Small Set Of Nodes Research Articles

Identifying critical nodes in interdependent networks by GA-XGBoost

Once a critical node is destroyed, the interdependent network is prone to experience severe cascading failure. Due to the coupling, traditional methods are challenging to apply to interdependent networks. Here, we propose a novel comprehensive model based on machine learning. The main work of this data-driven approach is to train the model on a small set of nodes (5 % of the graph) and do the critical node identification on the rest. We collect node centrality indicators to describe the node features and provide informative input data from different dimensions. The uniform node sampling is improved to cluster oversampling, which combines K-means and Synthetic Minority Over-sampling Technique (SMOTE) to select and recreate uniformly distributed training samples. We optimize the XGBoost based on the Genetic algorithm (GA) to overcome the instability of manual parameters. Kendall's τ correlation coefficient, Jaccard similarity coefficient, R2, and RMSE are used as the model performance evaluation metrics. Experiment results confirm that the proposed GA-XGBoost model outperforms others, demonstrating higher adaptability and stability in various situations. The heuristic algorithm-optimized machine learning model offers a viable solution for identifying critical nodes in interdependent networks, which is of great significance for controlling virus propagation and preventing failures.

On the approximate solution of dynamic systems derived from the HIV infection of CD[formula omitted]T cells using the LRBF-collocation scheme

Human immunodeficiency virus (HIV) infection may cause death by damaging some of the patient’s vital organs through weakening the body’s immune system, including CD4+T cells. In the meantime, mathematical models can be useful in dealing with this deadly virus by providing effective strategies based on the examination of different infection states. The major aim pursued in this paper is to present a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from the HIV infection models of CD4+T cells. The offered method is developed according to the use of local radial basis functions (LRBFs) as shape functions in the discrete collocation scheme. The new technique approximates the solution by a small set of nodes instead of all points located in the domain where the HIV mathematical model is given. Thus the presented method uses less computing volume compared to the globally supported radial basis functions, and as a result, its algorithm can be quickly run on a computer with relatively low memory. The computational efficiency of the scheme is studied by several test examples.

An Information-Theoretic Bound on p-Values for Detecting Communities Shared between Weighted Labeled Graphs

Extraction of subsets of highly connected nodes (“communities” or modules) is a standard step in the analysis of complex social and biological networks. We here consider the problem of finding a relatively small set of nodes in two labeled weighted graphs that is highly connected in both. While many scoring functions and algorithms tackle the problem, the typically high computational cost of permutation testing required to establish the p-value for the observed pattern presents a major practical obstacle. To address this problem, we here extend the recently proposed CTD (“Connect the Dots”) approach to establish information-theoretic upper bounds on the p-values and lower bounds on the size and connectedness of communities that are detectable. This is an innovation on the applicability of CTD, broadening its use to pairs of graphs.

Network models of posttraumatic stress disorder: A meta-analysis.

Posttraumatic stress disorder (PTSD) researchers have increasingly used psychological network models to investigate PTSD symptom interactions, as well as to identify central driver symptoms. It is unclear, however, how generalizable such results are. We have developed a meta-analytic framework for aggregating network studies while taking between-study heterogeneity into account and applied this framework in the first-ever meta-analytic study of PTSD symptom networks. We analyzed the correlational structures of 52 different samples with a total sample size of n = 29,561 and estimated a single pooled network model underlying the data sets, investigated the scope of between-study heterogeneity, and assessed the performance of network models estimated from single studies. Our main findings are that: (a) We identified large between-study heterogeneity, indicating that it should be expected for networks of single studies to not perfectly align with one-another, and meta-analytic approaches are vital for the study of PTSD networks. (b) While several clear symptom-links, interpretable clusters, and significant differences between strength of edges and centrality of nodes can be identified in the network, no single or small set of nodes that clearly played a more central role than other nodes could be pinpointed, except for the symptom "amnesia" that was clearly the least central symptom. (c) Despite large between-study heterogeneity, we found that network models estimated from single samples can lead to similar network structures as the pooled network model. We discuss the implications of these findings for both the PTSD literature as well as methodological literature on network psychometrics. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Region-Specific Network Analysis Reveals That Epigenetic Modifications Outside Transcriptional Start Sites Are Tightly Linked to mRNA

