Adaptive Synchronization in Small-World Dynamical Networks
Institute of Scientific and Technical Information of China (English)
ZOU Yan-li; ZHU Jie; LUO Xiao-shu
2007-01-01
Adaptive synchronization in NW small-world dynamical networks was studied. Firstly, an adaptive synchronization method is presented and explained. Then, it is applied to two different classes of dynamical networks,one is a class-B network, small-world connected R(o)ssler oscillators, the other is a class-A network, small-world connected Chua's circuits. The simulation verifies the validity of the presented method. It also shows that the adaptive synchronization method is robust to the variations of the node systems parameters. So the presented method can be used in networks whose node systems have unknown or time-varying parameters.
Collective Relaxation Dynamics of Small-World Networks
Grabow, Carsten; Kurths, Jürgen; Timme, Marc
2015-01-01
Complex networks exhibit a wide range of collective dynamic phenomena, including synchronization, diffusion, relaxation, and coordination processes. Their asymptotic dynamics is generically characterized by the local Jacobian, graph Laplacian or a similar linear operator. The structure of networks with regular, small-world and random connectivities are reasonably well understood, but their collective dynamical properties remain largely unknown. Here we present a two-stage mean-field theory to derive analytic expressions for network spectra. A single formula covers the spectrum from regular via small-world to strongly randomized topologies in Watts-Strogatz networks, explaining the simultaneous dependencies on network size N, average degree k and topological randomness q. We present simplified analytic predictions for the second largest and smallest eigenvalue, and numerical checks confirm our theoretical predictions for zero, small and moderate topological randomness q, including the entire small-world regime...
Phase multistability in a dynamical small world network
Energy Technology Data Exchange (ETDEWEB)
Shabunin, A. V., E-mail: shabuninav@info.sgu.ru [Radiophysics and Nonlinear Dynamics Department, Saratov State University, Saratov (Russian Federation)
2015-01-15
The effect of phase multistability is explored in a small world network of periodic oscillators with diffusive couplings. The structure of the network represents a ring with additional non-local links, which spontaneously arise and vanish between arbitrary nodes. The dynamics of random couplings is modeled by “birth” and “death” stochastic processes by means of the cellular automate approach. The evolution of the network under gradual increasing of the number of random couplings goes through stages of phases fluctuations and spatial cluster formation. Finally, in the presence of non-local couplings the phase multistability “dies” and only the in-phase regime survives.
Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics
Watanabe, Akitomo; Mizutaka, Shogo; Yakubo, Kousuke
2015-11-01
We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. In contrast, networks far from criticality have small-world structures. We also observe the crossover behavior from fractal to small-world structure in the network evolution.
Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics
Watanabe, Akitomo; Yakubo, Kousuke
2015-01-01
We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. In contrast, networks far from criticality have small-world structures. We also observe the crossover behavior from fractal to small-world structure in the network evolution.
Institute of Scientific and Technical Information of China (English)
ZOU Zhi-Yun; MAO Bao-Hua; HAO Hai-Ming; GAO Jian-Zhi; YANG Jie-Jiao
2009-01-01
According to the deficiencies in Watts and Strogatz's small-world network model, we present a new regular model to establish the small-world network. Besides the property of the small-world, this model has other properties such as accuracy in controlling the average shortest path length L, and the average clustering coefficient C, also regular network topology as well as enhanced network robustness. This method improves the construction of the small-world network essentially, so that the regular small-world network closely resembles the actual network. We also present studies on the relationships among the quantities of a variety of edges, L and C in regular small-world network in detail. This research lays the foundation for the establishment of the regular small-world network and acts as a good guidance for further research of this model and its applications.
Self-Organized Criticality in Small-World Networks Based on the Social Balance Dynamics
Institute of Scientific and Technical Information of China (English)
MENG Qing-Kuan
2011-01-01
A node model is proposed to study the self-organized criticality in the small-world networks which represent the social networks. Based on the node model and the social balance dynamics, the social networks are mapped to the thermodynamic systems and the phenomena are studied with physical methods. It is found that the avalanche in the small-world networks at the critical state satisfies the power-law distribution spatially and temporally.%A node model is proposed to study the self-organized criticality in the small-world networks which represent the social networks.Based on the node model and the social balance dynamics,the social networks are mapped to the thermodynamic systems and the phenomena are studied with physical methods.It is found that the avalanche in the small-world networks at the critical state satisfies the power-law distribution spatially and temporally.The balance dynamics on social networks[1] based on the notion of social balance has been studied.[2-4]In Ref.[2],the authors studied the triad balance dynamic on a completely connected network representing a social network.At each step,they choose a triad relation from the social network and let it evolve.When the network gets dynamically balanced,they will reach the distributions of each triad relation.Moreover,other researchers subsequently carried out several studies on balance dynamics.[5,6]In this Letter,a node model is proposed to describe the triad relations,so the edge relations in Ref.[2] are changed to node relations,which may be more a universal method to study the phenomena in social networks.We will introduce the node model later.
Directory of Open Access Journals (Sweden)
Sinisa Pajevic
2009-01-01
Full Text Available Cascading activity is commonly found in complex systems with directed interactions such as metabolic networks, neuronal networks, or disease spreading in social networks. Substantial insight into a system's organization can be obtained by reconstructing the underlying functional network architecture from the observed activity cascades. Here we focus on Bayesian approaches and reduce their computational demands by introducing the Iterative Bayesian (IB and Posterior Weighted Averaging (PWA methods. We introduce a special case of PWA, cast in nonparametric form, which we call the normalized count (NC algorithm. NC efficiently reconstructs random and small-world functional network topologies and architectures from subcritical, critical, and supercritical cascading dynamics and yields significant improvements over commonly used correlation methods. With experimental data, NC identified a functional and structural small-world topology and its corresponding traffic in cortical networks with neuronal avalanche dynamics.
Directed Dynamic Small-World Network Model for Worm Epidemics in Mobile ad hoc Networks
Institute of Scientific and Technical Information of China (English)
ZHU Chen-Ping; WANG Li; LIU Xiao-Ting; YAN Zhi-Jun
2012-01-01
We investigate the worm spreading process in mobile ad hoc networks with a susceptible-infected-recovered model on a two-dimensional plane.A medium access control mechanism operates within it,inhibiting transmission and relaying a message by using other nodes inside the node's transmitting circle during speaking.We measure the rewiring probability p with the transmitting range r and the average relative velocity (v) of the moving nodes,and map the problem into a directed dynamic small-world network.A new scaling relation for the recovered portion of the nodes reveals the effect caused by geometric distance,which has been ignored by previous models.%We investigate the worm spreading process in mobile ad hoc networks with a susceptible-infected-recovered model on a two-dimensional plane. A medium access control mechanism operates within it, inhibiting transmission and relaying a message by using other nodes inside the node's transmitting circle during speaking. We measure the rewiring probability p with the transmitting range r and the average relative velocity (v) of the moving nodes, and map the problem into a directed dynamic small-world network. A new scaling relation for the recovered portion of the nodes reveals the effect caused by geometric distance, which has been ignored by previous models.
Dynamics of organizational rumor communication on connecting multi-small-world networks
Institute of Scientific and Technical Information of China (English)
Xing Qi-Bin; Zhang Yuan-Biao; Liang Zhi-Ning; ZhangFan
2011-01-01
We study the dynamics of an epidemic-like model for the spread of a rumor on a connecting multi-small-world-network (CM-SWN) model,which represents organizational communication in the real world.It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of network randomness.Here,by numerical means,we perform a quantitative characterization of the evolution in the three groups under two evolution rules,namely the conformity and obeying principles.The variant of a dynamic CM-SWN,where the quenched disorder of small-world networks is replaced by randomly changing connections between individuals in a single network and stable connection by star nodes between networks,is also analysed in detail and compared with a mean-field approximation.
Institute of Scientific and Technical Information of China (English)
ZHANG Xue; YANG Qiu-Ying; ZHENG Tai-Yu; ZHANG Ying-Yue; ZHENG Li; ZHANG Gui-Qing; CHEN Tian-Lun
2008-01-01
In this paper, we investigate the effect due to the change of topology structure of network on the nonlinear dynamical behavior, by virtue of the OFC neuron evolution model with attack and repair strategy based on the small world. In particular, roles of various parameters relating to the dynamical behavior are carefully studied and analyzed. In addition, the avalanche and EEG-like wave activities with attack and repair strategy are also explored in detail in this work.
Dynamic range in small-world networks of Hodgkin-Huxley neurons with chemical synapses
Batista, C. A. S.; Viana, R. L.; Lopes, S. R.; Batista, A. M.
2014-09-01
According to Stevens' law the relationship between stimulus and response is a power-law within an interval called the dynamic range. The dynamic range of sensory organs is found to be larger than that of a single neuron, suggesting that the network structure plays a key role in the behavior of both the scaling exponent and the dynamic range of neuron assemblies. In order to verify computationally the relationships between stimulus and response for spiking neurons, we investigate small-world networks of neurons described by the Hodgkin-Huxley equations connected by chemical synapses. We found that the dynamic range increases with the network size, suggesting that the enhancement of the dynamic range observed in sensory organs, with respect to single neurons, is an emergent property of complex network dynamics.
Wei, Zong-Wen; Han, Xiao-Pu
2011-01-01
Quantum networks are critical to quantum communication and distributed quantum computing. Here we propose a small-world model of large-scale quantum repeater networks, where "small-world" is a fundamental concept rooted in complex networks, which describe a broad range of real systems. The core of the model is to relate the hierarchical fashion of measurements to coarse-graining process, when quantum repeater protocols are implemented. We demonstrate that quantum repeater networks with fractal structure can be enlarged with certain length scale in geographic space, while preserving topology by performing renormalization. Actually, renormalization here serves as an organizing principle determining the distribution of long-range entangled links over quantum networks, which gives rise to fractal to small-world transition. Furthermore, by iterative implementation of renormalization on the former coarse-grained network, we eventually obtain an onion-like, hierarchical quantum small-world network, where the distanc...
Dynamics in small worlds of tree topologies of wireless sensor networks
DEFF Research Database (Denmark)
Li, Qiao; Zhang, Baihai; Fan, Zhun
2012-01-01
Tree topologies, which construct spatial graphs with large characteristic path lengths and small clustering coefficients, are ubiquitous in deployments of wireless sensor networks. Small worlds are investigated in tree-based networks. Due to link additions, characteristic path lengths reduce...
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we introduce a modified small-world network added with new links with preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. Several dynamical character of the model such as the evolution graph, fo avalanche, the critical exponent D and τ, and the distribution of mutation times of all the nodes, show particular behaviors different from those of the model based on the regular network and the small-world network.
The dynamic consequences of cooperation and competition in small-world networks.
Fernández-Rosales, Iván Y; Liebovitch, Larry S; Guzmán-Vargas, Lev
2015-01-01
We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.
The dynamic consequences of cooperation and competition in small-world networks.
Directory of Open Access Journals (Sweden)
Iván Y Fernández-Rosales
Full Text Available We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.
Directory of Open Access Journals (Sweden)
Tun-Wei Hsu
Full Text Available Hepatic encephalopathy (HE is a complex neuropsychiatric syndrome and a major complication of liver cirrhosis. Dysmetabolism of the brain, related to elevated ammonia levels, interferes with intercortical connectivity and cognitive function. For evaluation of network efficiency, a 'small-world' network model can quantify the effectiveness of information transfer within brain networks. This study aimed to use small-world topology to investigate abnormalities of neuronal connectivity among widely distributed brain regions in patients with liver cirrhosis using resting-state functional magnetic resonance imaging (rs-fMRI. Seventeen cirrhotic patients without HE, 9 with minimal HE, 9 with overt HE, and 35 healthy controls were compared. The interregional correlation matrix was obtained by averaging the rs-fMRI time series over all voxels in each of the 90 regions using the automated anatomical labeling model. Cost and correlation threshold values were then applied to construct the functional brain network. The absolute and relative network efficiencies were calculated; quantifying distinct aspects of the local and global topological network organization. Correlations between network topology parameters, ammonia levels, and the severity of HE were determined using linear regression and ANOVA. The local and global topological efficiencies of the functional connectivity network were significantly disrupted in HE patients; showing abnormal small-world properties. Alterations in regional characteristics, including nodal efficiency and nodal strength, occurred predominantly in the association, primary, and limbic/paralimbic regions. The degree of network organization disruption depended on the severity of HE. Ammonia levels were also significantly associated with the alterations in local network properties. Results indicated that alterations in the rs-fMRI network topology of the brain were associated with HE grade; and that focal or diffuse lesions
Institute of Scientific and Technical Information of China (English)
ZHANG Ying-Yue; YANG Qiu-Ying; CHEN Tian-Lun
2007-01-01
We introduce a modified small-world network adding new links with nonlinearly preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. We study several important structural properties of our network such as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important critical value fc, the f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors.
Epidemics in interconnected small-world networks
Liu, M.; Li, D.; Qin, P.; Liu, C.; Wang, H.; Wang, F.
2015-01-01
Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks
Impact of Partial Time Delay on Temporal Dynamics of Watts-Strogatz Small-World Neuronal Networks
Yan, Hao; Sun, Xiaojuan
2017-06-01
In this paper, we mainly discuss effects of partial time delay on temporal dynamics of Watts-Strogatz (WS) small-world neuronal networks by controlling two parameters. One is the time delay τ and the other is the probability of partial time delay pdelay. Temporal dynamics of WS small-world neuronal networks are discussed with the aid of temporal coherence and mean firing rate. With the obtained simulation results, it is revealed that for small time delay τ, the probability pdelay could weaken temporal coherence and increase mean firing rate of neuronal networks, which indicates that it could improve neuronal firings of the neuronal networks while destroying firing regularity. For large time delay τ, temporal coherence and mean firing rate do not have great changes with respect to pdelay. Time delay τ always has great influence on both temporal coherence and mean firing rate no matter what is the value of pdelay. Moreover, with the analysis of spike trains and histograms of interspike intervals of neurons inside neuronal networks, it is found that the effects of partial time delays on temporal coherence and mean firing rate could be the result of locking between the period of neuronal firing activities and the value of time delay τ. In brief, partial time delay could have great influence on temporal dynamics of the neuronal networks.
Hybrid Control of Delay Induced Hopf Bifurcation of Dynamical Small-World Network
Institute of Scientific and Technical Information of China (English)
DING Dawei; ZHANG Xiaoyun; WANG Nian; LIANG Dong
2017-01-01
In this paper,we focus on the Hopf bifurcation control of a small-world network model with time-delay.With emphasis on the relationship between the Hopf bifurcation and the time-delay,we investigate the effect of time-delay by choosing it as the bifurcation parameter.By using tools from control and bifurcation theory,it is proved that there exists a critical value of time-delay for the stability of the model.When the time-delay passes through the critical value,the model loses its stability and a Hopf bifurcation occurs.To enhance the stability of the model,we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used.Through linear stability analysis,we show that by adjusting the control parameter properly,the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model.Finally,numerical simulations are given to verify the theoretical analysis.
The ubiquity of small-world networks
Telesford, Qawi K; Hayasaka, Satoru; Burdette, Jonathan H; Laurienti, Paul J
2011-01-01
Small-world networks by Watts and Strogatz are a class of networks that are highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. These characteristics result in networks with unique properties of regional specialization with efficient information transfer. Social networks are intuitive examples of this organization with cliques or clusters of friends being interconnected, but each person is really only 5-6 people away from anyone else. While this qualitative definition has prevailed in network science theory, in application, the standard quantitative application is to compare path length (a surrogate measure of distributed processing) and clustering (a surrogate measure of regional specialization) to an equivalent random network. It is demonstrated here that comparing network clustering to that of a random network can result in aberrant findings and networks once thought to exhibit small-world properties may not. We propose a new small-world metric, {\\omega}...
Energy Technology Data Exchange (ETDEWEB)
Wu Hao; Jiang Huijun [Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Hou Zhonghuai, E-mail: hzhlj@ustc.edu.cn [Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2011-10-15
Highlights: > We compare neuronal dynamics in dependence on two types of delayed coupling. > Distinct results induced by different delayed coupling can be achieved. > Time delays in type 1 coupling can induce a most spatiotemporal ordered state. > For type 2 coupling, the systems exhibit synchronization transitions with delay. - Abstract: We investigate temporal coherence and spatial synchronization on small-world networks consisting of noisy Terman-Wang (TW) excitable neurons in dependence on two types of time-delayed coupling: {l_brace}x{sub j}(t - {tau}) - x{sub i}(t){r_brace} and {l_brace}x{sub j}(t - {tau}) - x{sub i}(t - {tau}){r_brace}. For the former case, we show that time delay in the coupling can dramatically enhance temporal coherence and spatial synchrony of the noise-induced spike trains. In addition, if the delay time {tau} is tuned to nearly match the intrinsic spike period of the neuronal network, the system dynamics reaches a most ordered state, which is both periodic in time and nearly synchronized in space, demonstrating an interesting resonance phenomenon with delay. For the latter case, however, we cannot achieve a similar spatiotemporal ordered state, but the neuronal dynamics exhibits interesting synchronization transitions with time delay from zigzag fronts of excitations to dynamic clustering anti-phase synchronization (APS), and further to clustered chimera states which have spatially distributed anti-phase coherence separated by incoherence. Furthermore, we also show how these findings are influenced by the change of the noise intensity and the rewiring probability of the small-world networks. Finally, qualitative analysis is given to illustrate the numerical results.
Small-world network spectra in mean-field theory.
Grabow, Carsten; Grosskinsky, Stefan; Timme, Marc
2012-05-25
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean-field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering, and social science.
Using probabilistic cache scheme to construct the small world network
Institute of Scientific and Technical Information of China (English)
ZOU Fu-tai; YI Ping; MA Fan-yuan; LI Jian-hua
2007-01-01
Recently some P2P systems have constructed the small world network using the small world model so as to improve the routing performance. In this paper, we propose a novel probabilistic cache scheme to construct the small world network based on the small world model and use it to improve CAN, that is, PCCAN ( Probabilistic Cache - based CAN). PCCAN caches the long contact. It uses the worm routing replacing mechanism and probabilistic replacing strategy on the cache. The probabilistic cache scheme proves to be an efficient approach to model the small world phenomenon. Experiments in both the static and the dynamic network show that PCCAN can converge to the steady state with the cache scheme, and the routing performance is significantly improved with additional low overheads in the network compared with CAN.
Population synchrony in small-world networks.
Ranta, Esa; Fowler, Mike S; Kaitala, Veijo
2008-02-22
Network topography ranges from regular graphs (linkage between nearest neighbours only) via small-world graphs (some random connections between nodes) to completely random graphs. Small-world linkage is seen as a revolutionary architecture for a wide range of social, physical and biological networks, and has been shown to increase synchrony between oscillating subunits. We study small-world topographies in a novel context: dispersal linkage between spatially structured populations across a range of population models. Regular dispersal between population patches interacting with density-dependent renewal provides one ecological explanation for the large-scale synchrony seen in the temporal fluctuations of many species, for example, lynx populations in North America, voles in Fennoscandia and grouse in the UK. Introducing a small-world dispersal kernel leads to a clear reduction in synchrony with both increasing dispersal rate and small-world dispersal probability across a variety of biological scenarios. Synchrony is also reduced when populations are affected by globally correlated noise. We discuss ecological implications of small-world dispersal in the frame of spatial synchrony in population fluctuations.
Scaling in small-world resistor networks
Energy Technology Data Exchange (ETDEWEB)
Korniss, G. [Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590 (United States)]. E-mail: korniss@rpi.edu; Hastings, M.B. [Center for Non-linear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Bassler, K.E. [Department of Physics, 617 Science and Research Blvd I, Univesity of Houston, Houston, TX 77204-5005 (United States); Berryman, M.J. [Centre for Biomedical Engineering (CBME) and School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005 (Australia); Kozma, B. [Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180-3590 (United States); Abbott, D. [Centre for Biomedical Engineering (CBME) and School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005 (Australia)
2006-02-13
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged two-point resistance in the large system-size limit. We find that the small-world structure suppresses large network resistances: both the average resistance and its standard deviation approaches a finite value in the large system-size limit for any non-zero density of random links. We also consider a scenario where the link conductance decays as a power of the length of the random links, l{sup -{alpha}}. In this case we find that the average effective system resistance diverges for any non-zero value of {alpha}.
Small-world networks on a sphere
Corso, Gilberto; Torres Cruz, Claudia P.
2017-01-01
The Small-World Network on a Sphere SWNS is a non-crossing network that has no hubs and presents the small-world property diam log N with diam being the maximal distance between any two vertices and N being the number of vertices. The SWNS is constructed using a partition of the sphere and the parallels are regular sections of the sphere with constant latitude. The number of cells on the parallels, however, increases exponentially from the pole to the equator of the sphere. We analytically compute the distribution of connectivity, the clustering coefficient and the SWNS distances. The resilience of the model against selective attacks is also discussed.
Interface motion and pinning in small-world networks.
Boyer, Denis; Miramontes, Octavio
2003-03-01
We show that the nonequilibrium dynamics of systems with many interacting elements located on a small-world network can be much slower than on regular networks. As an example, we study the phase ordering dynamics of the Ising model on a Watts-Strogatz network, after a quench in the ferromagnetic phase at zero temperature. In one and two dimensions, small-world features produce dynamically frozen configurations, disordered at large length scales, analogous to random field models. This picture differs from the common knowledge (supported by equilibrium results) that ferromagnetic shortcut connections favor order and uniformity. We briefly discuss some implications of these results regarding the dynamics of social changes.
Disrupted Small-World Networks in Schizophrenia
Liu, Yong; Liang, Meng; Zhou, Yuan; He, Yong; Hao, Yihui; Song, Ming; Yu, Chunshui; Liu, Haihong; Liu, Zhening; Jiang, Tianzi
2008-01-01
The human brain has been described as a large, sparse, complex network characterized by efficient small-world properties, which assure that the brain generates and integrates information with high efficiency. Many previous neuroimaging studies have provided consistent evidence of "dysfunctional connectivity" among the brain regions in…
Hodge Decomposition of Information Flow on Small-World Networks
Haruna, Taichi; Fujiki, Yuuya
2016-01-01
We investigate the influence of the small-world topology on the composition of information flow on networks. By appealing to the combinatorial Hodge theory, we decompose information flow generated by random threshold networks on the Watts-Strogatz model into three components: gradient, harmonic and curl flows. The harmonic and curl flows represent globally circular and locally circular components, respectively. The Watts-Strogatz model bridges the two extreme network topologies, a lattice network and a random network, by a single parameter that is the probability of random rewiring. The small-world topology is realized within a certain range between them. By numerical simulation we found that as networks become more random the ratio of harmonic flow to the total magnitude of information flow increases whereas the ratio of curl flow decreases. Furthermore, both quantities are significantly enhanced from the level when only network structure is considered for the network close to a random network and a lattice network, respectively. Finally, the sum of these two ratios takes its maximum value within the small-world region. These findings suggest that the dynamical information counterpart of global integration and that of local segregation are the harmonic flow and the curl flow, respectively, and that a part of the small-world region is dominated by internal circulation of information flow. PMID:27733817
Multiobjective Bak-Sneppen model on a small-world network
Energy Technology Data Exchange (ETDEWEB)
Elettreby, M.F. [Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)] e-mail: mohfathy@mans.edu.eg
2005-11-01
Small-world networks (SWN) are relevant to biological systems. We study the dynamics of the Bak-Sneppen (BS) model on small-world network, including the concepts of extremal dynamics, multiobjective optimization and coherent noise. We find that the small-world structure stabilizes the system. Also, it is more realistic to augment the Bak-Sneppen model by these concepts.
Social influence in small-world networks
Institute of Scientific and Technical Information of China (English)
孙锴; 毛晓明; 欧阳颀
2002-01-01
We report on our numerical studies of the Axelrod model for social influence in small-world networks. Our simulation results show that the topology of thenetwork has a crucial effect on the evolution of cultures. As the randomness of the network increases, the system undergoes a transition from a highly fragmented phase to a uniform phase. We also find that the power-law distribution at the transition point, reported by Castellano et al, is not a critical phenomenon; it exists not only at the onset of transition but also for almost any control parameters. All these power-law distributions are stable against perturbations. A mean-field theory is developed to explain these phenomena.
A new small-world network created by Cellular Automata
Ruan, Yuhong; Li, Anwei
2016-08-01
In this paper, we generate small-world networks by the Cellular Automaton based on starting with one-dimensional regular networks. Besides the common properties of small-world networks with small average shortest path length and large clustering coefficient, the small-world networks generated in this way have other properties: (i) The edges which are cut in the regular network can be controlled that whether the edges are reconnected or not, and (ii) the number of the edges of the small-world network model equals the number of the edges of the original regular network. In other words, the average degree of the small-world network model equals to the average degree of the original regular network.
Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.
Chung, H-Y; Chung, C-Y; Ou, S-C
2012-10-01
The study will apply Lyapunov principle to construct a dynamic model for tuberculosis (TB). The Lyapunov principle is commonly used to examine and determine the stability of a dynamic system. To simulate the transmissions of vector-borne diseases and discuss the related health policies effects on vector-borne diseases, the authors combine the multi-agent-based system, social network and compartmental model to develop an epidemic simulation model. In the identity level, the authors use the multi-agent-based system and the mirror identity concept to describe identities with social network features such as daily visits, long-distance movement, high degree of clustering, low degree of separation and local clustering. The research will analyse the complex dynamic mathematic model of TB epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages. Facing the current TB epidemic situation, the development of TB and its developing trend through constructing a dynamic bio-mathematical system model of TB is investigated. After simulating the development of epidemic situation with the solution of the SMIR epidemic model, the authors will come up with a good scheme to control epidemic situation to analyse the parameter values of a model that influence epidemic situation evolved. The authors will try to find the quarantining parameters that are the most important factors to control epidemic situation. The SMIR epidemic model and the results via numerical analysis may offer effective prevention with reference to controlling epidemic situation of TB.
Phase Synchronization in Small World Chaotic Neural Networks
Institute of Scientific and Technical Information of China (English)
WANG Qing-Yun; LU Qi-Shao
2005-01-01
@@ To understand collective motion of realneural networks very well, we investigate collective phase synchronization of small world chaotic Hindmarsh-Rose (HR) neural networks. By numerical simulations, we conclude that small world chaotic HR neural networks can achieve collective phase synchronization. Furthermore, it is shown that phase synchronization of small world chaotic HR neural networks is dependent on the coupling strength,the connection topology (which is determined by the probability p), as well as the coupling number. These phenomena are important to guide us to understand the synchronization of real neural networks.
Small-world networks in neuronal populations: a computational perspective.
Zippo, Antonio G; Gelsomino, Giuliana; Van Duin, Pieter; Nencini, Sara; Caramenti, Gian Carlo; Valente, Maurizio; Biella, Gabriele E M
2013-08-01
The analysis of the brain in terms of integrated neural networks may offer insights on the reciprocal relation between structure and information processing. Even with inherent technical limits, many studies acknowledge neuron spatial arrangements and communication modes as key factors. In this perspective, we investigated the functional organization of neuronal networks by explicitly assuming a specific functional topology, the small-world network. We developed two different computational approaches. Firstly, we asked whether neuronal populations actually express small-world properties during a definite task, such as a learning task. For this purpose we developed the Inductive Conceptual Network (ICN), which is a hierarchical bio-inspired spiking network, capable of learning invariant patterns by using variable-order Markov models implemented in its nodes. As a result, we actually observed small-world topologies during learning in the ICN. Speculating that the expression of small-world networks is not solely related to learning tasks, we then built a de facto network assuming that the information processing in the brain may occur through functional small-world topologies. In this de facto network, synchronous spikes reflected functional small-world network dependencies. In order to verify the consistency of the assumption, we tested the null-hypothesis by replacing the small-world networks with random networks. As a result, only small world networks exhibited functional biomimetic characteristics such as timing and rate codes, conventional coding strategies and neuronal avalanches, which are cascades of bursting activities with a power-law distribution. Our results suggest that small-world functional configurations are liable to underpin brain information processing at neuronal level.
Small-World Propensity and Weighted Brain Networks.
Muldoon, Sarah Feldt; Bridgeford, Eric W; Bassett, Danielle S
2016-02-25
Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.
Small-World Propensity and Weighted Brain Networks
Muldoon, Sarah Feldt; Bridgeford, Eric W.; Bassett, Danielle S.
2016-02-01
Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.
Structured information in small-world neural networks
Dominguez, David; González, Mario; Serrano, Eduardo; Rodríguez, Francisco B.
2009-02-01
The retrieval abilities of spatially uniform attractor networks can be measured by the global overlap between patterns and neural states. However, we found that nonuniform networks, for instance, small-world networks, can retrieve fragments of patterns (blocks) without performing global retrieval. We propose a way to measure the local retrieval using a parameter that is related to the fluctuation of the block overlaps. Simulation of neural dynamics shows a competition between local and global retrieval. The phase diagram shows a transition from local retrieval to global retrieval when the storage ratio increases and the topology becomes more random. A theoretical approach confirms the simulation results and predicts that the stability of blocks can be improved by dilution.
