Hierarchy Measure for Complex Networks
Mones, Enys; Vicsek, Lilla; Vicsek, Tamás
2012-01-01
Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the m-reach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the controllability of the given system. We also propose a visualization procedure for large complex networks that can be used to obtain an overall qualitative picture about the nature of their hierarchical structure. PMID:22470477
Hierarchy measure for complex networks.
Mones, Enys; Vicsek, Lilla; Vicsek, Tamás
2012-01-01
Nature, technology and society are full of complexity arising from the intricate web of the interactions among the units of the related systems (e.g., proteins, computers, people). Consequently, one of the most successful recent approaches to capturing the fundamental features of the structure and dynamics of complex systems has been the investigation of the networks associated with the above units (nodes) together with their relations (edges). Most complex systems have an inherently hierarchical organization and, correspondingly, the networks behind them also exhibit hierarchical features. Indeed, several papers have been devoted to describing this essential aspect of networks, however, without resulting in a widely accepted, converging concept concerning the quantitative characterization of the level of their hierarchy. Here we develop an approach and propose a quantity (measure) which is simple enough to be widely applicable, reveals a number of universal features of the organization of real-world networks and, as we demonstrate, is capable of capturing the essential features of the structure and the degree of hierarchy in a complex network. The measure we introduce is based on a generalization of the m-reach centrality, which we first extend to directed/partially directed graphs. Then, we define the global reaching centrality (GRC), which is the difference between the maximum and the average value of the generalized reach centralities over the network. We investigate the behavior of the GRC considering both a synthetic model with an adjustable level of hierarchy and real networks. Results for real networks show that our hierarchy measure is related to the controllability of the given system. We also propose a visualization procedure for large complex networks that can be used to obtain an overall qualitative picture about the nature of their hierarchical structure.
Measure of robustness for complex networks
NASA Astrophysics Data System (ADS)
Youssef, Mina Nabil
Critical infrastructures are repeatedly attacked by external triggers causing tremendous amount of damages. Any infrastructure can be studied using the powerful theory of complex networks. A complex network is composed of extremely large number of different elements that exchange commodities providing significant services. The main functions of complex networks can be damaged by different types of attacks and failures that degrade the network performance. These attacks and failures are considered as disturbing dynamics, such as the spread of viruses in computer networks, the spread of epidemics in social networks, and the cascading failures in power grids. Depending on the network structure and the attack strength, every network differently suffers damages and performance degradation. Hence, quantifying the robustness of complex networks becomes an essential task. In this dissertation, new metrics are introduced to measure the robustness of technological and social networks with respect to the spread of epidemics, and the robustness of power grids with respect to cascading failures. First, we introduce a new metric called the Viral Conductance (VCSIS ) to assess the robustness of networks with respect to the spread of epidemics that are modeled through the susceptible/infected/susceptible (SIS) epidemic approach. In contrast to assessing the robustness of networks based on a classical metric, the epidemic threshold, the new metric integrates the fraction of infected nodes at steady state for all possible effective infection strengths. Through examples, VCSIS provides more insights about the robustness of networks than the epidemic threshold. In addition, both the paradoxical robustness of Barabasi-Albert preferential attachment networks and the effect of the topology on the steady state infection are studied, to show the importance of quantifying the robustness of networks. Second, a new metric VCSIR is introduced to assess the robustness of networks with respect
Measuring multiple evolution mechanisms of complex networks
Zhang, Qian-Ming; Xu, Xiao-Ke; Zhu, Yu-Xiao; Zhou, Tao
2015-01-01
Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real-world networks, which show that real-world networks are usually jointly driven by a hybrid mechanism of multiplex features instead of a single pure mechanism. To get an accurate simulation for real networks, some researchers proposed a few hybrid models by mixing multiple evolution mechanisms. Nevertheless, how a hybrid mechanism of multiplex features jointly influence the network evolution is not very clear. In this study, we introduce two methods (link prediction and likelihood analysis) to measure multiple evolution mechanisms of complex networks. Through tremendous experiments on artificial networks, which can be controlled to follow multiple mechanisms with different weights, we find the method based on likelihood analysis performs much better and gives very accurate estimations. At last, we apply this method to some real-world networks which are from different domains (including technology networks and social networks) and different countries (e.g., USA and China), to see how popularity and clustering co-evolve. We find most of them are affected by both popularity and clustering, but with quite different weights. PMID:26065382
Spectral measures of bipartivity in complex networks.
Estrada, Ernesto; Rodríguez-Velázquez, Juan A
2005-10-01
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.
Riemannian-geometric entropy for measuring network complexity.
Franzosi, Roberto; Felice, Domenico; Mancini, Stefano; Pettini, Marco
2016-06-01
A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a-in principle, any-network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.
Riemannian-geometric entropy for measuring network complexity
NASA Astrophysics Data System (ADS)
Franzosi, Roberto; Felice, Domenico; Mancini, Stefano; Pettini, Marco
2016-06-01
A central issue in the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate with a—in principle, any—network a differentiable object (a Riemannian manifold) whose volume is used to define the entropy. The effectiveness of the latter in measuring network complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale-free networks, as well as of characterizing small exponential random graphs, configuration models, and real networks.
Efficient calculation of the robustness measure R for complex networks
NASA Astrophysics Data System (ADS)
Hong, Chen; He, Ning; Lordan, Oriol; Liang, Bo-Yuan; Yin, Nai-Yu
2017-07-01
In a recent work, Schneider et al. (2011) proposed a new measure R for network robustness, where the value of R is calculated within the entire process of malicious node attacks. In this paper, we present an approach to improve the calculation efficiency of R, in which a computationally efficient robustness measure R‧ is introduced when the fraction of failed nodes reaches to a critical threshold qc. Simulation results on three different types of network models and three real networks show that these networks all exhibit a computationally efficient robustness measure R‧. The relationships between R‧ and the network size N and the network average degree < k > are also explored. It is found that the value of R‧ decreases with N while increases with < k > . Our results would be useful for improving the calculation efficiency of network robustness measure R for complex networks.
Pruning artificial neural networks using neural complexity measures.
Jorgensen, Thomas D; Haynes, Barry P; Norlund, Charlotte C F
2008-10-01
This paper describes a new method for pruning artificial neural networks, using a measure of the neural complexity of the neural network. This measure is used to determine the connections that should be pruned. The measure computes the information-theoretic complexity of a neural network, which is similar to, yet different from previous research on pruning. The method proposed here shows how overly large and complex networks can be reduced in size, whilst retaining learnt behaviour and fitness. The technique proposed here helps to discover a network topology that matches the complexity of the problem it is meant to solve. This novel pruning technique is tested in a robot control domain, simulating a racecar. It is shown, that the proposed pruning method is a significant improvement over the most commonly used pruning method Magnitude Based Pruning. Furthermore, some of the pruned networks prove to be faster learners than the benchmark network that they originate from. This means that this pruning method can also help to unleash hidden potential in a network, because the learning time decreases substantially for a pruned a network, due to the reduction of dimensionality of the network.
A complex network-based importance measure for mechatronics systems
NASA Astrophysics Data System (ADS)
Wang, Yanhui; Bi, Lifeng; Lin, Shuai; Li, Man; Shi, Hao
2017-01-01
In view of the negative impact of functional dependency, this paper attempts to provide an alternative importance measure called Improved-PageRank (IPR) for measuring the importance of components in mechatronics systems. IPR is a meaningful extension of the centrality measures in complex network, which considers usage reliability of components and functional dependency between components to increase importance measures usefulness. Our work makes two important contributions. First, this paper integrates the literature of mechatronic architecture and complex networks theory to define component network. Second, based on the notion of component network, a meaningful IPR is brought into the identifying of important components. In addition, the IPR component importance measures, and an algorithm to perform stochastic ordering of components due to the time-varying nature of usage reliability of components and functional dependency between components, are illustrated with a component network of bogie system that consists of 27 components.
Optimized texture classification by using hierarchical complex network measurements
NASA Astrophysics Data System (ADS)
Chalumeau, T.; da F. Costa, L.; Laligant, O.; Meriaudeau, F.
2006-02-01
Texture characterization and classification remains an important issue in image processing and analysis. Much attention has been focused on methods involving spectral analysis and co-occurrence matrix, as well as more modern approaches such as those involving fractal dimension, entropy and criteria based in multiresolution. The present work addresses the problem of texture characterization in terms of complex networks: image pixels are represented as nodes and similarities between such pixels are mapped as links between the network nodes. It is verified that several types of textures present node degree distributions which are far distinct from those observed for random networks, suggesting complex organization of those textures. Traditional measurements of the network connectivity, including their respective hierarchical extensions, are then applied in order to obtain feature vectors from which the textures can be characterized and classified. The performance of such an approach is compared to co-occurrence methods, suggesting promising complementary perspectives.
Range-limited centrality measures in complex networks
NASA Astrophysics Data System (ADS)
Ercsey-Ravasz, Mária; Lichtenwalter, Ryan N.; Chawla, Nitesh V.; Toroczkai, Zoltán
2012-06-01
Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ℓ=1,...,L in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than wℓ=ℓΔ, ℓ=1,2...,L=R/Δ. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of N nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs (˜5.5×106 nodes and ˜2.7×107 edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality measures in
Measuring robustness of community structure in complex networks
NASA Astrophysics Data System (ADS)
Li, Hui-Jia; Wang, Hao; Chen, Luonan
2014-12-01
The theory of community structure is a powerful tool for real networks, which can simplify their topological and functional analysis considerably. However, since community detection methods have random factors and real social networks derived from complex systems always contain error edges, evaluating the robustness of community structure is an urgent and important task. In this letter, we employ the critical threshold of resolution parameter in Hamiltonian function, γC , to measure the robustness of a network. According to spectral theory, a rigorous proof shows that the index we proposed is inversely proportional to robustness of community structure. Furthermore, by utilizing the co-evolution model, we provides a new efficient method for computing the value of γC . The research can be applied to broad clustering problems in network analysis and data mining due to its solid mathematical basis and experimental effects.
Measurement of organization in complex and co-evolving networks
NASA Astrophysics Data System (ADS)
Georgiev, Georgi
2012-02-01
We apply a new method for measurement of organization of complex and co-evolving networks using the quantity of physical action. We consider simple arrangements of elements in a network and constraints to their motion along paths and calculate the amount of organization in each system using the following measure: organization is the inverse of the average sum of physical actions of all elements in a system per unit motion multiplied by the Planck's constant. The meaning of quantity of organization here is the number of quanta of action per one unit motion along a path of an element. A unit motion along a path for a network, such as internet, is the transmission of one bit of information. The calculation can be expanded to systems consisting of many elements and constraints and also can be followed as a function of time with improvement of the organization of a system or connected systems and networks. Thus, the principle of least action becomes the driving force, and the least action state of the system, the attractor for all of the paths of its elements and states of its constraints. We consider also the rate of constraint minimization, or decrease of action per element and motion, as a function of the number of elements i.e. quality as a function of quantity. Increase of quantity, within specified limits, leads to increase of level of organization and vice versa.
Mitigating wildland fire hazard using complex network centrality measures
NASA Astrophysics Data System (ADS)
Russo, Lucia; Russo, Paola; Siettos, Constantinos I.
2016-12-01
We show how to distribute firebreaks in heterogeneous forest landscapes in the presence of strong wind using complex network centrality measures. The proposed framework is essentially a two-tire one: at the inner part a state-of- the-art Cellular Automata model is used to compute the weights of the underlying lattice network while at the outer part the allocation of the fire breaks is scheduled in terms of a hierarchy of centralities which influence the most the spread of fire. For illustration purposes we applied the proposed framework to a real-case wildfire that broke up in Spetses Island, Greece in 1990. We evaluate the scheme against the benchmark of random allocation of firebreaks under the weather conditions of the real incident i.e. in the presence of relatively strong winds.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity
NASA Astrophysics Data System (ADS)
Cao, Hongduo; Li, Ying
2014-03-01
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity
Cao, Hongduo; Li, Ying
2014-03-15
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel–Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
Unraveling chaotic attractors by complex networks and measurements of stock market complexity.
Cao, Hongduo; Li, Ying
2014-03-01
We present a novel method for measuring the complexity of a time series by unraveling a chaotic attractor modeled on complex networks. The complexity index R, which can potentially be exploited for prediction, has a similar meaning to the Kolmogorov complexity (calculated from the Lempel-Ziv complexity), and is an appropriate measure of a series' complexity. The proposed method is used to research the complexity of the world's major capital markets. None of these markets are completely random, and they have different degrees of complexity, both over the entire length of their time series and at a level of detail. However, developing markets differ significantly from mature markets. Specifically, the complexity of mature stock markets is stronger and more stable over time, whereas developing markets exhibit relatively low and unstable complexity over certain time periods, implying a stronger long-term price memory process.
An application of a measure for organization of complex networks
NASA Astrophysics Data System (ADS)
Georgiev, Georgi; Daly, Michael
2013-03-01
In order to measure self-organization in complex networks a quantitative measure for organization is necessary. This will allow us to measure their degree of organization and rate of self-organization. We apply as a measure for quantity of organization the inverse of the average sum of physical actions of all elements in a system per unit motion multiplied by the Planck's constant, using the principle of least action. The meaning of quantity of organization here is the inverse of average number of quanta of action per one node crossing of an element of the system. We apply this measure to the central processing unit (CPU) of computers. The organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has, S-shaped structure, suggesting some of the mechanisms of self-organization. We also study the dependence of organization on the number of transistors. This method helps us explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help to describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self-organization to improve their quality.
NASA Astrophysics Data System (ADS)
Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.
2017-01-01
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval [0 ,1 ]. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for SF networks with γ and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors.
Jacob, Rinku; Misra, R.
2017-01-01
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all types of network topology with ease and increases with the diversity of node degrees in the network. The measure is applied to compute the heterogeneity of synthetic (both random and scale free (SF)) and real-world networks with its value normalized in the interval [0,1]. To define the measure, we introduce a limiting network whose heterogeneity can be expressed analytically with the value tending to 1 as the size of the network N tends to infinity. We numerically study the variation of heterogeneity for random graphs (as a function of p and N) and for SF networks with γ and N as variables. Finally, as a specific application, we show that the proposed measure can be used to compare the heterogeneity of recurrence networks constructed from the time series of several low-dimensional chaotic attractors, thereby providing a single index to compare the structural complexity of chaotic attractors. PMID:28280579
Offdiagonal complexity: A computationally quick complexity measure for graphs and networks
NASA Astrophysics Data System (ADS)
Claussen, Jens Christian
2007-02-01
A vast variety of biological, social, and economical networks shows topologies drastically differing from random graphs; yet the quantitative characterization remains unsatisfactory from a conceptual point of view. Motivated from the discussion of small scale-free networks, a biased link distribution entropy is defined, which takes an extremum for a power-law distribution. This approach is extended to the node-node link cross-distribution, whose nondiagonal elements characterize the graph structure beyond link distribution, cluster coefficient and average path length. From here a simple (and computationally cheap) complexity measure can be defined. This offdiagonal complexity (OdC) is proposed as a novel measure to characterize the complexity of an undirected graph, or network. While both for regular lattices and fully connected networks OdC is zero, it takes a moderately low value for a random graph and shows high values for apparently complex structures as scale-free networks and hierarchical trees. The OdC approach is applied to the Helicobacter pylori protein interaction network and randomly rewired surrogates.
Measuring the significance of community structure in complex networks
NASA Astrophysics Data System (ADS)
Hu, Yanqing; Nie, Yuchao; Yang, Hua; Cheng, Jie; Fan, Ying; di, Zengru
2010-12-01
Many complex systems can be represented as networks, and separating a network into communities could simplify functional analysis considerably. Many approaches have recently been proposed to detect communities, but a method to determine whether the detected communities are significant is still lacking. In this paper, an index to evaluate the significance of communities in networks is proposed based on perturbation of the network. In contrast to previous approaches, the network is disturbed gradually, and the index is defined by integrating all of the similarities between the community structures before and after perturbation. Moreover, by taking the null model into account, the index eliminates scale effects. Thus, it can evaluate and compare the significance of communities in different networks. The method has been tested in many artificial and real-world networks. The results show that the index is in fact independent of the size of the network and the number of communities. With this approach, clear communities are found to always exist in social networks, but significant communities cannot be found in protein interactions and metabolic networks.
Multi-attribute integrated measurement of node importance in complex networks
NASA Astrophysics Data System (ADS)
Wang, Shibo; Zhao, Jinlou
2015-11-01
The measure of node importance in complex networks is very important to the research of networks stability and robustness; it also can ensure the security of the whole network. Most researchers have used a single indicator to measure the networks node importance, so that the obtained measurement results only reflect certain aspects of the networks with a loss of information. Meanwhile, because of the difference of networks topology, the nodes' importance should be described by combining the character of the networks topology. Most of the existing evaluation algorithms cannot completely reflect the circumstances of complex networks, so this paper takes into account the degree of centrality, the relative closeness centrality, clustering coefficient, and topology potential and raises an integrated measuring method to measure the nodes' importance. This method can reflect nodes' internal and outside attributes and eliminate the influence of network structure on the node importance. The experiments of karate network and dolphin network show that networks topology structure integrated measure has smaller range of metrical result than a single indicator and more universal. Experiments show that attacking the North American power grid and the Internet network with the method has a faster convergence speed than other methods.
An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks
Cabessa, Jérémie; Villa, Alessandro E. P.
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits. PMID:24727866
An attractor-based complexity measurement for Boolean recurrent neural networks.
Cabessa, Jérémie; Villa, Alessandro E P
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then translating the most refined classification of ω-automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits.
FALCON or how to compute measures time efficiently on dynamically evolving dense complex networks?
Franke, R; Ivanova, G
2014-02-01
A large number of topics in biology, medicine, neuroscience, psychology and sociology can be generally described via complex networks in order to investigate fundamental questions of structure, connectivity, information exchange and causality. Especially, research on biological networks like functional spatiotemporal brain activations and changes, caused by neuropsychiatric pathologies, is promising. Analyzing those so-called complex networks, the calculation of meaningful measures can be very long-winded depending on their size and structure. Even worse, in many labs only standard desktop computers are accessible to perform those calculations. Numerous investigations on complex networks regard huge but sparsely connected network structures, where most network nodes are connected to only a few others. Currently, there are several libraries available to tackle this kind of networks. A problem arises when not only a few big and sparse networks have to be analyzed, but hundreds or thousands of smaller and conceivably dense networks (e.g. in measuring brain activation over time). Then every minute per network is crucial. For these cases there several possibilities to use standard hardware more efficiently. It is not sufficient to apply just standard algorithms for dense graph characteristics. This article introduces the new library FALCON developed especially for the exploration of dense complex networks. Currently, it offers 12 different measures (like clustering coefficients), each for undirected-unweighted, undirected-weighted and directed-unweighted networks. It uses a multi-core approach in combination with comprehensive code and hardware optimizations. There is an alternative massively parallel GPU implementation for the most time-consuming measures, too. Finally, a comparing benchmark is integrated to support the choice of the most suitable library for a particular network issue. Copyright © 2013 Elsevier Inc. All rights reserved.
McDonough, Ian M.; Nashiro, Kaoru
2014-01-01
An emerging field of research focused on fluctuations in brain signals has provided evidence that the complexity of those signals, as measured by entropy, conveys important information about network dynamics (e.g., local and distributed processing). While much research has focused on how neural complexity differs in populations with different age groups or clinical disorders, substantially less research has focused on the basic understanding of neural complexity in populations with young and healthy brain states. The present study used resting-state fMRI data from the Human Connectome Project (Van Essen et al., 2013) to test the extent that neural complexity in the BOLD signal, as measured by multiscale entropy (1) would differ from random noise, (2) would differ between four major resting-state networks previously associated with higher-order cognition, and (3) would be associated with the strength and extent of functional connectivity—a complementary method of estimating information processing. We found that complexity in the BOLD signal exhibited different patterns of complexity from white, pink, and red noise and that neural complexity was differentially expressed between resting-state networks, including the default mode, cingulo-opercular, left and right frontoparietal networks. Lastly, neural complexity across all networks was negatively associated with functional connectivity at fine scales, but was positively associated with functional connectivity at coarse scales. The present study is the first to characterize neural complexity in BOLD signals at a high temporal resolution and across different networks and might help clarify the inconsistencies between neural complexity and functional connectivity, thus informing the mechanisms underlying neural complexity. PMID:24959130
Directed clustering coefficient as a measure of systemic risk in complex banking networks
NASA Astrophysics Data System (ADS)
Tabak, Benjamin M.; Takami, Marcelo; Rocha, Jadson M. C.; Cajueiro, Daniel O.; Souza, Sergio R. S.
2014-01-01
Recent literature has focused on the study of systemic risk in complex networks. It is clear now, after the crisis of 2008, that the aggregate behavior of the interaction among agents is not straightforward and it is very difficult to predict. Contributing to this debate, this paper shows that the directed clustering coefficient may be used as a measure of systemic risk in complex networks. Furthermore, using data from the Brazilian interbank network, we show that the directed clustering coefficient is negatively correlated with domestic interest rates.
Local Difference Measures between Complex Networks for Dynamical System Model Evaluation
Lange, Stefan; Donges, Jonathan F.; Volkholz, Jan; Kurths, Jürgen
2015-01-01
A faithful modeling of real-world dynamical systems necessitates model evaluation. A recent promising methodological approach to this problem has been based on complex networks, which in turn have proven useful for the characterization of dynamical systems. In this context, we introduce three local network difference measures and demonstrate their capabilities in the field of climate modeling, where these measures facilitate a spatially explicit model evaluation. Building on a recent study by Feldhoff et al. [1] we comparatively analyze statistical and dynamical regional climate simulations of the South American monsoon system. Three types of climate networks representing different aspects of rainfall dynamics are constructed from the modeled precipitation space-time series. Specifically, we define simple graphs based on positive as well as negative rank correlations between rainfall anomaly time series at different locations, and such based on spatial synchronizations of extreme rain events. An evaluation against respective networks built from daily satellite data provided by the Tropical Rainfall Measuring Mission 3B42 V7 reveals far greater differences in model performance between network types for a fixed but arbitrary climate model than between climate models for a fixed but arbitrary network type. We identify two sources of uncertainty in this respect. Firstly, climate variability limits fidelity, particularly in the case of the extreme event network; and secondly, larger geographical link lengths render link misplacements more likely, most notably in the case of the anticorrelation network; both contributions are quantified using suitable ensembles of surrogate networks. Our model evaluation approach is applicable to any multidimensional dynamical system and especially our simple graph difference measures are highly versatile as the graphs to be compared may be constructed in whatever way required. Generalizations to directed as well as edge- and node
Correlation dimension of complex networks.
Lacasa, Lucas; Gómez-Gardeñes, Jesús
2013-04-19
We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synthetic networks and real-world networks such as the world air-transportation network or urban networks, and provides a computationally fast way for estimating the dimensionality of networks which only relies on the local information provided by the walkers.
Zhou, Renjie; Yang, Chen; Wan, Jian; Zhang, Wei; Guan, Bo; Xiong, Naixue
2017-01-01
Measurement of time series complexity and predictability is sometimes the cornerstone for proposing solutions to topology and congestion control problems in sensor networks. As a method of measuring time series complexity and predictability, multiscale entropy (MSE) has been widely applied in many fields. However, sample entropy, which is the fundamental component of MSE, measures the similarity of two subsequences of a time series with either zero or one, but without in-between values, which causes sudden changes of entropy values even if the time series embraces small changes. This problem becomes especially severe when the length of time series is getting short. For solving such the problem, we propose flexible multiscale entropy (FMSE), which introduces a novel similarity function measuring the similarity of two subsequences with full-range values from zero to one, and thus increases the reliability and stability of measuring time series complexity. The proposed method is evaluated on both synthetic and real time series, including white noise, 1/f noise and real vibration signals. The evaluation results demonstrate that FMSE has a significant improvement in reliability and stability of measuring complexity of time series, especially when the length of time series is short, compared to MSE and composite multiscale entropy (CMSE). The proposed method FMSE is capable of improving the performance of time series analysis based topology and traffic congestion control techniques. PMID:28383496
Zhou, Renjie; Yang, Chen; Wan, Jian; Zhang, Wei; Guan, Bo; Xiong, Naixue
2017-04-06
Measurement of time series complexity and predictability is sometimes the cornerstone for proposing solutions to topology and congestion control problems in sensor networks. As a method of measuring time series complexity and predictability, multiscale entropy (MSE) has been widely applied in many fields. However, sample entropy, which is the fundamental component of MSE, measures the similarity of two subsequences of a time series with either zero or one, but without in-between values, which causes sudden changes of entropy values even if the time series embraces small changes. This problem becomes especially severe when the length of time series is getting short. For solving such the problem, we propose flexible multiscale entropy (FMSE), which introduces a novel similarity function measuring the similarity of two subsequences with full-range values from zero to one, and thus increases the reliability and stability of measuring time series complexity. The proposed method is evaluated on both synthetic and real time series, including white noise, 1/f noise and real vibration signals. The evaluation results demonstrate that FMSE has a significant improvement in reliability and stability of measuring complexity of time series, especially when the length of time series is short, compared to MSE and composite multiscale entropy (CMSE). The proposed method FMSE is capable of improving the performance of time series analysis based topology and traffic congestion control techniques.
Eigencentrality based on dissimilarity measures reveals central nodes in complex networks.
Alvarez-Socorro, A J; Herrera-Almarza, G C; González-Díaz, L A
2015-11-25
One of the most important problems in complex network's theory is the location of the entities that are essential or have a main role within the network. For this purpose, the use of dissimilarity measures (specific to theory of classification and data mining) to enrich the centrality measures in complex networks is proposed. The centrality method used is the eigencentrality which is based on the heuristic that the centrality of a node depends on how central are the nodes in the immediate neighbourhood (like rich get richer phenomenon). This can be described by an eigenvalues problem, however the information of the neighbourhood and the connections between neighbours is not taken in account, neglecting their relevance when is one evaluates the centrality/importance/influence of a node. The contribution calculated by the dissimilarity measure is parameter independent, making the proposed method is also parameter independent. Finally, we perform a comparative study of our method versus other methods reported in the literature, obtaining more accurate and less expensive computational results in most cases.
Growing complex network of citations of scientific papers: Modeling and measurements.
Golosovsky, Michael; Solomon, Sorin
2017-01-01
We consider the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on the copying-redirection-triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such validation is performed by measuring citation dynamics of physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including nonstationary citation distributions, diverging citation trajectories of similar papers, runaways or "immortal papers" with infinite citation lifetime, etc. Thus nonlinearity in complex network growth is our most important finding. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.
Growing complex network of citations of scientific papers: Modeling and measurements
NASA Astrophysics Data System (ADS)
Golosovsky, Michael; Solomon, Sorin
2017-01-01
We consider the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on the copying-redirection-triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such validation is performed by measuring citation dynamics of physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including nonstationary citation distributions, diverging citation trajectories of similar papers, runaways or "immortal papers" with infinite citation lifetime, etc. Thus nonlinearity in complex network growth is our most important finding. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.
Eigencentrality based on dissimilarity measures reveals central nodes in complex networks
NASA Astrophysics Data System (ADS)
Alvarez-Socorro, A. J.; Herrera-Almarza, G. C.; González-Díaz, L. A.
2015-11-01
One of the most important problems in complex network’s theory is the location of the entities that are essential or have a main role within the network. For this purpose, the use of dissimilarity measures (specific to theory of classification and data mining) to enrich the centrality measures in complex networks is proposed. The centrality method used is the eigencentrality which is based on the heuristic that the centrality of a node depends on how central are the nodes in the immediate neighbourhood (like rich get richer phenomenon). This can be described by an eigenvalues problem, however the information of the neighbourhood and the connections between neighbours is not taken in account, neglecting their relevance when is one evaluates the centrality/importance/influence of a node. The contribution calculated by the dissimilarity measure is parameter independent, making the proposed method is also parameter independent. Finally, we perform a comparative study of our method versus other methods reported in the literature, obtaining more accurate and less expensive computational results in most cases.
Eigencentrality based on dissimilarity measures reveals central nodes in complex networks
Alvarez-Socorro, A. J.; Herrera-Almarza, G. C.; González-Díaz, L. A.
2015-01-01
One of the most important problems in complex network’s theory is the location of the entities that are essential or have a main role within the network. For this purpose, the use of dissimilarity measures (specific to theory of classification and data mining) to enrich the centrality measures in complex networks is proposed. The centrality method used is the eigencentrality which is based on the heuristic that the centrality of a node depends on how central are the nodes in the immediate neighbourhood (like rich get richer phenomenon). This can be described by an eigenvalues problem, however the information of the neighbourhood and the connections between neighbours is not taken in account, neglecting their relevance when is one evaluates the centrality/importance/influence of a node. The contribution calculated by the dissimilarity measure is parameter independent, making the proposed method is also parameter independent. Finally, we perform a comparative study of our method versus other methods reported in the literature, obtaining more accurate and less expensive computational results in most cases. PMID:26603652
Measuring complex behaviors of local oscillatory networks in deep brain local field potentials.
Huang, Yongzhi; Geng, Xinyi; Li, Luming; Stein, John F; Aziz, Tipu Z; Green, Alexander L; Wang, Shouyan
2016-05-01
Multiple oscillations emerging from the same neuronal substrate serve to construct a local oscillatory network. The network usually exhibits complex behaviors of rhythmic, balancing and coupling between the oscillations, and the quantification of these behaviors would provide valuable insight into organization of the local network related to brain states. An integrated approach to quantify rhythmic, balancing and coupling neural behaviors based upon power spectral analysis, power ratio analysis and cross-frequency power coupling analysis was presented. Deep brain local field potentials (LFPs) were recorded from the thalamus of patients with neuropathic pain and dystonic tremor. t-Test was applied to assess the difference between the two patient groups. The rhythmic behavior measured by power spectral analysis showed significant power spectrum difference in the high beta band between the two patient groups. The balancing behavior measured by power ratio analysis showed significant power ratio differences at high beta band to 8-20 Hz, and 30-40 Hz to high beta band between the patient groups. The coupling behavior measured by cross-frequency power coupling analysis showed power coupling differences at (theta band, high beta band) and (45-55 Hz, 70-80 Hz) between the patient groups. The study provides a strategy for studying the brain states in a multi-dimensional behavior space and a framework to screen quantitative characteristics for biomarkers related to diseases or nuclei. The work provides a comprehensive approach for understanding the complex behaviors of deep brain LFPs and identifying quantitative biomarkers for brain states related to diseases or nuclei. Copyright © 2016 Elsevier B.V. All rights reserved.
Towards a methodology for validation of centrality measures in complex networks.
Batool, Komal; Niazi, Muaz A
2014-01-01
Living systems are associated with Social networks - networks made up of nodes, some of which may be more important in various aspects as compared to others. While different quantitative measures labeled as "centralities" have previously been used in the network analysis community to find out influential nodes in a network, it is debatable how valid the centrality measures actually are. In other words, the research question that remains unanswered is: how exactly do these measures perform in the real world? So, as an example, if a centrality of a particular node identifies it to be important, is the node actually important? The goal of this paper is not just to perform a traditional social network analysis but rather to evaluate different centrality measures by conducting an empirical study analyzing exactly how do network centralities correlate with data from published multidisciplinary network data sets. We take standard published network data sets while using a random network to establish a baseline. These data sets included the Zachary's Karate Club network, dolphin social network and a neural network of nematode Caenorhabditis elegans. Each of the data sets was analyzed in terms of different centrality measures and compared with existing knowledge from associated published articles to review the role of each centrality measure in the determination of influential nodes. Our empirical analysis demonstrates that in the chosen network data sets, nodes which had a high Closeness Centrality also had a high Eccentricity Centrality. Likewise high Degree Centrality also correlated closely with a high Eigenvector Centrality. Whereas Betweenness Centrality varied according to network topology and did not demonstrate any noticeable pattern. In terms of identification of key nodes, we discovered that as compared with other centrality measures, Eigenvector and Eccentricity Centralities were better able to identify important nodes.
Towards a Methodology for Validation of Centrality Measures in Complex Networks
2014-01-01
Background Living systems are associated with Social networks — networks made up of nodes, some of which may be more important in various aspects as compared to others. While different quantitative measures labeled as “centralities” have previously been used in the network analysis community to find out influential nodes in a network, it is debatable how valid the centrality measures actually are. In other words, the research question that remains unanswered is: how exactly do these measures perform in the real world? So, as an example, if a centrality of a particular node identifies it to be important, is the node actually important? Purpose The goal of this paper is not just to perform a traditional social network analysis but rather to evaluate different centrality measures by conducting an empirical study analyzing exactly how do network centralities correlate with data from published multidisciplinary network data sets. Method We take standard published network data sets while using a random network to establish a baseline. These data sets included the Zachary's Karate Club network, dolphin social network and a neural network of nematode Caenorhabditis elegans. Each of the data sets was analyzed in terms of different centrality measures and compared with existing knowledge from associated published articles to review the role of each centrality measure in the determination of influential nodes. Results Our empirical analysis demonstrates that in the chosen network data sets, nodes which had a high Closeness Centrality also had a high Eccentricity Centrality. Likewise high Degree Centrality also correlated closely with a high Eigenvector Centrality. Whereas Betweenness Centrality varied according to network topology and did not demonstrate any noticeable pattern. In terms of identification of key nodes, we discovered that as compared with other centrality measures, Eigenvector and Eccentricity Centralities were better able to identify important nodes
NASA Astrophysics Data System (ADS)
Walker, David N.; Fernsler, Richard F.; Blackwell, David D.; Amatucci, William E.
2008-11-01
In earlier work, using a network analyzer, we have shown the existence of collisionless resistance (CR) in the sheath of a spherical probe when driven by a small rf signal. As shown in that paper the CR depends on the plasma density gradient at a given location. Because of this there is a cutoff in the CR which is proportional to the applied bias level and which will occur at the plasma frequency at the surface of the probe, r = r0. We show that, in the frequency regime φpi<<φ<<φpe(r0), the complex impedance measurements made with a network analyzer can be used to determine electron temperature. We present an overview of the theory used along with comparisons to data sets made using three small spherical probes of different sizes. The numerical algorithm requires only a solution of the Poisson equation to determine the approximate sheath dimensions and integrals to determine approximate plasma and sheath inductances. We compare the results of the temperature measurements to those made by conventional Langmuir probe sweeps. Walker, D.N., R.F. Fernsler, D.D. Blackwell, W.E. Amatucci, S.J. Messer, Phys of Plasmas, 13, 032108 (2006)
Measuring microscopic evolution processes of complex networks based on empirical data
NASA Astrophysics Data System (ADS)
Chi, Liping
2015-04-01
Aiming at understanding the microscopic mechanism of complex systems in real world, we perform the measurement that characterizes the evolution properties on two empirical data sets. In the Autonomous Systems Internet data, the network size keeps growing although the system suffers a high rate of node deletion (r = 0.4) and link deletion (q = 0.81). However, the average degree keeps almost unchanged during the whole time range. At each time step the external links attached to a new node are about c = 1.1 and the internal links added between existing nodes are approximately m = 8. For the Scientific Collaboration data, it is a cumulated result of all the authors from 1893 up to the considered year. There is no deletion of nodes and links, r = q = 0. The external and internal links at each time step are c = 1.04 and m = 0, correspondingly. The exponents of degree distribution p(k) ∼ k-γ of these two empirical datasets γdata are in good agreement with that obtained theoretically γtheory. The results indicate that these evolution quantities may provide an insight into capturing the microscopic dynamical processes that govern the network topology.
Forman curvature for complex networks
NASA Astrophysics Data System (ADS)
Sreejith, R. P.; Mohanraj, Karthikeyan; Jost, Jürgen; Saucan, Emil; Samal, Areejit
2016-06-01
We adapt Forman’s discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.
Emergent Complex Network Geometry
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems. PMID:25985280
NASA Astrophysics Data System (ADS)
Walker, D. N.; Fernsler, R. F.; Blackwell, D. D.; Amatucci, W. E.
2008-12-01
In earlier work, using a network analyzer, it was shown that collisionless resistance (CR) exists in the sheath of a spherical probe when driven by a small rf signal. The CR is inversely proportional to the plasma density gradient at the location where the applied angular frequency equals the plasma frequency ωpe. Recently, efforts have concentrated on a study of the low-to-intermediate frequency response of the probe to the rf signal. At sufficiently low frequencies, the CR is beyond cutoff, i.e., below the plasma frequency at the surface of the probe. Since the electron density at the probe surface decreases as a function of applied (negative) bias, the CR will extend to lower frequencies as the magnitude of negative bias increases. Therefore to eliminate both CR and ion current contributions, the frequencies presently being considered are much greater than the ion plasma frequency, ωpi, but less than the plasma frequency, ωpe(r0), where r0 is the probe radius. It is shown that, in this frequency regime, the complex impedance measurements made with a network analyzer can be used to determine electron temperature. An overview of the theory is presented along with comparisons to data sets made using three stainless steel spherical probes of different sizes in different experimental environments and different plasma parameter regimes. The temperature measurements made by this method are compared to those made by conventional Langmuir probe sweeps; the method shown here requires no curve fitting as is the usual procedure with Langmuir probes when a Maxwell-Boltzmann electron distribution is assumed. The new method requires, however, a solution of the Poisson equation to determine the approximate sheath dimensions and integrals to determine approximate plasma and sheath inductances. The solution relies on the calculation of impedance for a spherical probe immersed in a collisionless plasma and is based on a simple circuit analogy for the plasma. Finally, the
Gong, Weiqiang; Liang, Jinling; Cao, Jinde
2015-10-01
In this paper, based on the matrix measure method and the Halanay inequality, global exponential stability problem is investigated for the complex-valued recurrent neural networks with time-varying delays. Without constructing any Lyapunov functions, several sufficient criteria are obtained to ascertain the global exponential stability of the addressed complex-valued neural networks under different activation functions. Here, the activation functions are no longer assumed to be derivative which is always demanded in relating references. In addition, the obtained results are easy to be verified and implemented in practice. Finally, two examples are given to illustrate the effectiveness of the obtained results.
Complexity measures of the central respiratory networks during wakefulness and sleep
NASA Astrophysics Data System (ADS)
Dragomir, Andrei; Akay, Yasemin; Curran, Aidan K.; Akay, Metin
2008-06-01
Since sleep is known to influence respiratory activity we studied whether the sleep state would affect the complexity value of the respiratory network output. Specifically, we tested the hypothesis that the complexity values of the diaphragm EMG (EMGdia) activity would be lower during REM compared to NREM. Furthermore, since REM is primarily generated by a homogeneous population of neurons in the medulla, the possibility that REM-related respiratory output would be less complex than that of the awake state was also considered. Additionally, in order to examine the influence of neuron vulnerabilities within the rostral ventral medulla (RVM) on the complexity of the respiratory network output, we inhibited respiratory neurons in the RVM by microdialysis of GABAA receptor agonist muscimol. Diaphragm EMG, nuchal EMG, EEG, EOG as well as other physiological signals (tracheal pressure, blood pressure and respiratory volume) were recorded from five unanesthetized chronically instrumented intact piglets (3-10 days old). Complexity of the diaphragm EMG (EMGdia) signal during wakefulness, NREM and REM was evaluated using the approximate entropy method (ApEn). ApEn values of the EMGdia during NREM and REM sleep were found significantly (p < 0.05 and p < 0.001, respectively) lower than those of awake EMGdia after muscimol inhibition. In the absence of muscimol, only the differences between REM and wakefulness ApEn values were found to be significantly different.
Combining Classification with fMRI-Derived Complex Network Measures for Potential Neurodiagnostics
Rubin, Denis; Edelman, Shimon; Malach, Rafael; Mujica-Parodi, Lilianne R.
2013-01-01
Complex network analysis (CNA), a subset of graph theory, is an emerging approach to the analysis of functional connectivity in the brain, allowing quantitative assessment of network properties such as functional segregation, integration, resilience, and centrality. Here, we show how a classification framework complements complex network analysis by providing an efficient and objective means of selecting the best network model characterizing given functional connectivity data. We describe a novel kernel-sum learning approach, block diagonal optimization (BDopt), which can be applied to CNA features to single out graph-theoretic characteristics and/or anatomical regions of interest underlying discrimination, while mitigating problems of multiple comparisons. As a proof of concept for the method’s applicability to future neurodiagnostics, we apply BDopt classification to two resting state fMRI data sets: a trait (between-subjects) classification of patients with schizophrenia vs. controls, and a state (within-subjects) classification of wake vs. sleep, demonstrating powerful discriminant accuracy for the proposed framework. PMID:23671641
Organization of complex networks
NASA Astrophysics Data System (ADS)
Kitsak, Maksim
Many large complex systems can be successfully analyzed using the language of graphs and networks. Interactions between the objects in a network are treated as links connecting nodes. This approach to understanding the structure of networks is an important step toward understanding the way corresponding complex systems function. Using the tools of statistical physics, we analyze the structure of networks as they are found in complex systems such as the Internet, the World Wide Web, and numerous industrial and social networks. In the first chapter we apply the concept of self-similarity to the study of transport properties in complex networks. Self-similar or fractal networks, unlike non-fractal networks, exhibit similarity on a range of scales. We find that these fractal networks have transport properties that differ from those of non-fractal networks. In non-fractal networks, transport flows primarily through the hubs. In fractal networks, the self-similar structure requires any transport to also flow through nodes that have only a few connections. We also study, in models and in real networks, the crossover from fractal to non-fractal networks that occurs when a small number of random interactions are added by means of scaling techniques. In the second chapter we use k-core techniques to study dynamic processes in networks. The k-core of a network is the network's largest component that, within itself, exhibits all nodes with at least k connections. We use this k-core analysis to estimate the relative leadership positions of firms in the Life Science (LS) and Information and Communication Technology (ICT) sectors of industry. We study the differences in the k-core structure between the LS and the ICT sectors. We find that the lead segment (highest k-core) of the LS sector, unlike that of the ICT sector, is remarkably stable over time: once a particular firm enters the lead segment, it is likely to remain there for many years. In the third chapter we study how
Immunization of complex networks
NASA Astrophysics Data System (ADS)
Pastor-Satorras, Romualdo; Vespignani, Alessandro
2002-03-01
Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity provides an ideal environment for the spreading of infective agents. Here we show that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. The absence of any critical immunization threshold is due to the unbounded connectivity fluctuations of scale-free networks. Successful immunization strategies can be developed only by taking into account the inhomogeneous connectivity properties of scale-free networks. In particular, targeted immunization schemes, based on the nodes' connectivity hierarchy, sharply lower the network's vulnerability to epidemic attacks.
Oscillations of complex networks
NASA Astrophysics Data System (ADS)
Wang, Xingang; Lai, Ying-Cheng; Lai, Choy Heng
2006-12-01
A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such quantities respond to sudden changes caused by attacks or disturbances in recoverable networks, i.e., functions of the affected nodes are only temporarily disabled or partially limited. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to oscillate persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.
Hyperbolic geometry of complex networks.
Krioukov, Dmitri; Papadopoulos, Fragkiskos; Kitsak, Maksim; Vahdat, Amin; Boguñá, Marián
2010-09-01
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.
NASA Astrophysics Data System (ADS)
Gao, Zhong-Ke; Dang, Wei-Dong; Xue, Le; Zhang, Shan-Shan
2017-03-01
Characterizing the flow structure underlying the evolution of oil-in-water bubbly flow remains a contemporary challenge of great interests and complexity. In particular, the oil droplets dispersing in a water continuum with diverse size make the study of oil-in-water bubbly flow really difficult. To study this issue, we first design a novel complex impedance sensor and systematically conduct vertical oil-water flow experiments. Based on the multivariate complex impedance measurements, we define modalities associated with the spatial transient flow structures and construct modality transition-based network for each flow condition to study the evolution of flow structures. In order to reveal the unique flow structures underlying the oil-in-water bubbly flow, we filter the inferred modality transition-based network by removing the edges with small weight and resulting isolated nodes. Then, the weighted clustering coefficient entropy and weighted average path length are employed for quantitatively assessing the original network and filtered network. The differences in network measures enable to efficiently characterize the evolution of the oil-in-water bubbly flow structures.
Multiscale vulnerability of complex networks.
Boccaletti, Stefano; Buldú, Javier; Criado, Regino; Flores, Julio; Latora, Vito; Pello, Javier; Romance, Miguel
2007-12-01
We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links' betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined.
The Solar Flare Complex Network
NASA Astrophysics Data System (ADS)
Gheibi, Akbar; Safari, Hossein; Javaherian, Mohsen
2017-10-01
We investigate the characteristics of the solar flare complex network. The limited predictability, nonlinearity, and self-organized criticality of the flares allow us to study systems of flares in the field of the complex systems. Both the occurrence time and the location of flares detected from 2006 January 1 to 2016 July 21 are used to design the growing flares network. The solar surface is divided into cells with equal areas. The cells, which include flares, are considered nodes of the network. The related links are equivalent to sympathetic flaring. The extracted features demonstrate that the network of flares follows quantitative measures of complexity. The power-law nature of the connectivity distribution with a degree exponent greater than three reveals that flares form a scale-free and small-world network. A large value for the clustering coefficient, a small characteristic path length, and a slow change of the diameter are all characteristics of the flares network. We show that the degree correlation of the flares network has the characteristics of a disassortative network. About 11% of the large energetic flares (M and X types in GOES classification) that occurred in the network hubs cover 3% of the solar surface.
Compressively sensed complex networks.
Dunlavy, Daniel M.; Ray, Jaideep; Pinar, Ali
2010-07-01
The aim of this project is to develop low dimension parametric (deterministic) models of complex networks, to use compressive sensing (CS) and multiscale analysis to do so and to exploit the structure of complex networks (some are self-similar under coarsening). CS provides a new way of sampling and reconstructing networks. The approach is based on multiresolution decomposition of the adjacency matrix and its efficient sampling. It requires preprocessing of the adjacency matrix to make it 'blocky' which is the biggest (combinatorial) algorithm challenge. Current CS reconstruction algorithm makes no use of the structure of a graph, its very general (and so not very efficient/customized). Other model-based CS techniques exist, but not yet adapted to networks. Obvious starting point for future work is to increase the efficiency of reconstruction.
Synchronization in complex networks
Arenas, A.; Diaz-Guilera, A.; Moreno, Y.; Zhou, C.; Kurths, J.
2007-12-12
Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization phenomena in natural systems take now advantage of the recent theory of complex networks. In this review, we report the advances in the comprehension of synchronization phenomena when oscillating elements are constrained to interact in a complex network topology. We also overview the new emergent features coming out from the interplay between the structure and the function of the underlying pattern of connections. Extensive numerical work as well as analytical approaches to the problem are presented. Finally, we review several applications of synchronization in complex networks to different disciplines: biological systems and neuroscience, engineering and computer science, and economy and social sciences.
NASA Astrophysics Data System (ADS)
Teixeira, G. M.; Aguiar, M. S. F.; Carvalho, C. F.; Dantas, D. R.; Cunha, M. V.; Morais, J. H. M.; Pereira, H. B. B.; Miranda, J. G. V.
Verbal language is a dynamic mental process. Ideas emerge by means of the selection of words from subjective and individual characteristics throughout the oral discourse. The goal of this work is to characterize the complex network of word associations that emerge from an oral discourse from a discourse topic. Because of that, concepts of associative incidence and fidelity have been elaborated and represented the probability of occurrence of pairs of words in the same sentence in the whole oral discourse. Semantic network of words associations were constructed, where the words are represented as nodes and the edges are created when the incidence-fidelity index between pairs of words exceeds a numerical limit (0.001). Twelve oral discourses were studied. The networks generated from these oral discourses present a typical behavior of complex networks and their indices were calculated and their topologies characterized. The indices of these networks obtained from each incidence-fidelity limit exhibit a critical value in which the semantic network has maximum conceptual information and minimum residual associations. Semantic networks generated by this incidence-fidelity limit depict a pattern of hierarchical classes that represent the different contexts used in the oral discourse.