While most data analysis of epigenetic modifications has focused on the transcriptional start site proximal region (TPR), the non-TPR has received less attention. The understanding of interaction relationships of epigenetic modifications and their effects is incomplete, especially for the non-TPR. To study the interaction relationships among epigenetic modifications within the TPR and non-TPR, we presented an original analysis framework, that is, the region-specific epigenetic interaction network, where each gene element was introduced as a new dimension that can be separately analyzed based on region-specific signals. We derived the epigenetic interaction network (EIN) based on the Pearson correlation coefficient and partial correlation coefficient. Our analysis of the data of CD4+ cells showed that the majority of edges relate to a small set of nodes in the identified EIN. Most strikingly, we found that modifications in the non-TPR, especially introns, exhibit frequent and important interactions and are closely linked to mRNA. Moreover, we found that epigenetic modifications exhibit more consistent behavior in different regions of genes. Finally, we showed that these modifications can be easily divided into three categories, namely, (i) the class of less interaction, (ii) the class of negative effect and (iii) the class of positive effect, where the last two classes perfectly match previous results. Our results provide a new perspective for exploring the functional mechanisms of epigenetic modification.

I/O efficient structural clustering and maintenance of clusters for large-scale graphs

In recent years, the size of graph data has increased significantly, but most existing graph clustering algorithms do not consider the case where the size of main memory is not sufficient to handle large amount of graph data. Exploring entire region of graph for clustering causes too many random disk accesses to use data that are not loaded into memory, resulting in excessive disk I/O and thrashing. To address this problem, we propose an I/O-efficient algorithm for structural clustering of a graph, called pm-SCAN. In the proposed method, if memory is insufficient, an input graph is partitioned into several subgraphs smaller than memory, and clustering is first performed for each subgraph. And then clusters from the subgraphs are merged based on connectivity between clusters so that global results can be obtained in the point of view of an original input graph. Not only does pm-SCAN produce scalable performance even for very large graphs, i.e., significant shortage of available memory, but also the result of pm-SCAN is the same as that of the original structural clustering algorithm SCAN. We also propose a cluster maintenance method for large-scale dynamic graphs that change over time. Instead of reclustering with a whole graph, only a small set of nodes whose structural connectivities are subject to change by a given update operation is first identified, and we access only those nodes in disk and update their clusters to reduce maintenance costs. This dynamic graph handling mechanism shows significant performance improvement compared to the existing method and the baseline that performs clustering from scratch.

An efficient path-based approach for influence maximization in social networks

It is no secret that the word-of-mouth has very powerful effect on the social interconnections, but the question is “which factors influence the word-of-mouth effectiveness?” The answer hinges on a small set of nodes if activated, would spread information all over the network. This is a major issue in the social network analysis, known as the influence maximization, through which the influence spreading through a small set of seed nodes is maximized. Finding this highly influential node set has still remained challenging due to the non-deterministic polynomial-time (NP)-hard nature of the influence maximization problem and the significant increase in the size of social networks. Thus, in this paper, an efficient path-based algorithm was proposed to address this problem from two complementary perspectives adapting the proposed algorithm in the large-scale networks. One perspective is approximating the influence spread efficiently using two features of the nodes: the degrees and the independent influence path. The second perspective is pruning out the uninfluential nodes and reducing the computation volume in approximating the influence spread using a practical preprocessing heuristic method. Extensive empirical experiments were conducted to evaluate the performance of the proposed algorithm in the seven real-world networks and the results were compared with a plenty of the state-of-the-art algorithms. The results revealed that the proposed algorithm outperforms its counterparts, by offering an outstanding trade-off between the quality and efficiency.