Geometric Assortative Growth Model for Small-World Networks
Directory of Open Access Journals (Sweden)
Yilun Shang
2014-01-01
Full Text Available It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.
Geometric assortative growth model for small-world networks.
Shang, Yilun
2014-01-01
It has been shown that both humanly constructed and natural networks are often characterized by small-world phenomenon and assortative mixing. In this paper, we propose a geometrically growing model for small-world networks. The model displays both tunable small-world phenomenon and tunable assortativity. We obtain analytical solutions of relevant topological properties such as order, size, degree distribution, degree correlation, clustering, transitivity, and diameter. It is also worth noting that the model can be viewed as a generalization for an iterative construction of Farey graphs.
Small-world brain networks in schizophrenia
Institute of Scientific and Technical Information of China (English)
Mingli LI; Zhuangfei CHEN; Tao LI
2012-01-01
Over the last decade the combination of brain neuroimaging techniques and graph theoretical analysis of the complex anatomical and functional networks in the brain have provided an exciting new platform for exploring the etiology of mental disorders such as schizophrenia. This review introduces the current status of this work, focusing on these networks in schizophrenia. The evidence supporting the findings of reduced efficiency of information exchange in schizophrenia both within local brain regions and globally throughout the brain is reviewed and the potential relationship of these changes to cognitive and clinical symptoms is discussed. Finally we propose some suggestions for future research.
From brain to earth and climate systems: small-world interaction networks or not?
Bialonski, Stephan; Horstmann, Marie-Therese; Lehnertz, Klaus
2010-03-01
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.
Deterministic multidimensional growth model for small-world networks
Peng, Aoyuan
2011-01-01
We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses small-world effect: larger clustering coefficient and smaller characteristic path length. We also obtain some accurate results for its properties including degree distribution, clustering coefficient and network diameter and discuss them. It is also worth noting that we get an accurate analytical expression for calculating the characteristic path length. We verify numerically and experimentally these main features.
The Efficiency of a Small-World Functional Brain Network
Institute of Scientific and Technical Information of China (English)
ZHAO Qing-Bai; ZHANG Xiao-Fei; SUI Dan-Ni; ZHOU Zhi-Jin; CHEN Qi-Cai; TANG Yi-Yuan
2012-01-01
We investigate whether the small-world topology of a functional brain network means high information processing efficiency by calculating the correlation between the small-world measures of a functional brain network and behavioral reaction during an imagery task.Functional brain networks are constructed by multichannel eventrelated potential data,in which the electrodes are the nodes and the functional connectivities between them are the edges.The results show that the correlation between small-world measures and reaction time is task-specific,such that in global imagery,there is a positive correlation between the clustering coefficient and reaction time,while in local imagery the average path length is positively correlated with the reaction time.This suggests that the efficiency of a functional brain network is task-dependent.%We investigate whether the small-world topology of a functional brain network means high information processing efficiency by calculating the correlation between the small-world measures of a functional brain network and behavioral reaction during an imagery task. Functional brain networks are constructed by multichannel event-related potential data, in which the electrodes are the nodes and the functional connectivities between them are the edges. The results show that the correlation between small-world measures and reaction time is task-specific, such that in global imagery, there is a positive correlation between the clustering coefficient and reaction time, while in local imagery the average path length is positively correlated with the reaction time. This suggests that the efficiency of a functional brain network is task-dependent.
Cascading failures of interdependent modular small-world networks
Zhu, Guowei; Wang, Xianpei; Tian, Meng; Dai, Dangdang; Long, Jiachuan; Zhang, Qilin
2016-07-01
Much empirical evidence shows that many real-world networks fall into the broad class of small-world networks and have a modular structure. The modularity has been revealed to have an important effect on cascading failure in isolated networks. However, the corresponding results for interdependent modular small-world networks remain missing. In this paper, we investigate the relationship between cascading failures and the intra-modular rewiring probabilities and inter-modular connections under different coupling preferences, i.e. random coupling with modules (RCWM), assortative coupling in modules (ACIM) and assortative coupling with modules (ACWM). The size of the largest connected component is used to evaluate the robustness from global and local perspectives. Numerical results indicate that increasing intra-modular rewiring probabilities and inter-modular connections can improve the robustness of interdependent modular small-world networks under intra-attacks and inter-attacks. Meanwhile, experiments on three coupling strategies demonstrate that ACIM has a better effect on preventing the cascading failures compared with RCWM and ACWM. These results can be helpful to allocate and optimize the topological structure of interdependent modular small-world networks to improve the robustness of such networks.
A small-world network model of facial emotion recognition.
Takehara, Takuma; Ochiai, Fumio; Suzuki, Naoto
2016-01-01
Various models have been proposed to increase understanding of the cognitive basis of facial emotions. Despite those efforts, interactions between facial emotions have received minimal attention. If collective behaviours relating to each facial emotion in the comprehensive cognitive system could be assumed, specific facial emotion relationship patterns might emerge. In this study, we demonstrate that the frameworks of complex networks can effectively capture those patterns. We generate 81 facial emotion images (6 prototypes and 75 morphs) and then ask participants to rate degrees of similarity in 3240 facial emotion pairs in a paired comparison task. A facial emotion network constructed on the basis of similarity clearly forms a small-world network, which features an extremely short average network distance and close connectivity. Further, even if two facial emotions have opposing valences, they are connected within only two steps. In addition, we show that intermediary morphs are crucial for maintaining full network integration, whereas prototypes are not at all important. These results suggest the existence of collective behaviours in the cognitive systems of facial emotions and also describe why people can efficiently recognize facial emotions in terms of information transmission and propagation. For comparison, we construct three simulated networks--one based on the categorical model, one based on the dimensional model, and one random network. The results reveal that small-world connectivity in facial emotion networks is apparently different from those networks, suggesting that a small-world network is the most suitable model for capturing the cognitive basis of facial emotions.
Can recurrence networks show small-world property?
Energy Technology Data Exchange (ETDEWEB)
Jacob, Rinku, E-mail: rinku.jacob.vallanat@gmail.com [Department of Physics, The Cochin College, Cochin, 682002 (India); Harikrishnan, K.P., E-mail: kp_hk2002@yahoo.co.in [Department of Physics, The Cochin College, Cochin, 682002 (India); Misra, R., E-mail: rmisra@iucaa.in [Inter University Centre for Astronomy and Astrophysics, Pune, 411007 (India); Ambika, G., E-mail: g.ambika@iiserpune.ac.in [Indian Institute of Science Education and Research, Pune, 411008 (India)
2016-08-12
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value ϵ chosen at or just above the percolation threshold of the network are quite well understood, what happens as the threshold increases beyond the usual operational window is still not clear from a complex network perspective. The present Letter is focused mainly on the network properties at intermediate-to-large values of the recurrence threshold, for which no systematic study has been performed so far. We argue, with numerical support, that recurrence networks constructed from chaotic attractors with ϵ equal to the usual recurrence threshold or slightly above cannot, in general, show small-world property. However, if the threshold is further increased, the recurrence network topology initially changes to a small-world structure and finally to that of a classical random graph as the threshold approaches the size of the strange attractor. - Highlights: • Properties of recurrence networks at intermediate-to-large values of recurrence threshold are analyzed from a complex network perspective. • Using a combined plot of characteristic path length and clustering coefficient, it is shown that the recurrence network constructed with recurrence threshold equal to or just above the percolation threshold cannot, in general, display small-world property. • As the recurrence threshold is increased from its usual operational window, the resulting network makes a smooth transition initially to a small-world network for an intermediate range of thresholds and finally to the classical random graph as the threshold becomes comparable to the size of the attractor.
The problem of thresholding in small-world network analysis.
Directory of Open Access Journals (Sweden)
Nicolas Langer
Full Text Available Graph theory deterministically models networks as sets of vertices, which are linked by connections. Such mathematical representation of networks, called graphs are increasingly used in neuroscience to model functional brain networks. It was shown that many forms of structural and functional brain networks have small-world characteristics, thus, constitute networks of dense local and highly effective distal information processing. Motivated by a previous small-world connectivity analysis of resting EEG-data we explored implications of a commonly used analysis approach. This common course of analysis is to compare small-world characteristics between two groups using classical inferential statistics. This however, becomes problematic when using measures of inter-subject correlations, as it is the case in commonly used brain imaging methods such as structural and diffusion tensor imaging with the exception of fibre tracking. Since for each voxel, or region there is only one data point, a measure of connectivity can only be computed for a group. To empirically determine an adequate small-world network threshold and to generate the necessary distribution of measures for classical inferential statistics, samples are generated by thresholding the networks on the group level over a range of thresholds. We believe that there are mainly two problems with this approach. First, the number of thresholded networks is arbitrary. Second, the obtained thresholded networks are not independent samples. Both issues become problematic when using commonly applied parametric statistical tests. Here, we demonstrate potential consequences of the number of thresholds and non-independency of samples in two examples (using artificial data and EEG data. Consequently alternative approaches are presented, which overcome these methodological issues.
Small Worlds in the Tree Topologies of Wireless Sensor Networks
DEFF Research Database (Denmark)
Qiao, Li; Lingguo, Cui; Baihai, Zhang
2010-01-01
In this study, the characteristics of small worlds are investigated in the context of the tree topologies of wireless sensor networks. Tree topologies, which construct spatial graphs with larger characteristic path lengths than random graphs and small clustering coefficients, are ubiquitous...... in wireless sensor networks. Suffering from the link rewiring or the link addition, the characteristic path length of the tree topology reduces rapidly and the clustering coefficient increases greatly. The variety of characteristic path length influences the time synchronization characteristics of wireless...... sensor networks greatly. With the increase of the link rewiring or the link addition probability, the time synchronization error decreases drastically. Two novel protocols named LEACH-SW and TREEPSI-SW are proposed to improve the performances of the sensor networks, in which the small world...
Optimal Routing in a Small-World Network
Institute of Scientific and Technical Information of China (English)
Jian-Yang Zeng; Wen-Jing Hsu
2006-01-01
Substantial research has been devoted to the modelling of the small-world phenomenon that arises in nature as well as human society. Earlier work has focused on the static properties of various small-world models. To examine the routing aspects, Kleinberg proposes a model based on a d-dimensional toroidal lattice with long-range links chosen at random according to the d-harmonic distribution. Kleinberg shows that, by using only local information, the greedy routing algorithm performs in O(lg2 n) expected number of hops. We extend Kleinberg's small-world model by allowing each node x to have two more random links to nodes chosen uniformly and randomly within (lg n)-d Manhattan distance from x. Basedon this extended model, we then propose an oblivious algorithm that can route messages between any two nodes in O(lg n)expected number of hops. Our routing algorithm keeps only O((lg n)β+1) bits of information on each node, where 1 ＜β＜ 2,thus being scalable w.r.t. the network size. To our knowledge, our result is the first to achieve the optimal routing complexity while still keeping a poly-logarithmic number of bits of information stored on each node in the small-world networks.
Exploring the Critical Sensitivity in Small-World Networks
Institute of Scientific and Technical Information of China (English)
罗嘉元; 欧阳颀
2004-01-01
Catastrophic phenomena such as earthquakes, avalanches, and critical points in the stock market are hard to predict. Recently, Xia et al. [Pure Appl. Geophys. 159 (2002)2491] showed that a geometrical system near catastrophic rupture presents a general critical sensitivity: the system becomes significantly sensitive near the catastrophe transition. Here we report that the phenomenon of critical sensitivity also exists in small-world network systems. With the increase of the small-world rewiring probability p, from the regular network p = 0 to the random one p = 1, the system performs more sensitively before the critical point while remaining in better organization through the evolutional progress, and the prediction threshold Ps performs more in advance. The concept of critical sensitivity can be applied to other complex network systems.
Scaling and percolation in the small-world network model
Energy Technology Data Exchange (ETDEWEB)
Newman, M. E. J. [Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 (United States); Watts, D. J. [Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 (United States)
1999-12-01
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one nontrivial length-scale in the model, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. This length-scale governs the crossover from large- to small-world behavior in the model, as well as the number of vertices in a neighborhood of given radius on the network. We derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex-vertex distance on the network, and, using series expansion and Pade approximants, find an approximate analytic form for the scaling function. We calculate the effective dimension of small-world graphs and show that this dimension varies as a function of the length-scale on which it is measured, in a manner reminiscent of multifractals. We also study the problem of site percolation on small-world networks as a simple model of disease propagation, and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms (in epidemiological terms, the point at which an epidemic occurs). The typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph. All our analytic results are confirmed by extensive numerical simulations of the model. (c) 1999 The American Physical Society.
Small-world patterns in Chinese phrase networks
Institute of Scientific and Technical Information of China (English)
LI Yong; WEI Luoxia; LI Wei; NIU Yi; LUO Shiyu
2005-01-01
@@ Recently, the structure and function of complex networks have become one of the hottest topics in statistical physics and interdisciplinary sciences[1-5]. Studies have shown that real networks containing a huge mount of nodes do not form and evolve in a random way as expected, but they display peculiar features. The most surprising one is the small-world effect, which is commonly shared by food webs[1], the web of human sexual contacts[2], word networks[3], etc. Moreover, the scale-free property of degree distributions also emerges on Internet and protein networks[6,7].
Small world in a seismic network: the California case
Directory of Open Access Journals (Sweden)
A. Jiménez
2008-05-01
Full Text Available Recent work has shown that disparate systems can be described as complex networks i.e. assemblies of nodes and links with nontrivial topological properties. Examples include technological, biological and social systems. Among them, earthquakes have been studied from this perspective. In the present work, we divide the Southern California region into cells of 0.1°, and calculate the correlation of activity between them to create functional networks for that seismic area, in the same way that the brain activity is studied from the complex network perspective. We found that the network shows small world features.
Bifurcations and chaos control in discrete small-world networks
Institute of Scientific and Technical Information of China (English)
Li Ning; Sun Hai-Yi; Zhang Qing-Ling
2012-01-01
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed.The control method is then applied to a discrete small-world network model.Qualitative analyses and simulations show that under a generic condition,the bifurcations and the chaos can be delayed or eliminated completely.In addition,the periodic orbits embedded in the chaotic attractor can be stabilized.
Growing homophilic networks are natural optimal navigable small worlds
Malkov, Yury A
2015-01-01
Navigability, an ability to find a short path between elements using only local information is one of the most fascinating properties of real-life networks. However the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in majority of networks: network growth and local homophily, giving the answer why the navigation feature appears in real-life networks. Incremental insertion of metric elements in random order by adding connections to the closest neighbors produces a self-similar optimally wired navigable small world network with an exponential degree distribution. Adding a preferential attachment produces a scale-free network which has shorter greedy paths, but worse (polynomial) scaling of the information extraction locality. Several features of the proposed model are observed in real-life networks, in particular in the brain neural networks, supporting earlier suggestions that they are navi...
Structure of Small World Innovation Network and Learning Performance
Directory of Open Access Journals (Sweden)
Shuang Song
2014-01-01
Full Text Available This paper examines the differences of learning performance of 5 MNCs (multinational corporations that filed the largest number of patents in China. We establish the innovation network with the patent coauthorship data by these 5 MNCs and classify the networks by the tail of distribution curve of connections. To make a comparison of the learning performance of these 5 MNCs with differing network structures, we develop an organization learning model by regarding the reality as having m dimensions, which denotes the heterogeneous knowledge about the reality. We further set n innovative individuals that are mutually interactive and own unique knowledge about the reality. A longer (shorter distance between the knowledge of the individual and the reality denotes a lower (higher knowledge level of that individual. Individuals interact with and learn from each other within the small-world network. By making 1,000 numerical simulations and averaging the simulated results, we find that the differing structure of the small-world network leads to the differences of learning performance between these 5 MNCs. The network monopolization negatively impacts and network connectivity positively impacts learning performance. Policy implications in the conclusion section suggest that to improve firm learning performance, it is necessary to establish a flat and connective network.
Characteristics of Preferentially Attached Network Grown from Small World
Lee, Seungyoung
2015-01-01
We introduce a model for a preferentially attached network which has grown from a small world network. Here, the average path length and the clustering coefficient are estimated, and the topological properties of modeled networks are compared as the initial conditions are changed. As a result, it is shown that the topological properties of the initial network remain even after the network growth. However, the vulnerability of each to preferentially attached nodes being added is not the same. It is found that the average path length rapidly decreases as the ratio of preferentially attached nodes increases and that the characteristics of the initial network can be easily disappeared. On the other hand, the clustering coefficient of the initial network slowly decreases with the ratio of preferentially attached nodes and its clustering characteristic remains much longer.
Mandala Networks: ultra-small-world and highly sparse graphs
Sampaio Filho, Cesar I. N.; Moreira, André A.; Andrade, Roberto F. S.; Herrmann, Hans J.; Andrade, José S.
2015-03-01
The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are robust against random failures. Furthermore, as the size of the network increases, its shortest path becomes asymptotically invariant and the density of links goes to zero, making it ultra-small world and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically. Finally, we show that some simple changes on the original network formulation can lead to an improved topology against malicious attacks.
Modular Epidemic Spreading in Small-World Networks
Institute of Scientific and Technical Information of China (English)
ZHAO Hui; GAO Zi-You
2007-01-01
We study the epidemic spreading of the susceptible-infected-susceptible model on small-world networks with modular structure.It is found that the epidemic threshold increases linearly with the modular strength.Furthermore,the modular structure may influence the infected density in the steady state and the spreading velocity at the beginning of propagation.Practically,the propagation can be hindered by strengthening the modular structure in the view of network topology.In addition,to reduce the probability of reconnection between modules may also help to control the propagation.
Corona graphs as a model of small-world networks
Lv, Qian; Yi, Yuhao; Zhang, Zhongzhi
2015-11-01
We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.
Delay Induced Hopf Bifurcation of Small-World Networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stability and the Hopf bifurcation of small-world networks with time delay are studied. By analyzing the change of delay, we obtain several sufficient conditions on stable and unstable properties. When the delay passes a critical value, a Hopf bifurcation may appear. Furthermore, the direction and the stability of bifurcating periodic solutions are investigated by the normal form theory and the center manifold reduction. At last, by numerical simulations, we further illustrate the effectiveness of theorems in this paper.
Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes
Institute of Scientific and Technical Information of China (English)
LINMin; CHENTian-Lun
2004-01-01
We introduce the Olami-Feder-Christensen (OFC) model on a square lattice with some "rewired" longrange connections having the properties of small world networks. We find that our model displays the power-law behavior, and connectivity topologies are very important to model's avalanche dynamical behaviors. Our model has some behaviors different from the OFC model on a small world network with "added" long-range connections in our previous work [LIN Min, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].
Influence of Different Connectivity Topologies in Small World Networks Modeling Earthquakes
Institute of Scientific and Technical Information of China (English)
LIN Min; CHEN Tian-Lun
2004-01-01
We introduce the Olami-Feder-Christensen (OFC) model on a squarelattice with some "rewired" long-range connections having the properties of small world networks. We find that our model displays the power-law behavior,and connectivity topologies are very important to model's avalanche dynamical behaviors. Our model has some behaviorsdifferent from the OFC model on a small world network with "added" long-range connections in our previous work [LINMin, ZHAO Xiao-Wei, and CHEN Tian-Lun, Commun. Theor. Phys. (Beijing, China) 41 (2004) 557.].
Synchronization of time-delay chaotic systems on small-world networks with delayed coupling
Institute of Scientific and Technical Information of China (English)
Qi Wei; Wang Ying-Hai
2009-01-01
By using the well-known Ikeda model as the node dynamics,this paper studies synchronization of time-delay systems on small-world networks where the connections between units involve time delays.It shows that,in contrast with the undelayed case,networks with delays can actually synchronize more easily.Specifically,for randomly distributed delays,time-delayed mutual coupling suppresses the chaotic behaviour by stabilizing a fixed point that is unstable for the uncoupled dynamical system.
Growing Homophilic Networks Are Natural Navigable Small Worlds.
Directory of Open Access Journals (Sweden)
Yury A Malkov
Full Text Available Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in the majority of networks: network growth and local homophily, giving a persuasive answer how the navigation appears in real-life networks. A very simple algorithm produces hierarchical self-similar optimally wired navigable small world networks with exponential degree distribution by using only local information. Adding preferential attachment produces a scale-free network which has shorter greedy paths, but worse (power law scaling of the information extraction locality (algorithmic complexity of a search. Introducing saturation of the preferential attachment leads to truncated scale-free degree distribution that offers a good tradeoff between these parameters and can be useful for practical applications. Several features of the model are observed in real-life networks, in particular in the brain neural networks, supporting the earlier suggestions that they are navigable.
Growing Homophilic Networks Are Natural Navigable Small Worlds.
Malkov, Yury A; Ponomarenko, Alexander
2016-01-01
Navigability, an ability to find a logarithmically short path between elements using only local information, is one of the most fascinating properties of real-life networks. However, the exact mechanism responsible for the formation of navigation properties remained unknown. We show that navigability can be achieved by using only two ingredients present in the majority of networks: network growth and local homophily, giving a persuasive answer how the navigation appears in real-life networks. A very simple algorithm produces hierarchical self-similar optimally wired navigable small world networks with exponential degree distribution by using only local information. Adding preferential attachment produces a scale-free network which has shorter greedy paths, but worse (power law) scaling of the information extraction locality (algorithmic complexity of a search). Introducing saturation of the preferential attachment leads to truncated scale-free degree distribution that offers a good tradeoff between these parameters and can be useful for practical applications. Several features of the model are observed in real-life networks, in particular in the brain neural networks, supporting the earlier suggestions that they are navigable.
Damage Spreading in Spatial and Small-world Random Boolean Networks
Energy Technology Data Exchange (ETDEWEB)
Lu, Qiming [Fermilab; Teuscher, Christof [Portland State U.
2014-02-18
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ($\\bar{K} \\ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\\bar{K}$, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.
Braess like Paradox in a Small World Network
Toyota, Norihito
2013-01-01
Braess \\cite{1} has been studied about a traffic flow on a diamond type network and found that introducing new edges to the networks always does not achieve the efficiency. Some researchers studied the Braess' paradox in similar type networks by introducing various types of cost functions. But whether such paradox occurs or not is not scarcely studied in complex networks. In this article, I analytically and numerically study whether Braess like paradox occurs or not on Dorogovtsev-Mendes network\\cite{2}, which is a sort of small world networks. The cost function needed to go along an edge is postulated to be equally identified with the length between two nodes, independently of an amount of traffic on the edge. It is also assumed the it takes a certain cost $c$ to pass through the center node in Dorogovtsev-Mendes network. If $c$ is small, then bypasses have the function to provide short cuts. As result of numerical and theoretical analyses, while I find that any Braess' like paradox will not occur when the n...
Damage spreading in spatial and small-world random boolean networks
Energy Technology Data Exchange (ETDEWEB)
Lu, Qiming [Los Alamos National Laboratory; Teuscher, Christof [Los Alamos National Laboratory
2008-01-01
Random Boolean Networks (RBNs) are often used as generic models for certain dynamics of complex systems, ranging from social networks, neural networks, to gene or protein interaction networks. Traditionally, RBNs are interconnected randomly and without considering any spatial arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ({bar K} << 1) and that the critical connectivity of stability K{sub s} changes compared to random networks. At higher {bar K}, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key trade-offs between damage spreading (robustness), the network wiring cost, and the network's communication characteristics.
Extraction of network topology from multi-electrode recordings: Is there a small-world effect?
Directory of Open Access Journals (Sweden)
Felipe eGerhard
2011-02-01
Full Text Available The simultaneous recording of the activity of many neurons poses challenges for multivariate data analysis. Here, we propose a general scheme of reconstruction of the functional network from spike train recordings. Effective, causal interactions are estimated by fitting Generalized Linear Models (GLMs on the neural responses, incorporating effects of the neurons' self-history, of input from other neurons in the recorded network and of modulation by an external stimulus. The coupling terms arising from synaptic input can be transformed by thresholding into a binary connectivity matrix which is directed. Each link between two neurons represents a causal influence from one neuron to the other, given the observation of all other neurons from the population. The resulting graph is analyzed with respect to small-world and scale-free properties using quantitative measures for directed networks. Such graph-theoretic analyses have been performed on many complex dynamic networks, including the connectivity structure between different brain areas. Only few studies have attempted to look at the structure of cortical neural networks on the level of individual neurons. Here, using multi-electrode recordings from the visual system of the awake monkey, we find that cortical networks lack scale-free behavior, but show a small, but significant small-world structure. Assuming a simple distance-dependent probabilistic wiring between neurons, we find that this connectivity structure can account for all of the networks' observed small-world-ness. Moreover, for multi-electrode recordings the sampling of neurons is not uniform across the population. We show that the small-world-ness obtained by such a localized sub-sampling overestimates the strength of the true small-world-structure of the network. This bias is likely to be present in all previous experiments based on multi-electrode recordings.
Small-World Effect of Complex Network and Its Application toProtein Folding
Institute of Scientific and Technical Information of China (English)
卢全国; 陈宝方; 彭华魁; 祖巧红
2004-01-01
The famous "six letters" experiment carried out by Milgram demonstrated the existence of small-world effect in a complex network. One vertex tends to be connected to another by a shortest path through network because of the small-world effect. This paper uses the small-world effect to study protein folding pathway.
Wang, Qingyun; Duan, Zhisheng; Perc, Matjaž; Chen, Guanrong
2008-09-01
Synchronization transitions are investigated in small-world neuronal networks that are locally modeled by the Rulkov map with additive spatiotemporal noise. In particular, we investigate the impact of different information transmission delays and rewiring probability. We show that short delays induce zigzag fronts of excitations, whereas intermediate delays can further detriment synchrony in the network due to a dynamic clustering anti-phase synchronization transition. Detailed investigations reveal, however, that for longer delay lengths the synchrony of excitations in the network can again be enhanced due to the emergence of in-phase synchronization. In addition, we show that an appropriate small-world topology can restore synchronized behavior provided information transmission delays are either short or long. On the other hand, within the intermediate delay region, which is characterized by anti-phase synchronization and clustering, differences in the network topology do not notably affect the synchrony of neuronal activity.
Algebraic approach to small-world network models
Rudolph-Lilith, Michelle; Muller, Lyle E.
2014-01-01
We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.
Chaos in complex motor networks induced byNewman-Watts small-world connections
Institute of Scientific and Technical Information of China (English)
WeiDu-Qu; Luo Xiao-Shu; Zhang Bo
2011-01-01
We investigate how dynamical behaviours of complex motor networks depend on the Newman-Watts small-world (NWSW) connections.Network elements are described by the permanent magnet synchronous motor (PMSM) with the values of parameters at which each individual PMSM is stable.It is found that with the increase of connection probability p,the motor in networks becomes periodic and falls into chaotic motion as p further increases.These phenomena imply that NWSW connections can induce and enhance chaos in motor networks.The possible mechanism behind the action of NWSW connections is addressed based on stability theory.
Optimal convergence in naming game with geography-based negotiation on small-world networks
Liu, Run-Ran; Wang, Wen-Xu; Lai, Ying-Cheng; Chen, Guanrong; Wang, Bing-Hong
2011-01-01
We propose a negotiation strategy to address the effect of geography on the dynamics of naming games over small-world networks. Communication and negotiation frequencies between two agents are determined by their geographical distance in terms of a parameter characterizing the correlation between interaction strength and the distance. A finding is that there exists an optimal parameter value leading to fastest convergence to global consensus on naming. Numerical computations and a theoretical analysis are provided to substantiate our findings.
Influence of choice of null network on small-world parameters of structural correlation networks.
Hosseini, S M Hadi; Kesler, Shelli R
2013-01-01
In recent years, coordinated variations in brain morphology (e.g., volume, thickness) have been employed as a measure of structural association between brain regions to infer large-scale structural correlation networks. Recent evidence suggests that brain networks constructed in this manner are inherently more clustered than random networks of the same size and degree. Thus, null networks constructed by randomizing topology are not a good choice for benchmarking small-world parameters of these networks. In the present report, we investigated the influence of choice of null networks on small-world parameters of gray matter correlation networks in healthy individuals and survivors of acute lymphoblastic leukemia. Three types of null networks were studied: 1) networks constructed by topology randomization (TOP), 2) networks matched to the distributional properties of the observed covariance matrix (HQS), and 3) networks generated from correlation of randomized input data (COR). The results revealed that the choice of null network not only influences the estimated small-world parameters, it also influences the results of between-group differences in small-world parameters. In addition, at higher network densities, the choice of null network influences the direction of group differences in network measures. Our data suggest that the choice of null network is quite crucial for interpretation of group differences in small-world parameters of structural correlation networks. We argue that none of the available null models is perfect for estimation of small-world parameters for correlation networks and the relative strengths and weaknesses of the selected model should be carefully considered with respect to obtained network measures.
Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology
Institute of Scientific and Technical Information of China (English)
LIU Qiang; FANG Jin-Qing; LI Yong
2007-01-01
The synchronous conditions of two kinds of the small-world (SW) network are studied.The small world topology can affect on dynamical behaviors of the beam transport network (BTN) largely,if the BTN is constructed with the SWtopology,the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology,respectively.This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems,and may have potential use in prospective applications for halo-chaos secure communication.
Synchronization of Coupled Oscillators on Newman-Watts Small-World Networks
Institute of Scientific and Technical Information of China (English)
GUAN Jian-Yue; XU Xin-Jian; WU Zhi-Xi; WANG Ying-Hai
2006-01-01
We investigate the collection behaviour of coupled phase oscillators on Newman- Watts small-world networks in one and two dimensions. Each component of the network is assumed as an oscillator and each interacts with the others following the Kuramoto model. We then study the onset of global synchronization of phases and frequencies based on dynamic simulations and finite-size scah'ng. Both the phase and frequency synchronization are observed to emerge in the presence of a tiny fraction of shortcuts and enhanced with the increases of nearest neighbours and lattice dimensions.
A multi-community homogeneous small-world network and its fundamental characteristics
Tanimoto, Jun
2016-10-01
We introduce a new small-world network-which we call the multi-community homogeneous-small-world network-that is divided into multiple communities that are relatively isolated, similar to sparsely connected islands. A generating algorithm is presented and its network parameters are explored. To elucidate the fundamental characteristics of the proposed topology, we adopt spatial prisoner's dilemma games as a template for discussion. Comparing with a conventional homogeneous small-world network, more enhanced network reciprocity is observed in games where a stag hunt-type dilemma is large. With intensive analysis, we find how this enhancement is brought about.
Zhou, Guangye; Li, Chengren; Li, Tingting; Yang, Yi; Wang, Chen; He, Fangjun; Sun, Jingchang
2016-09-01
Some typical dual-ring erbium-doped fiber lasers with hyperchaos behaviors are taken as nodes to construct two kinds of small-world networks-NW and WS networks. Based on Lyapunov stability theorem, the appropriate controllers are designed and the outer synchronization between the small-world networks with diverse structures and different node numbers is further investigated. The simulation results show that the perfect synchronization between the complex small-world networks is realized, which is of potential application for all optical communication network.
Growing small-world networks based on a modified BA model
Xu, Xinping; Li, Wei
2006-01-01
We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found that this model can produce small-world networks with power-law degree distributions. Properties of our model, including the degree distribution, clustering, and the average path length are compared with that of the BA model. Since most real networks are both scale-free and small-world networks, our model may provide a satisfactory description for empirical characteristics of real networks.
Small-world topology of functional connectivity in randomly connected dynamical systems.
Hlinka, J; Hartman, D; Paluš, M
2012-09-01
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths together with high clustering of the network, is one of the most discussed and studied. When dealing with coupled dynamical systems, links among units of the system are commonly quantified by a measure of pairwise statistical dependence of observed time series (functional connectivity). We argue that the functional connectivity approach leads to upwardly biased estimates of small-world characteristics (with respect to commonly used random graph models) due to partial transitivity of the accepted functional connectivity measures such as the correlation coefficient. In particular, this may lead to observation of small-world characteristics in connectivity graphs estimated from generic randomly connected dynamical systems. The ubiquity and robustness of the phenomenon are documented by an extensive parameter study of its manifestation in a multivariate linear autoregressive process, with discussion of the potential relevance for nonlinear processes and measures.
Emergence of the small-world architecture in neural networks by activity dependent growth
Gafarov, F. M.
2016-11-01
In this paper, we propose a model describing the growth and development of neural networks based on the latest achievements of experimental neuroscience. The model is based on two evolutionary equations. The first equation is for the evolution of the neurons state and the second is for the growth of axon tips. By using the model, we demonstrated the neuronal growth process from disconnected neurons to fully connected three-dimensional networks. For the analysis of the network's connections structure, we used the random graphs theory methods. It is shown that the growth in neural networks results in the formation of a well-known "small-world" network model. The analysis of the connectivity distribution shows the presence of a strictly non-Gaussian but no scale-free degree distribution for the in-degree node distribution. In terms of the graphs theory, this study developed a new model of dynamic graph.
Local Interactions and the Emergence of a Twitter Small-World Network
Ch'ng, Eugene
2015-01-01
The small-world phenomenon is found in many self-organising systems. Systems configured in small-world networks spread information more easily than in random or regular lattice-type networks. Whilst it is a known fact that small-world networks have short average path length and high clustering coefficient in self-organising systems, the ego centralities that maintain the cohesiveness of small-world network have not been formally defined. Here we show that instantaneous events such as the release of news items via Twitter, coupled with active community arguments related to the news item form a particular type of small-world network. Analysis of the centralities in the network reveals that community arguments maintain the small-world network whilst actively maintaining the cohesiveness and boundary of the group. The results demonstrate how an active Twitter community unconsciously forms a small-world network whilst interacting locally with a bordering community. Over time, such local interactions brought about ...
A geometric growth model interpolating between regular and small-world networks
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zhongzhi [Department of Computer Science and Engineering, Fudan University, Shanghai 200433 (China); Zhou, Shuigeng [Department of Computer Science and Engineering, Fudan University, Shanghai 200433 (China); Wang, Zhiyong [Department of Computer Science and Engineering, Fudan University, Shanghai 200433 (China); Shen, Zhen [Department of Computer Science and Engineering, Fudan University, Shanghai 200433 (China)
2007-09-28
We propose a geometric growth model which interpolates between one-dimensional linear graphs and small-world networks. The model undergoes a transition from large to small worlds. We study the topological characteristics by both theoretical predictions and numerical simulations, which are in good accordance with each other. Our geometrically growing model is a complementarity for the static WS model.
Effects of Different Connectivity Topologies in Small World Networks on EEG-Like Activities
Lin, Min; Zhang, Gui-Qing; Chen, Tian-Lun
2006-02-01
Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension, and the Hurst exponent within the rescaled range analysis (R/S). We find that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.
Effects of Different Connectivity Topologies in Small World Networks on EEG-Like Activities
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investi gate the effects of different connectivity topologies on complex behavior of electroencephalographic-like signals produced by this model. We show that several times series analysis methods that are often used for analyzing complex behavior of electroencephalographic-like signals, such as reconstruction of the phase space, correlation dimension, fractal dimension,and the Hurst exponent within the rescaled range analysis (R/S). We find that the different connectivity topologies lead to different dynamical behaviors in models of integrate-and-fire neurons.
Effects of hybrid synapses on the vibrational resonance in small-world neuronal networks.
Yu, Haitao; Wang, Jiang; Sun, Jianbing; Yu, Haifeng
2012-09-01
We investigate the effect of vibrational resonance in small-world neuronal networks with hybrid chemical and electrical synapses. It is shown that, irrespective of the probability of chemical synapses, an optimal amplitude of high-frequency component of the signal can optimize the dynamical response of neuron populations to the low-frequency component, which encodes the information. This effect of vibrational resonance of neuronal systems depends extensively on the network structure and parameters, which determine the ability of neuronal networks to enhance the outreach of localized subthreshold low-frequency signal. In particular, chemical synaptic coupling is more efficient than the electrical coupling for the transmission of local input signal due to its selective coupling. Moreover, there exists an optimal small-world topology characterized by an optimal value of rewiring probability, warranting the largest peak value of the system response. Considering that two-frequency signals are ubiquity in brain dynamics, we expect the presented results could have important implications for signal processing in neuronal systems.
Liu, Hongxiao; Zhang, Zhongzhi
2013-03-21
A central issue in the study of polymer physics is to understand the relation between the geometrical properties of macromolecules and various dynamics, most of which are encoded in the Laplacian spectra of a related graph describing the macrostructural structure. In this paper, we introduce a family of treelike polymer networks with a parameter, which has the same size as the Vicsek fractals modeling regular hyperbranched polymers. We study some relevant properties of the networks and show that they have an exponentially decaying degree distribution and exhibit the small-world behavior. We then study the Laplacian eigenvalues and their corresponding eigenvectors of the networks under consideration, with both quantities being determined through the recursive relations deduced from the network structure. Using the obtained recursive relations we can find all the eigenvalues and eigenvectors for the networks with any size. Finally, as some applications, we use the eigenvalues to study analytically or semi-analytically three dynamical processes occurring in the networks, including random walks, relaxation dynamics in the framework of generalized Gaussian structure, as well as the fluorescence depolarization under quasiresonant energy transfer. Moreover, we compare the results with those corresponding to Vicsek fractals, and show that the dynamics differ greatly for the two network families, which thus enables us to distinguish between them.
Latching chains in K-nearest-neighbor and modular small-world networks.
Song, Sanming; Yao, Hongxun; Simonov, Alexander Yurievich
2015-01-01
Latching dynamics retrieve pattern sequences successively by neural adaption and pattern correlation. We have previously proposed a modular latching chain model in Song et al. (2014) to better accommodate the structured transitions in the brain. Different cortical areas have different network structures. To explore how structural parameters like rewiring probability, threshold, noise and feedback connections affect the latching dynamics, two different connection schemes, K-nearest-neighbor network and modular network both having modular structure are considered. Latching chains are measured using two proposed measures characterizing length of intra-modular latching chains and sequential inter-modular association transitions. Our main findings include: (1) With decreasing threshold coefficient and rewiring probability, both the K-nearest-neighbor network and the modular network experience quantitatively similar phase change processes. (2) The modular network exhibits selectively enhanced latching in the small-world range of connectivity. (3) The K-nearest-neighbor network is more robust to changes in rewiring probability, while the modular network is more robust to the presence of noise pattern pairs and to changes in the strength of feedback connections. According to our findings, the relationships between latching chains in K-nearest-neighbor and modular networks and different forms of cognition and information processing emerging in the brain are discussed.
Immunizations on small worlds of tree-based wireless sensor networks
DEFF Research Database (Denmark)
Li, Qiao; Zhang, Bai-Hai; Cui, Ling-Guo
2012-01-01
, are conducted on small worlds of tree-based wireless sensor networks to combat the sensor viruses. With the former strategy, the infection extends exponentially, although the immunization effectively reduces the contagion speed. With the latter strategy, recurrent contagion oscillations occur in the small world......The sensor virus is a serious threat, as an attacker can simply send a single packet to compromise the entire sensor network. Epidemics become drastic with link additions among sensors when the small world phenomena occur. Two immunization strategies, uniform immunization and temporary immunization...
Achieving Small World Properties using Bio-Inspired Techniques in Wireless Networks
Agarwal, Rachit; Gauthier, Vincent; Becker, Monique; Yeo, Chai Kiat; Lee, Bu Sung
2011-01-01
Self-Organization properties of the nodes play an important role in an autonomous wireless sensor environment in achieving network wide characteristics. Self-Organization can be used to achieve small world characteristics in a network. In real networks, however, where there is non-uniform distribution of nodes and overall connectivity of the network is less, achieving small world properties while increasing connectivity must be studied. We believe that network connectivity can be increased and small world properties can be achieved with the help of beamforming, biologically inspired algorithms and using local information. Most of the researches performed in direction of achieving above mentioned goals in wireless networks assume knowledge of network with either heterogeneous or hybrid uniform deployment. We propose that without the knowledge of the global environment or introduction of any special features in the network, we can achieve our goal with the help of inspirations from the nature in a non-uniform n...
Continuous opinion model in small world directed networks
Gandica, Yérali; Vázquez, Gerardo J; Rojas, Sergio
2010-01-01
In the compromise model of continuous opinions proposed by Deffuant et al, the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance $\\epsilon$. In directed networks, if agent i is a neighbor of agent j, j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions $$ and their distribution as a function of $\\epsilon$ and of the network structural disorder. In directed networks $$ exhibits a rich structure, being larger than in undirected networks for higher values of $\\epsilon$, and smaller for lower values of $\\epsilon$.
Trade-offs between robustness and small-world effect in complex networks
Peng, Guan-Sheng; Tan, Suo-Yi; Wu, Jun; Holme, Petter
2016-11-01
Robustness and small-world effect are two crucial structural features of complex networks and have attracted increasing attention. However, little is known about the relation between them. Here we demonstrate that, there is a conflicting relation between robustness and small-world effect for a given degree sequence. We suggest that the robustness-oriented optimization will weaken the small-world effect and vice versa. Then, we propose a multi-objective trade-off optimization model and develop a heuristic algorithm to obtain the optimal trade-off topology for robustness and small-world effect. We show that the optimal network topology exhibits a pronounced core-periphery structure and investigate the structural properties of the optimized networks in detail.
Graph analysis of structural brain networks in Alzheimer's disease: beyond small world properties.
John, Majnu; Ikuta, Toshikazu; Ferbinteanu, Janina
2017-03-01
Changes in brain connectivity in patients with early Alzheimer's disease (AD) have been investigated using graph analysis. However, these studies were based on small data sets, explored a limited range of network parameters, and did not focus on more restricted sub-networks, where neurodegenerative processes may introduce more prominent alterations. In this study, we constructed structural brain networks out of 87 regions using data from 135 healthy elders and 100 early AD patients selected from the Open Access Series of Imaging Studies (OASIS) database. We evaluated the graph properties of these networks by investigating metrics of network efficiency, small world properties, segregation, product measures of complexity, and entropy. Because degenerative processes take place at different rates in different brain areas, analysis restricted to sub-networks may reveal changes otherwise undetected. Therefore, we first analyzed the graph properties of a network encompassing all brain areas considered together, and then repeated the analysis after dividing the brain areas into two sub-networks constructed by applying a clustering algorithm. At the level of large scale network, the analysis did not reveal differences between AD patients and controls. In contrast, the same analysis performed on the two sub-networks revealed that small worldness diminished with AD only in the sub-network containing the areas of medial temporal lobe known to be heaviest and earliest affected. The second sub-network, which did not present significant AD-induced modifications of 'classical' small world parameters, nonetheless showed a trend towards an increase in small world propensity, a novel metric that unbiasedly quantifies small world structure. Beyond small world properties, complexity and entropy measures indicated that the intricacy of connection patterns and structural diversity decreased in both sub-networks. These results show that neurodegenerative processes impact volumetric
Evolutionary snowdrift game on heterogeneous Newman-Watts small-world network
Institute of Scientific and Technical Information of China (English)
Yang Han-Xin; Gao Kun; Han Xiao-Pu; Wang Bing-Hong
2008-01-01
We study the evolutionary snowdrift game in a heterogeneous Newman-Watts small-world network. The hetero-geneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman-Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.
Current Redistribution in Resistor Networks: Fat-Tail Statistics in Regular and Small-World Networks
Lehmann, Jörg
2016-01-01
The redistribution of electrical currents in resistor networks after single-bond failures is analyzed in terms of current-redistribution factors that are shown to depend only on the topology of the network and on the values of the bond resistances. We investigate the properties of these current-redistribution factors for regular network topologies (e.g. $d$-dimensional hypercubic lattices) as well as for small-world networks. In particular, we find that the statistics of the current redistribution factors exhibits a fat-tail behavior, which reflects the long-range nature of the current redistribution as determined by Kirchhoff's circuit laws.
Lehmann, Jörg; Bernasconi, Jakob
2017-03-01
The redistribution of electrical currents in resistor networks after single-bond failures is analyzed in terms of current-redistribution factors that are shown to depend only on the topology of the network and on the values of the bond resistances. We investigate the properties of these current-redistribution factors for regular network topologies (e.g., d-dimensional hypercubic lattices) as well as for small-world networks. In particular, we find that the statistics of the current redistribution factors exhibits a fat-tail behavior, which reflects the long-range nature of the current redistribution as determined by Kirchhoff's circuit laws.
The conundrum of functional brain networks: small-world or fractal modularity
Gallos, Lazaros K; Sigman, Mariano
2011-01-01
The human brain is organized in functional modules. Such an organization poses a conundrum: modules ought to be sufficiently independent to guarantee functional specialization and sufficiently connected to bind multiple processors for efficient information transfer. It is commonly accepted that small-world architecture may solve this problem. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modules. Here we provide a solution to this puzzle. We show that the functional brain network formed by percolation of strong links is highly modular. Contrary to the common view, modules are self-similar and therefore are very far from being small-world. Incorporating the weak ties to the network converts it into a small-world preserving an underlying backbone of well-defined modules. Weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs. This trade-off architecture is reminiscent of the "strength of weak ties"...
Tekin, Ramazan; Tagluk, Mehmet Emin
2017-03-01
Physiological rhythms play a critical role in the functional development of living beings. Many biological functions are executed with an interaction of rhythms produced by internal characteristics of scores of cells. While synchronized oscillations may be associated with normal brain functions, anomalies in these oscillations may cause or relate the emergence of some neurological or neuropsychological pathologies. This study was designed to investigate the effects of topological structure and synaptic conductivity noise on the spatial synchronization and temporal rhythmicity of the waves generated by cells in the network. Because of holding the ability of clustering and randomizing with change of parameters, small-world (SW) network topology was chosen. The oscillatory activity of network was tried out by manipulating an insulated SW, cortical network model whose morphology is very close to real world. According to the obtained results, it was observed that at the optimal probabilistic rates of conductivity noise and rewiring of SW, powerful synchronized oscillatory small waves are generated in relation to the internal dynamics of cells, which are in line with the network's input. These two parameters were observed to be quite effective on the excitation-inhibition balance of the network. Accordingly, it may be suggested that the topological dynamics of SW and noisy synaptic conductivity may be associated with the normal and abnormal development of neurobiological structure.
Complex Behavior in a Selective Aging Neuron Model Based on Small World Networks
Institute of Scientific and Technical Information of China (English)
LUO Min-Jie; ZHANG Gui-Qing; LIU Qiu-Yu; CHEN Tian-Lun
2008-01-01
Complex behavior in a selective aging simple neuron model based on small world networks is investigated. The basic elements of the model are endowed with the main features of a neuron function. The structure of the selective aging neuron model is discussed. We also give some properties of the new network and find that the neuron model displays a power-law behavior. If the brain network is small world-like network, the mean avalanche size is almost the same unless the aging parameter is big enough.
Growing Small-World Networks Based on a Modified BA Model
Institute of Scientific and Technical Information of China (English)
XU Xin-Ping; LIU Feng; LI Wei
2006-01-01
@@ We modify the (Barabási-Albert) BA model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new node are made locally to the old node and its nearest neighbours. It is found that this model can produce small-world networks with power-law degree distributions. Properties of our model, including the degree distribution, clustering, average path length and degree correlation coefficient are compared with that of the BA model. Since most real networks are both scale free and small-world networks, our model may provide a satisfactory description for empirical characteristics of real networks.
Predicting Hierarchical Structure in Small World Social Networks
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar
2009-01-01
Typisk analytisk foranstaltninger i grafteori gerne grad centralitet, betweenness og nærhed centralities er meget almindelige og har lang tradition for deres vellykkede brug. Men modellering af skjult, terrorister eller kriminelle netværk gennem sociale grafer ikke rigtig give den hierarkiske str...... udnyttet til at forudsige den kommandostruktur af nettet. Nøgleord: Social Networks Analyse, Bayes Teorem, entropi, hierarkisk struktur.......Typisk analytisk foranstaltninger i grafteori gerne grad centralitet, betweenness og nærhed centralities er meget almindelige og har lang tradition for deres vellykkede brug. Men modellering af skjult, terrorister eller kriminelle netværk gennem sociale grafer ikke rigtig give den hierarkiske...
Small-world to fractal transition in complex networks: a renormalization group approach.
Rozenfeld, Hernán D; Song, Chaoming; Makse, Hernán A
2010-01-15
We show that renormalization group (RG) theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world-fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a nontrivial point of a pure fractal topology that is stable or unstable according to the amount of long-range links in the network, and (iii) another stable point of a fractal with shortcuts that exist exactly at the small-world-fractal transition. As a collateral, the RG technique explains the coexistence of the seemingly contradicting fractal and small-world phases and allows us to extract information on the distribution of shortcuts in real-world networks, a problem of importance for information flow in the system.
Spatial and Temporal Behaviors in a Modified Evolution Model Based on Small World Network
Institute of Scientific and Technical Information of China (English)
ZHAO Xiao-Wei; ZHOU Li-Ming; CHEN Tian-Lun
2004-01-01
In this paper, we introduce a new modified evolution model on a small world network. In our model,the spatial and temporal correlations and the spatial-temporal evolve pattern of mutating nodes exhibit some particular behaviors different from those of the original BS evolution model. More importantly, these behaviors will change with φ, the density of short paths in our network.
A Modified Earthquake Model of Self-Organized Criticality on Small World Networks
Institute of Scientific and Technical Information of China (English)
LIN Min; ZHAO Xiao-Wei; CHEN Tian-Lun
2004-01-01
A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.
Synchronizability of Small-World Networks Generated from a Two-Dimensional Kleinberg Model
Directory of Open Access Journals (Sweden)
Yi Zhao
2013-01-01
Full Text Available This paper investigates the synchronizability of small-world networks generated from a two-dimensional Kleinberg model, which is more general than NW small-world network. The three parameters of the Kleinberg model, namely, the distance of neighbors, the number of edge-adding, and the edge-adding probability, are analyzed for their impacts on its synchronizability and average path length. It can be deduced that the synchronizability becomes stronger as the edge-adding probability increases, and the increasing edge-adding probability could make the average path length of the Kleinberg small-world network go smaller. Moreover, larger distance among neighbors and more edges to be added could play positive roles in enhancing the synchronizability of the Kleinberg model. The lorentz oscillators are employed to verify the conclusions numerically.
Self-Organization of Wireless Ad Hoc Networks as Small Worlds Using Long Range Directional Beams
Banerjee, Abhik; Gauthier, Vincent; Yeo, Chai Kiat; Afifi, Hossam; Lee, Bu Sung
2011-01-01
We study how long range directional beams can be used for self-organization of a wireless network to exhibit small world properties. Using simulation results for randomized beamforming as a guideline, we identify crucial design issues for algorithm design. Subsequently, we propose an algorithm for deterministic creation of small worlds. We define a new centrality measure that estimates the structural importance of nodes based on traffic flow in the network, which is used to identify the optimum nodes for beamforming. This results in significant reduction in path length while maintaining connectivity.
Investigation of the forest-fire model on a small-world network.
Graham, I; Matthai, C C
2003-09-01
It is shown that the forest-fire model of Bak et al. run on a square lattice network with additional long-range interactions in the spirit of a small-world network results in a scale-free system reminiscent of self-organized criticality without recourse to fine tuning. As the number of these long-range interactions is increased, the cluster size distribution exponent is found to decrease in magnitude as the small-world regime is entered, indicating a change in its universality class. It is suggested that such a model could have applicability in the study of disease spreading in human populations.
Renormalization and small-world model of fractal quantum repeater networks
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. PMID:23386977
Renormalization and small-world model of fractal quantum repeater networks.
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
SWER: small world-based efficient routing for wireless sensor networks with mobile sinks
Institute of Scientific and Technical Information of China (English)
Xuejun LIU; Jihong GUAN; Guangwei BAI; Haiming LU
2009-01-01
The interest in small-world network has high-lighted the applicability of both the graph theory and the scaling theory to the analysis of network systems. In this pa-per, we introduce a new routing protocol, small world-based efficient routing (SWER), dedicated to supporting sink mo-bility and small transfers. The method is based on the con-cept of the small worlds where the addition of a small num-ber of long-range links in highly clustered networks results in significant reduction in the average path length. Based on the characteristic of sensor networks, a cluster-based small world network is presented, and an analytical model is de-veloped to analyze the expected path length. SWER adopts a simple and effective routing strategy to forward data to the mobile sink in a small transfer scene and avoid expensive mechanisms to construct a high quality route. We also study the routing scheme and analyze the expected path length in the case where every node is aware of the existence ofp long-range links. In addition, we develop a hierarchical mech-anism in which the mobile sink only transmits its location information to the cluster heads when it enters a new cluster. Thus we also avoid expensive cost to flood the location of the mobile sink to the whole network.
Small worlds and semantic network growth in typical and late talkers.
Beckage, Nicole; Smith, Linda; Hills, Thomas
2011-05-11
Network analysis has demonstrated that systems ranging from social networks to electric power grids often involve a small world structure-with local clustering but global ac cess. Critically, small world structure has also been shown to characterize adult human semantic networks. Moreover, the connectivity pattern of these mature networks is consistent with lexical growth processes in which children add new words to their vocabulary based on the structure of the language-learning environment. However, thus far, there is no direct evidence that a child's individual semantic network structure is associated with their early language learning. Here we show that, while typically developing children's early networks show small world structure as early as 15 months and with as few as 55 words, children with language delay (late talkers) have this structure to a smaller degree. This implicates a maladaptive bias in word acquisition for late talkers, potentially indicating a preference for "oddball" words. The findings provide the first evidence of a link between small-world connectivity and lexical development in individual children.
Small worlds and semantic network growth in typical and late talkers.
Directory of Open Access Journals (Sweden)
Nicole Beckage
Full Text Available Network analysis has demonstrated that systems ranging from social networks to electric power grids often involve a small world structure-with local clustering but global ac cess. Critically, small world structure has also been shown to characterize adult human semantic networks. Moreover, the connectivity pattern of these mature networks is consistent with lexical growth processes in which children add new words to their vocabulary based on the structure of the language-learning environment. However, thus far, there is no direct evidence that a child's individual semantic network structure is associated with their early language learning. Here we show that, while typically developing children's early networks show small world structure as early as 15 months and with as few as 55 words, children with language delay (late talkers have this structure to a smaller degree. This implicates a maladaptive bias in word acquisition for late talkers, potentially indicating a preference for "oddball" words. The findings provide the first evidence of a link between small-world connectivity and lexical development in individual children.
Small-world network model of propagation of the AIDS epidemic
Shi, Pengliang; Small, Michael
2004-03-01
Sexual contact and intravenus drug-use are the most common modes of transmission of HIV-AIDS. In this paper, homogenerous and heterogeneous models are proposed to model the dynamics in a system contains Small-World clusters. Four high risk groups: intravenus drug-users (D); homosexuals (H); individuals with multiple-sexual partners (M) and prostitutes (P), are classified using two models. Both networks are embedded among a background (low-risk) population using rich-get-richer preferential attachment. When a network is established, an epidemic is simulated in it by seeding randomly. We compare the two epidemic networks in detail and consider the effect of different levels of control policies in both. This study highlights two main conclusions: (i) set high protection coefficient for a massive-linkage-vertex (i.e. protect the highly connected individuals); and, (ii) a quick removal for the infected massive-linkage-veterx from the network is essential (rapidly quarantine infected individuals). While these conclusions may be intuitive, they indicate a necessary change of public policy toward prostitution in some developing countries such as China and India. An active effort to prevent possible infection from super-spreader is recommended.
Massobrio, Paolo; Pasquale, Valentina; Martinoia, Sergio
2015-06-01
The spontaneous activity of cortical networks is characterized by the emergence of different dynamic states. Although several attempts were accomplished to understand the origin of these dynamics, the underlying factors continue to be elusive. In this work, we specifically investigated the interplay between network topology and spontaneous dynamics within the framework of self-organized criticality (SOC). The obtained results support the hypothesis that the emergence of critical states occurs in specific complex network topologies. By combining multi-electrode recordings of spontaneous activity of in vitro cortical assemblies with theoretical models, we demonstrate that different 'connectivity rules' drive the network towards different dynamic states. In particular, scale-free architectures with different degree of small-worldness account better for the variability observed in experimental data, giving rise to different dynamic states. Moreover, in relationship with the balance between excitation and inhibition and percentage of inhibitory hubs, the simulated cortical networks fall in a critical regime.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jianbao [School of Science, Hangzhou Dianzi University, Hangzhou 310018 (China); Ma, Zhongjun, E-mail: mzj1234402@163.com [School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004 (China); Chen, Guanrong [Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong (China)
2014-06-15
All edges in the classical Watts and Strogatz's small-world network model are unweighted and cooperative (positive). By introducing competitive (negative) inter-cluster edges and assigning edge weights to mimic more realistic networks, this paper develops a modified model which possesses co-competitive weighted couplings and cluster structures while maintaining the common small-world network properties of small average shortest path lengths and large clustering coefficients. Based on theoretical analysis, it is proved that the new model with inter-cluster co-competition balance has an important dynamical property of robust cluster synchronous pattern formation. More precisely, clusters will neither merge nor split regardless of adding or deleting nodes and edges, under the condition of inter-cluster co-competition balance. Numerical simulations demonstrate the robustness of the model against the increase of the coupling strength and several topological variations.
Fast and robust image segmentation by small-world neural oscillator networks.
