Average Node Degree Research Articles

Bioinformatics Analysis of the Expression of ATP Binding Cassette Subfamily C Member 3 (ABCC3) in Human Glioma.

ObjectiveTo investigate the expression of the ABCC3 gene in human glioma and its correlation with the patient’s prognosis.MethodsThe cancer genome atlas (TCGA) database was used to analyze the differential expression of the ABCC3 gene in human glioma. The STRING database was used to construct the protein-protein interaction (PPI) network of the ABCC3 gene coding protein. The co-expression genes relevant to the ABCC3 gene were analyzed by the Pearson correlation test. A log-rank test was used to analyze the difference of overall survival (OS) and disease-free survival (DFS) between the high and low ABCC3 gene expression groups.ResultsThe expression level of the ABCC3 gene in glioma tissues was lower than that of corresponding normal brain tissues. The PPI network contains 51 nodes with the average node degree of 13.3 and the local clustering coefficient of 0.72 which indicated that the PPI enrichment was significant (p<0.001). Ten hub genes (ABCC3,NR1I2,NR1H4,-CYP7A1,SLC10A1,CYP3A4,UGT1A1,UGT1A8,UGT1A6 and ALB) were identified by the cytoscape software. The KEGG analysis was enriched in drug metabolism - cytochrome P450 and PPAR signaling pathway. CFI gene expression level was positive correlated with the ABCC3 expression level (r=0.71, p<0.05). And the CNRIP1 gene expressed was negative correlated with ABCC3 expression (r=-0.43, p<0.05). The overall survival (HR=2.8, P<0.05) and disease-free survival rates (HR=2.0, P<0.05) of patients with ABCC3 low expression glioma were significantly higher than those of patients with high expression of ABCC3. Conclusion The expression level of the ABCC3 gene in glioma was decreased compared to normal brain tissue. The overall survival and disease-free survival of in the ABCC3 low-expression group was significant decreased.

Dual‐failure restorability analysis of span‐restorable meta‐mesh networks

AbstractThe span‐restorable meta‐mesh model was previously designed as a cutting‐edge technique that enhanced the spare capacity efficiency in low average nodal degree networks. In this technique, lightpaths that fully traverse chains of degree‐2 nodes are provided with a logical express bypass span allowing a distinction between the internal and external working flow capacity that transit the chain. In the event of span failure, lightpaths which would normally traverse the chain in its entirety are allowed to fail back to its anchor nodes such that only the intrachain flow requires allocation of spare capacity. Previous work on the meta‐mesh design considered only single failure restorability. The work herein analyzes dual span failure situations by developing two new integer linear programming models. The first model provides the minimum total cost of designing a meta‐mesh network capable of withstanding dual span failure scenarios. The second model offers a maximization of the dual failure restorability by minimizing the number of nonrestored working capacities with a given limit of total spare capacity investment. Experiments are performed on six master test‐case networks of various topologies and scales.

Exploring the transition behavior of nodes in temporal networks based on dynamic community detection

Community detection and community evolution tracking are two important tasks in dynamic complex network analysis. Recently, a variety of models and methods have been proposed for detecting the community structure and analyzing their evolution. However, all these methods are only committed to improving the performance of community detection or identifying evolutionary events, ignoring the internal relevance between the structure of each snapshot of the dynamic network and the evolution pattern of communities, especially the structural features of nodes and their dynamic transition behavior. To cope with this problem, we firstly conduct experiments on 15 real-world dynamic networks to explore the transition behavior of nodes in dynamic networks, which is one of the most influential evolutionary patterns in temporal community detection. Firstly, we obtain the temporal community structure based on very successful temporal community detection methods. Secondly, we extract features of nodes based on the structure of the dynamic network, and take the community transition behavior of nodes as the binary classification problem. Finally, we use the decision tree to find the node-level features that have a general impact on node transition. Experiments indicate that the degree and average neighbor degree of nodes have the most common indispensable impact on the node transition behavior, which are very helpful for modeling dynamic complex networks in future.

Efficient EP Detectors Based on Channel Sparsification for Massive MIMO Systems

Multiuser detection based on the expectation propagation (EP) algorithm for the massive multiple-input multiple-output (M-MIMO) system has received considerable attention in recent years due to its good performance-complexity tradeoff. However, its performance degrades when the system is highly overloaded. Furthermore, the computational complexity increases fast as the number of receive antennas increases. In this work, we propose an improved EP detector via channel sparsification based approach, which is shortened as S-EP. The key idea is to sparsify the channel first, such that the average degree of the variable node (VN) and function node (FN) in the associated factor graph (FG) is significantly decreased, thus rendering a reduced effective interference. Therefore, the inference accuracy can be enhanced. The associated computational complexity of the message computation can also be eliminated. Analytical and simulation results illustrate that the proposed S-EP based detection scheme achieves noticeable performance gains compared with the conventional EP based one while requiring even a lower computational complexity.