Structural inequalities emerging from a large wire transfers network

We aim to explore the connections between structural network inequalities and bank’s customer spending behaviours, within an entire national ecosystem made of natural persons (i.e., an individual human being) and legal entities (i.e., private or public organisations), different business sectors, and supply chains that span distinct geographical regions. We focus on Italy, that is among the wealthiest nations in the world, and also an example of a complex economic system. In particular, we had access to a large subset of anonymised and GDPR-compliant wire transfer data recorded from Jan 2016 to Dec 2017 by Intesa Sanpaolo, a leading banking group in the Eurozone, and the most important one in Italy.Intesa Sanpaolo wire transfers network exhibits a strong heavy-tailed behaviour and a giant component that grows continuously around the same core of the 1% highest degree nodes, and it also shows a general disassortative pattern, even if some ranges of degrees’ values stand out from the trend. Structural heterogeneity is explored further by means of a bow-tie analysis, that shows clearly that the majority of relevant, in terms of transferred amount, transactions is settled between a smaller set of nodes that are associated to legal entities and that mostly belong to the strongly connected component. This observation brings to a more comprehensive inspection of differences between Italian regions and business sectors, that could support the detection and the understanding of the interplay between supply chains.Our results suggest that there is a general flow of money that seems to stream down from higher degree legal entities to lower degree natural persons, crossing Italian regions and connecting different business sectors, and that is finally redistributed through expenses sharing within families and smaller communities. We also describe a reference dataset and an empirical contribution to the study on financial networks, focusing on finer-grained information concerned about spending behaviour through wire transfers.

Achieving High Throughput for Heterogeneous Networks With Consecutive Caching and Adaptive Retrieval

Heterogeneous networks raise the challenge on ubiquitous connections among heterogeneous devices and networking protocols. As a promising approach to meet this challenge, Information-centric networking (ICN) offers a new communication paradigm which can conceal the heterogeneity of underlying networks. However, it suffers from the problem of segmented cached chunks, which results in low throughput caused by high frequency of switching among different nodes holding chunk copies, and the large Interest packet overhead (IPO). Although the studies on in-network caching or Interest pipelining based on delay estimation help to improve ICN performance, they cannot address such problem and further improve ICN performance fundamentally, because of their insufficient considerations on the interplay between caching and transport protocols. We conduct the experiments and observe that 1) data chunks are cached in a distributed manner with ICN, and 2) range-based data retrieval can reduce switch-over frequency and IPO. Based on these observations, we propose the adaptive retrieval with consecutive caching (ARCC) scheme, which is composed of the consecutive data chunk caching (ConCaching) and adaptive data chunk retrieval (ACUR). ARCC bridges the gap between caching and transport, where intermediate nodes on transmission path only cache the consecutive data chunks with the size above a threshold, while users can adjust the range of requested data chunks to maximize the throughput. This way, at most a range of consecutive data chunks can be retrieved by one Interest , and users retrieve data from the small set of nodes with low switch-over frequency. The intensive simulations show that the proposed mechanisms can achieve the objectives of consecutive chunk caching, in terms of substantial reduction in IPO and switch-over frequency and higher throughput compared with the existing pipeline mechanism in ICN.

An Equilibrated a Posteriori Error Estimator for Arbitrary-Order N\xe9d\xe9lec Elements for Magnetostatic Problems

We present a novel a posteriori error estimator for Nédélec elements for magnetostatic problems that is constant-free, i.e. it provides an upper bound on the error that does not involve a generic constant. The estimator is based on equilibration of the magnetic field and only involves small local problems that can be solved in parallel. Such an error estimator is already available for the lowest-degree Nédélec element (Braess and Schöberl in Math Comput 77(262):651-672, 2008) and requires solving local problems on vertex patches. The novelty of our estimator is that it can be applied to Nédélec elements of arbitrary degree. Furthermore, our estimator does not require solving problems on vertex patches, but instead requires solving problems on only single elements, single faces, and very small sets of nodes. We prove reliability and efficiency of the estimator and present several numerical examples that confirm this.

A neighborhood link sensitive dismantling method for social networks

Network dismantling aims to find the minimal set of nodes that, if removed, will break the network into small components with their largest one limited to a certain threshold. This problem underlies many practical applications in various areas, such as bioinformatics, transportation and the Internet. There are two major kinds of network dismantling methods, i.e. centrality measure based methods and network decycling based methods. The former ignores the influence of the loop structure in network topology, while the latter massively deletes irrelevant nodes in the loop removal step, both resulting in poor performance. To solve these problems, this paper proposes a neighborhood link sensitive dismantling method for social networks. The proposed method contains two key steps, namely node deleting step and node re-inserting step. In node deleting step, a neighborhood link sensitive centrality measure is defined to identify the nodes that are really crucial to destroy the connectivity of network. In the following node re-inserting step, an appropriate greedy strategy is selected to refine the node set of network dismantling as much as possible to the theoretical optimal solution. Experimental results on real-world networks and synthetic networks demonstrate that the proposed method can break down networks by deleting only a smaller set of nodes, outperforming the existing state-of-the-art methods. Furthermore, our proposed method shows stable performance and strong adaptability on networks with different scales and structural characteristics.

