Edge Connectivity Research Articles

Reliability Assessment of Multiprocessor System Based on Exchanged Crossed Cube Networks

ABSTRACTWith the increasingly widespread application of multiprocessor systems, some processors in multiprocessor systems are inevitably prone to malfunctions. The reliability and effectiveness of the system are key issues. As a standard for measuring system fault tolerance, connectivity, and edge connectivity have many drawbacks. Therefore, Haray proposed conditional connectivity by restricting the connected components in disconnected subgraphs to satisfy certain properties, where and represent the interconnection network and its set of faulty vertices, respectively. Restricted connectivity is a special type of conditional connectivity. Exchanged crossed cube, as a deformation of hypercube, has more favorable properties, such as smaller diameter, smaller link size, and lower cost. We prove that the 2‐restricted connectivity of the exchanged crossed cubes is for .

Altered default-mode and frontal-parietal network pattern underlie adaptiveness of emotion regulation flexibility following task-switch training.

Emotion regulation flexibility (ERF) refers to one's ability to respond flexibly in complex environments. Adaptiveness of ERF has been associated with cognitive flexibility, which can be improved by task-switching training. However, the impact of task-switching training on ERF and its underlying neural mechanisms remains unclear. To address this issue, we examined the effects of training on individuals' adaptiveness of ERF by assessing altered brain network patterns. Two groups of participants completed behavioral experiments and resting-state fMRI before and after training. Behavioral results showed higher adaptiveness scores and network analysis observed a higher number of connectivity edges, in the training group compared to the control group. Moreover, we found decreased connectivity strength within the default mode network (DMN) and increased connectivity strength within the frontoparietal network (FPN) in the training group. Furthermore, the task-switch training also led to decreased DMN-FPN interconnectivity, which was significantly correlated to increased adaptiveness of ERF scores. These findings suggest that the adaptiveness of ERF can be supported by altered patterns with the brain network through task-switch training, especially the increased network segregation between the DMN and FPN.

Metaplasticity and memory in multilevel recurrent feed-forward networks.

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and subnetworks. To a first approximation, this memory can be modeled through a "plastic" Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multilevel network structures and "metaplastic" effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional metaplastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The metaplastic term acts on a second network level in which edges are grouped together, simulating local, longer timescale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a metaplastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the metareinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, metareinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.

Enabling high reliability via matroidal connectivity and conditional matroidal connectivity on arrangement graph networks

Connectivity indicators are commonly used to evaluate system fault tolerance and reliability. However, with the high demand for multi-processor systems in high-performance computing and data center networks, the number of processors is getting larger, and the network is getting more complex. Thus, traditional connectivity and other indicators are hardly competent in assessing the reliability of complex networks. The matroidal connectivity and conditional matroidal connectivity are novel connectivity metrics that measure the actual fault-tolerant capability based on the constraints of each network dimension. In this paper, we study matroidal connectivity and conditional matroidal connectivity of the (n,k)-arrangement graph network An,k from the natural perspective of the partition of edge dimension and obtain their theoretically accurate values. Moreover, we conduct numerical analysis to compare matroidal connectivity with other conditional edge connectivities in An,k. Additionally, we explore the distribution pattern of edge failure through simulation experiments in An,k and attain the relation of conditional matroidal connectivity related to network scales. Our investigations include two famous network classes: alternating group graphs and star graphs.

Experimental and numerical investigation of H-beam to recycled aggregate concrete column edge connections under cyclic loading

Experimental and numerical investigation of H-beam to recycled aggregate concrete column edge connections under cyclic loading

A network analysis of voice hearing, emotional distress and subjective recovery before and after cognitive behavioural interventions.