Simplified computational model for generating biological networks.

A method to generate and simulate biological networks is discussed. An expanded Wooten–Winer–Weaire bond switching methods is proposed which allows for a distribution of node degrees in the network while conserving the mean average node degree. The networks are characterised in terms of their polygon structure and assortativities (a measure of local ordering). A wide range of experimental images are analysed and the underlying networks quantified in an analogous manner. Limitations in obtaining the network structure are discussed. A “network landscape” of the experimentally observed and simulated networks is constructed from the underlying metrics. The enhanced bond switching algorithm is able to generate networks spanning the full range of experimental observations.

Bisection and Exact Algorithms Based on the Lagrangian Dual for a Single-Constrained Shortest Path Problem

We propose two new algorithms called BiLAD and ExactBiLAD for the well-known Single-Constrained Shortest Path (SCSP) problem. It is a fundamental problem in quality-of-service (QoS) routing, where one seeks a source-destination path with the least cost satisfying a delay QoS constraint in a network. As pointed out by Juttner et al. , there is no widely accepted algorithm with polynomial time to the SCSP problem because the SCSP problem is NP-hard. The remarkable feature of BiLAD is that it ensures that the length of iteratively updated angle interval is shrunk at least at a constant ratio. With the help of this feature, we prove its polynomial time complexity. To the best of our knowledge, this is the first time that the polynomial time complexity is proved in details. The numerical results show that, in most QoS routing test instances, the performance of BiLAD is close to their primal optimal solutions. The proposed modified Dijkstra procedure, whose complexity is the same as that of the Dijkstra algorithm, also accelerates BiLAD. In the second part of the paper, based on the information obtained by BiLAD, we design an exact algorithm–ExactBiLAD, in which an optimal solution to the SCSP problem is finally obtained by scanning the steadily reduced optimal-path-candidate triangle area. The simulation results indicate that ExactBiLAD needs only a dozen times of executing the modified Dijkstra algorithm regardless of the network size or the average node degree. Distinguished from many other exact algorithms, ExactBiLAD has a satisfactory performance in the practical computation.

Effects of two channels on explosive information spreading

Information spreading has been studied for decades, but the underlying mechanism why the information can be accepted by a large number of people overnight is still under debate, especially in the aspects of two-channel effects for information transmission and theoretical analysis. In this study, based on a susceptible-accepted-recovered (SAR) model, we examine the effects of two channels represented by a two-layered network, in which one channel is the intra-links within the same layer and the other is inter-links between layers. Different with the case of one single channel on a one-layered network, in the case of two channels, the spreading can be speeded up by the increase in the coupling strength, i.e., average node degree and transmission probability between the two layers. Strikingly, even if the parameter (social reinforcement) is small, the strongly coupling strength can induce explosive transition in the information spreading process. Additionally, a big gap closed to the critical point for the explosive transition was found in the phase space of theoretical analysis, which indicates the emergency of a global large-scope outbreak. These findings may be of significance on the understanding and controlling explosive information spreading in modern society.

Concurrent Multipath Routing Optimization in Named Data Networks

To achieve maximum throughput in named data networking (NDN) with consideration of fairness among each source-sink pair, we model the routing problem in NDN as a mixed-integer maximum concurrent flow problem. Taking advantage of the smart forwarding framework in NDN, we obtain an approximate optimal routing and forwarding solution with our improved Fleischer and random rounding (FRR) algorithm. We analyze the complexity of the Fleischer algorithm more comprehensively and give the best scaling method to achieve the least iterations. In addition, we further reduce the complexity of the Fleischer algorithm so that it iterates only once, thus getting a heuristic algorithm which is called multicommodity multipath (MCMP). Using ndnSIM-based simulation, we compare our proposed routing algorithms with the existing routing algorithms, including flooding, k-shortest path, and best single path routing, and the simulation results prove that FRR and MCMP can outperform other algorithms both in throughput and latency, and it can also be concluded that the best number of paths for k-shortest path routing should be close to and less than the average node degree of the network. For studying routing optimization with caching, we conduct simulations with different in-network cache capacity and different caching policies. The simulation results show that although the LRU can achieve the best performance under the same cache capacity, the cache capacity plays a decisive role. All routing algorithms produce better performance with caching, but the FRR still achieves the best performance, and follows by MCMP.