A Method for Finding Constrained Driver Nodes in Target Control of Network

One of the ultimate goals of studying network dynamics and its properties is to control it. In the past 20 years, with the joint efforts of many scientists, the theory of controlling a whole network through a small set of nodes, which are called driver nodes (DN) has made great progress. However, the full control of networks may be neither feasible nor necessary in some real systems with huge size and high complexity, which motivate scientists to explore target control theory, i.e., the efficient control for a subset of nodes in a network through a small node set. And in a real network, there is another common situation, which is not each node can be easily accessed. Therefore, it is meaningful to explore the target control strategy under the condition that the driver nodes are constrained. In this paper, an effective method is proposed to make more DN be included in the constrained node set (CNs). We adopt the strategy of greedy algorithm to gradually constrain DN into CNs in the iterative process of target control. In each iteration, we will adjust the strategy of how to choose driver nodes according to some network properties. And a few experiments were presented to prove that the proposed method can make DN into CNs effectively in both Scale-free networks (SF) and Erdös-Rényi (ER) networks. Then, we explored the performance of this method in the case of local and random selection of target nodes, respectively. In addition, some factors that will affect the effects of this method were also explored in this paper. In the end, this method is proved valid through the verification of the real network data sets.

Bitcoin's dynamic peer‐to‐peer topology

SummaryTopology discovery is a prerequisite when investigating the network properties; with the enormous number of Bitcoin users and performance issues, it becomes critical to analyse the network in a fashion that makes it possible to detect all Bitcoin's nodes and understand their behaviour. In massive, dynamic, and distributed peer‐to‐peer (P2P) networks like Bitcoin, where thousands of updates occur per second, it is hard to obtain an accurate topology representing the structure of the network as a graph with nodes and links by using the traditional local measurement approaches based on batches, offline data, or on the discovery of the topology around a small set of nodes and then combine them to discover an approximate network topology. All of which present some limitation when applying them on blockchain‐based networks. In this paper, we propose a topology discovery system that performs a real‐time data collection and analysis for Bitcoin P2P links, which assembles incoming nodes information for deeper graph analysis processing. The topology discovery system allows us to gain knowledge on the Bitcoin network size, the network stability in terms of reachable, churn, and well‐connected nodes, as well as some data regarding the effects of some countries' Internet infrastructure on Bitcoin traffic.

A General Framework for Sensor Placement in Source Localization

When an epidemic spreads in a given network of individuals or communities, can we detect its source using only the information provided by a small set of nodes? We propose a general framework that incorporates two dimensions. First, we can either rely exclusively on a set of selected nodes (i.e., sensors) which always reveal their state independently of any particular epidemic (these are called static), or we can add some sensors (called dynamic) as an epidemic spreads, depending on which additional information is required. Second, the method can either localizes the source after an epidemic has spread through the entire network (offline), or while the epidemic is ongoing (online). We empirically study the performance of offline and online localization both with and without dynamic sensors. Our analysis shows that, by using dynamic sensors, the number of sensors necessary to localize the source is reduced by up to a factor of 10 and that, even with high-variance transmission delays, the source can be localized by using fewer than $5\%$5% of the nodes as sensors.

A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines

This paper presents a numerical method for solving logarithmic Fredholm integral equations which occur as a reformulation of two-dimensional Helmholtz equations over the unit circle with the Robin boundary conditions. The method approximates the solution utilizing the discrete collocation method based on the locally supported thin plate splines as a type of free shape parameter radial basis functions. The local thin plate splines establish an efficient and stable technique to estimate an unknown function by a small set of nodes instead of all points over the solution domain. To compute logarithm-like singular integrals appeared in the method, we use a particular nonuniform Gauss–Legendre quadrature rule. Since the scheme does not require any mesh generations on the domain, it can be identified as a meshless method. The error estimate of the proposed method is presented. Numerical results are included to show the validity and efficiency of the new technique. These results also confirm that the proposed method uses much less computer memory in comparison with the method established on the globally supported thin plate splines. Moreover, it seems that the algorithm of the presented approach is attractive and easy to implement on computers.

