Residual Graph Research Articles

Reliable Spanners for Metric Spaces

A spanner is reliable if it can withstand large, catastrophic failures in the network. More precisely, any failure of some nodes can only cause a small damage in the remaining graph in terms of the dilation. In other words, the spanner property is maintained for almost all nodes in the residual graph. Constructions of reliable spanners of near linear size are known in the low-dimensional Euclidean settings. Here, we present new constructions of reliable spanners for planar graphs, trees, and (general) metric spaces.

MSResG: Using GAE and Residual GCN to Predict Drug-Drug Interactions Based on Multi-source Drug Features.

Drug-drug interaction refers to taking the two drugs may produce certain reaction which may be a threat to patients' health, or enhance the efficacy helpful for medical work. Therefore, it is necessary to study and predict it. In fact, traditional experimental methods can be used for drug-drug interaction prediction, but they are time-consuming and costly, so we prefer to use more accurate and convenient calculation methods to predict the unknown drug-drug interaction. In this paper, we proposed a deep learning framework called MSResG that considers multi-sources features of drugs and combines them with Graph Auto-Encoder to predicting. Firstly, the model obtains four feature representations of drugs from the database, namely, chemical substructure, target, pathway and enzyme, and then calculates the Jaccard similarity of the drugs. To balance different drug features, we perform similarity integration by finding the mean value. Then we will be comprehensive similarity network combined with drug interaction network, and encodes and decodes it using the graph auto-encoder based on residual graph convolution network. Encoding is to learn the potential feature vectors of drugs, which contain similar information and interaction information. Decoding is to reconstruct the network to predict unknown drug-drug interaction. The experimental results show that our model has advanced performance and is superior to other existing advanced methods. Case study also shows that MSResG has practical significance.

Spatial adaptive graph convolutional network for skeleton-based action recognition

In recent years, great achievements have been made in graph convolutional network (GCN) for non-Euclidean spatial data feature extraction, especially the skeleton-based feature extraction. However, the fixed graph structure determined by the fixed adjacency matrix usually causes the problems such as the weak spatial modeling ability, the unsatisfactory generalization performance, the excessively large number of model parameters, and so on. In this paper, a spatially adaptive residual graph convolutional network (SARGCN) is proposed for action recognition based on skeleton feature extraction. Firstly, the uniform and fixed topology is not required in our graph. Secondly, a learnable parameter matrix is added to the GCN operation, which can enhance the model’s capabilities of feature extraction and generalization, while reducing the number of parameters. Therefore, compared with the several existing models mentioned in this paper, the least number of parameters are used in our model while ensuring the comparable recognition accuracy. Finally, inspired by the ResNet architecture, a residual connection is introduced in GCN to obtain higher accuracy at lower computational costs and learning difficulties. Extensive experimental on two large-scale datasets results validate the effectiveness of our proposed approach, namely NTU RGB+D 60 and NTU RGB+D 120.

A classification method of gastric cancer subtype based on residual graph convolution network.

Background: Clinical diagnosis and treatment of tumors are greatly complicated by their heterogeneity, and the subtype classification of cancer frequently plays a significant role in the subsequent treatment of tumors. Presently, the majority of studies rely far too heavily on gene expression data, omitting the enormous power of multi-omics fusion data and the potential for patient similarities. Method: In this study, we created a gastric cancer subtype classification model called RRGCN based on residual graph convolutional network (GCN) using multi-omics fusion data and patient similarity network. Given the multi-omics data's high dimensionality, we built an artificial neural network Autoencoder (AE) to reduce the dimensionality of the data and extract hidden layer features. The model is then built using the feature data. In addition, we computed the correlation between patients using the Pearson correlation coefficient, and this relationship between patients forms the edge of the graph structure. Four graph convolutional network layers and two residual networks with skip connections make up RRGCN, which reduces the amount of information lost during transmission between layers and prevents model degradation. Results: The results show that RRGCN significantly outperforms other classification methods with an accuracy as high as 0.87 when compared to four other traditional machine learning methods and deep learning models. Conclusion: In terms of subtype classification, RRGCN excels in all areas and has the potential to offer fresh perspectives on disease mechanisms and disease progression. It has the potential to be used for a broader range of disorders and to aid in clinical diagnosis.