Li, Chunguang; Li, Yuke
2011-06-01
Inspired by the temporal correlation theory of brain functions, researchers have presented a number of neural oscillator networks to implement visual scene segmentation problems. Recently, it is shown that many biological neural networks are typical small-world networks. In this paper, we propose and investigate two small-world models derived from the well-known LEGION (locally excitatory and globally inhibitory oscillator network) model. To form a small-world network, we add a proper proportion of unidirectional shortcuts (random long-range connections) to the original LEGION model. With local connections and shortcuts, the neural oscillators can not only communicate with neighbors but also exchange phase information with remote partners. Model 1 introduces excitatory shortcuts to enhance the synchronization within an oscillator group representing the same object. Model 2 goes further to replace the global inhibitor with a sparse set of inhibitory shortcuts. Simulation results indicate that the proposed small-world models could achieve synchronization faster than the original LEGION model and are more likely to bind disconnected image regions belonging together. In addition, we argue that these two models are more biologically plausible.
Inquiring the Potential of Evoking Small-World Properties for Self-Organizing Communication Networks
Brust, Matthias R; Ribeiro, Carlos H C
2007-01-01
Mobile multi-hop ad hoc networks allow establishing local groups of communicating devices in a self-organizing way. However, in a global setting such networks fail to work properly due to network partitioning. Providing that devices are capable of communicating both locally-e.g. using Wi-Fi or Bluetooth-and additionally also with arbitrary remote devices-e.g. using GSM/UMTS links-the objective is to find efficient ways of inter-linking multiple network partitions. Tackling this problem of topology control, we focus on the class of small-world networks that obey two distinguishing characteristics: they have a strong local clustering while still retaining a small average distance between two nodes. This paper reports on results gained investigating the question if small-world properties are indicative for an efficient link management in multiple multi-hop ad hoc network partitions.
The conundrum of functional brain networks: small-world efficiency or fractal modularity
Gallos, Lazaros K; Makse, Hernan A
2012-01-01
The human brain has been studied at multiple scales, from neurons, circuits, areas with well defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology. Here, we provide more details on the use of network science tools to elaborate on this behavior. We indicate the importance of using percolation theory to highlight the modular character of the functional brain network. These modules present a fractal, self-similar topology, identified through fractal network methods. When we lower the threshold of correlations to include weaker ties, the network as a whole assumes a small-world character. These weak ties are organized precisely as predicted by theory maximizing information transfer with minimal wiring costs.
Complete and phase synchronization in a heterogeneous small-world neuronal network
Institute of Scientific and Technical Information of China (English)
Han Fang; Lu Qi-Shao; Wiercigroch Marian; Ji Quan-Bao
2009-01-01
Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh-Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal nctworks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The cffect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an advcrse effect on synchrony.
Monomer-dimer model on a scale-free small-world network
Zhang, Zhongzhi; Sheng, Yibin; Jiang, Qiang
2012-02-01
The explicit determination of the number of monomer-dimer arrangements on a network is a theoretical challenge, and exact solutions to monomer-dimer problem are available only for few limiting graphs with a single monomer on the boundary, e.g., rectangular lattice and quartic lattice; however, analytical research (even numerical result) for monomer-dimer problem on scale-free small-world networks is still missing despite the fact that a vast variety of real systems display simultaneously scale-free and small-world structures. In this paper, we address the monomer-dimer problem defined on a scale-free small-world network and obtain the exact formula for the number of all possible monomer-dimer arrangements on the network, based on which we also determine the asymptotic growth constant of the number of monomer-dimer arrangements in the network. We show that the obtained asymptotic growth constant is much less than its counterparts corresponding to two-dimensional lattice and Sierpinski fractal having the same average degree as the studied network, which indicates from another aspect that scale-free networks have a fundamentally distinct architecture as opposed to regular lattices and fractals without power-law behavior.
Directory of Open Access Journals (Sweden)
Qingling Huang
Full Text Available BACKGROUND: Brain tumor patients often associated with losses of the small-world configuration and neurocognitive functions before operations. However, few studies were performed on the impairments of frontal lobe low-grade gliomas (LGG after tumor resection using small-world network features. METHODOLOGY/PRINCIPAL FINDINGS: To detect differences in the whole brain topology among LGG patients before and after operation, a combined study of neurocognitive assessment and graph theoretical network analysis of fMRI data was performed. We collected resting-state fMRI data of 12 carefully selected frontal lobe LGG patients before and after operation. We calculated the topological properties of brain functional networks in the 12 LGG, and compared with 12 healthy controls (HCs. We also applied Montreal Cognitive Assessment (MoCA in a subset of patients (n = 12, including before and after operation groups and HCs (n = 12. The resulting functional connectivity matrices were constructed for all 12 patients, and binary network analysis was performed. In the range of 0.05 ≤ Kcos t ≤ 0.35, the functional networks in preoperative LGG and postoperative one both fitted the definition of small-worldness. We proposed Knet = 0.20 as small-world network interval, and the results showed that the topological properties were found to be disrupted in the two LGG groups, meanwhile the global efficiency increased and the local efficiency decreased. Lnet in the two LGG groups both were longer than HCs. Cnet in the LGG groups were smaller than HCs. Compared with the Hcs, MoCA in the two LGG groups were lower than HCs with significant difference, and the disturbed networks in the LGG were negatively related to worse MoCA scores. CONCLUSIONS: Disturbed small-worldness preperty in the two LGG groups was found and widely spread in the strength and spatial organization of brain networks, and the alterated small-world network may be responsible for cognitive
The Phase Transitions of Self-similar Small-world Networks
Brunson, Trent; Boettcher, Stefan
2010-03-01
A novel set of self-similar networks called Hanoi networksfootnotetextS. Boettcher, B Goncalves, Europhysics Letters 84, 30002 (2008). (HN) have been developed to study the critical phenomena of small-world networks using the renormalization group (RG). Physically, HNs contain a more desirable geometry than random small-world networks. Their structure consists of a one-dimensional backbone with a hierarchy of long-range bonds, which allows the flexibility of studying planar and non-planar networks with either a regular or exponential degree distribution. The RG and Ising model simulation results for HNs reveal unique phase transitions and non-universal behavior, which can be attributed to their hierarchical structure.footnotetextSee also http://www.physics.emory.edu/faculty/boettcher/.
Small-World and Scale-Free Network Models for IoT Systems
Directory of Open Access Journals (Sweden)
Insoo Sohn
2017-01-01
Full Text Available It is expected that Internet of Things (IoT revolution will enable new solutions and business for consumers and entrepreneurs by connecting billions of physical world devices with varying capabilities. However, for successful realization of IoT, challenges such as heterogeneous connectivity, ubiquitous coverage, reduced network and device complexity, enhanced power savings, and enhanced resource management have to be solved. All these challenges are heavily impacted by the IoT network topology supported by massive number of connected devices. Small-world networks and scale-free networks are important complex network models with massive number of nodes and have been actively used to study the network topology of brain networks, social networks, and wireless networks. These models, also, have been applied to IoT networks to enhance synchronization, error tolerance, and more. However, due to interdisciplinary nature of the network science, with heavy emphasis on graph theory, it is not easy to study the various tools provided by complex network models. Therefore, in this paper, we attempt to introduce basic concepts of graph theory, including small-world networks and scale-free networks, and provide system models that can be easily implemented to be used as a powerful tool in solving various research problems related to IoT.
IMDB network revisited: unveiling fractal and modular properties from a typical small-world network.
Directory of Open Access Journals (Sweden)
Lazaros K Gallos
Full Text Available We study a subset of the movie collaboration network, http://www.imdb.com, where only adult movies are included. We show that there are many benefits in using such a network, which can serve as a prototype for studying social interactions. We find that the strength of links, i.e., how many times two actors have collaborated with each other, is an important factor that can significantly influence the network topology. We see that when we link all actors in the same movie with each other, the network becomes small-world, lacking a proper modular structure. On the other hand, by imposing a threshold on the minimum number of links two actors should have to be in our studied subset, the network topology becomes naturally fractal. This occurs due to a large number of meaningless links, namely, links connecting actors that did not actually interact. We focus our analysis on the fractal and modular properties of this resulting network, and show that the renormalization group analysis can characterize the self-similar structure of these networks.
Institute of Scientific and Technical Information of China (English)
李娜; 杨晓丽
2015-01-01
In this paper, by using the Terman-Wang small-world neuronal network with electrical synapse coupling, we inves-tigate the synchronous dynamics of neuronal network system subjected to spatially correlated white noise. First, the dynamical mean-field approximation theory is extended to the small-world network system under spatially correlated white noise, through which the original 2N-dimensional stochastic differential equations of the network system are trans-formed to 11-dimensional deterministic moment differential equations. Then, based on this set of moment differential equations, the key effects of spatially correlated noise and network structure on the synchronous firing property are dis-cussed in the Terman-Wang neuronal network system. The results show that the synchronization ratio of this considered neuronal network system becomes higher not only as the noise correlation coeﬃcient is increased but also as the coupling strength and the average vertex degree are added. Those results imply that the noise spatial correlation coeﬃcient, the coupling strength, and the average vertex degree can play a positive role in inducing synchronous neuronal behaviors. Furthermore, the synchronous dynamics of the original neuronal network system, obtained by direct numerical simula-tions, is compared with those obtained by the dynamical mean-field approximation theory, and good consistence between them is revealed.
a Small-World and Scale-Free Network Generated by Sierpinski Tetrahedron
Chen, Jin; Gao, Fei; Le, Anbo; Xi, Lifeng; Yin, Shuhua
2016-12-01
The Sierpinski tetrahedron is used to construct evolving networks, whose vertexes are all solid regular tetrahedra in the construction of the Sierpinski tetrahedron up to the stage t and any two vertexes are neighbors if and only if the corresponding tetrahedra are in contact with each other on boundary. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.
Critical properties of a dissipative sandpile model on small-world networks
Bhaumik, Himangsu; Santra, S. B.
2013-12-01
A dissipative sandpile model is constructed and studied on small-world networks (SWNs). SWNs are generated by adding extra links between two arbitrary sites of a two-dimensional square lattice with different shortcut densities ϕ. Three regimes are identified: regular lattice (RL) for ϕ ≲2-12, SWN for 2-12<ϕ<0.1, and random network (RN) for ϕ ≥0.1. In the RL regime, the sandpile dynamics is characterized by the usual Bak, Tang, and Weisenfeld (BTW)-type correlated scaling, whereas in the RN regime it is characterized by mean-field scaling. On SWNs, both scaling behaviors are found to coexist. Small compact avalanches below a certain characteristic size sc are found to belong to the BTW universality class, whereas large, sparse avalanches above sc are found to belong to the mean-field universality class. A scaling theory for the coexistence of two scaling forms on a SWN is developed and numerically verified. Though finite-size scaling is not valid for the dissipative sandpile model on RLs or on SWNs, it is found to be valid on RNs for the same model. Finite-size scaling on RNs appears to be an outcome of super diffusive sand transport and uncorrelated toppling waves.
Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile
2015-10-01
The phenomenon of vibrational resonance is investigated in adaptive Newman-Watts small-world neuronal networks, where the strength of synaptic connections between neurons is modulated based on spike-timing-dependent plasticity. Numerical results demonstrate that there exists appropriate amplitude of high-frequency driving which is able to optimize the neural ensemble response to the weak low-frequency periodic signal. The effect of networked vibrational resonance can be significantly affected by spike-timing-dependent plasticity. It is shown that spike-timing-dependent plasticity with dominant depression can always improve the efficiency of vibrational resonance, and a small adjusting rate can promote the transmission of weak external signal in small-world neuronal networks. In addition, the network topology plays an important role in the vibrational resonance in spike-timing-dependent plasticity-induced neural systems, where the system response to the subthreshold signal is maximized by an optimal network structure. Furthermore, it is demonstrated that the introduction of inhibitory synapses can considerably weaken the phenomenon of vibrational resonance in the hybrid small-world neuronal networks with spike-timing-dependent plasticity.
Toyota, Norihito
2011-01-01
We reformulated the string formalism given by Aoyama, using an adjacent matrix of a network and introduced a series of generalized clustering coefficients based on it. Furthermore we numerically evaluated Milgram condition proposed by their article in order to explore $q$-$th$ degrees of separation in scale free networks. In this article, we apply the reformulation to small world networks and numerically evaluate Milgram condition, especially the separation number of small world networks and its relation to cycle structures are discussed. Considering the number of non-zero elements of an adjacent matrix, the average path length and Milgram condition, we show that the formalism proposed by us is effective to analyze the six degrees of separation, especially effective for analyzing the relation between the separation number and cycle structures in a network. By this analysis of small world networks, it proves that a sort of power low holds between $M_n$, which is a key quantity in Milgram condition, and the gen...
A Self-Organization Framework for Wireless Ad Hoc Networks as Small Worlds
Banerjee, Abhik; Gauthier, Vincent; Yeo, Chai Kiat; Afifi, Hossam; Lee, Bu Sung
2012-01-01
Motivated by the benefits of small world networks, we propose a self-organization framework for wireless ad hoc networks. We investigate the use of directional beamforming for creating long-range short cuts between nodes. Using simulation results for randomized beamforming as a guideline, we identify crucial design issues for algorithm design. Our results show that, while significant path length reduction is achievable, this is accompanied by the problem of asymmetric paths between nodes. Subsequently, we propose a distributed algorithm for small world creation that achieves path length reduction while maintaining connectivity. We define a new centrality measure that estimates the structural importance of nodes based on traffic flow in the network, which is used to identify the optimum nodes for beamforming. We show, using simulations, that this leads to significant reduction in path length while maintaining connectivity.
Small-world network effects on innovation: evidences from nanotechnology patenting
Shi, Yuan; Guan, JianCheng
2016-11-01
This paper explores the effects of collaboration network on innovation in nanotechnology. We extend the idea of small-world to the heterogeneous network positions of actors by capturing the variation of how closely a given actor is connected to others in the same network and how clustered its neighbors are. We test the effects of small-world network in the context of nanotechnology patenting in China. Empirical results reveal that small-worldness, or the co-existence of high clustering and low path length in the network, displays inverse U-shape relationships with future patent output of the individual inventors and the system. Interestingly, the inflection point of the nonlinear relationship is significantly higher at the individual level. Based on these findings, we suggest that researchers of nanotechnology maintain a balance between friends in close-knit inner circles and colleagues in distant areas in their collaboration decisions and that policymakers interested in furthering the field offer collaboration opportunities for researchers in distant locations and areas.
Research on P2P Overlay Network Model with Small-world Features
Liu, Hao; Chen, Zhigang
2013-01-01
Topology structure of P2P network decides its system performance. However, the existing P2P network models don’t take clustering and symmetry of nodes into account. Based on the algebra and graph theory method of Cayley graph, this paper proposes a novel P2P overlay network model with small-world features. Its simplicity and symmetry can ensure the self-organization and scalability of P2P network. The results of analysis and experiment shows that this model provides better robustness, h...
Driving and driven architectures of directed small-world human brain functional networks.
Directory of Open Access Journals (Sweden)
Chaogan Yan
Full Text Available Recently, increasing attention has been focused on the investigation of the human brain connectome that describes the patterns of structural and functional connectivity networks of the human brain. Many studies of the human connectome have demonstrated that the brain network follows a small-world topology with an intrinsically cohesive modular structure and includes several network hubs in the medial parietal regions. However, most of these studies have only focused on undirected connections between regions in which the directions of information flow are not taken into account. How the brain regions causally influence each other and how the directed network of human brain is topologically organized remain largely unknown. Here, we applied linear multivariate Granger causality analysis (GCA and graph theoretical approaches to a resting-state functional MRI dataset with a large cohort of young healthy participants (n = 86 to explore connectivity patterns of the population-based whole-brain functional directed network. This directed brain network exhibited prominent small-world properties, which obviously improved previous results of functional MRI studies showing weak small-world properties in the directed brain networks in terms of a kernel-based GCA and individual analysis. This brain network also showed significant modular structures associated with 5 well known subsystems: fronto-parietal, visual, paralimbic/limbic, subcortical and primary systems. Importantly, we identified several driving hubs predominantly located in the components of the attentional network (e.g., the inferior frontal gyrus, supplementary motor area, insula and fusiform gyrus and several driven hubs predominantly located in the components of the default mode network (e.g., the precuneus, posterior cingulate gyrus, medial prefrontal cortex and inferior parietal lobule. Further split-half analyses indicated that our results were highly reproducible between two
A small-world network derived from the deterministic uniform recursive tree by line graph operation
Hou, Pengfeng; Zhao, Haixing; Mao, Yaping; Wang, Zhao
2016-03-01
The deterministic uniform recursive tree ({DURT}) is one of the deterministic versions of the uniform recursive tree ({URT}). Zhang et al (2008 Eur. Phys. J. B 63 507-13) studied the properties of DURT, including its topological characteristics and spectral properties. Although DURT shows a logarithmic scaling with the size of the network, DURT is not a small-world network since its clustering coefficient is zero. Lu et al (2012 Physica A 391 87-92) proposed a deterministic small-world network by adding some edges with a simple rule in each DURT iteration. In this paper, we intoduce a method for constructing a new deterministic small-world network by the line graph operation in each DURT iteration. The line graph operation brings about cliques at each node of the previous given graph, and the resulting line graph possesses larger clustering coefficients. On the other hand, this operation can decrease the diameter at almost one, then giving the analytic solutions to several topological characteristics of the model proposed. Supported by The Ministry of Science and Technology 973 project (No. 2010C B334708); National Science Foundation of China (Nos. 61164005, 11161037, 11101232, 11461054, 11551001); The Ministry of education scholars and innovation team support plan of Yangtze River (No. IRT1068); Qinghai Province Nature Science Foundation Project (Nos. 2012-Z-943, 2014-ZJ-907).
Bhaumik, Himangsu; Santra, S. B.
2016-12-01
A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities ϕ , where ϕ =0 represents regular lattice and ϕ =1 represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at ϕ =0 and mean-field scaling at ϕ =1 , the dissipative avalanches display nontrivial critical properties at ϕ =0 and 1 in both one and two dimensions. In the small-world regime (2-12≤ϕ ≤0.1 ) , the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size sc. Stochastic scaling is found to occur for s sc . As different scaling forms are found to coexist in a single probability distribution, a coexistence scaling theory on small world network is developed and numerically verified.
Altered small-world brain networks in schizophrenia patients during working memory performance.
He, Hao; Sui, Jing; Yu, Qingbao; Turner, Jessica A; Ho, Beng-Choon; Sponheim, Scott R; Manoach, Dara S; Clark, Vincent P; Calhoun, Vince D
2012-01-01
Impairment of working memory (WM) performance in schizophrenia patients (SZ) is well-established. Compared to healthy controls (HC), SZ patients show aberrant blood oxygen level dependent (BOLD) activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI) data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP) at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs) defined by group independent component analysis (ICA). The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1) at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2) in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3) the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.
Altered small-world brain networks in schizophrenia patients during working memory performance.
Directory of Open Access Journals (Sweden)
Hao He
Full Text Available Impairment of working memory (WM performance in schizophrenia patients (SZ is well-established. Compared to healthy controls (HC, SZ patients show aberrant blood oxygen level dependent (BOLD activations and disrupted functional connectivity during WM performance. In this study, we examined the small-world network metrics computed from functional magnetic resonance imaging (fMRI data collected as 35 HC and 35 SZ performed a Sternberg Item Recognition Paradigm (SIRP at three WM load levels. Functional connectivity networks were built by calculating the partial correlation on preprocessed time courses of BOLD signal between task-related brain regions of interest (ROIs defined by group independent component analysis (ICA. The networks were then thresholded within the small-world regime, resulting in undirected binarized small-world networks at different working memory loads. Our results showed: 1 at the medium WM load level, the networks in SZ showed a lower clustering coefficient and less local efficiency compared with HC; 2 in SZ, most network measures altered significantly as the WM load level increased from low to medium and from medium to high, while the network metrics were relatively stable in HC at different WM loads; and 3 the altered structure at medium WM load in SZ was related to their performance during the task, with longer reaction time related to lower clustering coefficient and lower local efficiency. These findings suggest brain connectivity in patients with SZ was more diffuse and less strongly linked locally in functional network at intermediate level of WM when compared to HC. SZ show distinctly inefficient and variable network structures in response to WM load increase, comparing to stable highly clustered network topologies in HC.
Phase Transitions of an Epidemic Spreading Model in Small-World Networks
Institute of Scientific and Technical Information of China (English)
HUA Da-Yin; GAO Ke
2011-01-01
We propose a modified susceptible-infected-refractory-susceptible (SIRS) model to investigate the global oscillations of the epidemic spreading in Watts-Strogatz (WS) small-world networks. It is found that when an individual immunity does not change or decays slowly in an immune period, the system can exhibit complex transition from an infecting stationary state to a large amplitude sustained oscillation or an absorbing state with no infection. When the immunity decays rapidly in the immune period, the transition to the global oscillation disappears and there is no oscillation. Furthermore, based on the spatio-temporal evolution patterns and the phase diagram, it is disclosed that a long immunity period takes an important role in the emergence of the global oscillation in small-world networks.
Complex Behavior in an Integrate-and-Fire Neuron Model Based on Small World Networks
Institute of Scientific and Technical Information of China (English)
LIN Min; CHEN Tian-Lun
2005-01-01
Based on our previously pulse-coupled integrate-and-fire neuron model in small world networks, we investigate the complex behavior of electroencephalographic (EEG)-like activities produced by such a model. We find EEG-like activities have obvious chaotic characteristics. We also analyze the complex behaviors of EEG-like signals,such as spectral analysis, reconstruction of the phase space, the correlation dimension, and so on.
Small World Effects in a Harmonious Unifying Hybrid Preferential Model Networks
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Small world effects in the harmonious unifying hybrid preferential model (HUHPM) networks are studied both numerically and analytically. The idea and method of the HUHPM is applied to three typical examples of unweighted BA model, weighted BBV model, and the TDE model, so-called HUHPM-BA, HUHPM-BBV and HUHPM-TDE networks. Comparing the HUHPM with current typical models above, it is found that the HUHPM networks has the smallest average path length and the biggest average clustering coefficient. The results demonstrate that the HUHPM is more suitable not only for the un-weighted models but also for the weighted models.
The Peculiar Phase Transitions of the Ising Model on a Small-World Network
Brunson, Trent; Boettcher, Stefan
2009-11-01
To describe many collective phenomena on networks, the Ising model again plays a fundamental role. Here, we study a new network with small-world properties that can be studied exactly with the renormalization group. The network is non-planar and has a recursive design combining a one-dimensional backbone with a hierarchy of long-range bonds. Varying the relative strength between nearest-neighbor and long-range bonds, we can define a one-parameter family of models that exhibits a rich variety of critical phenomena, quite distinct from those on lattice models. Exact results and numerical simulations reveal this behavior in great detail.
Small-world anatomical networks in the human brain revealed by cortical thickness from MRI.
He, Yong; Chen, Zhang J; Evans, Alan C
2007-10-01
An important issue in neuroscience is the characterization for the underlying architectures of complex brain networks. However, little is known about the network of anatomical connections in the human brain. Here, we investigated large-scale anatomical connection patterns of the human cerebral cortex using cortical thickness measurements from magnetic resonance images. Two areas were considered anatomically connected if they showed statistically significant correlations in cortical thickness and we constructed the network of such connections using 124 brains from the International Consortium for Brain Mapping database. Significant short- and long-range connections were found in both intra- and interhemispheric regions, many of which were consistent with known neuroanatomical pathways measured by human diffusion imaging. More importantly, we showed that the human brain anatomical network had robust small-world properties with cohesive neighborhoods and short mean distances between regions that were insensitive to the selection of correlation thresholds. Additionally, we also found that this network and the probability of finding a connection between 2 regions for a given anatomical distance had both exponentially truncated power-law distributions. Our results demonstrated the basic organizational principles for the anatomical network in the human brain compatible with previous functional networks studies, which provides important implications of how functional brain states originate from their structural underpinnings. To our knowledge, this study provides the first report of small-world properties and degree distribution of anatomical networks in the human brain using cortical thickness measurements.
Neural progenitors organize in small-world networks to promote cell proliferation.
Malmersjö, Seth; Rebellato, Paola; Smedler, Erik; Planert, Henrike; Kanatani, Shigeaki; Liste, Isabel; Nanou, Evanthia; Sunner, Hampus; Abdelhady, Shaimaa; Zhang, Songbai; Andäng, Michael; El Manira, Abdeljabbar; Silberberg, Gilad; Arenas, Ernest; Uhlén, Per
2013-04-16
Coherent network activity among assemblies of interconnected cells is essential for diverse functions in the adult brain. However, cellular networks before formations of chemical synapses are poorly understood. Here, embryonic stem cell-derived neural progenitors were found to form networks exhibiting synchronous calcium ion (Ca(2+)) activity that stimulated cell proliferation. Immature neural cells established circuits that propagated electrical signals between neighboring cells, thereby activating voltage-gated Ca(2+) channels that triggered Ca(2+) oscillations. These network circuits were dependent on gap junctions, because blocking prevented electrotonic transmission both in vitro and in vivo. Inhibiting connexin 43 gap junctions abolished network activity, suppressed proliferation, and affected embryonic cortical layer formation. Cross-correlation analysis revealed highly correlated Ca(2+) activities in small-world networks that followed a scale-free topology. Graph theory predicts that such network designs are effective for biological systems. Taken together, these results demonstrate that immature cells in the developing brain organize in small-world networks that critically regulate neural progenitor proliferation.
Stochastic resonance enhancement of small-world neural networks by hybrid synapses and time delay
Yu, Haitao; Guo, Xinmeng; Wang, Jiang
2017-01-01
The synergistic effect of hybrid electrical-chemical synapses and information transmission delay on the stochastic response behavior in small-world neuronal networks is investigated. Numerical results show that, the stochastic response behavior can be regulated by moderate noise intensity to track the rhythm of subthreshold pacemaker, indicating the occurrence of stochastic resonance (SR) in the considered neural system. Inheriting the characteristics of two types of synapses-electrical and chemical ones, neural networks with hybrid electrical-chemical synapses are of great improvement in neuron communication. Particularly, chemical synapses are conducive to increase the network detectability by lowering the resonance noise intensity, while the information is better transmitted through the networks via electrical coupling. Moreover, time delay is able to enhance or destroy the periodic stochastic response behavior intermittently. In the time-delayed small-world neuronal networks, the introduction of electrical synapses can significantly improve the signal detection capability by widening the range of optimal noise intensity for the subthreshold signal, and the efficiency of SR is largely amplified in the case of pure chemical couplings. In addition, the stochastic response behavior is also profoundly influenced by the network topology. Increasing the rewiring probability in pure chemically coupled networks can always enhance the effect of SR, which is slightly influenced by information transmission delay. On the other hand, the capacity of information communication is robust to the network topology within the time-delayed neuronal systems including electrical couplings.
Studies on the signal amplification in weighted and unweighted small-world networks
Gao, Yang; Wang, Jianjun; Ma, Fuqiu
2017-02-01
Weighted and unweighted networks composed of coupled bistable oscillators with small-world topology are investigated under the co-presence of a weak signal and multiplicative Gaussian white noise. As the noise intensity is adjusted to one or two optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of stochastic resonance (SR) or stochastic bi-resonance (SBR). The resonance behavior is strongly-dependent on the coupling strength in both networks. At a weak coupling, SR more likely takes place; whereas at a strong coupling, SBR is prone to occur. Compared with unweighted networks, the span of coupling strength for SBR is narrower in weighted networks. In addition, the weak signal cannot be amplified so effectively in the weighted networks as in the unweighted networks, attributing to the weakening effect of the link weight on the coupling between oscillators and the heterogeneity of the whole network connectivity caused by the weight distribution.
The Griffiths Phase on Hierarchical Modular Networks with Small-world Edges
Li, Shanshan
2016-01-01
The Griffiths phase has been proposed to induce a stretched critical regime that facilitates self organizing of brain networks for optimal function. This phase stems from the intrinsic structural heterogeneity of brain networks, such as the hierarchical modular structure. In this work, we extend this concept to modified hierarchical networks with small-world connections based on Hanoi networks [1]. Through extensive simulations, we identify the essential role played by the exponential distribution of the inter-moduli connectivity probability across hierarchies on the emergence of the Griffiths phase in this network. Additionally, the spectral analysis on the adjacency matrix of the relevant networks [2] shows that a localized principle eigenvector is not necessarily the fingerprint of the Griffiths phase.
Power-Aware Anycast Routing in Wireless Sensor Network Exploiting Small World Effect
Institute of Scientific and Technical Information of China (English)
JIANG Nan; YANG Shu-qun; LI Ling-zhi; DING Qiu-lin
2008-01-01
By considering energy-efficient anycast routing in wireless sensor network (WSN), and combining small world characteristics of WSN with the properties of the ant algorithm, a power-aware anycast routing algorithm (SWPAR) with multi-sink nodes is proposed and evaluated. By SWPAR, the optimal sink node is found and the problem of routing path is effectively solved. Simulation results show that compared with the sink-based anycast routing protocol (SARP) and the hierarchy-based anycast routing protocol (HARP), the proposed algorithm improves network lifetime and reduces power consumption.