There is a need to identify and to better understand key processes involved in voice hearing, which can inform the targeting and development of psychological interventions for distressing voices. The current study aimed to examine interrelations between the negative impact of voices, voice characteristics, emotional distress and recovery before and after cognitive behavioural interventions for voices (Coping Strategy Enhancement, guided self-help Cognitive Behavioural Therapy, Relating Therapy and Person-Based Cognitive Therapy). The sample consisted of 172 participants from the Sussex Voices Clinic who completed pre- and post-treatment assessments. The negative impact of voices, voice characteristics, emotional distress and recovery were used to estimate two networks, before and after cognitive behavioural interventions, using the graphical lasso method with the extended Bayesian information criterion. Centrality indices were also computed, and the two networks were compared on connectivity, structure and individual edge weights. Depression, anxiety and the negative impact of voices were identified as key central symptoms and acted as bridge symptoms in pre- and post-treatment networks. There were no significant differences in network structure (M = 0.155, p = .57), global strength (S = 0.188, p = .07) and centralities (C = -0.318, p = -.06) between the two networks. Our findings suggest that anxiety and depression are promising treatment targets, that can lead to reductions in voice-related distress, whereas the characteristics of voices and subjective recovery play little role in the network structure. Limitations include the lack of a control group and the lack of diversity within the sample.

Weighted graph convolutional network with feature mask for low back pain prediction

Low back pain (LBP) is one of the most common physical disabilities worldwide, imposing a heavy medical economic burden. To help medical experts make disease predictions at an early stage, this paper proposes an LBP abnormality diagnosis model based on a weighted graph convolutional network with feature mask. Unlike popular neural network architectures, we represent the biomechanical characteristics of the spine as a weighted feature graph. The potential relationship between patients is mined through edge connections, and the importance of features for different patients is dynamically captured through the internal feature weighting of nodes. Finally, the importance score of each feature is calculated according to its identification and independence to generate the feature importance mask. It realizes feature sparsification and reinforces important features at the same time, so as to improve the accuracy and stability of the model. The proposed model is verified on a public dataset available in the Kaggle repository, and the classification accuracy achieves 90.2%, which is 2.14% higher than the current best result. Furthermore, when compared for stability against several commonly used machine learning algorithms, the standard deviation of accuracy over ten experiments is only about 1/3 of that of other algorithms.

Enhancing Knowledge-Aware Recommendation with Dual-Graph Contrastive Learning

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

Research on maximizing real demand response based on link addition in social networks

The impact of social networks on real-life scenarios is intensifying with the diversification of the information they disseminate. Consequently, the interconnection between social networks and tangible networks is strengthening. Notably, we have observed that messages disseminated on social networks, particularly those soliciting aid, exert a significant influence on the underlying network structure. This study aims to investigate the role and importance of social networks in the information dissemination process, as well as to construct a linear threshold model tailored for the dissemination of emergency information across both real and social networks, leveraging conventional models of information spread. We have developed a model to increase the number of connection edges in social networks in order to enhance their worth. Additionally, we discovered that the objective function possesses submodular features and thus the created problem is NP-hard. As a result, we can use algorithms with approximative assurances of 1−e−1−θ′ to solve our problem and ensures the accuracy of the solution. We also analyze the complexity of the algorithm in solving this problem. Finally we validated our conclusions with three publicly available datasets and one real data set to analysis the results of the solution.

Squares of graphs are optimally [formula omitted]-supereulerian

For two integers s≥0,t≥0, a graph G is (s,t)-supereulerian, if for every pair of disjoint subsets X,Y⊂E(G), with |X|≤s,|Y|≤t, G has a spanning eulerian subgraph H with X⊂E(H) and Y∩E(H)=0̸. Pulleyblank (1979) proved that even within planar graphs, determining if a graph G is (0,0)-supereulerian is NP-complete. Xiong et al. (2021) identified a function j0(s,t) such that every (s,t)-supereulerian graph must have edge connectivity at least j0(s,t). Examples have been found that having edge connectivity at least j0(s,t) is not sufficient to warrant the graph to be (s,t)-supereulerian. A graph family S is optimally(s,t)-supereulerian if for every pair of given non-negative integers (s,t), a graph G∈S is (s,t)-supereulerian if and only if κ′(G)≥j0(s,t). Hence the (s,t)-supereulerian problem in such a graph family can be solved in polynomial time with minimally required edge-connectivity. In this research, we prove that the family of all squares of graphs of order at least 5 is optimally (s,t)-supereulerian.

Percolation Transitions in Edge-Coupled Interdependent Networks with Reinforced Inter-Layer Links.

