Adjacency Matrix Research Articles

A novel approach for ASD recognition based on graph attention networks.

Early detection and diagnosis of Autism Spectrum Disorder (ASD) can significantly improve the quality of life for affected individuals. Identifying ASD based on brain functional connectivity (FC) poses a challenge due to the high heterogeneity of subjects' fMRI data in different sites. Meanwhile, deep learning algorithms show efficacy in ASD identification but lack interpretability. In this paper, a novel approach for ASD recognition is proposed based on graph attention networks. Specifically, we treat the region of interest (ROI) of the subjects as node, conduct wavelet decomposition of the BOLD signal in each ROI, extract wavelet features, and utilize them along with the mean and variance of the BOLD signal as node features, and the optimized FC matrix as the adjacency matrix, respectively. We then employ the self-attention mechanism to capture long-range dependencies among features. To enhance interpretability, the node-selection pooling layers are designed to determine the importance of ROI for prediction. The proposed framework are applied to fMRI data of children (younger than 12 years old) from the Autism Brain Imaging Data Exchange datasets. Promising results demonstrate superior performance compared to recent similar studies. The obtained ROI detection results exhibit high correspondence with previous studies and offer good interpretability.

DHONE: Density-based higher-order network embedding

Studies have indicated that focusing solely on pairwise interactions between two nodes disregards the associativity among multi-nodes in the network’s local structure. This associativity can be seen as dependencies among nodes, where certain edges’ presence depends on the path leading to it. Examinations on diverse datasets have approved that the variable order of chained dependencies allows for the preservation of structure information, which enables the reconstruction of the original network into a Higher-Order Network (HON) with improved quality of network representation. This paper proposes a Density-based Higher-Order Network Embedding (DHONE) algorithm, which integrates the concept of higher-order density into the network-embedding process in order to classify the contribution of different orders of dependencies. Through the construction of a novel and effective higher-order adjacency matrix, DHONE steadily improves the accuracy of network representation learning. Experimental results demonstrate DHONEs proficiency in improving embedding accuracy and overall algorithm robustness. Furthermore, grounded in the concept of higher-order density proposed herein, numerous dependencies have been discerned within the network generated from trajectories, potentially indicating the role of multi-node structures in networks.

A Novel Approach on Energy of λJ-dominating Single-Valued Neutrosophic Graph Structure

The concept of dominance is one of the most important ideas in graph theory for handling random events, and it has drawn the interest from many scholars. Research related to graph energy has garnered a lot focus recently. The application of single-valued neutrosophic graphs (SVNGs) for energy, Laplacian energy, and dominating energy has been recommended by previous studies. In this research, we apply the concepts of single-valued neutrosophic sets (SVNS) to graph structures (GSs) and investigate some intriguing features of single-valued neutrosophic graph structures (SVNGS). Moreover, the notions of λJ-dominating energy GS in an SVNGS environment are analyzed in this study. More specifically, illustrative examples are used to develop the adjacency matrix of a λJ-dominating SVNGS, as well as the spectrum of the adjacency matrix and their related theory. Further, the SVNGS λJ-dominating energy is determined. We go over various characteristics and constraints for the energy of SVNGS with λJ-dominating. Further, we introduce the idea of isomorphic and identical λJ-dominating SVNGS energy, which has been studied using relevant examples, and some of its established properties are presented.

The Graft Transformation and Their Application on the Spectral Radius of Block Graphs

Let [Formula: see text] be a connected graph and [Formula: see text] be the adjacency matrix of [Formula: see text]. Suppose that [Formula: see text] are the eigenvalues of [Formula: see text]. In this paper, we first give a graft transformation on the spectral radius of graphs and then as their application, we determine the extremal graphs with maximum and minimum spectral radii among all clique trees. Furthermore, we also determine the unique graph with maximum spectral radius among all block graphs by using different methods.