Research on P2P Overlay Network Model with Small-world Features
Directory of Open Access Journals (Sweden)
Hao LIU
2013-09-01
Full Text Available Topology structure of P2P network decides its system performance. However, the existing P2P network models don’t take clustering and symmetry of nodes into account. Based on the algebra and graph theory method of Cayley graph, this paper proposes a novel P2P overlay network model with small-world features. Its simplicity and symmetry can ensure the self-organization and scalability of P2P network. The results of analysis and experiment shows that this model provides better robustness, higher enquiry efficiency and better load balance than the existing P2P Overlay Network models such as Chord and CAN. Furthermore, it possesses the property of high clustering.
EXTENDED CLUSTERING COEFFICIENTS:GENERALIZATION OF CLUSTERING COEFFICIENTS IN SMALL-WORLD NETWORKS
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 (for no connectivity) to 1 (for full connectivity). We define extended clustering coefficients C(h) of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C(1). Based on known results about the distance distribution Pδ(h) in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law Pδ(h)C(h) ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ(h)C(h) is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ(h) and C(h). Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.
Critical behavior of the XY-rotor model on regular and small-world networks.
De Nigris, Sarah; Leoncini, Xavier
2013-07-01
We study the XY rotors model on small networks whose number of links scales with the system size N(links)~N(γ), where 1≤γ≤2. We first focus on regular one-dimensional rings in the microcanonical ensemble. For γ1.5, the system equilibrium properties are found to be identical to the mean field, which displays a second-order phase transition at a critical energy density ε=E/N,ε(c)=0.75. Moreover, for γ(c)~/=1.5 we find that a nontrivial state emerges, characterized by an infinite susceptibility. We then consider small-world networks, using the Watts-Strogatz mechanism on the regular networks parametrized by γ. We first analyze the topology and find that the small-world regime appears for rewiring probabilities which scale as p(SW)[proportionality]1/N(γ). Then considering the XY-rotors model on these networks, we find that a second-order phase transition occurs at a critical energy ε(c) which logarithmically depends on the topological parameters p and γ. We also define a critical probability p(MF), corresponding to the probability beyond which the mean field is quantitatively recovered, and we analyze its dependence on γ.
Small-world bias of correlation networks: From brain to climate
Hlinka, Jaroslav; Hartman, David; Jajcay, Nikola; Tomeček, David; Tintěra, Jaroslav; Paluš, Milan
2017-03-01
Complex systems are commonly characterized by the properties of their graph representation. Dynamical complex systems are then typically represented by a graph of temporal dependencies between time series of state variables of their subunits. It has been shown recently that graphs constructed in this way tend to have relatively clustered structure, potentially leading to spurious detection of small-world properties even in the case of systems with no or randomly distributed true interactions. However, the strength of this bias depends heavily on a range of parameters and its relevance for real-world data has not yet been established. In this work, we assess the relevance of the bias using two examples of multivariate time series recorded in natural complex systems. The first is the time series of local brain activity as measured by functional magnetic resonance imaging in resting healthy human subjects, and the second is the time series of average monthly surface air temperature coming from a large reanalysis of climatological data over the period 1948-2012. In both cases, the clustering in the thresholded correlation graph is substantially higher compared with a realization of a density-matched random graph, while the shortest paths are relatively short, showing thus distinguishing features of small-world structure. However, comparable or even stronger small-world properties were reproduced in correlation graphs of model processes with randomly scrambled interconnections. This suggests that the small-world properties of the correlation matrices of these real-world systems indeed do not reflect genuinely the properties of the underlying interaction structure, but rather result from the inherent properties of correlation matrix.
Yu, Qingbao; Sui, Jing; Rachakonda, Srinivas; He, Hao; Gruner, William; Pearlson, Godfrey; Kiehl, Kent A; Calhoun, Vince D
2011-01-01
Aberrant topological properties of small-world human brain networks in patients with schizophrenia (SZ) have been documented in previous neuroimaging studies. Aberrant functional network connectivity (FNC, temporal relationships among independent component time courses) has also been found in SZ by a previous resting state functional magnetic resonance imaging (fMRI) study. However, no study has yet determined if topological properties of FNC are also altered in SZ. In this study, small-world network metrics of FNC during the resting state were examined in both healthy controls (HCs) and SZ subjects. FMRI data were obtained from 19 HCs and 19 SZ. Brain images were decomposed into independent components (ICs) by group independent component analysis (ICA). FNC maps were constructed via a partial correlation analysis of ICA time courses. A set of undirected graphs were built by thresholding the FNC maps and the small-world network metrics of these maps were evaluated. Our results demonstrated significantly altered topological properties of FNC in SZ relative to controls. In addition, topological measures of many ICs involving frontal, parietal, occipital and cerebellar areas were altered in SZ relative to controls. Specifically, topological measures of whole network and specific components in SZ were correlated with scores on the negative symptom scale of the Positive and Negative Symptom Scale (PANSS). These findings suggest that aberrant architecture of small-world brain topology in SZ consists of ICA temporally coherent brain networks.
Integration of neuroblasts into a two-dimensional small world neuronal network
Schneider-Mizell, Casey; Zochowski, Michal; Sander, Leonard
2009-03-01
Neurogenesis in the adult brain has been suggested to be important for learning and functional robustness to the neuronal death. New neurons integrate themselves into existing neuronal networks by moving into a target destination, extending axonal and dendritic processes, and inducing synaptogenesis to connect to active neurons. We hypothesize that increased plasticity of the network to novel stimuli can arise from activity-dependent cell and process motility rules. In complement to a similar in vitro model, we investigate a computational model of a two-dimensional small world network of integrate and fire neurons. After steady-state activity is reached in the extant network, we introduce new neurons which move, stop, and connect themselves through rules governed by position and firing rate.
Abe, Jun; Bomze, David; Cremasco, Viviana; Scandella, Elke; Stein, Jens V.; Turley, Shannon J.; Ludewig, Burkhard
2016-01-01
Fibroblastic reticular cells (FRCs) form the cellular scaffold of lymph nodes (LNs) and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8+ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses. PMID:27415420
Impact of mobility structure on the optimization of small-world networks of mobile agents
Lee, Eun
2015-01-01
In ad hoc wireless networking, units are connected to each other rather than to a central, fixed, infrastructure. Constructing and maintaining such networks create several trade-off problems between robustness, communication speed, power consumption, etc., that bridges engineering, computer science and the physics of complex systems. In this work, we address the role of mobility patterns of the agents on the optimal tuning of a small-world type network construction method. By this method, the network is updated periodically and held static between the updates. We investigate the optimal updating times for different scenarios of the movement of agents (modeling, for example, the fat-tailed trip distances, and periodicities, of human travel). We find that these mobility patterns affect the power consumption in non-trivial ways and discuss how these effects can best be handled.
Novkovic, Mario; Onder, Lucas; Cupovic, Jovana; Abe, Jun; Bomze, David; Cremasco, Viviana; Scandella, Elke; Stein, Jens V; Bocharov, Gennady; Turley, Shannon J; Ludewig, Burkhard
2016-07-01
Fibroblastic reticular cells (FRCs) form the cellular scaffold of lymph nodes (LNs) and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8+ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses.
Directory of Open Access Journals (Sweden)
Mario Novkovic
2016-07-01
Full Text Available Fibroblastic reticular cells (FRCs form the cellular scaffold of lymph nodes (LNs and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8+ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses.
Impact of mobility structure on optimization of small-world networks of mobile agents
Lee, Eun; Holme, Petter
2016-06-01
In ad hoc wireless networking, units are connected to each other rather than to a central, fixed, infrastructure. Constructing and maintaining such networks create several trade-off problems between robustness, communication speed, power consumption, etc., that bridges engineering, computer science and the physics of complex systems. In this work, we address the role of mobility patterns of the agents on the optimal tuning of a small-world type network construction method. By this method, the network is updated periodically and held static between the updates. We investigate the optimal updating times for different scenarios of the movement of agents (modeling, for example, the fat-tailed trip distances, and periodicities, of human travel). We find that these mobility patterns affect the power consumption in non-trivial ways and discuss how these effects can best be handled.
Scale-free and small-world properties of earthquake network in Chile
Pasten, Denisse; Munoz, Victor; Suzuki, Norikazu
2010-01-01
The properties of earthquake networks have been studied so far mainly for the seismic data sets taken from California, Japan and Iran, and features common in these regions have been reported in the literature. Here, an earthquake network is constructed and analyzed for the Chilean data to examine if the scale-free and small-world properties of the earthquake networks constructed in the other geographical regions can also be found in seismicity in Chile. It is shown that the result is affirmative: in all the regions both the exponent "gamma" of the power-law connectivity distribution and the clustering coefficient C take the universal invariant values "gamma ~1" and "C~0.85", respectively, as the cell size becomes larger than a certain value, which is the scale of coarse graining needed for constructing earthquake network. An interpretation for this remarkable result is presented based on physical considerations.
Kim, Sang-Yoon; Lim, Woochang
2015-11-01
We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength Jinter and the average number of intermodular links per interneuron Msyn(inter ). In contrast to the case of nonclustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intramodular dynamics of subnetworks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intramodular dynamics of subnetworks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching degree between the instantaneous subpopulation spike rates of the subnetworks, and examine whether the sparse synchronization is global or modular. Depending on its magnitude, the intermodular coupling strength Jinter seems to play "dual" roles for the pacing between spikes in each subnetwork. For large Jinter, due to strong inhibition it plays a destructive role to "spoil" the pacing between spikes, while for small Jinter it plays a constructive role to "favor" the pacing between spikes. Through competition between the constructive and the destructive roles of Jinter, there exists an intermediate optimal Jinter at which the pacing degree between spikes becomes maximal. In contrast, the average number of intermodular links per interneuron Msyn(inter ) seems to play a role just to favor the pacing between spikes. With increasing Msyn(inter ), the pacing degree between spikes increases monotonically thanks to the increase in the degree of effectiveness of global communication between spikes. Furthermore, we
Robustness of Diversity Induced Synchronization Transition in a Delayed Small-World Neuronal Network
Institute of Scientific and Technical Information of China (English)
TANG Jun; QU Li-Cheng; LUO Jin-Ming
2011-01-01
In a diverse and delayed small-world neuronal network, we have identified the oscillatory-like synchronization transition between anti-phase and complete synchronization [Phys. Rev. E 83(2011)046207]. Here we study the influence of the network topology and noise on the synchronization transition. The robustness of this transition is investigated. The results show that: (I) the synchronization transition is robust to the neuron number N in the network; (ii) only when the coupled neighbor number k is in the region [4,10], does the synchronization transition exist; (iii) to some extent, the synchronization is destroyed by noise and the oscillatory-like synchronization transition exists for relatively weak noise (D <0.003).%In a diverse and delayed small-world neuronal network,we have identified the oscillatory-like synchronization transition between anti-phase and complete synchronization [Phys.Rev.E 83 (2011) 046207].Here we study the influence of the network topology and noise on the synchronization transition.The robustness of this transition is investigated.The results show that:(i) the synchronization transition is robust to the neuron number N in the network;(ii) only when the coupled neighbor number k is in the region [4,10],does the synchronization transition exist;(iii) to some extent,the synchronization is destroyed by noise and the oscillatory-like synchronization transition exists for relatively weak noise (D ＜0.003).In the theoretical study of neuron systems,the synchronized behavior of a population of interacting neurons,namely,a neuronal network,is a hot issue due to its importance to the processing and transmission of information.[1] Many types of synchronization are identified in neuronal networks,such as complete synchronization,phase synchronization,anti-phase synchronization,phase-lock synchronization,cluster synchronization and lag synchronization.[2
Quantification of degeneracy in Hodgkin-Huxley neurons on Newman-Watts small world network.
Man, Menghua; Zhang, Ya; Ma, Guilei; Friston, Karl; Liu, Shanghe
2016-08-07
Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin-Huxley neuronal networks with Newman-Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus - and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity - and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.
Small-World Connections to Induce Firing Activity and Phase Synchronization in Neural Networks
Institute of Scientific and Technical Information of China (English)
QIN Ying-Hua; LUO Xiao-Shu
2009-01-01
We investigate how the firing activity and the subsequent phase synchronization of neural networks with small-world topological connections depend on the probability p of adding-links. Network elements are described by two-dimensional map neurons (2DMNs) in a quiescent original state. Neurons burst for a given coupling strength when the topological randomness p increases, which is absent in a regular-lattice neural network. The bursting activity becomes frequent and synchronization of neurons emerges as topological randomness further increases.The maximal firing frequency and phase synchronization appear at a particular value of p. However, if the randomness p further increases, the firing frequency decreases and synchronization is apparently destroyed.
Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures
de Santos-Sierra, Daniel; Leyva, Inmaculada; Almendral, Juan A; Anava, Sarit; Ayali, Amir; Papo, David; Boccaletti, Stefano
2014-01-01
In vitro primary cultures of dissociated invertebrate neurons from locust ganglia are used to experimentally investigate the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. At all the different stages of the culture's development, identification of neurons' and neurites' location by means of a dedicated software allows to ultimately extract an adjacency matrix from each image of the culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main network's characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graph's micro- and meso-scale properties emerge. Finally, we identify the main physical processes ruling the culture's morphological transformati...
Altered small-world properties of gray matter networks in breast cancer
Directory of Open Access Journals (Sweden)
Hosseini S M
2012-05-01
Full Text Available Abstract Background Breast cancer survivors, particularly those treated with chemotherapy, are at significantly increased risk for long-term cognitive and neurobiologic impairments. These deficits tend to involve skills that are subserved by distributed brain networks. Additionally, neuroimaging studies have shown a diffuse pattern of brain structure changes in chemotherapy-treated breast cancer survivors that might impact large-scale brain networks. Methods We therefore applied graph theoretical analysis to compare the gray matter structural networks of female breast cancer survivors with a history of chemotherapy treatment and healthy age and education matched female controls. Results Results revealed reduced clustering coefficient and small-world index in the brain network of the breast cancer patients across a range of network densities. In addition, the network of the breast cancer group had less highly interactive nodes and reduced degree/centrality in the frontotemporal regions compared to controls, which may help explain the common impairments of memory and executive functioning among these patients. Conclusions These results suggest that breast cancer and chemotherapy may decrease regional connectivity as well as global network organization and integration, reducing efficiency of the network. To our knowledge, this is the first report of altered large-scale brain networks associated with breast cancer and chemotherapy.
Prisoner's Dilemma Game with Heterogeneous Influential Effect on Regular Small-World Networks
Institute of Scientific and Technical Information of China (English)
WU Zhi-Xi; XU Xin-Jian; WANG Ying-Hai
2006-01-01
@@ The effect of heterogeneous influence of different individuals on the maintenance of co-operative behaviour is studied in an evolutionary Prisoner's Dilemma game with players located on the sites of regular small-world networks. The players interacting with their neighbours can either co-operate or defect and update their states by choosing one of the neighbours and adopting its strategy with a probability depending on the payoff difference.The selection of the neighbour obeys a preferential rule: the more influential a neighbour, the larger the probability it is picked. It is found that this simple preferential selection rule can promote continuously the co-operation of the whole population with the strengthening of the disorder of the underlying network.
Migration in a Small World: A Network Approach to Modeling Immigration Processes
Fotouhi, Babak
2012-01-01
Existing theories of migration either focus on micro- or macroscopic behavior of populations; that is, either the average behavior of entire population is modeled directly, or decisions of individuals are modeled directly. In this work, we seek to bridge these two perspectives by modeling individual agents decisions to migrate while accounting for the social network structure that binds individuals into a population. Pecuniary considerations combined with the decisions of peers are the primary elements of the model, being the main driving forces of migration. People of the home country are modeled as nodes on a small-world network. A dichotomous state is associated with each node, indicating whether it emigrates to the destination country or it stays in the home country. We characterize the emigration rate in terms of the relative welfare and population of the home and destination countries. The time evolution and the steady-state fraction of emigrants are also derived.
Directory of Open Access Journals (Sweden)
Wei Li
2013-10-01
Full Text Available The patent cooperation network which enterprises join is a very important network platform for enterprises’ open innovation. However, very limited work has been done to empirically investigate the dynamic change process of the network in China. To address this issue, this paper analyzes dynamic change process of cooperation network of enterprises and the small-world effect of the biggest subgroup according to the data of 36731 items of cooperative patents between enterprises from 1985 to 2010 published by the State Intellectual Property Office of China. A conclusion can be drawn from the analysis results that the biggest subgroup has the characteristics of small-world effect, but the overall network structure also has some defects, which limit the development of open innovation. For the first time, suggestions on open innovation strategies are put forward to provide theoretical reference for both the government and enterprises.
Navigation on Power-Law Small World Network with Incomplete Information
Institute of Scientific and Technical Information of China (English)
CHEN Jian-Zhen; ZHU Jian-Yang
2007-01-01
We investigate the navigation process on a variant of the Watts-Strogatz small-world network model with local information. In the network construction, each vertex of an N × N square lattice sends out a long-range link with probability p. The other end of the link falls on a randomly chosen vertex with probability proportional to r-α, where r is the lattice distance between the two vertices, and α ≥ 0. The average actual path length,i.e. the expected number of steps for passing messages between randomly chosen vertex pairs, is found to scale as a power-law function of the network size Nβ, except when α is close to a specific value αmin, which gives the highest efficiency of message navigation. For a finite network, the exponent β depends on both α and p, and αmin drops to zero at a critical value of p which depends on N. When the network size goes to infinity,β depends only on α, and αmin is equal to the network dimensionality.
Effects of distance-dependent delay on small-world neuronal networks.
Zhu, Jinjie; Chen, Zhen; Liu, Xianbin
2016-04-01
We study firing behaviors and the transitions among them in small-world noisy neuronal networks with electrical synapses and information transmission delay. Each neuron is modeled by a two-dimensional Rulkov map neuron. The distance between neurons, which is a main source of the time delay, is taken into consideration. Through spatiotemporal patterns and interspike intervals as well as the interburst intervals, the collective behaviors are revealed. It is found that the networks switch from resting state into intermittent firing state under Gaussian noise excitation. Initially, noise-induced firing behaviors are disturbed by small time delays. Periodic firing behaviors with irregular zigzag patterns emerge with an increase of the delay and become progressively regular after a critical value is exceeded. More interestingly, in accordance with regular patterns, the spiking frequency doubles compared with the former stage for the spiking neuronal network. A growth of frequency persists for a larger delay and a transition to antiphase synchronization is observed. Furthermore, it is proved that these transitions are generic also for the bursting neuronal network and the FitzHugh-Nagumo neuronal network. We show these transitions due to the increase of time delay are robust to the noise strength, coupling strength, network size, and rewiring probability.
Waldorp, Lourens J
2016-01-01
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To analyse changes over time and characterise possible future behaviour is rather difficult for large graphs. We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We show that we can use variations of the mean field of the grid to describe the dynamics of the PCA on a random and small-world graph. Bifurcation diagrams for the mean field of the grid, random, and small-world graphs indicate possible phase transitions for certain parameter settings. Extensive simulations indicate for di...
Directory of Open Access Journals (Sweden)
Zhekang Dong
2014-01-01
Full Text Available In this paper, we present an implementation scheme of memristor-based multilayer feedforward small-world neural network (MFSNN inspirited by the lack of the hardware realization of the MFSNN on account of the need of a large number of electronic neurons and synapses. More specially, a mathematical closed-form charge-governed memristor model is presented with derivation procedures and the corresponding Simulink model is presented, which is an essential block for realizing the memristive synapse and the activation function in electronic neurons. Furthermore, we investigate a more intelligent memristive PID controller by incorporating the proposed MFSNN into intelligent PID control based on the advantages of the memristive MFSNN on computation speed and accuracy. Finally, numerical simulations have demonstrated the effectiveness of the proposed scheme.
Modeling and Analysis of Epidemic Diffusion within Small-World Network
Directory of Open Access Journals (Sweden)
Ming Liu
2012-01-01
Full Text Available To depict the rule of epidemic diffusion, two different models, the Susceptible-Exposure-Infected-Recovered-Susceptible (SEIRS model and the Susceptible-Exposure-Infected-Quarantine-Recovered-Susceptible (SEIQRS model, are proposed and analyzed within small-world network in this paper. Firstly, the epidemic diffusion models are constructed with mean-filed theory, and condition for the occurrence of disease diffusion is explored. Then, the existence and global stability of the disease-free equilibrium and the endemic equilibrium for these two complex epidemic systems are proved by differential equations knowledge and Routh-Hurwiz theory. At last, a numerical example which includes key parameters analysis and critical topic discussion is presented to test how well the proposed two models may be applied in practice. These works may provide some guidelines for decision makers when coping with epidemic diffusion controlling problems.
The Public Opinion Control Model Based on the Connecting Multi-Small-World-Network
Directory of Open Access Journals (Sweden)
Wen-Qi Zhong
2013-09-01
Full Text Available Based on the propagation mechanism of the rumor control, this study proposes a mode of propagation found on the information content to describe the dissemination of two opposite rumors on the same subject among crowds and sets up public opinion control model on the basis of this mode. Two opposite rumors on the same subject in our mode of propagation can respectively represent rumor and truth, so we investigate their interactions during the dissemination among crowd and simulate it in the connecting multi-small-world-network. Finally, by adjusting the factors which can affect the control effect of the model, we propose a corresponding rumor immunization strategy. Based on that, we conduct the analogy analysis of interactions of many opposite rumors on the same subject when they spread among crowds.
Disrupted small-world brain networks in moderate Alzheimer's disease: a resting-state FMRI study.
Directory of Open Access Journals (Sweden)
Xiaohu Zhao
Full Text Available The small-world organization has been hypothesized to reflect a balance between local processing and global integration in the human brain. Previous multimodal imaging studies have consistently demonstrated that the topological architecture of the brain network is disrupted in Alzheimer's disease (AD. However, these studies have reported inconsistent results regarding the topological properties of brain alterations in AD. One potential explanation for these inconsistent results lies with the diverse homogeneity and distinct progressive stages of the AD involved in these studies, which are thought to be critical factors that might affect the results. We investigated the topological properties of brain functional networks derived from resting functional magnetic resonance imaging (fMRI of carefully selected moderate AD patients and normal controls (NCs. Our results showed that the topological properties were found to be disrupted in AD patients, which showing increased local efficiency but decreased global efficiency. We found that the altered brain regions are mainly located in the default mode network, the temporal lobe and certain subcortical regions that are closely associated with the neuropathological changes in AD. Of note, our exploratory study revealed that the ApoE genotype modulates brain network properties, especially in AD patients.
Networks of neuroblastoma cells on porous silicon substrates reveal a small world topology
Marinaro, Giovanni
2015-01-01
The human brain is a tightly interweaving network of neural cells where the complexity of the network is given by the large number of its constituents and its architecture. The topological structure of neurons in the brain translates into its increased computational capabilities, low energy consumption, and nondeterministic functions, which differentiate human behavior from artificial computational schemes. In this manuscript, we fabricated porous silicon chips with a small pore size ranging from 8 to 75 nm and large fractal dimensions up to Df ∼ 2.8. In culturing neuroblastoma N2A cells on the described substrates, we found that those cells adhere more firmly to and proliferate on the porous surfaces compared to the conventional nominally flat silicon substrates, which were used as controls. More importantly, we observed that N2A cells on the porous substrates create highly clustered, small world topology patterns. We conjecture that neurons with a similar architecture may elaborate information more efficiently than in random or regular grids. Moreover, we hypothesize that systems of neurons on nano-scale geometry evolve in time to form networks in which the propagation of information is maximized. This journal is
Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures.
Directory of Open Access Journals (Sweden)
Daniel de Santos-Sierra
Full Text Available In vitro primary cultures of dissociated invertebrate neurons from locust ganglia are used to experimentally investigate the morphological evolution of assemblies of living neurons, as they self-organize from collections of separated cells into elaborated, clustered, networks. At all the different stages of the culture's development, identification of neurons' and neurites' location by means of a dedicated software allows to ultimately extract an adjacency matrix from each image of the culture. In turn, a systematic statistical analysis of a group of topological observables grants us the possibility of quantifying and tracking the progression of the main network's characteristics during the self-organization process of the culture. Our results point to the existence of a particular state corresponding to a small-world network configuration, in which several relevant graph's micro- and meso-scale properties emerge. Finally, we identify the main physical processes ruling the culture's morphological transformations, and embed them into a simplified growth model qualitatively reproducing the overall set of experimental observations.
Abnormal small-world architecture of top–down control networks in obsessive–compulsive disorder
Zhang, Tijiang; Wang, Jinhui; Yang, Yanchun; Wu, Qizhu; Li, Bin; Chen, Long; Yue, Qiang; Tang, Hehan; Yan, Chaogan; Lui, Su; Huang, Xiaoqi; Chan, Raymond C.K.; Zang, Yufeng; He, Yong; Gong, Qiyong
2011-01-01
Background Obsessive–compulsive disorder (OCD) is a common neuropsychiatric disorder that is characterized by recurrent intrusive thoughts, ideas or images and repetitive ritualistic behaviours. Although focal structural and functional abnormalities in specific brain regions have been widely studied in populations with OCD, changes in the functional relations among them remain poorly understood. This study examined OCD–related alterations in functional connectivity patterns in the brain’s top–down control network. Methods We applied resting-state functional magnetic resonance imaging to investigate the correlation patterns of intrinsic or spontaneous blood oxygen level–dependent signal fluctuations in 18 patients with OCD and 16 healthy controls. The brain control networks were first constructed by thresholding temporal correlation matrices of 39 brain regions associated with top–down control and then analyzed using graph theory-based approaches. Results Compared with healthy controls, the patients with OCD showed decreased functional connectivity in the posterior temporal regions and increased connectivity in various control regions such as the cingulate, precuneus, thalamus and cerebellum. Furthermore, the brain’s control networks in the healthy controls showed small-world architecture (high clustering coefficients and short path lengths), suggesting an optimal balance between modularized and distributed information processing. In contrast, the patients with OCD showed significantly higher local clustering, implying abnormal functional organization in the control network. Further analysis revealed that the changes in network properties occurred in regions of increased functional connectivity strength in patients with OCD. Limitations The patient group in the present study was heterogeneous in terms of symptom clusters, and most of the patients with OCD were medicated. Conclusion Our preliminary results suggest that the organizational patterns of
Abnormal small-world architecture of top-down control networks in obsessive-compulsive disorder.
Zhang, Tijiang; Wang, Jinhui; Yang, Yanchun; Wu, Qizhu; Li, Bin; Chen, Long; Yue, Qiang; Tang, Hehan; Yan, Chaogan; Lui, Su; Huang, Xiaoqi; Chan, Raymond C K; Zang, Yufeng; He, Yong; Gong, Qiyong
2011-01-01
Obsessive-compulsive disorder (OCD) is a common neuropsychiatric disorder that is characterized by recurrent intrusive thoughts, ideas or images and repetitive ritualistic behaviours. Although focal structural and functional abnormalities in specific brain regions have been widely studied in populations with OCD, changes in the functional relations among them remain poorly understood. This study examined OCD-related alterations in functional connectivity patterns in the brain's top-down control network. We applied resting-state functional magnetic resonance imaging to investigate the correlation patterns of intrinsic or spontaneous blood oxygen level-dependent signal fluctuations in 18 patients with OCD and 16 healthy controls. The brain control networks were first constructed by thresholding temporal correlation matrices of 39 brain regions associated with top-down control and then analyzed using graph theory-based approaches. Compared with healthy controls, the patients with OCD showed decreased functional connectivity in the posterior temporal regions and increased connectivity in various control regions such as the cingulate, precuneus, thalamus and cerebellum. Furthermore, the brain's control networks in the healthy controls showed small-world architecture (high clustering coefficients and short path lengths), suggesting an optimal balance between modularized and distributed information processing. In contrast, the patients with OCD showed significantly higher local clustering, implying abnormal functional organization in the control network. Further analysis revealed that the changes in network properties occurred in regions of increased functional connectivity strength in patients with OCD. The patient group in the present study was heterogeneous in terms of symptom clusters, and most of the patients with OCD were medicated. Our preliminary results suggest that the organizational patterns of intrinsic brain activity in the control networks are altered in
Yilmaz, Ergin; Baysal, Veli; Ozer, Mahmut; Perc, Matjaž
2016-02-01
We study the effects of an autapse, which is mathematically described as a self-feedback loop, on the propagation of weak, localized pacemaker activity across a Newman-Watts small-world network consisting of stochastic Hodgkin-Huxley neurons. We consider that only the pacemaker neuron, which is stimulated by a subthreshold periodic signal, has an electrical autapse that is characterized by a coupling strength and a delay time. We focus on the impact of the coupling strength, the network structure, the properties of the weak periodic stimulus, and the properties of the autapse on the transmission of localized pacemaker activity. Obtained results indicate the existence of optimal channel noise intensity for the propagation of the localized rhythm. Under optimal conditions, the autapse can significantly improve the propagation of pacemaker activity, but only for a specific range of the autaptic coupling strength. Moreover, the autaptic delay time has to be equal to the intrinsic oscillation period of the Hodgkin-Huxley neuron or its integer multiples. We analyze the inter-spike interval histogram and show that the autapse enhances or suppresses the propagation of the localized rhythm by increasing or decreasing the phase locking between the spiking of the pacemaker neuron and the weak periodic signal. In particular, when the autaptic delay time is equal to the intrinsic period of oscillations an optimal phase locking takes place, resulting in a dominant time scale of the spiking activity. We also investigate the effects of the network structure and the coupling strength on the propagation of pacemaker activity. We find that there exist an optimal coupling strength and an optimal network structure that together warrant an optimal propagation of the localized rhythm.