Benford's Distribution in Complex Networks.
Morzy, Mikołaj; Kajdanowicz, Tomasz; Szymański, Bolesław K
2016-10-17
Many collections of numbers do not have a uniform distribution of the leading digit, but conform to a very particular pattern known as Benford's distribution. This distribution has been found in numerous areas such as accounting data, voting registers, census data, and even in natural phenomena. Recently it has been reported that Benford's law applies to online social networks. Here we introduce a set of rigorous tests for adherence to Benford's law and apply it to verification of this claim, extending the scope of the experiment to various complex networks and to artificial networks created by several popular generative models. Our findings are that neither for real nor for artificial networks there is sufficient evidence for common conformity of network structural properties with Benford's distribution. We find very weak evidence suggesting that three measures, degree centrality, betweenness centrality and local clustering coefficient, could adhere to Benford's law for scalefree networks but only for very narrow range of their parameters.
Northey, G W; Oliver, M L; Rittenhouse, D M
2006-01-01
Biomechanics studies often require the analysis of position and orientation. Although a variety of transducer and camera systems can be utilized, a common inexpensive alternative is the Hall effect sensor. Hall effect sensors have been used extensively for one-dimensional position analysis but their non-linear behavior and cross-talk effects make them difficult to calibrate for effective and accurate two- and three-dimensional position and orientation analysis. The aim of this study was to develop and calibrate a displacement measurement system for a hydraulic-actuation joystick used for repetitive motion analysis of heavy equipment operators. The system utilizes an array of four Hall effect sensors that are all active during any joystick movement. This built-in redundancy allows the calibration to utilize fully connected feed forward neural networks in conjunction with a Microscribe 3D digitizer. A fully connected feed forward neural network with one hidden layer containing five neurons was developed. Results indicate that the ability of the neural network to accurately predict the x, y and z coordinates of the joystick handle was good with r(2) values of 0.98 and higher. The calibration technique was found to be equally as accurate when used on data collected 5 days after the initial calibration, indicating the system is robust and stable enough to not require calibration every time the joystick is used. This calibration system allowed an infinite number of joystick orientations and positions to be found within the range of joystick motion.
Accessibility in complex networks
NASA Astrophysics Data System (ADS)
Travençolo, B. A. N.; da F. Costa, L.
2008-12-01
This Letter describes a method for the quantification of the diversity of non-linear dynamics in complex networks as a consequence of self-avoiding random walks. The methodology is analyzed in the context of theoretical models and illustrated with respect to the characterization of the accessibility in urban streets.
Reactive immunization on complex networks
NASA Astrophysics Data System (ADS)
Alfinito, Eleonora; Beccaria, Matteo; Fachechi, Alberto; Macorini, Guido
2017-01-01
Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent of the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks.
Articulation points in complex networks
NASA Astrophysics Data System (ADS)
Tian, Liang; Bashan, Amir; Shi, Da-Ning; Liu, Yang-Yu
2017-01-01
An articulation point in a network is a node whose removal disconnects the network. Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. Here we develop analytical tools to study key issues pertinent to articulation points, such as the expected number of them and the network vulnerability against their removal, in an arbitrary complex network. We find that a greedy articulation point removal process provides us a different perspective on the organizational principles of complex networks. Moreover, this process results in a rich phase diagram with two fundamentally different types of percolation transitions. Our results shed light on the design of more resilient infrastructure networks and the effective destruction of terrorist communication networks.
Articulation points in complex networks
Tian, Liang; Bashan, Amir; Shi, Da-Ning; Liu, Yang-Yu
2017-01-01
An articulation point in a network is a node whose removal disconnects the network. Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. Here we develop analytical tools to study key issues pertinent to articulation points, such as the expected number of them and the network vulnerability against their removal, in an arbitrary complex network. We find that a greedy articulation point removal process provides us a different perspective on the organizational principles of complex networks. Moreover, this process results in a rich phase diagram with two fundamentally different types of percolation transitions. Our results shed light on the design of more resilient infrastructure networks and the effective destruction of terrorist communication networks. PMID:28139697
Target recovery in complex networks
NASA Astrophysics Data System (ADS)
Sun, Weiman; Zeng, An
2017-01-01
The invulnerability of complex networks is an important issue which has been widely analyzed in different fields. A lot of works have been done to measure and improve the stability of complex networks when being attacked. Recently, how to recover networks after attack was intensively studied. The existing methods are mainly designed to recover the overall functionality of networks, yet in many real cases the recovery of important nodes should be given priority, to which we refer target recovery. For example, when the cold wave paralyses the railway networks, target recovery means to repair those stations or railways such that the transport capacity of densely-populated cities can be recovered as fast as possible. In this paper, we first compare the impact of attacks on the whole network and target nodes respectively, and then study the efficiency of traditional recovery methods that are proposed based on global centrality metrics. Furthermore, based on target centrality metrics, we introduce a local betweenness recovery method and we find it has better performance than the traditional methods. We finally propose a hybrid recovery method which includes local betweenness metric and local closeness metric. The performance of the hybrid method is shown to be similar to that of the greedy algorithm.
Physical controllability of complex networks
Wang, Le-Zhi; Chen, Yu-Zhong; Wang, Wen-Xu; Lai, Ying-Cheng
2017-01-01
A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control. PMID:28074900
Physical controllability of complex networks
NASA Astrophysics Data System (ADS)
Wang, Le-Zhi; Chen, Yu-Zhong; Wang, Wen-Xu; Lai, Ying-Cheng
2017-01-01
A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.
Complex Networks and Socioeconomic Applications
NASA Astrophysics Data System (ADS)
Almendral, Juan A.; López, Luis; Mendes, Jose F.; Sanjuán, Miguel A. F.
2003-04-01
The study and characterization of complex systems is a fruitful research area nowadays. Special attention has been paid recently to complex networks, where graph and network analysis plays an important role since they reduce a given system to a simpler problem. Using a simple model for the information flow on social networks, we show that the traditional hierarchical topologies frequently used by companies and organizations, are poorly designed in terms of efficiency. Moreover, we prove that this type of structures are the result of the individual aim of monopolizing as much information as possible within the network. As the information is an appropriate measurement of centrality, we conclude that this kind of topology is so attractive for leaders because the global influence each actor has within the network is completely determined by the hierarchical level occupied. The effect on the efficiency caused by a change in a traditional hierarchical topology is also analyzed. In particular, by introducing the possibility of communication on the same level of the hierarchy.
Structural complexity of quantum networks
Siomau, Michael
2016-06-10
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e. mutual position of nodes and channels connecting them. We show here that the classical structural complexity of a quantum network does not restrict the structural complexity of entanglement graphs, which may be created in the quantum network with local operations and classical communication. We show, in particular, that 1D quantum network can simulate both simple entanglement graphs such as lattices and random graphs and complex small-world graphs.
Jun Kang, Yang; Yeom, Eunseop; Lee, Sang-Joon
2013-01-01
Blood viscosity has been considered as one of important biophysical parameters for effectively monitoring variations in physiological and pathological conditions of circulatory disorders. Standard previous methods make it difficult to evaluate variations of blood viscosity under cardiopulmonary bypass procedures or hemodialysis. In this study, we proposed a unique microfluidic device for simultaneously measuring viscosity and flow rate of whole blood circulating in a complex fluidic network including a rat, a reservoir, a pinch valve, and a peristaltic pump. To demonstrate the proposed method, a twin-shaped microfluidic device, which is composed of two half-circular chambers, two side channels with multiple indicating channels, and one bridge channel, was carefully designed. Based on the microfluidic device, three sequential flow controls were applied to identify viscosity and flow rate of blood, with label-free and sensorless detection. The half-circular chamber was employed to achieve mechanical membrane compliance for flow stabilization in the microfluidic device. To quantify the effect of flow stabilization on flow fluctuations, a formula of pulsation index (PI) was analytically derived using a discrete fluidic circuit model. Using the PI formula, the time constant contributed by the half-circular chamber is estimated to be 8 s. Furthermore, flow fluctuations resulting from the peristaltic pumps are completely removed, especially under periodic flow conditions within short periods (T < 10 s). For performance demonstrations, the proposed method was applied to evaluate blood viscosity with respect to varying flow rate conditions [(a) known blood flow rate via a syringe pump, (b) unknown blood flow rate via a peristaltic pump]. As a result, the flow rate and viscosity of blood can be simultaneously measured with satisfactory accuracy. In addition, the proposed method was successfully applied to identify the viscosity of rat blood, which circulates in a
Jun Kang, Yang; Yeom, Eunseop; Lee, Sang-Joon
2013-01-01
Blood viscosity has been considered as one of important biophysical parameters for effectively monitoring variations in physiological and pathological conditions of circulatory disorders. Standard previous methods make it difficult to evaluate variations of blood viscosity under cardiopulmonary bypass procedures or hemodialysis. In this study, we proposed a unique microfluidic device for simultaneously measuring viscosity and flow rate of whole blood circulating in a complex fluidic network including a rat, a reservoir, a pinch valve, and a peristaltic pump. To demonstrate the proposed method, a twin-shaped microfluidic device, which is composed of two half-circular chambers, two side channels with multiple indicating channels, and one bridge channel, was carefully designed. Based on the microfluidic device, three sequential flow controls were applied to identify viscosity and flow rate of blood, with label-free and sensorless detection. The half-circular chamber was employed to achieve mechanical membrane compliance for flow stabilization in the microfluidic device. To quantify the effect of flow stabilization on flow fluctuations, a formula of pulsation index (PI) was analytically derived using a discrete fluidic circuit model. Using the PI formula, the time constant contributed by the half-circular chamber is estimated to be 8 s. Furthermore, flow fluctuations resulting from the peristaltic pumps are completely removed, especially under periodic flow conditions within short periods (T < 10 s). For performance demonstrations, the proposed method was applied to evaluate blood viscosity with respect to varying flow rate conditions [(a) known blood flow rate via a syringe pump, (b) unknown blood flow rate via a peristaltic pump]. As a result, the flow rate and viscosity of blood can be simultaneously measured with satisfactory accuracy. In addition, the proposed method was successfully applied to identify the viscosity of rat blood, which circulates in a
Role models for complex networks
NASA Astrophysics Data System (ADS)
Reichardt, J.; White, D. R.
2007-11-01
We present a framework for automatically decomposing (“block-modeling”) the functional classes of agents within a complex network. These classes are represented by the nodes of an image graph (“block model”) depicting the main patterns of connectivity and thus functional roles in the network. Using a first principles approach, we derive a measure for the fit of a network to any given image graph allowing objective hypothesis testing. From the properties of an optimal fit, we derive how to find the best fitting image graph directly from the network and present a criterion to avoid overfitting. The method can handle both two-mode and one-mode data, directed and undirected as well as weighted networks and allows for different types of links to be dealt with simultaneously. It is non-parametric and computationally efficient. The concepts of structural equivalence and modularity are found as special cases of our approach. We apply our method to the world trade network and analyze the roles individual countries play in the global economy.
Dynamics of and on complex networks
NASA Astrophysics Data System (ADS)
Halu, Arda
Complex networks are dynamic, evolving structures that can host a great number of dynamical processes. In this thesis, we address current challenges regarding the dynamics of and dynamical processes on complex networks. First, we study complex network dynamics from the standpoint of network growth. As a quantitative measure of the complexity and information content of networks generated by growing network models, we define and evaluate their entropy rate. We propose stochastic growth models inspired by the duplication-divergence mechanism to generate epistatic interaction networks and find that they exhibit the property of monochromaticity as a result of their dynamical evolution. Second, we explore the dynamics of quantum mechanical processes on complex networks. We investigate the Bose-Hubbard model on annealed and quenched scale-free networks as well as Apollonian networks and show that their phase diagram changes significantly in the presence of complex topologies, depending on the second degree of the degree distribution and the maximal eigenvalue of the adjacency matrix. We then study the Jaynes-Cummings-Hubbard model on various complex topologies and demonstrate the importance of the maximal eigenvalue of the hopping matrix in determining the phase diagram of the model. Third, we investigate dynamical processes on interacting and multiplex networks. We study opinion dynamics in a simulated setting of two antagonistically interacting networks and recover the importance of connectivity and committed agents. We propose a multiplex centrality measure that takes into account the connectivity patterns within and across different layers and find that the dynamics of biased random walks on multiplex networks gives rise to a centrality ranking that is different from univariate centrality measures. Finally, we study the statistical mechanics of multilayered spatial networks and demonstrate the emergence of significant link overlap and improved navigability in
Graph distance for complex networks
NASA Astrophysics Data System (ADS)
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-10-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions.
Graph distance for complex networks
Shimada, Yutaka; Hirata, Yoshito; Ikeguchi, Tohru; Aihara, Kazuyuki
2016-01-01
Networks are widely used as a tool for describing diverse real complex systems and have been successfully applied to many fields. The distance between networks is one of the most fundamental concepts for properly classifying real networks, detecting temporal changes in network structures, and effectively predicting their temporal evolution. However, this distance has rarely been discussed in the theory of complex networks. Here, we propose a graph distance between networks based on a Laplacian matrix that reflects the structural and dynamical properties of networked dynamical systems. Our results indicate that the Laplacian-based graph distance effectively quantifies the structural difference between complex networks. We further show that our approach successfully elucidates the temporal properties underlying temporal networks observed in the context of face-to-face human interactions. PMID:27725690
Online Community Detection for Large Complex Networks
Pan, Gang; Zhang, Wangsheng; Wu, Zhaohui; Li, Shijian
2014-01-01
Complex networks describe a wide range of systems in nature and society. To understand complex networks, it is crucial to investigate their community structure. In this paper, we develop an online community detection algorithm with linear time complexity for large complex networks. Our algorithm processes a network edge by edge in the order that the network is fed to the algorithm. If a new edge is added, it just updates the existing community structure in constant time, and does not need to re-compute the whole network. Therefore, it can efficiently process large networks in real time. Our algorithm optimizes expected modularity instead of modularity at each step to avoid poor performance. The experiments are carried out using 11 public data sets, and are measured by two criteria, modularity and NMI (Normalized Mutual Information). The results show that our algorithm's running time is less than the commonly used Louvain algorithm while it gives competitive performance. PMID:25061683
Control Capacity in Complex Networks
NASA Astrophysics Data System (ADS)
Jia, Tao; Liu, Yang-Yu; Slotine, Jean-Jacques; Barabasi, Albert-Laszlo
2012-02-01
By combining tools from control theory and network science, an efficient methodology was proposed to identify the minimum sets of driver nodes, whose time-dependent control can guide the whole network to any desired final state. Yet, this minimum driver set (MDS) is usually not unique, but one can often achieve multiple potential control configurations with the same number of driver nodes. Given that some nodes may appear in some MDSs but not in other, a crucial question remain unanswered: what is the role of individual node in controlling a complex system? We first classify a node as critical, redundant, or ordinary if it appears in all, no, or some MDSs. Then we introduce the concept of control capacity as a measure of the frequency that a node is in the MDSs, which quantifies the importance of a given node in maintaining Controllability. To avoid impractical enumeration of all MDSs, we propose an algorithm that uniformly samples the MDS. We use it to explore the control capacity of nodes in complex networks and study how it is related to other characteristics of the network topology.
Coupled adaptive complex networks
NASA Astrophysics Data System (ADS)
Shai, S.; Dobson, S.
2013-04-01
Adaptive networks, which combine topological evolution of the network with dynamics on the network, are ubiquitous across disciplines. Examples include technical distribution networks such as road networks and the internet, natural and biological networks, and social science networks. These networks often interact with or depend upon other networks, resulting in coupled adaptive networks. In this paper we study susceptible-infected-susceptible (SIS) epidemic dynamics on coupled adaptive networks, where susceptible nodes are able to avoid contact with infected nodes by rewiring their intranetwork connections. However, infected nodes can pass the disease through internetwork connections, which do not change with time: The dependencies between the coupled networks remain constant. We develop an analytical formalism for these systems and validate it using extensive numerical simulation. We find that stability is increased by increasing the number of internetwork links, in the sense that the range of parameters over which both endemic and healthy states coexist (both states are reachable depending on the initial conditions) becomes smaller. Finally, we find a new stable state that does not appear in the case of a single adaptive network but only in the case of weakly coupled networks, in which the infection is endemic in one network but neither becomes endemic nor dies out in the other. Instead, it persists only at the nodes that are coupled to nodes in the other network through internetwork links. We speculate on the implications of these findings.
Exact controllability of complex networks
Yuan, Zhengzhong; Zhao, Chen; Di, Zengru; Wang, Wen-Xu; Lai, Ying-Cheng
2013-01-01
Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems. PMID:24025746
Complex networks analysis of language complexity
NASA Astrophysics Data System (ADS)
Amancio, Diego R.; Aluisio, Sandra M.; Oliveira, Osvaldo N., Jr.; Costa, Luciano da F.
2012-12-01
Methods from statistical physics, such as those involving complex networks, have been increasingly used in the quantitative analysis of linguistic phenomena. In this paper, we represented pieces of text with different levels of simplification in co-occurrence networks and found that topological regularity correlated negatively with textual complexity. Furthermore, in less complex texts the distance between concepts, represented as nodes, tended to decrease. The complex networks metrics were treated with multivariate pattern recognition techniques, which allowed us to distinguish between original texts and their simplified versions. For each original text, two simplified versions were generated manually with increasing number of simplification operations. As expected, distinction was easier for the strongly simplified versions, where the most relevant metrics were node strength, shortest paths and diversity. Also, the discrimination of complex texts was improved with higher hierarchical network metrics, thus pointing to the usefulness of considering wider contexts around the concepts. Though the accuracy rate in the distinction was not as high as in methods using deep linguistic knowledge, the complex network approach is still useful for a rapid screening of texts whenever assessing complexity is essential to guarantee accessibility to readers with limited reading ability.
2010-02-18
social network (DS), (8) network of American football games among colleges (AFC), (9) social network of friendships of a karate club (FKC), (10...Ax2 = 12 book karate football ’•■ electronic circuit dolphins a C. Elegans 102 Figure 8: For Universal scaling law for six real-world
Synchronization in uncertain complex networks
NASA Astrophysics Data System (ADS)
Chen, Maoyin; Zhou, Donghua
2006-03-01
We consider the problem of synchronization in uncertain generic complex networks. For generic complex networks with unknown dynamics of nodes and unknown coupling functions including uniform and nonuniform inner couplings, some simple linear feedback controllers with updated strengths are designed using the well-known LaSalle invariance principle. The state of an uncertain generic complex network can synchronize an arbitrary assigned state of an isolated node of the network. The famous Lorenz system is stimulated as the nodes of the complex networks with different topologies. We found that the star coupled and scale-free networks with nonuniform inner couplings can be in the state of synchronization if only a fraction of nodes are controlled.
Synchronization in uncertain complex networks.
Chen, Maoyin; Zhou, Donghua
2006-03-01
We consider the problem of synchronization in uncertain generic complex networks. For generic complex networks with unknown dynamics of nodes and unknown coupling functions including uniform and nonuniform inner couplings, some simple linear feedback controllers with updated strengths are designed using the well-known LaSalle invariance principle. The state of an uncertain generic complex network can synchronize an arbitrary assigned state of an isolated node of the network. The famous Lorenz system is stimulated as the nodes of the complex networks with different topologies. We found that the star coupled and scale-free networks with nonuniform inner couplings can be in the state of synchronization if only a fraction of nodes are controlled.
Approaching human language with complex networks.
Cong, Jin; Liu, Haitao
2014-12-01
The interest in modeling and analyzing human language with complex networks is on the rise in recent years and a considerable body of research in this area has already been accumulated. We survey three major lines of linguistic research from the complex network approach: 1) characterization of human language as a multi-level system with complex network analysis; 2) linguistic typological research with the application of linguistic networks and their quantitative measures; and 3) relationships between the system-level complexity of human language (determined by the topology of linguistic networks) and microscopic linguistic (e.g., syntactic) features (as the traditional concern of linguistics). We show that the models and quantitative tools of complex networks, when exploited properly, can constitute an operational methodology for linguistic inquiry, which contributes to the understanding of human language and the development of linguistics. We conclude our review with suggestions for future linguistic research from the complex network approach: 1) relationships between the system-level complexity of human language and microscopic linguistic features; 2) expansion of research scope from the global properties to other levels of granularity of linguistic networks; and 3) combination of linguistic network analysis with other quantitative studies of language (such as quantitative linguistics).
Approaching human language with complex networks
NASA Astrophysics Data System (ADS)
Cong, Jin; Liu, Haitao
2014-12-01
The interest in modeling and analyzing human language with complex networks is on the rise in recent years and a considerable body of research in this area has already been accumulated. We survey three major lines of linguistic research from the complex network approach: 1) characterization of human language as a multi-level system with complex network analysis; 2) linguistic typological research with the application of linguistic networks and their quantitative measures; and 3) relationships between the system-level complexity of human language (determined by the topology of linguistic networks) and microscopic linguistic (e.g., syntactic) features (as the traditional concern of linguistics). We show that the models and quantitative tools of complex networks, when exploited properly, can constitute an operational methodology for linguistic inquiry, which contributes to the understanding of human language and the development of linguistics. We conclude our review with suggestions for future linguistic research from the complex network approach: 1) relationships between the system-level complexity of human language and microscopic linguistic features; 2) expansion of research scope from the global properties to other levels of granularity of linguistic networks; and 3) combination of linguistic network analysis with other quantitative studies of language (such as quantitative linguistics).
Aging, frailty and complex networks.
Mitnitski, A B; Rutenberg, A D; Farrell, S; Rockwood, K
2017-03-02
When people age their mortality rate increases exponentially, following Gompertz's law. Even so, individuals do not die from old age. Instead, they accumulate age-related illnesses and conditions and so become increasingly vulnerable to death from various external and internal stressors. As a measure of such vulnerability, frailty can be quantified using the frailty index (FI). Larger values of the FI are strongly associated with mortality and other adverse health outcomes. This association, and the insensitivity of the FI to the particular health variables that are included in its construction, makes it a powerful, convenient, and increasingly popular integrative health measure. Still, little is known about why the FI works so well. Our group has recently developed a theoretical network model of health deficits to better understand how changes in health are captured by the FI. In our model, health-related variables are represented by the nodes of a complex network. The network has a scale-free shape or "topology": a few nodes have many connections with other nodes, whereas most nodes have few connections. These nodes can be in two states, either damaged or undamaged. Transitions between damaged and non-damaged states are governed by the stochastic environment of individual nodes. Changes in the degree of damage of connected nodes change the local environment and make further damage more likely. Our model shows how age-dependent acceleration of the FI and of mortality emerges, even without specifying an age-damage relationship or any other time-dependent parameter. We have also used our model to assess how informative individual deficits are with respect to mortality. We find that the information is larger for nodes that are well connected than for nodes that are not. The model supports the idea that aging occurs as an emergent phenomenon, and not as a result of age-specific programming. Instead, aging reflects how damage propagates through a complex network of
ERIC Educational Resources Information Center
Doskey, Steven Craig
2014-01-01
This research presents an innovative means of gauging Systems Engineering effectiveness through a Systems Engineering Relative Effectiveness Index (SE REI) model. The SE REI model uses a Bayesian Belief Network to map causal relationships in government acquisitions of Complex Information Systems (CIS), enabling practitioners to identify and…
ERIC Educational Resources Information Center
Doskey, Steven Craig
2014-01-01
This research presents an innovative means of gauging Systems Engineering effectiveness through a Systems Engineering Relative Effectiveness Index (SE REI) model. The SE REI model uses a Bayesian Belief Network to map causal relationships in government acquisitions of Complex Information Systems (CIS), enabling practitioners to identify and…
Quantization Effects on Complex Networks
Wang, Ying; Wang, Lin; Yang, Wen; Wang, Xiaofan
2016-01-01
Weights of edges in many complex networks we constructed are quantized values of the real weights. To what extent does the quantization affect the properties of a network? In this work, quantization effects on network properties are investigated based on the spectrum of the corresponding Laplacian. In contrast to the intuition that larger quantization level always implies a better approximation of the quantized network to the original one, we find a ubiquitous periodic jumping phenomenon with peak-value decreasing in a power-law relationship in all the real-world weighted networks that we investigated. We supply theoretical analysis on the critical quantization level and the power laws. PMID:27226049
Language Networks as Complex Systems
ERIC Educational Resources Information Center
Lee, Max Kueiming; Ou, Sheue-Jen
2008-01-01
Starting in the late eighties, with a growing discontent with analytical methods in science and the growing power of computers, researchers began to study complex systems such as living organisms, evolution of genes, biological systems, brain neural networks, epidemics, ecology, economy, social networks, etc. In the early nineties, the research…
The physics of communicability in complex networks
NASA Astrophysics Data System (ADS)
Estrada, Ernesto; Hatano, Naomichi; Benzi, Michele
2012-05-01
A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.
"Conjectural" links in complex networks
NASA Astrophysics Data System (ADS)
Snarskii, A. A.; Zorinets, D. I.; Lande, D. V.
2016-11-01
This paper introduces the concept of Conjectural Link for Complex Networks, in particular, social networks. Conjectural Link we understand as an implicit link, not available in the network, but supposed to be present, based on the characteristics of its topology. It is possible, for example, when in the formal description of the network some connections are skipped due to errors, deliberately hidden or withdrawn (e.g. in the case of partial destruction of the network). Introduced a parameter that allows ranking the Conjectural Link. The more this parameter - the more likely that this connection should be present in the network. This paper presents a method of recovery of partially destroyed Complex Networks using Conjectural Links finding. Presented two methods of finding the node pairs that are not linked directly to one another, but have a great possibility of Conjectural Link communication among themselves: a method based on the determination of the resistance between two nodes, and method based on the computation of the lengths of routes between two nodes. Several examples of real networks are reviewed and performed a comparison to know network links prediction methods, not intended to find the missing links in already formed networks.
2014-10-21
networks. With economists Larry Blume and David Easley, and computer scientists Jon Kleinberg and Éva Tardos, we investigated so-called threshold...and Nicole Immorlica [13], we investigated Schelling’s segregation model, a famous model of residential segregation that has been observed, in...approximation ratio achieves the first provable improvement upon the approximation ratio of the famous algorithm introduced by Christofides in 1976 (which
Griffiths phases on complex networks.
Muñoz, Miguel A; Juhász, Róbert; Castellano, Claudio; Odor, Géza
2010-09-17
Quenched disorder is known to play a relevant role in dynamical processes and phase transitions. Its effects on the dynamics of complex networks have hardly been studied. Aimed at filling this gap, we analyze the contact process, i.e., the simplest propagation model, with quenched disorder on complex networks. We find Griffiths phases and other rare-region effects, leading rather generically to anomalously slow (algebraic, logarithmic, …) relaxation, on Erdos-Rényi networks. Similar effects are predicted to exist for other topologies with a finite percolation threshold. More surprisingly, we find that Griffiths phases can also emerge in the absence of quenched disorder, as a consequence of topological heterogeneity in networks with finite topological dimension. These results have a broad spectrum of implications for propagation phenomena and other dynamical processes on networks.
Heat diffusion: Thermodynamic depth complexity of networks
NASA Astrophysics Data System (ADS)
Escolano, Francisco; Hancock, Edwin R.; Lozano, Miguel A.
2012-03-01
In this paper we use the Birkhoff-von Neumann decomposition of the diffusion kernel to compute a polytopal measure of graph complexity. We decompose the diffusion kernel into a series of weighted Birkhoff combinations and compute the entropy associated with the weighting proportions (polytopal complexity). The maximum entropy Birkhoff combination can be expressed in terms of matrix permanents. This allows us to introduce a phase-transition principle that links our definition of polytopal complexity to the heat flowing through the network at a given diffusion time. The result is an efficiently computed complexity measure, which we refer to as flow complexity. Moreover, the flow complexity measure allows us to analyze graphs and networks in terms of the thermodynamic depth. We compare our method with three alternative methods described in the literature (Estrada's heterogeneity index, the Laplacian energy, and the von Neumann entropy). Our study is based on 217 protein-protein interaction (PPI) networks including histidine kinases from several species of bacteria. We find a correlation between structural complexity and phylogeny (more evolved species have statistically more complex PPIs). Although our methods outperform the alternatives, we find similarities with Estrada's heterogeneity index in terms of network size independence and predictive power.
Control efficacy of complex networks
NASA Astrophysics Data System (ADS)
Gao, Xin-Dong; Wang, Wen-Xu; Lai, Ying-Cheng
2016-06-01
Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.
Control efficacy of complex networks
Gao, Xin-Dong; Wang, Wen-Xu; Lai, Ying-Cheng
2016-01-01
Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks. PMID:27324438
Information communication on complex networks
NASA Astrophysics Data System (ADS)
Igarashi, Akito; Kawamoto, Hiroki; Maruyama, Takahiro; Morioka, Atsushi; Naganuma, Yuki
2013-02-01
Since communication networks such as the Internet, which is regarded as a complex network, have recently become a huge scale and a lot of data pass through them, the improvement of packet routing strategies for transport is one of the most significant themes in the study of computer networks. It is especially important to find routing strategies which can bear as many traffic as possible without congestion in complex networks. First, using neural networks, we introduce a strategy for packet routing on complex networks, where path lengths and queue lengths in nodes are taken into account within a framework of statistical physics. Secondly, instead of using shortest paths, we propose efficient paths which avoid hubs, nodes with a great many degrees, on scale-free networks with a weight of each node. We improve the heuristic algorithm proposed by Danila et. al. which optimizes step by step routing properties on congestion by using the information of betweenness, the probability of paths passing through a node in all optimal paths which are defined according to a rule, and mitigates the congestion. We confirm the new heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in much smaller number of iteration steps. Finally, We model virus spreading and data transfer on peer-to-peer (P2P) networks. Using mean-field approximation, we obtain an analytical formulation and emulate virus spreading on the network and compare the results with those of simulation. Moreover, we investigate the mitigation of information traffic congestion in the P2P networks.
Ranking in evolving complex networks
NASA Astrophysics Data System (ADS)
Liao, Hao; Mariani, Manuel Sebastian; Medo, Matúš; Zhang, Yi-Cheng; Zhou, Ming-Yang
2017-05-01
Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Many popular ranking algorithms (such as Google's PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. At the same time, recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of network traffic, prediction of future links, and identification of significant nodes.
Dynamic and interacting complex networks
NASA Astrophysics Data System (ADS)
Dickison, Mark E.
This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of dynamic and interacting complex networks. The mapping of various social and physical phenomena to complex networks has been a rich field in the past few decades. Subjects as broad as petroleum engineering, scientific collaborations, and the structure of the internet have all been analyzed in a network physics context, with useful and universal results. In the first chapter we introduce basic concepts in networks, including the two types of network configurations that are studied and the statistical physics and epidemiological models that form the framework of the network research, as well as covering various previously-derived results in network theory that are used in the work in the following chapters. In the second chapter we introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the time evolution of the network. We show that the dynamic network undergoes a percolation phase transition at a critical concentration pc, that decreases with the rate r at which the network links are changed. The behavior near criticality is universal and independent of r. We find that for dynamic random networks fundamental laws are changed: i) The size of the giant component at criticality scales with the network size N for all values of r, rather than as N2/3 in static network, ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as N1/2, compared to N1/3 in a static network. The third chapter consists of a study of the effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible
Spreading dynamics in complex networks
NASA Astrophysics Data System (ADS)
Pei, Sen; Makse, Hernán A.
2013-12-01
Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from epidemic control, innovation diffusion, viral marketing, and social movement to idea propagation. In this paper, we first display some of the most important theoretical models that describe spreading processes, and then discuss the problem of locating both the individual and multiple influential spreaders respectively. Recent approaches in these two topics are presented. For the identification of privileged single spreaders, we summarize several widely used centralities, such as degree, betweenness centrality, PageRank, k-shell, etc. We investigate the empirical diffusion data in a large scale online social community—LiveJournal. With this extensive dataset, we find that various measures can convey very distinct information of nodes. Of all the users in the LiveJournal social network, only a small fraction of them are involved in spreading. For the spreading processes in LiveJournal, while degree can locate nodes participating in information diffusion with higher probability, k-shell is more effective in finding nodes with a large influence. Our results should provide useful information for designing efficient spreading strategies in reality.
Fractional dynamics of complex networks
NASA Astrophysics Data System (ADS)
Turalska, Malgorzata; West, Bruce J.
2014-03-01
The relation between the behavior of a single element and the global dynamics of its host network is an open problem in the science of complex networks. Typically one attempts to infer the global dynamics by combining the behavior of single elements within the system, following a bottom-up approach. Here we address an inverse problem. We show that for a generic model within the Ising universality class it is possible to construct a description of the dynamics of an individual element, given the information about the network's global behavior. We demonstrate that the individual trajectory response to the collective motion of the network is described by a linear fractional differential equation, whose analytic solution is the Mittag-Leffler function. This solution is obtained through a subordination procedure without the necessity of linearizing the underlying dynamics, that is, the solution retains the influence of the nonlinear network dynamics on the individual. Moreover the solutions to the fractional equation of motion suggest a new direction for designing control mechanisms for complex networks. The implications of this new perspective are explored by introducing a control signal into a small number of network elements and analyzing the subsequent change in the network dynamics.
Attack Robustness and Centrality of Complex Networks
Iyer, Swami; Killingback, Timothy; Sundaram, Bala; Wang, Zhen
2013-01-01
Many complex systems can be described by networks, in which the constituent components are represented by vertices and the connections between the components are represented by edges between the corresponding vertices. A fundamental issue concerning complex networked systems is the robustness of the overall system to the failure of its constituent parts. Since the degree to which a networked system continues to function, as its component parts are degraded, typically depends on the integrity of the underlying network, the question of system robustness can be addressed by analyzing how the network structure changes as vertices are removed. Previous work has considered how the structure of complex networks change as vertices are removed uniformly at random, in decreasing order of their degree, or in decreasing order of their betweenness centrality. Here we extend these studies by investigating the effect on network structure of targeting vertices for removal based on a wider range of non-local measures of potential importance than simply degree or betweenness. We consider the effect of such targeted vertex removal on model networks with different degree distributions, clustering coefficients and assortativity coefficients, and for a variety of empirical networks. PMID:23565156
Composing Music with Complex Networks
NASA Astrophysics Data System (ADS)
Liu, Xiaofan; Tse, Chi K.; Small, Michael
In this paper we study the network structure in music and attempt to compose music artificially. Networks are constructed with nodes and edges corresponding to musical notes and their co-occurrences. We analyze sample compositions from Bach, Mozart, Chopin, as well as other types of music including Chinese pop music. We observe remarkably similar properties in all networks constructed from the selected compositions. Power-law exponents of degree distributions, mean degrees, clustering coefficients, mean geodesic distances, etc. are reported. With the network constructed, music can be created by using a biased random walk algorithm, which begins with a randomly chosen note and selects the subsequent notes according to a simple set of rules that compares the weights of the edges, weights of the nodes, and/or the degrees of nodes. The newly created music from complex networks will be played in the presentation.
Complex Networks in Psychological Models
NASA Astrophysics Data System (ADS)
Wedemann, R. S.; Carvalho, L. S. A. V. D.; Donangelo, R.
We develop schematic, self-organizing, neural-network models to describe mechanisms associated with mental processes, by a neurocomputational substrate. These models are examples of real world complex networks with interesting general topological structures. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, we propose neural network models to explain development of cortical map structure and dynamics of memory access, and unify different mental processes into a single neurocomputational substrate. Based on our neural network models, neurotic behavior may be understood as an associative memory process in the brain, and the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The models are illustrated through computer simulations, where we varied dopaminergic modulation and observed the self-organizing emergent patterns at the resulting semantic map, interpreting them as different manifestations of mental functioning, from psychotic through to normal and neurotic behavior, and creativity.
Porous Soil as Complex Network
NASA Astrophysics Data System (ADS)
Benito, R. M.; Santiago, A.; Cárdenas, J. P.; Tarquis, A. M.; Borondo, F.; Losada, J. C.
2009-04-01
We present a complex network model based on a heterogeneous preferential attachment scheme [1,2] to quantify the structure of porous soils [3]. Under this perspective pores are represented by nodes and the space for the flow of fluids between them are represented by links. Pore properties such as position and size are described by fixed states in a metric space, while an affinity function is introduced to bias the attachment probabilities of links according to these properties. We perform an analytical and numerical study of the degree distributions in the soil model and show that under reasonable conditions all the model variants yield a multiscaling behavior in the connectivity degrees, leaving a empirically testable signature of heterogeneity in the topology of pore networks. References [1] A. Santiago and R. M. Benito, "Emergence of multiscaling in heterogeneous complex networks". Int. J. Mod. Phys. C 18, 1591 (2007). [2] A. Santiago and R. M. Benito, "An extended formalism for preferential attachment in heterogeneous complex networks". Europhys. Lett. 82, 58004 (2008). [3] A. Santiago, R. M. Benito, J. P. Cárdenas, J. C. Losada, A. M. Tarquis and F. Borondo, "Multiscaling of porous soils as heterogeneous complex networks". Nonl. Proc. Geophys. 15, 1-10 (2008).
Robustness Elasticity in Complex Networks
Matisziw, Timothy C.; Grubesic, Tony H.; Guo, Junyu
2012-01-01
Network robustness refers to a network’s resilience to stress or damage. Given that most networks are inherently dynamic, with changing topology, loads, and operational states, their robustness is also likely subject to change. However, in most analyses of network structure, it is assumed that interaction among nodes has no effect on robustness. To investigate the hypothesis that network robustness is not sensitive or elastic to the level of interaction (or flow) among network nodes, this paper explores the impacts of network disruption, namely arc deletion, over a temporal sequence of observed nodal interactions for a large Internet backbone system. In particular, a mathematical programming approach is used to identify exact bounds on robustness to arc deletion for each epoch of nodal interaction. Elasticity of the identified bounds relative to the magnitude of arc deletion is assessed. Results indicate that system robustness can be highly elastic to spatial and temporal variations in nodal interactions within complex systems. Further, the presence of this elasticity provides evidence that a failure to account for nodal interaction can confound characterizations of complex networked systems. PMID:22808060
Dynamic information routing in complex networks
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2016-01-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function. PMID:27067257
Dynamic information routing in complex networks
NASA Astrophysics Data System (ADS)
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2016-04-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how such systems may specifically communicate and dynamically route information is not well understood. Here we identify a generic mechanism to route information on top of collective dynamical reference states in complex networks. Switching between collective dynamics induces flexible reorganization of information sharing and routing patterns, as quantified by delayed mutual information and transfer entropy measures between activities of a network's units. We demonstrate the power of this mechanism specifically for oscillatory dynamics and analyse how individual unit properties, the network topology and external inputs co-act to systematically organize information routing. For multi-scale, modular architectures, we resolve routing patterns at all levels. Interestingly, local interventions within one sub-network may remotely determine nonlocal network-wide communication. These results help understanding and designing information routing patterns across systems where collective dynamics co-occurs with a communication function.
Quantum physics and complex networks
NASA Astrophysics Data System (ADS)
Biamonte, Jacob
2014-03-01
There is a widely used and successful theory of ``chemical reaction networks,'' which provides a framework describing systems governed by mass action kinetics. Computer science and population biology use the same ideas under a different name: ``stochastic Petri nets.'' But if we look at these theories from the perspective of quantum theory, they turn out to involve creation and annihilation operators, coherent states and other well-known ideas--yet in a context where probabilities replace amplitudes. I will explain this connection as part of a detailed analogy between quantum mechanics and stochastic mechanics which we've produced several results on recently, including the recent analytical results uniting quantum physics and complex networks. Our general idea is about merging concepts from quantum physics and complex network theory to provide a bidirectional bridge between both disciplines. Support is acknowledged from the Foundational Questions Institute (FQXi) and the Compagnia di San Paolo Foundation.
2005-04-01
the topological specification of a network in the form of a connection matrix and the branches of mathematics known as continuous group theory and...Connection Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2.2 Dynamical Network Changes...essential aspects of the network into just a few metrics (functions of the network matrix values). It is well known that a network is characterized
Adaptive walk on complex networks.
Campos, Paulo R A; Moreira, F G Brady
2005-06-01
We investigate the properties of adaptive walks on an uncorrelated fitness landscape which is established in sequence spaces of complex structure. In particular, we perform numerical simulations of adaptive walks on random graphs and scale-free networks. For the former, we also derive some analytical approximations for the density of local optima of the fitness landscape and the mean length walk. We compare our results with those obtained for regular lattices. We obtain that the density of local optima decreases as 1/z, where z is the mean connectivity, for all networks we have investigated. In random graphs, the mean length walk L reaches the asymptotic value e - 1 for large z, which corresponds to the result for regular networks. Although we could not find an exact estimate, we derive an underestimated value for L. Unlike random graphs, scale-free networks show an upper asymptotic value of L.
Wealth dynamics on complex networks
NASA Astrophysics Data System (ADS)
Garlaschelli, Diego; Loffredo, Maria I.
2004-07-01
We study a model of wealth dynamics (Physica A 282 (2000) 536) which mimics transactions among economic agents. The outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network. The extreme cases of a fully connected and a fully disconnected network yield power-law and log-normal forms of the wealth distribution, respectively. We perform numerical simulations in order to test the model on more complex network topologies. We show that the mixed form of most empirical distributions (displaying a non-smooth transition from a log-normal to a power-law form) can be traced back to a heterogeneous topology with varying link density, which on the other hand is a recently observed property of real networks.
Multilevel Complex Networks and Systems
NASA Astrophysics Data System (ADS)
Caldarelli, Guido
2014-03-01
Network theory has been a powerful tool to model isolated complex systems. However, the classical approach does not take into account the interactions often present among different systems. Hence, the scientific community is nowadays concentrating the efforts on the foundations of new mathematical tools for understanding what happens when multiple networks interact. The case of economic and financial networks represents a paramount example of multilevel networks. In the case of trade, trade among countries the different levels can be described by the different granularity of the trading relations. Indeed, we have now data from the scale of consumers to that of the country level. In the case of financial institutions, we have a variety of levels at the same scale. For example one bank can appear in the interbank networks, ownership network and cds networks in which the same institution can take place. In both cases the systemically important vertices need to be determined by different procedures of centrality definition and community detection. In this talk I will present some specific cases of study related to these topics and present the regularities found. Acknowledged support from EU FET Project ``Multiplex'' 317532.
Role of Edges in Complex Network Epidemiology
NASA Astrophysics Data System (ADS)
Zhang, Hao; Jiang, Zhi-Hong; Wang, Hui; Xie, Fei; Chen, Chao
2012-09-01
In complex network epidemiology, diseases spread along contacting edges between individuals and different edges may play different roles in epidemic outbreaks. Quantifying the efficiency of edges is an important step towards arresting epidemics. In this paper, we study the efficiency of edges in general susceptible-infected-recovered models, and introduce the transmission capability to measure the efficiency of edges. Results show that deleting edges with the highest transmission capability will greatly decrease epidemics on scale-free networks. Basing on the message passing approach, we get exact mathematical solution on configuration model networks with edge deletion in the large size limit.
Epidemic processes in complex networks
NASA Astrophysics Data System (ADS)
Pastor-Satorras, Romualdo; Castellano, Claudio; Van Mieghem, Piet; Vespignani, Alessandro
2015-07-01
In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.
Viral quasispecies complexity measures.
Gregori, Josep; Perales, Celia; Rodriguez-Frias, Francisco; Esteban, Juan I; Quer, Josep; Domingo, Esteban
2016-06-01
Mutant spectrum dynamics (changes in the related mutants that compose viral populations) has a decisive impact on virus behavior. The several platforms of next generation sequencing (NGS) to study viral quasispecies offer a magnifying glass to study viral quasispecies complexity. Several parameters are available to quantify the complexity of mutant spectra, but they have limitations. Here we critically evaluate the information provided by several population diversity indices, and we propose the introduction of some new ones used in ecology. In particular we make a distinction between incidence, abundance and function measures of viral quasispecies composition. We suggest a multidimensional approach (complementary information contributed by adequately chosen indices), propose some guidelines, and illustrate the use of indices with a simple example. We apply the indices to three clinical samples of hepatitis C virus that display different population heterogeneity. Areas of virus biology in which population complexity plays a role are discussed.
Competitive Dynamics on Complex Networks
NASA Astrophysics Data System (ADS)
Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan
2014-07-01
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition.
Competitive Dynamics on Complex Networks
Zhao, Jiuhua; Liu, Qipeng; Wang, Xiaofan
2014-01-01
We consider a dynamical network model in which two competitors have fixed and different states, and each normal agent adjusts its state according to a distributed consensus protocol. The state of each normal agent converges to a steady value which is a convex combination of the competitors' states, and is independent of the initial states of agents. This implies that the competition result is fully determined by the network structure and positions of competitors in the network. We compute an Influence Matrix (IM) in which each element characterizing the influence of an agent on another agent in the network. We use the IM to predict the bias of each normal agent and thus predict which competitor will win. Furthermore, we compare the IM criterion with seven node centrality measures to predict the winner. We find that the competitor with higher Katz Centrality in an undirected network or higher PageRank in a directed network is most likely to be the winner. These findings may shed new light on the role of network structure in competition and to what extent could competitors adjust network structure so as to win the competition. PMID:25068622
Statistical physics of complex networks
NASA Astrophysics Data System (ADS)
Xie, Huafeng
We live in a connected world. It is of great practical importance and intellectual appeal to understand the networks surrounding us. In this work we study ranking of the nodes in complex networks. In large networks such as World Wide Web (WWW) and citation networks of scientific literature, searching by keywords is a common practice to retrieve useful information. On the WWW, apart from the contents of webpages, the topology of the network itself can be a rich source of information about their relative importance and relevancy to the search query. It is the effective utilization of this topological information [50] which advanced the Google search engine to its present position of the most popular tool on the WWW. The World-Wide Web (WWW) is characterized by a strong community structure in which communities of webpages are densely interconnected by hyperlinks. We study how such network architecture affects the average Google ranking of individual webpages in the community. Using a mean-field approximation, we quantify how the average Google rank of community's webpages depends on the degree to which it is isolated from the rest of the world in both incoming and outgoing directions, and alpha -- the only intrinsic parameter of Google's PageRank algorithm. We proceed with numerical study of simulated networks and empirical study of several internal web-communities within two US universities. The predictions of our mean-field treatment were qualitatively verified in those real-life networks. Furthermore, the value alpha = 0.15 used by Google seems to be optimized for the degree of isolation of communities as they exist in the actual WWW. We then extend Google's PageRank algorithm to citation networks of scientific literature. Unlike hyperlinks, citations cannot be updated after the point of publication. This results in strong aging characteristics of citation networks that affect the performance of the PageRank algorithm. To rectify this we modify the Page
Congestion phenomena on complex networks.
De Martino, Daniele; Dall'asta, Luca; Bianconi, Ginestra; Marsili, Matteo
2009-01-01
We define a minimal model of traffic flows in complex networks in order to study the trade-off between topological-based and traffic-based routing strategies. The resulting collective behavior is obtained analytically for an ensemble of uncorrelated networks and summarized in a rich phase diagram presenting second-order as well as first-order phase transitions between a free-flow phase and a congested phase. We find that traffic control improves global performance, enlarging the free-flow region in parameter space only in heterogeneous networks. Traffic control introduces nonlinear effects and, beyond a critical strength, may trigger the appearance of a congested phase in a discontinuous manner. The model also reproduces the crossover in the scaling of traffic fluctuations empirically observed on the Internet.