Highly efficient family of two-step simultaneous method for all polynomial roots

<abstract><p>In this article, we constructed a derivative-free family of iterative techniques for extracting simultaneously all the distinct roots of a non-linear polynomial equation. Convergence analysis is discussed to show that the proposed family of iterative method has fifth order convergence. Nonlinear test models including fractional conversion, predator-prey, chemical reactor and beam designing models are included. Also many other interesting results concerning symmetric problems with application of group symmetry are also described. The simultaneous iterative scheme is applied starting with the initial estimates to get the exact roots within the given tolerance. The proposed iterative scheme requires less function evaluations and computation time as compared to existing classical methods. Dynamical planes are exhibited in CAS-MATLAB (R2011B) to show how the simultaneous iterative approach outperforms single roots finding methods that might confine the divergence zone in terms of global convergence. Furthermore, convergence domains, namely basins of attraction that are symmetrical through fractal-like edges, are analyzed using the graphical tool. Numerical results and residual graphs are presented in detail for the simultaneous iterative method. An extensive study has been made for the newly developed simultaneous iterative scheme, which is found to be efficient, robust and authentic in its domain.</p></abstract>

ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS

This research paper introduces a novel fractional Caputo-type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using suitable correction, the order of convergence of the basic Aberth–Ehrlich simultaneous method has been increased from three to [Formula: see text]. In terms of accuracy, residual graph, computational efficiency and computation CPU time, the newly proposed families of simultaneous methods outperforms existing methods in numerical applications.

A Novel Radar Signals Sorting Method via Residual Graph Convolutional Network

The dense, complex and variable electromagnetic environment poses a serious challenge to radar signal sorting (RSS) in modern electronic reconnaissance systems. In order to improve RSS performance, this letter proposes a semi-supervised learning framework-based RSS method via a residual graph convolutional network (ResGCN-RSS) to effectively improve the generalization ability of the signal sorting models in small data scenarios. Firstly, the graph structure construction of intercepted radar signals is performed via K-nearest neighbor algorithm. Then, the three-layer ResGCN is designed to adaptively improve the features learning. Finally, RSS can be effectively and efficiently implemented through an end-to-end ResGCN with small labeled graph data of interleaved radar signals. The simulation experimental results show that our proposed method can achieve better average accuracy with little computational cost increasing when the labeled data is very small, compared to some existing methods.

DGRNet: A Dual-level Graph Relation Network for Video Object Detection.

Video object detection is a fundamental and important task in computer vision. One mainstay solution for this task is to aggregate features from different frames to enhance the detection on the current frame. Off-the-shelf feature aggregation paradigms for video object detection typically rely on inferring feature-to-feature (Fea2Fea) relations. However, most existing methods are unable to stably estimate Fea2Fea relations due to the appearance deterioration caused by object occlusion, motion blur or rare poses, resulting in limited detection performance. In this paper, we study Fea2Fea relations from a new perspective, and propose a novel dual-level graph relation network (DGRNet) for high-performance video object detection. Different from previous methods, our DGRNet innovatively leverages the residual graph convolutional network to simultaneously model Fea2Fea relations at two different levels including frame level and proposal level, which facilitates performing better feature aggregation in the temporal domain. To prune unreliable edge connections in the graph, we introduce a node topology affinity measure to adaptively evolve the graph structure by mining the local topological information of pairwise nodes. To the best of our knowledge, our DGRNet is the first video object detection method that leverages dual-level graph relations to guide feature aggregation. We conduct experiments on the ImageNet VID dataset and the results demonstrate the superiority of our DGRNet against state-of-the-art methods. Especially, our DGRNet achieves 85.0% mAP and 86.2% mAP with ResNet-101 and ResNeXt-101, respectively.