Continuous Forest Fire Propagation in a Local Small World Network Model
Aguayo, F; Clerc, J -P; Porterie, B
2013-01-01
This paper presents the development of a new continuous forest fire model implemented as a weighted local small-world network approach. This new approach was designed to simulate fire patterns in real, heterogeneous landscapes. The wildland fire spread is simulated on a square lattice in which each cell represents an area of the land's surface. The interaction between burning and non-burning cells, in the present work induced by flame radiation, may be extended well beyond nearest neighbors. It depends on local conditions of topography and vegetation types. An approach based on a solid flame model is used to predict the radiative heat flux from the flame generated by the burning of each site towards its neighbors. The weighting procedure takes into account the self-degradation of the tree and the ignition processes of a combustible cell through time. The model is tested on a field presenting a range of slopes and with data collected from a real wildfire scenario. The critical behavior of the spreading process...
Yu, Haitao; Wang, Jiang; Du, Jiwei; Deng, Bin; Wei, Xile; Liu, Chen
2013-05-01
The effects of time delay and rewiring probability on stochastic resonance and spatiotemporal order in small-world neuronal networks are studied in this paper. Numerical results show that, irrespective of the pacemaker introduced to one single neuron or all neurons of the network, the phenomenon of stochastic resonance occurs. The time delay in the coupling process can either enhance or destroy stochastic resonance on small-world neuronal networks. In particular, appropriately tuned delays can induce multiple stochastic resonances, which appear intermittently at integer multiples of the oscillation period of the pacemaker. More importantly, it is found that the small-world topology can significantly affect the stochastic resonance on excitable neuronal networks. For small time delays, increasing the rewiring probability can largely enhance the efficiency of pacemaker-driven stochastic resonance. We argue that the time delay and the rewiring probability both play a key role in determining the ability of the small-world neuronal network to improve the noise-induced outreach of the localized subthreshold pacemaker.
Luongo, Francisco J; Zimmerman, Chris A; Horn, Meryl E; Sohal, Vikaas S
2016-05-01
Sequential patterns of prefrontal activity are believed to mediate important behaviors, e.g., working memory, but it remains unclear exactly how they are generated. In accordance with previous studies of cortical circuits, we found that prefrontal microcircuits in young adult mice spontaneously generate many more stereotyped sequences of activity than expected by chance. However, the key question of whether these sequences depend on a specific functional organization within the cortical microcircuit, or emerge simply as a by-product of random interactions between neurons, remains unanswered. We observed that correlations between prefrontal neurons do follow a specific functional organization-they have a small-world topology. However, until now it has not been possible to directly link small-world topologies to specific circuit functions, e.g., sequence generation. Therefore, we developed a novel analysis to address this issue. Specifically, we constructed surrogate data sets that have identical levels of network activity at every point in time but nevertheless represent various network topologies. We call this method shuffling activity to rearrange correlations (SHARC). We found that only surrogate data sets based on the actual small-world functional organization of prefrontal microcircuits were able to reproduce the levels of sequences observed in actual data. As expected, small-world data sets contained many more sequences than surrogate data sets with randomly arranged correlations. Surprisingly, small-world data sets also outperformed data sets in which correlations were maximally clustered. Thus the small-world functional organization of cortical microcircuits, which effectively balances the random and maximally clustered regimes, is optimal for producing stereotyped sequential patterns of activity.
Energy Technology Data Exchange (ETDEWEB)
Yu, Haitao; Guo, Xinmeng; Wang, Jiang, E-mail: jiangwang@tju.edu.cn; Deng, Bin; Wei, Xile [School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 (China)
2014-09-01
The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.
Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile
2014-09-01
The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.
SYNCHRONIZATION IN COMPLEX DYNAMICAL NETWORKS
Institute of Scientific and Technical Information of China (English)
WANG Xiaofan; CHEN Guanrong
2003-01-01
In the past few years, the discovery of small-world and scale-free properties of many natural and artificial complex networks has stimulated increasing interest in further studying the underlying organizing principles of various complex networks. This has led to significant advances in understanding the relationship between the topology and the dynamics of such complex networks. This paper reviews some recent research works on the synchronization phenomenon in various dynamical networks with small-world and scalefree connections.
Chen, Yong; Qin, Shao-Meng; Yu, Lianchun; Zhang, Shengli
2008-03-01
We studied synchronization between prisoner’s dilemma games with voluntary participation in two Newman-Watts small-world networks. It was found that there are three kinds of synchronization: partial phase synchronization, total phase synchronization, and complete synchronization, for varied coupling factors. Besides, two games can reach complete synchronization for the large enough coupling factor. We also discussed the effect of the coupling factor on the amplitude of oscillation of cooperator density.
Yu, Haitao; Wang, Jiang; Du, Jiwei; Deng, Bin; Wei, Xile
2015-02-01
Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.
Institute of Scientific and Technical Information of China (English)
YUAN Wu-Jie; LUO Xiao-Shu; JIANG Pin-Qun
2007-01-01
In this paper,we propose a new model of weighted small-world biological neural networks based on biophysical Hodgkin-Huxley neurons with side-restrain mechanism.Then we study excitement properties of the model under alternating current (AC) stimulation.The study shows that the excitement properties in the networks are preferably consistent with the behavior properties of a brain nervous system under different AC stimuli,such as refractory period and the brain neural excitement response induced by different intensities of nolse and coupling.The results of the study have reference worthiness for the brain nerve electrophysiology and epistemological science.
Liu, Tian; Chen, Yanni; Lin, Pan; Wang, Jue
2015-07-01
We investigated the topologic properties of human brain attention-related functional networks associated with Multi-Source Interference Task (MSIT) performance using electroencephalography (EEG). Data were obtained from 13 children diagnosed with attention-deficit/hyperactivity disorder (ADHD) and 13 normal control children. Functional connectivity between all pairwise combinations of EEG channels was established by calculating synchronization likelihood (SL). The cluster coefficients and path lengths were computed as a function of degree K. The results showed that brain attention functional networks of normal control subjects had efficient small-world topologic properties, whereas these topologic properties were altered in ADHD. In particular, increased local characteristics combined with decreased global characteristics in ADHD led to a disorder-related shift of the network topologic structure toward ordered networks. These findings are consistent with a hypothesis of dysfunctional segregation and integration of the brain in ADHD, and enhance our understanding of the underlying pathophysiologic mechanism of this illness.
Ma, Fei; Yao, Bing
2017-10-01
It is always an open, demanding and difficult task for generating available model to simulate dynamical functions and reveal inner principles from complex systems and networks. In this article, due to lots of real-life and artificial networks are built from series of simple and small groups (components), we discuss some interesting and helpful network-operation to generate more realistic network models. In view of community structure (modular topology), we present a class of sparse network models N(t , m) . At the moment, we capture the fact the N(t , 4) has not only scale-free feature, which means that the probability that a randomly selected vertex with degree k decays as a power-law, following P(k) ∼k-γ, where γ is the degree exponent, but also small-world property, which indicates that the typical distance between two uniform randomly chosen vertices grows proportionally to logarithm of the order of N(t , 4) , namely, relatively shorter diameter and lower average path length, simultaneously displays higher clustering coefficient. Next, as a new topological parameter correlating to reliability, synchronization capability and diffusion properties of networks, the number of spanning trees over a network is studied in more detail, an exact analytical solution for the number of spanning trees of the N(t , 4) is obtained. Based on the network-operation, part hub-vertex linking with each other will be helpful for structuring various network models and investigating the rules related with real-life networks.
Altered small-world anatomical networks in Apolipoprotein-E4 (ApoE4) carriers using MRI.
Goryawala, Mohammed; Zhou, Qi; Duara, Ranjan; Loewenstein, David; Cabrerizo, Mercedes; Barker, Warren; Adjouadi, Malek
2014-01-01
Apolipoprotein E (ApoE) gene and primarily its allele e4 have been identified as a risk factor for Alzheimer's disease (AD). The prevalence of the gene in 25-30% in the population makes it essential to estimate its role in neuroregulation and its impact on distributed brain networks. In this study, we provide computational neuroanatomy based interpretation of large-scale and small-world cortical networks in cognitive normal (CN) subjects with differing Apolipoprotein-E4 (ApoE4) gene expression. We estimated large-scale anatomical networks from cortical thickness measurements derived from magnetic resonance imaging in 147 CN subjects explored in relation to ApoE4 genotype (e4+ carriers (n=41) versus e4- non-carriers (n=106)). Brain networks were constructed by thresholding cortical thickness correlation matrices of 68 bilateral regions of the brain analyzed using well-established graph theoretical approaches. Compared to ApoE4 non-carriers, carriers showed increased interregional correlation coefficients in regions like precentral, superior frontal and inferior temporal regions. Interestingly most of the altered connections were intra-hemispheric limited primarily to the right hemisphere. Furthermore, ApoE4 carriers demonstrated abnormal small-world architecture in the cortical networks with increased clustering coefficient and path lengths as compared to non-carrier, suggesting a less optimal topological organization. Additionally non-carriers demonstrated higher betweenness in regions such as middle temporal, para-hippocampal gyrus, posterior cingulate and insula of the default mode network (DMN), also seen in subjects with AD and mild cognitive impairment (MCI). The results suggest that the complex morphological cortical connectivity patterns are altered in ApoE4 carriers as compared to non-carriers, providing evidence for disruption of integrity in large-scale anatomical brain networks.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Long Jiang, E-mail: kevinzhlj@163.com [Department of Medical Imaging, Jinling Hospital, Medical School of Nanjing University, Nanjing, Jiangsu 210002 (China); Zheng, Gang [Department of Medical Imaging, Jinling Hospital, Medical School of Nanjing University, Nanjing, Jiangsu 210002 (China); College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016 (China); Zhang, Liping [College of Natural Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016 (China); Zhong, Jianhui [Department of Biomedical Engineering, Zhejiang University, Hangzhou, Zhejiang 310027 (China); Li, Qiang [College of Natural Science, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016 (China); Zhao, Tie Zhu [Department of Medical Imaging, Jinling Hospital, Medical School of Nanjing University, Nanjing, Jiangsu 210002 (China); College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 210016 (China); Lu, Guang Ming, E-mail: cjr.luguangming@vip.163.com [Department of Medical Imaging, Jinling Hospital, Medical School of Nanjing University, Nanjing, Jiangsu 210002 (China)
2014-10-15
Purpose: To explore changes in functional connectivity and topological organization of brain functional networks in cirrhotic patients with minimal hepatic encephalopathy (MHE) and non hepatic encephalopathy (nonHE) and their relationship with clinical markers. Materials and methods: Resting-state functional MR imaging was acquired in 22 MHE, 29 nonHE patients and 33 healthy controls. Functional connectivity networks were obtained by computing temporal correlations between any pairs of 90 cortical and subcortical regions. Graph analysis measures were quantitatively assessed for each subject. One-way analysis of covariance was applied to identify statistical differences of functional connectivity and network parameters among three groups. Correlations between clinical markers, such as Child–Pugh scores, venous blood ammonia level, and number connection test type A (NCT-A)/digit symbol test (DST) scores, and connectivity/graph metrics were calculated. Results: Thirty functional connectivities represented by edges were found to be abnormal (P < 0.05, FDR corrected) in cirrhotic patients, in which 16 edges (53.3%) were related with sub-cortical regions. MHE patients showed abnormal small-world attributes in the functional connectivity networks. Cirrhotic patients had significantly reduced nodal degree in 8 cortical regions and increased nodal centrality in 3 cortical regions. Twenty edges were correlated with either NCT-A or DST scores, in which 13 edges were related with sub-cortical regions. No correlation was found between Child–Pugh scores and graph theoretical measures in cirrhotic patients. Conclusion: Disturbances of brain functional connectivity and small world property loss are associated with neurocognitive impairment of cirrhotic patients. Reorganization of brain network occurred during disease progression from nonHE to MHE.
Multistage Random Growing Small-World Networks with Power-Law Degree Distribution
Institute of Scientific and Technical Information of China (English)
LIU Jian-Guo; DANG Yan-Zhong; WANG Zhong-Tuo
2006-01-01
@@ We present a simple rule which could generate scale-free networks with very large clustering coefficient and very small average distance. These networks, called the multistage random growing networks (MRGNs), are constructed by a two-stage adding process for each new node. The analytic results of the power-law exponentγ = 3 and the clustering coefficient C = 0.81 are obtained, which agree with the simulation results approximately.
Percha, B; Zochowski, M; Percha, Bethany; Dzakpasu, Rhonda; Zochowski, Micha{\\l} \\.
2004-01-01
Temporal correlations in the brain are thought to have very dichotomic roles. On one hand they are ubiquitously present in the healthy brain and are thought to underlie feature binding during information processing. On the other hand large scale synchronization is an underlying mechanism of epileptic seizures. In this paper we show a possible mechanism of transition to pathological coherence underlying seizure generation. We show that properties of phase synchronization in the 2-D lattice of non-identical coupled Hindmarsh-Rose neurons change radically depending on the connectivity structure. We modify the connectivity using the small world network paradigm and measure properties of phase synchronization using previously developed measure based on assessment of the distributions of relative interspike intervals. We show that the phase synchronization undergoes a dramatic change as a function of locality of network connections from local coherence strongly dependent on the distance between two neurons to globa...
Energy Technology Data Exchange (ETDEWEB)
Shao Zhigang [Department of Physics, Wuhan University, Wuhan 430072 (China); Zou Xianwu [Department of Physics, Wuhan University, Wuhan 430072 (China)]. E-mail: xwzou@whu.edu.cn; Tan Zhijie [Department of Physics, Wuhan University, Wuhan 430072 (China); Huang Shengyou [Department of Physics, Wuhan University, Wuhan 430072 (China); Jin Zhunzhi [Department of Physics, Wuhan University, Wuhan 430072 (China)
2004-10-11
Deposition, diffusion, and aggregation (DDA) on a two-dimensional small-world network have been investigated by computer simulations. This model is characterized by two parameters: the clustering exponent {alpha} and long-range connection rate {phi}. The results show that as {alpha} and {phi} vary there exists a continuous crossover in the fractal dimension Df from 1.65 to 2, which corresponds to the crossover from the DDA pattern to dense one. The change of the aggregation pattern results from the long-range connection in the network, which reduces the effect of screening during the aggregation. With primitive analysis, we obtain the expressions of the fractal dimension Df and the crossover point {alpha}c. These results may be useful to describe the vapor deposition, molecular-beam epitaxy, and similar experiments on defective substrates.
Kim, Sang-Yoon
2016-01-01
We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons. By varying the fraction of LR interneurons $p_{long}$, we investigate the effect of network architecture on emergence of sparsely synchronized rhythms, and make comparison with that in the Watts-Strogatz SWN. Although SR and LR interneurons have the same average in- and out-degrees, their betweenness centralities (characterizing the potentiality in controlling communication between other interneurons) are distinctly different. Hence, in view of the betweenness, SWNs we consider are inhomogeneous, unlike the "canonical" Watts-Strogatz SWN with nearly same betweenness centralities. As $p_{long}$ is increased, the average path length becomes shorter, and the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Eventually, when passing a critical value $p_{long}^{(c)}$ $(\\simeq 0.16)$, spars...
SIR model on a small-world network and the endemic state of an infectious disease
Dottori, Martin
2014-01-01
In this work we performed a numerical study of an epidemic model that mimics the endemic state of whooping cough in the pre-vaccine era. We considered a stochastic SIR model on two-dimensional Watts-Strogatz-type networks and analyzed the influence of the network properties on the characterization of the quasi-stationary state. We computed probability density functions (PDF) for infected fraction of individuals and found that they are well fitted by gamma functions, excepted the tails of the distributions that are q-exponentials. We also computed the fluctuation power spectra of infective time series for different networks. We found that network effects can be partially absorbed by rescaling the rate of infective contacts of the model. An explicit relation between the effective transmission rate of the disease and the correlation of susceptible individuals with their infective nearest neighbours was obtained. This relation quantifies the known screening of infective individuals observed in these networks. We ...
The small world of osteocytes: connectomics of the lacuno-canalicular network in bone
Kollmannsberger, Philip; Kerschnitzki, Michael; Repp, Felix; Wagermaier, Wolfgang; Weinkamer, Richard; Fratzl, Peter
2017-07-01
Osteocytes and their cell processes reside in a large, interconnected network of voids pervading the mineralized bone matrix of most vertebrates. This osteocyte lacuno-canalicular network (OLCN) is believed to play important roles in mechanosensing, mineral homeostasis, and for the mechanical properties of bone. While the extracellular matrix structure of bone is extensively studied on ultrastructural and macroscopic scales, there is a lack of quantitative knowledge on how the cellular network is organized. Using a recently introduced imaging and quantification approach, we analyze the OLCN in different bone types from mouse and sheep that exhibit different degrees of structural organization not only of the cell network but also of the fibrous matrix deposited by the cells. We define a number of robust, quantitative measures that are derived from the theory of complex networks. These measures enable us to gain insights into how efficient the network is organized with regard to intercellular transport and communication. Our analysis shows that the cell network in regularly organized, slow-growing bone tissue from sheep is less connected, but more efficiently organized compared to irregular and fast-growing bone tissue from mice. On the level of statistical topological properties (edges per node, edge length and degree distribution), both network types are indistinguishable, highlighting that despite pronounced differences at the tissue level, the topological architecture of the osteocyte canalicular network at the subcellular level may be independent of species and bone type. Our results suggest a universal mechanism underlying the self-organization of individual cells into a large, interconnected network during bone formation and mineralization.
Tian, Lixia; Wang, Jinhui; Yan, Chaogan; He, Yong
2011-01-01
We employed resting-state functional MRI (R-fMRI) to investigate hemisphere- and gender-related differences in the topological organization of human brain functional networks. Brain networks were first constructed by measuring inter-regional temporal correlations of R-fMRI data within each hemisphere in 86 young, healthy, right-handed adults (38 males and 48 females) followed by a graph-theory analysis. The hemispheric networks exhibit small-world attributes (high clustering and short paths) that are compatible with previous results in the whole-brain functional networks. Furthermore, we found that compared with females, males have a higher normalized clustering coefficient in the right hemispheric network but a lower clustering coefficient in the left hemispheric network, suggesting a gender-hemisphere interaction. Moreover, we observed significant hemisphere-related differences in the regional nodal characteristics in various brain regions, such as the frontal and occipital regions (leftward asymmetry) and the temporal regions (rightward asymmetry), findings that are consistent with previous studies of brain structural and functional asymmetries. Together, our results suggest that the topological organization of human brain functional networks is associated with gender and hemispheres, and they provide insights into the understanding of functional substrates underlying individual differences in behaviors and cognition.
Tse, A; Verkhivker, G M
2015-07-01
The human protein kinases play a fundamental regulatory role in orchestrating functional processes in complex cellular networks. Understanding how conformational equilibrium between functional kinase states can be modulated by ligand binding or mutations is critical for quantifying molecular basis of allosteric regulation and drug resistance. In this work, molecular dynamics simulations of the Abl kinase complexes with cancer drugs (Imatinib and Dasatinib) were combined with structure-based network modeling to characterize dynamics of the residue interaction networks in these systems. The results have demonstrated that structural architecture of kinase complexes can produce a small-world topology of the interaction networks. Our data have indicated that specific Imatinib binding to a small number of highly connected residues could lead to network-bridging effects and allow for efficient allosteric communication, which is mediated by a dominant pathway sensitive to the unphosphorylated Abl state. In contrast, Dasatinib binding to the active kinase form may activate a broader ensemble of allosteric pathways that are less dependent on the phosphorylation status of Abl and provide a better balance between the efficiency and resilience of signaling routes. Our results have unveiled how differences in the residue interaction networks and allosteric communications of the Abl kinase complexes can be directly related to drug resistance effects. This study offers a plausible perspective on how efficiency and robustness of the residue interaction networks and allosteric pathways in kinase structures may be associated with protein responses to drug binding.
A small world of citations? The influence of collaboration networks on citation practices.
Directory of Open Access Journals (Sweden)
Matthew L Wallace
Full Text Available This paper examines the proximity of authors to those they cite using degrees of separation in a co-author network, essentially using collaboration networks to expand on the notion of self-citations. While the proportion of direct self-citations (including co-authors of both citing and cited papers is relatively constant in time and across specialties in the natural sciences (10% of references and the social sciences (20%, the same cannot be said for citations to authors who are members of the co-author network. Differences between fields and trends over time lie not only in the degree of co-authorship which defines the large-scale topology of the collaboration network, but also in the referencing practices within a given discipline, computed by defining a propensity to cite at a given distance within the collaboration network. Overall, there is little tendency to cite those nearby in the collaboration network, excluding direct self-citations. These results are interpreted in terms of small-scale structure, field-specific citation practices, and the value of local co-author networks for the production of knowledge and for the accumulation of symbolic capital. Given the various levels of integration between co-authors, our findings shed light on the question of the availability of 'arm's length' expert reviewers of grant applications and manuscripts.
A small world of citations? The influence of collaboration networks on citation practices.
Wallace, Matthew L; Larivière, Vincent; Gingras, Yves
2012-01-01
This paper examines the proximity of authors to those they cite using degrees of separation in a co-author network, essentially using collaboration networks to expand on the notion of self-citations. While the proportion of direct self-citations (including co-authors of both citing and cited papers) is relatively constant in time and across specialties in the natural sciences (10% of references) and the social sciences (20%), the same cannot be said for citations to authors who are members of the co-author network. Differences between fields and trends over time lie not only in the degree of co-authorship which defines the large-scale topology of the collaboration network, but also in the referencing practices within a given discipline, computed by defining a propensity to cite at a given distance within the collaboration network. Overall, there is little tendency to cite those nearby in the collaboration network, excluding direct self-citations. These results are interpreted in terms of small-scale structure, field-specific citation practices, and the value of local co-author networks for the production of knowledge and for the accumulation of symbolic capital. Given the various levels of integration between co-authors, our findings shed light on the question of the availability of 'arm's length' expert reviewers of grant applications and manuscripts.
Beyond Scale-Free Small-World Networks: Cortical Columns for Quick Brains
Stoop, Ralph; Saase, Victor; Wagner, Clemens; Stoop, Britta; Stoop, Ruedi
2013-03-01
We study to what extent cortical columns with their particular wiring boost neural computation. Upon a vast survey of columnar networks performing various real-world cognitive tasks, we detect no signs of enhancement. It is on a mesoscopic—intercolumnar—scale that the existence of columns, largely irrespective of their inner organization, enhances the speed of information transfer and minimizes the total wiring length required to bind distributed columnar computations towards spatiotemporally coherent results. We suggest that brain efficiency may be related to a doubly fractal connectivity law, resulting in networks with efficiency properties beyond those by scale-free networks.
A small world of citations? The influence of collaboration networks on citation practices
Wallace, Matthew L; Gingras, Yves
2011-01-01
This paper examines the proximity of authors to those they cite using degrees of separation in a co-author network, essentially using collaboration networks to expand on the notion of self-citations. While the proportion of direct self-citations (including co-authors of both citing and cited papers) is relatively constant in time and across specialties in the natural sciences (10% of citations) and the social sciences (20%), the same cannot be said for citations to authors who are members of the co-author network. Differences between fields and trends over time lie not only in the degree of co-authorship which defines the large-scale topology of the collaboration network, but also in the referencing practices within a given discipline, computed by defining a propensity to cite at a given distance within the collaboration network. Overall, there is little tendency to cite those nearby in the collaboration network, excluding direct self-citations. By analyzing these social references, we characterize the social...
Epidemic dynamics on complex networks
Institute of Scientific and Technical Information of China (English)
ZHOU Tao; FU Zhongqian; WANG Binghong
2006-01-01
Recently, motivated by the pioneer work in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. One of the ultimate goals is to understand how the topological structures affect the dynamics upon networks. In this paper, we give a brief review on the studies of epidemic dynamics on complex networks, including the description of classical epidemic models, the epidemic spread on small-world and scale-free networks, and network immunization. Finally, perspectives and some interesting problems are proposed.
CHC: A Robust P2P Overlay Network with Simple Routing and Small-World Features
Directory of Open Access Journals (Sweden)
Wenjun Xiao
2011-08-01
Full Text Available Almost all recent researches on P2P systems focus on howto build a highly usable P2P overlay network. Researchersinclude small routing table, short query path and goodrobustness into their design objectives of overlay topology. Inthis paper, we present a general group theory method anddefine a new Cayley graph. Based on this Cayley graph, wepropose a novel P2P overlay network called CHC, which hassimple routing (searching scheme and many other excellentproperties such as short query path, high clustering and goodrobustness because of its symmetry. The performance isevaluated by simulation to show that CHC possesses shorterquery path length and higher clustering and better robustnessthan several popular P2P overlay networks such as Chord andUlysses.
Energy Technology Data Exchange (ETDEWEB)
Ozer, Mahmut [Zonguldak Karaelmas University, Engineering Faculty, Department of Electrical and Electronics Engineering, 67100 Zonguldak (Turkey); Laboratory of Neurophysics and Physiology, UMR 8119 CNRS, Universite Paris Descartes, 45 rue des Saint-Peres, 75006 Paris (France)], E-mail: mahmutozer2002@yahoo.com; Uzuntarla, Muhammet [Zonguldak Karaelmas University, Engineering Faculty, Department of Electrical and Electronics Engineering, 67100 Zonguldak (Turkey); Kayikcioglu, Temel [Karadeniz Technical University, Department of Electrical and Electronics Engineering, Trabzon (Turkey); Graham, Lyle J. [Laboratory of Neurophysics and Physiology, UMR 8119 CNRS, Universite Paris Descartes, 45 rue des Saint-Peres, 75006 Paris (France)
2008-10-20
We study the collective temporal coherence of a small-world network of coupled stochastic Hodgkin-Huxley neurons. Previous reports have shown that network coherence in response to a subthreshold periodic stimulus, thus subthreshold signal encoding, is maximal for a specific range of the fraction of randomly added shortcuts relative to all possible shortcuts, p, added to an initially locally connected network. We investigated this behavior further as a function of channel noise, stimulus frequency and coupling strength. We show that temporal coherence peaks when the frequency of the external stimulus matches that of the intrinsic subthreshold oscillations. We also find that large values of the channel noise, corresponding to small cell sizes, increases coherence for optimal values of the stimulus frequency and the topology parameter p. For smaller values of the channel noise, thus larger cell sizes, network coherence becomes insensitive to these parameters. Finally, the degree of coupling between neurons in the network modulates the sensitivity of coherence to topology, such that for stronger coupling the peak coherence is achieved with fewer added short cuts.
Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji
2012-09-01
We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.
Evolutionary Games on Weighted Newman-Watts Small-World Networks
Institute of Scientific and Technical Information of China (English)
DU Wen-Bo; CAO Xian-Bin; ZHAO Lin; ZHOU Hong
2009-01-01
We investigate the evolutionary prisoner's dilemma game (PDG) on weighted Newman-Watts (NW) networks. In weighted NW networks, the link weight wij is assigned to the link between the nodes i and j as: wij = (ki · kj)β,where ki(kj) is the degree of node i(j) and β represents the strength of the correlations. Obviously, the link weight can be tuned by only one parameter β. We focus on the cooperative behavior and wealth distribution in the system. Simulation results show that the cooperator frequency is promoted by a large range of β and there is a minimal cooperation frequency around β = - 1. Moreover, we also employ the Gini coefficient to study the wealth distribution in the population. Numerical results show that the Gini coefficient reaches its minimum when β≈ -1. Our work may be helpful in understanding the emergence of cooperation and unequal wealth distribution in society.
Small-World Effect of Complex Network and Its Application to Protein Folding%复杂网络的小世界影响及其在蛋白质折叠中的运用
Institute of Scientific and Technical Information of China (English)
卢全国; 陈定方; 彭华魁; 祖巧红
2004-01-01
The famous "six letters" experiment carried out by Milgram demonstrated the existence of small-world effect in a complex network. One vertex tends to be connected to another by a shortest path through network because of the small-world effect. This paper uses the small-world effect to study protein folding pathway.