Differently Expressed Genes (DEGs) Relevant to Type 2 Diabetes Mellitus Identification and Pathway Analysis via Integrated Bioinformatics Analysis.

BackgroundThe aim of this study was to evaluate the differently expressed genes (DEGs) relevant to type 2 diabetes mellitus (T2DM) and pathway by performing integrated bioinformatics analysis.Material/MethodsThe gene expression datasets GSE7014 and GSE29221 were downloaded in GEO database, and DEGs from type 2 diabetes mellitus and normal skeletal muscle tissues were identified. Biological function analysis of the DEGs was enriched by GO and KEEG pathway. A PPI network for the identified DEGs was built using the STRING database.ResultsThirty top DEGs were identified from 2 datasets: GSE7014 and GSE29221. Of the 30 top DEGs, 20 were up-regulated and 10 were down-regulated. The 20 up-regulated genes were enriched in regulation of mRNA, protein biding, and phospholipase D signaling pathway. The 10 down-regulated genes were enriched in telomere maintenance via semi-conservative replication, AGE-RAGE signaling pathway in diabetic complications, and insulin resistance pathway. In the PPI network of 20 up-regulated DEGs, there were 40 nodes and 84 edges, with an average node degree of 4.2. For the 10 down-regulated DEGs, we found a total of 30 nodes and 105 edges, with an average node degree of 7.0 and local clustering coefficient of 0.812. Among the 30 DEGs, 10 hub genes (CNOT6L, CNOT6, CNOT1, CNOT7, RQCD1, RFC2, PRIM1, RFC4, RFC5, and RFC1) were also identified through Cytoscape.ConclusionsDEGs of T2DM may play an essential role in disease development and may be potential pathogeneses of T2DM.

Efficient computation of loop-free alternates

Network failures may lead to serious packet loss and degrade network performance. Therefore, loop-free alternates (LFA) have been widely deployed by many Internet service providers to cope with single network component failure in large Internet backbones. However, the efficiency of LFA has not been sufficiently studied. Some existing methods have extremely large computational overhead, and their computational complexity is linear with the average node degree of the network. The current methods consume a large amount of central processing unit resources, thereby aggravating the burden on the router. To improve the routing resilience without introducing significant extra overhead, this study proposes an incremental alternate computation with negative augmentation algorithm (IAC), which is based on incremental shortest path first algorithm. First, IAC turns the problem of quick implementation of LFA into efficiently calculating the minimum cost of all its neighbors to all other network nodes on the shortest path tree rooted at the computing node. Then, several theorems for calculating the cost are presented and their correctness is validated. Finally, we evaluate IAC through simulations with real-world and generated topologies. Compared with TBFH, DMPA, and DMPA-e, which are algorithms optimized for limited scenarios, IAC finds approximately 50% more available alternates, is more than three times faster, and provides node protection capabilities that TBFH, DMPA, and DMPA-e cannot provide. These advantages make IAC a good candidate for traditional telecommunication networks and emerging complex networks that require failure repair and load balancing in a highly dynamic environment.

Modelling and Prediction of Financial Trading Networks: An Application to the New York Mercantile Exchange Natural Gas Futures Market

SummaryOver recent years there has been a growing interest in using financial trading networks to understand the microstructure of financial markets. Most of the methodologies that have been developed so far for this have been based on the study of descriptive summaries of the networks such as the average node degree and the clustering coefficient. In contrast, this paper develops novel statistical methods for modelling sequences of financial trading networks. Our approach uses a stochastic block model to describe the structure of the network during each period, and then links multiple time periods by using a hidden Markov model. This structure enables us to identify events that affect the structure of the market and make accurate short-term prediction of future transactions. The methodology is illustrated by using data from the New York Mercantile Exchange natural gas futures market from January 2005 to December 2008.