Prior research on cascading failures within interdependent networks has predominantly emphasized the coupling of nodes. Nevertheless, in practical networks, interactions often exist not just through the nodes themselves but also via the connections (edges) linking them, a configuration referred to as edge-coupled interdependent networks. Past research has shown that introducing a certain percentage of reinforced nodes or connecting edges can prevent catastrophic network collapses. However, the effect of reinforced inter-layer links in edge-coupled interdependent networks has yet to be addressed. Here, we develop a theoretical framework for studying percolation models in edge-coupled interdependent networks by introducing a proportion of reinforced inter-layer links and deriving detailed expressions for the giant and finite components and the percolation phase transition threshold. We find that there exists a required minimum proportion of the reinforced inter-layer links to prevent abrupt network collapse, which serves as a boundary to distinguish different phase transition types of a network. We provide both analytical and numerical solutions for random and scale-free networks, demonstrating that the proposed method exhibits superior reinforcement efficiency compared to intra-layer link reinforcement strategies. Theoretical analysis, simulation results, and real network systems validate our model and indicate that introducing a specific proportion of reinforced inter-layer links can prevent abrupt system failure and enhance network robustness in edge-coupled interdependent networks.

Improved time complexity for spintronic oscillator ising machines compared to a popular classical optimization algorithm for the Max-Cut problem.

Solving certain combinatorial optimization problems like Max-Cut becomes challenging once the graph size and edge connectivity increase beyond a threshold, with brute-force algorithms which solve such problems exactly on conventional digital computers having the bottleneck of exponential time complexity. Hence currently, such problems are instead solved approximately using algorithms like Goemans-Williamson (GW) algorithm, run on conventional computers with polynomial time complexity. Phase binarized oscillators (PBOs), also often known as oscillator Ising machines, have been proposed as an alternative to solve such problems. In this paper, restricting ourselves to the combinatorial optimization problem Max-Cut solved on three kinds of graphs (Mobius Ladder, random cubic, Erdös Rényi) up to 100 nodes, we empirically show that computation time/time to solution (TTS) for PBOs (captured through Kuramoto model) grows at a much lower rate (logarithmically:O(log(N)), with respect to graph sizeN) compared to GW algorithm, for which TTS increases as square of graph size (O(N2)). However, Kuramoto model being a physics-agnostic mathematical model, this time complexity/ TTS trend for PBOs is a general trend and is device-physics agnostic. So for more specific results, we choose spintronic oscillators, known for their high operating frequency (in GHz), and model them through Slavin's model which captures the physics of their coupled magnetization oscillation dynamics. We thereby empirically show that TTS of spintronic oscillators also grows logarithmically with graph size (O(log(N)), while their accuracy is comparable to that of GW. So spintronic oscillators have improved time complexity over GW algorithm. For large graphs, they are expected to compute Max-Cut values much faster than GW algorithm, as well as other oscillators operating at lower frequencies, while maintaining the same level of accuracy.

Multi-order graph clustering with adaptive node-level weight learning

Current graph clustering methods emphasize individual node and edge connections, while ignoring higher-order organization at the level of motif. Recently, higher-order graph clustering approaches have been designed by motif-based hypergraphs. However, these approaches often suffer from hypergraph fragmentation issue seriously, which degrades the clustering performance greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes participating in multiple motifs. A key challenge is how to achieve precise clustering results by integrating information from multiple motifs at the node level. In this paper, we propose a multi-order graph clustering model (MOGC) to integrate multiple higher-order structures and edge connections at node level. MOGC employs an adaptive weight learning mechanism to automatically adjust the contributions of different motifs for each node. This not only tackles hypergraph fragmentation issue but enhances clustering accuracy. MOGC is efficiently solved by an alternating minimization algorithm. Experiments on seven real-world datasets illustrate the effectiveness of MOGC.

Neighborhood structure-guided brain functional networks estimation for mild cognitive impairment identification.