Directory of Open Access Journals (Sweden)
Bo Liu
Full Text Available BACKGROUND: Acupuncture in humans can produce clinical effects via the central nervous system. However, the neural substrates of acupuncture's effects remain largely unknown. RESULTS: We utilized functional MRI to investigate the topological efficiency of brain functional networks in eighteen healthy young adults who were scanned before and after acupuncture at the ST36 acupoints (ACUP and its sham point (SHAM. Whole-brain functional networks were constructed by thresholding temporal correlations matrices of ninety brain regions, followed by a graph theory-based analysis. We showed that brain functional networks exhibited small-world attributes (high local and global efficiency regardless of the order of acupuncture and stimulus points, a finding compatible with previous studies of brain functional networks. Furthermore, the brain networks had increased local efficiency after ACUP stimulation but there were no significant differences after SHAM, indicating a specificity of acupuncture point in coordinating local information flow over the whole brain. Moreover, significant (P<0.05, corrected by false discovery rate approach effects of only acupuncture point were detected on nodal degree of the left hippocampus (higher nodal degree at ACUP as compared to SHAM. Using an uncorrected P<0.05, point-related effects were also observed in the anterior cingulate cortex, frontal and occipital regions while stimulation-related effects in various brain regions of frontal, parietal and occipital cortex regions. In addition, we found that several limbic and subcortical brain regions exhibited point- and stimulation-related alterations in their regional homogeneity (P<0.05, uncorrected. CONCLUSIONS: Our results suggest that acupuncture modulates topological organization of whole-brain functional brain networks and the modulation has point specificity. These findings provide new insights into neuronal mechanism of acupuncture from the perspective of functional
Rock-scissors-paper game on regular small-world networks
Energy Technology Data Exchange (ETDEWEB)
Szabo, Gyoergy [Research Institute for Technical Physics and Materials Science, PO Box 49, H-1525 Budapest (Hungary); Szolnoki, Attila [Research Institute for Technical Physics and Materials Science, PO Box 49, H-1525 Budapest (Hungary); Izsak, Rudolf [Institute for Theoretical Physics, Eoetvoes University, PO Box 32, H-1518 Budapest (Hungary)
2004-02-20
The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.
Qian, Yu
2014-01-01
The synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs) induced by time delay and long-range connection (LRC) probability have been investigated by synchronization parameter and space-time plots. Four distinct parameter regions, that is, asynchronous region, transition region, synchronous region, and oscillatory region have been discovered at certain LRC probability as time delay is increased. Interestingly, desynchronization is observed in oscillatory region. More importantly, we consider the spatiotemporal patterns obtained in delayed Newman-Watts SWNNs are the competition results between long-range drivings (LRDs) and neighboring interactions. In addition, for moderate time delay, the synchronization of neuronal network can be enhanced remarkably by increasing LRC probability. Furthermore, lag synchronization has been found between weak synchronization and complete synchronization as LRC probability is a little less than 1.0. Finally, the two necessary conditions, moderate time delay and large numbers of LRCs, are exposed explicitly for synchronization in delayed Newman-Watts SWNNs. PMID:24810595
Qian, Yu
2014-01-01
The synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs) induced by time delay τ and long-range connection (LRC) probability P have been investigated by synchronization parameter and space-time plots. Four distinct parameter regions, that is, asynchronous region, transition region, synchronous region, and oscillatory region have been discovered at certain LRC probability P = 1.0 as time delay is increased. Interestingly, desynchronization is observed in oscillatory region. More importantly, we consider the spatiotemporal patterns obtained in delayed Newman-Watts SWNNs are the competition results between long-range drivings (LRDs) and neighboring interactions. In addition, for moderate time delay, the synchronization of neuronal network can be enhanced remarkably by increasing LRC probability. Furthermore, lag synchronization has been found between weak synchronization and complete synchronization as LRC probability P is a little less than 1.0. Finally, the two necessary conditions, moderate time delay and large numbers of LRCs, are exposed explicitly for synchronization in delayed Newman-Watts SWNNs.
Li, Ting; Hong, Jun; Zhang, Jinhua; Guo, Feng
2014-03-15
The improvement of the resolution of brain signal and the ability to control external device has been the most important goal in BMI research field. This paper describes a non-invasive brain-actuated manipulator experiment, which defined a paradigm for the motion control of a serial manipulator based on motor imagery and shared control. The techniques of component selection, spatial filtering and classification of motor imagery were involved. Small-world neural network (SWNN) was used to classify five brain states. To verify the effectiveness of the proposed classifier, we replace the SWNN classifier by a radial basis function (RBF) networks neural network, a standard multi-layered feed-forward backpropagation network (SMN) and a multi-SVM classifier, with the same features for the classification. The results also indicate that the proposed classifier achieves a 3.83% improvement over the best results of other classifiers. We proposed a shared control method consisting of two control patterns to expand the control of BMI from the software angle. The job of path building for reaching the 'end' point was designated as an assessment task. We recorded all paths contributed by subjects and picked up relevant parameters as evaluation coefficients. With the assistance of two control patterns and series of machine learning algorithms, the proposed BMI originally achieved the motion control of a manipulator in the whole workspace. According to experimental results, we confirmed the feasibility of the proposed BMI method for 3D motion control of a manipulator using EEG during motor imagery. Copyright © 2013 Elsevier B.V. All rights reserved.
具有高对称性的小世界网络模型研究%Research on Small World Network Model with High Symmetry
Institute of Scientific and Technical Information of China (English)
张付仁; 刘浩
2011-01-01
Based on research of small-world network and Cayley graph, it adopts the algebra and graph theory method of Cayley graph, a model of small-world network with high symmetry is proposed. Some properties of small-world such as clustering coefficient and characteristic path length are analyzed. A routing algorithm is developed. Results of analysis and simulation testify this model provides high local clustering and low network diameter, possesses the property of small-world.%在研究小世界网络和Cayley图的基础上,采用基于Cayley图的代数图论方法,给出一种具有高对称性的小世界网络模型,分析该模型的聚类系数和特征路径长度等小世界性质,给出其路由算法.分析结果表明,该模型聚类性高、网络直径小,具有小世界特性.
极小Cayley图的确定性小世界网络模型%Deterministic small-world network model based on minimal Cayley graph
Institute of Scientific and Technical Information of China (English)
刘艳霞; 奚建清; 张芩
2014-01-01
小世界网络的确定性模型研究是复杂网络建模领域的重要分支，通过分析Cayley图的极小性与小世界特性的关联，提出一种基于极小Cayley图构造小世界网络的确定性模型。模型通过选择满足条件的极小Cayley图，恰当地扩展其生成集，构造出一类对称性强且结构规则的小世界网络。结果表明，和现有模型不同，该模型可根据需求构造常数度或非常数度网络，且生成网络不仅具有较高的聚集系数和低的网络直径，而且是节点对称的，在通信网络、结构化P2P 覆盖网络等实际领域的拓扑结构设计中具有重要应用。%The research on deterministic small-world network model is an important branch of complex network modeling. This paper analyzes the small-world property of the minimal Cayley graph and proposes a deterministic small-world network model based on minimal Cayley graph. The model constructs a class of small-world networks with high symmetry by selecting a minimal Cayley graph, and appropriately expands its generating set. Compared with the existing models, this model can be used flexibly to get small-world networks with const degree or variable degree, which is adaptable for the disign and analysis of the real networks such as communication network and P2P overlay network.
Institute of Scientific and Technical Information of China (English)
ZHANG Gui-Qing; ZHANG Ying-Yue; CHEN Tian-Lun
2007-01-01
Effects of aging and self-organized criticality in a pulse-coupled integrate-and-fire neuron model based on small world networks have been studied. We give the degree distribution of aging network, average shortest path length,the diameter of our network, and the clustering coefficient, and find that our neuron model displays the power-law behavior, and with the number of added links increasing, the effects of aging become smaller and smaller. This shows that if the brain works at the self-organized criticality state, it can relieve some effects caused by aging.
Trust Propagation in Small Worlds
DEFF Research Database (Denmark)
Gray, Elizabeth; Seigneur, Jean-Marc; Chen, Yong
2003-01-01
The possibility of a massive, networked infrastructure of diverse entities partaking in collaborative applications with each other increases more and more with the proliferation of mobile devices and the development of ad hoc networking technologies. In this context, traditional security measures...... do not scale well. We aim to develop trust-based security mechanisms using small world concepts to optimise formation and propagation of trust amongst entities in these vast networks. In this regard, we surmise that in a very large mobile ad hoc network, trust, risk, and recommendations can...
Anderson, Ariana; Cohen, Mark S
2013-01-01
Functional network connectivity (FNC) is a method of analyzing the temporal relationship of anatomical brain components, comparing the synchronicity between patient groups or conditions. We use functional-connectivity measures between independent components to classify between Schizophrenia patients and healthy controls during resting-state. Connectivity is measured using a variety of graph-theoretic connectivity measures such as graph density, average path length, and small-worldness. The Schizophrenia patients showed significantly less clustering (transitivity) among components than healthy controls (p COBRE dataset of 146 Schizophrenia patients and healthy controls, provided as part of the 1000 Functional Connectomes Project. We demonstrate preprocessing, using independent component analysis (ICA) to nominate networks, computing graph-theoretic connectivity measures, and finally using these connectivity measures to either classify between patient groups or assess between-group differences using formal hypothesis testing. All necessary code is provided for both running command-line FSL preprocessing, and for computing all statistical measures and SVM classification within R. Collectively, this work presents not just findings of diminished FNC among resting-state networks in Schizophrenia, but also a practical connectivity tutorial.
Information Diffusion in Small-world Social Networks%小世界社会网络中的信息传播
Institute of Scientific and Technical Information of China (English)
唐泳; 马永开
2006-01-01
Small-world social network model is one of the best ways to describe the real social system. An information diffusion model was proposed in small-world social networks. In the model, every social participant has a continuous parameter to represents his attitude to the information, and the attitude can be positive or negative and cause positive and negative feedbacks respectively. Concepts of local information and global information were introduced to describe the information acquiring ability of a social participant. Computational experiments of the information diffusion model were also carried in the small-world social networks with different randomness and scales. The simulation results show that the topological structure of the network, the feedbacks caused by the attitudes of the participants and the weight of the global information have great influence on the process that networks evolve into a uniform situation in which all participants hold a same attitude.%小世界社会网络模型是一种描述现实社会系统的理想模型,基于此模型,提出小世界社会网络中的信息传播模型.模型中,每个社会参与者都具有一个连续型参数来描述其对于信息的态度,正的态度对信息传播有正反馈作用,而负的态度对于信息传播有负反馈作用.同时,引入局部信息和全局信息概念用以描速社会参与者对于信息的获取能力.信息传播模型在不同随机度和规模的小世界社会网络上进行了计算仿真.仿真结果表明网络的拓扑结构和参与者态度的正负反馈作用以及对于全局信息的权重对于信息的传播均衡结果有显著的影响.
Cluster-size entropy in the Axelrod model of social influence: small-world networks and mass media.
Gandica, Y; Charmell, A; Villegas-Febres, J; Bonalde, I
2011-10-01
We study the Axelrod's cultural adaptation model using the concept of cluster-size entropy S(c), which gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is given by the maximum of the S(c)(q) distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first or second order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait q(c) and the number F of cultural features in two-dimensional regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a partially ordered phase whose largest cultural cluster is not aligned with the external field, in contrast with a recent suggestion that this type of phase cannot be formed in regular networks. We draw a q-B phase diagram for the Axelrod model in regular networks.
具有小世界特性的语义覆盖网络模型%Semantic Overlay Network Model with Small-world Features
Institute of Scientific and Technical Information of China (English)
刘浩; 贺文华
2012-01-01
The topology structure of P2P overlay network decides its system performance. However, the existing P2P overlay network models do not take clustering and symmetry of nodes into account, and support only precise resource locating scheme. A Semantic Overlay Network(SON) model with small-world features is proposed in the paper. It adopts the mechanism of distinctly grouping, semantic search edge and Group Flooding(GF). Results of analysis and experiment show that this model provides better network performance and higher search efficiency than the existing overlay network models such as Chord and CAN. Furthermore, it has the querying capability of multi-matching results.%目前大多数的结构化覆盖网络模型忽略节点的聚类性和对称性,并且只能提供精确的资源查询机制.为此,给出一种具有小世界特性的语义覆盖网络模型.该模型采用显式分区机制、语义搜索链和组扩散机制.分析和实验结果表明,该模型比现有的覆盖网络模型Chord和CAN具有更好的网络性能,搜索效率更高,且具有较好的多匹配结果查询能力.
Directory of Open Access Journals (Sweden)
Marcel eAusloos
2015-06-01
Full Text Available Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP, on one hand, and the Darwinian Evolution Defenders (DED, on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter- and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues; the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed network to its counterpart, the time aggregated (undirected network, - which has real eigenvalues. In order to do so, small world networks which both contain an $odd$ number of nodes are studied and compared to similar networks with an even number of nodes. It is found that (i the diffusion of knowledge is more difficult on the largest networks; (ii the network size influences the slowing-down or speeding-up diffusion process. Interestingly, it is observed that (iii the diffusion of knowledge is slower in IDP and faster in DED communities. It is suggested that the finding can be rationalized, if some scientific quality and publication habit is attributed to the agents, as common sense would guess. This finding offers some opening discussion toward tying scientific knowledge to belief.
Ausloos, Marcel
2015-06-01
Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter- and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues; the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) network, - which has real eigenvalues. In order to do so, small world networks which both contain an odd number of nodes are studied and compared to similar networks with an even number of nodes. It is found that (i) the diffusion of knowledge is more difficult on the largest networks; (ii) the network size influences the slowing-down or speeding-up diffusion process. Interestingly, it is observed that (iii) the diffusion of knowledge is slower in IDP and faster in DED communities. It is suggested that the finding can be "rationalized", if some "scientific quality" and "publication habit" is attributed to the agents, as common sense would guess. This finding offers some opening discussion toward tying scientific knowledge to belief.
Cluster size entropy in the Axelrod model of social influence: small-world networks and mass media
Gandica, Yérali; Villegas-Febres, J; Bonalde, I
2011-01-01
We study the Axelrod's cultural adaptation model using the concept of cluster size entropy, $S_{c}$ that gives information on the variability of the cultural cluster size present in the system. Using networks of different topologies, from regular to random, we find that the critical point of the well-known nonequilibrium monocultural-multicultural (order-disorder) transition of the Axelrod model is unambiguously given by the maximum of the $S_{c}(q)$ distributions. The width of the cluster entropy distributions can be used to qualitatively determine whether the transition is first- or second-order. By scaling the cluster entropy distributions we were able to obtain a relationship between the critical cultural trait $q_c$ and the number $F$ of cultural features in regular networks. We also analyze the effect of the mass media (external field) on social systems within the Axelrod model in a square network. We find a new partially ordered phase whose largest cultural cluster is not aligned with the external fiel...
阿尔茨海默病患者的大脑功能网络小世界性%Small-worldness of functional networks in Alzheimer's disease
Institute of Scientific and Technical Information of China (English)
赵小虎; 王湘彬; 席芊; 江虹; 郭起浩; 刘勇; 王培军
2012-01-01
目的 利用静息态血氧水平依赖功能磁共振(BOLD-fMRI)数据,构建大脑功能网络,探讨阿尔茨海默病(AD)患者脑功能网络的小世界属性是否改变.方法 收集2009年1月至2010年6月复旦大学上海医学院附属华山医院神经内科门诊33例AD患者和20名健康老年志愿者参加试验.受试者行简易智能状态检查( MMSE)和Mattis痴呆评定量表(DRS)测试,评估其认知水平.采集静息态BOLD-fMRI数据,计算90个区域之间的相关系数,构建N×N(N =90)的相关性Z值矩阵.检验AD患者和正常老年人大脑网络的小世界属性,通过双样本t检验探索AD患者相关参数变化.结果 行为学结果:AD组和正常对照组MMSE平均分值分别为20.6±2.3、28.2±1.8.AD组和正常对照组DRS平均分值分别为96 ±11、123±14.两组差异均有统计学意义(均P＜0.01).在0.1≤Sparsity≤0.4范围内,AD组和正常对照组均符合小世界属性.但AD患者的聚类系数和平均路径长度在所有阈值点均显著大于正常对照组(P＜0.05).结论 AD患者的大脑功能网络仍具有小世界属性,但聚类系数和平均路径长度均高于正常人,提示AD患者脑功能网络信息传递能力和脑区之间信息整合能力受损,该发现对从网络角度研究AD病理机制具有重要意义.%Objective To construct the functional networks of human brains by resting-state functional magnetic resonance imaging (fMRI) and examine whether or not the small-world property of functional brain networks changes in patients with Alzheimer disease (AD).Methods A total of 33 AD patients and 20 healthy old volunteers were recruited.Their cognitive functions were evaluated by the minimental state examination (MMSE) and Mattis dementia rating scale (DRS).The resting-state BOLD-fMRI data were acquired and preprocessed. Then the correlation coefficient of every pair of 90 regions was calculated and correlation matrix Z ( N × N,N =90) generated by Fisher Z
Li, Meiling; Wang, Junping; Liu, Feng; Chen, Heng; Lu, Fengmei; Wu, Guorong; Yu, Chunshui; Chen, Huafu
2015-05-01
The human brain has been described as a complex network, which integrates information with high efficiency. However, the relationships between the efficiency of human brain functional networks and handedness and brain size remain unclear. Twenty-one left-handed and 32 right-handed healthy subjects underwent a resting-state functional magnetic resonance imaging scan. The whole brain functional networks were constructed by thresholding Pearson correlation matrices of 90 cortical and subcortical regions. Graph theory-based methods were employed to further analyze their topological properties. As expected, all participants demonstrated small-world topology, suggesting a highly efficient topological structure. Furthermore, we found that smaller brains showed higher local efficiency, whereas larger brains showed higher global efficiency, reflecting a suitable efficiency balance between local specialization and global integration of brain functional activity. Compared with right-handers, significant alterations in nodal efficiency were revealed in left-handers, involving the anterior and median cingulate gyrus, middle temporal gyrus, angular gyrus, and amygdala. Our findings indicated that the functional network organization in the human brain was associated with handedness and brain size.
Analysis of Small-World Model to a Tendentious Ring Network%带有倾向性的环状网络Small-World现象的分析
Institute of Scientific and Technical Information of China (English)
张帆
2011-01-01
一个环状网络可以由马尔科夫链来描述,并且通过求解该马尔科夫链的平均首达时间等指标来描述该网络的特点.一个带有倾向性的环状网络,其上马尔科夫链的平均首达时问解可以被精确求出.带有倾向性的环状网络上的Small-world现象与对称环状网络也有一定的差异.%A ring network can be modeled by a Markov chain and its characteristics can be described by several indicators such as the mean first passage times of the Markov chain. The exact results for a tendentions ring network Markov chain model is provided and the difference of Small-World phenomenon between tendentious ring network and a symmetric one is given.
Structurally Dynamic Spin Market Networks
Horváth, Denis; Kuscsik, Zoltán
The agent-based model of stock price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. The inherent structure of node agent "brain" is modeled by a recursive neural network with local and global inputs and feedback connections. For specific parametric combination the complex network displays small-world phenomenon combined with scale-free behavior. The identification of a local leader (network hub, agent whose strategies are frequently adapted by its neighbors) is carried out by repeated random walk process through network. The simulations show empirically relevant dynamics of price returns and volatility clustering. The additional emerging aspects of stylized market statistics are Zipfian distributions of fitness.
Yao, Yuangen; Deng, Haiyou; Ma, Chengzhang; Yi, Ming; Ma, Jun
2017-01-01
Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed.
Yao, Yuangen; Deng, Haiyou; Ma, Chengzhang; Yi, Ming
2017-01-01
Spiral waves are observed in the chemical, physical and biological systems, and the emergence of spiral waves in cardiac tissue is linked to some diseases such as heart ventricular fibrillation and epilepsy; thus it has importance in theoretical studies and potential medical applications. Noise is inevitable in neuronal systems and can change the electrical activities of neuron in different ways. Many previous theoretical studies about the impacts of noise on spiral waves focus an unbounded Gaussian noise and even colored noise. In this paper, the impacts of bounded noise and rewiring of network on the formation and instability of spiral waves are discussed in small-world (SW) network of Hodgkin-Huxley (HH) neurons through numerical simulations, and possible statistical analysis will be carried out. Firstly, we present SW network of HH neurons subjected to bounded noise. Then, it is numerically demonstrated that bounded noise with proper intensity σ, amplitude A, or frequency f can facilitate the formation of spiral waves when rewiring probability p is below certain thresholds. In other words, bounded noise-induced resonant behavior can occur in the SW network of neurons. In addition, rewiring probability p always impairs spiral waves, while spiral waves are confirmed to be robust for small p, thus shortcut-induced phase transition of spiral wave with the increase of p is induced. Furthermore, statistical factors of synchronization are calculated to discern the phase transition of spatial pattern, and it is confirmed that larger factor of synchronization is approached with increasing of rewiring probability p, and the stability of spiral wave is destroyed. PMID:28129401
静息态人脑功能网络的小世界特性%Small-World Properties of Resting State Human Brain Functional Networks
Institute of Scientific and Technical Information of China (English)
黄文涛; 冯又层
2011-01-01
研究了静息态下健康人脑的功能连接模式有助于理解人脑在正常或疾病状态下的功能活动规律.利用小波变换从健康志愿者静息态的功能磁共振成像中提取时间序列,计算90个脑区的相关性,设定阈值建立脑功能网络的无向简单图,然后计算特征路径长度和聚类系数,并对度分布进行拟合.结果显示：脑功能网络具有规则网络的大聚集系数又具有随机网络的小特征路径长度,度的拟合显示具有指数截断幂律分布,即脑功能网络具有小世界特性.%It is important to study the resting state functional pattern of healthy human brain because it will aid us to understand the law of functional activities of human brain in normal or disease states.Using wavelet transformation,time series of 90 brain regions were extracted from functional magnetic resonance imagines of resting state healthy volunteers.Functional correlations between brain regions were calculated,and the threshold was set to establish the simple undirected graph,then characteristic path length and clustering coefficient were computed,finally the degree distribution was fitted.The results demonstrated that the brain functional networks had both big clustering coefficients like regular networks and small characteristic path lengths similar as random networks,degree distribution met exponentially truncated power-law distribution.Taken together,the human brain functional networks have small world properties.
A small world model for the spread of HIV infection
Directory of Open Access Journals (Sweden)
Israel T. Vieira
2011-08-01
Full Text Available It has long been recognised that the structure of social networks plays an important role in the dynamics of disease propagation. The spread of HIV usually results from a complex network of social interactions and other factors related to culture, sexual behaviour, demography, geography and disease characteristics, as well as the availability, accessibility and delivery of healthcare. The small world phenomenon has been used for representing social network interactions. It states that, given some random connections, the degrees of separation between any two individuals within a population can be very small. In this paper we present a discrete event simulation model which uses a variant of the small world network model to represent social interactions and the sexual transmission of HIV within a population. We use the model to demonstrate the importance of the choice of topology and initial distribution of infection, and capture the direct and non-linear relationship between the probability of a casual partnership (small world randomness parameter and the spread of HIV.
Is the Semantic Web a Small World?
Bachlechner , Daniel; Strang, Thomas
2007-01-01
In this paper, we describe a comprehensive analysis of graph-theoretical properties of online social networks based on the Friend-of-a-Friend (FOAF) ontology. Of particular interest for this work were properties related to the small-world phenomenon. More than 1.6 million of the FOAF documents collected on the Semantic Web met our requirements and were analyzed in depth. Most FOAF documents are created and published by social networking services, blog hosting services, or combinations of the ...
Structurally dynamic spin market networks
Horváth, D
2007-01-01
The agent-based model of price dynamics on a directed evolving complex network is suggested and studied by direct simulation. The resulting stationary regime is maintained as a result of the balance between the extremal dynamics, adaptivity of strategic variables and reconnection rules. For some properly selected parametric combination the network displays small-world phenomenon with high mean clustering coefficient and power-law node degree distribution. The mechanism of repeated random walk through network combined with a fitness recognition is proposed and tested to generate modular multi-leader market. The simulations suggest that dynamics of fitness is the slowest process that manifests itself in the volatility clustering of the log-price returns.
基于小世界网络的大学生社交网络模型研究%Research of College Students' social network model of small-world networks
Institute of Scientific and Technical Information of China (English)
林晓
2015-01-01
随着大学生社交网络使用的日趋频繁，有关大学生社交网络应用的研究也日益增多，本文采用在复杂网络研究中运用广泛的小世界网络理论，通过分析大学生社交网络的静态网络统计量，提出一种构造简单的大学生社交网络模型，并对其小世界特性进行了验证。%With the development of College Students' social network,the research on College Students' social network applications are increasing,Based on the deep research of WS and NW small-world network,put forward a new kind of simple structure social network model,through the analysis of the static network statistics, verify its small world properties.
The small-world effect is a modern phenomenon
Marvel, Seth A; Doering, Charles R; Lusseau, David; Newman, M E J
2013-01-01
The "small-world effect" is the observation that one can find a short chain of acquaintances, often of no more than a handful of individuals, connecting almost any two people on the planet. It is often expressed in the language of networks, where it is equivalent to the statement that most pairs of individuals are connected by a short path through the acquaintance network. Although the small-world effect is well-established empirically for contemporary social networks, we argue here that it is a relatively recent phenomenon, arising only in the last few hundred years: for most of mankind's tenure on Earth the social world was large, with most pairs of individuals connected by relatively long chains of acquaintances, if at all. Our conclusions are based on observations about the spread of diseases, which travel over contact networks between individuals and whose dynamics can give us clues to the structure of those networks even when direct network measurements are not available. As an example we consider the s...
Complex networks: Dynamics and security
Indian Academy of Sciences (India)
Ying-Cheng Lai; Adilson Motter; Takashi Nishikawa; Kwangho Park; Liang Zhao
2005-04-01
This paper presents a perspective in the study of complex networks by focusing on how dynamics may affect network security under attacks. In particular, we review two related problems: attack-induced cascading breakdown and range-based attacks on links. A cascade in a network means the failure of a substantial fraction of the entire network in a cascading manner, which can be induced by the failure of or attacks on only a few nodes. These have been reported for the internet and for the power grid (e.g., the August 10, 1996 failure of the western United States power grid). We study a mechanism for cascades in complex networks by constructing a model incorporating the flows of information and physical quantities in the network. Using this model we can also show that the cascading phenomenon can be understood as a phase transition in terms of the key parameter characterizing the node capacity. For a parameter value below the phase-transition point, cascading failures can cause the network to disintegrate almost entirely. We will show how to obtain a theoretical estimate for the phase-transition point. The second problem is motivated by the fact that most existing works on the security of complex networks consider attacks on nodes rather than on links. We address attacks on links. Our investigation leads to the finding that many scale-free networks are more sensitive to attacks on short-range than on long-range links. Considering that the small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance, our result, besides its importance concerning network efficiency and security, has the striking implication that the small-world property of scale-free networks is mainly due to short-range links.
Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes
Institute of Scientific and Technical Information of China (English)
LI Yong; FANG Jin-Qing; LIU Qiang; LIANG Yong
2006-01-01
Based on the model of the same degree of all nodes we proposed before, a new algorithm, the so-called"spread all over vertices" (SAV) algorithm, is proposed for generating small-world properties from a regular ring lattices.During randomly rewiring connections the SAV is used to keep the unchanged number of links. Comparing the SAV algorithm with the Watts-Strogatz model and the "spread all over boundaries" algorithm, three methods can have the same topological properties of the small world networks. These results offer diverse formation of small world networks.It is helpful to the research of some applications for dynamics of mutual oscillator inside nodes and interacting automata associated with networks.
Institute of Scientific and Technical Information of China (English)
LIN Min; CHEN Tian-Lun
2005-01-01
A lattice model for a set of pulse-coupled integrate-and-fire neurons with small world structure is introduced.We find that our model displays the power-law behavior accompanied with the large-scale synchronized activities among the units. And the different connectivity topologies lead to different behaviors in models of integrate-and-fire neurons.
A dynamic network model for interbank market
Xu, Tao; He, Jianmin; Li, Shouwei
2016-12-01
In this paper, a dynamic network model based on agent behavior is introduced to explain the formation mechanism of interbank market network. We investigate the impact of credit lending preference on interbank market network topology, the evolution of interbank market network and stability of interbank market. Experimental results demonstrate that interbank market network is a small-world network and cumulative degree follows the power-law distribution. We find that the interbank network structure keeps dynamic stability in the network evolution process. With the increase of bank credit lending preference, network clustering coefficient increases and average shortest path length decreases monotonously, which improves the stability of the network structure. External shocks are main threats for the interbank market and the reduction of bank external investment yield rate and deposits fluctuations contribute to improve the resilience of the banking system.
Economics: An Emerging Small World?