Spectral coarse grained controllability of complex networks
NASA Astrophysics Data System (ADS)
Wang, Pei; Xu, Shuang
2017-07-01
With the accumulation of interaction data from various systems, a fundamental question in network science is how to reduce the sizes while keeping certain properties of complex networks. Combined the spectral coarse graining theory and the structural controllability of complex networks, we explore the structural controllability of undirected complex networks during coarse graining processes. We evidence that the spectral coarse grained controllability (SCGC) properties for the Erdös-Rényi (ER) random networks, the scale-free (SF) random networks and the small-world (SW) random networks are distinct from each other. The SW networks are very robust, while the SF networks are sensitive during the coarse graining processes. As an emergent properties for the dense ER networks, during the coarse graining processes, there exists a threshold value of the coarse grained sizes, which separates the controllability of the reduced networks into robust and sensitive to coarse graining. Investigations on some real-world complex networks indicate that the SCGC properties are varied among different categories and different kinds of networks, some highly organized social or biological networks are more difficult to be controlled, while many man-made power networks and infrastructure networks can keep the controllability properties during the coarse graining processes. Furthermore, we speculate that the SCGC properties of complex networks may depend on their degree distributions. The associated investigations have potential implications in the control of large-scale complex networks, as well as in the understanding of the organization of complex networks.
Blockmodeling techniques for complex networks
NASA Astrophysics Data System (ADS)
Ball, Brian Joseph
The class of network models known as stochastic blockmodels has recently been gaining popularity. In this dissertation, we present new work that uses blockmodels to answer questions about networks. We create a blockmodel based on the idea of link communities, which naturally gives rise to overlapping vertex communities. We derive a fast and accurate algorithm to fit the model to networks. This model can be related to another blockmodel, which allows the method to efficiently find nonoverlapping communities as well. We then create a heuristic based on the link community model whose use is to find the correct number of communities in a network. The heuristic is based on intuitive corrections to likelihood ratio tests. It does a good job finding the correct number of communities in both real networks and synthetic networks generated from the link communities model. Two commonly studied types of networks are citation networks, where research papers cite other papers, and coauthorship networks, where authors are connected if they've written a paper together. We study a multi-modal network from a large dataset of Physics publications that is the combination of the two, allowing for directed links between papers as citations, and an undirected edge between a scientist and a paper if they helped to write it. This allows for new insights on the relation between social interaction and scientific production. We also have the publication dates of papers, which lets us track our measures over time. Finally, we create a stochastic model for ranking vertices in a semi-directed network. The probability of connection between two vertices depends on the difference of their ranks. When this model is fit to high school friendship networks, the ranks appear to correspond with a measure of social status. Students have reciprocated and some unreciprocated edges with other students of closely similar rank that correspond to true friendship, and claim an aspirational friendship with a much
Controlling centrality in complex networks
Nicosia, V.; Criado, R.; Romance, M.; Russo, G.; Latora, V.
2012-01-01
Spectral centrality measures allow to identify influential individuals in social groups, to rank Web pages by popularity, and even to determine the impact of scientific researches. The centrality score of a node within a network crucially depends on the entire pattern of connections, so that the usual approach is to compute node centralities once the network structure is assigned. We face here with the inverse problem, that is, we study how to modify the centrality scores of the nodes by acting on the structure of a given network. We show that there exist particular subsets of nodes, called controlling sets, which can assign any prescribed set of centrality values to all the nodes of a graph, by cooperatively tuning the weights of their out-going links. We found that many large networks from the real world have surprisingly small controlling sets, containing even less than 5 – 10% of the nodes. PMID:22355732
Robustness surfaces of complex networks
NASA Astrophysics Data System (ADS)
Manzano, Marc; Sahneh, Faryad; Scoglio, Caterina; Calle, Eusebi; Marzo, Jose Luis
2014-09-01
Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the R*-value and introducing the concept of robustness surface (Ω). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.
Network representations of immune system complexity
Subramanian, Naeha; Torabi-Parizi, Parizad; Gottschalk, Rachel A.; Germain, Ronald N.; Dutta, Bhaskar
2015-01-01
The mammalian immune system is a dynamic multi-scale system composed of a hierarchically organized set of molecular, cellular and organismal networks that act in concert to promote effective host defense. These networks range from those involving gene regulatory and protein-protein interactions underlying intracellular signaling pathways and single cell responses to increasingly complex networks of in vivo cellular interaction, positioning and migration that determine the overall immune response of an organism. Immunity is thus not the product of simple signaling events but rather non-linear behaviors arising from dynamic, feedback-regulated interactions among many components. One of the major goals of systems immunology is to quantitatively measure these complex multi-scale spatial and temporal interactions, permitting development of computational models that can be used to predict responses to perturbation. Recent technological advances permit collection of comprehensive datasets at multiple molecular and cellular levels while advances in network biology support representation of the relationships of components at each level as physical or functional interaction networks. The latter facilitate effective visualization of patterns and recognition of emergent properties arising from the many interactions of genes, molecules, and cells of the immune system. We illustrate the power of integrating ‘omics’ and network modeling approaches for unbiased reconstruction of signaling and transcriptional networks with a focus on applications involving the innate immune system. We further discuss future possibilities for reconstruction of increasingly complex cellular and organism-level networks and development of sophisticated computational tools for prediction of emergent immune behavior arising from the concerted action of these networks. PMID:25625853
Factors determining nestedness in complex networks.
Jonhson, Samuel; Domínguez-García, Virginia; Muñoz, Miguel A
2013-01-01
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks. Indeed, Bastolla et al. introduced a simple measure of network nestedness which opened the door to analytical understanding, allowing them to conclude that biodiversity is strongly enhanced in highly nested mutualistic networks. Here, we suggest a slightly refined version of such a measure of nestedness and study how it is influenced by the most basic structural properties of networks, such as degree distribution and degree-degree correlations (i.e. assortativity). We find that most of the empirically found nestedness stems from heterogeneity in the degree distribution. Once such an influence has been discounted - as a second factor - we find that nestedness is strongly correlated with disassortativity and hence - as random networks have been recently found to be naturally disassortative - they also tend to be naturally nested just as the result of chance.
Factors Determining Nestedness in Complex Networks
Jonhson, Samuel; Domínguez-García, Virginia; Muñoz, Miguel A.
2013-01-01
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks. Indeed, Bastolla et al. introduced a simple measure of network nestedness which opened the door to analytical understanding, allowing them to conclude that biodiversity is strongly enhanced in highly nested mutualistic networks. Here, we suggest a slightly refined version of such a measure of nestedness and study how it is influenced by the most basic structural properties of networks, such as degree distribution and degree-degree correlations (i.e. assortativity). We find that most of the empirically found nestedness stems from heterogeneity in the degree distribution. Once such an influence has been discounted – as a second factor – we find that nestedness is strongly correlated with disassortativity and hence – as random networks have been recently found to be naturally disassortative – they also tend to be naturally nested just as the result of chance. PMID:24069264
Characterizing the Community Structure of Complex Networks
Lancichinetti, Andrea; Kivelä, Mikko; Saramäki, Jari; Fortunato, Santo
2010-01-01
Background Community structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks. Methodology/Principal Findings We present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as “fingerprints” of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category. Conclusions/Significance Our findings, verified by the use of two fundamentally different community detection methods, allow for a classification of real networks and pave the way to a realistic modelling of networks' evolution. PMID:20711338
Complex Networks and Critical Infrastructures
NASA Astrophysics Data System (ADS)
Setola, Roberto; de Porcellinis, Stefano
The term “Critical Infrastructures” indicates all those technological infrastructures such as: electric grids, telecommunication networks, railways, healthcare systems, financial circuits, etc. that are more and more relevant for the welfare of our countries. Each one of these infrastructures is a complex, highly non-linear, geographically dispersed cluster of systems, that interact with their human owners, operators, users and with the other infrastructures. Their augmented relevance and the actual political and technological scenarios, which have increased their exposition to accidental failure and deliberate attacks, demand for different and innovative protection strategies (generally indicate as CIP - Critical Infrastructure Protection). To this end it is mandatory to understand the mechanisms that regulate the dynamic of these infrastructures. In this framework, an interesting approach is those provided by the complex networks. In this paper we illustrate some results achieved considering structural and functional properties of the corresponding topological networks both when each infrastructure is assumed as an autonomous system and when we take into account also the dependencies existing among the different infrastructures.
Anomalous Transport in Complex Networks
NASA Astrophysics Data System (ADS)
Lopez, Eduardo; Buldyrev, Sergey; Havlin, Shlomo; Stanley, H. Eugene
2005-03-01
To study transport properties of complex networks, we analyze the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)˜k^-λ in which each link has the same unit resistance. We predict a broad range of values of G, with a power-law tail distribution φSF(G)˜G^-gG, where gG=2λ-1, and confirm our predictions by simulations. The power-law tail in φSF(G) leads to large values of G, thereby significantly improving the transport in scale-free networks, compared to Erdos-R'enyi random graphs where the tail of the conductivity distribution decays exponentially. Based on a simple physical ``transport backbone'' picture we show that the conductances are well approximated by ckAkB/(kA+kB) for any pair of nodes A and B with degrees kA and kB. Thus, a single parameter c characterizes transport on scale-free networks.
Fuzzy Entropy Method for Quantifying Supply Chain Networks Complexity
NASA Astrophysics Data System (ADS)
Zhang, Jihui; Xu, Junqin
Supply chain is a special kind of complex network. Its complexity and uncertainty makes it very difficult to control and manage. Supply chains are faced with a rising complexity of products, structures, and processes. Because of the strong link between a supply chain’s complexity and its efficiency the supply chain complexity management becomes a major challenge of today’s business management. The aim of this paper is to quantify the complexity and organization level of an industrial network working towards the development of a ‘Supply Chain Network Analysis’ (SCNA). By measuring flows of goods and interaction costs between different sectors of activity within the supply chain borders, a network of flows is built and successively investigated by network analysis. The result of this study shows that our approach can provide an interesting conceptual perspective in which the modern supply network can be framed, and that network analysis can handle these issues in practice.
Spatial Network Representation Of Complex Living Tissues
NASA Astrophysics Data System (ADS)
Korošak, Dean; Rupnik, Marjan
2008-11-01
Networks were widely used to describe organizational and functional principles of living organisms across various scales. The topology of such biological complex networks often turned out to be "scale-free," with the power-law distribution of number of links per node, robust and modular with underlying self-similar structure. However, the topology of cytoarchitecture in living tissues has not yet received wide attention from the network perspective. Here we discuss the spatial complex network model of coupled clusters of beta cells in pancreatic islets. Networks of cells in pancreatic islets were constructed from the 2D section images presenting fluorescently labelled intercellular spaces obtained by two-photon laser scanning microscopy of whole pancreas tissue slices, and cells conductances measured electrophysiologically using whole-cell patch-clamp. We find that the heterogeneity of beta cells in intact living islets induces scale-free topology of the tissue network. Furthermore, we show that the islet-like structures visually similar to 2D section images can be obtained using Voronoi diagrams of random points.
Exploring Statistical and Population Aspects of Network Complexity
Emmert-Streib, Frank; Dehmer, Matthias
2012-01-01
The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples. PMID:22590495
Modeling phototaxis in complex networks
NASA Astrophysics Data System (ADS)
Kuksenok, Olga; Balazs, Anna C.
2006-03-01
Phototaxis is the movement of organisms towards or away from light. It is one of the most important photo-biological processes, which in turn are responsible for light reception and the use of photons as a source of information. We briefly review current models of phototaxis of biological organisms and we develop a simple, minimal model for synthetic microscale units that can undergo phototactic motion. We then use this model to simulate the collective motion of such photosensitive artificial objects within a complex network, which is illuminated in a non-uniform manner by an external light.
Kinetic analysis of complex metabolic networks
Stephanopoulos, G.
1996-12-31
A new methodology is presented for the analysis of complex metabolic networks with the goal of metabolite overproduction. The objective is to locate a small number of reaction steps in a network that have maximum impact on network flux amplification and whose rate can also be increased without functional network derangement. This method extends the concepts of Metabolic Control Analysis to groups of reactions and offers the means for calculating group control coefficients as measures of the control exercised by groups of reactions on the overall network fluxes and intracellular metabolite pools. It is further demonstrated that the optimal strategy for the effective increase of network fluxes, while maintaining an uninterrupted supply of intermediate metabolites, is through the coordinated amplification of multiple (as opposed to a single) reaction steps. Satisfying this requirement invokes the concept of the concentration control to coefficient, which emerges as a critical parameter in the identification of feasible enzymatic modifications with maximal impact on the network flux. A case study of aromatic aminoacid production is provided to illustrate these concepts.
Geometry of complex networks and topological centrality
NASA Astrophysics Data System (ADS)
Ranjan, Gyan; Zhang, Zhi-Li
2013-09-01
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L). The squared distance of a node i to the origin in this n-dimensional space (lii+), yields a topological centrality index, defined as C∗(i)=1/lii+. In turn, the sum of reciprocals of individual node centralities, ∑i1/C∗(i)=∑ilii+, or the trace of L, yields the well-known Kirchhoff index (K), an overall structural descriptor for the network. To put into context this geometric definition of centrality, we provide alternative interpretations of the proposed indices that connect them to meaningful topological characteristics - first, as forced detour overheads and frequency of recurrences in random walks that has an interesting analogy to voltage distributions in the equivalent electrical network; and then as the average connectedness of i in all the bi-partitions of the graph. These interpretations respectively help establish the topological centrality (C∗(i)) of node i as a measure of its overall position as well as its overall connectedness in the network; thus reflecting the robustness of i to random multiple edge failures. Through empirical evaluations using synthetic and real world networks, we demonstrate how the topological centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchhoff index, is appropriately sensitive to perturbations/re-wirings in the network.
The Correlation Fractal Dimension of Complex Networks
NASA Astrophysics Data System (ADS)
Wang, Xingyuan; Liu, Zhenzhen; Wang, Mogei
2013-05-01
The fractality of complex networks is studied by estimating the correlation dimensions of the networks. Comparing with the previous algorithms of estimating the box dimension, our algorithm achieves a significant reduction in time complexity. For four benchmark cases tested, that is, the Escherichia coli (E. Coli) metabolic network, the Homo sapiens protein interaction network (H. Sapiens PIN), the Saccharomyces cerevisiae protein interaction network (S. Cerevisiae PIN) and the World Wide Web (WWW), experiments are provided to demonstrate the validity of our algorithm.
Advances in the Theory of Complex Networks
NASA Astrophysics Data System (ADS)
Peruani, Fernando
An exhaustive and comprehensive review on the theory of complex networks would imply nowadays a titanic task, and it would result in a lengthy work containing plenty of technical details of arguable relevance. Instead, this chapter addresses very briefly the ABC of complex network theory, visiting only the hallmarks of the theoretical founding, to finally focus on two of the most interesting and promising current research problems: the study of dynamical processes on transportation networks and the identification of communities in complex networks.
Ranking important nodes in complex networks by simulated annealing
NASA Astrophysics Data System (ADS)
Sun, Yu; Yao, Pei-Yang; Wan, Lu-Jun; Shen, Jian; Zhong, Yun
2017-02-01
In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented. First, the concept of an importance sequence (IS) to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks. Project supported by the National Natural Science Foundation of China (Grant No. 61573017) and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2016JQ6062).
Robustness and structure of complex networks
NASA Astrophysics Data System (ADS)
Shao, Shuai
This dissertation covers the two major parts of my PhD research on statistical physics and complex networks: i) modeling a new type of attack -- localized attack, and investigating robustness of complex networks under this type of attack; ii) discovering the clustering structure in complex networks and its influence on the robustness of coupled networks. Complex networks appear in every aspect of our daily life and are widely studied in Physics, Mathematics, Biology, and Computer Science. One important property of complex networks is their robustness under attacks, which depends crucially on the nature of attacks and the structure of the networks themselves. Previous studies have focused on two types of attack: random attack and targeted attack, which, however, are insufficient to describe many real-world damages. Here we propose a new type of attack -- localized attack, and study the robustness of complex networks under this type of attack, both analytically and via simulation. On the other hand, we also study the clustering structure in the network, and its influence on the robustness of a complex network system. In the first part, we propose a theoretical framework to study the robustness of complex networks under localized attack based on percolation theory and generating function method. We investigate the percolation properties, including the critical threshold of the phase transition pc and the size of the giant component Pinfinity. We compare localized attack with random attack and find that while random regular (RR) networks are more robust against localized attack, Erdoḧs-Renyi (ER) networks are equally robust under both types of attacks. As for scale-free (SF) networks, their robustness depends crucially on the degree exponent lambda. The simulation results show perfect agreement with theoretical predictions. We also test our model on two real-world networks: a peer-to-peer computer network and an airline network, and find that the real-world networks
Autoscoring Essays Based on Complex Networks
ERIC Educational Resources Information Center
Ke, Xiaohua; Zeng, Yongqiang; Luo, Haijiao
2016-01-01
This article presents a novel method, the Complex Dynamics Essay Scorer (CDES), for automated essay scoring using complex network features. Texts produced by college students in China were represented as scale-free networks (e.g., a word adjacency model) from which typical network features, such as the in-/out-degrees, clustering coefficient (CC),…
Autoscoring Essays Based on Complex Networks
ERIC Educational Resources Information Center
Ke, Xiaohua; Zeng, Yongqiang; Luo, Haijiao
2016-01-01
This article presents a novel method, the Complex Dynamics Essay Scorer (CDES), for automated essay scoring using complex network features. Texts produced by college students in China were represented as scale-free networks (e.g., a word adjacency model) from which typical network features, such as the in-/out-degrees, clustering coefficient (CC),…
Energy complexity of recurrent neural networks.
Síma, Jiří
2014-05-01
Recently a new so-called energy complexity measure has been introduced and studied for feedforward perceptron networks. This measure is inspired by the fact that biological neurons require more energy to transmit a spike than not to fire, and the activity of neurons in the brain is quite sparse, with only about 1% of neurons firing. In this letter, we investigate the energy complexity of recurrent networks, which counts the number of active neurons at any time instant of a computation. We prove that any deterministic finite automaton with m states can be simulated by a neural network of optimal size [Formula: see text] with the time overhead of [Formula: see text] per one input bit, using the energy O(e), for any e such that [Formula: see text] and e=O(s), which shows the time-energy trade-off in recurrent networks. In addition, for the time overhead [Formula: see text] satisfying [Formula: see text], we obtain the lower bound of [Formula: see text] on the energy of such a simulation for some constant c>0 and for infinitely many s.
A Complexity Theory of Neural Networks
1990-04-14
Significant results have been obtained on the computation complexity of analog neural networks , and distribute voting. The computing power and...learning algorithms for limited precision analog neural networks have been investigated. Lower bounds for constant depth, polynomial size analog neural ... networks , and a limited version of discrete neural networks have been obtained. The work on distributed voting has important applications for distributed
Benford’s Distribution in Complex Networks
Morzy, Mikołaj; Kajdanowicz, Tomasz; Szymański, Bolesław K.
2016-01-01
Many collections of numbers do not have a uniform distribution of the leading digit, but conform to a very particular pattern known as Benford’s distribution. This distribution has been found in numerous areas such as accounting data, voting registers, census data, and even in natural phenomena. Recently it has been reported that Benford’s law applies to online social networks. Here we introduce a set of rigorous tests for adherence to Benford’s law and apply it to verification of this claim, extending the scope of the experiment to various complex networks and to artificial networks created by several popular generative models. Our findings are that neither for real nor for artificial networks there is sufficient evidence for common conformity of network structural properties with Benford’s distribution. We find very weak evidence suggesting that three measures, degree centrality, betweenness centrality and local clustering coefficient, could adhere to Benford’s law for scalefree networks but only for very narrow range of their parameters. PMID:27748398
Benford’s Distribution in Complex Networks
NASA Astrophysics Data System (ADS)
Morzy, Mikołaj; Kajdanowicz, Tomasz; Szymański, Bolesław K.
2016-10-01
Many collections of numbers do not have a uniform distribution of the leading digit, but conform to a very particular pattern known as Benford’s distribution. This distribution has been found in numerous areas such as accounting data, voting registers, census data, and even in natural phenomena. Recently it has been reported that Benford’s law applies to online social networks. Here we introduce a set of rigorous tests for adherence to Benford’s law and apply it to verification of this claim, extending the scope of the experiment to various complex networks and to artificial networks created by several popular generative models. Our findings are that neither for real nor for artificial networks there is sufficient evidence for common conformity of network structural properties with Benford’s distribution. We find very weak evidence suggesting that three measures, degree centrality, betweenness centrality and local clustering coefficient, could adhere to Benford’s law for scalefree networks but only for very narrow range of their parameters.
Structural measures for multiplex networks
NASA Astrophysics Data System (ADS)
Battiston, Federico; Nicosia, Vincenzo; Latora, Vito
2014-03-01
Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular, we propose a series of measures to characterize the multiplexicity of the systems in terms of (i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, (ii) local properties such as the clustering coefficient and the transitivity, and (iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuinely multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications, and business relationships.
Complexity Characteristics of Currency Networks
NASA Astrophysics Data System (ADS)
Gorski, A. Z.; Drozdz, S.; Kwapien, J.; Oswiecimka, P.
2006-11-01
A large set of daily FOREX time series is analyzed. The corresponding correlation matrices (CM) are constructed for USD, EUR and PLN used as the base currencies. The triangle rule is interpreted as constraints reducing the number of independent returns. The CM spectrum is computed and compared with the cases of shuffled currencies and a fictitious random currency taken as a base currency. The Minimal Spanning Tree (MST) graphs are calculated and the clustering effects for strong currencies are found. It is shown that for MSTs the node rank has power like, scale free behavior. Finally, the scaling exponents are evaluated and found in the range analogous to those identified recently for various complex networks.
Community structure of complex networks based on continuous neural network
NASA Astrophysics Data System (ADS)
Dai, Ting-ting; Shan, Chang-ji; Dong, Yan-shou
2017-09-01
As a new subject, the research of complex networks has attracted the attention of researchers from different disciplines. Community structure is one of the key structures of complex networks, so it is a very important task to analyze the community structure of complex networks accurately. In this paper, we study the problem of extracting the community structure of complex networks, and propose a continuous neural network (CNN) algorithm. It is proved that for any given initial value, the continuous neural network algorithm converges to the eigenvector of the maximum eigenvalue of the network modularity matrix. Therefore, according to the stability of the evolution of the network symbol will be able to get two community structure.
Spatially Distributed Social Complex Networks
NASA Astrophysics Data System (ADS)
Frasco, Gerald F.; Sun, Jie; Rozenfeld, Hernán D.; ben-Avraham, Daniel
2014-01-01
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrat's law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008).]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.
The noisy voter model on complex networks
Carro, Adrián; Toral, Raúl; San Miguel, Maxi
2016-01-01
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for uncorrelated networks, allowing to deal with the network structure as parametric heterogeneity. As an illustration, we study the noisy voter model, a modification of the original voter model including random changes of state. The proposed method is able to unfold the dependence of the model not only on the mean degree (the mean-field prediction) but also on more complex averages over the degree distribution. In particular, we find that the degree heterogeneity—variance of the underlying degree distribution—has a strong influence on the location of the critical point of a noise-induced, finite-size transition occurring in the model, on the local ordering of the system, and on the functional form of its temporal correlations. Finally, we show how this latter point opens the possibility of inferring the degree heterogeneity of the underlying network by observing only the aggregate behavior of the system as a whole, an issue of interest for systems where only macroscopic, population level variables can be measured. PMID:27094773
Defining nodes in complex brain networks
Stanley, Matthew L.; Moussa, Malaak N.; Paolini, Brielle M.; Lyday, Robert G.; Burdette, Jonathan H.; Laurienti, Paul J.
2013-01-01
Network science holds great promise for expanding our understanding of the human brain in health, disease, development, and aging. Network analyses are quickly becoming the method of choice for analyzing functional MRI data. However, many technical issues have yet to be confronted in order to optimize results. One particular issue that remains controversial in functional brain network analyses is the definition of a network node. In functional brain networks a node represents some predefined collection of brain tissue, and an edge measures the functional connectivity between pairs of nodes. The characteristics of a node, chosen by the researcher, vary considerably in the literature. This manuscript reviews the current state of the art based on published manuscripts and highlights the strengths and weaknesses of three main methods for defining nodes. Voxel-wise networks are constructed by assigning a node to each, equally sized brain area (voxel). The fMRI time-series recorded from each voxel is then used to create the functional network. Anatomical methods utilize atlases to define the nodes based on brain structure. The fMRI time-series from all voxels within the anatomical area are averaged and subsequently used to generate the network. Functional activation methods rely on data from traditional fMRI activation studies, often from databases, to identify network nodes. Such methods identify the peaks or centers of mass from activation maps to determine the location of the nodes. Small (~10–20 millimeter diameter) spheres located at the coordinates of the activation foci are then applied to the data being used in the network analysis. The fMRI time-series from all voxels in the sphere are then averaged, and the resultant time series is used to generate the network. We attempt to clarify the discussion and move the study of complex brain networks forward. While the “correct” method to be used remains an open, possibly unsolvable question that deserves
Defining nodes in complex brain networks.
Stanley, Matthew L; Moussa, Malaak N; Paolini, Brielle M; Lyday, Robert G; Burdette, Jonathan H; Laurienti, Paul J
2013-11-22
Network science holds great promise for expanding our understanding of the human brain in health, disease, development, and aging. Network analyses are quickly becoming the method of choice for analyzing functional MRI data. However, many technical issues have yet to be confronted in order to optimize results. One particular issue that remains controversial in functional brain network analyses is the definition of a network node. In functional brain networks a node represents some predefined collection of brain tissue, and an edge measures the functional connectivity between pairs of nodes. The characteristics of a node, chosen by the researcher, vary considerably in the literature. This manuscript reviews the current state of the art based on published manuscripts and highlights the strengths and weaknesses of three main methods for defining nodes. Voxel-wise networks are constructed by assigning a node to each, equally sized brain area (voxel). The fMRI time-series recorded from each voxel is then used to create the functional network. Anatomical methods utilize atlases to define the nodes based on brain structure. The fMRI time-series from all voxels within the anatomical area are averaged and subsequently used to generate the network. Functional activation methods rely on data from traditional fMRI activation studies, often from databases, to identify network nodes. Such methods identify the peaks or centers of mass from activation maps to determine the location of the nodes. Small (~10-20 millimeter diameter) spheres located at the coordinates of the activation foci are then applied to the data being used in the network analysis. The fMRI time-series from all voxels in the sphere are then averaged, and the resultant time series is used to generate the network. We attempt to clarify the discussion and move the study of complex brain networks forward. While the "correct" method to be used remains an open, possibly unsolvable question that deserves extensive
Synchronization of fractional order complex dynamical networks
NASA Astrophysics Data System (ADS)
Wang, Yu; Li, Tianzeng
2015-06-01
In this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied. A fractional order controller for synchronization of complex network is presented. Some new sufficient synchronization criteria are proposed based on the Lyapunov stability theory and the LaSalle invariance principle. These synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling-configuration matrix and the inner-coupling matrix are not assumed to be symmetric or irreducible. It means that this method is more general and effective. Numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method.
Exploring the Morphospace of Communication Efficiency in Complex Networks
Goñi, Joaquín; Avena-Koenigsberger, Andrea; Velez de Mendizabal, Nieves; van den Heuvel, Martijn P.; Betzel, Richard F.; Sporns, Olaf
2013-01-01
Graph theoretical analysis has played a key role in characterizing global features of the topology of complex networks, describing diverse systems such as protein interactions, food webs, social relations and brain connectivity. How system elements communicate with each other depends not only on the structure of the network, but also on the nature of the system's dynamics which are constrained by the amount of knowledge and resources available for communication processes. Complementing widely used measures that capture efficiency under the assumption that communication preferentially follows shortest paths across the network (“routing”), we define analytic measures directed at characterizing network communication when signals flow in a random walk process (“diffusion”). The two dimensions of routing and diffusion efficiency define a morphospace for complex networks, with different network topologies characterized by different combinations of efficiency measures and thus occupying different regions of this space. We explore the relation of network topologies and efficiency measures by examining canonical network models, by evolving networks using a multi-objective optimization strategy, and by investigating real-world network data sets. Within the efficiency morphospace, specific aspects of network topology that differentially favor efficient communication for routing and diffusion processes are identified. Charting regions of the morphospace that are occupied by canonical, evolved or real networks allows inferences about the limits of communication efficiency imposed by connectivity and dynamics, as well as the underlying selection pressures that have shaped network topology. PMID:23505455
Network Motifs: Simple Building Blocks of Complex Networks
NASA Astrophysics Data System (ADS)
Milo, R.; Shen-Orr, S.; Itzkovitz, S.; Kashtan, N.; Chklovskii, D.; Alon, U.
2002-10-01
Complex networks are studied across many fields of science. To uncover their structural design principles, we defined ``network motifs,'' patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks. We found such motifs in networks from biochemistry, neurobiology, ecology, and engineering. The motifs shared by ecological food webs were distinct from the motifs shared by the genetic networks of Escherichia coli and Saccharomyces cerevisiae or from those found in the World Wide Web. Similar motifs were found in networks that perform information processing, even though they describe elements as different as biomolecules within a cell and synaptic connections between neurons in Caenorhabditis elegans. Motifs may thus define universal classes of networks. This approach may uncover the basic building blocks of most networks.
The complex network reliability and influential nodes
NASA Astrophysics Data System (ADS)
Li, Kai; He, Yongfeng
2017-08-01
In order to study the complex network node important degree and reliability, considering semi-local centrality, betweenness centrality and PageRank algorithm, through the simulation method to gradually remove nodes and recalculate the importance in the random network, small world network and scale-free network. Study the relationship between the largest connected component and node removed proportion, the research results show that betweenness centrality and PageRank algorithm based on the global information network are more effective for evaluating the importance of nodes, and the reliability of the network is related to the network topology.
Higher-order organization of complex networks
Benson, Austin R.; Gleich, David F.; Leskovec, Jure
2016-01-01
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be captured at the level of individual nodes and edges. However, higher-order organization of complex networks—at the level of small network subgraphs—remains largely unknown. Here, we develop a generalized framework for clustering networks on the basis of higher-order connectivity patterns. This framework provides mathematical guarantees on the optimality of obtained clusters and scales to networks with billions of edges. The framework reveals higher-order organization in a number of networks, including information propagation units in neuronal networks and hub structure in transportation networks. Results show that networks exhibit rich higher-order organizational structures that are exposed by clustering based on higher-order connectivity patterns. PMID:27387949
Small-time Scale Network Traffic Prediction Based on Complex-valued Neural Network
NASA Astrophysics Data System (ADS)
Yang, Bin
2017-07-01
Accurate models play an important role in capturing the significant characteristics of the network traffic, analyzing the network dynamic, and improving the forecasting accuracy for system dynamics. In this study, complex-valued neural network (CVNN) model is proposed to further improve the accuracy of small-time scale network traffic forecasting. Artificial bee colony (ABC) algorithm is proposed to optimize the complex-valued and real-valued parameters of CVNN model. Small-scale traffic measurements data namely the TCP traffic data is used to test the performance of CVNN model. Experimental results reveal that CVNN model forecasts the small-time scale network traffic measurement data very accurately
Realizing actual feedback control of complex network
NASA Astrophysics Data System (ADS)
Tu, Chengyi; Cheng, Yuhua
2014-06-01
In this paper, we present the concept of feedbackability and how to identify the Minimum Feedbackability Set of an arbitrary complex directed network. Furthermore, we design an estimator and a feedback controller accessing one MFS to realize actual feedback control, i.e. control the system to our desired state according to the estimated system internal state from the output of estimator. Last but not least, we perform numerical simulations of a small linear time-invariant dynamics network and a real simple food network to verify the theoretical results. The framework presented here could make an arbitrary complex directed network realize actual feedback control and deepen our understanding of complex systems.
Realizing actual feedback control of complex network
NASA Astrophysics Data System (ADS)
Tu, Chengyi; Cheng, Yuhua
2014-06-01
In this paper, we present the concept of feedbackability and how to identify the Minimum Feedbackability Set of an arbitrary complex directed network. Furthermore, we design an estimator and a feedback controller accessing one MFS to realize actual feedback control, i.e. control the system to our desired state according to the estimated system internal state from the output of estimator. Last but not least, we perform numerical simulations of a small linear time-invariant dynamics network and a real simple food network to verify the theoretical results. The framework presented here could make an arbitrary complex directed network realize actual feedback control and deepen our understanding of complex systems.
Grip on complexity in chemical reaction networks
2017-01-01
A new discipline of “systems chemistry” is emerging, which aims to capture the complexity observed in natural systems within a synthetic chemical framework. Living systems rely on complex networks of chemical reactions to control the concentration of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. To truly understand how living systems function, we need a complete understanding of how chemical reaction networks (CRNs) create function. We propose the development of a bottom-up approach to design and construct CRNs where we can follow the influence of single chemical entities on the properties of the network as a whole. Ultimately, this approach should allow us to not only understand such complex networks but also to guide and control their behavior. PMID:28845192
Synchronization in complex networks with adaptive coupling
NASA Astrophysics Data System (ADS)
Zhang, Rong; Hu, Manfeng; Xu, Zhenyuan
2007-08-01
Generally it is very difficult to realized synchronization for some complex networks. In order to synchronize, the coupling coefficient of networks has to be very large, especially when the number of coupled nodes is larger. In this Letter, we consider the problem of synchronization in complex networks with adaptive coupling. A new concept about asymptotic stability is presented, then we proved by using the well-known LaSalle invariance principle, that the state of such a complex network can synchronize an arbitrary assigned state of an isolated node of the network as long as the feedback gain is positive. Unified system is simulated as the nodes of adaptive coupling complex networks with different topologies.
Grip on complexity in chemical reaction networks.
Wong, Albert S Y; Huck, Wilhelm T S
2017-01-01
A new discipline of "systems chemistry" is emerging, which aims to capture the complexity observed in natural systems within a synthetic chemical framework. Living systems rely on complex networks of chemical reactions to control the concentration of molecules in space and time. Despite the enormous complexity in biological networks, it is possible to identify network motifs that lead to functional outputs such as bistability or oscillations. To truly understand how living systems function, we need a complete understanding of how chemical reaction networks (CRNs) create function. We propose the development of a bottom-up approach to design and construct CRNs where we can follow the influence of single chemical entities on the properties of the network as a whole. Ultimately, this approach should allow us to not only understand such complex networks but also to guide and control their behavior.
Chaos synchronization of general complex dynamical networks
NASA Astrophysics Data System (ADS)
Lü, Jinhu; Yu, Xinghuo; Chen, Guanrong
2004-03-01
Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical network model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization of a time-varying complex network is determined by means of the inner coupled link matrix, the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix, rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network. Especially, we do not assume that the coupled configuration matrix is symmetric and its off-diagonal elements are nonnegative, which in a way generalizes the related results existing in the literature.
Pinning impulsive control algorithms for complex network
Sun, Wen; Lü, Jinhu; Chen, Shihua; Yu, Xinghuo
2014-03-15
In this paper, we further investigate the synchronization of complex dynamical network via pinning control in which a selection of nodes are controlled at discrete times. Different from most existing work, the pinning control algorithms utilize only the impulsive signals at discrete time instants, which may greatly improve the communication channel efficiency and reduce control cost. Two classes of algorithms are designed, one for strongly connected complex network and another for non-strongly connected complex network. It is suggested that in the strongly connected network with suitable coupling strength, a single controller at any one of the network's nodes can always pin the network to its homogeneous solution. In the non-strongly connected case, the location and minimum number of nodes needed to pin the network are determined by the Frobenius normal form of the coupling matrix. In addition, the coupling matrix is not necessarily symmetric or irreducible. Illustrative examples are then given to validate the proposed pinning impulsive control algorithms.
Effective Augmentation of Complex Networks
Wang, Jinjian; Yu, Xinghuo; Stone, Lewi
2016-01-01
Networks science plays an enormous role in many aspects of modern society from distributing electrical power across nations to spreading information and social networking amongst global populations. While modern networks constantly change in size, few studies have sought methods for the difficult task of optimising this growth. Here we study theoretical requirements for augmenting networks by adding source or sink nodes, without requiring additional driver-nodes to accommodate the change i.e., conserving structural controllability. Our “effective augmentation” algorithm takes advantage of clusters intrinsic to the network topology, and permits rapidly and efficient augmentation of a large number of nodes in one time-step. “Effective augmentation” is shown to work successfully on a wide range of model and real networks. The method has numerous applications (e.g. study of biological, social, power and technological networks) and potentially of significant practical and economic value. PMID:27165120
Effective Augmentation of Complex Networks
NASA Astrophysics Data System (ADS)
Wang, Jinjian; Yu, Xinghuo; Stone, Lewi
2016-05-01
Networks science plays an enormous role in many aspects of modern society from distributing electrical power across nations to spreading information and social networking amongst global populations. While modern networks constantly change in size, few studies have sought methods for the difficult task of optimising this growth. Here we study theoretical requirements for augmenting networks by adding source or sink nodes, without requiring additional driver-nodes to accommodate the change i.e., conserving structural controllability. Our “effective augmentation” algorithm takes advantage of clusters intrinsic to the network topology, and permits rapidly and efficient augmentation of a large number of nodes in one time-step. “Effective augmentation” is shown to work successfully on a wide range of model and real networks. The method has numerous applications (e.g. study of biological, social, power and technological networks) and potentially of significant practical and economic value.
Contagion on complex networks with persuasion.
Huang, Wei-Min; Zhang, Li-Jie; Xu, Xin-Jian; Fu, Xinchu
2016-03-31
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.
Contagion on complex networks with persuasion
NASA Astrophysics Data System (ADS)
Huang, Wei-Min; Zhang, Li-Jie; Xu, Xin-Jian; Fu, Xinchu
2016-03-01
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense.
A Complexity Theory of Neural Networks
1991-08-09
Significant progress has been made in laying the foundations of a complexity theory of neural networks . The fundamental complexity classes have been...identified and studied. The class of problems solvable by small, shallow neural networks has been found to be the same class even if (1) probabilistic...behaviour (2)Multi-valued logic, and (3)analog behaviour, are allowed (subject to certain resonable technical assumptions). Neural networks can be
Constrained target controllability of complex networks
NASA Astrophysics Data System (ADS)
Guo, Wei-Feng; Zhang, Shao-Wu; Wei, Ze-Gang; Zeng, Tao; Liu, Fei; Zhang, Jingsong; Wu, Fang-Xiang; Chen, Luonan
2017-06-01
It is of great theoretical interest and practical significance to study how to control a system by applying perturbations to only a few driver nodes. Recently, a hot topic of modern network researches is how to determine driver nodes that allow the control of an entire network. However, in practice, to control a complex network, especially a biological network, one may know not only the set of nodes which need to be controlled (i.e. target nodes), but also the set of nodes to which only control signals can be applied (i.e. constrained control nodes). Compared to the general concept of controllability, we introduce the concept of constrained target controllability (CTC) of complex networks, which concerns the ability to drive any state of target nodes to their desirable state by applying control signals to the driver nodes from the set of constrained control nodes. To efficiently investigate the CTC of complex networks, we further design a novel graph-theoretic algorithm called CTCA to estimate the ability of a given network to control targets by choosing driver nodes from the set of constrained control nodes. We extensively evaluate the CTC of numerous real complex networks. The results indicate that biological networks with a higher average degree are easier to control than biological networks with a lower average degree, while electronic networks with a lower average degree are easier to control than web networks with a higher average degree. We also show that our CTCA can more efficiently produce driver nodes for target-controlling the networks than existing state-of-the-art methods. Moreover, we use our CTCA to analyze two expert-curated bio-molecular networks and compare to other state-of-the-art methods. The results illustrate that our CTCA can efficiently identify proven drug targets and new potentials, according to the constrained controllability of those biological networks.
Revealing the Hidden Language of Complex Networks
NASA Astrophysics Data System (ADS)
Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Davis, Darren; Levnajic, Zoran; Janjic, Vuk; Karapandza, Rasa; Stojmirovic, Aleksandar; Pržulj, Nataša
2014-04-01
Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network's structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a country's role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists.
Revealing the Hidden Language of Complex Networks
Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Davis, Darren; Levnajic, Zoran; Janjic, Vuk; Karapandza, Rasa; Stojmirovic, Aleksandar; Pržulj, Nataša
2014-01-01
Sophisticated methods for analysing complex networks promise to be of great benefit to almost all scientific disciplines, yet they elude us. In this work, we make fundamental methodological advances to rectify this. We discover that the interaction between a small number of roles, played by nodes in a network, can characterize a network's structure and also provide a clear real-world interpretation. Given this insight, we develop a framework for analysing and comparing networks, which outperforms all existing ones. We demonstrate its strength by uncovering novel relationships between seemingly unrelated networks, such as Facebook, metabolic, and protein structure networks. We also use it to track the dynamics of the world trade network, showing that a country's role of a broker between non-trading countries indicates economic prosperity, whereas peripheral roles are associated with poverty. This result, though intuitive, has escaped all existing frameworks. Finally, our approach translates network topology into everyday language, bringing network analysis closer to domain scientists. PMID:24686408
Jamming in complex networks with degree correlation
NASA Astrophysics Data System (ADS)
Pastore Y Piontti, Ana; Braunstein, Lidia; Macri, Pablo
2012-02-01
We study the effects of the degree-degree correlations on the pressure congestion J for a diffusive transport process on scale free complex networks. Using the gradient network approach we find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally, we apply our transportation process to real world networks, and the results agree with our findings for model networks.
CORRELATION PROFILES AND MOTIFS IN COMPLEX NETWORKS.
MASLOV,S.SNEPPEN,K.ALON,U.
2004-01-16
Networks have recently emerged as a unifying theme in complex systems research [1]. It is in fact no coincidence that networks and complexity are so heavily intertwined. Any future definition of a complex system should reflect the fact that such systems consist of many mutually interacting components. These components are far from being identical as say electrons in systems studied by condensed matter physics. In a truly complex system each of them has a unique identity allowing one to separate it from the others. The very first question one may ask about such a system is which other components a given component interacts with? This information system wide can be visualized as a graph, whose nodes correspond to individual components of the complex system in question and edges to their mutual interactions. Such a network can be thought of as a backbone of the complex system. Of course, system's dynamics depends not only on the topology of an underlying network but also on the exact form of interaction of components with each other, which can be very different in various complex systems. However, the underlying network may contain clues about the basic design principles and/or evolutionary history of the complex system in question. The goal of this article is to provide readers with a set of useful tools that would help to decide which features of a complex network are there by pure chance alone, and which of them were possibly designed or evolved to their present state.
Center of mass in complex networks
NASA Astrophysics Data System (ADS)
Fu, Chuanji; Gao, Yachun; Cai, Shimin; Yang, Hongchun; Yang, Chun
2017-01-01
Network dynamics is always a big challenge in nonlinear dynamics. Although great advancements have been made in various types of complex systems, an universal theoretical framework is required. In this paper, we introduce the concept of center of ‘mass’ of complex networks, where ‘mass’ stands for node importance or centrality in contrast to that of particle systems, and further prove that the phase transition and evolutionary state of the system can be characterized by the activity of center of ‘mass’. The steady states of several complex networks (gene regulatory networks and epidemic spreading systems) are then studied by analytically calculating the decoupled equation of the dynamic activity of center of ‘mass’, which is derived from the dynamic equation of the complex networks. The limitations of this method are also pointed out, such as the dynamical problems that related with the relative activities among components, and those systems that consist of oscillatory or chaotic motions.
A random interacting network model for complex networks
Goswami, Bedartha; Shekatkar, Snehal M.; Rheinwalt, Aljoscha; Ambika, G.; Kurths, Jürgen
2015-01-01
We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems. PMID:26657032
Percolation of localized attack on complex networks
NASA Astrophysics Data System (ADS)
Shao, Shuai; Huang, Xuqing; Stanley, H. Eugene; Havlin, Shlomo
2015-02-01
The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erdős-Rényi networks, random-regular networks, and scale-free networks. Our results provide insight into how to better protect networks, enhance cybersecurity, and facilitate the design of more robust infrastructures.
Complex Networks: from Graph Theory to Biology
NASA Astrophysics Data System (ADS)
Lesne, Annick
2006-12-01
The aim of this text is to show the central role played by networks in complex system science. A remarkable feature of network studies is to lie at the crossroads of different disciplines, from mathematics (graph theory, combinatorics, probability theory) to physics (statistical physics of networks) to computer science (network generating algorithms, combinatorial optimization) to biological issues (regulatory networks). New paradigms recently appeared, like that of ‘scale-free networks’ providing an alternative to the random graph model introduced long ago by Erdös and Renyi. With the notion of statistical ensemble and methods originally introduced for percolation networks, statistical physics is of high relevance to get a deep account of topological and statistical properties of a network. Then their consequences on the dynamics taking place in the network should be investigated. Impact of network theory is huge in all natural sciences, especially in biology with gene networks, metabolic networks, neural networks or food webs. I illustrate this brief overview with a recent work on the influence of network topology on the dynamics of coupled excitable units, and the insights it provides about network emerging features, robustness of network behaviors, and the notion of static or dynamic motif.
Controlling complex networks with conformity behavior
NASA Astrophysics Data System (ADS)
Wang, Xu-Wen; Nie, Sen; Wang, Wen-Xu; Wang, Bing-Hong
2015-09-01
Controlling complex networks accompanied by common conformity behavior is a fundamental problem in social and physical science. Conformity behavior that individuals tend to follow the majority in their neighborhood is common in human society and animal communities. Despite recent progress in understanding controllability of complex networks, the existent controllability theories cannot be directly applied to networks associated with conformity. Here we propose a simple model to incorporate conformity-based decision making into the evolution of a network system, which allows us to employ the exact controllability theory to explore the controllability of such systems. We offer rigorous theoretical results of controllability for representative regular networks. We also explore real networks in different fields and some typical model networks, finding some interesting results that are different from the predictions of structural and exact controllability theory in the absence of conformity. We finally present an example of steering a real social network to some target states to further validate our controllability theory and tools. Our work offers a more realistic understanding of network controllability with conformity behavior and can have potential applications in networked evolutionary games, opinion dynamics and many other complex networked systems.
Managing Complex Network Operation with Predictive Analytics
Huang, Zhenyu; Wong, Pak C.; Mackey, Patrick S.; Chen, Yousu; Ma, Jian; Schneider, Kevin P.; Greitzer, Frank L.
2008-03-26
Complex networks play an important role in modern societies. Their failures, such as power grid blackouts, would lead to significant disruption of people’s life, industry and commercial activities, and result in massive economic losses. Operation of these complex networks is an extremely challenging task due to their complex structures, wide geographical coverage, complex data/information technology systems, and highly dynamic and nonlinear behaviors. None of the complex network operation is fully automated; human-in-the-loop operation is critical. Given the complexity involved, there may be thousands of possible topological configurations at any given time. During an emergency, it is not uncommon for human operators to examine thousands of possible configurations in near real-time to choose the best option and operate the network effectively. In today’s practice, network operation is largely based on experience with very limited real-time decision support, resulting in inadequate management of complex predictions and inability to anticipate, recognize, and respond to situations caused by human errors, natural disasters, and cyber attacks. A systematic approach is needed to manage the complex operation paradigms and choose the best option in a near-real-time manner. This paper applies predictive analytics techniques to establish a decision support system for complex network operation management and help operators to predict potential network failures and adapt the network to adverse situations. The resultant decision support system enables continuous monitoring of network performance and turns large amounts of data into actionable information. Examples with actual power grid data are presented to demonstrate the capability of this proposed decision support system.
Detecting link failures in complex network processes using remote monitoring
NASA Astrophysics Data System (ADS)
Dhal, R.; Abad Torres, J.; Roy, S.