The adoption and growth of functional magnetic resonance imaging (fMRI) technology, especially through the use of Pearson's correlation (PC) for constructing brain functional networks (BFN), has significantly advanced brain disease diagnostics by uncovering the brain's operational mechanisms and offering biomarkers for early detection. However, the PC always tends to make for a dense BFN, which violates the biological prior. Therefore, in practice, researchers use hard-threshold to remove weak connection edges or introduce l 1-norm as a regularization term to obtain sparse BFNs. However, these approaches neglect the spatial neighborhood information between regions of interest (ROIs), and ROI with closer distances has higher connectivity prospects than ROI with farther distances due to the principle of simple wiring costs in resent studies. Thus, we propose a neighborhood structure-guided BFN estimation method in this article. In detail, we figure the ROIs' Euclidean distances and sort them. Then, we apply the K-nearest neighbor (KNN) to find out the top K neighbors closest to the current ROIs, where each ROI's K neighbors are independent of each other. We establish the connection relationship between the ROIs and these K neighbors and construct the global topology adjacency matrix according to the binary network. Connect ROI nodes with k nearest neighbors using edges to generate an adjacency graph, forming an adjacency matrix. Based on adjacency matrix, PC calculates the correlation coefficient between ROIs connected by edges, and generates the BFN. With the purpose of evaluating the performance of the introduced method, we utilize the estimated BFN for distinguishing individuals with mild cognitive impairment (MCI) from the healthy ones. Experimental outcomes imply this method attains better classification performance than the baselines. Additionally, we compared it with the most commonly used time series methods in deep learning. Results of the performance of K-nearest neighbor-Pearson's correlation (K-PC) has some advantage over deep learning.

A Novel Technical Framework for the Evaluation of Node Significance and Edge Connectivity in Global Shipping Network

Marine transportation is pivotal in the rapid development of global trade, significantly enhancing international economic and trade connectivity and impacting the sustainable development of the global economy. In this study, we developed a novel technical framework based on the Laplacian matrix to evaluate the node significance and edge connectivity of the global shipping network using 2019 vessel schedule data from the top 30 liner shipping companies, as ranked by Alphaliner. Our analyses were conducted in both L-space, characterizing the connectivity function, and P-space, characterizing the transfer function. The findings indicate the following. (1) There is no consistent relationship between node significance and centrality for most ports. Ports with high node significance are mainly located in the Asia–Pacific region, with Singapore Port being the port with the highest node significance in L-space and Shanghai Port being the port with the highest node significance in P-space. (2) In L-space, the structures with significant improvements in edge connectivity in the shipping network have at least one port node that exhibits both low degree centrality and low betweenness centrality; these are primarily found on East African routes. (3) In P-space, the structures with significant improvements in edge connectivity in the shipping network are more complex but are notably linked to the ports of Assaluyeh and Bandar Abbas in Iran. The proposed node evaluation and edge addition strategy effectively analyze port significance and edge connectivity, providing decision-making support for optimizing port layouts, supporting container route planning, and enhancing the overall performance of the shipping network.

Coupling Fault Diagnosis Based on Dynamic Vertex Interpretable Graph Neural Network.

Mechanical equipment is composed of several parts, and the interaction between parts exists throughout the whole life cycle, leading to the widespread phenomenon of fault coupling. The diagnosis of independent faults cannot meet the requirements of the health management of mechanical equipment under actual working conditions. In this paper, the dynamic vertex interpretable graph neural network (DIGNN) is proposed to solve the problem of coupling fault diagnosis, in which dynamic vertices are defined in the data topology. First, in the date preprocessing phase, wavelet transform is utilized to make input features interpretable and reduce the uncertainty of model training. In the fault topology, edge connections are made between nodes according to the fault coupling information, and edge connections are established between dynamic nodes and all other nodes. Second the data topology with dynamic vertices is used in the training phase and in the testing phase, the time series data are only fed into dynamic vertices for classification and analysis, which makes it possible to realize coupling fault diagnosis in an industrial production environment. The features extracted in different layers of DIGNN interpret how the model works. The method proposed in this paper can realize the accurate diagnosis of independent faults in the dataset with an accuracy of 100%, and can effectively judge the coupling mode of coupling faults with a comprehensive accuracy of 88.3%.

Good r-divisions Imply Optimal Amortized Decremental Biconnectivity

We present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in O(m+n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(m+n)$$\\end{document} time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in worst-case O(1) time. In case the vertices are not biconnected, the data structure can return a cutvertex separating them in worst-case O(1) time. As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, including planar graphs and other minor free graphs.