Control of multiconsensus in multi-agent systems based on eigenvector centrality

In multiconsensus (or group consensus) the units of a multi-agent system split into clusters, with the agents of the same group converging towards the same consensus value, which, in general, is different from cluster to cluster. In this brief paper, we develop a new technique to achieve multiconsensus among agents described by second-order dynamics. To do this, we introduce a communication protocol where interactions between agents are directed and weighted. Our approach consists of two steps. First, the weights of the interaction network are assigned so that the network adjacency matrix has a given leading eigenvector. This allows the formation of clusters of nodes that have the same value of eigenvector centrality. Second, the gains of the communication protocols are selected to guarantee the stability of the error dynamics. We study both the cases of leaderless and leader–follower multiconsensus, providing analytical conditions for multiconsensus, and discuss a few numerical examples to illustrate our theoretical results.

Graph-based EEG approach for depression prediction: integrating time-frequency complexity and spatial topology.

Depression has become the prevailing global mental health concern. The accuracy of traditional depression diagnosis methods faces challenges due to diverse factors, making primary identification a complex task. Thus, the imperative lies in developing a method that fulfills objectivity and effectiveness criteria for depression identification. Current research underscores notable disparities in brain activity between individuals with depression and those without. The Electroencephalogram (EEG), as a biologically reflective and easily accessible signal, is widely used to diagnose depression. This article introduces an innovative depression prediction strategy that merges time-frequency complexity and electrode spatial topology to aid in depression diagnosis. Initially, time-frequency complexity and temporal features of the EEG signal are extracted to generate node features for a graph convolutional network. Subsequently, leveraging channel correlation, the brain network adjacency matrix is employed and calculated. The final depression classification is achieved by training and validating a graph convolutional network with graph node features and a brain network adjacency matrix based on channel correlation. The proposed strategy has been validated using two publicly available EEG datasets, MODMA and PRED+CT, achieving notable accuracy rates of 98.30 and 96.51%, respectively. These outcomes affirm the reliability and utility of our proposed strategy in predicting depression using EEG signals. Additionally, the findings substantiate the effectiveness of EEG time-frequency complexity characteristics as valuable biomarkers for depression prediction.

The impact of pollution transmission networks in a transboundary pollution game

To explore transboundary pollution games with network externalities, this study develops a multi-region differential game which investigates the interaction and co-evolution of multiple pollution stocks across a continuous horizon. Pollution transmission networks are incorporated into the model via an adjacency matrix, detailing transmission paths of pollution across regions. Equilibrium strategies for emissions and investments in pollution control are obtained through a system of coupled differential equations. Our study demonstrates that these equilibrium strategies and the corresponding discounted net welfare of regions depend crucially on the structure of pollution transmission networks. The spectral properties of networks can effectively discern the evolutionary stability of equilibrium strategies. Through a numerical simulation of multiregional pollution dynamics, we also show that regions' motivation for pollution control decreases continuously as their influence in pollution transmission networks (i.e., network influence) increases; Nevertheless, an increase in a region's network influence can significantly reduce local pollution stocks in cycle networks but increase them in tree networks.

Structural deep multi-view clustering with integrated abstraction and detail

Deep multi-view clustering, which can obtain complementary information from different views, has received considerable attention in recent years. Although some efforts have been made and achieve decent performances, most of them overlook the structural information and are susceptible to poor quality views, which may seriously restrict the capacity for clustering. To this end, we propose Structural deep Multi-View Clustering with integrated abstraction and detail (SMVC). Specifically, multi-layer perceptrons are used to extract features from specific views, which are then concatenated to form the global features. Besides, a global target distribution is constructed and guides the soft cluster assignments of specific views. In addition to the exploitation of the top-level abstraction, we also design the mining of the underlying details. We construct instance-level contrastive learning using high-order adjacency matrices, which has an equivalent effect to graph attention network and reduces feature redundancy. By integrating the top-level abstraction and underlying detail into a unified framework, our model can jointly optimize the cluster assignments and feature embeddings. Extensive experiments on four benchmark datasets have demonstrated that the proposed SMVC consistently outperforms the state-of-the-art methods.

A Novel Local-Global Graph Convolutional Method for Point Cloud Semantic Segmentation.