2015-11-01
We study whether local structural changes in a complex network can be distinguished from passive remote time-course measurements of the network's dynamics. Specifically the detection of link failures in a network synchronization process from noisy measurements at a single network component is considered. By phrasing the detection task as a Maximum A Posteriori Probability hypothesis testing problem, we are able to obtain conditions under which the detection is (1) improved over the a priori and (2) asymptotically perfect, in terms of the network spectrum and graph. We find that, in the case where the detector has knowledge of the network's state, perfect detection is possible under general connectivity conditions regardless of the measurement location. When the detector does not have state knowledge, a remote signature permits improved but not perfect detection, under the same connectivity conditions. At its essence, detectability is achieved because of the close connection between a network's topology, its eigenvalues and local response characteristics.
Covered conductors fault behavior studied by features of complex networks
NASA Astrophysics Data System (ADS)
Vantuch, Tomas; Zelinka, Ivan
2017-07-01
The representation of analyzed data by complex network brings different views on the problem which could lead into the increase of the number of valuable features. The study described in this paper aims on the representation of the similarities of pulses from the classified signal into the complex network. The analysis of signals' pulses is purposed by correct classification of the signals measured on medium voltage (MV) overhead lines with application of covered conductors (CC). There is plenty of features available to extract from complex network, therefore they should be properly analyzed and evaluated according their relevancy.
Optimization of spatial complex networks
NASA Astrophysics Data System (ADS)
Guillier, S.; Muñoz, V.; Rogan, J.; Zarama, R.; Valdivia, J. A.
2017-02-01
First, we estimate the connectivity properties of a predefined (fixed node locations) spatial network which optimizes a connectivity functional that balances construction and transportation costs. In this case we obtain a Gaussian distribution for the connectivity. However, when we consider these spatial networks in a growing process, we obtain a power law distribution for the connectivity. If the transportation costs in the functional involve the shortest geometrical path, we obtain a scaling exponent γ = 2.5. However, if the transportation costs in the functional involve just the shortest path, we obtain γ = 2.2. Both cases may be useful to analyze in some real networks.
Power grid vulnerability: A complex network approach
NASA Astrophysics Data System (ADS)
Arianos, S.; Bompard, E.; Carbone, A.; Xue, F.
2009-03-01
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.
Power grid vulnerability: a complex network approach.
Arianos, S; Bompard, E; Carbone, A; Xue, F
2009-03-01
Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.
Statistically Validated Networks in Bipartite Complex Systems
Tumminello, Michele; Miccichè, Salvatore; Lillo, Fabrizio; Piilo, Jyrki; Mantegna, Rosario N.
2011-01-01
Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved. PMID:21483858
Measurement of Online Social Networks
ERIC Educational Resources Information Center
Gjoka, Mina
2010-01-01
In recent years, the popularity of online social networks (OSN) has risen to unprecedented levels, with the most popular ones having hundreds of millions of users. This success has generated interest within the networking community and has given rise to a number of measurement and characterization studies, which provide a first step towards their…
Measurement of Online Social Networks
ERIC Educational Resources Information Center
Gjoka, Mina
2010-01-01
In recent years, the popularity of online social networks (OSN) has risen to unprecedented levels, with the most popular ones having hundreds of millions of users. This success has generated interest within the networking community and has given rise to a number of measurement and characterization studies, which provide a first step towards their…
Benchmarking Measures of Network Influence
NASA Astrophysics Data System (ADS)
Bramson, Aaron; Vandermarliere, Benjamin
2016-09-01
Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.
Benchmarking Measures of Network Influence
Bramson, Aaron; Vandermarliere, Benjamin
2016-01-01
Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures. PMID:27670635
Universality in complex networks: random matrix analysis.
Bandyopadhyay, Jayendra N; Jalan, Sarika
2007-08-01
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world, and random networks follow universal Gaussian orthogonal ensemble statistics of random matrix theory. Second, we show an analogy between the onset of small-world behavior, quantified by the structural properties of networks, and the transition from Poisson to Gaussian orthogonal ensemble statistics, quantified by Brody parameter characterizing a spectral property. We also present our analysis for a protein-protein interaction network in budding yeast.
Fluctuations in percolation of sparse complex networks
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra
2017-07-01
We study the role of fluctuations in percolation of sparse complex networks. To this end we consider two random correlated realizations of the initial damage of the nodes and we evaluate the fraction of nodes that are expected to remain in the giant component of the network in both cases or just in one case. Our framework includes a message-passing algorithm able to predict the fluctuations in a single network, and an analytic prediction of the expected fluctuations in ensembles of sparse networks. This approach is applied to real ecological and infrastructure networks and it is shown to characterize the expected fluctuations in their response to external damage.
Optimal dynamic bandwidth allocation for complex networks
NASA Astrophysics Data System (ADS)
Jiang, Zhong-Yuan; Liang, Man-Gui; Li, Qian; Guo, Dong-Chao
2013-03-01
Traffic capacity of one network strongly depends on the link’s bandwidth allocation strategy. In previous bandwidth allocation mechanisms, once one link’s bandwidth is allocated, it will be fixed throughout the overall traffic transmission process. However, the traffic load of every link changes from time to time. In this paper, with finite total bandwidth resource of the network, we propose to dynamically allocate the total bandwidth resource in which each link’s bandwidth is proportional to the queue length of the output buffer of the link per time step. With plenty of data packets in the network, the traffic handling ability of all links of the network achieves full utilization. The theoretical analysis and the extensive simulation results on complex networks are consistent. This work is valuable for network service providers to improve network performance or to do reasonable network design efficiently.
Jamming in complex networks with degree correlation
NASA Astrophysics Data System (ADS)
Pastore y Piontti, Ana L.; Braunstein, Lidia A.; Macri, Pablo A.
2010-10-01
We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model.
Error and attack tolerance of complex networks
NASA Astrophysics Data System (ADS)
Albert, Réka; Jeong, Hawoong; Barabási, Albert-László
2000-07-01
Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network. Complex communication networks display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.
Measuring and modeling correlations in multiplex networks
NASA Astrophysics Data System (ADS)
Nicosia, Vincenzo; Latora, Vito
2015-09-01
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multilayer networks, i.e., networks where each layer stands for a different type of interaction between the same set of nodes. There is today a growing interest in understanding when and why a description in terms of a multiplex network is necessary and more informative than a single-layer projection. Here we contribute to this debate by presenting a comprehensive study of correlations in multiplex networks. Correlations in node properties, especially degree-degree correlations, have been thoroughly studied in single-layer networks. Here we extend this idea to investigate and characterize correlations between the different layers of a multiplex network. Such correlations are intrinsically multiplex, and we first study them empirically by constructing and analyzing several multiplex networks from the real world. In particular, we introduce various measures to characterize correlations in the activity of the nodes and in their degree at the different layers and between activities and degrees. We show that real-world networks exhibit indeed nontrivial multiplex correlations. For instance, we find cases where two layers of the same multiplex network are positively correlated in terms of node degrees, while other two layers are negatively correlated. We then focus on constructing synthetic multiplex networks, proposing a series of models to reproduce the correlations observed empirically and/or to assess their relevance.
Measuring and modeling correlations in multiplex networks.
Nicosia, Vincenzo; Latora, Vito
2015-09-01
The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multilayer networks, i.e., networks where each layer stands for a different type of interaction between the same set of nodes. There is today a growing interest in understanding when and why a description in terms of a multiplex network is necessary and more informative than a single-layer projection. Here we contribute to this debate by presenting a comprehensive study of correlations in multiplex networks. Correlations in node properties, especially degree-degree correlations, have been thoroughly studied in single-layer networks. Here we extend this idea to investigate and characterize correlations between the different layers of a multiplex network. Such correlations are intrinsically multiplex, and we first study them empirically by constructing and analyzing several multiplex networks from the real world. In particular, we introduce various measures to characterize correlations in the activity of the nodes and in their degree at the different layers and between activities and degrees. We show that real-world networks exhibit indeed nontrivial multiplex correlations. For instance, we find cases where two layers of the same multiplex network are positively correlated in terms of node degrees, while other two layers are negatively correlated. We then focus on constructing synthetic multiplex networks, proposing a series of models to reproduce the correlations observed empirically and/or to assess their relevance.
Traffic congestion in interconnected complex networks
NASA Astrophysics Data System (ADS)
Tan, Fei; Wu, Jiajing; Xia, Yongxiang; Tse, Chi K.
2014-06-01
Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic congestion in coupled complex networks, however, is still relatively unexplored. In this paper, we try to explore the effect of interconnections on traffic congestion in interconnected Barabási-Albert scale-free networks. We find that assortative coupling can alleviate traffic congestion more readily than disassortative and random coupling when the node processing capacity is allocated based on node usage probability. Furthermore, the optimal coupling probability can be found for assortative coupling. However, three types of coupling preferences achieve similar traffic performance if all nodes share the same processing capacity. We analyze interconnected Internet autonomous-system-level graphs of South Korea and Japan and obtain similar results. Some practical suggestions are presented to optimize such real-world interconnected networks accordingly.
Epidemic outbreaks in complex heterogeneous networks
NASA Astrophysics Data System (ADS)
Moreno, Y.; Pastor-Satorras, R.; Vespignani, A.
2002-04-01
We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures.
Traffic congestion in interconnected complex networks.
Tan, Fei; Wu, Jiajing; Xia, Yongxiang; Tse, Chi K
2014-06-01
Traffic congestion in isolated complex networks has been investigated extensively over the last decade. Coupled network models have recently been developed to facilitate further understanding of real complex systems. Analysis of traffic congestion in coupled complex networks, however, is still relatively unexplored. In this paper, we try to explore the effect of interconnections on traffic congestion in interconnected Barabási-Albert scale-free networks. We find that assortative coupling can alleviate traffic congestion more readily than disassortative and random coupling when the node processing capacity is allocated based on node usage probability. Furthermore, the optimal coupling probability can be found for assortative coupling. However, three types of coupling preferences achieve similar traffic performance if all nodes share the same processing capacity. We analyze interconnected Internet autonomous-system-level graphs of South Korea and Japan and obtain similar results. Some practical suggestions are presented to optimize such real-world interconnected networks accordingly.
Distinguishing fiction from non-fiction with complex networks
NASA Astrophysics Data System (ADS)
Larue, David M.; Carr, Lincoln D.; Jones, Linnea K.; Stevanak, Joe T.
2014-03-01
Complex Network Measures are applied to networks constructed from texts in English to demonstrate an initial viability in textual analysis. Texts from novels and short stories obtained from Project Gutenberg and news stories obtained from NPR are selected. Unique word stems in a text are used as nodes in an associated unweighted undirected network, with edges connecting words occurring within a certain number of words somewhere in the text. Various combinations of complex network measures are computed for each text's network. Fisher's Linear Discriminant analysis is used to build a parameter optimizing the ability to separate the texts according to their genre. Success rates in the 70% range for correctly distinguishing fiction from non-fiction were obtained using edges defined as within four words, using 400 word samples from 400 texts from each of the two genres with some combinations of measures such as the power-law exponents of degree distributions and clustering coefficients.
Topological structural classes of complex networks
NASA Astrophysics Data System (ADS)
Estrada, Ernesto
2007-01-01
We use theoretical principles to study how complex networks are topologically organized at large scale. Using spectral graph theory we predict the existence of four different topological structural classes of networks. These classes correspond, respectively, to highly homogenous networks lacking structural bottlenecks, networks organized into highly interconnected modules with low inter-community connectivity, networks with a highly connected central core surrounded by a sparser periphery, and networks displaying a combination of highly connected groups (quasicliques) and groups of nodes partitioned into disjoint subsets (quasibipartites). Here we show by means of the spectral scaling method that these classes really exist in real-world ecological, biological, informational, technological, and social networks. We show that neither of three network growth mechanisms—random with uniform distribution, preferential attachment, and random with the same degree sequence as real network—is able to reproduce the four structural classes of complex networks. These models reproduce two of the network classes as a function of the average degree but completely fail in reproducing the other two classes of networks.
Experimental flux measurements on a network scale
Schwender, J.
2011-10-11
Metabolic flux is a fundamental property of living organisms. In recent years, methods for measuring metabolic flux in plants on a network scale have evolved further. One major challenge in studying flux in plants is the complexity of the plant's metabolism. In particular, in the presence of parallel pathways in multiple cellular compartments, the core of plant central metabolism constitutes a complex network. Hence, a common problem with the reliability of the contemporary results of {sup 13}C-Metabolic Flux Analysis in plants is the substantial reduction in complexity that must be included in the simulated networks; this omission partly is due to limitations in computational simulations. Here, I discuss recent emerging strategies that will better address these shortcomings.
Competing epidemics on complex networks
NASA Astrophysics Data System (ADS)
Karrer, Brian; Newman, M. E. J.
2011-09-01
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.
Synchronization reveals topological scales in complex networks.
Arenas, Alex; Díaz-Guilera, Albert; Pérez-Vicente, Conrad J
2006-03-24
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.
An Adaptive Complex Network Model for Brain Functional Networks
Gomez Portillo, Ignacio J.; Gleiser, Pablo M.
2009-01-01
Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution. PMID:19738902
Localized recovery of complex networks against failure
NASA Astrophysics Data System (ADS)
Shang, Yilun
2016-07-01
Resilience of complex networks to failure has been an important issue in network research for decades, and recent studies have begun to focus on the inverse recovery of network functionality through strategically healing missing nodes or edges. However, the effect of network recovery is far from fully understood, and a general theory is still missing. Here we propose and study a general model of localized recovery, where a group of neighboring nodes are restored in an invasive way from a seed node. We develop a theoretical framework to compare the effect of random recovery (RR) and localized recovery (LR) in complex networks including Erdős-Rényi networks, random regular networks, and scale-free networks. We find detailed phase diagrams for the subnetwork of occupied nodes and the “complement network” of failed nodes under RR and LR. By identifying the two competitive forces behind LR, we present an analytical and numerical approach to guide us in choosing the appropriate recovery strategy and provide estimation on its effect by using the degree distribution of the original network as the only input. Our work therefore provides insight for quantitatively understanding recovery process and its implications in infrastructure protection in various complex systems.
Localized recovery of complex networks against failure
Shang, Yilun
2016-01-01
Resilience of complex networks to failure has been an important issue in network research for decades, and recent studies have begun to focus on the inverse recovery of network functionality through strategically healing missing nodes or edges. However, the effect of network recovery is far from fully understood, and a general theory is still missing. Here we propose and study a general model of localized recovery, where a group of neighboring nodes are restored in an invasive way from a seed node. We develop a theoretical framework to compare the effect of random recovery (RR) and localized recovery (LR) in complex networks including Erdős-Rényi networks, random regular networks, and scale-free networks. We find detailed phase diagrams for the subnetwork of occupied nodes and the “complement network” of failed nodes under RR and LR. By identifying the two competitive forces behind LR, we present an analytical and numerical approach to guide us in choosing the appropriate recovery strategy and provide estimation on its effect by using the degree distribution of the original network as the only input. Our work therefore provides insight for quantitatively understanding recovery process and its implications in infrastructure protection in various complex systems. PMID:27456202
Applications of Complex Networks on Analysis of World Trade Network
NASA Astrophysics Data System (ADS)
Lee, Jae Woo; Maeng, Seong Eun; Ha, Gyeong-Gyun; Hyeok Lee, Moon; Cho, Eun Seong
2013-02-01
We consider the wealth and the money flow of the world trade data. We analyze the world trade data from year 1948 to 2000 which include the total amounts of the import and export for every country per year. We apply the analyzing methods of the complex networks to the world trade network. We define the wealth as the gross domestic products (GDP) of each country. We defined the backbone network of the world trade network. We generate the backbone network keeping the link with the largest wealth flowing out each country by the import and deleting all remaining links. We observed that the wealth was transferred from the poorer countries to the wealthier countries. We found the asymmetry of the world trade flow by the disparity of the networks. From the backbone network of the world trade we can identify the regional economic connections and wealth flow among the countries.
Maximizing information exchange between complex networks
NASA Astrophysics Data System (ADS)
West, Bruce J.; Geneston, Elvis L.; Grigolini, Paolo
2008-10-01
Science is not merely the smooth progressive interaction of hypothesis, experiment and theory, although it sometimes has that form. More realistically the scientific study of any given complex phenomenon generates a number of explanations, from a variety of perspectives, that eventually requires synthesis to achieve a deep level of insight and understanding. One such synthesis has created the field of out-of-equilibrium statistical physics as applied to the understanding of complex dynamic networks. Over the past forty years the concept of complexity has undergone a metamorphosis. Complexity was originally seen as a consequence of memory in individual particle trajectories, in full agreement with a Hamiltonian picture of microscopic dynamics and, in principle, macroscopic dynamics could be derived from the microscopic Hamiltonian picture. The main difficulty in deriving macroscopic dynamics from microscopic dynamics is the need to take into account the actions of a very large number of components. The existence of events such as abrupt jumps, considered by the conventional continuous time random walk approach to describing complexity was never perceived as conflicting with the Hamiltonian view. Herein we review many of the reasons why this traditional Hamiltonian view of complexity is unsatisfactory. We show that as a result of technological advances, which make the observation of single elementary events possible, the definition of complexity has shifted from the conventional memory concept towards the action of non-Poisson renewal events. We show that the observation of crucial processes, such as the intermittent fluorescence of blinking quantum dots as well as the brain’s response to music, as monitored by a set of electrodes attached to the scalp, has forced investigators to go beyond the traditional concept of complexity and to establish closer contact with the nascent field of complex networks. Complex networks form one of the most challenging areas of
Static pairwise annihilation in complex networks
NASA Astrophysics Data System (ADS)
Laguna, M. F.; Aldana, M.; Larralde, H.; Parris, P. E.; Kenkre, V. M.
2005-08-01
We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the “hubs” have been annihilated, the network disintegrates and only isolated sites are left.
Onset of traffic congestion in complex networks.
Zhao, Liang; Lai, Ying-Cheng; Park, Kwangho; Ye, Nong
2005-02-01
Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.
Correlated measurement error hampers association network inference.
Kaduk, Mateusz; Hoefsloot, Huub C J; Vis, Daniel J; Reijmers, Theo; van der Greef, Jan; Smilde, Age K; Hendriks, Margriet M W B
2014-09-01
Modern chromatography-based metabolomics measurements generate large amounts of data in the form of abundances of metabolites. An increasingly popular way of representing and analyzing such data is by means of association networks. Ideally, such a network can be interpreted in terms of the underlying biology. A property of chromatography-based metabolomics data is that the measurement error structure is complex: apart from the usual (random) instrumental error there is also correlated measurement error. This is intrinsic to the way the samples are prepared and the analyses are performed and cannot be avoided. The impact of correlated measurement errors on (partial) correlation networks can be large and is not always predictable. The interplay between relative amounts of uncorrelated measurement error, correlated measurement error and biological variation defines this impact. Using chromatography-based time-resolved lipidomics data obtained from a human intervention study we show how partial correlation based association networks are influenced by correlated measurement error. We show how the effect of correlated measurement error on partial correlations is different for direct and indirect associations. For direct associations the correlated measurement error usually has no negative effect on the results, while for indirect associations, depending on the relative size of the correlated measurement error, results can become unreliable. The aim of this paper is to generate awareness of the existence of correlated measurement errors and their influence on association networks. Time series lipidomics data is used for this purpose, as it makes it possible to visually distinguish the correlated measurement error from a biological response. Underestimating the phenomenon of correlated measurement error will result in the suggestion of biologically meaningful results that in reality rest solely on complicated error structures. Using proper experimental designs that allow
Controlling extreme events on complex networks
NASA Astrophysics Data System (ADS)
Chen, Yu-Zhong; Huang, Zi-Gang; Lai, Ying-Cheng
2014-08-01
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network ``mobile'' can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
Topology identification of complex dynamical networks
NASA Astrophysics Data System (ADS)
Zhao, Junchan; Li, Qin; Lu, Jun-An; Jiang, Zhong-Ping
2010-06-01
Recently, some researchers investigated the topology identification for complex networks via LaSalle's invariance principle. The principle cannot be directly applied to time-varying systems since the positive limit sets are generally not invariant. In this paper, we study the topology identification problem for a class of weighted complex networks with time-varying node systems. Adaptive identification laws are proposed to estimate the coupling parameters of the networks with and without communication delays. We prove that the asymptotic identification is ensured by a persistently exciting condition. Numerical simulations are given to demonstrate the effectiveness of the proposed approach.
Construction of ontology augmented networks for protein complex prediction.
Zhang, Yijia; Lin, Hongfei; Yang, Zhihao; Wang, Jian
2013-01-01
Protein complexes are of great importance in understanding the principles of cellular organization and function. The increase in available protein-protein interaction data, gene ontology and other resources make it possible to develop computational methods for protein complex prediction. Most existing methods focus mainly on the topological structure of protein-protein interaction networks, and largely ignore the gene ontology annotation information. In this article, we constructed ontology augmented networks with protein-protein interaction data and gene ontology, which effectively unified the topological structure of protein-protein interaction networks and the similarity of gene ontology annotations into unified distance measures. After constructing ontology augmented networks, a novel method (clustering based on ontology augmented networks) was proposed to predict protein complexes, which was capable of taking into account the topological structure of the protein-protein interaction network, as well as the similarity of gene ontology annotations. Our method was applied to two different yeast protein-protein interaction datasets and predicted many well-known complexes. The experimental results showed that (i) ontology augmented networks and the unified distance measure can effectively combine the structure closeness and gene ontology annotation similarity; (ii) our method is valuable in predicting protein complexes and has higher F1 and accuracy compared to other competing methods.
The price of complexity in financial networks
May, Robert M.; Roukny, Tarik; Stiglitz, Joseph E.
2016-01-01
Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises. PMID:27555583
Travel and tourism: Into a complex network
NASA Astrophysics Data System (ADS)
Miguéns, J. I. L.; Mendes, J. F. F.
2008-05-01
It is discussed how the worldwide tourist arrivals, about 10% of the world’s domestic product, form a largely heterogeneous and directed complex network. Remarkably the random network of connectivity is converted into a scale-free network of intensities. The importance of weights on network connections is brought into discussion. It is also shown how strategic positioning particularly benefits from market diversity and that interactions among countries prevail on a technological and economic pattern, questioning the backbone of driving forces in traveling.
The price of complexity in financial networks.
Battiston, Stefano; Caldarelli, Guido; May, Robert M; Roukny, Tarik; Stiglitz, Joseph E
2016-09-06
Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.
The price of complexity in financial networks
NASA Astrophysics Data System (ADS)
Battiston, Stefano; Caldarelli, Guido; May, Robert M.; Roukny, Tarik; Stiglitz, Joseph E.
2016-09-01
Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.
Analysis of complex networks using aggressive abstraction.
Colbaugh, Richard; Glass, Kristin.; Willard, Gerald
2008-10-01
This paper presents a new methodology for analyzing complex networks in which the network of interest is first abstracted to a much simpler (but equivalent) representation, the required analysis is performed using the abstraction, and analytic conclusions are then mapped back to the original network and interpreted there. We begin by identifying a broad and important class of complex networks which admit abstractions that are simultaneously dramatically simplifying and property preserving we call these aggressive abstractions -- and which can therefore be analyzed using the proposed approach. We then introduce and develop two forms of aggressive abstraction: 1.) finite state abstraction, in which dynamical networks with uncountable state spaces are modeled using finite state systems, and 2.) onedimensional abstraction, whereby high dimensional network dynamics are captured in a meaningful way using a single scalar variable. In each case, the property preserving nature of the abstraction process is rigorously established and efficient algorithms are presented for computing the abstraction. The considerable potential of the proposed approach to complex networks analysis is illustrated through case studies involving vulnerability analysis of technological networks and predictive analysis for social processes.
Predicting and Controlling Complex Networks
2015-06-22
networks and control . . . . . . . . . . . . . . . . . . . 7 3.4 Pattern formation, synchronization and outbreak of biodiversity in cyclically...Ni, Y.-C. Lai, and C. Grebogi, “Pattern formation, synchronization and outbreak of biodiversity in cyclically competing games,” Physical Review E 83...of Physics B 76, 179-183 (2010). 3.4 Pattern formation, synchronization and outbreak of biodiversity in cyclically competing games Biodiversity is
Quantum Navigation and Ranking in Complex Networks
NASA Astrophysics Data System (ADS)
Sánchez-Burillo, Eduardo; Duch, Jordi; Gómez-Gardeñes, Jesús; Zueco, David
2012-08-01
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.
Quantum Navigation and Ranking in Complex Networks
Sánchez-Burillo, Eduardo; Duch, Jordi; Gómez-Gardeñes, Jesús; Zueco, David
2012-01-01
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems. PMID:22930671
Identifying influential nodes in complex networks based on AHP
NASA Astrophysics Data System (ADS)
Bian, Tian; Hu, Jiantao; Deng, Yong
2017-08-01
In the field of complex networks, how to identify influential nodes in the network is still an important research topic. In this paper, a method to identify the influence of the node based on Analytic Hierarchy Process (AHP) is proposed. AHP, as a multiple attribute decision making (MADM) technique has become an important branch of decision making since then. Every centrality measure has its own disadvantages and limitations, thus we consider several different centrality measures as the multi-attribute of complex network in AHP application. AHP is used to aggregate the multi-attribute to obtain the evaluation of the influence of each node. The experiments on four real networks and an informative network show the efficiency and practicability of the proposed method.
Shock waves on complex networks
Mones, Enys; Araújo, Nuno A. M.; Vicsek, Tamás; Herrmann, Hans J.
2014-01-01
Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and affect a significant fraction of the network. Almost discontinuous perturbations can be modeled by shock waves which can eventually interfere constructively and endanger the normal functionality of the infrastructure. We study their dynamics by solving the Burgers equation under random perturbations on several real and artificial directed graphs. Even for graphs with a narrow distribution of node properties (e.g., degree or betweenness), a steady state is reached exhibiting a heterogeneous load distribution, having a difference of one order of magnitude between the highest and average loads. Unexpectedly we find for the European power grid and for finite Watts-Strogatz networks a broad pronounced bimodal distribution for the loads. To identify the most vulnerable nodes, we introduce the concept of node-basin size, a purely topological property which we show to be strongly correlated to the average load of a node. PMID:24821422
Phase transitions in complex network dynamics
NASA Astrophysics Data System (ADS)
Squires, Shane
Two phase transitions in complex networks are analyzed. The first of these is a percolation transition, in which the network develops a macroscopic connected component as edges are added to it. Recent work has shown that if edges are added "competitively" to an undirected network, the onset of percolation is abrupt or "explosive." A new variant of explosive percolation is introduced here for directed networks, whose critical behavior is explored using numerical simulations and finite-size scaling theory. This process is also characterized by a very rapid percolation transition, but it is not as sudden as in undirected networks. The second phase transition considered here is the emergence of instability in Boolean networks, a class of dynamical systems that are widely used to model gene regulation. The dynamics, which are determined by the network topology and a set of update rules, may be either stable or unstable, meaning that small perturbations to the state of the network either die out or grow to become macroscopic. Here, this transition is analytically mapped onto a well-studied percolation problem, which can be used to predict the average steady-state distance between perturbed and unperturbed trajectories. This map applies to specific Boolean networks with few restrictions on network topology, but can only be applied to two commonly used types of update rules. Finally, a method is introduced for predicting the stability of Boolean networks with a much broader range of update rules. The network is assumed to have a given complex topology, subject only to a locally tree-like condition, and the update rules may be correlated with topological features of the network. While past work has addressed the separate effects of topology and update rules on stability, the present results are the first widely applicable approach to studying how these effects interact. Numerical simulations agree with the theory and show that such correlations between topology and update
Towards a trustworthy distributed architecture for complex sensing networks
NASA Astrophysics Data System (ADS)
Schubert, Heidi; Luke, Jahn A.
2012-06-01
Fast, efficient distributed computing enables much more capable sensing systems for defense and commercial applications. However, distributed systems face distributed threats. These threats can be countered with a distributed trustworthiness architecture that measures and enforces trust across a network. Currently, there are no designs for distributed trust architectures suitable for complex systems. We present such an architecture, which measures nodes' trustworthiness before they join the network and while they are operational. In order to facilitate the computation and enforcement of trust, a distributed sensing network has to integrate a new type of component. We define the trust agents in terms of capabilities that support trustworthiness measurements.
Evolution of Complex Modular Biological Networks
Hintze, Arend; Adami, Christoph
2008-01-01
Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein–protein interaction network, synthetic lethal gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks. PMID:18266463
Complex Cooperative Networks from Evolutionary Preferential Attachment
Poncela, Julia; Gómez-Gardeñes, Jesús; Floría, Luis M.; Sánchez, Angel; Moreno, Yamir
2008-01-01
In spite of its relevance to the origin of complex networks, the interplay between form and function and its role during network formation remains largely unexplored. While recent studies introduce dynamics by considering rewiring processes of a pre-existent network, we study network growth and formation by proposing an evolutionary preferential attachment model, its main feature being that the capacity of a node to attract new links depends on a dynamical variable governed in turn by the node interactions. As a specific example, we focus on the problem of the emergence of cooperation by analyzing the formation of a social network with interactions given by the Prisoner's Dilemma. The resulting networks show many features of real systems, such as scale-free degree distributions, cooperative behavior and hierarchical clustering. Interestingly, results such as the cooperators being located mostly on nodes of intermediate degree are very different from the observations of cooperative behavior on static networks. The evolutionary preferential attachment mechanism points to an evolutionary origin of scale-free networks and may help understand similar feedback problems in the dynamics of complex networks by appropriately choosing the game describing the interaction of nodes. PMID:18560601
Characterizing time series: when Granger causality triggers complex networks
NASA Astrophysics Data System (ADS)
Ge, Tian; Cui, Yindong; Lin, Wei; Kurths, Jürgen; Liu, Chong
2012-08-01
In this paper, we propose a new approach to characterize time series with noise perturbations in both the time and frequency domains by combining Granger causality and complex networks. We construct directed and weighted complex networks from time series and use representative network measures to describe their physical and topological properties. Through analyzing the typical dynamical behaviors of some physical models and the MIT-BIHMassachusetts Institute of Technology-Beth Israel Hospital. human electrocardiogram data sets, we show that the proposed approach is able to capture and characterize various dynamics and has much potential for analyzing real-world time series of rather short length.
Cascade defense via routing in complex networks
NASA Astrophysics Data System (ADS)
Xu, Xiao-Lan; Du, Wen-Bo; Hong, Chen
2015-05-01
As the cascading failures in networked traffic systems are becoming more and more serious, research on cascade defense in complex networks has become a hotspot in recent years. In this paper, we propose a traffic-based cascading failure model, in which each packet in the network has its own source and destination. When cascade is triggered, packets will be redistributed according to a given routing strategy. Here, a global hybrid (GH) routing strategy, which uses the dynamic information of the queue length and the static information of nodes' degree, is proposed to defense the network cascade. Comparing GH strategy with the shortest path (SP) routing, efficient routing (ER) and global dynamic (GD) routing strategies, we found that GH strategy is more effective than other routing strategies in improving the network robustness against cascading failures. Our work provides insight into the robustness of networked traffic systems.
Epidemic extinction paths in complex networks
NASA Astrophysics Data System (ADS)
Hindes, Jason; Schwartz, Ira B.
2017-05-01
We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.
Distributed multiple path routing in complex networks
NASA Astrophysics Data System (ADS)
Chen, Guang; Wang, San-Xiu; Wu, Ling-Wei; Mei, Pan; Yang, Xu-Hua; Wen, Guang-Hui
2016-12-01
Routing in complex transmission networks is an important problem that has garnered extensive research interest in the recent years. In this paper, we propose a novel routing strategy called the distributed multiple path (DMP) routing strategy. For each of the O-D node pairs in a given network, the DMP routing strategy computes and stores multiple short-length paths that overlap less with each other in advance. And during the transmission stage, it rapidly selects an actual routing path which provides low transmission cost from the pre-computed paths for each transmission task, according to the real-time network transmission status information. Computer simulation results obtained for the lattice, ER random, and scale-free networks indicate that the strategy can significantly improve the anti-congestion ability of transmission networks, as well as provide favorable routing robustness against partial network failures.
Random matrix analysis of complex networks.
Jalan, Sarika; Bandyopadhyay, Jayendra N
2007-10-01
We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of the adjacency matrix of various model networks, namely, random, scale-free, and small-world networks. These distributions follow the Gaussian orthogonal ensemble statistic of RMT. To probe long-range correlations in the eigenvalues we study spectral rigidity via the Delta_{3} statistic of RMT as well. It follows RMT prediction of linear behavior in semilogarithmic scale with the slope being approximately 1pi;{2} . Random and scale-free networks follow RMT prediction for very large scale. A small-world network follows it for sufficiently large scale, but much less than the random and scale-free networks.
Chain motifs: the tails and handles of complex networks.
Boas, Paulino R Villas; Rodrigues, Francisco A; Travieso, Gonzalo; Costa, Luciano da Fontoura
2008-02-01
A great part of the interest in complex networks has been motivated by the presence of structured, frequently nonuniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they provide the means to identify and classify several types of complex network, it becomes important to obtain meaningful measurements of the local network topology. In addition to traditional features such as the node degree, clustering coefficient, and shortest path, motifs have been introduced in the literature in order to provide complementary descriptions of the network connectivity. The current work proposes a different type of motif, namely, chains of nodes, that is, sequences of connected nodes with degree 2. These chains have been subdivided into cords, tails, rings, and handles, depending on the type of their extremities (e.g., open or connected). A theoretical analysis of the density of such motifs in random and scale-free networks is described, and an algorithm for identifying these motifs in general networks is presented. The potential of considering chains for network characterization has been illustrated with respect to five categories of real-world networks including 16 cases. Several interesting findings were obtained, including the fact that several chains were observed in real-world networks, especially the world wide web, books, and the power grid. The possibility of chains resulting from incompletely sampled networks is also investigated.
Common neighbour structure and similarity intensity in complex networks
NASA Astrophysics Data System (ADS)
Hou, Lei; Liu, Kecheng
2017-10-01
Complex systems as networks always exhibit strong regularities, implying underlying mechanisms governing their evolution. In addition to the degree preference, the similarity has been argued to be another driver for networks. Assuming a network is randomly organised without similarity preference, the present paper studies the expected number of common neighbours between vertices. A symmetrical similarity index is accordingly developed by removing such expected number from the observed common neighbours. The developed index can not only describe the similarities between vertices, but also the dissimilarities. We further apply the proposed index to measure of the influence of similarity on the wring patterns of networks. Fifteen empirical networks as well as artificial networks are examined in terms of similarity intensity and degree heterogeneity. Results on real networks indicate that, social networks are strongly governed by the similarity as well as the degree preference, while the biological networks and infrastructure networks show no apparent similarity governance. Particularly, classical network models, such as the Barabási-Albert model, the Erdös-Rényi model and the Ring Lattice, cannot well describe the social networks in terms of the degree heterogeneity and similarity intensity. The findings may shed some light on the modelling and link prediction of different classes of networks.
Network model of bilateral power markets based on complex networks
NASA Astrophysics Data System (ADS)
Wu, Yang; Liu, Junyong; Li, Furong; Yan, Zhanxin; Zhang, Li
2014-06-01
The bilateral power transaction (BPT) mode becomes a typical market organization with the restructuring of electric power industry, the proper model which could capture its characteristics is in urgent need. However, the model is lacking because of this market organization's complexity. As a promising approach to modeling complex systems, complex networks could provide a sound theoretical framework for developing proper simulation model. In this paper, a complex network model of the BPT market is proposed. In this model, price advantage mechanism is a precondition. Unlike other general commodity transactions, both of the financial layer and the physical layer are considered in the model. Through simulation analysis, the feasibility and validity of the model are verified. At same time, some typical statistical features of BPT network are identified. Namely, the degree distribution follows the power law, the clustering coefficient is low and the average path length is a bit long. Moreover, the topological stability of the BPT network is tested. The results show that the network displays a topological robustness to random market member's failures while it is fragile against deliberate attacks, and the network could resist cascading failure to some extent. These features are helpful for making decisions and risk management in BPT markets.
Opinion control in complex networks
NASA Astrophysics Data System (ADS)
Masuda, Naoki
2015-03-01
In many political elections, the electorate appears to be a composite of partisan and independent voters. Given that partisans are not likely to convert to a different party, an important goal for a political party could be to mobilize independent voters toward the party with the help of strong leadership, mass media, partisans, and the effects of peer-to-peer influence. Based on the exact solution of classical voter model dynamics in the presence of perfectly partisan voters (i.e., zealots), we propose a computational method that uses pinning control strategy to maximize the share of a party in a social network of independent voters. The party, corresponding to the controller or zealots, optimizes the nodes to be controlled given the information about the connectivity of independent voters and the set of nodes that the opposing party controls. We show that controlling hubs is generally a good strategy, but the optimized strategy is even better. The superiority of the optimized strategy is particularly eminent when the independent voters are connected as directed (rather than undirected) networks.
Finding instabilities in the community structure of complex networks
NASA Astrophysics Data System (ADS)
Gfeller, David; Chappelier, Jean-Cédric; de Los Rios, Paolo
2005-11-01
The problem of finding clusters in complex networks has been studied by mathematicians, computer scientists, and, more recently, by physicists. Many of the existing algorithms partition a network into clear clusters without overlap. Here we introduce a method to identify the nodes lying “between clusters,” allowing for a general measure of the stability of the clusters. This is done by adding noise over the edge weights. Our method can in principle be used with almost any clustering algorithm able to deal with weighted networks. We present several applications on real-world networks using two different clustering algorithms.
Assembly of complex plant–fungus networks
Toju, Hirokazu; Guimarães, Paulo R.; Olesen, Jens M.; Thompson, John N.
2014-01-01
Species in ecological communities build complex webs of interaction. Although revealing the architecture of these networks is fundamental to understanding ecological and evolutionary dynamics in nature, it has been difficult to characterize the structure of most species-rich ecological systems. By overcoming this limitation through next-generation sequencing technology, we herein uncover the network architecture of below-ground plant–fungus symbioses, which are ubiquitous to terrestrial ecosystems. The examined symbiotic network of a temperate forest in Japan includes 33 plant species and 387 functionally and phylogenetically diverse fungal taxa, and the overall network architecture differs fundamentally from that of other ecological networks. In contrast to results for other ecological networks and theoretical predictions for symbiotic networks, the plant–fungus network shows moderate or relatively low levels of interaction specialization and modularity and an unusual pattern of ‘nested’ network architecture. These results suggest that species-rich ecological networks are more architecturally diverse than previously recognized. PMID:25327887
Contagion on complex networks with persuasion
Huang, Wei-Min; Zhang, Li-Jie; Xu, Xin-Jian; Fu, Xinchu
2016-01-01
The threshold model has been widely adopted as a classic model for studying contagion processes on social networks. We consider asymmetric individual interactions in social networks and introduce a persuasion mechanism into the threshold model. Specifically, we study a combination of adoption and persuasion in cascading processes on complex networks. It is found that with the introduction of the persuasion mechanism, the system may become more vulnerable to global cascades, and the effects of persuasion tend to be more significant in heterogeneous networks than those in homogeneous networks: a comparison between heterogeneous and homogeneous networks shows that under weak persuasion, heterogeneous networks tend to be more robust against random shocks than homogeneous networks; whereas under strong persuasion, homogeneous networks are more stable. Finally, we study the effects of adoption and persuasion threshold heterogeneity on systemic stability. Though both heterogeneities give rise to global cascades, the adoption heterogeneity has an overwhelmingly stronger impact than the persuasion heterogeneity when the network connectivity is sufficiently dense. PMID:27029498
Complex networks repair strategies: Dynamic models
NASA Astrophysics Data System (ADS)
Fu, Chaoqi; Wang, Ying; Gao, Yangjun; Wang, Xiaoyang
2017-09-01
Network repair strategies are tactical methods that restore the efficiency of damaged networks; however, unreasonable repair strategies not only waste resources, they are also ineffective for network recovery. Most extant research on network repair focuses on static networks, but results and findings on static networks cannot be applied to evolutionary dynamic networks because, in dynamic models, complex network repair has completely different characteristics. For instance, repaired nodes face more severe challenges, and require strategic repair methods in order to have a significant effect. In this study, we propose the Shell Repair Strategy (SRS) to minimize the risk of secondary node failures due to the cascading effect. Our proposed method includes the identification of a set of vital nodes that have a significant impact on network repair and defense. Our identification of these vital nodes reduces the number of switching nodes that face the risk of secondary failures during the dynamic repair process. This is positively correlated with the size of the average degree < k > and enhances network invulnerability.
Complex Network for Solar Active Regions
NASA Astrophysics Data System (ADS)
Daei, Farhad; Safari, Hossein; Dadashi, Neda
2017-08-01
In this paper we developed a complex network of solar active regions (ARs) to study various local and global properties of the network. The values of the Hurst exponent (0.8-0.9) were evaluated by both the detrended fluctuation analysis and the rescaled range analysis applied on the time series of the AR numbers. The findings suggest that ARs can be considered as a system of self-organized criticality (SOC). We constructed a growing network based on locations, occurrence times, and the lifetimes of 4227 ARs recorded from 1999 January 1 to 2017 April 14. The behavior of the clustering coefficient shows that the AR network is not a random network. The logarithmic behavior of the length scale has the characteristics of a so-called small-world network. It is found that the probability distribution of the node degrees for undirected networks follows the power law with exponents of about 3.7-4.2. This indicates the scale-free nature of the AR network. The scale-free and small-world properties of the AR network confirm that the system of ARs forms a system of SOC. Our results show that the occurrence probability of flares (classified by GOES class C> 5, M, and X flares) in the position of the AR network hubs takes values greater than that obtained for other nodes.
Robust Reconstruction of Complex Networks from Sparse Data
NASA Astrophysics Data System (ADS)
Han, Xiao; Shen, Zhesi; Wang, Wen-Xu; Di, Zengru
2015-01-01
Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust reconstruction of complex networks from sparse and noisy data. Specifically, we decompose the task of reconstructing the whole network into recovering local structures centered at each node. Thus, the natural sparsity of complex networks ensures a conversion from the local structure reconstruction into a sparse signal reconstruction problem that can be addressed by using the lasso, a convex optimization method. We apply our method to evolutionary games, transportation, and communication processes taking place in a variety of model and real complex networks, finding that universal high reconstruction accuracy can be achieved from sparse data in spite of noise in time series and missing data of partial nodes. Our approach opens new routes to the network reconstruction problem and has potential applications in a wide range of fields.
Self-organized topology of recurrence-based complex networks
Yang, Hui Liu, Gang
2013-12-15
With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article is to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., “what is the self-organizing geometry of a recurrence network?” and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.
Self-organized topology of recurrence-based complex networks
NASA Astrophysics Data System (ADS)
Yang, Hui; Liu, Gang
2013-12-01
With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article is to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., "what is the self-organizing geometry of a recurrence network?" and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.
Self-organized topology of recurrence-based complex networks.
Yang, Hui; Liu, Gang
2013-12-01
With the rapid technological advancement, network is almost everywhere in our daily life. Network theory leads to a new way to investigate the dynamics of complex systems. As a result, many methods are proposed to construct a network from nonlinear time series, including the partition of state space, visibility graph, nearest neighbors, and recurrence approaches. However, most previous works focus on deriving the adjacency matrix to represent the complex network and extract new network-theoretic measures. Although the adjacency matrix provides connectivity information of nodes and edges, the network geometry can take variable forms. The research objective of this article is to develop a self-organizing approach to derive the steady geometric structure of a network from the adjacency matrix. We simulate the recurrence network as a physical system by treating the edges as springs and the nodes as electrically charged particles. Then, force-directed algorithms are developed to automatically organize the network geometry by minimizing the system energy. Further, a set of experiments were designed to investigate important factors (i.e., dynamical systems, network construction methods, force-model parameter, nonhomogeneous distribution) affecting this self-organizing process. Interestingly, experimental results show that the self-organized geometry recovers the attractor of a dynamical system that produced the adjacency matrix. This research addresses a question, i.e., "what is the self-organizing geometry of a recurrence network?" and provides a new way to reproduce the attractor or time series from the recurrence plot. As a result, novel network-theoretic measures (e.g., average path length and proximity ratio) can be achieved based on actual node-to-node distances in the self-organized network topology. The paper brings the physical models into the recurrence analysis and discloses the spatial geometry of recurrence networks.
Analytical and experimental study on complex compressed air pipe network
NASA Astrophysics Data System (ADS)
Gai, Yushou; Cai, Maolin; Shi, Yan
2015-09-01
To analyze the working characteristics of complex compressed air networks, numerical methods are widely used which are based on finite element technology or intelligent algorithms. However, the effectiveness of the numerical methods is limited. In this paper, to provide a new method to optimize the design and the air supply strategy of the complex compressed air pipe network, firstly, a novel method to analyze the topology structure of the compressed air flow in the pipe network is initially proposed. A matrix is used to describe the topology structure of the compressed air flow. Moreover, based on the analysis of the pressure loss of the pipe network, the relationship between the pressure and the flow of the compressed air is derived, and a prediction method of pressure fluctuation and air flow in a segment in a complex pipe network is proposed. Finally, to inspect the effectiveness of the method, an experiment with a complex network is designed. The pressure and the flow of airflow in the network are measured and studied. The results of the study show that, the predicted results with the proposed method have a good consistency with the experimental results, and that verifies the air flow prediction method of the complex pipe network. This research proposes a new method to analyze the compressed air network and a prediction method of pressure fluctuation and air flow in a segment, which can predicate the fluctuation of the pressure according to the flow of compressed air, and predicate the fluctuation of the flow according to the pressure in a segment of a complex pipe network.
Social Synchrony on Complex Networks.
Xuan, Qi; Zhang, Zhi-Yuan; Fu, Chenbo; Hu, Hong-Xiang; Filkov, Vladimir
2017-05-09
Social synchrony (SS) is an emergent phenomenon in human society. People often mimic others which, over time, can result in large groups behaving similarly. Drawing from prior empirical studies of SS in online communities, here we propose a discrete network model of SS based on four attributes: 1) depth of action; 2) breadth of impact, i.e., a large number of actions are performed with a large group of people involved; 3) heterogeneity of role, i.e., people of higher degree play more important roles; and 4) lastly, emergence of phenomenon, i.e., it is far from random. We analyze our model both analytically and with simulations, and find good agreement between the two. We find this model can well explain the four characters of SS, and thus hope it can help researchers better understand human collective behavior.
Social networks as embedded complex adaptive systems.
Benham-Hutchins, Marge; Clancy, Thomas R
2010-09-01
As systems evolve over time, their natural tendency is to become increasingly more complex. Studies in the field of complex systems have generated new perspectives on management in social organizations such as hospitals. Much of this research appears as a natural extension of the cross-disciplinary field of systems theory. This is the 15th in a series of articles applying complex systems science to the traditional management concepts of planning, organizing, directing, coordinating, and controlling. In this article, the authors discuss healthcare social networks as a hierarchy of embedded complex adaptive systems. The authors further examine the use of social network analysis tools as a means to understand complex communication patterns and reduce medical errors.
Predictive Control of Large Complex Networks
NASA Astrophysics Data System (ADS)
Haber, Aleksandar; Motter, Adilson E.
Networks of coupled dynamical subsystems are increasingly used to represent complex natural and engineered systems. While recent technological developments give us improved means to actively control the dynamics of individual subsystems in various domains, network control remains a challenging problem due to difficulties imposed by intrinsic nonlinearities, control constraints, and the large-scale nature of the systems. In this talk, we will present a model predictive control approach that is effective while accounting for these realistic properties of complex networks. Our method can systematically identify control interventions that steer the trajectory to a desired state, even in the presence of strong nonlinearities and constraints. Numerical tests show that the method is applicable to a variety of networks, ranging from power grids to chemical reaction systems.