Resolving Power Equipment Data Inconsistency via Heterogeneous Network Alignment

This paper studies the problem of resolving data inconsistency from multiple sources in managing data related to power equipment for China’s state grid corporation. This paper proposes to automatically align inconsistent devices from multiple sources, i.e., the same devices that have multiple entries with different values in each source, by HENGE, a HEtetrogeneous Network GEneration model. HENGE builds multiple data sources into a heterogeneous graph, and captures complex physical and semantic relationships among devices. HENGE combines both feature and relational information and improves alignment accuracy by feature-enhanced residual graph encoder and disentangled representation learning. HENGE is capable to learn from a small amount of labeled data, through a uniformity autoencoder trained on an unsupervised generation task. Experiments on two real-world datasets demonstrate the capability of HENGE in resolving inconsistent device entries in multiple sources.

GCNCPR-ACPs: a novel graph convolution network method for ACPs prediction

BackgroundAnticancer peptide (ACP) inhibits and kills tumor cells. Research on ACP is of great significance for the development of new drugs, and the prediction of ACPs and non-ACPs is the new hotspot.ResultsWe propose a new machine learning-based method named GCNCPR-ACPs (a Graph Convolutional Neural Network Method based on collapse pooling and residual network to predict the ACPs), which automatically and accurately predicts ACPs using residual graph convolution networks, differentiable graph pooling, and features extracted using peptide sequence information extraction. The GCNCPR-ACPs method can effectively capture different levels of node attributes for amino acid node representation learning, GCNCPR-ACPs uses node2vec and one-hot embedding methods to extract initial amino acid features for ACP prediction.ConclusionsExperimental results of ten-fold cross-validation and independent validation based on different metrics showed that GCNCPR-ACPs significantly outperformed state-of-the-art methods. Specifically, the evaluation indicators of Matthews Correlation Coefficient (MCC) and AUC of our predicator were 69.5% and 90%, respectively, which were 4.3% and 2% higher than those of the other predictors, respectively, in ten-fold cross-validation. And in the independent test, the scores of MCC and SP were 69.6% and 93.9%, respectively, which were 37.6% and 5.5% higher than those of the other predictors, respectively. The overall results showed that the GCNCPR-ACPs method proposed in the current paper can effectively predict ACPs.

ON INVERSE ITERATION PROCESS FOR FINDING ALL ROOTS OF NONLINEAR EQUATIONS WITH APPLICATIONS

In this work, we construct a new family of inverse iterative numerical technique for extracting all roots of nonlinear equation simultaneously. Convergence analysis verifies that the proposed family of methods has local 10th-order convergence. Among the test models investigated are blood rheology, a fractional nonlinear equation model, fluid permeability in biogels, and beam localization models. In comparison to other methods, the family of inverse simultaneous iterative techniques gets initial estimations to exact roots within a given tolerance while using less function evaluations in each iterative step. Numerical results, basins of attraction for fractional nonlinear equation, residual graphs are presented in detail for the simultaneous iterative techniques. The newly developed simultaneous iterative techniques were thoroughly investigated and proven to be efficient, robust, and authentic in their domain.

A fast tri-individual memetic search approach for the distance-based critical node problem

The distance-based critical node problem involves identifying a subset of nodes in a graph such that the removal of these nodes leads to a residual graph with the minimum distance-based connectivity. Due to its NP-hard nature, solving this problem using exact algorithms has proved to be highly challenging. Moreover, existing heuristic algorithms are typically time-consuming. In this work, we introduce a fast tri-individual memetic search approach to solve the problem. The proposed approach maintains a small population of only three individuals during the whole search. At each generation, it sequentially executes an inherit-repair recombination operator to generate a promising offspring solution, a fast betweenness centrality-based late-acceptance search to find high-quality local optima, and a simple population updating strategy to maintain a healthy population. Extensive experiments on both real-world and synthetic benchmarks show our method significantly outperforms state-of-the-art algorithms. In particular, it can steadily find the known optimal solutions for all 22 real-world instances with known optima in only one minute, and new upper bounds on the remaining 22 large real-world instances. For 54 synthetic instances, it finds new upper bounds on 36 instances, and matches the previous best-known upper bounds on 15 other instances in ten minutes. Finally, we investigate the usefulness of each key algorithmic ingredient.