Consensus Subspace Graph Regularization based on prior information for multiplex network clustering

Multiplex network clustering can identify the common cluster structure shared by all layers, which is of great significance for downstream research such as personalized recommendations of social relationships and the mining of social media communication behaviors. Traditional multiplex network clustering methods rely only on the topological structure and are suitable for networks with clear structures. However, real-world networks often suffer from sparse connectivity and noisy edges. In addition, the current methods based on prior information only use the obtained consensus prior information as a preprocessing method for multiplex networks, and do not fully utilize and integrate the prior information in the clustering process, resulting in a low accuracy. To solve the problem of insufficient utilization of prior information, we propose a Consensus Subspace Graph Regularization (CSGR) approach for multiplex network clustering, which integrates topological information with the consensus prior information of a network. We first construct the consensus prior matrix of a network by a non-overlapping greedy search method, which represents a subset of the network that consists of nodes with high edge density. Then we construct a graph regularization term, which encodes the consensus prior information, to optimize the generation of a joint low-dimensional representation within the consensus subspace for the entire multiplex network. Finally, we employ the consensus prior matrix to denoise each network layer, thereby yielding a precise low-dimensional representation of each layer for consensus subspace fusion. In addition, comprehensive experiments have demonstrated that CSGR improves the clustering accuracy of real-world networks by an average of 1.56%.

Rational construction of surface doping of Cu in WO3 nano platelets with Fe rich layer oxyhydroxide on the porous BiVO4 catalyst: A solar driven heterostructure photoanode for efficient water oxidation

The (Cu:WO3/BiVO4/FeOOH) photoanode heterostructure is a significant semiconductor for solar water splitting owing to its wide absorption of visible light photons. The bulk particles are experiencing charge recombination, which limits the PEC performance of the WO3 and BiVO4. Wherein, the heterostructure Cu:WO3/BiVO4/FeOOH catalysts have a staggered connection of band edges and morphological variation that outperforms the photoelectrochemical properties. The FeOOH layer on the surface of the PEC catalyst efficiently boosts water oxidation and quickens water splitting under light illumination. As anticipated, the doping in the WO3 and BiVO4 loading on the WO3 plates attains an outstanding increase in the water splitting performance. The 2% copper doping in the WO3 exhibits 1.2 mA/cm2, which is increasing by 40 cycles of coated BiVO4 to 2.0 mA/cm2. The FeOOH-grown heterostructure photoanode results in a higher overall photocurrent density (2.8 mA/cm2) at water oxidation potential. Moreover, the photoanode exhibits good stability and low resistance (385.7 Ohm/cm2). The photon-to-electron conversion efficiency has been attained at 1.2% at the applied potential of 0.4 V vs. RHE. These results from the photoanode could be a good candidate for high-performance PEC applications.

Individual cerebellar metabolic connectome in patients with MTLE and NTLE associated with surgical prognosis.

This study aimed to comprehensively explore the different metabolic connectivity topological changes in MTLE and NTLE, as well as their association with surgical outcomes. This study enrolled a cohort of patients with intractable MTLE and NTLE. Each individual's metabolic connectome, as determined by Kullback-Leibler divergence similarity estimation for the [18F]FDG PET image, was employed to conduct a comprehensive analysis of the cerebral metabolic network. Alterations in network connectivity were assessed by extracting and evaluating the strength of edge and weighted connectivity. By utilizing these two connectivity strength metrics with the cerebellum, we explored the network properties of connectivity and its association with prognosis in surgical patients. Both MTLE and NTLE patients exhibited substantial alterations in the connectivity of the metabolic network at the edge and nodal levels (p < 0.01, FDR corrected). The key disparity between MTLE and NTLE was observed in the cerebellum. In MTLE, there was a predominance of increased connectivity strength in the cerebellum. Whereas, a decrease in cerebellar connectivity was identified in NTLE. It was found that in MTLE, higher edge connectivity and weighted connectivity strength in the contralateral cerebellar hemisphere correlated with improved surgical outcomes. Conversely, in NTLE, a higher edge metabolic connectivity strength in the ipsilateral cerebellar hemisphere suggested a worse surgical prognosis. The cerebellum exhibits distinct topological characteristics in the metabolic networks between MTLE and NTLE. The hyper- or hypo-metabolic connectivity in the cerebellum may be a prognostic biomarker of surgical prognosis, which might aid in therapeutic decision-making for TLE individuals.