Probing Limits of Information Spread with Sequential Seeding

We consider here information spread which propagates with certain probability from nodes just activated to their not yet activated neighbors. Diffusion cascades can be triggered by activation of even a small set of nodes. Such activation is commonly performed in a single stage. A novel approach based on sequential seeding is analyzed here resulting in three fundamental contributions. First, we propose a coordinated execution of randomized choices to enable precise comparison of different algorithms in general. We apply it here when the newly activated nodes at each stage of spreading attempt to activate their neighbors. Then, we present a formal proof that sequential seeding delivers at least as good spread coverage as the single stage seeding does. Moreover, we also show that, under modest assumptions, sequential seeding performs provably better than the single stage seeding using the same number of seeds and node ranking. Finally, we present experimental results comparing single stage and sequential approaches on directed and undirected graphs to the well-known greedy approach to provide the objective measure of the sequential seeding benefits. Surprisingly, applying sequential seeding to a simple degree-based selection leads to higher coverage than achieved by the computationally expensive greedy approach currently considered to be the best heuristic.

On the numerical solution of Fredholm integral equations utilizing the local radial basis function method

ABSTRACTThe current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method.

Optimal stabilization of Boolean networks through collective influence.

Boolean networks have attracted much attention due to their wide applications in describing dynamics of biological systems. During past decades, much effort has been invested in unveiling how network structure and update rules affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. For locally treelike Boolean networks with biased truth tables, we propose a greedy algorithm to identify influential nodes in Boolean networks by minimizing the largest eigenvalue of a modified nonbacktracking matrix. We test the performance of the proposed collective influence algorithm on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes compared with other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying virulence genes that lead to serious diseases.

Power aware malicious nodes detection for securing MANETs against packet forwarding misbehavior attack

A power aware detection procedure for securing mobile ad hoc networks (MANETs) against packet forwarding misbehavior attack is introduced. Packet forwarding misbehavior attack is one of the security attacks in which malicious nodes make MANETs weak by showing packet dropping misconduct. The proposed protocol is named as power aware malicious detection for security (PAMDS) protocol. The feature of power aware is desirable to prolong MANET lifetime as under certain conditions, it is impracticable to replace or recharge the nodes’ batteries. The protocol employs intrusion detection system (IDS) for the detection and exclusion of the nodes inducing packet forwarding misbehavior attack in the network. The detection procedure reacts quickly in detecting and isolating malicious nodes. The detection procedure is power aware as only a small set of nodes that have enough energy and that cover the entire network are selected for running IDS. Also, IDS nodes are not required to work in promiscuous listening mode 100% of the time, this further saves power. PAMDS protocol emphasizes on security of the mobile ad hoc environment and power saving of the battery powered hand held devices. The protocol has been extensively simulated using network simulator NS-2. The findings indicate that PAMDS protocol is effective in terms of power saving, quick malicious node isolation and packet delivery ratio percentage.

Exploring temporal networks with greedy walks

Temporal networks come with a wide variety of heterogeneities, from burstiness of event sequences to correlations between timings of node and link activations. In this paper, we set to explore the latter by using greedy walks as probes of temporal network structure. Given a temporal network (a sequence of contacts), greedy walks proceed from node to node by always following the first available contact. Because of this, their structure is particularly sensitive to temporal-topological patterns involving repeated contacts between sets of nodes. This becomes evident in their small coverage per step as compared to a temporal reference model -- in empirical temporal networks, greedy walks often get stuck within small sets of nodes because of correlated contact patterns. While this may also happen in static networks that have pronounced community structure, the use of the temporal reference model takes the underlying static network structure out of the equation and indicates that there is a purely temporal reason for the observations. Further analysis of the structure of greedy walks indicates that burst trains, sequences of repeated contacts between node pairs, are the dominant factor. However, there are larger patterns too, as shown with non-backtracking greedy walks. We proceed further to study the entropy rates of greedy walks, and show that the sequences of visited nodes are more structured and predictable in original data as compared to temporally uncorrelated references. Taken together, these results indicate a richness of correlated temporal-topological patterns in temporal networks.