Large $$p$$-Core $$p'$$-Partitions and Walks on the Additive Residue Graph

This paper investigates partitions which have neither parts nor hook lengths divisible by $$p$$ , referred to as $$p$$ -core $$p'$$ -partitions. We show that the largest $$p$$ -core $$p'$$ -partition corresponds to the longest walk on a graph with vertices $$\{0, 1, \ldots , p-1\}$$ and labelled edges defined via addition modulo $$p$$ . We also exhibit an explicit family of large $$p$$ -core $$p'$$ -partitions, giving a lower bound on the size of the largest such partition which is of the same degree as the upper bound found by McSpirit and Ono.

An interactive game for rehabilitation based on real-time hand gesture recognition.

Currently, cardiovascular and cerebrovascular diseases have become serious global health problems related to their high incidence and fatality rate. Some patients with cardiovascular cerebro-cardiovascular diseases even may face motor or cognitive dysfunction after surgery. In recent years, human-computer interactive systems with artificial intelligence have become an important part of human well-being because they enable novel forms of rehabilitation therapies. We propose an interactive game utilizing real-time skeleton-based hand gesture recognition, which aims to assist rehabilitation exercises by improving the hand-eye coordination of the patients during a game-like experience. For this purpose, we propose a lightweight residual graph convolutional architecture for hand gesture recognition. Furthermore, we designed the whole system using the proposed gesture recognition module and some third-party modules. Finally, some participants were invited to test our system and most of them showed an improvement in their passing rate of the game during the test process.

On-Admission Anemia and Survival Rate in COVID-19 Patients

Anemia often worsens the severity of respiratory illnesses, and few studies have so far elucidated the impact of anemia on COVID-19 infection. This study aimed to evaluate the effect of anemia at admission on the overall survival of COVID-19 patients using accelerated failure time (AFT) models.This registry-based, single-center retrospective cohort study was conducted in a university hospital in Ilam, the southwest of Iran, between March 2020 and September 2021. AFT models were applied to set the data of 2,441 COVID-19 patients. Performance of AFT models was assessed using Akaike’s information criterion (AIC) and Cox-Snell residual. On-admission anemia was defined as hemoglobin (Hb) concentration <120 g/l in men, <110 g/l in women, and <100 g/l in pregnant women.The median in-hospital survival times for anemic and non-anemic patients were 27 and 31 days, respectively. Based on the AIC and Cox-Snell residual graph, the Weibull model had the lowest AIC and it was the best fitted model to the data set among AFT models. In the adjusted model, the results of the Weibull model suggested that the anemia (adjusted time ratio: 1.04; 95% CI: 1.00-1.08; p = 0.03) was the accelerated factor for progression to death in COVID-19 patients. Each unit of increase in hemoglobin in COVID-19 patients enhanced the survival rate by 4%.Anemia is an independent risk factor associated with the risk of mortality from COVID-19 infection. Therefore, healthcare professionals should be more sensitive to the Hb level of COVID-19 patients upon admission.

Ligand Binding Prediction Using Protein Structure Graphs and Residual Graph Attention Networks.

Computational prediction of ligand–target interactions is a crucial part of modern drug discovery as it helps to bypass high costs and labor demands of in vitro and in vivo screening. As the wealth of bioactivity data accumulates, it provides opportunities for the development of deep learning (DL) models with increasing predictive powers. Conventionally, such models were either limited to the use of very simplified representations of proteins or ineffective voxelization of their 3D structures. Herein, we present the development of the PSG-BAR (Protein Structure Graph-Binding Affinity Regression) approach that utilizes 3D structural information of the proteins along with 2D graph representations of ligands. The method also introduces attention scores to selectively weight protein regions that are most important for ligand binding. Results: The developed approach demonstrates the state-of-the-art performance on several binding affinity benchmarking datasets. The attention-based pooling of protein graphs enables identification of surface residues as critical residues for protein–ligand binding. Finally, we validate our model predictions against an experimental assay on a viral main protease (Mpro)—the hallmark target of SARS-CoV-2 coronavirus.