Although convolutional neural networks (CNNs) have shown good performance on grid data, they are limited in the semantic segmentation of irregular point clouds. This article proposes a novel and effective graph CNN framework, referred to as the local-global graph convolutional method (LGGCM), which can achieve short- and long-range dependencies on point clouds. The key to this framework is the design of local spatial attention convolution (LSA-Conv). The design includes two parts: generating a weighted adjacency matrix of the local graph composed of neighborhood points, and updating and aggregating the features of nodes to obtain the spatial geometric features of the local point cloud. In addition, a smooth module for central points is incorporated into the process of LSA-Conv to enhance the robustness of the convolution against noise interference by adjusting the position coordinates of the points adaptively. The learned robust LSA-Conv features are then fed into a global spatial attention module with the gated unit to extract long-range contextual information and dynamically adjust the weights of features from different stages. The proposed framework, consisting of both encoding and decoding branches, is an end-to-end trainable network for semantic segmentation of 3-D point clouds. The theoretical analysis of the approximation capabilities of LSA-Conv is discussed to determine whether the features of the point cloud can be accurately represented. Experimental results on challenging benchmarks of the 3-D point cloud demonstrate that the proposed framework achieves excellent performance.

Retraction Note: The Sachs theorem and its application on extended adjacency matrix of graphs

Retraction Note: The Sachs theorem and its application on extended adjacency matrix of graphs

On Low-Rank Directed Acyclic Graphs and Causal Structure Learning.

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high-dimensional settings when the graphs to be learned are not sparse. In this article, we propose to exploit a low-rank assumption regarding the (weighted) adjacency matrix of a DAG causal model to help address this problem. We utilize existing low-rank techniques to adapt causal structure learning methods to take advantage of this assumption and establish several useful results relating interpretable graphical conditions to the low-rank assumption. Specifically, we show that the maximum rank is highly related to hubs, suggesting that scale-free (SF) networks, which are frequently encountered in practice, tend to be low rank. Our experiments demonstrate the utility of the low-rank adaptations for a variety of data models, especially with relatively large and dense graphs. Moreover, with a validation procedure, the adaptations maintain a superior or comparable performance even when graphs are not restricted to be low rank.

Physics-informed deep learning with Kalman filter mixture for traffic state prediction

Accurate traffic forecasting is crucial for understanding and managing congestion for efficient transportation planning. However, conventional approaches often neglect epistemic uncertainty, which arises from incomplete knowledge across different spatiotemporal scales. This study addresses this challenge by introducing a novel methodology to establish dynamic spatiotemporal correlations that captures the unobserved heterogeneity in travel time through distinct peaks in probability density functions, guided by physics-based principles. We propose an innovative approach to modifying both prediction and correction steps of the Kalman Filter (KF) algorithm by leveraging established spatiotemporal correlations. Central to our approach is the development of a novel deep learning model called the Physics Informed-Graph Convolutional Gated Recurrent Neural Network (PI-GRNN). Functioning as the state-space model within the KF, the PI-GRNN exploits established correlations to construct dynamic adjacency matrices that utilize the inherent structure and relationships within the transportation network to capture sequential patterns and dependencies over time. Furthermore, our methodology integrates insights gained from correlations into the correction step of the KF algorithm that helps in enhancing its correctional capabilities. This integrated approach proves instrumental in alleviating the inherent model drift associated with data-driven methods, as periodic corrections through update step of KF refine the predictions generated by PI-GRNN. To the best of our knowledge, this study represents a pioneering effort in integrating deep learning and KF algorithms in this unique symbiotic manner. Through extensive experimentation with real-world traffic data, we demonstrate the superior performance of our model compared to the benchmark approaches.

Spatial-temporal graph neural ODE networks for skeleton-based action recognition.

In the field of skeleton-based action recognition, accurately recognizing human actions is crucial for applications such as virtual reality and motion analysis. However, this task faces challenges such intraindividual action differences and long-term temporal dependencies. To address these challenges, we propose an innovative model called spatial-temporal graph neural ordinary differential equations (STG-NODE). First, in the data preprocessing stage, the dynamic time warping (DTW) algorithm is used to normalize and calculate 3D skeleton data to facilitate the derivation of customized adjacency matrices for improving the influence of intraindividual action differences. Secondly, a custom ordinary differential equation (ODE) integrator is applied based on the initial conditions of the temporal features, producing a solution function that simulates the dynamic evolution trend of the events of interest. Finally, the outstanding ODE solver is used to numerically solve the time features based on the solution function to increase the influence of long-term dependencies on the recognition accuracy of the model and provide it with a more powerful temporal modeling ability. Through extensive experiments conducted on the NTU RGB+D 60 and Kinetics Skeleton 400 benchmark datasets, we demonstrate the superior performance of STG-NODE in the action recognition domain. The success of the STG-NODE model also provides new ideas and methods for the future development of the action recognition field.