Complex Dynamics in Information Sharing Networks
NASA Astrophysics Data System (ADS)
Cronin, Bruce
This study examines the roll-out of an electronic knowledge base in a medium-sized professional services firm over a six year period. The efficiency of such implementation is a key business problem in IT systems of this type. Data from usage logs provides the basis for analysis of the dynamic evolution of social networks around the depository during this time. The adoption pattern follows an "s-curve" and usage exhibits something of a power law distribution, both attributable to network effects, and network position is associated with organisational performance on a number of indicators. But periodicity in usage is evident and the usage distribution displays an exponential cut-off. Further analysis provides some evidence of mathematical complexity in the periodicity. Some implications of complex patterns in social network data for research and management are discussed. The study provides a case study demonstrating the utility of the broad methodological approach.
Complex network analysis of time series
NASA Astrophysics Data System (ADS)
Gao, Zhong-Ke; Small, Michael; Kurths, Jürgen
2016-12-01
Revealing complicated behaviors from time series constitutes a fundamental problem of continuing interest and it has attracted a great deal of attention from a wide variety of fields on account of its significant importance. The past decade has witnessed a rapid development of complex network studies, which allow to characterize many types of systems in nature and technology that contain a large number of components interacting with each other in a complicated manner. Recently, the complex network theory has been incorporated into the analysis of time series and fruitful achievements have been obtained. Complex network analysis of time series opens up new venues to address interdisciplinary challenges in climate dynamics, multiphase flow, brain functions, ECG dynamics, economics and traffic systems.
Structurally robust control of complex networks
NASA Astrophysics Data System (ADS)
Nacher, Jose C.; Akutsu, Tatsuya
2015-01-01
Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called controllers. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on complex networks including scale-free topologies. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations, and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard nonrobust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in Caenorhabditis elegans, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.
Micro-Macro Analysis of Complex Networks
Marchiori, Massimo; Possamai, Lino
2015-01-01
Complex systems have attracted considerable interest because of their wide range of applications, and are often studied via a “classic” approach: study a specific system, find a complex network behind it, and analyze the corresponding properties. This simple methodology has produced a great deal of interesting results, but relies on an often implicit underlying assumption: the level of detail on which the system is observed. However, in many situations, physical or abstract, the level of detail can be one out of many, and might also depend on intrinsic limitations in viewing the data with a different level of abstraction or precision. So, a fundamental question arises: do properties of a network depend on its level of observability, or are they invariant? If there is a dependence, then an apparently correct network modeling could in fact just be a bad approximation of the true behavior of a complex system. In order to answer this question, we propose a novel micro-macro analysis of complex systems that quantitatively describes how the structure of complex networks varies as a function of the detail level. To this extent, we have developed a new telescopic algorithm that abstracts from the local properties of a system and reconstructs the original structure according to a fuzziness level. This way we can study what happens when passing from a fine level of detail (“micro”) to a different scale level (“macro”), and analyze the corresponding behavior in this transition, obtaining a deeper spectrum analysis. The obtained results show that many important properties are not universally invariant with respect to the level of detail, but instead strongly depend on the specific level on which a network is observed. Therefore, caution should be taken in every situation where a complex network is considered, if its context allows for different levels of observability. PMID:25635812
Competitive cluster growth in complex networks
NASA Astrophysics Data System (ADS)
Moreira, André A.; Paula, Demétrius R.; Costa Filho, Raimundo N.; Andrade, José S., Jr.
2006-06-01
In this work we propose an idealized model for competitive cluster growth in complex networks. Each cluster can be thought of as a fraction of a community that shares some common opinion. Our results show that the cluster size distribution depends on the particular choice for the topology of the network of contacts among the agents. As an application, we show that the cluster size distributions obtained when the growth process is performed on hierarchical networks, e.g., the Apollonian network, have a scaling form similar to what has been observed for the distribution of a number of votes in an electoral process. We suggest that this similarity may be due to the fact that social networks involved in the electoral process may also possess an underlining hierarchical structure.
Characterizing English Poetic Style Using Complex Networks
NASA Astrophysics Data System (ADS)
Roxas-Villanueva, Ranzivelle Marianne; Nambatac, Maelori Krista; Tapang, Giovanni
Complex networks have been proven useful in characterizing written texts. Here, we use networks to probe if there exist a similarity within, and difference across, era as reflected within the poem's structure. In literary history, boundary lines are set to distinguish the change in writing styles through time. We obtain the network parameters and motif frequencies of 845 poems published from 1522 to 1931 and relate this to the writing of the Elizabethan, 17th Century, Augustan, Romantic and Victorian eras. Analysis of the different network parameters shows a significant difference of the Augustan era (1667-1780) with the rest. The network parameters and the convex hull and centroids of the motif frequencies reflect the adjectival sequence pattern of the poems of the Augustan era.
Identifying community structure in complex networks
NASA Astrophysics Data System (ADS)
Shao, Chenxi; Duan, Yubing
2015-07-01
A wide variety of applications could be formulated to resolve the problem of finding all communities from a given network, ranging from social and biological network analysis to web mining and searching. In this study, we propose the concept of virtual attractive strength between each pair of node in networks, and then give the definition of community structure based on the proposed attractive strength. Furthermore, we present a community detection method by moving vertices to the clusters that produce the largest attractive strengths to them until the division of network reaches unchanged. Experimental results on synthetic and real networks indicate that the proposed approach has favorite effectiveness and fast convergence speed, which provides an efficient method for exploring and analyzing complex systems.
The complexity of Chinese syntactic dependency networks
NASA Astrophysics Data System (ADS)
Liu, Haitao
2008-05-01
This paper proposes how to build a syntactic network based on syntactic theory and presents some statistical properties of Chinese syntactic dependency networks based on two Chinese treebanks with different genres. The results show that the two syntactic networks are small-world networks, and their degree distributions obey a power law. The finding, that the two syntactic networks have the same diameter and different average degrees, path lengths, clustering coefficients and power exponents, can be seen as an indicator that complexity theory can work as a means of stylistic study. The paper links the degree of a vertex with a valency of a word, the small world with the minimized average distance of a language, that reinforces the explanations of the findings from linguistics.
Center of mass in complex networks
Fu, Chuanji; Gao, Yachun; Cai, Shimin; Yang, Hongchun; Yang, Chun
2017-01-01
Network dynamics is always a big challenge in nonlinear dynamics. Although great advancements have been made in various types of complex systems, an universal theoretical framework is required. In this paper, we introduce the concept of center of ‘mass’ of complex networks, where ‘mass’ stands for node importance or centrality in contrast to that of particle systems, and further prove that the phase transition and evolutionary state of the system can be characterized by the activity of center of ‘mass’. The steady states of several complex networks (gene regulatory networks and epidemic spreading systems) are then studied by analytically calculating the decoupled equation of the dynamic activity of center of ‘mass’, which is derived from the dynamic equation of the complex networks. The limitations of this method are also pointed out, such as the dynamical problems that related with the relative activities among components, and those systems that consist of oscillatory or chaotic motions. PMID:28106109
Size reduction of complex networks preserving modularity
NASA Astrophysics Data System (ADS)
Arenas, A.; Duch, J.; Fernández, A.; Gómez, S.
2007-06-01
The ubiquity of modular structure in real-world complex networks is the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the non-deterministic polynomial-time hard (NP-hard) class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining their modularity. This size reduction allows use of heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the extremal optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.
Complexity, dynamic cellular network, and tumorigenesis.
Waliszewski, P
1997-01-01
A holistic approach to tumorigenesis is proposed. The main element of the model is the existence of dynamic cellular network. This network comprises a molecular and an energetistic structure of a cell connected through the multidirectional flow of information. The interactions within dynamic cellular network are complex, stochastic, nonlinear, and also involve quantum effects. From this non-reductionist perspective, neither tumorigenesis can be limited to the genetic aspect, nor the initial event must be of molecular nature, nor mutations and epigenetic factors are mutually exclusive, nor a link between cause and effect can be established. Due to complexity, an unstable stationary state of dynamic cellular network rather than a group of unrelated genes determines the phenotype of normal and transformed cells. This implies relativity of tumor suppressor genes and oncogenes. A bifurcation point is defined as an unstable state of dynamic cellular network leading to the other phenotype-stationary state. In particular, the bifurcation point may be determined by a change of expression of a single gene. Then, the gene is called bifurcation point gene. The unstable stationary state facilitates the chaotic dynamics. This may result in a fractal dimension of both normal and tumor tissues. The co-existence of chaotic dynamics and complexity is the essence of cellular processes and shapes differentiation, morphogenesis, and tumorigenesis. In consequence, tumorigenesis is a complex, unpredictable process driven by the interplay between self-organisation and selection.
Size reduction of complex networks preserving modularity
Arenas, A.; Duch, J.; Fernandez, A.; Gomez, S.
2008-12-24
The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.
Studies on a network of complex neurons
NASA Astrophysics Data System (ADS)
Chakravarthy, Srinivasa V.; Ghosh, Joydeep
1993-08-01
In the last decade, much effort has been directed towards understanding the role of chaos in the brain. Work with rabbits reveals that in the resting state the electrical activity on the surface of the olfactory bulb is chaotic. But, when the animal is involved in a recognition task, the activity shifts to a specific pattern corresponding to the odor that is being recognized. Unstable, quasiperiodic behavior can be found in a class of conservative, deterministic physical systems called the Hamiltonian systems. In this paper, we formulate a complex version of Hopfield's network os real parameters and show that a variation on this model is a conservative system. Conditions under which the complex network can be used as a Content Addressable memory are studied. We also examine the effect of singularities of the complex sigmoid function on the network dynamics. The network exhibits unpredictable behavior at the singularities due to the failure of a uniqueness condition for the solution of the dynamic equations. On incorporating a weight adaptation rule, the structure of the resulting complex network equations is shown to have an interesting similarity with Kosko's Adaptive Bidirectional Associative Memory.
Studies on a network of complex neurons
NASA Astrophysics Data System (ADS)
Chakravarthy, Srinivasa V.; Ghosh, Joydeep
1993-09-01
In the last decade, much effort has been directed towards understanding the role of chaos in the brain. Work with rabbits reveals that in the resting state the electrical activity on the surface of the olfactory bulb is chaotic. But, when the animal is involved in a recognition task, the activity shifts to a specific pattern corresponding to the odor that is being recognized. Unstable, quasiperiodic behavior can be found in a class of conservative, deterministic physical systems called the Hamiltonian systems. In this paper, we formulate a complex version of Hopfield's network of real parameters and show that a variation on this model is a conservative system. Conditions under which the complex network can be used as a Content Addressable memory are studied. We also examine the effect of singularities of the complex sigmoid function on the network dynamics. The network exhibits unpredictable behavior at the singularities due to the failure of a uniqueness condition for the solution of the dynamic equations. On incorporating a weight adaptation rule, the structure of the resulting complex network equations is shown to have an interesting similarity with Kosko's Adaptive Bidirectional Associative Memory.
Controlling congestion on complex networks: fairness, efficiency and network structure.
Buzna, Ľuboš; Carvalho, Rui
2017-08-22
We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow allocation, and the location of bottleneck edges. The more realistic proportional fairness and max-min fairness algorithms have similar throughput, but path flow allocations are more unequal in scale-free than in random regular networks. Scale-free networks have lower throughput than their random regular counterparts in the uniform-flow algorithm, which is favoured in the complex networks literature. We show, however, that this relation is reversed on all other congestion control algorithms for a region of the parameter space given by the degree exponent γ and average degree 〈k〉. Moreover, the uniform-flow algorithm severely underestimates the network throughput of congested networks, and a rich phenomenology of path flow allocations is only present in the more realistic α-fair family of algorithms. Finally, we show that the number of paths passing through an edge characterises the location of a wide range of bottleneck edges in these algorithms. Such identification of bottlenecks could provide a bridge between the two fields of complex networks and congestion control.
Complex root networks of Chinese characters
NASA Astrophysics Data System (ADS)
Lee, Po-Han; Chen, Jia-Ling; Wang, Po-Cheng; Chi, Ting-Ting; Xiao, Zhi-Ren; Jhang, Zih-Jian; Yeh, Yeong-Nan; Chen, Yih-Yuh; Hu, Chin-Kun
There are several sets of Chinese characters still available today, including Oracle Bone Inscriptions (OBI) in Shang Dynasty, Chu characters (CC) used in Chu of Warring State Period, Small Seal Script in dictionary Shuowen Jiezi (SJ) in Eastern Han Dynasty, and Kangxi Dictionary (KD) in Qing Dynasty. Such as Chinese characters were all constructed via combinations of meaningful patterns, called roots. Our studies for the complex networks of all roots indicate that the roots of the characters in OBI, CC, SJ and KD have characteristics of small world networks and scale-free networks.
Spatial price dynamics: From complex network perspective
NASA Astrophysics Data System (ADS)
Li, Y. L.; Bi, J. T.; Sun, H. J.
2008-10-01
The spatial price problem means that if the supply price plus the transportation cost is less than the demand price, there exists a trade. Thus, after an amount of exchange, the demand price will decrease. This process is continuous until an equilibrium state is obtained. However, how the trade network structure affects this process has received little attention. In this paper, we give a evolving model to describe the levels of spatial price on different complex network structures. The simulation results show that the network with shorter path length is sensitive to the variation of prices.
Composite centrality: A natural scale for complex evolving networks
NASA Astrophysics Data System (ADS)
Joseph, A. C.; Chen, G.
2014-01-01
We derive a composite centrality measure for general weighted and directed complex networks, based on measure standardisation and invariant statistical inheritance schemes. Different schemes generate different intermediate abstract measures providing additional information, while the composite centrality measure tends to the standard normal distribution. This offers a unified scale to measure node and edge centralities for complex evolving networks under a uniform framework. Considering two real-world cases of the world trade web and the world migration web, both during a time span of 40 years, we propose a standard set-up to demonstrate its remarkable normative power and accuracy. We illustrate the applicability of the proposed framework for large and arbitrary complex systems, as well as its limitations, through extensive numerical simulations.
Dynamic information routing in complex networks
NASA Astrophysics Data System (ADS)
Kirst, Christoph; Timme, Marc; Battaglia, Demian
2015-03-01
Flexible information routing fundamentally underlies the function of many biological and artificial networks. Yet, how information may be specifically communicated and dynamically routed in these systems is not well understood. Here we demonstrate that collective dynamical states systematically control patterns of information sharing and transfer in networks, as measured by delayed mutual information and transfer entropies between activities of a network's units. For oscillatory networks we analyze how individual unit properties, the connectivity structure and external inputs all provide means to flexibly control information routing. For multi-scale, modular architectures, we resolve communication patterns at all levels and show how local interventions within one sub-network may remotely control the non-local network-wide routing of information. This theory helps understanding information routing patterns across systems where collective dynamics co-occurs with a communication function.
Extractive summarization using complex networks and syntactic dependency
NASA Astrophysics Data System (ADS)
Amancio, Diego R.; Nunes, Maria G. V.; Oliveira, Osvaldo N.; Costa, Luciano da F.
2012-02-01
The realization that statistical physics methods can be applied to analyze written texts represented as complex networks has led to several developments in natural language processing, including automatic summarization and evaluation of machine translation. Most importantly, so far only a few metrics of complex networks have been used and therefore there is ample opportunity to enhance the statistics-based methods as new measures of network topology and dynamics are created. In this paper, we employ for the first time the metrics betweenness, vulnerability and diversity to analyze written texts in Brazilian Portuguese. Using strategies based on diversity metrics, a better performance in automatic summarization is achieved in comparison to previous work employing complex networks. With an optimized method the Rouge score (an automatic evaluation method used in summarization) was 0.5089, which is the best value ever achieved for an extractive summarizer with statistical methods based on complex networks for Brazilian Portuguese. Furthermore, the diversity metric can detect keywords with high precision, which is why we believe it is suitable to produce good summaries. It is also shown that incorporating linguistic knowledge through a syntactic parser does enhance the performance of the automatic summarizers, as expected, but the increase in the Rouge score is only minor. These results reinforce the suitability of complex network methods for improving automatic summarizers in particular, and treating text in general.
An exploration of graph metric reproducibility in complex brain networks
Telesford, Qawi K.; Burdette, Jonathan H.; Laurienti, Paul J.
2013-01-01
The application of graph theory to brain networks has become increasingly popular in the neuroimaging community. These investigations and analyses have led to a greater understanding of the brain's complex organization. More importantly, it has become a useful tool for studying the brain under various states and conditions. With the ever expanding popularity of network science in the neuroimaging community, there is increasing interest to validate the measurements and calculations derived from brain networks. Underpinning these studies is the desire to use brain networks in longitudinal studies or as clinical biomarkers to understand changes in the brain. A highly reproducible tool for brain imaging could potentially prove useful as a clinical tool. In this review, we examine recent studies in network reproducibility and their implications for analysis of brain networks. PMID:23717257
Discriminating complex networks through supervised NDR and Bayesian classifier
NASA Astrophysics Data System (ADS)
Yan, Ke-Sheng; Rong, Li-Li; Yu, Kai
2016-12-01
Discriminating complex networks is a particularly important task for the purpose of the systematic study of networks. In order to discriminate unknown networks exactly, a large set of network measurements are needed to be taken into account for comprehensively considering network properties. However, as we demonstrate in this paper, these measurements are nonlinear correlated with each other in general, resulting in a wide variety of redundant measurements which unintentionally explain the same aspects of network properties. To solve this problem, we adopt supervised nonlinear dimensionality reduction (NDR) to eliminate the nonlinear redundancy and visualize networks in a low-dimensional projection space. Though unsupervised NDR can achieve the same aim, we illustrate that supervised NDR is more appropriate than unsupervised NDR for discrimination task. After that, we perform Bayesian classifier (BC) in the projection space to discriminate the unknown network by considering the projection score vectors as the input of the classifier. We also demonstrate the feasibility and effectivity of this proposed method in six extensive research real networks, ranging from technological to social or biological. Moreover, the effectiveness and advantage of the proposed method is proved by the contrast experiments with the existing method.
The complex network of musical tastes
NASA Astrophysics Data System (ADS)
Buldú, Javier M.; Cano, P.; Koppenberger, M.; Almendral, Juan A.; Boccaletti, S.
2007-06-01
We present an empirical study of the evolution of a social network constructed under the influence of musical tastes. The network is obtained thanks to the selfless effort of a broad community of users who share playlists of their favourite songs with other users. When two songs co-occur in a playlist a link is created between them, leading to a complex network where songs are the fundamental nodes. In this representation, songs in the same playlist could belong to different musical genres, but they are prone to be linked by a certain musical taste (e.g. if songs A and B co-occur in several playlists, an user who likes A will probably like also B). Indeed, playlist collections such as the one under study are the basic material that feeds some commercial music recommendation engines. Since playlists have an input date, we are able to evaluate the topology of this particular complex network from scratch, observing how its characteristic parameters evolve in time. We compare our results with those obtained from an artificial network defined by means of a null model. This comparison yields some insight on the evolution and structure of such a network, which could be used as ground data for the development of proper models. Finally, we gather information that can be useful for the development of music recommendation engines and give some hints about how top-hits appear.
Neural networks and dynamic complex systems
Fox, G.; Furmanski, Wojtek; Ho, Alex; Koller, J.; Simic, P.; Wong, Isaac
1989-01-01
We describe the use of neural networks for optimization and inference associated with a variety of complex systems. We show how a string formalism can be used for parallel computer decomposition, message routing and sequential optimizing compilers. We extend these ideas to a general treatment of spatial assessment and distributed artificial intelligence. 34 refs., 12 figs.
Realizing Wisdom Theory in Complex Learning Networks
ERIC Educational Resources Information Center
Kok, Ayse
2009-01-01
The word "wisdom" is rarely seen in contemporary technology and learning discourse. This conceptual paper aims to provide some clear principles that answer the question: How can we establish wisdom in complex learning networks? By considering the nature of contemporary calls for wisdom the paper provides a metatheoretial framework to evaluate the…
The Kuramoto model in complex networks
NASA Astrophysics Data System (ADS)
Rodrigues, Francisco A.; Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen
2016-01-01
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.
Controlling extreme events on complex networks
Chen, Yu-Zhong; Huang, Zi-Gang; Lai, Ying-Cheng
2014-01-01
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed. PMID:25131344
Amplitude dynamics favors synchronization in complex networks
Gambuzza, Lucia Valentina; Gómez-Gardeñes, Jesus; Frasca, Mattia
2016-01-01
In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics. PMID:27108847
Amplitude dynamics favors synchronization in complex networks
NASA Astrophysics Data System (ADS)
Gambuzza, Lucia Valentina; Gómez-Gardeñes, Jesus; Frasca, Mattia
2016-04-01
In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics.
Emergence of fractal scaling in complex networks.
Wei, Zong-Wen; Wang, Bing-Hong
2016-09-01
Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.
Emergence of fractal scaling in complex networks
NASA Astrophysics Data System (ADS)
Wei, Zong-Wen; Wang, Bing-Hong
2016-09-01
Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.
Disease Surveillance on Complex Social Networks.
Herrera, Jose L; Srinivasan, Ravi; Brownstein, John S; Galvani, Alison P; Meyers, Lauren Ancel
2016-07-01
As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors-sampling the most connected, random, and friends of random individuals-in three complex social networks-a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals-early and accurate detection of epidemic emergence and peak, and general situational awareness-we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.
Distribution of Node Characteristics in Complex Networks
NASA Astrophysics Data System (ADS)
Park, Juyong; Barabasi, A.-L.
2008-03-01
Our enhanced ability to map the structure of various complex networks is accompanied by the capability to independently identify the functional characteristics of each node, leading to the observation that nodes with similar characteristics show tendencies to link to each other. Examples can be easily found in biological, technological, and social networks. Here we propose a tool to quantify the interplay between node properties and the structure of the underlying network. We show that when nodes in a network belong to two distinct classes, two independent parameters are needed. We find that the network structure limits the values of these parameters, requiring a phase diagram to uniquely characterize the configurations available to the system. The phase diagram shows independence from the network size, a finding that allows us to estimate its shape for large networks from their samples. We study biological and socioeconomic systems, finding that the proposed parameters have a strong discriminating power. ootnotetextJ. Park and A.-L. Barab'asi, Proc. Nat. Acad. Sci. 104, pp. 17916--17920 (2007)
Markovian dynamics on complex reaction networks
NASA Astrophysics Data System (ADS)
Goutsias, J.; Jenkinson, G.
2013-08-01
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underlying population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions and the large size of the underlying state-spaces, computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.
Surprise maximization reveals the community structure of complex networks
Aldecoa, Rodrigo; Marín, Ignacio
2013-01-01
How to determine the community structure of complex networks is an open question. It is critical to establish the best strategies for community detection in networks of unknown structure. Here, using standard synthetic benchmarks, we show that none of the algorithms hitherto developed for community structure characterization perform optimally. Significantly, evaluating the results according to their modularity, the most popular measure of the quality of a partition, systematically provides mistaken solutions. However, a novel quality function, called Surprise, can be used to elucidate which is the optimal division into communities. Consequently, we show that the best strategy to find the community structure of all the networks examined involves choosing among the solutions provided by multiple algorithms the one with the highest Surprise value. We conclude that Surprise maximization precisely reveals the community structure of complex networks. PMID:23320141
A graph clustering method for community detection in complex networks
NASA Astrophysics Data System (ADS)
Zhou, HongFang; Li, Jin; Li, JunHuai; Zhang, FaCun; Cui, YingAn
2017-03-01
Information mining from complex networks by identifying communities is an important problem in a number of research fields, including the social sciences, biology, physics and medicine. First, two concepts are introduced, Attracting Degree and Recommending Degree. Second, a graph clustering method, referred to as AR-Cluster, is presented for detecting community structures in complex networks. Third, a novel collaborative similarity measure is adopted to calculate node similarities. In the AR-Cluster method, vertices are grouped together based on calculated similarity under a K-Medoids framework. Extensive experimental results on two real datasets show the effectiveness of AR-Cluster.
Complexity Measures in Magnetoencephalography: Measuring "Disorder" in Schizophrenia
Brookes, Matthew J.; Hall, Emma L.; Robson, Siân E.; Price, Darren; Palaniyappan, Lena; Liddle, Elizabeth B.; Liddle, Peter F.; Robinson, Stephen E.; Morris, Peter G.
2015-01-01
This paper details a methodology which, when applied to magnetoencephalography (MEG) data, is capable of measuring the spatio-temporal dynamics of ‘disorder’ in the human brain. Our method, which is based upon signal entropy, shows that spatially separate brain regions (or networks) generate temporally independent entropy time-courses. These time-courses are modulated by cognitive tasks, with an increase in local neural processing characterised by localised and transient increases in entropy in the neural signal. We explore the relationship between entropy and the more established time-frequency decomposition methods, which elucidate the temporal evolution of neural oscillations. We observe a direct but complex relationship between entropy and oscillatory amplitude, which suggests that these metrics are complementary. Finally, we provide a demonstration of the clinical utility of our method, using it to shed light on aberrant neurophysiological processing in schizophrenia. We demonstrate significantly increased task induced entropy change in patients (compared to controls) in multiple brain regions, including a cingulo-insula network, bilateral insula cortices and a right fronto-parietal network. These findings demonstrate potential clinical utility for our method and support a recent hypothesis that schizophrenia can be characterised by abnormalities in the salience network (a well characterised distributed network comprising bilateral insula and cingulate cortices). PMID:25886553
Universal resilience patterns in complex networks.
Gao, Jianxi; Barzel, Baruch; Barabási, Albert-László
2016-02-18
Resilience, a system's ability to adjust its activity to retain its basic functionality when errors, failures and environmental changes occur, is a defining property of many complex systems. Despite widespread consequences for human health, the economy and the environment, events leading to loss of resilience--from cascading failures in technological systems to mass extinctions in ecological networks--are rarely predictable and are often irreversible. These limitations are rooted in a theoretical gap: the current analytical framework of resilience is designed to treat low-dimensional models with a few interacting components, and is unsuitable for multi-dimensional systems consisting of a large number of components that interact through a complex network. Here we bridge this theoretical gap by developing a set of analytical tools with which to identify the natural control and state parameters of a multi-dimensional complex system, helping us derive effective one-dimensional dynamics that accurately predict the system's resilience. The proposed analytical framework allows us systematically to separate the roles of the system's dynamics and topology, collapsing the behaviour of different networks onto a single universal resilience function. The analytical results unveil the network characteristics that can enhance or diminish resilience, offering ways to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems resilient to both internal failures and environmental changes.
Disease Surveillance on Complex Social Networks
Herrera, Jose L.; Srinivasan, Ravi; Brownstein, John S.; Galvani, Alison P.; Meyers, Lauren Ancel
2016-01-01
As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors—sampling the most connected, random, and friends of random individuals—in three complex social networks—a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals—early and accurate detection of epidemic emergence and peak, and general situational awareness—we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information. PMID:27415615
Predicting links based on knowledge dissemination in complex network
NASA Astrophysics Data System (ADS)
Zhou, Wen; Jia, Yifan
2017-04-01
Link prediction is the task of mining the missing links in networks or predicting the next vertex pair to be connected by a link. A lot of link prediction methods were inspired by evolutionary processes of networks. In this paper, a new mechanism for the formation of complex networks called knowledge dissemination (KD) is proposed with the assumption of knowledge disseminating through the paths of a network. Accordingly, a new link prediction method-knowledge dissemination based link prediction (KDLP)-is proposed to test KD. KDLP characterizes vertex similarity based on knowledge quantity (KQ) which measures the importance of a vertex through H-index. Extensive numerical simulations on six real-world networks demonstrate that KDLP is a strong link prediction method which performs at a higher prediction accuracy than four well-known similarity measures including common neighbors, local path index, average commute time and matrix forest index. Furthermore, based on the common conclusion that an excellent link prediction method reveals a good evolving mechanism, the experiment results suggest that KD is a considerable network evolving mechanism for the formation of complex networks.
Transport and percolation in complex networks
NASA Astrophysics Data System (ADS)
Li, Guanliang
To design complex networks with optimal transport properties such as flow efficiency, we consider three approaches to understanding transport and percolation in complex networks. We analyze the effects of randomizing the strengths of connections, randomly adding long-range connections to regular lattices, and percolation of spatially constrained networks. Various real-world networks often have links that are differentiated in terms of their strength, intensity, or capacity. We study the distribution P(σ) of the equivalent conductance for Erdoḧs-Rényi (ER) and scale-free (SF) weighted resistor networks with N nodes, for which links are assigned with conductance σ i ≡ e-axi, where xi is a random variable with 0 < xi < 1. We find, both analytically and numerically, that P(σ) for ER networks exhibits two regimes: (i) For σ < e-apc, P(σ) is independent of N and scales as a power law P(σ) ˜ sk/a-1 . Here pc = 1/
Post Disaster Governance, Complexity and Network Theory
Lassa, Jonatan A.
2015-01-01
This research aims to understand the organizational network typology of large-scale disaster intervention in developing countries and to understand the complexity of post-disaster intervention, through the use of network theory based on empirical data from post-tsunami reconstruction in Aceh, Indonesia, during 2005/2007. The findings suggest that the ‘ degrees of separation’ (or network diameter) between any two organizations in the field is 5, thus reflecting ‘small world’ realities and therefore making no significant difference with the real human networks, as found in previous experiments. There are also significant loops in the network reflecting the fact that some actors tend to not cooperate, which challenges post disaster coordination. The findings show the landscape of humanitarian actors is not randomly distributed. Many actors were connected to each other through certain hubs, while hundreds of actors make ‘scattered’ single ‘principal-client’ links. The paper concludes that by understanding the distribution of degree, centrality, ‘degrees of separation’ and visualization of the network, authorities can improve their understanding of the realities of coordination, from macro to micro scales. PMID:26236562
Robust Multiobjective Controllability of Complex Neuronal Networks.
Tang, Yang; Gao, Huijun; Du, Wei; Lu, Jianquan; Vasilakos, Athanasios V; Kurths, Jurgen
2016-01-01
This paper addresses robust multiobjective identification of driver nodes in the neuronal network of a cat's brain, in which uncertainties in determination of driver nodes and control gains are considered. A framework for robust multiobjective controllability is proposed by introducing interval uncertainties and optimization algorithms. By appropriate definitions of robust multiobjective controllability, a robust nondominated sorting adaptive differential evolution (NSJaDE) is presented by means of the nondominated sorting mechanism and the adaptive differential evolution (JaDE). The simulation experimental results illustrate the satisfactory performance of NSJaDE for robust multiobjective controllability, in comparison with six statistical methods and two multiobjective evolutionary algorithms (MOEAs): nondominated sorting genetic algorithms II (NSGA-II) and nondominated sorting composite differential evolution. It is revealed that the existence of uncertainties in choosing driver nodes and designing control gains heavily affects the controllability of neuronal networks. We also unveil that driver nodes play a more drastic role than control gains in robust controllability. The developed NSJaDE and obtained results will shed light on the understanding of robustness in controlling realistic complex networks such as transportation networks, power grid networks, biological networks, etc.
Universality at Breakdown of Quantum Transport on Complex Networks.
Kulvelis, Nikolaj; Dolgushev, Maxim; Mülken, Oliver
2015-09-18
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by the time-averaged return probability. For treelike networks, we show analytically that a transition from efficient to inefficient transport occurs depending on the (average) functionality of the nodes of the network. In the infinite system size limit, this transition can be characterized by an exponent which is universal for all treelike networks. Our findings are corroborated by analytic results for specific deterministic networks, dendrimers and Vicsek fractals, and by Monte Carlo simulations of iteratively built scale-free trees.
The generalization complexity measure for continuous input data.
Gómez, Iván; Cannas, Sergio A; Osenda, Omar; Jerez, José M; Franco, Leonardo
2014-01-01
We introduce in this work an extension for the generalization complexity measure to continuous input data. The measure, originally defined in Boolean space, quantifies the complexity of data in relationship to the prediction accuracy that can be expected when using a supervised classifier like a neural network, SVM, and so forth. We first extend the original measure for its use with continuous functions to later on, using an approach based on the use of the set of Walsh functions, consider the case of having a finite number of data points (inputs/outputs pairs), that is, usually the practical case. Using a set of trigonometric functions a model that gives a relationship between the size of the hidden layer of a neural network and the complexity is constructed. Finally, we demonstrate the application of the introduced complexity measure, by using the generated model, to the problem of estimating an adequate neural network architecture for real-world data sets.
The Generalization Complexity Measure for Continuous Input Data
Cannas, Sergio A.; Osenda, Omar; Jerez, José M.
2014-01-01
We introduce in this work an extension for the generalization complexity measure to continuous input data. The measure, originally defined in Boolean space, quantifies the complexity of data in relationship to the prediction accuracy that can be expected when using a supervised classifier like a neural network, SVM, and so forth. We first extend the original measure for its use with continuous functions to later on, using an approach based on the use of the set of Walsh functions, consider the case of having a finite number of data points (inputs/outputs pairs), that is, usually the practical case. Using a set of trigonometric functions a model that gives a relationship between the size of the hidden layer of a neural network and the complexity is constructed. Finally, we demonstrate the application of the introduced complexity measure, by using the generated model, to the problem of estimating an adequate neural network architecture for real-world data sets. PMID:24983000
Study of complex networks using statistical physics methods
NASA Astrophysics Data System (ADS)
Chen, Yiping
The goal of this thesis is to study the behaviors of complex networks in several aspects using methods from statistical physics. Networks are structures that consist of nodes and links. By changing the way links connect to nodes, different complex network structures can be constructed such as Erdḧs-Renyi (ER) networks and scale-free (SF) networks. Complex networks have wide relevance to many real world problems, including the spread of disease in human society, message routing in the Internet, etc. In this thesis analytical and simulation results are obtained regarding optimal paths in disordered networks, fragmentation of social networks, and improved strategies for immunization against diseases. In the study of disordered systems, of particular current interest is the scaling behavior of the optimal path length ℓopt from strong disorder to weak disorder state for different weight distributions P(w). Here we derive analytically a new criterion. Using this criterion we find that for all P(w) that possess a strong-weak disorder crossover, the distributions p(ℓ) of the optimal path lengths display the same universal behavior. Fragmentation in social networks is also studied using methods from percolation theory. Recently, a new measure of fragmentation F has been developed in social network studies. For each removal of a subset of links or nodes, F is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removal, and the total number of pairs in the original fully connected network. We study the statistical behavior of F using both analytical and numerical methods and relate it to the traditional measure of fragmentation, the relative size of the largest cluster, Pinfinity, used in percolation theory. Finally, we tried to find a better immunization strategy. It is widely accepted that the most efficient immunization strategies are based on "targeted" strategies. Here we propose a novel "equal graph
Quantum Google in a Complex Network
Paparo, Giuseppe Davide; Müller, Markus; Comellas, Francesc; Martin-Delgado, Miguel Angel
2013-01-01
We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks. PMID:24091980
Stochastic competitive learning in complex networks.
Silva, Thiago Christiano; Zhao, Liang
2012-03-01
Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning..
The complex networks approach for authorship attribution of books
NASA Astrophysics Data System (ADS)
Mehri, Ali; Darooneh, Amir H.; Shariati, Ashrafalsadat
2012-04-01
Authorship analysis by means of textual features is an important task in linguistic studies. We employ complex networks theory to tackle this disputed problem. In this work, we focus on some measurable quantities of word co-occurrence network of each book for authorship characterization. Based on the network features, attribution probability is defined for authorship identification. Furthermore, two scaling exponents, q-parameter and α-exponent, are combined to classify personal writing style with acceptable high resolution power. The q-parameter, generally known as the nonextensivity measure, is calculated for degree distribution and the α-exponent comes from a power law relationship between number of links and number of nodes in the co-occurrence network constructed for different books written by each author. The applicability of the presented method is evaluated in an experiment with thirty six books of five Persian litterateurs. Our results show high accuracy rate in authorship attribution.
Preferential urn model and nongrowing complex networks.
Ohkubo, Jun; Yasuda, Muneki; Tanaka, Kazuyuki
2005-12-01
A preferential urn model, which is based on the concept "the rich get richer," is proposed. From a relationship between a nongrowing model for complex networks and the preferential urn model in regard to degree distributions, it is revealed that a fitness parameter in the nongrowing model is interpreted as an inverse local temperature in the preferential urn model. Furthermore, it is clarified that the preferential urn model with randomness generates a fat-tailed occupation distribution; the concept of the local temperature enables us to understand the fat-tailed occupation distribution intuitively. Since the preferential urn model is a simple stochastic model, it can be applied to research on not only the nongrowing complex networks, but also many other fields such as econophysics and social sciences.
Complex network approach to fractional time series
Manshour, Pouya
2015-10-15
In order to extract correlation information inherited in stochastic time series, the visibility graph algorithm has been recently proposed, by which a time series can be mapped onto a complex network. We demonstrate that the visibility algorithm is not an appropriate one to study the correlation aspects of a time series. We then employ the horizontal visibility algorithm, as a much simpler one, to map fractional processes onto complex networks. The degree distributions are shown to have parabolic exponential forms with Hurst dependent fitting parameter. Further, we take into account other topological properties such as maximum eigenvalue of the adjacency matrix and the degree assortativity, and show that such topological quantities can also be used to predict the Hurst exponent, with an exception for anti-persistent fractional Gaussian noises. To solve this problem, we take into account the Spearman correlation coefficient between nodes' degrees and their corresponding data values in the original time series.
Complex networks analysis of obstructive nephropathy data
NASA Astrophysics Data System (ADS)
Zanin, M.; Boccaletti, S.
2011-09-01
Congenital obstructive nephropathy (ON) is one of the most frequent and complex diseases affecting children, characterized by an abnormal flux of the urine, due to a partial or complete obstruction of the urinary tract; as a consequence, urine may accumulate in the kidney and disturb the normal operation of the organ. Despite important advances, pathological mechanisms are not yet fully understood. In this contribution, the topology of complex networks, based on vectors of features of control and ON subjects, is related with the severity of the pathology. Nodes in these networks represent genetic and metabolic profiles, while connections between them indicate an abnormal relation between their expressions. Resulting topologies allow discriminating ON subjects and detecting which genetic or metabolic elements are responsible for the malfunction.
Different Epidemic Models on Complex Networks
NASA Astrophysics Data System (ADS)
Zhang, Hai-Feng; Small, Michael; Fu, Xin-Chu
2009-07-01
Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals' relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each case. Finally, we present numerical simulations for each case to verify our results.
Mathematical modeling of complex regulatory networks.
Stelling, Jörg; Gilles, Ernst Dieter
2004-09-01
Cellular regulation comprises overwhelmingly complex interactions between genes and proteins that ultimately will only be rendered understandable by employing formal approaches. Developing large-scale mathematical models of such systems in an efficient and reliable way, however, requires careful evaluation of structuring principles for the models, of the description of the system dynamics, and of the experimental data basis for adjusting the models to reality. We discuss these three aspects of model development using the example of cell cycle regulation in yeast and suggest that capturing complex dynamic networks is feasible despite incomplete (quantitative) biological knowledge.
Strong correlations between text quality and complex networks features
NASA Astrophysics Data System (ADS)
Antiqueira, L.; Nunes, M. G. V.; Oliveira, O. N., Jr.; F. Costa, L. da
2007-01-01
Concepts of complex networks have been used to obtain metrics that were correlated to text quality established by scores assigned by human judges. Texts produced by high-school students in Portuguese were represented as scale-free networks (word adjacency model), from which typical network features such as the in/outdegree, clustering coefficient and shortest path were obtained. Another metric was derived from the dynamics of the network growth, based on the variation of the number of connected components. The scores assigned by the human judges according to three text quality criteria (coherence and cohesion, adherence to standard writing conventions and theme adequacy/development) were correlated with the network measurements. Text quality for all three criteria was found to decrease with increasing average values of outdegrees, clustering coefficient and deviation from the dynamics of network growth. Among the criteria employed, cohesion and coherence showed the strongest correlation, which probably indicates that the network measurements are able to capture how the text is developed in terms of the concepts represented by the nodes in the networks. Though based on a particular set of texts and specific language, the results presented here point to potential applications in other instances of text analysis.
The topology and dynamics of complex networks
NASA Astrophysics Data System (ADS)
Dezso, Zoltan
We start with a brief introduction about the topological properties of real networks. Most real networks are scale-free, being characterized by a power-law degree distribution. The scale-free nature of real networks leads to unexpected properties such as the vanishing epidemic threshold. Traditional methods aiming to reduce the spreading rate of viruses cannot succeed on eradicating the epidemic on a scale-free network. We demonstrate that policies that discriminate between the nodes, curing mostly the highly connected nodes, can restore a finite epidemic threshold and potentially eradicate the virus. We find that the more biased a policy is towards the hubs, the more chance it has to bring the epidemic threshold above the virus' spreading rate. We continue by studying a large Web portal as a model system for a rapidly evolving network. We find that the visitation pattern of a news document decays as a power law, in contrast with the exponential prediction provided by simple models of site visitation. This is rooted in the inhomogeneous nature of the browsing pattern characterizing individual users: the time interval between consecutive visits by the same user to the site follows a power law distribution, in contrast with the exponential expected for Poisson processes. We show that the exponent characterizing the individual user's browsing patterns determines the power-law decay in a document's visitation. Finally, we turn our attention to biological networks and demonstrate quantitatively that protein complexes in the yeast, Saccharomyces cerevisiae, are comprised of a core in which subunits are highly coexpressed, display the same deletion phenotype (essential or non-essential) and share identical functional classification and cellular localization. The results allow us to define the deletion phenotype and cellular task of most known complexes, and to identify with high confidence the biochemical role of hundreds of proteins with yet unassigned functionality.
Complex growing networks with intrinsic vertex fitness
Bedogne, C.; Rodgers, G. J.
2006-10-15
One of the major questions in complex network research is to identify the range of mechanisms by which a complex network can self organize into a scale-free state. In this paper we investigate the interplay between a fitness linking mechanism and both random and preferential attachment. In our models, each vertex is assigned a fitness x, drawn from a probability distribution {rho}(x). In Model A, at each time step a vertex is added and joined to an existing vertex, selected at random, with probability p and an edge is introduced between vertices with fitnesses x and y, with a rate f(x,y), with probability 1-p. Model B differs from Model A in that, with probability p, edges are added with preferential attachment rather than randomly. The analysis of Model A shows that, for every fixed fitness x, the network's degree distribution decays exponentially. In Model B we recover instead a power-law degree distribution whose exponent depends only on p, and we show how this result can be generalized. The properties of a number of particular networks are examined.
Structural and dynamical properties of complex networks
NASA Astrophysics Data System (ADS)
Ghoshal, Gourab
Recent years have witnessed a substantial amount of interest within the physics community in the properties of networks. Techniques from statistical physics coupled with the widespread availability of computing resources have facilitated studies ranging from large scale empirical analysis of the worldwide web, social networks, biological systems, to the development of theoretical models and tools to explore the various properties of these systems. Following these developments, in this dissertation, we present and solve for a diverse set of new problems, investigating the structural and dynamical properties of both model and real world networks. We start by defining a new metric to measure the stability of network structure to disruptions, and then using a combination of theory and simulation study its properties in detail on artificially generated networks; we then compare our results to a selection of networks from the real world and find good agreement in most cases. In the following chapter, we propose a mathematical model that mimics the structure of popular file-sharing websites such as Flickr and CiteULike and demonstrate that many of its properties can solved exactly in the limit of large network size. The remaining part of the dissertation primarily focuses on the dynamical properties of networks. We first formulate a model of a network that evolves under the addition and deletion of vertices and edges, and solve for the equilibrium degree distribution for a variety of cases of interest. We then consider networks whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with some mild constraints, it is possible by a suitable choice of rules to arrange for the network to have any degree distribution we desire. In addition we define a simple local algorithm by which appropriate rules can be implemented in practice. Finally, we conclude our
Complex Networks Unveiling Spatial Patterns in Turbulence
NASA Astrophysics Data System (ADS)
Scarsoglio, Stefania; Iacobello, Giovanni; Ridolfi, Luca
2016-12-01
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on the complex network theory, offering a powerful framework to explore complex systems with a huge number of interacting elements. Although interest in complex networks has been increasing in the past years, few recent studies have been applied to turbulence. We propose an investigation starting from a two-point correlation for the kinetic energy of a forced isotropic field numerically solved. Among all the metrics analyzed, the degree centrality is the most significant, suggesting the formation of spatial patterns which coherently move with similar vorticity over the large eddy turnover time scale. Pattern size can be quantified through a newly-introduced parameter (i.e. average physical distance) and varies from small to intermediate scales. The network analysis allows a systematic identification of different spatial regions, providing new insights into the spatial characterization of turbulent flows. Based on present findings, the application to highly inhomogeneous flows seems promising and deserves additional future investigation.
Universal resilience patterns in complex networks
NASA Astrophysics Data System (ADS)
Gao, Jianxi; Barzel, Baruch; Barabási, Albert-László
2016-02-01
Resilience, a system’s ability to adjust its activity to retain its basic functionality when errors, failures and environmental changes occur, is a defining property of many complex systems. Despite widespread consequences for human health, the economy and the environment, events leading to loss of resilience—from cascading failures in technological systems to mass extinctions in ecological networks—are rarely predictable and are often irreversible. These limitations are rooted in a theoretical gap: the current analytical framework of resilience is designed to treat low-dimensional models with a few interacting components, and is unsuitable for multi-dimensional systems consisting of a large number of components that interact through a complex network. Here we bridge this theoretical gap by developing a set of analytical tools with which to identify the natural control and state parameters of a multi-dimensional complex system, helping us derive effective one-dimensional dynamics that accurately predict the system’s resilience. The proposed analytical framework allows us systematically to separate the roles of the system’s dynamics and topology, collapsing the behaviour of different networks onto a single universal resilience function. The analytical results unveil the network characteristics that can enhance or diminish resilience, offering ways to prevent the collapse of ecological, biological or economic systems, and guiding the design of technological systems resilient to both internal failures and environmental changes.
Vulnerability of complex networks under path-based attacks
NASA Astrophysics Data System (ADS)
Pu, Cun-Lai; Cui, Wei
2015-02-01
We investigate vulnerability of complex networks including model networks and real-world networks subject to path-based attacks. Specifically, we remove approximately the longest simple path from a network iteratively until there are no paths left in the network. We propose two algorithms, the random augmenting approach (RPA) and the Hamilton-path based approach (HPA), for finding the approximately longest simple path in a network. Results demonstrate that steps of longest-path attacks increase with network density linearly for random networks, while exponentially increasing for scale-free networks. The more homogeneous the degree distribution is, the more fragile the network, which is different from the previous results of node or edge attacks. HPA is generally more efficient than RPA in the longest-path attacks of complex networks. These findings further help us understand the vulnerability of complex systems, better protect complex systems, and design more tolerant complex systems.
Simulating Operation of a Complex Sensor Network
NASA Technical Reports Server (NTRS)
Jennings, Esther; Clare, Loren; Woo, Simon
2008-01-01
Simulation Tool for ASCTA Microsensor Network Architecture (STAMiNA) ["ASCTA" denotes the Advanced Sensors Collaborative Technology Alliance.] is a computer program for evaluating conceptual sensor networks deployed over terrain to provide military situational awareness. This or a similar program is needed because of the complexity of interactions among such diverse phenomena as sensing and communication portions of a network, deployment of sensor nodes, effects of terrain, data-fusion algorithms, and threat characteristics. STAMiNA is built upon a commercial network-simulator engine, with extensions to include both sensing and communication models in a discrete-event simulation environment. Users can define (1) a mission environment, including terrain features; (2) objects to be sensed; (3) placements and modalities of sensors, abilities of sensors to sense objects of various types, and sensor false alarm rates; (4) trajectories of threatening objects; (5) means of dissemination and fusion of data; and (6) various network configurations. By use of STAMiNA, one can simulate detection of targets through sensing, dissemination of information by various wireless communication subsystems under various scenarios, and fusion of information, incorporating such metrics as target-detection probabilities, false-alarm rates, and communication loads, and capturing effects of terrain and threat.