Underlying and Persistence Fault Diagnosis in Wireless Sensor Networks Using Majority Neighbors Co-ordination Approach

The faults in wireless sensor network are classified according to the underlying causes, behavior, and persistence with respect to the observation time. Due to underlying causes, faults are classified as fail and stop, crash, omission, timing, and incorrect computation fault. Due to behavior, faults are classified as hard and soft fault. Due to persistence, faults are classified as permanent, intermittent, and transient fault. As the recent state-of-art fault diagnosis is a significant requirement for each application of wireless sensor network. In this research paper, we have proposed a fault diagnosis protocol using majority neighbors coordination based approach for wireless sensor network. Precisely, a multiple-hop data received technique, timeout period mechanism, timeout request and response message exchange, timeout early and delay message exchange, and degree of belongingness using Gaussian function mechanism are used for the detection of faults such as fail and stop, crash, omission, timing, and incorrect computation. The mean difference and standard error comparison with different threshold condition are used for soft (permanent, intermittent, and transient) fault detection, and timeout response mechanism with different threshold condition is used for hard (permanent, intermittent, and transient) fault detection. After fault detection, the actual fault status of the sensor node is confirmed by the one-hop majority neighbor sensor nodes. For validation of the proposed fault detection algorithms, simulation experiments are conducted by the network simulator NS-2.35. The experimental results show the substantially parameters performance such as fault detection accuracy, false alarm rate, false positive rate, and false classification rate with increasing the fault probability for different average degree of the sensor nodes in the network.

Structural Robustness to Noise in Consensus Networks: Impact of Degrees and Distances, Fundamental Limits, and Extremal Graphs

We investigate how the graph topology influences the robustness to noise in undirected linear consensus networks. We measure the structural robustness by using the smallest possible value of steady-state population variance of states under the noisy consensus dynamics with edge weights from the unit interval. We derive tight upper and lower bounds on the structural robustness of networks based on the average distance between nodes and the average node degree. Using the proposed bounds, we characterize the networks with different types of robustness scaling under increasing size. Furthermore, we present a fundamental tradeoff between the structural robustness and the average degree of networks. While this tradeoff implies that a desired level of structural robustness can only be achieved by graphs with a sufficiently large average degree, we also show that there exist dense graphs with poor structural robustness. We then show that random <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -regular graphs (the degree of each node is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> ) with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> nodes typically have near-optimal structural robustness among all the graphs with size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> and average degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> for sufficiently large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> . We also show that when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> increases properly with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> , random <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -regular graphs maintain a structural robustness within a constant factor of the complete graph's while also having the minimum average degree required for such robustness.

Urban spatial order: street network orientation, configuration, and entropy

Street networks may be planned according to clear organizing principles or they may evolve organically through accretion, but their configurations and orientations help define a city’s spatial logic and order. Measures of entropy reveal a city’s streets’ order and disorder. Past studies have explored individual cases of orientation and entropy, but little is known about broader patterns and trends worldwide. This study examines street network orientation, configuration, and entropy in 100 cities around the world using OpenStreetMap data and OSMnx. It measures the entropy of street bearings in weighted and unweighted network models, along with each city’s typical street segment length, average circuity, average node degree, and the network’s proportions of four-way intersections and dead-ends. It also develops a new indicator of orientation-order that quantifies how a city’s street network follows the geometric ordering logic of a single grid. A cluster analysis is performed to explore similarities and differences among these study sites in multiple dimensions. Significant statistical relationships exist between city orientation-order and other indicators of spatial order, including street circuity and measures of connectedness. On average, US/Canadian study sites are far more grid-like than those elsewhere, exhibiting less entropy and circuity. These indicators, taken in concert, help reveal the extent and nuance of the grid. These methods demonstrate automatic, scalable, reproducible tools to empirically measure and visualize city spatial order, illustrating complex urban transportation system patterns and configurations around the world.

The Extended Directed Friendship Paradox

The friendship paradox says that on average your friends have more friends than you. Equivalently, in an undirected graph, the average degree of the nodes is no greater than the average degree of the terminal node of a random walk of length one. We generalize this result in two ways: (1) by considering directed graphs, which also allow one-sided relations, such as between followers and leaders; and (2) by characterizing the relations between the expected values of the in and out degrees of the terminal nodes of random alternating walks of length 2k and 2k+1, where k is nonnegative. The limiting value of these averages is proportional to the largest singular value of the associated adjacency matrix, and to its largest eigenvalue in the special case of an undirected graph. We interpret the results for one-sided relations (e.g., between leaders and followers) and two-sided relations (e.g., between friends). We further relate such extension to centrality measures. We show that beta centrality approaches eigenvector centrality when the inverse of the weighting parameter becomes arbitrarily close to the limiting value of the expected degree of the terminal node of a random walk of length k. When relations are asymmetric, this observation extends to the singular vectors of the associated directed graph.

