methods. [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]

The Rubik's Cube mechanism (RCM) is a kind of reconfigurable mechanism with multiple characteristics such as multiple configurations, variable topology, strong coupling, and reconfigurability. Crossover research on the RCM with mathematics, chemistry, cryptography, and other disciplines has led to important breakthroughs and progress. It is obvious that the invention and creation of a new RCM can provide important ideological inspiration and theoretical guidance for the accelerated iterative updating of Rubik's Cube products and the expansion of their applications. This paper investigates the type synthesis method for a regular hexagonal prism (RHP) RCM (RHPRCM). Through analysis of the reconfigurable movement process of the RCM, two mechanism factors are abstracted, a type synthesis process for the RHPRCM is proposed, a symmetry layout method for the RCM's revolute axis based on the RHP space polyhedron is proposed, and an analysis method for the intersection of the revolute pair contact surfaces (RPCSs) based on the adjacency matrix is proposed. Taking a revolute axis passing through the center of an RHP and having only one RPCS for each revolute axis as an example, an RHPRCM with different topological structures is synthesized. The relevant research in this paper can provide methodological guidance for the synthesis of other spatial RCMs. [ABSTRACT FROM AUTHOR]

In the paper, we introduce the signless Laplacian ABC-matrix Q̃(G)=D¯(G)+Ã(G), where D¯(G) is the diagonal matrix of ABC-degrees and Ã(G) is the ABC-matrix of G. The eigenvalues of the matrix Q̃(G) are the signless Laplacian ABC-eigenvalues of G. We give some basic properties of the matrix Q̃(G), which includes relating independence number and clique number with signless Laplacian ABC-eigenvalues. For bipartite graphs, we show that the signless Laplacian ABC-spectrum and the Laplacian ABC-spectrum are the same. We characterize the graphs with exactly two distinct signless Laplacian ABC-eigenvalues. Also, we consider the problem of the characterization of the graphs with exactly three distinct signless Laplacian ABC-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 Q̃(G)−tr(Q̃(G))nI, called the signless Laplacian ABC-energy of G. We obtain some upper and lower bounds for signless Laplacian ABC-energy and characterize the extremal graphs attaining it. Further, for graphs of order at most 6, we compare the signless Laplacian energy and the ABC-energy with the signless Laplacian ABC-energy and found that the latter behaves well, as there is a single pair of graphs with the same signless Laplacian ABC-energy unlike the 26 pairs of graphs with same signless Laplacian energy and eight pairs of graphs with the same ABC-energy.

In addressing the challenges of trajectory prediction in multi-ship interaction scenarios and aiming to improve the accuracy of multi-ship trajectory prediction, this paper proposes a multi-ship trajectory prediction model, GL-STGCNN. The GL-STGCNN model employs a ship interaction adjacency matrix extraction module to obtain a more reasonable ship interaction adjacency matrix. Additionally, after obtaining the distribution of predicted trajectories using the model, a model predictive control trajectory correction method is introduced to enhance the accuracy and reasonability of the predicted trajectories. Through quantitative analysis of different datasets, it was observed that GL-STGCNN outperforms previous prediction models with a 31.8% improvement in the average displacement error metric and a 16.8% improvement in the final displacement error metric. Furthermore, trajectory correction through model predictive control shows a performance boost of 44.5% based on the initial predicted trajectory distribution. While GL-STGCNN excels in multi-ship interaction trajectory prediction by reasonably modeling ship interaction adjacency matrices and employing trajectory correction, its performance may vary in different datasets and ship motion patterns. Future work could focus on adapting the model’s ship interaction adjacency matrix modeling to diverse environmental scenarios for enhanced performance.

Campus safety is related to the healthy growth of students, and the research focus of this paper is to explore the impact of Internet of Things (IoT) technology on campus safety prevention and control. Based on the correlation between ISM and DEMATEL methods, this paper constitutes an integrated DEMATEL-ISM model by using neighbor matrix and reachable matrix to transform each other. It constructs a risk factor model for campus security prevention and control evaluation based on Internet of Things technology according to the modeling steps after soliciting experts’ suggestions through questionnaires. Combined with the SEM model to estimate students’ campus risk identification ability, the path index was used to construct the college security awareness score index to explore the relationship between latent variables (influencing factors) and observed variables (risk identification ability). The results show that every 1% increase in the safety climate of the social environment will lead to the rise of 0.58%, 0.20%, and 0.52% in the on-campus environment factor, the campus safety management team building factor, and the students’ literacy factor, respectively. A 0.17% increase in the on-campus environment will occur with every 1% increase in students’ literacy in higher education. This study contributes to a deeper understanding of the role of IoT technology in enhancing campus security prevention and control. It can provide deep research references for subsequent risk grading evaluation, risk warning prevention and control, and supervision in campus risk management.