Spectral dynamic causal modeling: A didactic introduction and its relationship with functional connectivity.

We present a didactic introduction to spectral dynamic causal modeling (DCM), a Bayesian state-space modeling approach used to infer effective connectivity from noninvasive neuroimaging data. Spectral DCM is currently the most widely applied DCM variant for resting-state functional MRI analysis. Our aim is to explain its technical foundations to an audience with limited expertise in state-space modeling and spectral data analysis. Particular attention will be paid to cross-spectral density, which is the most distinctive feature of spectral DCM and is closely related to functional connectivity, as measured by (zero-lag) Pearson correlations. In fact, the model parameters estimated by spectral DCM are those that best reproduce the cross-correlations between all measurements-at all time lags-including the zero-lag correlations that are usually interpreted as functional connectivity. We derive the functional connectivity matrix from the model equations and show how changing a single effective connectivity parameter can affect all pairwise correlations. To complicate matters, the pairs of brain regions showing the largest changes in functional connectivity do not necessarily coincide with those presenting the largest changes in effective connectivity. We discuss the implications and conclude with a comprehensive summary of the assumptions and limitations of spectral DCM.

Complete synchronization of three-layer Rulkov neuron network coupled by electrical and chemical synapses.

This paper analyzes the complete synchronization of a three-layer Rulkov neuron network model connected by electrical synapses in the same layers and chemical synapses between adjacent layers. The outer coupling matrix of the network is not Laplacian as in linear coupling networks. We develop the master stability function method, in which the invariant manifold of the master stability equations (MSEs) does not correspond to the zero eigenvalues of the connection matrix. After giving the existence conditions of the synchronization manifold about the nonlinear chemical coupling, we investigate the dynamics of the synchronization manifold, which will be identical to that of a synchronous network by fixing the same parameters and initial values. The waveforms show that the transient chaotic windows and the transient approximate periodic windows with increased or decreased periods occur alternatively before asymptotic behaviors. Furthermore, the Lyapunov exponents of the MSEs indicate that the network with a periodic synchronization manifold can achieve complete synchronization, while the network with a chaotic synchronization manifold can not. Finally, we simulate the effects of small perturbations on the asymptotic regimes and the evolution routes for the synchronous periodic and the non-synchronous chaotic network.

The Index Weighted Hermitian Adjacency Matrices for Mixed Graphs

Based on the Hermitian adjacency matrices of second kind introduced by Mohar [1] and weighted adjacency matrices introduced in [2], we define a kind of index weighted Hermitian adjacency matrices of mixed graphs. In this paper we characterize the structure of mixed graphs which are cospectral to their underlying graphs, then we determine a upper bound on the spectral radius of mixed graphs with maximum degree Δ , and characterize the corresponding extremal graphs.

INTEGRATED APPROACH TO PAIN MANAGEMENT: YOGA, MANUAL THERAPY, FASCIA RELEASE, NERVE MOBILIZATION TECHNIQUES, OSTEOPATHIC MANIPULATIVE TREATMENT, CHIROPRACTIC CARE AND KINEMATIC AND KINETIC CHAINSANALYSIS& MUSCULOSKELETAL DYNAMICS