Multi-mode dynamic residual graph convolution network for traffic flow prediction

Urban traffic congestion is not only an important cause of traffic accidents, but also a major hinder to urban development. By learning the historical traffic flow data, we can forecast the traffic flow of some regions in the future, which is of great significance to urban road planning, traffic management, traffic control and many more. However, due to the complex topology of traffic network and the diversity of influencing factors to traffic flow, the traffic modes are usually complicated and volatile, which makes traffic flow prediction very difficult. In this paper, we propose a new graph convolution neural network, namely Multi-mode Dynamic Residual Graph Convolution Network (MDRGCN), to capture the dynamic impact of different factors on traffic flow in a road network simultaneously. Firstly, we design a multi-mode dynamic graph convolution module (MDGCN), which is employed to capture the impact of different traffic modes by learning two types of relationship matrices. Then, we design a multi-mode dynamic graph convolution gated recurrent unit (MDGRU) to realize the combination of spatial and temporal dependences. Finally, we use a dynamic residual module (DRM) to integrate the orginal traffic data and the spatio-temporal features extracted by the MDGRU module to forecast the future traffic flow. Experimental reulsts conducted on the NYCTaxi and NYCBike datasets validate that the MDRGCN model performs better than the other eight baselines.

N-strain epidemic model using bond percolation.

In this paper we examine the emergent structures of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process, in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations, and a collaborative branching process, where percolation is performed on the giant connected component (GCC) instead. We investigate the behavior of these models, including the expected size of the GCC for a given generation, the critical percolation probability, and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erdős-Renyi and scale-free random graphs. This model can be interpreted as a seasonal N-strain model of disease spreading.

The Application of Grey Relational Analysis in the Evaluation of Financial Auditing Effect and Improvement

Financial institutions are confronting more complicated risks as a result of the current financial crisis. Financial auditing is an essential aspect of government auditing since it serves to protect the security and stability of the national financial system by evaluating financial systemic vulnerabilities. Therefore, this paper combines the grey relational analysis to carry out research work on the financial auditing effect and improvement evaluation. Firstly, we conducted a preliminary selection of relevant financial audit impact indicators and identified the design of the influencing factor system as well as appropriate data for the influencing factors, resulting in the first evaluation system of the evaluation indicators. Secondly, we created a factor set for evaluating the financial audit improvement effect. The completed task proportion component and the task completion quality factor are the two kinds of improvement impact evaluation factors. On this foundation, this research develops a grey correlation-based assessment model for audit effect enhancement. The residual graph fitting findings indicate that the scheme has a good implementation impact and may be utilised to assess the financial auditing improvement effect.

Simulated annealing in feature selection approach for modeling aboveground carbon stock at the transition between Brazilian Savanna and Atlantic Forest biomes

Forest ecosystems are important in the carbon storage process. Thus, the objective was to investigate the effectiveness of the Simulated Annealing meta-heuristic analysis for selecting variables to maximize the accuracy of the aboveground carbon prediction at the tree level. We used data from uneven-aged forests located in the Rio Grande Basin - Minas Gerais, Brazil, where 227 trees had their carbon stock measured. The classic Spurr linear model, stepwise linear regression and pan-tropical coverage, Random Forest (RF), and the hybrid SARF method (Simulated Annealing and Random Forest) were used to estimate the carbon stock from the selection of variables for the different compartments of the tree (total, stem, branch, and leaf). The SARF consisted of the metaheuristic to select the variables to be used in the RF. These methods were evaluated by the root mean square error (RMSE), coefficient of determination (R²), and residual graph. As a result, the pan-tropical equation demonstrated superior performance than the Spurr model due to its greater homogeneity of residues. The stepwise technique reduced the number of variables and the error of the estimates, mainly for the validation set. SARF showed better adjustments than RF, as it reduced in on average 99.2% of the number of variables and 9% of the error of estimates considering all compartments. In general, variables such as volume, basic wood density, canopy projection area, diameter at 0%, diameter at breast height, height, and latitude contributed strongly to the carbon independent of the tree compartment. Among the methods, SARF is an alternative to the traditional method, as it can extract accurate information from a large data set.