Sampling of Complex Networks: A Datamining Approach
NASA Astrophysics Data System (ADS)
Loecher, Markus; Dohrmann, Jakob; Bauer, Gernot
2007-03-01
Efficient and accurate sampling of big complex networks is still an unsolved problem. As the degree distribution is one of the most commonly used attributes to characterize a network, there have been many attempts in recent papers to derive the original degree distribution from the data obtained during a traceroute- like sampling process. This talk describes a strategy for predicting the original degree of a node using the data obtained from a network by traceroute-like sampling making use of datamining techniques. Only local quantities (the sampled degree k, the redundancy of node detection r, the time of the first discovery of a node t and the distance to the sampling source d) are used as input for the datamining models. Global properties like the betweenness centrality are ignored. These local quantities are examined theoretically and in simulations to increase their value for the predictions. The accuracy of the models is discussed as a function of the number of sources used in the sampling process and the underlying topology of the network. The purpose of this work is to introduce the techniques of the relatively young field of datamining to the discussion on network sampling.
Diffusive capture process on complex networks
NASA Astrophysics Data System (ADS)
Lee, Sungmin; Yook, Soon-Hyung; Kim, Yup
2006-10-01
We study the dynamical properties of a diffusing lamb captured by a diffusing lion on the complex networks with various sizes of N . We find that the lifetime ⟨T⟩ of a lamb scales as ⟨T⟩˜N and the survival probability S(N→∞,t) becomes finite on scale-free networks with degree exponent γ>3 . However, S(N,t) for γ<3 has a long-living tail on tree-structured scale-free networks and decays exponentially on looped scale-free networks. This suggests that the second moment of degree distribution ⟨k2⟩ is the relevant factor for the dynamical properties in the diffusive capture process. We numerically find that the normalized number of capture events at a node with degree k , n(k) , decreases as n(k)˜k-σ . When γ<3 , n(k) still increases anomalously for k≈kmax , where kmax is the maximum value of k of given networks with size N . We analytically show that n(k) satisfies the relation n(k)˜k2P(k) for any degree distribution P(k) and the total number of capture events Ntot is proportional to ⟨k2⟩ , which causes the γ -dependent behavior of S(N,t) and ⟨T⟩ .
Competitive seeds-selection in complex networks
NASA Astrophysics Data System (ADS)
Zhao, Jiuhua; Liu, Qipeng; Wang, Lin; Wang, Xiaofan
2017-02-01
This paper investigates a competitive diffusion model where two competitors simultaneously select a set of nodes (seeds) in the network to influence. We focus on the problem of how to select these seeds such that, when the diffusion process terminates, a competitor can obtain more supports than its opponent. Instead of studying this problem in the game-theoretic framework as in the existing work, in this paper we design several heuristic seed-selection strategies inspired by commonly used centrality measures-Betweenness Centrality (BC), Closeness Centrality (CC), Degree Centrality (DC), Eigenvector Centrality (EC), and K-shell Centrality (KS). We mainly compare three centrality-based strategies, which have better performances in competing with the random selection strategy, through simulations on both real and artificial networks. Even though network structure varies across different networks, we find certain common trend appearing in all of these networks. Roughly speaking, BC-based strategy and DC-based strategy are better than CC-based strategy. Moreover, if a competitor adopts CC-based strategy, then BC-based strategy is a better strategy than DC-based strategy for his opponent, and the superiority of BC-based strategy decreases as the heterogeneity of the network decreases.
Complex Network Structure Influences Processing in Long-Term and Short-Term Memory
ERIC Educational Resources Information Center
Vitevitch, Michael S.; Chan, Kit Ying; Roodenrys, Steven
2012-01-01
Complex networks describe how entities in systems interact; the structure of such networks is argued to influence processing. One measure of network structure, clustering coefficient, C, measures the extent to which neighbors of a node are also neighbors of each other. Previous psycholinguistic experiments found that the C of phonological…
Complex Network Structure Influences Processing in Long-Term and Short-Term Memory
ERIC Educational Resources Information Center
Vitevitch, Michael S.; Chan, Kit Ying; Roodenrys, Steven
2012-01-01
Complex networks describe how entities in systems interact; the structure of such networks is argued to influence processing. One measure of network structure, clustering coefficient, C, measures the extent to which neighbors of a node are also neighbors of each other. Previous psycholinguistic experiments found that the C of phonological…
Boolean modeling of collective effects in complex networks
Norrell, Johannes; Socolar, Joshua E. S.
2009-01-01
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may, however, introduce dynamical possibilities that are not accessible to the original system. We show that large random networks of variables coupled through continuous transfer functions often fail to exhibit the complex dynamics of corresponding Boolean models in the disordered (chaotic) regime, even when each individual function appears to be a good candidate for Boolean idealization. A suitably modified Boolean theory explains the behavior of systems in which information does not propagate faithfully down certain chains of nodes. Model networks incorporating calculated or directly measured transfer functions reported in the literature on transcriptional regulation of genes are described by the modified theory. PMID:19658525
Activity-Dependent Neuronal Model on Complex Networks
de Arcangelis, Lucilla; Herrmann, Hans J.
2012-01-01
Neuronal avalanches are a novel mode of activity in neuronal networks, experimentally found in vitro and in vivo, and exhibit a robust critical behavior: these avalanches are characterized by a power law distribution for the size and duration, features found in other problems in the context of the physics of complex systems. We present a recent model inspired in self-organized criticality, which consists of an electrical network with threshold firing, refractory period, and activity-dependent synaptic plasticity. The model reproduces the critical behavior of the distribution of avalanche sizes and durations measured experimentally. Moreover, the power spectra of the electrical signal reproduce very robustly the power law behavior found in human electroencephalogram (EEG) spectra. We implement this model on a variety of complex networks, i.e., regular, small-world, and scale-free and verify the robustness of the critical behavior. PMID:22470347
Synchronization in node of complex networks consist of complex chaotic system
Wei, Qiang; Xie, Cheng-jun; Liu, Hong-jun; Li, Yan-hui
2014-07-15
A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.
Complex quantum network geometries: Evolution and phase transitions
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao
2015-08-01
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
Spreading to localized targets in complex networks
Sun, Ye; Ma, Long; Zeng, An; Wang, Wen-Xu
2016-01-01
As an important type of dynamics on complex networks, spreading is widely used to model many real processes such as the epidemic contagion and information propagation. One of the most significant research questions in spreading is to rank the spreading ability of nodes in the network. To this end, substantial effort has been made and a variety of effective methods have been proposed. These methods usually define the spreading ability of a node as the number of finally infected nodes given that the spreading is initialized from the node. However, in many real cases such as advertising and news propagation, the spreading only aims to cover a specific group of nodes. Therefore, it is necessary to study the spreading ability of nodes towards localized targets in complex networks. In this paper, we propose a reversed local path algorithm for this problem. Simulation results show that our method outperforms the existing methods in identifying the influential nodes with respect to these localized targets. Moreover, the influential spreaders identified by our method can effectively avoid infecting the non-target nodes in the spreading process. PMID:27966613
Spreading to localized targets in complex networks
NASA Astrophysics Data System (ADS)
Sun, Ye; Ma, Long; Zeng, An; Wang, Wen-Xu
2016-12-01
As an important type of dynamics on complex networks, spreading is widely used to model many real processes such as the epidemic contagion and information propagation. One of the most significant research questions in spreading is to rank the spreading ability of nodes in the network. To this end, substantial effort has been made and a variety of effective methods have been proposed. These methods usually define the spreading ability of a node as the number of finally infected nodes given that the spreading is initialized from the node. However, in many real cases such as advertising and news propagation, the spreading only aims to cover a specific group of nodes. Therefore, it is necessary to study the spreading ability of nodes towards localized targets in complex networks. In this paper, we propose a reversed local path algorithm for this problem. Simulation results show that our method outperforms the existing methods in identifying the influential nodes with respect to these localized targets. Moreover, the influential spreaders identified by our method can effectively avoid infecting the non-target nodes in the spreading process.
Phase transitions in Pareto optimal complex networks
NASA Astrophysics Data System (ADS)
Seoane, Luís F.; Solé, Ricard
2015-09-01
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem, finding phase transitions of different kinds. Distinct phases are associated with different arrangements of the connections, but the need of drastic topological changes does not determine the presence or the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.
Complex network study of Brazilian soccer players
NASA Astrophysics Data System (ADS)
Onody, Roberto N.; de Castro, Paulo A.
2004-09-01
Although being a very popular sport in many countries, soccer has not received much attention from the scientific community. In this paper, we study soccer from a complex network point of view. First, we consider a bipartite network with two kinds of vertices or nodes: the soccer players and the clubs. Real data were gathered from the 32 editions of the Brazilian soccer championship, in a total of 13411 soccer players and 127 clubs. We find a lot of interesting and perhaps unsuspected results. The probability that a Brazilian soccer player has worked at N clubs or played M games shows an exponential decay while the probability that he has scored G goals is power law. Now, if two soccer players who have worked at the same club at the same time are connected by an edge, then a new type of network arises (composed exclusively by soccer player nodes). Our analysis shows that for this network the degree distribution decays exponentially. We determine the exact values of the clustering coefficient, the assortativity coefficient and the average shortest path length and compare them with those of the Erdös-Rényi and configuration model. The time evolution of these quantities are calculated and the corresponding results discussed.
Hybrid recommendation methods in complex networks.
Fiasconaro, A; Tumminello, M; Nicosia, V; Latora, V; Mantegna, R N
2015-07-01
We propose two recommendation methods, based on the appropriate normalization of already existing similarity measures, and on the convex combination of the recommendation scores derived from similarity between users and between objects. We validate the proposed measures on three data sets, and we compare the performance of our methods to other recommendation systems recently proposed in the literature. We show that the proposed similarity measures allow us to attain an improvement of performances of up to 20% with respect to existing nonparametric methods, and that the accuracy of a recommendation can vary widely from one specific bipartite network to another, which suggests that a careful choice of the most suitable method is highly relevant for an effective recommendation on a given system. Finally, we study how an increasing presence of random links in the network affects the recommendation scores, finding that one of the two recommendation algorithms introduced here can systematically outperform the others in noisy data sets.
Building and measuring a high performance network architecture
Kramer, William T.C.; Toole, Timothy; Fisher, Chuck; Dugan, Jon; Wheeler, David; Wing, William R; Nickless, William; Goddard, Gregory; Corbato, Steven; Love, E. Paul; Daspit, Paul; Edwards, Hal; Mercer, Linden; Koester, David; Decina, Basil; Dart, Eli; Paul Reisinger, Paul; Kurihara, Riki; Zekauskas, Matthew J; Plesset, Eric; Wulf, Julie; Luce, Douglas; Rogers, James; Duncan, Rex; Mauth, Jeffery
2001-04-20
Once a year, the SC conferences present a unique opportunity to create and build one of the most complex and highest performance networks in the world. At SC2000, large-scale and complex local and wide area networking connections were demonstrated, including large-scale distributed applications running on different architectures. This project was designed to use the unique opportunity presented at SC2000 to create a testbed network environment and then use that network to demonstrate and evaluate high performance computational and communication applications. This testbed was designed to incorporate many interoperable systems and services and was designed for measurement from the very beginning. The end results were key insights into how to use novel, high performance networking technologies and to accumulate measurements that will give insights into the networks of the future.
Complex Networks and Minimal Spanning Trees in International Trade Network
NASA Astrophysics Data System (ADS)
Maeng, Seong Eun; Choi, Hyung Wooc; Lee, Jae Woo
The wealth of a nation is changed by the internal economic growth of a nation and by the international trade among countries. Trade between countries are one of their most important interactions and thus expects to affect crucially the wealth distribution over countries. We reviewed the network properties of the international trade networks (ITN). We analyzed data sets of world trade. The data set include a total number of 190 countries from 1950 to 2000. We observed that the world trade network showed the uneven trading relationships which are measured by the disparity. The effective disparity followed a power law, < D(k) > tδ, for the import and export network. We also construct the minimal spanning tree(MST) of international trade network, where each node is a country and directed links connecting them represent money flow from a source node to a target one. The topology of the MST shows the flow patterns of the international trades. From the MST we can identify the sub-economic zone if we delete the hub node. We observed that the cumulative degree distribution functions follow the power law, P>(k) k-α, with the average exponent α = 1.1(1)). We also calculated the betweenness centrality(BC) of the MST. The cumulative probability distribution of the betweenness centrality follows the power law, P>(BC) BC-β, with the average exponent β = 1.09(7).
Complex networks analysis of obstructive nephropathy data.
Zanin, M; Boccaletti, S
2011-09-01
Congenital obstructive nephropathy (ON) is one of the most frequent nephropathy observed among newborns and children, and the first cause of end-stage renal diseases treated by dialysis or transplantation. This pathology is characterized by the presence of an obstacle in the urinary tract, e.g., stenosis or abnormal implantation of the urethra in the kidney. In spite of important advances, pathological mechanisms are not yet fully understood. In this contribution, the topology of complex networks created upon vectors of features for control and ON subjects is related with the severity of the pathology. Nodes in these networks represent genetic and metabolic profiles, while connections between them indicate an abnormal relation between their expressions. Resulting topologies allow discriminating ON subjects and detecting which genetic or metabolic elements are responsible for the malfunction.
Unveiling causal activity of complex networks
NASA Astrophysics Data System (ADS)
Williams-García, Rashid V.; Beggs, John M.; Ortiz, Gerardo
2017-07-01
We introduce a novel tool for analyzing complex network dynamics, allowing for cascades of causally-related events, which we call causal webs (c-webs), to be separated from other non-causally-related events. This tool shows that traditionally-conceived avalanches may contain mixtures of spatially-distinct but temporally-overlapping cascades of events, and dynamical disorder or noise. In contrast, c-webs separate these components, unveiling previously hidden features of the network and dynamics. We apply our method to mouse cortical data with resulting statistics which demonstrate for the first time that neuronal avalanches are not merely composed of causally-related events. The original version of this article was uploaded to the arXiv on March 17th, 2016 [1].
Cultural dissemination in a complex network
NASA Astrophysics Data System (ADS)
Xiao, X. H.; Ye, G. W.; Wang, B.; He, M. F.
2009-03-01
In this paper, a complex contact network is constructed as substrate for cultural diffusion. Agents are partitioned into “clusters”, interpreted as sub-cultural groups. Cultural dissemination works both within the cluster and across clusters. To reflect connection intensity, an extra-cluster interaction damping coefficient is defined. The probability of interaction between agents through the intra-cluster contact is higher than through extra-cluster. Dynamical behavior of the cultural diffusion model is studied in this contact network. It is found that there is a critical value of extra-interaction intensity that separates the system from a multicultural to mono-cultural state for low values of the number of vectors (options) per cultural feature (attribute).
Burstiness and fractional diffusion on complex networks
NASA Astrophysics Data System (ADS)
de Nigris, Sarah; Hastir, Anthony; Lambiotte, Renaud
2016-04-01
Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on distributions whose average inter-event time diverges, and study its impact on the dynamics of random walkers on networks. The process can naturally be described, in the long time limit, in terms of Riemann-Liouville fractional derivatives. We show that all the dynamical modes possess, in the asymptotic regime, the same power law relaxation, which implies that the dynamics does not exhibit time-scale separation between modes, and that no mode can be neglected versus another one, even for long times. Our results are then confirmed by numerical simulations.
System crash as dynamics of complex networks.
Yu, Yi; Xiao, Gaoxi; Zhou, Jie; Wang, Yubo; Wang, Zhen; Kurths, Jürgen; Schellnhuber, Hans Joachim
2016-10-18
Complex systems, from animal herds to human nations, sometimes crash drastically. Although the growth and evolution of systems have been extensively studied, our understanding of how systems crash is still limited. It remains rather puzzling why some systems, appearing to be doomed to fail, manage to survive for a long time whereas some other systems, which seem to be too big or too strong to fail, crash rapidly. In this contribution, we propose a network-based system dynamics model, where individual actions based on the local information accessible in their respective system structures may lead to the "peculiar" dynamics of system crash mentioned above. Extensive simulations are carried out on synthetic and real-life networks, which further reveal the interesting system evolution leading to the final crash. Applications and possible extensions of the proposed model are discussed.
Complex networks renormalization: flows and fixed points.
Radicchi, Filippo; Ramasco, José J; Barrat, Alain; Fortunato, Santo
2008-10-03
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.
Evaluation method of indoor GPS measurement network
NASA Astrophysics Data System (ADS)
Li, Yang; Zhou, Zili; Ma, Liqun; Li, Qian
2013-01-01
Indoor GPS measurement network is a space coordinate measuring system, which is composed of more than one transmitter. The number and location of the transmitter determine the measurement range and accuracy of the measurement network. Therefore, how to correctly evaluate the measurement network is a key issue. By analyzing the error model of a measuring system, which is composed of two transmitters, we acquired the main cause of the measurement uncertainty. Through MATLAB simulation, we are able to get the effective measurement conditions, in order to meet specific requirement of measurement uncertainty. Meanwhile, total uncertainty of the measurement network, which is composed of measurement uncertainty, location uncertainty, receiver uncertainty and other uncertainties, is analyzed. We proposed the evaluation method based on the reference length, and at the same time, optimized the position of the reference position, posture and length, in order to meet the evaluation requirements of the entire measurement space. Finally, we simulated the measurement network for aircraft assembly in measurement space of 20m×20m×5m, and the measurement network for car assembly in measurement space of 5m×5m×2m. We evaluated the measurement network according to the above principles and estimated the uncertainty of the measurement network trough measurement bias of reference length at different locations.
Detection of hierarchies and complex networks in cerebral synchronization patterns
NASA Astrophysics Data System (ADS)
Ivanov, Plamen Ch.; Hu, Kun; Dammers, Juergen; Fieseler, Thomas; Tass, Peter A.
2003-03-01
We study the synchronization patterns between local current signals obtained from magnetic field tomography at different source points in the human brain during externally and intrinsically driven finger tapping. Based on the estimate of cross-correlation measures we define a ``distance'' between each pair of source points to determine the degree of synchronization in their functional response, and we develop an optimization algorithm to investigate the relation between the functional and physiological structure of the observed complex network of interactions. We identify hierarchies of functional patterns in the network through clusters of source points with different levels of synchronization, and we map these patterns to the anatomical structure of the brain.
From time series to complex networks: the visibility graph.
Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; Luque, Jordi; Nuño, Juan Carlos
2008-04-01
In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view.
Complex Networks/Foundations of Information Systems
2013-03-06
Information Systems 6 March 2013 Robert J. Bonneau, Ph.D. Division Chief AFOSR/RTC Report Documentation Page Form ApprovedOMB No. 0704-0188 Public...if it does not display a currently valid OMB control number. 1. REPORT DATE 06 MAR 2013 2. REPORT TYPE 3. DATES COVERED 00-00-2013 to 00-00...2013 4. TITLE AND SUBTITLE Complex Networks/Foundations of Information Systems 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6
Intervality and coherence in complex networks
NASA Astrophysics Data System (ADS)
Domínguez-García, Virginia; Johnson, Samuel; Muñoz, Miguel A.
2016-06-01
Food webs—networks of predators and prey—have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals. Although the meaning of this axis—usually identified with a "niche" dimension—has remained a mystery, it is assumed to lie at the basis of the highly non-trivial structure of food webs. With this in mind, most trophic network modelling has for decades been based on assigning species a niche value by hand. However, we argue here that intervality should not be considered the cause but rather a consequence of food-web structure. First, analysing a set of 46 empirical food webs, we find that they also exhibit predator intervality: the predators of any given species are as likely to be contiguous as the prey are, but in a different ordering. Furthermore, this property is not exclusive of trophic networks: several networks of genes, neurons, metabolites, cellular machines, airports, and words are found to be approximately as interval as food webs. We go on to show that a simple model of food-web assembly which does not make use of a niche axis can nevertheless generate significant intervality. Therefore, the niche dimension (in the sense used for food-web modelling) could in fact be the consequence of other, more fundamental structural traits. We conclude that a new approach to food-web modelling is required for a deeper understanding of ecosystem assembly, structure, and function, and propose that certain topological features thought to be specific of food webs are in fact common to many complex networks.
Intervality and coherence in complex networks.
Domínguez-García, Virginia; Johnson, Samuel; Muñoz, Miguel A
2016-06-01
Food webs-networks of predators and prey-have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals. Although the meaning of this axis-usually identified with a "niche" dimension-has remained a mystery, it is assumed to lie at the basis of the highly non-trivial structure of food webs. With this in mind, most trophic network modelling has for decades been based on assigning species a niche value by hand. However, we argue here that intervality should not be considered the cause but rather a consequence of food-web structure. First, analysing a set of 46 empirical food webs, we find that they also exhibit predator intervality: the predators of any given species are as likely to be contiguous as the prey are, but in a different ordering. Furthermore, this property is not exclusive of trophic networks: several networks of genes, neurons, metabolites, cellular machines, airports, and words are found to be approximately as interval as food webs. We go on to show that a simple model of food-web assembly which does not make use of a niche axis can nevertheless generate significant intervality. Therefore, the niche dimension (in the sense used for food-web modelling) could in fact be the consequence of other, more fundamental structural traits. We conclude that a new approach to food-web modelling is required for a deeper understanding of ecosystem assembly, structure, and function, and propose that certain topological features thought to be specific of food webs are in fact common to many complex networks.
Review of Public Safety in Viewpoint of Complex Networks
NASA Astrophysics Data System (ADS)
Chengcheng, Gai; Wenguo, Weng; Hongyong, Yuan
2010-05-01
In this paper, a brief review of public safety in viewpoint of complex networks is presented. Public safety incidents are divided into four categories: natural disasters, industry accidents, public health and social security, in which the complex network approaches and theories are need. We review how the complex network methods was developed and used in the studies of the three kinds of public safety incidents. The typical public safety incidents studied by the complex network methods in this paper are introduced, including the natural disaster chains, blackouts on electric power grids and epidemic spreading. Finally, we look ahead to the application prospects of the complex network theory on public safety.
Review of Public Safety in Viewpoint of Complex Networks
Gai Chengcheng; Weng Wenguo; Yuan Hongyong
2010-05-21
In this paper, a brief review of public safety in viewpoint of complex networks is presented. Public safety incidents are divided into four categories: natural disasters, industry accidents, public health and social security, in which the complex network approaches and theories are need. We review how the complex network methods was developed and used in the studies of the three kinds of public safety incidents. The typical public safety incidents studied by the complex network methods in this paper are introduced, including the natural disaster chains, blackouts on electric power grids and epidemic spreading. Finally, we look ahead to the application prospects of the complex network theory on public safety.
Imaging complex nutrient dynamics in mycelial networks.
Fricker, M D; Lee, J A; Bebber, D P; Tlalka, M; Hynes, J; Darrah, P R; Watkinson, S C; Boddy, L
2008-08-01
Transport networks are vital components of multi-cellular organisms, distributing nutrients and removing waste products. Animal cardiovascular and respiratory systems, and plant vasculature, are branching trees whose architecture is thought to determine universal scaling laws in these organisms. In contrast, the transport systems of many multi-cellular fungi do not fit into this conceptual framework, as they have evolved to explore a patchy environment in search of new resources, rather than ramify through a three-dimensional organism. These fungi grow as a foraging mycelium, formed by the branching and fusion of threadlike hyphae, that gives rise to a complex network. To function efficiently, the mycelial network must both transport nutrients between spatially separated source and sink regions and also maintain its integrity in the face of continuous attack by mycophagous insects or random damage. Here we review the development of novel imaging approaches and software tools that we have used to characterise nutrient transport and network formation in foraging mycelia over a range of spatial scales. On a millimetre scale, we have used a combination of time-lapse confocal imaging and fluorescence recovery after photobleaching to quantify the rate of diffusive transport through the unique vacuole system in individual hyphae. These data then form the basis of a simulation model to predict the impact of such diffusion-based movement on a scale of several millimetres. On a centimetre scale, we have used novel photon-counting scintillation imaging techniques to visualize radiolabel movement in small microcosms. This approach has revealed novel N-transport phenomena, including rapid, preferential N-resource allocation to C-rich sinks, induction of simultaneous bi-directional transport, abrupt switching between different pre-existing transport routes, and a strong pulsatile component to transport in some species. Analysis of the pulsatile transport component using Fourier
Optimal localization of diffusion sources in complex networks
Hu, Zhao-Long; Han, Xiao; Lai, Ying-Cheng
2017-01-01
Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications. PMID:28484635
Optimal localization of diffusion sources in complex networks.
Hu, Zhao-Long; Han, Xiao; Lai, Ying-Cheng; Wang, Wen-Xu
2017-04-01
Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.
Complex network synchronization of chaotic systems with delay coupling
Theesar, S. Jeeva Sathya Ratnavelu, K.
2014-03-05
The study of complex networks enables us to understand the collective behavior of the interconnected elements and provides vast real time applications from biology to laser dynamics. In this paper, synchronization of complex network of chaotic systems has been studied. Every identical node in the complex network is assumed to be in Lur’e system form. In particular, delayed coupling has been assumed along with identical sector bounded nonlinear systems which are interconnected over network topology.
Complex quantum network model of energy transfer in photosynthetic complexes.
Ai, Bao-Quan; Zhu, Shi-Liang
2012-12-01
The quantum network model with real variables is usually used to describe the excitation energy transfer (EET) in the Fenna-Matthews-Olson (FMO) complexes. In this paper we add the quantum phase factors to the hopping terms and find that the quantum phase factors play an important role in the EET. The quantum phase factors allow us to consider the space structure of the pigments. It is found that phase coherence within the complexes would allow quantum interference to affect the dynamics of the EET. There exist some optimal phase regions where the transfer efficiency takes its maxima, which indicates that when the pigments are optimally spaced, the exciton can pass through the FMO with perfect efficiency. Moreover, the optimal phase regions almost do not change with the environments. In addition, we find that the phase factors are useful in the EET just in the case of multiple pathways. Therefore, we demonstrate that the quantum phases may bring the other two factors, the optimal space of the pigments and multiple pathways, together to contribute the EET in photosynthetic complexes with perfect efficiency.
Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks
NASA Astrophysics Data System (ADS)
Maletić, S.; Rajković, M.
2012-09-01
Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order analysis in complex networks and compare the results with ordinary graph spectra. Methods and results are obtained using social network of the Zachary karate club.
Topological Phenotypes in Complex Leaf Venation Networks
NASA Astrophysics Data System (ADS)
Ronellenfitsch, Henrik; Lasser, Jana; Daly, Douglas; Katifori, Eleni
2015-03-01
The leaves of vascular plants contain highly complex venation networks consisting of recursively nested, hierarchically organized loops. We analyze the topology of the venation of leaves from ca. 200 species belonging to ca. 10 families, defining topological metrics that quantify the hierarchical nestedness of the network cycles. We find that most of the venation variability can be described by a two dimensional phenotypic space, where one dimension consists of a linear combination of geometrical metrics and the other dimension of topological, previously uncharacterized metrics. We show how this new topological dimension in the phenotypic space significantly improves identification of leaves from fragments, by calculating a ``leaf fingerprint'' from the topology and geometry of the higher order veins. Further, we present a simple model suggesting that the topological phenotypic traits can be explained by noise effects and variations in the timing of higher order vein developmental events. This work opens the path to (a) new quantitative identification techniques for leaves which go beyond simple geometric traits such as vein density and (b) topological quantification of other planar or almost planar networks such as arterial vaculature in the neocortex and lung tissue.
Noncommutative Biology: Sequential Regulation of Complex Networks
Letsou, William; Cai, Long
2016-01-01
Single-cell variability in gene expression is important for generating distinct cell types, but it is unclear how cells use the same set of regulatory molecules to specifically control similarly regulated genes. While combinatorial binding of transcription factors at promoters has been proposed as a solution for cell-type specific gene expression, we found that such models resulted in substantial information bottlenecks. We sought to understand the consequences of adopting sequential logic wherein the time-ordering of factors informs the final outcome. We showed that with noncommutative control, it is possible to independently control targets that would otherwise be activated simultaneously using combinatorial logic. Consequently, sequential logic overcomes the information bottleneck inherent in complex networks. We derived scaling laws for two noncommutative models of regulation, motivated by phosphorylation/neural networks and chromosome folding, respectively, and showed that they scale super-exponentially in the number of regulators. We also showed that specificity in control is robust to the loss of a regulator. Lastly, we connected these theoretical results to real biological networks that demonstrate specificity in the context of promiscuity. These results show that achieving a desired outcome often necessitates roundabout steps. PMID:27560383
Wealth distribution on complex networks with losses
NASA Astrophysics Data System (ADS)
Wang, Fei; Fang, Weiguo
2015-07-01
Wealth distribution plays an important role in the field of econophysics. In this paper, this issue is investigated based on the Bouchaud and Mézard (BM) wealth distribution model by the method of complex networks in this paper. Previous reports usually assumed that wealth increased steadily or was transferred from one agent to another. However, wealth may be lost due to some natural disasters or incidents. Therefore, we introduce terms representing losses in the BM model to describe the economic behavior more precisely. We find that an anti-degree preference helps to create an equitable economic environment. The Gini coefficient of the wealth distribution is calculated, and an optimized preferential parameter is obtained for both the case with losses and the case without losses. For variable values of the parameter, the corresponding results are obtained and discussed. If network topologies are considered, we find that a homogeneous network prompts an equitable economic environment. Simulations prove that losses enlarge the rich-poor gap.
A Complex Network Approach to Stylometry.
Amancio, Diego Raphael
2015-01-01
Statistical methods have been widely employed to study the fundamental properties of language. In recent years, methods from complex and dynamical systems proved useful to create several language models. Despite the large amount of studies devoted to represent texts with physical models, only a limited number of studies have shown how the properties of the underlying physical systems can be employed to improve the performance of natural language processing tasks. In this paper, I address this problem by devising complex networks methods that are able to improve the performance of current statistical methods. Using a fuzzy classification strategy, I show that the topological properties extracted from texts complement the traditional textual description. In several cases, the performance obtained with hybrid approaches outperformed the results obtained when only traditional or networked methods were used. Because the proposed model is generic, the framework devised here could be straightforwardly used to study similar textual applications where the topology plays a pivotal role in the description of the interacting agents.
A Complex Network Approach to Stylometry
Amancio, Diego Raphael
2015-01-01
Statistical methods have been widely employed to study the fundamental properties of language. In recent years, methods from complex and dynamical systems proved useful to create several language models. Despite the large amount of studies devoted to represent texts with physical models, only a limited number of studies have shown how the properties of the underlying physical systems can be employed to improve the performance of natural language processing tasks. In this paper, I address this problem by devising complex networks methods that are able to improve the performance of current statistical methods. Using a fuzzy classification strategy, I show that the topological properties extracted from texts complement the traditional textual description. In several cases, the performance obtained with hybrid approaches outperformed the results obtained when only traditional or networked methods were used. Because the proposed model is generic, the framework devised here could be straightforwardly used to study similar textual applications where the topology plays a pivotal role in the description of the interacting agents. PMID:26313921
Rahman, Rezwanur; Taylor, P C; Scales, John A
2013-08-01
Quasi-optical (QO) methods of dielectric spectroscopy are well established in the millimeter and submillimeter frequency bands. These methods exploit standing wave structure in the sample produced by a transmitted Gaussian beam to achieve accurate, low-noise measurement of the complex permittivity of the sample [e.g., J. A. Scales and M. Batzle, Appl. Phys. Lett. 88, 062906 (2006); R. N. Clarke and C. B. Rosenberg, J. Phys. E 15, 9 (1982); T. M. Hirovnen, P. Vainikainen, A. Lozowski, and A. V. Raisanen, IEEE Trans. Instrum. Meas. 45, 780 (1996)]. In effect the sample itself becomes a low-Q cavity. On the other hand, for optically thin samples (films of thickness much less than a wavelength) or extremely low loss samples (loss tangents below 10(-5)) the QO approach tends to break down due to loss of signal. In such a case it is useful to put the sample in a high-Q cavity and measure the perturbation of the cavity modes. Provided that the average mode frequency divided by the shift in mode frequency is less than the Q (quality factor) of the mode, then the perturbation should be resolvable. Cavity perturbation techniques are not new, but there are technological difficulties in working in the millimeter/submillimeter wave region. In this paper we will show applications of cavity perturbation to the dielectric characterization of semi-conductor thin films of the type used in the manufacture of photovoltaics in the 100 and 350 GHz range. We measured the complex optical constants of hot-wire chemical deposition grown 1-μm thick amorphous silicon (a-Si:H) film on borosilicate glass substrate. The real part of the refractive index and dielectric constant of the glass-substrate varies from frequency-independent to linearly frequency-dependent. We also see power-law behavior of the frequency-dependent optical conductivity from 316 GHz (9.48 cm(-1)) down to 104 GHz (3.12 cm(-1)).
NASA Astrophysics Data System (ADS)
Rahman, Rezwanur; Taylor, P. C.; Scales, John A.
2013-08-01
Quasi-optical (QO) methods of dielectric spectroscopy are well established in the millimeter and submillimeter frequency bands. These methods exploit standing wave structure in the sample produced by a transmitted Gaussian beam to achieve accurate, low-noise measurement of the complex permittivity of the sample [e.g., J. A. Scales and M. Batzle, Appl. Phys. Lett. 88, 062906 (2006);, 10.1063/1.2172403 R. N. Clarke and C. B. Rosenberg, J. Phys. E 15, 9 (1982);, 10.1088/0022-3735/15/1/002 T. M. Hirovnen, P. Vainikainen, A. Lozowski, and A. V. Raisanen, IEEE Trans. Instrum. Meas. 45, 780 (1996)], 10.1109/19.516996. In effect the sample itself becomes a low-Q cavity. On the other hand, for optically thin samples (films of thickness much less than a wavelength) or extremely low loss samples (loss tangents below 10-5) the QO approach tends to break down due to loss of signal. In such a case it is useful to put the sample in a high-Q cavity and measure the perturbation of the cavity modes. Provided that the average mode frequency divided by the shift in mode frequency is less than the Q (quality factor) of the mode, then the perturbation should be resolvable. Cavity perturbation techniques are not new, but there are technological difficulties in working in the millimeter/submillimeter wave region. In this paper we will show applications of cavity perturbation to the dielectric characterization of semi-conductor thin films of the type used in the manufacture of photovoltaics in the 100 and 350 GHz range. We measured the complex optical constants of hot-wire chemical deposition grown 1-μm thick amorphous silicon (a-Si:H) film on borosilicate glass substrate. The real part of the refractive index and dielectric constant of the glass-substrate varies from frequency-independent to linearly frequency-dependent. We also see power-law behavior of the frequency-dependent optical conductivity from 316 GHz (9.48 cm-1) down to 104 GHz (3.12 cm-1).
The geometry of chaotic dynamics — a complex network perspective
NASA Astrophysics Data System (ADS)
Donner, R. V.; Heitzig, J.; Donges, J. F.; Zou, Y.; Marwan, N.; Kurths, J.
2011-12-01
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ɛ-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ɛ-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that ɛ-recurrence networks exhibit an important link between dynamical systems and graph theory.
NASA Astrophysics Data System (ADS)
Donner, R. V.; Zou, Y.; Donges, J. F.; Marwan, N.; Kurths, J.
2009-12-01
We present a new approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network which links different points in time if the evolution of the considered states is very similar. A critical comparison of these recurrence networks with similar existing techniques is presented, revealing strong conceptual benefits of the new approach which can be considered as a unifying framework for transforming time series into complex networks that also includes other methods as special cases. Based on different model systems, we demonstrate that there are fundamental interrelationships between the topological properties of recurrence networks and the statistical properties of the phase space density of the underlying dynamical system. Hence, the network description yields new quantitative characteristics of the dynamical complexity of a time series, which substantially complement existing measures of recurrence quantification analysis. Finally, we illustrate the potential of our approach for detecting hidden dynamical transitions from geoscientific time series by applying it to different paleoclimate records. In particular, we are able to resolve previously unknown climatic regime shifts in East Africa during the last about 4 million years, which might have had a considerable influence on the evolution of hominids in the area.
Complex Chebyshev-polynomial-based unified model (CCPBUM) neural networks
NASA Astrophysics Data System (ADS)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1998-03-01
In this paper, we propose complex Chebyshev Polynomial Based unified model neural network for the approximation of complex- valued function. Based on this approximate transformable technique, we have derived the relationship between the single-layered neural network and multi-layered perceptron neural network. It is shown that the complex Chebyshev Polynomial Based unified model neural network can be represented as a functional link network that are based on Chebyshev polynomial. We also derived a new learning algorithm for the proposed network. It turns out that the complex Chebyshev Polynomial Based unified model neural network not only has the same capability of universal approximator, but also has faster learning speed than conventional complex feedforward/recurrent neural network.
Module detection in complex networks using integer optimisation
2010-01-01
Background The detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks. Results We present a novel solution approach to identify community structure in large complex networks and address resolution limitations in module detection. The proposed algorithm employs modularity to express network community structure and it is based on mixed integer optimisation models. The solution procedure is extended through an iterative procedure to diminish effects that tend to agglomerate smaller modules (resolution limitations). Conclusions A comprehensive comparative analysis of methodologies for module detection based on modularity maximisation shows that our approach outperforms previously reported methods. Furthermore, in contrast to previous reports, we propose a strategy to handle resolution limitations in modularity maximisation. Overall, we illustrate ways to improve existing methodologies for community structure identification so as to increase its efficiency and applicability. PMID:21073720
Zhang, Songchuan; Xia, Youshen; Wang, Jun
2015-12-01
In this paper, we present a complex-valued projection neural network for solving constrained convex optimization problems of real functions with complex variables, as an extension of real-valued projection neural networks. Theoretically, by developing results on complex-valued optimization techniques, we prove that the complex-valued projection neural network is globally stable and convergent to the optimal solution. Obtained results are completely established in the complex domain and thus significantly generalize existing results of the real-valued projection neural networks. Numerical simulations are presented to confirm the obtained results and effectiveness of the proposed complex-valued projection neural network.
Community centrality for node's influential ranking in complex network
NASA Astrophysics Data System (ADS)
Cai, Biao; Tuo, Xian-Guo; Yang, Kai-Xue; Liu, Ming-Zhe
2014-10-01
Some tiny party of influential nodes may highly affect spread of information in complex networks. For the case of very high time complexity in the shortest path computation of global centralities, making use of local community centrality to identify influential nodes is an open and possible problem. Compared to degree and local centralities, a five-heartbeat forward community centrality is proposed in this paper, in which a five-step induced sub-graph of certain node in the network will be achieved. Next, we induce the minimal spanning tree (MMT) of the sub-graph. Finally, we take the sum of all weights of the MMT as community centrality measurement that needs to be the influential ranking of the node. We use the susceptible, infected and recovered (SIR) model to evaluate the performance of this method on several public test network data and explore the forward steps of community centrality by experiments. Simulative results show that our method with five steps can identify the influential ranking of nodes in complex network as well.
The new challenges of multiplex networks: Measures and models
NASA Astrophysics Data System (ADS)
Battiston, Federico; Nicosia, Vincenzo; Latora, Vito
2017-02-01
What do societies, the Internet, and the human brain have in common? They are all examples of complex relational systems, whose emerging behaviours are largely determined by the non-trivial networks of interactions among their constituents, namely individuals, computers, or neurons, rather than only by the properties of the units themselves. In the last two decades, network scientists have proposed models of increasing complexity to better understand real-world systems. Only recently we have realised that multiplexity, i.e. the coexistence of several types of interactions among the constituents of a complex system, is responsible for substantial qualitative and quantitative differences in the type and variety of behaviours that a complex system can exhibit. As a consequence, multilayer and multiplex networks have become a hot topic in complexity science. Here we provide an overview of some of the measures proposed so far to characterise the structure of multiplex networks, and a selection of models aiming at reproducing those structural properties and quantifying their statistical significance. Focusing on a subset of relevant topics, this brief review is a quite comprehensive introduction to the most basic tools for the analysis of multiplex networks observed in the real-world. The wide applicability of multiplex networks as a framework to model complex systems in different fields, from biology to social sciences, and the colloquial tone of the paper will make it an interesting read for researchers working on both theoretical and experimental analysis of networked systems.
Structural Measures for Network Biology Using QuACN
2011-01-01
Background Structural measures for networks have been extensively developed, but many of them have not yet demonstrated their sustainably. That means, it remains often unclear whether a particular measure is useful and feasible to solve a particular problem in network biology. Exemplarily, the classification of complex biological networks can be named, for which structural measures are used leading to a minimal classification error. Hence, there is a strong need to provide freely available software packages to calculate and demonstrate the appropriate usage of structural graph measures in network biology. Results Here, we discuss topological network descriptors that are implemented in the R-package QuACN and demonstrate their behavior and characteristics by applying them to a set of example graphs. Moreover, we show a representative application to illustrate their capabilities for classifying biological networks. In particular, we infer gene regulatory networks from microarray data and classify them by methods provided by QuACN. Note that QuACN is the first freely available software written in R containing a large number of structural graph measures. Conclusion The R package QuACN is under ongoing development and we add promising groups of topological network descriptors continuously. The package can be used to answer intriguing research questions in network biology, e.g., classifying biological data or identifying meaningful biological features, by analyzing the topology of biological networks. PMID:22195644
Dynamical complexity in the C.elegans neural network
NASA Astrophysics Data System (ADS)
Antonopoulos, C. G.; Fokas, A. S.; Bountis, T. C.
2016-09-01
We model the neuronal circuit of the C.elegans soil worm in terms of a Hindmarsh-Rose system of ordinary differential equations, dividing its circuit into six communities which are determined via the Walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical complexity, namely synchronicity, the largest Lyapunov exponent, and the ΦAR auto-regressive integrated information theory measure. We show that ΦAR provides a useful measure of the information contained in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans brain dynamic network generates more information than the sum of its constituent parts, and that attains higher levels of integrated information for couplings for which either all its communities are highly synchronized, or there is a mixed state of highly synchronized and desynchronized communities.
Characterizing global evolutions of complex systems via intermediate network representations.
Iwayama, Koji; Hirata, Yoshito; Takahashi, Kohske; Watanabe, Katsumi; Aihara, Kazuyuki; Suzuki, Hideyuki
2012-01-01
Recent developments in measurement techniques have enabled us to observe the time series of many components simultaneously. Thus, it is important to understand not only the dynamics of individual time series but also their interactions. Although there are many methods for analysing the interaction between two or more time series, there are very few methods that describe global changes of the interactions over time. Here, we propose an approach to visualise time evolution for the global changes of the interactions in complex systems. This approach consists of two steps. In the first step, we construct a meta-time series of networks. In the second step, we analyse and visualise this meta-time series by using distance and recurrence plots. Our two-step approach involving intermediate network representations elucidates the half-a-day periodicity of foreign exchange markets and a singular functional network in the brain related to perceptual alternations.
Properties of volume-capacity ratio in congested complex networks
NASA Astrophysics Data System (ADS)
Zhu, Zhi-Hong; Zheng, Jian-Feng; Gao, Zi-You; Du, Hao-Ming
2014-04-01
The volume-capacity ratio (v/c) is one of the most important indexes to measure the congestion of a traffic network. If v/c is very small, the traffic demand is deficient and/or the transportation supply or capacity is surplus, leading to a waste of capacity; on the contrary, a large value of v/c means that the traffic network is seriously congested. This paper investigates the properties of v/c in complex small-world and scale-free networks by introducing the congestion effects, described by link cost functions. The relationship between v/c and the degree of the node is mainly discussed. Finally, a simple strategy is presented to balance the tradeoff between traffic congestion and a waste of capacity.
Characterizing global evolutions of complex systems via intermediate network representations
NASA Astrophysics Data System (ADS)
Iwayama, Koji; Hirata, Yoshito; Takahashi, Kohske; Watanabe, Katsumi; Aihara, Kazuyuki; Suzuki, Hideyuki
2012-05-01
Recent developments in measurement techniques have enabled us to observe the time series of many components simultaneously. Thus, it is important to understand not only the dynamics of individual time series but also their interactions. Although there are many methods for analysing the interaction between two or more time series, there are very few methods that describe global changes of the interactions over time. Here, we propose an approach to visualise time evolution for the global changes of the interactions in complex systems. This approach consists of two steps. In the first step, we construct a meta-time series of networks. In the second step, we analyse and visualise this meta-time series by using distance and recurrence plots. Our two-step approach involving intermediate network representations elucidates the half-a-day periodicity of foreign exchange markets and a singular functional network in the brain related to perceptual alternations.
Analysis and Reduction of Complex Networks Under Uncertainty.
Ghanem, Roger G
2014-07-31
This effort was a collaboration with Youssef Marzouk of MIT, Omar Knio of Duke University (at the time at Johns Hopkins University) and Habib Najm of Sandia National Laboratories. The objective of this effort was to develop the mathematical and algorithmic capacity to analyze complex networks under uncertainty. Of interest were chemical reaction networks and smart grid networks. The statements of work for USC focused on the development of stochastic reduced models for uncertain networks. The USC team was led by Professor Roger Ghanem and consisted of one graduate student and a postdoc. The contributions completed by the USC team consisted of 1) methodology and algorithms to address the eigenvalue problem, a problem of significance in the stability of networks under stochastic perturbations, 2) methodology and algorithms to characterize probability measures on graph structures with random flows. This is an important problem in characterizing random demand (encountered in smart grid) and random degradation (encountered in infrastructure systems), as well as modeling errors in Markov Chains (with ubiquitous relevance !). 3) methodology and algorithms for treating inequalities in uncertain systems. This is an important problem in the context of models for material failure and network flows under uncertainty where conditions of failure or flow are described in the form of inequalities between the state variables.
The XIOM. Oceanographic measurement network
NASA Astrophysics Data System (ADS)
Jerez, F.; Gómez Aguar, J.; Espino, M.; Puigdefàbregas, J.; . Cateura, J.; López, J.