This study employs deep learning techniques to present a compelling approach for modeling brain connectivity in EEG motor imagery classification through graph embedding. The compelling aspect of this study lies in its combination of graph embedding, deep learning, and different brain connectivity types, which not only enhances classification accuracy but also enriches the understanding of brain function. The approach yields high accuracy, providing valuable insights into brain connections and has potential applications in understanding neurological conditions. The proposed models consist of two distinct graph-based convolutional neural networks, each leveraging different types of brain connectivities to enhance classification performance and gain a deeper understanding of brain connections. The first model, Adjacency-based Convolutional Neural Network Model (Adj-CNNM), utilizes a graph representation based on structural brain connectivity to embed spatial information, distinguishing it from prior spatial filtering approaches dependent on subjects and tasks. Extensive tests on a benchmark dataset-IV-2a demonstrate that an accuracy of 72.77% is achieved by the Adj-CNNM, surpassing baseline and state-of-the-art methods. The second model, Phase Locking Value Convolutional Neural Network Model (PLV-CNNM), incorporates functional connectivity to overcome structural connectivity limitations and identifies connections between distinct brain regions. The PLV-CNNM achieves an overall accuracy of 75.10% across the 1–51 Hz frequency range. In the preferred 8–30 Hz frequency band, known for motor imagery data classification (including α, μ, and β waves), individual accuracies of 91.9%, 90.2%, and 85.8% are attained for α, μ, and β, respectively. Moreover, the model performs admirably with 84.3% accuracy when considering the entire 8–30 Hz band. Notably, the PLV-CNNM reveals robust connections between different brain regions during motor imagery tasks, including the frontal and central cortex and the central and parietal cortex. These findings provide valuable insights into brain connectivity patterns, enriching the comprehension of brain function. Additionally, the study offers a comprehensive comparative analysis of diverse brain connectivity modeling methods.

Emotion is one of the most important higher cognitive functions of the human brain and plays an important role in transaction processing and decisions. In traditional emotion recognition studies, the frequency band features in EEG signals have been shown to have a high correlation with emotion production. However, traditional emotion recognition methods cannot satisfactorily solve the problem of individual differences in subjects and data heterogeneity in EEG, and subject-independent emotion recognition based on EEG signals has attracted extensive attention from researchers. In this paper, we propose a subject-independent emotion recognition model based on adaptive extraction of layer structure based on frequency bands (BFE-Net), which is adaptive in extracting EEG map features through the multi-graphic layer construction module to obtain a frequency band-based multi-graphic layer emotion representation. To evaluate the performance of the model in subject-independent emotion recognition studies, extensive experiments are conducted on two public datasets including SEED and SEED-IV. The experimental results show that in most experimental settings, our model has a more advanced performance than the existing studies of the same type. In addition, the visualization of brain connectivity patterns reveals that some of the findings are consistent with previous neuroscientific validations, further validating the model in subject-independent emotion recognition studies.

With the rapid advancement of deep learning, 3D human pose estimation has largely freed itself from reliance on manually annotated methods. The effective utilization of joint features has become significant. Utilizing 2D human joint information to predict 3D human skeletons is of paramount importance. Effectively leveraging 2D joint data can improve the accuracy of 3D human skeleton prediction. In this paper, we propose the SCGFormer model to reduce the error in predicting human skeletal poses in three-dimensional space. The network architecture of SCGFormer encompasses Transformer and two distinct types of graph convolution, organized into two interconnected modules: SGraAttention and AcChebGconv. SGraAttention extracts global feature information from each 2D human joint, thereby augmenting local feature learning by integrating prior knowledge of human joint relationships. Simultaneously, AcChebGconv broadens the receptive field for graph structure information and constructs implicit joint relationships to aggregate more valuable adjacent features. SCGraFormer is tested on widely recognized benchmark datasets such as Human3.6M and MPI-INF-3DHP and achieves excellent results. In particular, on Human3.6M, our method achieves the best results in 9 actions (out of a total of 15 actions), with an overall average error reduction of about 1.5 points compared to state-of-the-art methods, demonstrating the excellent performance of SCGFormer.

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.