Optimal Multiculture Network Design for Maximizing Resilience in the Face of Multiple Correlated Failures

Current data networks are highly homogeneous because of management, economic, and interoperability reasons. This technological homogeneity introduces shared risks, where correlated failures may entirely disrupt the network operation and impair multiple nodes. In this paper, we tackle the problem of improving the resilience of homogeneous networks, which are affected by correlated node failures, through optimal multiculture network design. Correlated failures regarded here are modeled by SRNG events. We propose three sequential optimization problems for maximizing the network resilience by selecting as different node technologies, which do not share risks, and placing such nodes in a given topology. Results show that in the 75% of real-world network topologies analyzed here, our optimal multiculture design yields networks whose probability that a pair of nodes, chosen at random, are connected is 1, i.e., its ATTR metric is 1. To do so, our method efficiently trades off the network heterogeneity, the number of nodes per technology, and their clustered location in the network. In the remaining 25% of the topologies, whose average node degree was less than 2, such probability was at least 0.7867. This means that both multiculture design and topology connectivity are necessary to achieve network resilience.

Protein-Protein interaction network analyses of human WNT proteins involved in neural development.

WNT proteins are involved from initial of neural tissue specification to the end of cell fate determination and organ development. The present work was carried out to understand the involvement of different WNT isoforms (WNT3a, WNT5a and WNT7b) in neural development. A total of 718, 546 and 1004 PPIs for WNT3a, WNT5a and WNT7b respectively, were predicted by STRING database with confidence score more than 0.400. A network carrying all the selected PPIs of targeted proteins was constructed by using Cytoscape by assigning source node, target node and combined score as edge attribute. A total 2268 interactions of WNT3a, WNT5a and WNT7b were predicted to be involved in multiple signaling pathways and developmental processes. 43 of 2268 PPIs were refined after analyzing role of targeted proteins specifically in brain and neural development. WNT3a, WNT5a and WNT7a were predicted to be interacting with 18, 17 and 11 proteins, respectively, with average node degree score of 1.89, 2.12 and 1.82 respectively. The CytoHubba algorithm identified WNT3a, WNT5a, and WNT7b as hub proteins in neural development ranked on the basis of EPC (Edge Percolated Component) score of 9.352, 9.258 and 8.387.

Early recovery of interhemispheric functional connectivity after corpus callosotomy.

To investigate whether interhemispheric functional connectivity (FC) recovers in the first year after total callosotomy. Eight epilepsy patients undergoing total callosotomy were recruited. Resting-state functional magnetic resonance imaging was acquired before and after surgery. The precallosotomy and postcallosotomy interhemispheric and intrahemispheric FC was analyzed by using graph theory and voxel-mirrored homotopic connectivity (VMHC). The seizure outcome was scored using the Engel surgical outcome scale. After callosotomy (mean postoperative interval = 4months), the network density, average node degree, characteristic path length, and global efficiency of the whole interhemispheric networks were significantly decreased, compared to those in the precallosotomy networks. However, postcallosotomy interhemispheric FC and homotopic VMHC were not significantly reduced in bilateral frontal and temporal lobes. The network density and average node degree of the intrahemispheric networks were significantly increased. The characteristic path length and global efficiency of intrahemispheric networks were unchanged. The interhemispheric FC may be preserved or recover early within the first postoperative year after total callosotomy, particularly in the frontal and anterior temporal lobes.

Analysis on topological features of deterministic hierarchical complex network

Real complex networks usually have small-world effect, scale-free features and hierarchical modularity, a construction method for deterministic hierarchical network is proposed in this paper. The network model with growth and global preferential attachment characteristic and connected by the copy network modules to establish hierarchical network model. By theoretical calculation and numerical simulation about the deterministic hierarchical complex network model, the results illustrate that the complex network model satisfy the small-world effect, scale-free feature and hierarchical modularity, the calculation results show that the size of the hierarchical network model for exponential growth with the network size increased, and the average degree of nodes is shown as linear growth; at the same time, the model of scale-free feature and the hierarchical modularity with network parameters do not have correlation which is an inherent attribute of network model itself; the clustering-degree correlations in the network model satisfy power-law characteristics and the nodes contact closely together in the modules which are connected by the Hub nodes in the complex network model. .

A modified efficiency centrality to identify influential nodes in weighted networks

It is still a crucial issue to identify influential nodes effectively in the study of complex networks. As for the existing efficiency centrality (EffC), it cannot be applied to a weighted network. In this paper, a modified efficiency centrality (EffC $$^\mathrm{m}$$ ) is proposed by extending EffC into weighted networks. The proposed measure trades off the node degree and global structure in a weighted network. The influence of both the sum of the average degree of nodes in the whole network and the average distance of the network is taken into account. Numerical examples are used to illustrate the efficiency of the proposed method.