2009-04-01
DESCRIPTION The XIOM network for oceanographic and coastal meteorological measurements (Xarxa d'Instrumentació Oceanogràfica I Meteorològica) is owned by the Catalan regional government. His deployment is to better understanding of processes that take place in the Spanish Catalan coast, in the NW Mediterranean. The XIOM sea measurement network is formed by the following equipment: 3 directional buoys. 1 scalar buoy. 4 meteo-oceanographical buoys (providing the currents measurements). 2 tide gauge stations. INSTRUMENTATION Wave buoys sends a HF radio signal to a receiver station at the coast and are equipped with ARGOS allocators to allow recovery in case on drift. The receiver stations area composed by antenna, A/D signal converter and the computer. The signal is processed ant the spectral and statistical parameters are sent through internet connection to the main computer. Meteo-oceanographical buoys sends data by satellite (ORBCOMM system) and it's received by e-mail directly in the main computer. Tidal gauges are locally connected to internet connection and sends the data to a main computer. A vast amount of data is collected. In case of waves the main parameters are Hs (significant wave height) spectral and statistical, Tp (peak period), and mean direction of waves in the peak of spectrum. Another parameters are: Tz (mean period), main directional spread, spectral width, and up to 25 different parameters obtained from spectral moments and statistical calculations. In case of meteo-oceanographical buoys, the parameters are velocity of the current, direction of the current and temperature, all of them at -1 m and -15 m. The buoys are equipped also with a standard meteorological station in its upper part that measures parameters like wind velocity and its direction. Tidal gauges measure sea level and water temperature. DATA FLOW In Xiom network, one ftp server centralizes all the directional and scalar buoy's data. It's located at the UPC (Universitat Polit
Liu, Rui; Wang, Xiangdong; Aihara, Kazuyuki; Chen, Luonan
2014-05-01
Many studies have been carried out for early diagnosis of complex diseases by finding accurate and robust biomarkers specific to respective diseases. In particular, recent rapid advance of high-throughput technologies provides unprecedented rich information to characterize various disease genotypes and phenotypes in a global and also dynamical manner, which significantly accelerates the study of biomarkers from both theoretical and clinical perspectives. Traditionally, molecular biomarkers that distinguish disease samples from normal samples are widely adopted in clinical practices due to their ease of data measurement. However, many of them suffer from low coverage and high false-positive rates or high false-negative rates, which seriously limit their further clinical applications. To overcome those difficulties, network biomarkers (or module biomarkers) attract much attention and also achieve better performance because a network (or subnetwork) is considered to be a more robust form to characterize diseases than individual molecules. But, both molecular biomarkers and network biomarkers mainly distinguish disease samples from normal samples, and they generally cannot ensure to identify predisease samples due to their static nature, thereby lacking ability to early diagnosis. Based on nonlinear dynamical theory and complex network theory, a new concept of dynamical network biomarkers (DNBs, or a dynamical network of biomarkers) has been developed, which is different from traditional static approaches, and the DNB is able to distinguish a predisease state from normal and disease states by even a small number of samples, and therefore has great potential to achieve "real" early diagnosis of complex diseases. In this paper, we comprehensively review the recent advances and developments on molecular biomarkers, network biomarkers, and DNBs in particular, focusing on the biomarkers for early diagnosis of complex diseases considering a small number of samples and high
Structural and functional clusters of complex brain networks
NASA Astrophysics Data System (ADS)
Zemanová, Lucia; Zhou, Changsong; Kurths, Jürgen
2006-12-01
Recent research using the complex network approach has revealed a rich and complicated network topology in the cortical connectivity of mammalian brains. It is of importance to understand the implications of such complex network structures in the functional organization of the brain activities. Here we study this problem from the viewpoint of dynamical complex networks. We investigate synchronization dynamics on the corticocortical network of the cat by modeling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behavior, and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex.
Yu, Xiangtian; Zeng, Tao; Wang, Xiangdong; Li, Guojun; Chen, Luonan
2015-06-13
In the conventional analysis of complex diseases, the control and case samples are assumed to be of great purity. However, due to the heterogeneity of disease samples, many disease genes are even not always consistently up-/down-regulated, leading to be under-estimated. This problem will seriously influence effective personalized diagnosis or treatment. The expression variance and expression covariance can address such a problem in a network manner. But, these analyses always require multiple samples rather than one sample, which is generally not available in clinical practice for each individual. To extract the common and specific network characteristics for individual patients in this paper, a novel differential network model, e.g. personalized dysfunctional gene network, is proposed to integrate those genes with different features, such as genes with the differential gene expression (DEG), genes with the differential expression variance (DEVG) and gene-pairs with the differential expression covariance (DECG) simultaneously, to construct personalized dysfunctional networks. This model uses a new statistic-like measurement on differential information, i.e., a differential score (DEVC), to reconstruct the differential expression network between groups of normal and diseased samples; and further quantitatively evaluate different feature genes in the patient-specific network for each individual. This DEVC-based differential expression network (DEVC-net) has been applied to the study of complex diseases for prostate cancer and diabetes. (1) Characterizing the global expression change between normal and diseased samples, the differential gene networks of those diseases were found to have a new bi-coloured topological structure, where their non hub-centred sub-networks are mainly composed of genes/proteins controlling various biological processes. (2) The differential expression variance/covariance rather than differential expression is new informative sources, and can
Robustness of complex networks with an improved breakdown probability against cascading failures
NASA Astrophysics Data System (ADS)
Liu, Jun; Xiong, Qingyu; Shi, Xin; Wang, Kai; Shi, Weiren
2016-08-01
The robustness of complex network is a core issue in complex network research. We agree that not all overload nodes will be removed from the network in real networks because some effective measures can be taken to protect them. But only a few researches consider this issue. Based on previous researches, we propose a cascading model with an improved breakdown probability. Different from previous breakdown probability model, the current model brings in some parameters to explore the optimal distribution strategy of the protection resources. Furthermore, we quantify the allocation of the protection resources. We explore the relationship between the parameters of our cascading model and the robustness of three networks (two typical networks and one real network), based on which we find out the optimal value of the parameter. It in turn helps us to quantify the allocation of protection resources and form an optimal protection strategy. Our work may be helpful for improving the robustness of complex networks.
Complex Gleason measures and the Nemytsky operator
NASA Astrophysics Data System (ADS)
Valles, Miguel A.
This thesis is devoted to generalize previous results on Gleason measures to complex Gleason measures, and to develop a functional calculus for complex measures in relation to the Nemytsky operator. Furthermore we present the interpretation of our results in the field of quantum mechanics, some concrete examples and further extensions of several theorems.
Exceptional reducibility of complex-valued neural networks.
Kobayashi, Masaki
2010-07-01
A neural network is referred to as minimal if it cannot reduce the number of hidden neurons that maintain the input-output map. The condition in which the number of hidden neurons can be reduced is referred to as reducibility. Real-valued neural networks have only three simple types of reducibility. It can be naturally extended to complex-valued neural networks without bias terms of hidden neurons. However, general complex-valued neural networks have another type of reducibility, referred to herein as exceptional reducibility. In this paper, another type of reducibility is presented, and a method by which to minimize complex-valued neural networks is proposed.
Reduced-Complexity Models for Network Performance Prediction
2005-05-01
traffic over the network . To understand such a complex system it is necessary to develop accurate, yet simple, models to describe the performance...interconnected in complex ways, with millions of users sending traffic over the network . To understand such a complex system, it is necessary to develop...number of downloaders . . . . . . . . . . . . . . . . . 17 11 A network of ISP clouds. In this figure, the ISPs are connected via peering points, denoted
Consistency of heterogeneous synchronization patterns in complex weighted networks
NASA Astrophysics Data System (ADS)
Malagarriga, D.; Villa, A. E. P.; Garcia-Ojalvo, J.; Pons, A. J.
2017-03-01
Synchronization within the dynamical nodes of a complex network is usually considered homogeneous through all the nodes. Here we show, in contrast, that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or asymmetries in small networks. We also analyze consistency, defined as the persistence of coexistent synchronization patterns regardless of the initial conditions. Our results show that complex weighted networks display richer consistency than regular networks, suggesting why certain functional network topologies are often constructed when experimental data are analyzed.
Context dependent preferential attachment model for complex networks
NASA Astrophysics Data System (ADS)
Pandey, Pradumn Kumar; Adhikari, Bibhas
2015-10-01
In this paper, we propose a growing random complex network model, which we call context dependent preferential attachment model (CDPAM), when the preference of a new node to get attached to old nodes is determined by the local and global property of the old nodes. We consider that local and global properties of a node as the degree and relative average degree of the node respectively. We prove that the degree distribution of complex networks generated by CDPAM follow power law with exponent lies in the interval [2,3] and the expected diameter grows logarithmically with the size of new nodes added to the initial small network. Numerical results show that the expected diameter stabilizes when alike weights to the local and global properties are assigned by the new nodes. Computing various measures including clustering coefficient, assortativity, number of triangles, algebraic connectivity, spectral radius, we show that the proposed model replicates properties of real networks when alike weights are given to local and global property. Finally, we observe that the BA model is a limiting case of CDPAM when new nodes tend to give large weight to the local property compared to the weight given to the global property during link formation.
Uncertainty quantification for quantum chemical models of complex reaction networks.
Proppe, Jonny; Husch, Tamara; Simm, Gregor N; Reiher, Markus
2016-12-22
For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.
PREFACE: Complex Networks: from Biology to Information Technology
NASA Astrophysics Data System (ADS)
Barrat, A.; Boccaletti, S.; Caldarelli, G.; Chessa, A.; Latora, V.; Motter, A. E.
2008-06-01
The field of complex networks is one of the most active areas in contemporary statistical physics. Ten years after seminal work initiated the modern study of networks, interest in the field is in fact still growing, as indicated by the ever increasing number of publications in network science. The reason for such a resounding success is most likely the simplicity and broad significance of the approach that, through graph theory, allows researchers to address a variety of different complex systems within a common framework. This special issue comprises a selection of contributions presented at the workshop 'Complex Networks: from Biology to Information Technology' held in July 2007 in Pula (Cagliari), Italy as a satellite of the general conference STATPHYS23. The contributions cover a wide range of problems that are currently among the most important questions in the area of complex networks and that are likely to stimulate future research. The issue is organised into four sections. The first two sections describe 'methods' to study the structure and the dynamics of complex networks, respectively. After this methodological part, the issue proceeds with a section on applications to biological systems. The issue closes with a section concentrating on applications to the study of social and technological networks. The first section, entitled Methods: The Structure, consists of six contributions focused on the characterisation and analysis of structural properties of complex networks: The paper Motif-based communities in complex networks by Arenas et al is a study of the occurrence of characteristic small subgraphs in complex networks. These subgraphs, known as motifs, are used to define general classes of nodes and their communities by extending the mathematical expression of the Newman-Girvan modularity. The same line of research, aimed at characterising network structure through the analysis of particular subgraphs, is explored by Bianconi and Gulbahce in Algorithm
Identification of hybrid node and link communities in complex networks.
He, Dongxiao; Jin, Di; Chen, Zheng; Zhang, Weixiong
2015-03-02
Identifying communities in complex networks is an effective means for analyzing complex systems, with applications in diverse areas such as social science, engineering, biology and medicine. Finding communities of nodes and finding communities of links are two popular schemes for network analysis. These schemes, however, have inherent drawbacks and are inadequate to capture complex organizational structures in real networks. We introduce a new scheme and an effective approach for identifying complex mixture structures of node and link communities, called hybrid node-link communities. A central piece of our approach is a probabilistic model that accommodates node, link and hybrid node-link communities. Our extensive experiments on various real-world networks, including a large protein-protein interaction network and a large network of semantically associated words, illustrated that the scheme for hybrid communities is superior in revealing network characteristics. Moreover, the new approach outperformed the existing methods for finding node or link communities separately.
Identification of hybrid node and link communities in complex networks
NASA Astrophysics Data System (ADS)
He, Dongxiao; Jin, Di; Chen, Zheng; Zhang, Weixiong
2015-03-01
Identifying communities in complex networks is an effective means for analyzing complex systems, with applications in diverse areas such as social science, engineering, biology and medicine. Finding communities of nodes and finding communities of links are two popular schemes for network analysis. These schemes, however, have inherent drawbacks and are inadequate to capture complex organizational structures in real networks. We introduce a new scheme and an effective approach for identifying complex mixture structures of node and link communities, called hybrid node-link communities. A central piece of our approach is a probabilistic model that accommodates node, link and hybrid node-link communities. Our extensive experiments on various real-world networks, including a large protein-protein interaction network and a large network of semantically associated words, illustrated that the scheme for hybrid communities is superior in revealing network characteristics. Moreover, the new approach outperformed the existing methods for finding node or link communities separately.
Identification of hybrid node and link communities in complex networks
He, Dongxiao; Jin, Di; Chen, Zheng; Zhang, Weixiong
2015-01-01
Identifying communities in complex networks is an effective means for analyzing complex systems, with applications in diverse areas such as social science, engineering, biology and medicine. Finding communities of nodes and finding communities of links are two popular schemes for network analysis. These schemes, however, have inherent drawbacks and are inadequate to capture complex organizational structures in real networks. We introduce a new scheme and an effective approach for identifying complex mixture structures of node and link communities, called hybrid node-link communities. A central piece of our approach is a probabilistic model that accommodates node, link and hybrid node-link communities. Our extensive experiments on various real-world networks, including a large protein-protein interaction network and a large network of semantically associated words, illustrated that the scheme for hybrid communities is superior in revealing network characteristics. Moreover, the new approach outperformed the existing methods for finding node or link communities separately. PMID:25728010
Complexity measurement based on information theory and kolmogorov complexity.
Lui, Leong Ting; Terrazas, Germán; Zenil, Hector; Alexander, Cameron; Krasnogor, Natalio
2015-01-01
In the past decades many definitions of complexity have been proposed. Most of these definitions are based either on Shannon's information theory or on Kolmogorov complexity; these two are often compared, but very few studies integrate the two ideas. In this article we introduce a new measure of complexity that builds on both of these theories. As a demonstration of the concept, the technique is applied to elementary cellular automata and simulations of the self-organization of porphyrin molecules.
Navigation by anomalous random walks on complex networks
NASA Astrophysics Data System (ADS)
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-11-01
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Navigation by anomalous random walks on complex networks
Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan
2016-01-01
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks. PMID:27876855
NASA Astrophysics Data System (ADS)
Hramov, Alexander E.; Kharchenko, Alexander A.; Khramova, Marina V.; Koronovskii, Alexey A.; Kurovskaya, Maria K.; Makarov, Vladimir V.; Moskalenko, Olga I.; Pavlov, Alexey N.; Dana, Syamal K.
2016-03-01
In the present paper the mechanism of the global synchronization onset through the formation of the synchronous clusters in complex networks with different topologies of links (scale-free networks, small-world networks, random networks) is studied. We consider the dependencies of integral characteristics of synchronous dynamics (synchronization measure, number of synchronous clusters, etc) on coupling strength between nodes. As a basic element of the node oscillator we consider Kuramoto phase oscillator.
Mutual information model for link prediction in heterogeneous complex networks
Shakibian, Hadi; Moghadam Charkari, Nasrollah
2017-01-01
Recently, a number of meta-path based similarity indices like PathSim, HeteSim, and random walk have been proposed for link prediction in heterogeneous complex networks. However, these indices suffer from two major drawbacks. Firstly, they are primarily dependent on the connectivity degrees of node pairs without considering the further information provided by the given meta-path. Secondly, most of them are required to use a single and usually symmetric meta-path in advance. Hence, employing a set of different meta-paths is not straightforward. To tackle with these problems, we propose a mutual information model for link prediction in heterogeneous complex networks. The proposed model, called as Meta-path based Mutual Information Index (MMI), introduces meta-path based link entropy to estimate the link likelihood and could be carried on a set of available meta-paths. This estimation measures the amount of information through the paths instead of measuring the amount of connectivity between the node pairs. The experimental results on a Bibliography network show that the MMI obtains high prediction accuracy compared with other popular similarity indices. PMID:28344326
Improving the Robustness of Complex Networks with Preserving Community Structure
Yang, Yang; Li, Zhoujun; Chen, Yan; Zhang, Xiaoming; Wang, Senzhang
2015-01-01
Complex networks are everywhere, such as the power grid network, the airline network, the protein-protein interaction network, and the road network. The networks are ‘robust yet fragile’, which means that the networks are robust against random failures but fragile under malicious attacks. The cascading failures, system-wide disasters and intentional attacks on these networks are deserving of in-depth study. Researchers have proposed many solutions to improve the robustness of these networks. However whilst many solutions preserve the degree distribution of the networks, little attention is paid to the community structure of these networks. We argue that the community structure of a network is a defining characteristic of a network which identifies its functionality and thus should be preserved. In this paper, we discuss the relationship between robustness and the community structure. Then we propose a 3-step strategy to improve the robustness of a network, while retaining its community structure, and also its degree distribution. With extensive experimentation on representative real-world networks, we demonstrate that our method is effective and can greatly improve the robustness of networks, while preserving community structure and degree distribution. Finally, we give a description of a robust network, which is useful not only for improving robustness, but also for designing robust networks and integrating networks. PMID:25674786
Limits on ecosystem trophic complexity: insights from ecological network analysis.
Ulanowicz, Robert E; Holt, Robert D; Barfield, Michael
2014-02-01
Articulating what limits the length of trophic food chains has remained one of the most enduring challenges in ecology. Mere counts of ecosystem species and transfers have not much illumined the issue, in part because magnitudes of trophic transfers vary by orders of magnitude in power-law fashion. We address this issue by creating a suite of measures that extend the basic indexes usually obtained by counting taxa and transfers so as to apply to networks wherein magnitudes vary by orders of magnitude. Application of the extended measures to data on ecosystem trophic networks reveals that the actual complexity of ecosystem webs is far less than usually imagined, because most ecosystem networks consist of a multitude of weak connections dominated by a relatively few strong flows. Although quantitative ecosystem networks may consist of hundreds of nodes and thousands of transfers, they nevertheless behave similarly to simpler representations of systems with fewer than 14 nodes or 40 flows. Both theory and empirical data point to an upper bound on the number of effective trophic levels at about 3-4 links. We suggest that several whole-system processes may be at play in generating these ecosystem limits and regularities. © 2013 John Wiley & Sons Ltd/CNRS.
Pattern recognition tool based on complex network-based approach
NASA Astrophysics Data System (ADS)
Casanova, Dalcimar; Backes, André Ricardo; Martinez Bruno, Odemir
2013-02-01
This work proposed a generalization of the method proposed by the authors: 'A complex network-based approach for boundary shape analysis'. Instead of modelling a contour into a graph and use complex networks rules to characterize it, here, we generalize the technique. This way, the work proposes a mathematical tool for characterization signals, curves and set of points. To evaluate the pattern description power of the proposal, an experiment of plat identification based on leaf veins image are conducted. Leaf vein is a taxon characteristic used to plant identification proposes, and one of its characteristics is that these structures are complex, and difficult to be represented as a signal or curves and this way to be analyzed in a classical pattern recognition approach. Here, we model the veins as a set of points and model as graphs. As features, we use the degree and joint degree measurements in a dynamic evolution. The results demonstrates that the technique has a good power of discrimination and can be used for plant identification, as well as other complex pattern recognition tasks.
Structure and function of complex brain networks.
Sporns, Olaf
2013-09-01
An increasing number of theoretical and empirical studies approach the function of the human brain from a network perspective. The analysis of brain networks is made feasible by the development of new imaging acquisition methods as well as new tools from graph theory and dynamical systems. This review surveys some of these methodological advances and summarizes recent findings on the architecture of structural and functional brain networks. Studies of the structural connectome reveal several modules or network communities that are interlinked by hub regions mediating communication processes between modules. Recent network analyses have shown that network hubs form a densely linked collective called a "rich club," centrally positioned for attracting and dispersing signal traffic. In parallel, recordings of resting and task-evoked neural activity have revealed distinct resting-state networks that contribute to functions in distinct cognitive domains. Network methods are increasingly applied in a clinical context, and their promise for elucidating neural substrates of brain and mental disorders is discussed.
Dynamical properties of transportation on complex networks
NASA Astrophysics Data System (ADS)
Shen, Bo; Gao, Zi-You
2008-02-01
We study the dynamical properties of transportation considering the topology structure of networks and congestion effects, based on a proposed simple model. We analyze the behavior of the model for finding out the relationship between the properties of transportation and the structure of network. Analysis and numerical results demonstrate that the transition from free flow to congested regime can be observed for both single link load and network load, but it is discontinuous for single link and continuous for network. We also find that networks with large average degree have small average link betweenness and are more tolerant to congestion, and networks with homogeneous structure can hold more vehicles in stationary state at the subcritical region. Furthermore, by allotting capacity with different mode to links, a manner of enhancing the performance of networks is introduced, which should be helpful in the design of traffic networks.
Synchronization between two coupled complex networks.
Li, Changpin; Sun, Weigang; Kurths, Jürgen
2007-10-01
We study synchronization for two unidirectionally coupled networks. This is a substantial generalization of several recent papers investigating synchronization inside a network. We derive analytically a criterion for the synchronization of two networks which have the same (inside) topological connectivity. Then numerical examples are given which fit the theoretical analysis. In addition, numerical calculations for two networks with different topological connections are presented and interesting synchronization and desynchronization alternately appear with increasing value of the coupling strength.
Collective Almost Synchronisation in Complex Networks
Baptista, Murilo S.; Ren, Hai-Peng; Swarts, Johen C. M.; Carareto, Rodrigo; Nijmeijer, Henk; Grebogi, Celso
2012-01-01
This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it. PMID:23144851
Graph theoretical analysis of complex networks in the brain.
Stam, Cornelis J; Reijneveld, Jaap C
2007-07-05
Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern.
Complexities and uncertainties of neuronal network function
Parker, David
2005-01-01
The nervous system generates behaviours through the activity in groups of neurons assembled into networks. Understanding these networks is thus essential to our understanding of nervous system function. Understanding a network requires information on its component cells, their interactions and their functional properties. Few networks come close to providing complete information on these aspects. However, even if complete information were available it would still only provide limited insight into network function. This is because the functional and structural properties of a network are not fixed but are plastic and can change over time. The number of interacting network components, their (variable) functional properties, and various plasticity mechanisms endows networks with considerable flexibility, but these features inevitably complicate network analyses. This review will initially discuss the general approaches and problems of network analyses. It will then examine the success of these analyses in a model spinal cord locomotor network in the lamprey, to determine to what extent in this relatively simple vertebrate system it is possible to claim detailed understanding of network function and plasticity. PMID:16553310
Algorithms and Requirements for Measuring Network Bandwidth
Jin, Guojun
2002-12-08
This report unveils new algorithms for actively measuring (not estimating) available bandwidths with very low intrusion, computing cross traffic, thus estimating the physical bandwidth, provides mathematical proof that the algorithms are accurate, and addresses conditions, requirements, and limitations for new and existing algorithms for measuring network bandwidths. The paper also discusses a number of important terminologies and issues for network bandwidth measurement, and introduces a fundamental parameter -Maximum Burst Size that is critical for implementing algorithms based on multiple packets.
NASA Astrophysics Data System (ADS)
An, Xin-lei; Zhang, Li; Li, Yin-zhen; Zhang, Jian-gang
2014-10-01
On the basis of traditional weighted network, we study a new complex network model with multi-weights, which has one or several different types of weights between any two nodes. According to the method of network split, we split the complex network with multi-weights into several different complex networks with single weight, and study its global synchronization. Taking bus lines as the network nodes, a new public traffic roads network model with multi-weights is established by the proposed network model and space R modeling approach. Then based on the Lyapunov stability theory, the criteria is designed for the global synchronization of the public traffic roads networks with multi-weights. By changing the different weights and taking the Lorenz chaotic system for example, some numerical examples are given to discuss the balance of the whole public traffic roads network.
Recent Progress in Some Active Topics on Complex Networks
NASA Astrophysics Data System (ADS)
Gu, J.; Zhu, Y.; Guo, L.; Jiang, J.; Chi, L.; Li, W.; Wang, Q. A.; Cai, X.
2015-04-01
Complex networks have been extensively studied across many fields, especially in interdisciplinary areas. It has since long been recognized that topological structures and dynamics are important aspects for capturing the essence of complex networks. The recent years have also witnessed the emergence of several new elements which play important roles in network study. By combining the results of different research orientations in our group, we provide here a review of the recent advances in regards to spectral graph theory, opinion dynamics, interdependent networks, graph energy theory and temporal networks. We hope this will be helpful for the newcomers of those fields to discover new intriguing topics.
Oscillations in interconnected complex networks under intentional attack
NASA Astrophysics Data System (ADS)
Zhang, Wen-Ping; Xia, Yongxiang; Tan, Fei
2016-01-01
Many real-world networks are interconnected with each other. In this paper, we study the traffic dynamics in interconnected complex networks under an intentional attack. We find that with the shortest time delay routing strategy, the traffic dynamics can show the stable state, periodic, quasi-periodic and chaotic oscillations, when the capacity redundancy parameter changes. Moreover, compared with isolated complex networks, oscillations always take place in interconnected networks more easily. Thirdly, in interconnected networks, oscillations are affected strongly by the coupling probability and coupling preference.
Sequential defense against random and intentional attacks in complex networks.
Chen, Pin-Yu; Cheng, Shin-Ming
2015-02-01
Network robustness against attacks is one of the most fundamental researches in network science as it is closely associated with the reliability and functionality of various networking paradigms. However, despite the study on intrinsic topological vulnerabilities to node removals, little is known on the network robustness when network defense mechanisms are implemented, especially for networked engineering systems equipped with detection capabilities. In this paper, a sequential defense mechanism is first proposed in complex networks for attack inference and vulnerability assessment, where the data fusion center sequentially infers the presence of an attack based on the binary attack status reported from the nodes in the network. The network robustness is evaluated in terms of the ability to identify the attack prior to network disruption under two major attack schemes, i.e., random and intentional attacks. We provide a parametric plug-in model for performance evaluation on the proposed mechanism and validate its effectiveness and reliability via canonical complex network models and real-world large-scale network topology. The results show that the sequential defense mechanism greatly improves the network robustness and mitigates the possibility of network disruption by acquiring limited attack status information from a small subset of nodes in the network.
Testing time series irreversibility using complex network methods
NASA Astrophysics Data System (ADS)
Donges, Jonathan F.; Donner, Reik V.; Kurths, Jürgen
2013-04-01
The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically, we statistically compare the distributions of time-directed variants of the common complex network measures degree and local clustering coefficient. Our approach does not involve surrogate data and is applicable to relatively short time series. We demonstrate its performance for paradigmatic model systems with known time-reversal properties as well as for picking up signatures of nonlinearity in neuro-physiological data.
Knowledge spillover processes as complex networks
NASA Astrophysics Data System (ADS)
Konno, Tomohiko
2016-11-01
We introduce the model of knowledge spillover on networks. Knowledge spillover is a major source of economic growth; and is a representative externality in economic phenomena. We show that the model has the following four characteristics: (1) the long-run growth rate is not relevant to the mean degree, but is determined by the mean degree of the nearest neighbors; (2) the productivity level of a firm is proportional to the degree of the firm; (3) the long-run growth rate increases with the increasing heterogeneity of the network; and (4) of three representative networks, the largest growth rate is in scale-free networks and the least in regular networks.
Invulnerability study of transit network based on complex network
NASA Astrophysics Data System (ADS)
Wang, Kui; Fu, Xiufen
2017-05-01
In order to ensure the normal operation of urban transit network (abbreviated as UTN) and improve the operating efficiency of UTN, this paper takes UTN of Guangzhou as an example, analyzes the topology characteristics of this transit network, studies the invulnerability of the network under random attack and deliberate attack. The simulation results show that under random attack and under attack based on node degree, continuously removing the number of nodes is almost no effect on network invulnerability, but under attack based on the node betweenness and efficiency, the number of consecutive removed nodes is less, the network invulnerability is worse; Influence on network invulnerability by attack based on node betweenness is more significant than influence on network invulnerability by both random attack and attack based on node degree and efficiency.
A simple model clarifies the complicated relationships of complex networks
Zheng, Bojin; Wu, Hongrun; Kuang, Li; Qin, Jun; Du, Wenhua; Wang, Jianmin; Li, Deyi
2014-01-01
Real-world networks such as the Internet and WWW have many common traits. Until now, hundreds of models were proposed to characterize these traits for understanding the networks. Because different models used very different mechanisms, it is widely believed that these traits origin from different causes. However, we find that a simple model based on optimisation can produce many traits, including scale-free, small-world, ultra small-world, Delta-distribution, compact, fractal, regular and random networks. Moreover, by revising the proposed model, the community-structure networks are generated. By this model and the revised versions, the complicated relationships of complex networks are illustrated. The model brings a new universal perspective to the understanding of complex networks and provide a universal method to model complex networks from the viewpoint of optimisation. PMID:25160506
Linear relation on the correlation in complex networks
NASA Astrophysics Data System (ADS)
Ma, C. W.; Szeto, K. Y.
2006-04-01
Correlation in complex networks follows a linear relation between the degree of a node and the total degrees of its neighbors for six different classes of real networks. This general linear relation is an extension of the Aboav-Weaire law in two-dimensional cellular structures and provides a simple and different perspective on the correlation in complex networks, which is complementary to an existing description using Pearson correlation coefficients and a power law fit. Analytical expression for this linear relation for three standard models of complex networks: the Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert networks is provided. The slope and intercept of this linear relation are described by a single parameter a together with the first and second moment of the degree distribution of the network. The assortivity of the network can be related to the sign of the intercept.
Effective distances for epidemics spreading on complex networks
NASA Astrophysics Data System (ADS)
Iannelli, Flavio; Koher, Andreas; Brockmann, Dirk; Hövel, Philipp; Sokolov, Igor M.
2017-01-01
We show that the recently introduced logarithmic metrics used to predict disease arrival times on complex networks are approximations of more general network-based measures derived from random walks theory. Using the daily air-traffic transportation data we perform numerical experiments to compare the infection arrival time with this alternative metric that is obtained by accounting for multiple walks instead of only the most probable path. The comparison with direct simulations reveals a higher correlation compared to the shortest-path approach used previously. In addition our method allows to connect fundamental observables in epidemic spreading with the cumulant-generating function of the hitting time for a Markov chain. Our results provides a general and computationally efficient approach using only algebraic methods.
From time series to complex networks: The visibility graph
Lacasa, Lucas; Luque, Bartolo; Ballesteros, Fernando; Luque, Jordi; Nuño, Juan Carlos
2008-01-01
In this work we present a simple and fast computational method, the visibility algorithm, that converts a time series into a graph. The constructed graph inherits several properties of the series in its structure. Thereby, periodic series convert into regular graphs, and random series do so into random graphs. Moreover, fractal series convert into scale-free networks, enhancing the fact that power law degree distributions are related to fractality, something highly discussed recently. Some remarkable examples and analytical tools are outlined to test the method's reliability. Many different measures, recently developed in the complex network theory, could by means of this new approach characterize time series from a new point of view. PMID:18362361
Complex Active Optical Networks as a New Laser Concept.
Lepri, Stefano; Trono, Cosimo; Giacomelli, Giovanni
2017-03-24
Complex optical networks containing one or more gain sections are investigated, and the evidence of lasing action is reported; the emission spectrum reflects the topological disorder induced by the connections. A theoretical description compares well with the measurements, mapping the networks to directed graphs and showing the analogies with the problem of quantum chaos on graphs. We show that the interplay of chaotic diffusion and amplification leads to an emission statistic with characteristic heavy tails: for different topologies, an unprecedented experimental demonstration of Lévy statistics expected for random lasers is here provided for a continuous-wave pumped system. This result is also supported by a Monte Carlo simulation based on the ray random walk on the graph.
Complex Active Optical Networks as a New Laser Concept
NASA Astrophysics Data System (ADS)
Lepri, Stefano; Trono, Cosimo; Giacomelli, Giovanni
2017-03-01
Complex optical networks containing one or more gain sections are investigated, and the evidence of lasing action is reported; the emission spectrum reflects the topological disorder induced by the connections. A theoretical description compares well with the measurements, mapping the networks to directed graphs and showing the analogies with the problem of quantum chaos on graphs. We show that the interplay of chaotic diffusion and amplification leads to an emission statistic with characteristic heavy tails: for different topologies, an unprecedented experimental demonstration of Lévy statistics expected for random lasers is here provided for a continuous-wave pumped system. This result is also supported by a Monte Carlo simulation based on the ray random walk on the graph.
Instantiating a Global Network Measurement Framework
Tierney, Brian L.; Boote, Jeff; Boyd, Eric; Brown, Aaron; Grigoriev, Maxim; Metzger, Joe; Swany, Martin; Zekauskas, Matt; Zurawski, Jason
2008-12-15
perfSONAR is a web services-based infrastructure for collecting and publishing network performance monitoring. A primary goal of perfSONAR is making it easier to solve end-to-end performance problems on paths crossing several networks. It contains a set of services delivering performance measurements in a federated environment. These services act as an intermediate layer, between the performance measurement tools and the diagnostic or visualization applications. This layer is aimed at making and exchanging performance measurements across multiple networks and multiple user communities, using well-defined protocols. This paper summarizes the key perfSONAR components, and describes how they are deployed by the US-LHC community to monitor the networks distributing LHC data from CERN. All monitoring data described herein is publicly available, and we hope the availability of this data via a standard schema will inspire others to contribute to the effort by building network data analysis applications that use perfSONAR.
Unification of theoretical approaches for epidemic spreading on complex networks.
Wang, Wei; Tang, Ming; Eugene Stanley, H; Braunstein, Lidia A
2017-03-01
Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.
Unification of theoretical approaches for epidemic spreading on complex networks
NASA Astrophysics Data System (ADS)
Wang, Wei; Tang, Ming; Stanley, H. Eugene; Braunstein, Lidia A.
2017-03-01
Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.
On the robustness of complex heterogeneous gene expression networks.
Gómez-Gardeñes, Jesús; Moreno, Yamir; Floría, Luis M
2005-04-01
We analyze a continuous gene expression model on the underlying topology of a complex heterogeneous network. Numerical simulations aimed at studying the chaotic and periodic dynamics of the model are performed. The results clearly indicate that there is a region in which the dynamical and structural complexity of the system avoid chaotic attractors. However, contrary to what has been reported for Random Boolean Networks, the chaotic phase cannot be completely suppressed, which has important bearings on network robustness and gene expression modeling.
Converting PSO dynamics into complex network - Initial study
NASA Astrophysics Data System (ADS)
Pluhacek, Michal; Janostik, Jakub; Senkerik, Roman; Zelinka, Ivan
2016-06-01
In this paper it is presented the initial study on the possibility of capturing the inner dynamic of Particle Swarm Optimization algorithm into a complex network structure. Inspired in previous works there are two different approaches for creating the complex network presented in this paper. Visualizations of the networks are presented and commented. The possibilities for future applications of the proposed design are given in detail.
Analysis of complex contagions in random multiplex networks
NASA Astrophysics Data System (ADS)
Yaǧan, Osman; Gligor, Virgil
2012-09-01
We study the diffusion of influence in random multiplex networks where links can be of r different types, and, for a given content (e.g., rumor, product, or political view), each link type is associated with a content-dependent parameter ci in [0,∞] that measures the relative bias type i links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their “perceived” proportion of active neighbors exceeds a threshold τ. Namely a node connected to mi active neighbors and ki-mi inactive neighbors via type i links will turn active if ∑cimi/∑ciki exceeds its threshold τ. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by (i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.
Temporal node centrality in complex networks
NASA Astrophysics Data System (ADS)
Kim, Hyoungshick; Anderson, Ross
2012-02-01
Many networks are dynamic in that their topology changes rapidly—on the same time scale as the communications of interest between network nodes. Examples are the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market. While we have good models of static networks, so far these have been lacking for the dynamic case. In this paper we present a simple but powerful model, the time-ordered graph, which reduces a dynamic network to a static network with directed flows. This enables us to extend network properties such as vertex degree, closeness, and betweenness centrality metrics in a very natural way to the dynamic case. We then demonstrate how our model applies to a number of interesting edge cases, such as where the network connectivity depends on a small number of highly mobile vertices or edges, and show that our centrality definition allows us to track the evolution of connectivity. Finally we apply our model and techniques to two real-world dynamic graphs of human contact networks and then discuss the implication of temporal centrality metrics in the real world.
Heterogeneous multidimensional scaling for complex networks
NASA Astrophysics Data System (ADS)
Xuan, Qi; Ma, Xiaodi; Fu, Chenbo; Dong, Hui; Zhang, Guijun; Yu, Li
2015-07-01
Many real-world networks are essentially heterogeneous, where the nodes have different abilities to gain connections. Such networks are difficult to be embedded into low-dimensional Euclidean space if we ignore the heterogeneity and treat all the nodes equally. In this paper, based on a newly defined heterogeneous distance and a generalized network distance under the constraints of network and triangle inequalities, respectively, we propose a new heterogeneous multidimensional scaling method (HMDS) to embed different networks into proper Euclidean spaces. We find that HMDS behaves much better than the traditional multidimensional scaling method (MDS) in embedding different artificial and real-world networks into Euclidean spaces. Besides, we also propose a method to estimate the appropriate dimensions of Euclidean spaces for different networks, and find that the estimated dimensions are quite close to the real dimensions for those geometrical networks under study. These methods thus can help to better understand the evolution of real-world networks, and have practical importance in network visualization, community detection, link prediction and localization of wireless sensors.
Synchronization for linear singularly perturbed complex networks with coupling delays
NASA Astrophysics Data System (ADS)
Cai, Chenxiao; Xu, Jing; Liu, Yurong; Zou, Yun
2015-02-01
This paper is concerned with the synchronization problem about linear singularly perturbed complex network system with coupling delay. The sufficient delay-dependent conditions for the synchronization of the network are established by introducing an equivalent network system with the Lyapunov stability theory. These conditions, which are formulated in terms of linear matrix inequalities, can be solved efficiently by the LMI toolbox of MATLAB. A simulation example is provided to show the validity of the proposed the synchronization conditions of the whole network.
Multiscale ensemble clustering for finding modules in complex networks.
Kim, Eun-Youn; Hwang, Dong-Uk; Ko, Tae-Wook
2012-02-01
The identification of modules in complex networks is important for the understanding of systems. Here, we propose an ensemble clustering method incorporating node groupings in various sizes and the sequential removal of weak ties between nodes which are rarely grouped together. This method successfully detects modules in various networks, such as hierarchical random networks and the American college football network, with known modular structures. Some of the results are compared with those obtained by modularity optimization and K-means clustering.
Network medicine approaches to the genetics of complex diseases.
Silverman, Edwin K; Loscalzo, Joseph
2012-08-01
Complex diseases are caused by perturbations of biological networks. Genetic analysis approaches focused on individual genetic determinants are unlikely to characterize the network architecture of complex diseases comprehensively. Network medicine, which applies systems biology and network science to complex molecular networks underlying human disease, focuses on identifying the interacting genes and proteins which lead to disease pathogenesis. The long biological path between a genetic risk variant and development of a complex disease involves a range of biochemical intermediates, including coding and non-coding RNA, proteins, and metabolites. Transcriptomics, proteomics, metabolomics, and other -omics technologies have the potential to provide insights into complex disease pathogenesis, especially if they are applied within a network biology framework. Most previous efforts to relate genetics to -omics data have focused on a single -omics platform; the next generation of complex disease genetics studies will require integration of multiple types of -omics data sets in a network context. Network medicine may also provide insight into complex disease heterogeneity, serve as the basis for new disease classifications that reflect underlying disease pathogenesis, and guide rational therapeutic and preventive strategies.
Network Medicine Approaches to the Genetics of Complex Diseases
Silverman, Edwin K.; Loscalzo, Joseph
2013-01-01
Complex diseases are caused by perturbations of biological networks. Genetic analysis approaches focused on individual genetic determinants are unlikely to characterize the network architecture of complex diseases comprehensively. Network medicine, which applies systems biology and network science to complex molecular networks underlying human disease, focuses on identifying the interacting genes and proteins which lead to disease pathogenesis. The long biological path between a genetic risk variant and development of a complex disease involves a range of biochemical intermediates, including coding and non-coding RNA, proteins, and metabolites. Transcriptomics, proteomics, metabolomics, and other –omics technologies have the potential to provide insights into complex disease pathogenesis, especially if they are applied within a network biology framework. Most previous efforts to relate genetics to –omics data have focused on a single –omics platform; the next generation of complex disease genetics studies will require integration of multiple types of –omics data sets in a network context. Network medicine may also provide insight into complex disease heterogeneity, serve as the basis for new disease classifications that reflect underlying disease pathogenesis, and guide rational therapeutic and preventive strategies. PMID:22935211
Natural Time Analysis and Complex Networks
NASA Astrophysics Data System (ADS)
Sarlis, Nicholas; Skordas, Efthimios; Lazaridou, Mary; Varotsos, Panayiotis
2013-04-01
Here, we review the analysis of complex time series in a new time domain, termed natural time, introduced by our group [1,2]. This analysis conforms to the desire to reduce uncertainty and extract signal information as much as possible [3]. It enables [4] the distinction between the two origins of self-similarity when analyzing data from complex systems, i.e., whether self-similarity solely results from long-range temporal correlations (the process's memory only) or solely from the process's increments infinite variance (heavy tails in their distribution). Natural time analysis captures the dynamical evolution of a complex system and identifies [5] when the system enters a critical stage. Hence, this analysis plays a key role in predicting forthcoming catastrophic events in general. Relevant examples, compiled in a recent monograph [6], have been presented in diverse fields, including Solid State Physics [7], Statistical Physics (for example systems exhibiting self-organized criticality [8]), Cardiology [9,10], Earth Sciences [11] (Geophysics, Seismology), Environmental Sciences (e.g. see Ref. [12]), etc. Other groups have proposed and developed a network approach to earthquake events with encouraging results. A recent study [13] reveals that this approach is strengthened if we combine it with natural time analysis. In particular, we find [13,14] that the study of the spatial distribution of the variability [15] of the order parameter fluctuations, defined in natural time, provides important information on the dynamical evolution of the system. 1. P. Varotsos, N. Sarlis, and E. Skordas, Practica of Athens Academy, 76, 294-321, 2001. 2. P.A. Varotsos, N.V. Sarlis, and E.S. Skordas, Phys. Rev. E, 66, 011902 , 2002. 3. S. Abe, N.V. Sarlis, E.S. Skordas, H.K. Tanaka and P.A. Varotsos, Phys. Rev. Lett. 94, 170601, 2005. 4. P.A. Varotsos, N.V. Sarlis, E.S. Skordas, H.K. Tanaka and M.S. Lazaridou, Phys. Rev. E, 74, 021123, 2006. 5. P.Varotsos, N. V. Sarlis, E. S. Skordas
Bypass rewiring and robustness of complex networks
NASA Astrophysics Data System (ADS)
Park, Junsang; Hahn, Sang Geun
2016-08-01
A concept of bypass rewiring is introduced, and random bypass rewiring is analytically and numerically investigated with simulations. Our results show that bypass rewiring makes networks robust against removal of nodes including random failures and attacks. In particular, random bypass rewiring connects all nodes except the removed nodes on an even degree infinite network and makes the percolation threshold 0 for arbitrary occupation probabilities. In our example, the even degree network is more robust than the original network with random bypass rewiring, while the original network is more robust than the even degree networks without random bypass. We propose a greedy bypass rewiring algorithm which guarantees the maximum size of the largest component at each step, assuming which node will be removed next is unknown. The simulation result shows that the greedy bypass rewiring algorithm improves the robustness of the autonomous system of the Internet under attacks more than random bypass rewiring.
Complex Network Modeling with an Emulab HPC
2012-09-01
field. Actual Joint Tactical Radio System (JTRS) radios, Operations Network ( OPNET ) emulations, and GNU (recursive definition for GNU is Not Unix...open-source software-defined-radio software/ firmware/ hardware emulations can be accommodated. Index Terms—network emulation, Emulab, OPNET I...other hand, simulation tools such as MATLAB, Optimized Network Engineering Tools ( OPNET ), NS2, and CORE (a modeling environment from Vitech
Measuring and Tracking Complexity in Science
NASA Astrophysics Data System (ADS)
Marczyk, Jacek; Deshpande, Balachandra
Recent years have seen the development of a new approach to the study of diverse problems in natural, social and technological fields: the science of complexity [Gell-Man 1994]. The objective of complex systems science is to comprehend how groups of agents, e.g. people, cells, animals, organizations, the economy, function collectively. The underlying concept of complexity science is that any system is an ensemble of agents that interact. As a result, the system exhibits characteristics different from that of each agent, leading to collective behavior [Gell-Man 1994]. This property is known as emergence [Morowitz 2002]. Moreover, complex systems can adapt to changing environments, and are able to spontaneously self-organize [Sornette 2000]. The dynamics of complex system tends to converge to time patterns, that are known as attractors [Sornette 2000] and is strongly influenced by the agent inter-relationships, which can be represented as networks [Barabasi 2002]. The topological properties of such networks are crucial for determining the collective behavior of the systems, with particular reference to their robustness to external perturbations or to agent failure [Barabasi, Albert 2000], [Dorogovtsev 2003]. Although the theoretical exploration of highly complex systems is usually very difficult, the creation of plausible computer models has been made possible in the past 10-15 years. These models yield new insights into how these systems function. Traditionally, such models were studied within the areas of cellular automata [Chopard 1998], neural networks [Haykin 1999] chaos theory [Sornette 2000], control theory [Aguirre 2000], non-linear dynamics [Sornette 2000] and evolutionary programming [Zhou 2003].
Identifying node importance in complex networks
NASA Astrophysics Data System (ADS)
Hu, Ping; Fan, Wenli; Mei, Shengwei
2015-07-01
In this paper, we propose a novel node importance evaluation method from the perspective of the existence of mutual dependence among nodes. The node importance comprises its initial importance and the importance contributions from both the adjacent and non-adjacent nodes according to the dependence strength between them. From the simulation analyses on an example network and the ARPA network, we observe that our method can well identify the node importance. Then, the cascading failures on the Netscience and E-mail networks demonstrate that the networks are more vulnerable when continuously removing the important nodes identified by our method, which further proves the accuracy of our method.
An anti-attack model based on complex network theory in P2P networks
NASA Astrophysics Data System (ADS)
Peng, Hao; Lu, Songnian; Zhao, Dandan; Zhang, Aixin; Li, Jianhua
2012-04-01
Complex network theory is a useful way to study many real systems. In this paper, an anti-attack model based on complex network theory is introduced. The mechanism of this model is based on a dynamic compensation process and a reverse percolation process in P2P networks. The main purpose of the paper is: (i) a dynamic compensation process can turn an attacked P2P network into a power-law (PL) network with exponential cutoff; (ii) a local healing process can restore the maximum degree of peers in an attacked P2P network to a normal level; (iii) a restoring process based on reverse percolation theory connects the fragmentary peers of an attacked P2P network together into a giant connected component. In this way, the model based on complex network theory can be effectively utilized for anti-attack and protection purposes in P2P networks.
Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison
NASA Astrophysics Data System (ADS)
De Domenico, Manlio; Biamonte, Jacob
2016-10-01
Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Rényi q entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First, we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed with appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral-based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory.
Decision support systems and methods for complex networks
Huang, Zhenyu [Richland, WA; Wong, Pak Chung [Richland, WA; Ma, Jian [Richland, WA; Mackey, Patrick S [Richland, WA; Chen, Yousu [Richland, WA; Schneider, Kevin P [Seattle, WA
2012-02-28
Methods and systems for automated decision support in analyzing operation data from a complex network. Embodiments of the present invention utilize these algorithms and techniques not only to characterize the past and present condition of a complex network, but also to predict future conditions to help operators anticipate deteriorating and/or problem situations. In particular, embodiments of the present invention characterize network conditions from operation data using a state estimator. Contingency scenarios can then be generated based on those network conditions. For at least a portion of all of the contingency scenarios, risk indices are determined that describe the potential impact of each of those scenarios. Contingency scenarios with risk indices are presented visually as graphical representations in the context of a visual representation of the complex network. Analysis of the historical risk indices based on the graphical representations can then provide trends that allow for prediction of future network conditions.
Balance between Noise and Information Flow Maximizes Set Complexity of Network Dynamics
Mäki-Marttunen, Tuomo; Kesseli, Juha; Nykter, Matti
2013-01-01
Boolean networks have been used as a discrete model for several biological systems, including metabolic and genetic regulatory networks. Due to their simplicity they offer a firm foundation for generic studies of physical systems. In this work we show, using a measure of context-dependent information, set complexity, that prior to reaching an attractor, random Boolean networks pass through a transient state characterized by high complexity. We justify this finding with a use of another measure of complexity, namely, the statistical complexity. We show that the networks can be tuned to the regime of maximal complexity by adding a suitable amount of noise to the deterministic Boolean dynamics. In fact, we show that for networks with Poisson degree distributions, all networks ranging from subcritical to slightly supercritical can be tuned with noise to reach maximal set complexity in their dynamics. For networks with a fixed number of inputs this is true for near-to-critical networks. This increase in complexity is obtained at the expense of disruption in information flow. For a large ensemble of networks showing maximal complexity, there exists a balance between noise and contracting dynamics in the state space. In networks that are close to critical the intrinsic noise required for the tuning is smaller and thus also has the smallest effect in terms of the information processing in the system. Our results suggest that the maximization of complexity near to the state transition might be a more general phenomenon in physical systems, and that noise present in a system may in fact be useful in retaining the system in a state with high information content. PMID:23516395
Measurement and Statistics of Application Business in Complex Internet
NASA Astrophysics Data System (ADS)
Wang, Lei; Li, Yang; Li, Yipeng; Wu, Shuhang; Song, Shiji; Ren, Yong
Owing to independent topologies and autonomic routing mechanism, the logical networks formed by Internet application business behavior cause the significant influence on the physical networks. In this paper, the backbone traffic of TUNET (Tsinghua University Networks) is measured, further more, the two most important application business: HTTP and P2P are analyzed at IP-packet level. It is shown that uplink HTTP and P2P packets behavior presents spatio-temporal power-law characteristics with exponents 1.25 and 1.53 respectively. Downlink HTTP packets behavior also presents power-law characteristics, but has more little exponents γ = 0.82 which differs from traditional complex networks research result. Moreover, downlink P2P packets distribution presents an approximate power-law which means that flow equilibrium profits little from distributed peer-to peer mechanism actually.