• A novel dynamic graph attention network is proposed for EEG emotion recognition. • The high accuracy can be obtained from the DGAT model in EEG emotion recognition. • The channel connectivity can reflect the synergistic relationships within the brain. Deep learning classification models based on electroencephalogram (EEG) emotion recognition have demonstrated considerable proficiency in the categorization of emotional states. However, these models have limitations in their capability to analyze the active states and cooperative relationships among distinct brain regions. This study proposes a dynamic graph attention network (DGAT) for EEG emotion recognition, which learns the features of each channel and leverages multiple-head self-attention mechanisms to capture non-Euclidean relationships between channels. Then, we use differential entropy features of emotions signals on the SJTU emotion EEG dataset (SEED). The DGAT model achieved improved subject-dependent and cross-subject classification accuracy compared to previous models. Moreover, ablation studies show that the channel weight matrix(CWM) and appropriate hyper-parameters can improve the performance of the DGAT model significantly. Furthermore, by conducting interpretable analysis of the new connections and electrode weights learned by the model, we find that these connection weight relationships reflect a certain degree of coordination within the brain for EEG-based emotion recognition. These findings provide a new method for EEG emotion recognition and highlights the potential for using deep learning models to analyze the active state and synergistic relationships among brain regions. [ABSTRACT FROM AUTHOR]

Power forecast for each renewable power plant (RPP) in the renewable energy clusters is essential. Though existing graph neural networks (GNN)-based models achieve satisfactory prediction performance by capturing dependencies among distinct RPPs, the static graph structure employed in these models ignores crucial lead-lag correlations among RPPs, resulting from the time difference of the air flow at spatially dispersed RPPs. To address this problem, this paper proposes a novel dynamic graph structure using multiple temporal granularity groups (TGGs) to characterize the lead-lag correlations among RPPs. A granular-based GNN called GGNet is designed to generate an optimal adjacency matrix for the proposed graph structure. Specifically, a two-dimensional convolutional neural network (2D-CNN) is used to quantify the uncertain lead-lag correlations among RPPs; secondly, a gate mechanism is used to calculate a dynamic adjacency matrix; Finally, a graph attention network (GAT) is used to aggregate the information on RPPs based on the well-learned adjacency matrix. Case studies conducted using real-world datasets, with wind power plants and photovoltaic power plants, show our method outperforms state-of-the-art (SoTA) ones with better performance. Compared with the SoTA models, the RMSE N and MAE N of wind power plants for 1–4 h forecast steps decreased on average by 22.925% and 13.18%, respectively; the RMSE N and MAE N of photovoltaic power plants for 1–4 h forecast steps decreased on average by 48.95% and 18.75%, respectively. The results show that the proposed framework can generate improved performance with accuracy and robustness. • Dynamic graph structure can clarify lead-lag power correlation of renewable plants. • A novel model can quantity the lead-lag power correlation of renewable plants. • Memory cell can make the adjacency matrix among renewable plants learnable. • A graph attention network can improve power forecast accuracy of renewable plants. [ABSTRACT FROM AUTHOR]

Ergonomic risk assessment (ERA) is commonly used to identify and analyze postures that are detrimental to the health of workers in industrial workplaces, which is vital to prevent work-related musculoskeletal disorders (WMSDs). Among the automatic approaches, algorithms based on graph convolutional networks (GCNs) have shown promising results in ERA using skeleton sequence as input. However, previous GCN-based methods still have certain limitations. First, the separated modeling of spatial and temporal information and the manually pre-defined topology of graph may restrict the representation diversity of the networks. Additionally, RNN-based temporal modeling often incurs high computational costs and fails to capture long-range temporal dependencies, thereby reducing flexibility in describing long videos. To overcome these challenges, in this study, we propose an attention-based adaptive spatial–temporal graph convolutional network (AAST-GCN), aiming to achieve effective and efficient action representation for ERA in long video. First, we employ an alternate modeling strategy to effectively capture the spatial–temporal information, and propose an improved adaptive adjacency matrix scheme to learn various coordination and relations of body-joints, thus enhancing the flexibility to model diverse postures. Furthermore, we introduce an efficient multi-scale temporal convolutional network as a replacement for RNN-based algorithms, enabling the network to extract various granularities of temporal features. Moreover, to make the network focuses on more valuable information, we employ a spatial–temporal interaction attention (STIA) module. Finally, the aforementioned modules are aggregated within a multi-task learning framework, with the action segmentation serving as the auxiliary task to further improve the accuracy of ERA. We conducted the ergonomic risk assessment on the UW-IOM and TUM Kitchen datasets using our network. Extensive experiments conducted on the most popular datasets UW-IOM and TUM Kitchen demonstrated that our proposed AAST-GCN outperforms other GCN-based methods. Ablation studies and visualization also prove the effectiveness of the individual sub-modules. [ABSTRACT FROM AUTHOR]