Chronic pain affects millions worldwide, presenting a complex challenge to conventional medical approaches. This abstract explores an integrated approach to pain management, amalgamating principles from yoga, manual therapy, fascia release, nerve mobilization, Osteopathic Manipulative Treatment, Chiropractic Careand Kinematic and Kinetic ChainsAnalysis and Musculoskeletal Dynamics. By synergizing these modalities, practitioners address pain comprehensively, targeting its multifaceted origins and manifestations.Yoga, renowned for its mind-body connection, offers a repertoire of postures and breathing exercises tailored to alleviate pain and enhance flexibility. Manual therapy techniques, including myofascial release and joint mobilization, address muscular imbalances and restore tissue integrity. Fascia release strategies delve deeper, releasing tension in the connective tissue matrix, thereby enhancing movement quality and reducing discomfort.Nerve mobilization practices target neural tension, promoting optimal nerve glide and alleviating symptoms associated with nerve compression. Concurrently, Osteopathic Manipulative Treatment, Chiropractic Care, Kinematic and Kinetic ChainsAnalysis and Musculoskeletal Dynamics to identify and rectify movement dysfunctions, ensuring harmonious joint mechanics and reducing stress on susceptible structures.Furthermore, this integrated approach extends beyond physical interventions, incorporating mindfulness practices and lifestyle adjustments to modulate pain perception and promote overall well-being. Multidisciplinary collaboration and patient education foster empowerment and long-term adherence to personalized pain management plans.In conclusion, theIntegration of Yoga, Manual Therapy, Fascia Release, Nerve Mobilization Techniques, Osteopathic Manipulative Treatment, Chiropractic Care and Kinematic and Kinetic Chains Analysis & Musculoskeletal Dynamicsrepresents a promising paradigm shift in pain management. By embracing the interconnectedness of mind, body, and environment, this holistic approach strives to restore function, alleviate suffering, and enhance the quality of life for individuals grappling with chronic pain.

Construction and evolutionary factors of spatial correlation network of China's provincial tourism resource conversion efficiency

Research objectiveTo explore the spatial correlation network characteristics and formation mechanisms of tourism resource conversion efficiency, and provide reference for the collaborative improvement of tourism resource conversion efficiency at the provincial level in China. Research methodsNon parametric SBM efficiency measurement method and social network analysis method. Research hypothesis: The spatial network correlation characteristics of tourism resource conversion efficiency are obvious, and regional connections are close. Research findings(i) during the research period, the spatial connection strength of China's tourism resource conversion efficiency continued to increase and the spatial network structure of tourism resource conversion efficiency tended to become more complex and significantly more stable. (ii) A spatially linked network with a stable tourism resource conversion efficiency structure formed in China. The number of network relations and density of the network fluctuated and increased, while the network efficiency continued to decrease; however, a strong small-world nature was observed. (iii) The economic development level difference matrix, tourism industry agglomeration difference matrix, human capital difference matrix, and marketization degree difference matrix significantly and positively affected spatial association relationship establishment, while the provincial adjacency matrix significantly and negatively affected such relationships.

Inverse of \(\alpha\)-Hermitian Adjacency Matrix of a Unicyclic Bipartite Graph

Let \(X\) be bipartite mixed graph and for a unit complex number \(\alpha\), \(H_\alpha\) be its \(\alpha\)-hermitian adjacency matrix. If \(X\) has a unique perfect matching, then \(H_\alpha\) has a hermitian inverse \(H_\alpha^{-1}\). In this paper we give a full description of the entries of \(H_\alpha^{-1}\) in terms of the paths between the vertices. Furthermore, for \(\alpha\) equals the primitive third root of unity \(\gamma\) and for a unicyclic bipartite graph \(X\) with unique perfect matching, we characterize when \(H_\gamma^{-1}\) is \(\pm 1\) diagonally similar to \(\gamma\)-hermitian adjacency matrix of a mixed graph. Through our work, we have provided a new construction for the \(\pm 1\) diagonal matrix.

Non-Compatible Action Graph and Its Adjacency Matrix for The Non-abelian Tensor Product for Groups of Prime Power Order

This article focused on the notion of the non-abelian tensor product of groups of prime power order. Particularly, it presented new graph named as Non-compatible action graph and discussed some of its properties. Moreover, this graph concentrated on the case of non-compatible actions of the tensor product of two finite -groups. Furthermore, its adjacency matrix has been determined and discussed in detail. Moreover, the adjacency matrix has been denoted by A(G) and its inputs are 1 whenever there is adjacency and 0 otherwise.