Identify influential spreaders in complex networks, the role of neighborhood
NASA Astrophysics Data System (ADS)
Liu, Ying; Tang, Ming; Zhou, Tao; Do, Younghae
2016-06-01
Identifying the most influential spreaders is an important issue in controlling the spreading processes in complex networks. Centrality measures are used to rank node influence in a spreading dynamics. Here we propose a node influence measure based on the centrality of a node and its neighbors' centrality, which we call the neighborhood centrality. By simulating the spreading processes in six real-world networks, we find that the neighborhood centrality greatly outperforms the basic centrality of a node such as the degree and coreness in ranking node influence and identifying the most influential spreaders. Interestingly, we discover a saturation effect in considering the neighborhood of a node, which is not the case of the larger the better. Specifically speaking, considering the 2-step neighborhood of nodes is a good choice that balances the cost and performance. If further step of neighborhood is taken into consideration, there is no obvious improvement and even decrease in the ranking performance. The saturation effect may be informative for studies that make use of the local structure of a node to determine its importance in the network.
Community detection based on significance optimization in complex networks
NASA Astrophysics Data System (ADS)
Xiang, Ju; Wang, Zhi-Zhong; Li, Hui-Jia; Zhang, Yan; Li, Fang; Dong, Li-Ping; Li, Jian-Ming; Guo, Li-Juan
2017-05-01
Community structure is an important topological property that extensively exists in various complex networks. In the past decade, much attention has been paid to the design of community-detection methods, while analyzing the behaviors of the methods is also of interest in theoretical research and real applications. Here, we focus on an important measure for community structure, i.e. significance (2013 Sci. Rep. 3 2930). Specifically, we study the effect of various network parameters on this measure, analyze the critical behaviors in partition transition, and then deduce the formula of the critical points and the phase diagrams theoretically. The results show that the critical number of communities in partition transition increases dramatically with the difference between inter-community and intra-community link densities, and thus significance optimization displays higher resolution in community detection than many other methods, but it also may lead to the excessive splitting of communities. By employing the Louvain algorithm to optimize the significance, we confirm the theoretical results on artificial and real-world networks, and further perform a series of comparisons with some classical methods.
Architecture of the Florida Power Grid as a Complex Network
NASA Astrophysics Data System (ADS)
Xu, Yan; Gurfinkel, Aleks Jacob; Rikvold, Per Arne
2014-03-01
Power grids are the largest engineered systems ever built. Our work presents a simple and self-consistent graph-theoretic analysis of the Florida high-voltage power grid as a technological network embedded in two-dimensional space. We take a new perspective on the mixing patterns of generators and loads in power grids, pointing out that the real grid is usually intermediate between the random mixing and semi-bipartite case (in which generator-generator power transmission lines are disallowed). We propose spatial network models for power grids, which are obtained via a Monte Carlo cooling optimization process. Our results suggest some possible design principles behind the complex architecture of the Florida grid, viz. balancing low construction cost (measured by the total length of transmission lines) and an indispensable redundancy (measured by the clustering coefficient and edge multiplicity) responsible for the robustness of the grid. We also study community structures (modularity) of the real and modeled power-grid networks. Such communities can be electrically separated from each other to limit cascading power failures, a technique known as intentional islanding. Supported by NSF Grant No. DMR-1104829.
Architecture of the Florida power grid as a complex network
NASA Astrophysics Data System (ADS)
Xu, Yan; Gurfinkel, Aleks Jacob; Rikvold, Per Arne
2014-05-01
We study the Florida high-voltage power grid as a technological network embedded in space. Measurements of geographical lengths of transmission lines, the mixing of generators and loads, the weighted clustering coefficient, as well as the organization of edge conductance weights show a complex architecture quite different from random-graph models usually considered. In particular, we introduce a parametrized mixing matrix to characterize the mixing pattern of generators and loads in the Florida Grid, which is intermediate between the random mixing case and the semi-bipartite case where generator-generator transmission lines are forbidden. Our observations motivate an investigation of optimization (design) principles leading to the structural organization of power grids. We thus propose two network optimization models for the Florida Grid as a case study. Our results show that the Florida Grid is optimized not only by reducing the construction cost (measured by the total length of power lines), but also through reducing the total pairwise edge resistance in the grid, which increases the robustness of power transmission between generators and loads against random line failures. We then embed our models in spatial areas of different aspect ratios and study how this geometric factor affects the network structure, as well as the box-counting fractal dimension of the grids generated by our models.
Structure and function of complex brain networks
Sporns, Olaf
2013-01-01
An increasing number of theoretical and empirical studies approach the function of the human brain from a network perspective. The analysis of brain networks is made feasible by the development of new imaging acquisition methods as well as new tools from graph theory and dynamical systems. This review surveys some of these methodological advances and summarizes recent findings on the architecture of structural and functional brain networks. Studies of the structural connectome reveal several modules or network communities that are interlinked by hub regions mediating communication processes between modules. Recent network analyses have shown that network hubs form a densely linked collective called a “rich club,” centrally positioned for attracting and dispersing signal traffic. In parallel, recordings of resting and task-evoked neural activity have revealed distinct resting-state networks that contribute to functions in distinct cognitive domains. Network methods are increasingly applied in a clinical context, and their promise for elucidating neural substrates of brain and mental disorders is discussed. PMID:24174898
A complex network representation of wind flows
NASA Astrophysics Data System (ADS)
Gelbrecht, Maximilian; Boers, Niklas; Kurths, Jürgen
2017-03-01
Climate networks have proven to be a valuable method to investigate spatial connectivity patterns of the climate system. However, so far such networks have mostly been applied to scalar observables. In this study, we propose a new method for constructing networks from atmospheric wind fields on two-dimensional isobaric surfaces. By connecting nodes along a spatial environment based on the local wind flow, we derive a network representation of the low-level circulation that captures its most important characteristics. In our approach, network links are placed according to a suitable statistical null model that takes into account the direction and magnitude of the flow. We compare a simulation-based (numerically costly) and a semi-analytical (numerically cheaper) approach to determine the statistical significance of possible connections, and find that both methods yield qualitatively similar results. As an application, we choose the regional climate system of South America and focus on the monsoon season in austral summer. Monsoon systems are generally characterized by substantial changes in the large-scale wind directions, and therefore provide ideal applications for the proposed wind networks. Based on these networks, we are able to reveal the key features of the low-level circulation of the South American Monsoon System, including the South American Low-Level Jet. Networks of the dry and the wet season are compared with each other and their differences are consistent with the literature on South American climate.
Marwan, Norbert; Kurths, Jürgen
2015-09-01
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.
Using Complex Networks to Characterize International Business Cycles
Caraiani, Petre
2013-01-01
Background There is a rapidly expanding literature on the application of complex networks in economics that focused mostly on stock markets. In this paper, we discuss an application of complex networks to study international business cycles. Methodology/Principal Findings We construct complex networks based on GDP data from two data sets on G7 and OECD economies. Besides the well-known correlation-based networks, we also use a specific tool for presenting causality in economics, the Granger causality. We consider different filtering methods to derive the stationary component of the GDP series for each of the countries in the samples. The networks were found to be sensitive to the detrending method. While the correlation networks provide information on comovement between the national economies, the Granger causality networks can better predict fluctuations in countries’ GDP. By using them, we can obtain directed networks allows us to determine the relative influence of different countries on the global economy network. The US appears as the key player for both the G7 and OECD samples. Conclusion The use of complex networks is valuable for understanding the business cycle comovements at an international level. PMID:23483979
Using complex networks to characterize international business cycles.
Caraiani, Petre
2013-01-01
There is a rapidly expanding literature on the application of complex networks in economics that focused mostly on stock markets. In this paper, we discuss an application of complex networks to study international business cycles. We construct complex networks based on GDP data from two data sets on G7 and OECD economies. Besides the well-known correlation-based networks, we also use a specific tool for presenting causality in economics, the Granger causality. We consider different filtering methods to derive the stationary component of the GDP series for each of the countries in the samples. The networks were found to be sensitive to the detrending method. While the correlation networks provide information on comovement between the national economies, the Granger causality networks can better predict fluctuations in countries' GDP. By using them, we can obtain directed networks allows us to determine the relative influence of different countries on the global economy network. The US appears as the key player for both the G7 and OECD samples. The use of complex networks is valuable for understanding the business cycle comovements at an international level.
Optimal structure of complex networks for minimizing traffic congestion.
Zhao, Liang; Cupertino, Thiago Henrique; Park, Kwangho; Lai, Ying-Cheng; Jin, Xiaogang
2007-12-01
To design complex networks to minimize traffic congestion, it is necessary to understand how traffic flow depends on network structure. We study data packet flow on complex networks, where the packet delivery capacity of each node is not fixed. The optimal configuration of capacities to minimize traffic congestion is derived and the critical packet generating rate is determined, below which the network is at a free flow state but above which congestion occurs. Our analysis reveals a direct relation between network topology and traffic flow. Optimal network structure, free of traffic congestion, should have two features: uniform distribution of load over all nodes and small network diameter. This finding is confirmed by numerical simulations. Our analysis also makes it possible to theoretically compare the congestion conditions for different types of complex networks. In particular, we find that network with low critical generating rate is more susceptible to congestion. The comparison has been made on the following complex-network topologies: random, scale-free, and regular.
Complex networks and simple models in biology
de Silva, Eric; Stumpf, Michael P.H
2005-01-01
The analysis of molecular networks, such as transcriptional, metabolic and protein interaction networks, has progressed substantially because of the power of models from statistical physics. Increasingly, the data are becoming so detailed—though not always complete or correct—that the simple models are reaching the limits of their usefulness. Here, we will discuss how network information can be described and to some extent quantified. In particular statistics offers a range of tools, such as model selection, which have not yet been widely applied in the analysis of biological networks. We will also outline a number of present challenges posed by biological network data in systems biology, and the extent to which these can be addressed by new developments in statistics, physics and applied mathematics. PMID:16849202
Entropic origin of disassortativity in complex networks.
Johnson, Samuel; Torres, Joaquín J; Marro, J; Muñoz, Miguel A
2010-03-12
Why are most empirical networks, with the prominent exception of social ones, generically degree-degree anticorrelated? To answer this long-standing question, we define the ensemble of correlated networks and obtain the associated Shannon entropy. Maximum entropy can correspond to either assortative (correlated) or disassortative (anticorrelated) configurations, but in the case of highly heterogeneous, scale-free networks a certain disassortativity is predicted--offering a parsimonious explanation for the question above. Our approach provides a neutral model from which, in the absence of further knowledge regarding network evolution, one can obtain the expected value of correlations. When empirical observations deviate from the neutral predictions--as happens for social networks--one can then infer that there are specific correlating mechanisms at work.
NASA Astrophysics Data System (ADS)
Donges, Jonathan F.; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V.; Marwan, Norbert; Dijkstra, Henk A.; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
Donges, Jonathan F; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V; Marwan, Norbert; Dijkstra, Henk A; Kurths, Jürgen
2015-11-01
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.
One Single Static Measurement Predicts Wave Localization in Complex Structures.
Lefebvre, Gautier; Gondel, Alexane; Dubois, Marc; Atlan, Michael; Feppon, Florian; Labbé, Aimé; Gillot, Camille; Garelli, Alix; Ernoult, Maxence; Mayboroda, Svitlana; Filoche, Marcel; Sebbah, Patrick
2016-08-12
A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.
Complex networks from lévy noise
NASA Astrophysics Data System (ADS)
Zhang, J.-Fang; Shao, Z.-Gang
2011-09-01
We construct complex networks from lévy noise (LN) using visibility algorithm proposed by Lucas lacasa el al. It is found that as the stability index α of the symmetric LN decreases, the corresponding complex network will transit from exponential network to long-tailed-degree-distribution one, and then to Gaussian one. The associated network for symmetric LN is the high clustering, hierarchy, and 18 community network. The properties of the associated networks for asymmetric LN except the skewness parameter β = -1 are similar with that for symmetric one. The associated network for the asymmetric LN with the skewness parameter β = -1 is always the exponential, high clustering, and hierarchy one with small k-clique communities.
Analysis of complex network performance and heuristic node removal strategies
NASA Astrophysics Data System (ADS)
Jahanpour, Ehsan; Chen, Xin
2013-12-01
Removing important nodes from complex networks is a great challenge in fighting against criminal organizations and preventing disease outbreaks. Six network performance metrics, including four new metrics, are applied to quantify networks' diffusion speed, diffusion scale, homogeneity, and diameter. In order to efficiently identify nodes whose removal maximally destroys a network, i.e., minimizes network performance, ten structured heuristic node removal strategies are designed using different node centrality metrics including degree, betweenness, reciprocal closeness, complement-derived closeness, and eigenvector centrality. These strategies are applied to remove nodes from the September 11, 2001 hijackers' network, and their performance are compared to that of a random strategy, which removes randomly selected nodes, and the locally optimal solution (LOS), which removes nodes to minimize network performance at each step. The computational complexity of the 11 strategies and LOS is also analyzed. Results show that the node removal strategies using degree and betweenness centralities are more efficient than other strategies.
Assessing Low-Intensity Relationships in Complex Networks
Spitz, Andreas; Gimmler, Anna; Stoeck, Thorsten; Zweig, Katharina Anna; Horvát, Emőke-Ágnes
2016-01-01
Many large network data sets are noisy and contain links representing low-intensity relationships that are difficult to differentiate from random interactions. This is especially relevant for high-throughput data from systems biology, large-scale ecological data, but also for Web 2.0 data on human interactions. In these networks with missing and spurious links, it is possible to refine the data based on the principle of structural similarity, which assesses the shared neighborhood of two nodes. By using similarity measures to globally rank all possible links and choosing the top-ranked pairs, true links can be validated, missing links inferred, and spurious observations removed. While many similarity measures have been proposed to this end, there is no general consensus on which one to use. In this article, we first contribute a set of benchmarks for complex networks from three different settings (e-commerce, systems biology, and social networks) and thus enable a quantitative performance analysis of classic node similarity measures. Based on this, we then propose a new methodology for link assessment called z* that assesses the statistical significance of the number of their common neighbors by comparison with the expected value in a suitably chosen random graph model and which is a consistently top-performing algorithm for all benchmarks. In addition to a global ranking of links, we also use this method to identify the most similar neighbors of each single node in a local ranking, thereby showing the versatility of the method in two distinct scenarios and augmenting its applicability. Finally, we perform an exploratory analysis on an oceanographic plankton data set and find that the distribution of microbes follows similar biogeographic rules as those of macroorganisms, a result that rejects the global dispersal hypothesis for microbes. PMID:27096435
Assessing Low-Intensity Relationships in Complex Networks.
Spitz, Andreas; Gimmler, Anna; Stoeck, Thorsten; Zweig, Katharina Anna; Horvát, Emőke-Ágnes
2016-01-01
Many large network data sets are noisy and contain links representing low-intensity relationships that are difficult to differentiate from random interactions. This is especially relevant for high-throughput data from systems biology, large-scale ecological data, but also for Web 2.0 data on human interactions. In these networks with missing and spurious links, it is possible to refine the data based on the principle of structural similarity, which assesses the shared neighborhood of two nodes. By using similarity measures to globally rank all possible links and choosing the top-ranked pairs, true links can be validated, missing links inferred, and spurious observations removed. While many similarity measures have been proposed to this end, there is no general consensus on which one to use. In this article, we first contribute a set of benchmarks for complex networks from three different settings (e-commerce, systems biology, and social networks) and thus enable a quantitative performance analysis of classic node similarity measures. Based on this, we then propose a new methodology for link assessment called z* that assesses the statistical significance of the number of their common neighbors by comparison with the expected value in a suitably chosen random graph model and which is a consistently top-performing algorithm for all benchmarks. In addition to a global ranking of links, we also use this method to identify the most similar neighbors of each single node in a local ranking, thereby showing the versatility of the method in two distinct scenarios and augmenting its applicability. Finally, we perform an exploratory analysis on an oceanographic plankton data set and find that the distribution of microbes follows similar biogeographic rules as those of macroorganisms, a result that rejects the global dispersal hypothesis for microbes.
Integrated Genomic and Network-Based Analyses of Complex Diseases and Human Disease Network.
Al-Harazi, Olfat; Al Insaif, Sadiq; Al-Ajlan, Monirah A; Kaya, Namik; Dzimiri, Nduna; Colak, Dilek
2016-06-20
A disease phenotype generally reflects various pathobiological processes that interact in a complex network. The highly interconnected nature of the human protein interaction network (interactome) indicates that, at the molecular level, it is difficult to consider diseases as being independent of one another. Recently, genome-wide molecular measurements, data mining and bioinformatics approaches have provided the means to explore human diseases from a molecular basis. The exploration of diseases and a system of disease relationships based on the integration of genome-wide molecular data with the human interactome could offer a powerful perspective for understanding the molecular architecture of diseases. Recently, subnetwork markers have proven to be more robust and reliable than individual biomarker genes selected based on gene expression profiles alone, and achieve higher accuracy in disease classification. We have applied one of these methodologies to idiopathic dilated cardiomyopathy (IDCM) data that we have generated using a microarray and identified significant subnetworks associated with the disease. In this paper, we review the recent endeavours in this direction, and summarize the existing methodologies and computational tools for network-based analysis of complex diseases and molecular relationships among apparently different disorders and human disease network. We also discuss the future research trends and topics of this promising field.
Structural Interrelationship in the Ecosystem Network Using Method of Complex Networks
NASA Astrophysics Data System (ADS)
Petrova, I.; Loew, A.
2012-04-01
Complex Networks have been recently successfully applied to problems in climate science. They have been used as an alternative method to reveal persistent structural features in the climate system based on observed and model simulated fields of temperature, precipitation and other meteorological fields. CCN provide information on the topology, dynamics and stability characteristic features in the climate system and help to e.g. identify regions with large importance for teleconnections. The present paper uses climate networks to analyze results from the Earth System Model of the Max-Planck-Institute for Meteorology, conducted in the frame of the Coupled Model Intercomparison Project Phase 5 (CMIP5). By analyzing local and global measures such as centralities and link distance the climate and especially terrestrial teleconnection patterns are revealed and investigated. To construct the network the 30- year time-series (1979-2009) of evaporation flux, gross and net primary production were retrieved from the two experimental setups of the MPI-ESM using either a full coupled climate model (ocean, atmosphere, land) or prescribed sea surface temperature fields (atmosphere, land only). The major teleconnection patterns discovered were associated with climate related energy information flow and material cycling functionality within the Earth system. Non-local spatial linkages to the main teleconnection patterns, like NAO and ENSO were analyzed, as well as spatial-temporal structures obtained by the community detection method were established. An outlook of using complex networks as an alternative tool for the evaluation of coupled Earth System models will be given.
Enhancing Traffic Capacity of Two-Layer Complex Networks
NASA Astrophysics Data System (ADS)
Jiang, Zhong-Yuan; Liang, Man-Gui; Zhang, Shuai; Zhou, Weixing; Jin, Huiqin
2013-08-01
As two-layer or multi-layer network model can more accurately reveal many real structures of complex systems such as peer-to-peer (P2P) networks on IP networks, to better understand the traffic dynamics and improve the network traffic capacity, we propose to efficiently construct the structure of upper logical layer network which can be possibly implemented. From the beginning, we assume that the logical layer network has the same structure as the lower physical layer network, and then we use link-removal strategy in which a fraction of links with maximal product (ki* kj) are removed from the logical layer, where ki and kj are the degrees of node i and node j, respectively. Traffic load is strongly redistributed from center nodes to noncenter nodes. The traffic capacity of whole complex system is enhanced several times at the expense of a little average path lengthening. In two-layer network model, the physical layer network structure is unchanged and the shortest path routing strategy is used. The structure of upper layer network can been constructed freely under our own methods. This mechanism can be employed in many real complex systems to improve the network traffic capacity.
Partial-Nodes-Based State Estimation for Complex Networks With Unbounded Distributed Delays.
Liu, Yurong; Wang, Zidong; Yuan, Yuan; Alsaadi, Fuad E
2017-09-07
In this brief, the new problem of partial-nodes-based (PNB) state estimation problem is investigated for a class of complex network with unbounded distributed delays and energy-bounded measurement noises. The main novelty lies in that the states of the complex network are estimated through measurement outputs of a fraction of the network nodes. Such fraction of the nodes is determined by either the practical availability or the computational necessity. The PNB state estimator is designed such that the error dynamics of the network state estimation is exponentially ultimately bounded in the presence of measurement errors. Sufficient conditions are established to ensure the existence of the PNB state estimators and then the explicit expression of the gain matrices of such estimators is characterized. When the network measurements are free of noises, the main results specialize to the case of exponential stability for error dynamics. Numerical examples are presented to verify the theoretical results.
NASA Astrophysics Data System (ADS)
Vargas, David L.
Emerging quantum simulator technologies provide a new challenge to quantum many body theory. Quantifying the emergent order in and predicting the dynamics of such complex quantum systems requires a new approach. We develop such an approach based on complex network analysis of quantum mutual information. First, we establish the usefulness of quantum mutual information complex networks by reproducing the phase diagrams of transverse Ising and Bose-Hubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to non-equilibrium quantum dynamics. We conclude with a study of student collaboration networks, correlating a student's role in a collaboration network with their grades. This work thus initiates a quantitative theory of quantum complexity and provides a new tool for physics education research. (Abstract shortened by ProQuest.).
Hierarchical organization unveiled by functional connectivity in complex brain networks.
Zhou, Changsong; Zemanová, Lucia; Zamora, Gorka; Hilgetag, Claus C; Kurths, Jürgen
2006-12-08
How do diverse dynamical patterns arise from the topology of complex networks? We study synchronization dynamics in the cortical brain network of the cat, which displays a hierarchically clustered organization, by modeling each node (cortical area) with a subnetwork of interacting excitable neurons. We find that in the biologically plausible regime the dynamics exhibits a hierarchical modular organization, in particular, revealing functional clusters coinciding with the anatomical communities at different scales. Our results provide insights into the relationship between network topology and functional organization of complex brain networks.
A CAD system based on complex networks theory to characterize mass in mammograms
NASA Astrophysics Data System (ADS)
Watanabe, Carolina Y. V.; Ramos, Jonathan S.; Traina, Agma J. M.; Traina, Caetano, Jr.
2012-03-01
This paper presents a Computer-Aided Diagnosis (CAD) system for mammograms, which is based on complex networks to shape boundary characterization of mass in mammograms, suggesting a "second opinion" to the health specialist. A region of interest (the mass) is automatically segmented using an improved algorithm based on EM/MPM and the shape is modeled into a scale-free complex network. Topological measurements of the resulting network are used to compose the shape descriptors. The experiments comparing the complex network approach with other traditional descriptors, in detecting breast cancer in mammograms, show that the proposed approach accomplish the best values of accuracy. Hence, the results indicate that complex networks are wellsuited to characterize mammograms.
Toward link predictability of complex networks
Lü, Linyuan; Pan, Liming; Zhou, Tao; Zhang, Yi-Cheng; Stanley, H. Eugene
2015-01-01
The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in the consistency of structural features before and after a random removal of a small set of links. Based on the perturbation of the adjacency matrix, we propose a universal structural consistency index that is free of prior knowledge of network organization. Extensive experiments on disparate real-world networks demonstrate that (i) structural consistency is a good estimation of link predictability and (ii) a derivative algorithm outperforms state-of-the-art link prediction methods in both accuracy and robustness. This analysis has further applications in evaluating link prediction algorithms and monitoring sudden changes in evolving network mechanisms. It will provide unique fundamental insights into the above-mentioned academic research fields, and will foster the development of advanced information filtering technologies of interest to information technology practitioners. PMID:25659742
Toward link predictability of complex networks.
Lü, Linyuan; Pan, Liming; Zhou, Tao; Zhang, Yi-Cheng; Stanley, H Eugene
2015-02-24
The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in the consistency of structural features before and after a random removal of a small set of links. Based on the perturbation of the adjacency matrix, we propose a universal structural consistency index that is free of prior knowledge of network organization. Extensive experiments on disparate real-world networks demonstrate that (i) structural consistency is a good estimation of link predictability and (ii) a derivative algorithm outperforms state-of-the-art link prediction methods in both accuracy and robustness. This analysis has further applications in evaluating link prediction algorithms and monitoring sudden changes in evolving network mechanisms. It will provide unique fundamental insights into the above-mentioned academic research fields, and will foster the development of advanced information filtering technologies of interest to information technology practitioners.
Immunizing complex networks with limited budget
NASA Astrophysics Data System (ADS)
Mirzasoleiman, Baharan; Babaei, Mahmoudreza; Jalili, Mahdi
2012-05-01
In this letter we studied the epidemic spreading on scale-free networks assuming a limited budget for immunization. We proposed a general model in which the immunity of an individual against the disease depends on its immunized friends in the network. Furthermore, we considered the possibility that each individual might be eager to pay a price to buy the vaccine and become immune against the disease. Under these assumptions we proposed an algorithm for improving the performance of all previous immunization algorithms. We also introduced a heuristic extension of the algorithm, which works well in scale-free networks.
Inhomogeneity induces relay synchronization in complex networks
NASA Astrophysics Data System (ADS)
Gambuzza, Lucia Valentina; Frasca, Mattia; Fortuna, Luigi; Boccaletti, Stefano
2016-04-01
Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.
Inhomogeneity induces relay synchronization in complex networks.
Gambuzza, Lucia Valentina; Frasca, Mattia; Fortuna, Luigi; Boccaletti, Stefano
2016-04-01
Relay synchronization is a collective state, originally found in chains of interacting oscillators, in which uncoupled dynamical units synchronize through the action of mismatched inner nodes that relay the information but do not synchronize with them. It is demonstrated herein that relay synchronization is not limited to such simple motifs, rather it can emerge in larger and arbitrary network topologies. In particular, we show how this phenomenon can be observed in networks of chaotic systems in the presence of some mismatched units, the relay nodes, and how it is actually responsible for an enhancement of synchronization in the network.
An Algebraic Approach to Inference in Complex Networked Structures
2015-07-09
AFRL-AFOSR-VA-TR-2015-0265 An Algebraic Approach to Inference in Complex Networked Structures Jose Moura CARNEGIE MELLON UNIVERSITY Final Report 07...31-03-2015 4. TITLE AND SUBTITLE An Algebraic Approach to Inference in Complex Networked Structures 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1...Final Report: An Algebraic Approach to Inference in Complex Networked Structures FA9550-12-1-0087 4/1/2012-3/31/2015 José M F Moura Carnegie Mellon
Network Compression as a Quality Measure for Protein Interaction Networks
Royer, Loic; Reimann, Matthias; Stewart, A. Francis; Schroeder, Michael
2012-01-01
With the advent of large-scale protein interaction studies, there is much debate about data quality. Can different noise levels in the measurements be assessed by analyzing network structure? Because proteomic regulation is inherently co-operative, modular and redundant, it is inherently compressible when represented as a network. Here we propose that network compression can be used to compare false positive and false negative noise levels in protein interaction networks. We validate this hypothesis by first confirming the detrimental effect of false positives and false negatives. Second, we show that gold standard networks are more compressible. Third, we show that compressibility correlates with co-expression, co-localization, and shared function. Fourth, we also observe correlation with better protein tagging methods, physiological expression in contrast to over-expression of tagged proteins, and smart pooling approaches for yeast two-hybrid screens. Overall, this new measure is a proxy for both sensitivity and specificity and gives complementary information to standard measures such as average degree and clustering coefficients. PMID:22719828
Locating influential nodes in complex networks
Malliaros, Fragkiskos D.; Rossi, Maria-Evgenia G.; Vazirgiannis, Michalis
2016-01-01
Understanding and controlling spreading processes in networks is an important topic with many diverse applications, including information dissemination, disease propagation and viral marketing. It is of crucial importance to identify which entities act as influential spreaders that can propagate information to a large portion of the network, in order to ensure efficient information diffusion, optimize available resources or even control the spreading. In this work, we capitalize on the properties of the K-truss decomposition, a triangle-based extension of the core decomposition of graphs, to locate individual influential nodes. Our analysis on real networks indicates that the nodes belonging to the maximal K-truss subgraph show better spreading behavior compared to previously used importance criteria, including node degree and k-core index, leading to faster and wider epidemic spreading. We further show that nodes belonging to such dense subgraphs, dominate the small set of nodes that achieve the optimal spreading in the network. PMID:26776455
Evolutionary vaccination dilemma in complex networks
NASA Astrophysics Data System (ADS)
Cardillo, Alessio; Reyes-Suárez, Catalina; Naranjo, Fernando; Gómez-Gardeñes, Jesús
2013-09-01
In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or do not take the vaccine upon their previous experience. Our framework thus puts in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect, scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns. However, when imperfection appears we find a crossover effect so that the number of infected (vaccinated) individuals increases (decreases) with respect to homogeneous networks, thus showing the competition between the aforementioned properties of scale-free graphs.
Data reliability in complex directed networks
NASA Astrophysics Data System (ADS)
Sanz, Joaquín; Cozzo, Emanuele; Moreno, Yamir
2013-12-01
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open problem. From Biology to Sociology and Economics, the identification of false and missing positives has become a problem that calls for a solution. In this work we extend one of the newest, best performing models—due to Guimerá and Sales-Pardo in 2009—to directed networks. The new methodology is able to identify missing and spurious directed interactions with more precision than previous approaches, which renders it particularly useful for analyzing data reliability in systems like trophic webs, gene regulatory networks, communication patterns and several social systems. We also show, using real-world networks, how the method can be employed to help search for new interactions in an efficient way.
Traffic of particles in complex networks.
Germano, Renato; de Moura, Alessandro P S
2006-09-01
The study of the information flow through communication networks, such as the Internet, is of great importance. In the Internet, information flows in discrete units ("packets"), and the capacity of storage and processing of information of computers is finite. Thus if there are many packets walking on the network at the same time, they will interfere with each other. To understand this, we propose an idealized model, in which many particles move randomly on the network, and the nodes support limited numbers of particles. The maximum number of packets supported by a node can be any positive integer, and can be different for each node. We analyze the statistical properties of this model, obtaining analytical expressions for the mean occupation of each node, for different network topologies. The analytical results are shown to be in agreement with numerical simulations.
Evolutionary vaccination dilemma in complex networks.
Cardillo, Alessio; Reyes-Suárez, Catalina; Naranjo, Fernando; Gómez-Gardeñes, Jesús
2013-09-01
In this work we analyze the evolution of voluntary vaccination in networked populations by entangling the spreading dynamics of an influenza-like disease with an evolutionary framework taking place at the end of each influenza season so that individuals take or do not take the vaccine upon their previous experience. Our framework thus puts in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors. Our results show that when vaccine is perfect, scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns. However, when imperfection appears we find a crossover effect so that the number of infected (vaccinated) individuals increases (decreases) with respect to homogeneous networks, thus showing the competition between the aforementioned properties of scale-free graphs.
Locating influential nodes in complex networks
NASA Astrophysics Data System (ADS)
Malliaros, Fragkiskos D.; Rossi, Maria-Evgenia G.; Vazirgiannis, Michalis
2016-01-01
Understanding and controlling spreading processes in networks is an important topic with many diverse applications, including information dissemination, disease propagation and viral marketing. It is of crucial importance to identify which entities act as influential spreaders that can propagate information to a large portion of the network, in order to ensure efficient information diffusion, optimize available resources or even control the spreading. In this work, we capitalize on the properties of the K-truss decomposition, a triangle-based extension of the core decomposition of graphs, to locate individual influential nodes. Our analysis on real networks indicates that the nodes belonging to the maximal K-truss subgraph show better spreading behavior compared to previously used importance criteria, including node degree and k-core index, leading to faster and wider epidemic spreading. We further show that nodes belonging to such dense subgraphs, dominate the small set of nodes that achieve the optimal spreading in the network.
Nonparametric Sparsification of Complex Multiscale Networks
Foti, Nicholas J.; Hughes, James M.; Rockmore, Daniel N.
2011-01-01
Many real-world networks tend to be very dense. Particular examples of interest arise in the construction of networks that represent pairwise similarities between objects. In these cases, the networks under consideration are weighted, generally with positive weights between any two nodes. Visualization and analysis of such networks, especially when the number of nodes is large, can pose significant challenges which are often met by reducing the edge set. Any effective “sparsification” must retain and reflect the important structure in the network. A common method is to simply apply a hard threshold, keeping only those edges whose weight exceeds some predetermined value. A more principled approach is to extract the multiscale “backbone” of a network by retaining statistically significant edges through hypothesis testing on a specific null model, or by appropriately transforming the original weight matrix before applying some sort of threshold. Unfortunately, approaches such as these can fail to capture multiscale structure in which there can be small but locally statistically significant similarity between nodes. In this paper, we introduce a new method for backbone extraction that does not rely on any particular null model, but instead uses the empirical distribution of similarity weight to determine and then retain statistically significant edges. We show that our method adapts to the heterogeneity of local edge weight distributions in several paradigmatic real world networks, and in doing so retains their multiscale structure with relatively insignificant additional computational costs. We anticipate that this simple approach will be of great use in the analysis of massive, highly connected weighted networks. PMID:21346815
Introduction to Focus Issue: synchronization in complex networks.
Suykens, Johan A K; Osipov, Grigory V
2008-09-01
Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon relevant for the understanding of working mechanisms in neuronal networks, genetic networks, coupled electrical and laser networks, coupled mechanical systems, networks in social sciences, and others. It relates to mathematical and computational analysis of the existence of different states and its stability, clustering, bifurcations and chaos, robustness and sensitivity analysis, etc., at the intersection between synchronization and pattern formation in complex networks. This interdisciplinary oriented Focus Issue presents recent progress in this area with contributions on generic methods, specific model studies, and applications.
Complex quantum networks as structured environments: engineering and probing
NASA Astrophysics Data System (ADS)
Nokkala, Johannes; Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina; Piilo, Jyrki
2016-05-01
We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity.
Inferring Complex Network Topology from Spatio-Temporal Spike Patterns
NASA Astrophysics Data System (ADS)
van Bussel, Frank; Kriener, Birgit; Timme, Marc
2011-03-01
The problem of reconstructing or reverse-engineering the connectivity of networks consisting of dynamically interacting units has become an active area of study in fields such as genetics, ecology, and neuroscience. The collective dynamics of such networks is often sensitive to the presence (or absence) of individual interactions, but there is commonly no direct way to probe for their existence. We present an explicit method for reconstructing neuronal networks from their spiking activity. The approach works well for networks in simple collective states, but is also applicable to networks exhibiting complex spatio-temporal spike patterns. In particular, stationarity of spiking time series is not required.
Complex quantum networks as structured environments: engineering and probing
Nokkala, Johannes; Galve, Fernando; Zambrini, Roberta; Maniscalco, Sabrina; Piilo, Jyrki
2016-01-01
We consider structured environments modeled by bosonic quantum networks and investigate the probing of their spectral density, structure, and topology. We demonstrate how to engineer a desired spectral density by changing the network structure. Our results show that the spectral density can be very accurately detected via a locally immersed quantum probe for virtually any network configuration. Moreover, we show how the entire network structure can be reconstructed by using a single quantum probe. We illustrate our findings presenting examples of spectral densities and topology probing for networks of genuine complexity. PMID:27230125
The guitar chord-generating algorithm based on complex network
NASA Astrophysics Data System (ADS)
Ren, Tao; Wang, Yi-fan; Du, Dan; Liu, Miao-miao; Siddiqi, Awais
2016-02-01
This paper aims to generate chords for popular songs automatically based on complex network. Firstly, according to the characteristics of guitar tablature, six chord networks of popular songs by six pop singers are constructed and the properties of all networks are concluded. By analyzing the diverse chord networks, the accompaniment regulations and features are shown, with which the chords can be generated automatically. Secondly, in terms of the characteristics of popular songs, a two-tiered network containing a verse network and a chorus network is constructed. With this network, the verse and chorus can be composed respectively with the random walk algorithm. Thirdly, the musical motif is considered for generating chords, with which the bad chord progressions can be revised. This method can make the accompaniments sound more melodious. Finally, a popular song is chosen for generating chords and the new generated accompaniment sounds better than those done by the composers.
The complexity and robustness of metro networks
NASA Astrophysics Data System (ADS)
Derrible, Sybil; Kennedy, Christopher
2010-09-01
Transportation systems, being real-life examples of networks, are particularly interesting to analyze from the viewpoint of the new and rapidly emerging field of network science. Two particular concepts seem to be particularly relevant: scale-free patterns and small-worlds. By looking at 33 metro systems in the world, this paper adapts network science methodologies to the transportation literature, and offers one application to the robustness of metros; here, metro refers to urban rail transit with exclusive right-of-way, whether it is underground, at grade or elevated. We find that most metros are indeed scale-free (with scaling factors ranging from 2.10 to 5.52) and small-worlds; they show atypical behaviors, however, with increasing size. In particular, the presence of transfer-hubs (stations hosting more than three lines) results in relatively large scaling factors. The analysis provides insights/recommendations for increasing the robustness of metro networks. Smaller networks should focus on creating transfer stations, thus generating cycles to offer alternative routes. For larger networks, few stations seem to detain a certain monopole on transferring, it is therefore important to create additional transfers, possibly at the periphery of city centers; the Tokyo system seems to remarkably incorporate these properties.
NASA Astrophysics Data System (ADS)
Cong, Jin; Liu, Haitao
2014-12-01
Amid the enthusiasm for real-world networks of the new millennium, the enquiry into linguistic networks is flourishing not only as a productive branch of the new networks science but also as a promising approach to linguistic research. Although the complex network approach constitutes a potential opportunity to make linguistics a science, the world of linguistics seems unprepared to embrace it. For one thing, linguistics has been largely unaffected by quantitative methods. Those who are accustomed to qualitative linguistic methods may find it hard to appreciate the application of quantitative properties of language such as frequency and length, not to mention quantitative properties of language modeled as networks. With this in mind, in our review [1] we restrict ourselves to the basics of complex networks and the new insights into human language with the application of complex networks. For another, while breaking new grounds and posing new challenges for linguistics, the complex network approach to human language as a new tradition of linguistic research is faced with challenges and unsolved issues of its own. It is no surprise that the comments on our review, especially their skepticism and suggestions, focus on various different aspects of the complex network approach to human language. We are grateful to all the insightful and penetrating comments, which, together with our review, mark a significant impetus to linguistic research from the complex network approach. In this reply, we would like to address four major issues of the complex network approach to human language, namely, a) its theoretical rationale, b) its application in linguistic research, c) interpretation of the results, and d) directions of future research.
Reduction of complex signaling networks to a representative kernel.
Kim, Jeong-Rae; Kim, Junil; Kwon, Yung-Keun; Lee, Hwang-Yeol; Heslop-Harrison, Pat; Cho, Kwang-Hyun
2011-05-31
The network of biomolecular interactions that occurs within cells is large and complex. When such a network is analyzed, it can be helpful to reduce the complexity of the network to a "kernel" that maintains the essential regulatory functions for the output under consideration. We developed an algorithm to identify such a kernel and showed that the resultant kernel preserves the network dynamics. Using an integrated network of all of the human signaling pathways retrieved from the KEGG (Kyoto Encyclopedia of Genes and Genomes) database, we identified this network's kernel and compared the properties of the kernel to those of the original network. We found that the percentage of essential genes to the genes encoding nodes outside of the kernel was about 10%, whereas ~32% of the genes encoding nodes within the kernel were essential. In addition, we found that 95% of the kernel nodes corresponded to Mendelian disease genes and that 93% of synthetic lethal pairs associated with the network were contained in the kernel. Genes corresponding to nodes in the kernel had low evolutionary rates, were ubiquitously expressed in various tissues, and were well conserved between species. Furthermore, kernel genes included many drug targets, suggesting that other kernel nodes may be potential drug targets. Owing to the simplification of the entire network, the efficient modeling of a large-scale signaling network and an understanding of the core structure within a complex framework become possible.
Mathematical modelling of complex contagion on clustered networks
NASA Astrophysics Data System (ADS)
O'sullivan, David J.; O'Keeffe, Gary; Fennell, Peter; Gleeson, James
2015-09-01
The spreading of behavior, such as the adoption of a new innovation, is influenced bythe structure of social networks that interconnect the population. In the experiments of Centola (Science, 2010), adoption of new behavior was shown to spread further and faster across clustered-lattice networks than across corresponding random networks. This implies that the “complex contagion” effects of social reinforcement are important in such diffusion, in contrast to “simple” contagion models of disease-spread which predict that epidemics would grow more efficiently on random networks than on clustered networks. To accurately model complex contagion on clustered networks remains a challenge because the usual assumptions (e.g. of mean-field theory) regarding tree-like networks are invalidated by the presence of triangles in the network; the triangles are, however, crucial to the social reinforcement mechanism, which posits an increased probability of a person adopting behavior that has been adopted by two or more neighbors. In this paper we modify the analytical approach that was introduced by Hebert-Dufresne et al. (Phys. Rev. E, 2010), to study disease-spread on clustered networks. We show how the approximation method can be adapted to a complex contagion model, and confirm the accuracy of the method with numerical simulations. The analytical results of the model enable us to quantify the level of social reinforcement that is required to observe—as in Centola’s experiments—faster diffusion on clustered topologies than on random networks.
The independent spreaders involved SIR Rumor model in complex networks
NASA Astrophysics Data System (ADS)
Qian, Zhen; Tang, Shaoting; Zhang, Xiao; Zheng, Zhiming
2015-07-01
Recent studies of rumor or information diffusion process in complex networks show that in contrast to traditional comprehension, individuals who participate in rumor spreading within one network do not always get the rumor from their neighbors. They can obtain the rumor from different sources like online social networks and then publish it on their personal sites. In our paper, we discuss this phenomenon in complex networks by adopting the concept of independent spreaders. Rather than getting the rumor from neighbors, independent spreaders learn it from other channels. We further develop the classic "ignorant-spreaders-stiflers" or SIR model of rumor diffusion process in complex networks. A steady-state analysis is conducted to investigate the final spectrum of the rumor spreading under various spreading rate, stifling rate, density of independent spreaders and average degree of the network. Results show that independent spreaders effectively enhance the rumor diffusion process, by delivering the rumor to regions far away from the current rumor infected regions. And though the rumor spreading process in SF networks is faster than that in ER networks, the final size of rumor spreading in ER networks is larger than that in SF networks.
Barrenas, Fredrik; Chavali, Sreenivas; Holme, Petter; Mobini, Reza; Benson, Mikael
2009-11-30
Previous studies of network properties of human disease genes have mainly focused on monogenic diseases or cancers and have suffered from discovery bias. Here we investigated the network properties of complex disease genes identified by genome-wide association studies (GWAs), thereby eliminating discovery bias. We derived a network of complex diseases (n = 54) and complex disease genes (n = 349) to explore the shared genetic architecture of complex diseases. We evaluated the centrality measures of complex disease genes in comparison with essential and monogenic disease genes in the human interactome. The complex disease network showed that diseases belonging to the same disease class do not always share common disease genes. A possible explanation could be that the variants with higher minor allele frequency and larger effect size identified using GWAs constitute disjoint parts of the allelic spectra of similar complex diseases. The complex disease gene network showed high modularity with the size of the largest component being smaller than expected from a randomized null-model. This is consistent with limited sharing of genes between diseases. Complex disease genes are less central than the essential and monogenic disease genes in the human interactome. Genes associated with the same disease, compared to genes associated with different diseases, more often tend to share a protein-protein interaction and a Gene Ontology Biological Process. This indicates that network neighbors of known disease genes form an important class of candidates for identifying novel genes for the same disease.
Complex network approach to classifying classical piano compositions
NASA Astrophysics Data System (ADS)
Xin, Chen; Zhang, Huishu; Huang, Jiping
2016-10-01
Complex network has been regarded as a useful tool handling systems with vague interactions. Hence, numerous applications have arised. In this paper we construct complex networks for 770 classical piano compositions of Mozart, Beethoven and Chopin based on musical note pitches and lengths. We find prominent distinctions among network edges of different composers. Some stylized facts can be explained by such parameters of network structures and topologies. Further, we propose two classification methods for music styles and genres according to the discovered distinctions. These methods are easy to implement and the results are sound. This work suggests that complex network could be a decent way to analyze the characteristics of musical notes, since it could provide a deep view into understanding of the relationships among notes in musical compositions and evidence for classification of different composers, styles and genres of music.
Introduction to focus issue: mesoscales in complex networks.
Almendral, Juan A; Criado, Regino; Leyva, Inmaculada; Buldú, Javier M; Sendiña-Nadal, Irene
2011-03-01
Although the functioning of real complex networks is greatly determined by modularity, the majority of articles have focused, until recently, on either their local scale structure or their macroscopical properties. However, neither of these descriptions can adequately describe the important features that complex networks exhibit due to their organization in modules. This Focus Issue precisely presents the state of the art on the study of complex networks at that intermediate level. The reader will find out why this mesoscale level has become an important topic of research through the latest advances carried out to improve our understanding of the dynamical behavior of modular networks. The contributions presented here have been chosen to cover, from different viewpoints, the many open questions in the field as different aspects of community definition and detection algorithms, moduli overlapping, dynamics on modular networks, interplay between scales, and applications to biological, social, and technological fields.
Measures of complexity in signal analysis
Kurths, J.; Schwarz, U.; Witt, A.; Krampe, R.T.; Abel, M.
1996-06-01
Observational data of natural systems, as measured in astrophysical, geophysical or physiological experiments are typically quite different from those obtained in laboratories. Due to the peculiarities with these data, well-known characteristics processes, such as periodicities or fractal dimension, often do not provide a suitable description. To study such data, we present here the use of measures of complexity, which are mainly basing on symbolic dynamics. We distinguish two types of such quantities: traditional measures (e.g. algorithmic complexity) which are measures of randomness and alternative measures (e.g. {epsilon}-complexity) which relate highest complexity to some critical points. It is important to note that there is no optimum measure of complexity. Its choice should depend on the context. Mostly, a combination of some such quantities is appropriate. Applying this concept to three examples in astrophysics, cardiology and cognitive psychology, we show that it can be helpful also in cases where other tools of data analysis fail. {copyright} {ital 1996 American Institute of Physics.}
Mapping Creativity: Creativity Measurements Network Analysis
ERIC Educational Resources Information Center
Pinheiro, Igor Reszka; Cruz, Roberto Moraes
2014-01-01
This article borrowed network analysis tools to discover how the construct formed by the set of all measures of creativity configures itself. To this end, using a variant of the meta-analytical method, a database was compiled simulating 42,381 responses to 974 variables centered on 64 creativity measures. Results, although preliminary, indicate…
Mapping Creativity: Creativity Measurements Network Analysis
ERIC Educational Resources Information Center
Pinheiro, Igor Reszka; Cruz, Roberto Moraes
2014-01-01
This article borrowed net