S. Goyal (Sanjeev); M.J. van der Leij (Marco); J.L. Moraga-Gonzalez (José Luis)
2004-01-01
textabstractThis paper examines the small world hypothesis. The first part of the paper presents empirical evidence on the evolution of a particular world: the world of journal publishing economists during the period 1970-2000. We find that in the 1970's the world of economics was a collection of is
Dynamic Network Analysis for Robust Uncertainty Management
2010-03-01
kpc , kgc are controller gains and A" is a constant skew symmetric matrix. Please see [11] for more details on the potential and gyroscropic...distilled from the study of statistical physics such as the small-world and the scale-free network (10,11), begin to see their application in gene ...dynamics of the nuclear factor NFKB, which regulates various genes important for pathogen or cytokine inflammation, immune re- 4 170 B.6. UNFOLDING
Small-World Characteristics of Cortical Connectivity Changes in Acute Stroke.
Caliandro, Pietro; Vecchio, Fabrizio; Miraglia, Francesca; Reale, Giuseppe; Della Marca, Giacomo; La Torre, Giuseppe; Lacidogna, Giordano; Iacovelli, Chiara; Padua, Luca; Bramanti, Placido; Rossini, Paolo Maria
2017-01-01
Background After cerebral ischemia, disruption and subsequent reorganization of functional connections occur both locally and remote to the lesion. Recently, complexity of brain connectivity has been described using graph theory, a mathematical approach that depicts important properties of complex systems by quantifying topologies of network representations. Functional and dynamic changes of brain connectivity can be reliably analyzed via electroencephalography (EEG) recordings even when they are not yet reflected in structural changes of connections. Objective We tested whether and how ischemic stroke in the acute stage may determine changes in small-worldness of cortical networks as measured by cortical sources of EEG. Methods Graph characteristics of EEG of 30 consecutive stroke patients in acute stage (no more than 5 days after the event) were examined. Connectivity analysis was performed using eLORETA in both hemispheres. Results Network rearrangements were mainly detected in delta, theta, and alpha bands when patients were compared with healthy subjects. In delta and alpha bands similar findings were observed in both hemispheres regardless of the side of ischemic lesion: bilaterally decreased small-worldness in the delta band and bilaterally increased small-worldness in the alpha2 band. In the theta band, bilaterally decreased small-worldness was observed only in patients with stroke in the left hemisphere. Conclusions After an acute stroke, brain cortex rearranges its network connections diffusely, in a frequency-dependent modality probably in order to face the new anatomical and functional frame.
Unifying evolutionary and network dynamics
Swarup, Samarth; Gasser, Les
2007-06-01
Many important real-world networks manifest small-world properties such as scale-free degree distributions, small diameters, and clustering. The most common model of growth for these networks is preferential attachment, where nodes acquire new links with probability proportional to the number of links they already have. We show that preferential attachment is a special case of the process of molecular evolution. We present a single-parameter model of network growth that unifies varieties of preferential attachment with the quasispecies equation (which models molecular evolution), and also with the Erdős-Rényi random graph model. We suggest some properties of evolutionary models that might be applied to the study of networks. We also derive the form of the degree distribution resulting from our algorithm, and we show through simulations that the process also models aspects of network growth. The unification allows mathematical machinery developed for evolutionary dynamics to be applied in the study of network dynamics, and vice versa.
Institute of Scientific and Technical Information of China (English)
张瑞成; 李冲
2011-01-01
关于优化神经网络模型的快速性和精度,为了寻找最优的神经网络结构,在复杂网络的研究方法对多层前向神经网络模型的基础上,提出一种在层次结构上处于规则型到随机型神经网络过渡的中间网络模型-NW型多层前向小世界人工神经网络模型.利用对多层前向规则神经网络中神经元以某一概率p随机化向后层跨层连接,构建新的神经网络模型,然后将不同跨层概率下的小世界人工神经网络应用于函数逼近.在设定精度相同情况下对不同概率下的收敛次数做比较,仿真发现随机化加边概率p处于p =0.08附近时的小世界人工神经网络比同规模的规则网络和随机网络具有更好的收敛速度,实验证实采用NW型小世界多层前向人工神经网络模型,在精度和收敛速度上均得到提高.%To find the optimal neural network structure, based on the research methods from the complex network , the structure of multi - layer forward neural networks model was studied, and a new neural networks model, NW multi-layer forward small world artificial neural networks was proposed, whose structure of layer was between the regular model and the stochastic model. At first, the regular of multilayer feed -forward neural network neurons randomized cross-layer link back layer with a probability p, and constructed the new neural network model. Second-ly, the cross -layer small world artificial neural networks were used for function approximation under different re-wiring probability. The count of convergence under different probability was compared by setting a same precision. Simulation shows that the small-world neural network has a better convergence speed than regular network and random network nearly p = 0. 08, and the optimum performance of the NW multi-layer forward small world artificial neural network is proved in the right side of probability increases.
Small Worldness in Dense and Weighted Connectomes
Colon-Perez, Luis; Couret, Michelle; Triplett, William; Price, Catherine; Mareci, Thomas
2016-05-01
The human brain is a heterogeneous network of connected functional regions; however, most brain network studies assume that all brain connections can be described in a framework of binary connections. The brain is a complex structure of white matter tracts connected by a wide range of tract sizes, which suggests a broad range of connection strengths. Therefore, the assumption that the connections are binary yields an incomplete picture of the brain. Various thresholding methods have been used to remove spurious connections and reduce the graph density in binary networks. But these thresholds are arbitrary and make problematic the comparison of networks created at different thresholds. The heterogeneity of connection strengths can be represented in graph theory by applying weights to the network edges. Using our recently introduced edge weight parameter, we estimated the topological brain network organization using a complimentary weighted connectivity framework to the traditional framework of a binary network. To examine the reproducibility of brain networks in a controlled condition, we studied the topological network organization of a single healthy individual by acquiring 10 repeated diffusion-weighted magnetic resonance image datasets, over a one-month period on the same scanner, and analyzing these networks with deterministic tractography. We applied a threshold to both the binary and weighted networks and determined that the extra degree of freedom that comes with the framework of weighting network connectivity provides a robust result as any threshold level. The proposed weighted connectivity framework provides a stable result and is able to demonstrate the small world property of brain networks in situations where the binary framework is inadequate and unable to demonstrate this network property.
Zhang, Z.-Z.; Zhou, S.-G.; Zou, T.
2007-04-01
In this paper, firstly, we study analytically the topological features of a family of hierarchical lattices (HLs) from the view point of complex networks. We derive some basic properties of HLs controlled by a parameter q: scale-free degree distribution with exponent γ=2+ln 2/(ln q), null clustering coefficient, power-law behavior of grid coefficient, exponential growth of average path length (non-small-world), fractal scaling with dimension dB=ln (2q)/(ln 2), and disassortativity. Our results show that scale-free networks are not always small-world, and support the conjecture that self-similar scale-free networks are not assortative. Secondly, we define a deterministic family of graphs called small-world hierarchical lattices (SWHLs). Our construction preserves the structure of hierarchical lattices, including its degree distribution, fractal architecture, clustering coefficient, while the small-world phenomenon arises. Finally, the dynamical processes of intentional attacks and collective synchronization are studied and the comparisons between HLs and Barabási-Albert (BA) networks as well as SWHLs are shown. We find that the self-similar property of HLs and SWHLs significantly increases the robustness of such networks against targeted damage on hubs, as compared to the very vulnerable non fractal BA networks, and that HLs have poorer synchronizability than their counterparts SWHLs and BA networks. We show that degree distribution of scale-free networks does not suffice to characterize their synchronizability, and that networks with smaller average path length are not always easier to synchronize.
Nonequilibrium phase transition in directed small-world-Voronoi-Delaunay random lattices
Lima, F. W. S.
2016-01-01
On directed small-world-Voronoi-Delaunay random lattices in two dimensions with quenched connectivity disorder we study the critical properties of the dynamics evolution of public opinion in social influence networks using a simple spin-like model. The system is treated by applying Monte Carlo simulations. We show that directed links on these random lattices may lead to phase diagram with first- and second-order social phase transitions out of equilibrium.
Directory of Open Access Journals (Sweden)
Xia Liang
Full Text Available Graph theoretical analysis of brain networks based on resting-state functional MRI (R-fMRI has attracted a great deal of attention in recent years. These analyses often involve the selection of correlation metrics and specific preprocessing steps. However, the influence of these factors on the topological properties of functional brain networks has not been systematically examined. Here, we investigated the influences of correlation metric choice (Pearson's correlation versus partial correlation, global signal presence (regressed or not and frequency band selection [slow-5 (0.01-0.027 Hz versus slow-4 (0.027-0.073 Hz] on the topological properties of both binary and weighted brain networks derived from them, and we employed test-retest (TRT analyses for further guidance on how to choose the "best" network modeling strategy from the reliability perspective. Our results show significant differences in global network metrics associated with both correlation metrics and global signals. Analysis of nodal degree revealed differing hub distributions for brain networks derived from Pearson's correlation versus partial correlation. TRT analysis revealed that the reliability of both global and local topological properties are modulated by correlation metrics and the global signal, with the highest reliability observed for Pearson's-correlation-based brain networks without global signal removal (WOGR-PEAR. The nodal reliability exhibited a spatially heterogeneous distribution wherein regions in association and limbic/paralimbic cortices showed moderate TRT reliability in Pearson's-correlation-based brain networks. Moreover, we found that there were significant frequency-related differences in topological properties of WOGR-PEAR networks, and brain networks derived in the 0.027-0.073 Hz band exhibited greater reliability than those in the 0.01-0.027 Hz band. Taken together, our results provide direct evidence regarding the influences of correlation metrics
Ausloos, Marcel
2015-01-01
Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter- and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues, the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) networ...
一种网络敏感的结构化小世界P2P覆盖网络%Network-aware structured P2P overlay based on small world
Institute of Scientific and Technical Information of China (English)
任平凡; 黄东军
2009-01-01
In recent years people have conducted massive research to the structured P2P overlay network. In the construction of structured P2P network, the lower level network's topology has not obtained the consideration. So in end-to-end correspondence, although the hops of path are very few, the actual latency can actually be very large. In view of this problem, this article applied the small world theory to propose a network-aware P2P overlay network, which could enable the nodes that were close in actual network to gather in a same cluster. And as a small world network, it could take its features of short average path and high clustering coefficient to make route choosing and congestion control. The simulation experiment indicates, comparing with the classic P2P overlay network, this network has higher inquiry efficiency.%近年来人们对结构化P2P覆盖网络进行了大量的研究,在结构化P2P网络的构建中,下层的网络拓扑结构并没有得到考虑,因此在端到端的通信中,尽管覆盖网上所反映出路径跳数很少,但实际的延迟却会很大.针对此问题,结合小世界理论提出一种网络敏感的新P2P覆盖网络,使实际网络中邻近的节点能聚集到同一簇中,并利用小世界网络平均距离小和大簇系数特性进行路由选择和拥塞控制.仿真实验表明,与经典的P2P覆盖网络相比,该网络具有更高的查询效率.
Batalle, Dafnis; Eixarch, Elisenda; Figueras, Francesc; Muñoz-Moreno, Emma; Bargallo, Nuria; Illa, Miriam; Acosta-Rojas, Ruthy; Amat-Roldan, Ivan; Gratacos, Eduard
2012-04-02
Intrauterine growth restriction (IUGR) due to placental insufficiency affects 5-10% of all pregnancies and it is associated with a wide range of short- and long-term neurodevelopmental disorders. Prediction of neurodevelopmental outcomes in IUGR is among the clinical challenges of modern fetal medicine and pediatrics. In recent years several studies have used magnetic resonance imaging (MRI) to demonstrate differences in brain structure in IUGR subjects, but the ability to use MRI for individual predictive purposes in IUGR is limited. Recent research suggests that MRI in vivo access to brain connectivity might have the potential to help understanding cognitive and neurodevelopment processes. Specifically, MRI based connectomics is an emerging approach to extract information from MRI data that exhaustively maps inter-regional connectivity within the brain to build a graph model of its neural circuitry known as brain network. In the present study we used diffusion MRI based connectomics to obtain structural brain networks of a prospective cohort of one year old infants (32 controls and 24 IUGR) and analyze the existence of quantifiable brain reorganization of white matter circuitry in IUGR group by means of global and regional graph theory features of brain networks. Based on global and regional analyses of the brain network topology we demonstrated brain reorganization in IUGR infants at one year of age. Specifically, IUGR infants presented decreased global and local weighted efficiency, and a pattern of altered regional graph theory features. By means of binomial logistic regression, we also demonstrated that connectivity measures were associated with abnormal performance in later neurodevelopmental outcome as measured by Bayley Scale for Infant and Toddler Development, Third edition (BSID-III) at two years of age. These findings show the potential of diffusion MRI based connectomics and graph theory based network characteristics for estimating differences in the
Trust Propagation in Small Worlds
DEFF Research Database (Denmark)
Gray, Elizabeth; Seigneur, Jean-Marc; Chen, Yong
2003-01-01
The possibility of a massive, networked infrastructure of diverse entities partaking in collaborative applications with each other increases more and more with the proliferation of mobile devices and the development of ad hoc networking technologies. In this context, traditional security measures...
Marcel eAusloos
2015-01-01
Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix bui...
Prisoner's Dilemma on Two-Dimension Heterogeneous Small-World Network%二维平面异质小世界网络上的囚徒博弈
Institute of Scientific and Technical Information of China (English)
佟庆涛; 周亚; 韩战钢; 李克强
2012-01-01
探讨了基于二维网格构建的异质小世界网络上的演化囚徒博弈,研究了该网络结构的异质性对合作水平的影响.研究发现,网络中异质节点和长程边数在中等水平时,网络的合作水平最高,过多和过少的异质节点和长程边数均不能使合作水平达到最高.此外,不同于同质网络,在特定的条件下,异质网络平均连接度的增加仍然会促进合作水平的提高.%We investigate an evolutionary prisoner s dilemma on a heterogeneous small-world network based on a two-dimension lattice. The main work is to study the influence of topological heterogeneity on cooperation level. We found that the cooperation level peaks when heterogeneity is intermediate, which means that the most heterogeneous cases and the most homogeneous ones did not favor the cooperators. Besides, increasing average degree of heterogeneous network can still promote cooperation under specified conditions, which is different from homogeneous net-work.
Small-world ProPerties of the brain structural networks in male schizoPhrenia%男性精神分裂症患者脑结构网络小世界属性研究
Institute of Scientific and Technical Information of China (English)
李影; 陈建淮; 阎锐; 花玲玲; 姚志剑
2014-01-01
目的：探讨男性精神分裂症患者脑结构网络小世界属性的特点。方法：对21例男性精神分裂症患者（患者组）进行弥散张量成像扫描（DTI），利用解剖学自动标记模板（AAL）将整个大脑划分为90个区域，采用纤维分配连续跟踪（FACT）方法构建脑结构二值网络；并与23名健康男性（对照组）比较。结果：两组脑结构网络均具有小世界属性（P ＝0.47）；患者组平均最短路径长度较对照组显著增加（P ＝0.001），经 FDR 校正主要位于右侧颞中回、左侧楔叶、右侧枕中回、左侧扣带回后部、右侧颞上回颞极、右侧颞中回颞极（P 均﹤0.001）。结论：男性精神分裂症患者脑结构形式和信息处理模式都具有小世界属性；但不同脑区间信息传递路径变长，提示其脑结构网络信息传递能力和脑区间信息整合能力受损。%To explore the characteristics of the small-world properties of the brain structural networks in male schizophrenia. Method:Twenty-one male schizophrenic patients(case group)were scanned with diffusion tensor imaging(DTI). The whole brain was divided into 90 districts by automated anatomical la-beling(AAL),and brain structure binary network was constructed by fiber distribution of continuous tracking (FACT)method. The result was compared with 23 healthy men(control group). Results:The brain struc-tural networks had small-world properties in both groups(P = 0. 47). The average shortest path length of the brain structural networks in case group was significantly increased than the control group(P = 0. 001). By the correction of FDR,mainly in the right middle temporal gyrus,the left cuneus,the right middle occipital gyrus, the left median cingulate gyri,the right superior temporal gyrus(temporal pole)and the right middle temporal gyrus(temporal pole). Conclusion:The brain structure form and the information processing model in male schizophrenic patients
基于小世界的传感器网络查询能量空洞问题%The Energy Hole Problem Based on Small World in Wireless Sensor Networks
Institute of Scientific and Technical Information of China (English)
刘学军; 陆海明; 周水庚; 白光伟
2012-01-01
Sensor nodes closer to the sink need to relay more traffic compared to other nodes in outer sub-regions, thus they suffer much faster energy consumption rates and have much shorter expected lifetime. This phenomenon of uneven energy consumption is called the "energy holes" problem. In this paper, we propose a new method to solve the "energy holes" problem. The method is based on the concept of small worlds where the addition of a small number of long-range links to Sink results in significant reduction in traffic of nodes closer to the Sink. This method balances the energy expenditure among sensors and alleviates the energy holes problem, thus prolongs the lifetime of the sensor network. We analyze the optimal location and quantity of long-range links theoretically. Moreover we further explore their influence on energy expenditure and network lifetime. On this basis, we present a practicable method to realize the small world network. Simulation experiments verify the results of theoretical analysis.%靠近Sink的传感器节点因为需要转发来自其它节点的数据而承担了更多的通信负载,这些节点往往更早地耗尽自身能量而有更短的生命周期,这种现象被称为“能量空洞”问题.文中基于小世界思想,通过向Sink节点添加一些长链,减少Sink周围节点转发数据的数量来缓解能量空洞的出现,从而延长网络的生命周期.首先对等距传输的网络进行了能耗分析,然后提出采用小世界的策略缓解能量洞的出现,从理论上分析了长链的位置和数量对能量消耗和网络生命周期的影响,提出了一种实用的小世界网络实现方法.仿真实验验证了理论分析结果.
Institute of Scientific and Technical Information of China (English)
周彬镔; 陈雪波
2015-01-01
Social network has a characteristic of small world , with high cluster coefficient and short average distance .In order to do some research on epidemic spread in small world network and points ’ voluntary suppressions under a global warning , a model based on CA ( cellular automaton ) is proposed .Combining with normal cloud model , we give the model some adaptive properties . Points in the model can break links and connect to others .Under a global warning , we let points abide by danger awareness func-tion.Using AHP model, they are inclined to avoid danger points .Simulation results show that this model is good at simulating epidemic spread and it gives us an explanation of why global warning can postpone the epidemic spread on a network .%人际网络具有小世界特征，拥有高聚类系数、短平均路径等特点。为研究病毒在小世界网络中的传播动力学及全局预警下节点的自主抑制行为，本文基于元胞自动机理论，提出一种小世界网络上的元胞自动机病毒传播模型。结合云模型，模型中节点在病毒传播过程中拥有断开与重连的自适应性，拥有节点危害性认识能力，可参照全局预警，运用层次分析法，对高危节点主动避让。仿真结果表明，该模型可较好模拟病毒的实际传播，通过全局预警可促使节点对高危节点进行规避，以延缓病毒传播。
A Structured P2P Overlay Network with Small-World Characteristics%一种具有小世界特征的结构化P2P覆盖网络
Institute of Scientific and Technical Information of China (English)
魏文红; 肖文俊
2009-01-01
现有的P 2P覆盖网络都难以把具有共同兴趣的对等点连接起来,不适用于文件浏览服务.为此,文中推广了立方连接圈(CCC)图,研究了推广立方连接圈(GCCC)图的拓扑性质,进而基于GCCC图定义了一种新的结构化P 2P覆盖网络--推广立方连接圈网络(GCNET).与其它的P 2P覆盖网络相比,GCNET具有良好的小世界特征和更好的鲁棒性.模拟实验结果表明,GCNET的路由表和查询长度能达到理论下界.%As the existing P2P overlay networks can not closely connect peers with the same interest together, it is not practical to provide browsing service in such systems. In order to solve this problem, the existing cube-connec-ted cycle (CCC) graph is generalized, and the topological properties of the generalized CCC (GCCC) graph are investigated. Afterwards, a novel structured P2P overlay network marked as GCNET (Generalized Cube-Connected Cycle network) is defined based on GCCC, which possesses better small-world characteristics and stronger robustness than other P2P overlay networks. Simulated results show that GCNET can reach the theoretical lower bounds of both the routing table size and the query path length.
Agent-based modeling and network dynamics
Namatame, Akira
2016-01-01
The book integrates agent-based modeling and network science. It is divided into three parts, namely, foundations, primary dynamics on and of social networks, and applications. The book begins with the network origin of agent-based models, known as cellular automata, and introduce a number of classic models, such as Schelling’s segregation model and Axelrod’s spatial game. The essence of the foundation part is the network-based agent-based models in which agents follow network-based decision rules. Under the influence of the substantial progress in network science in late 1990s, these models have been extended from using lattices into using small-world networks, scale-free networks, etc. The book also shows that the modern network science mainly driven by game-theorists and sociophysicists has inspired agent-based social scientists to develop alternative formation algorithms, known as agent-based social networks. The book reviews a number of pioneering and representative models in this family. Upon the gi...
Institute of Scientific and Technical Information of China (English)
林敏; 李南; 季旭
2012-01-01
By analyzing the behavior of knowledge communication in organizations, sufficiency index and equity index are proposed to measure the effectiveness of knowledge communication and explore the effect of partner selection mechanism. The process of knowledge communication on small - world network is simulated. Results show that the mechanism for selecting neighbors who have higher knowledge level could promote knowledge communication, on the other hand, the mechanism for selecting neighbors who have more work experiences results in a clustering effect and impedes knowledge communication in organizations.%本文在分析组织知识交流行为的基础上，提出了衡量知识交流效果的交流充分度指标和交流公平度指标。并探讨了知识交流对象选择机制对知识交流效果的影响。对小世界网络上的知识交流过程进行了模拟，并分析了结果。通过比较研究发现，就高选择机制是促进组织知识交流的积极因素，而工龄选择机制下会出现扎堆现象，妨碍组织的知识交流。
Pinning impulsive directed coupled delayed dynamical network and its applications
Lin, Chunnan; Wu, Quanjun; Xiang, Lan; Zhou, Jin
2015-01-01
The main objective of the present paper is to further investigate pinning synchronisation of a complex delayed dynamical network with directionally coupling by a single impulsive controller. By developing the analysis procedure of pinning impulsive stability for undirected coupled dynamical network previously, some simple yet general criteria of pinning impulsive synchronisation for such directed coupled network are derived analytically. It is shown that a single impulsive controller can always pin a given directed coupled network to a desired homogenous solution, including an equilibrium point, a periodic orbit, or a chaotic orbit. Subsequently, the theoretical results are illustrated by a directed small-world complex network which is a cellular neural network (CNN) and a directed scale-free complex network with the well-known Hodgkin-Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.
Yet another approach to the small world phenomenon
Medo, M
2006-01-01
We introduce a metrics to the random network of the human relationships. Obtained spatial graph allows us to calculate the average separation of people in a very simple manner. Acquired results agree with the well-known presence of the small-world phenomenon in human relationships. It indicates that this feature can be understood merely as the consequence of the probability composition. We will also examine how this phenomenon evolves with the development of the human society.
Armbruster, Benjamin
2011-01-01
We analyze random networks that change over time. First we analyze a dynamic Erdos-Renyi model, whose edges change over time. We describe its stationary distribution, its convergence thereto, and the SI contact process on the network, which has relevance for connectivity and the spread of infections. Second, we analyze the effect of node turnover, when nodes enter and leave the network, which has relevance for network models incorporating births, deaths, aging, and other demographic factors.
Vaccination intervention on epidemic dynamics in networks
Peng, Xiao-Long; Fu, Xinchu; Zhou, Tao
2013-01-01
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barab\\'asi-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.
Assimilation Dynamic Network (ADN) Project
National Aeronautics and Space Administration — The Assimilation Dynamic Network (ADN) is a dynamic inter-processor communication network that spans heterogeneous processor architectures, unifying components,...
Airborne Network Optimization with Dynamic Network Update
2015-03-26
AIRBORNE NETWORK OPTIMIZATION WITH DYNAMIC NETWORK UPDATE THESIS Bradly S. Paul, Capt, USAF AFIT-ENG-MS-15-M-030 DEPARTMENT OF THE AIR FORCE AIR...to copyright protection in the United States. AFIT-ENG-MS-15-M-030 AIRBORNE NETWORK OPTIMIZATION WITH DYNAMIC NETWORK UPDATE THESIS Presented to the...NETWORK OPTIMIZATION WITH DYNAMIC NETWORK UPDATE Bradly S. Paul, B.S.C.P. Capt, USAF Committee Membership: Maj Thomas E. Dube Chair Dr. Kenneth M. Hopkinson
On the relation between the small world structure and scientific activities.
Ebadi, Ashkan; Schiffauerova, Andrea
2015-01-01
The modern science has become more complex and interdisciplinary in its nature which might encourage researchers to be more collaborative and get engaged in larger collaboration networks. Various aspects of collaboration networks have been examined so far to detect the most determinant factors in knowledge creation and scientific production. One of the network structures that recently attracted much theoretical attention is called small world. It has been suggested that small world can improve the information transmission among the network actors. In this paper, using the data on 12 periods of journal publications of Canadian researchers in natural sciences and engineering, the co-authorship networks of the researchers are created. Through measuring small world indicators, the small worldiness of the mentioned network and its relation with researchers' productivity, quality of their publications, and scientific team size are assessed. Our results show that the examined co-authorship network strictly exhibits the small world properties. In addition, it is suggested that in a small world network researchers expand their team size through getting connected to other experts of the field. This team size expansion may result in higher productivity of the whole team as a result of getting access to new resources, benefitting from the internal referring, and exchanging ideas among the team members. Moreover, although small world network is positively correlated with the quality of the articles in terms of both citation count and journal impact factor, it is negatively related with the average productivity of researchers in terms of the number of their publications.
Veenstra, René; Dijkstra, Jan; Steglich, Christian; Van Zalk, Maarten H. W.
2013-01-01
Researchers have become increasingly interested in disentangling selection and influence processes. This literature review provides context for the special issue on network-behavior dynamics. It brings together important conceptual, methodological, and empirical contributions focusing on longitudina
Institute of Scientific and Technical Information of China (English)
丁尚文; 钱志余; 李韪韬; 陶玲; 胡光霞
2012-01-01
Differences of information transmission network hub. network aggregation and minimum path of information transmission under the states of photon stimulation and resting are studied- The brain functional network is constructed based on the small-world network theory. By analyzing the network connectivity of brain function, cluster coefficient and the minimum path, the conclusion is drawn that stronger functional areas of information transferring are the insula and the posterior cingulate state. Thalamus and hippocampus have a greater aggregation. The information amount of photon stimulation from superior frontal gyrus to the middle occipital gyrus is passed through middle temporal gyrus under the photon stimulation. Those are drawn under rest state that stronger functional areas of information transferring are the cuneus and the lingual gyrus, the central lobule and superior temporal gyrus have a greater aggregations the information amount of photon stimulation from left superior frontal gyrus to left the middle occipital gyrus is passed through middle temporal gyrus, cuneus and that from right superior frontal gyrus to right the middle occipital gyrus is passed through anterior cingulate gyrus and inferior occipital gyrus.%研究光诱发和静息两种状态下的脑功能网络的信息传输枢纽、网络聚合能力和信息传输的最小路径的差异性.采用小世界网络理论对脑功能网络进行建模,通过对脑功能网络连接度、簇系数和最小路径进行分析,得出光诱发状态下的信息传输重要枢纽为岛叶、后扣带回功能区；丘脑、海马两处功能网络有较大聚合能力.光诱发过程从额上回经颞中回传输到枕中回.静息状态下的信息传输重要枢纽为楔叶、舌回；中央旁小叶、颞上回脑功能网络有较大聚合能力.静息状态下的左半区最佳信息传输路径为左额上回、左颞中回、右楔叶最后到左枕中回；右脑半区
Dynamics and processing in finite self-similar networks.
DeDeo, Simon; Krakauer, David C
2012-09-07
A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.
Dynamical Crossover in Complex Networks near the Percolation Transition
Kawasaki, Fumiya; Yakubo, Kousuke
2011-10-01
The return probability P0(t) of random walkers is investigated numerically for several scale-free fractal networks. Our results show that P0(t) is proportional to t-ds/2 with the non-integer spectral dimension ds as in the case of non-scale free fractal networks. We also study how the diffusion process is affected by the structural crossover from a fractal to a small-world architecture in a network near the percolation transition. It is elucidated that the corresponding dynamical crossover is scaled only by the unique characteristic time tξ regardless of whether the network is scale free or not. In addition, the scaling relation ds= 2Df/dw is found to be valid even for scale-free fractal networks, where Df and dw are the fractal and the walk dimensions. These results suggest that qualitative properties of P0(t) are irrelevant to the scale-free nature of networks.
Optimizing Dynamical Network Structure for Pinning Control
Orouskhani, Yasin; Jalili, Mahdi; Yu, Xinghuo
2016-04-01
Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights.
Energy Technology Data Exchange (ETDEWEB)
Madduri, Kamesh; Bader, David A.
2009-02-15
Graph-theoretic abstractions are extensively used to analyze massive data sets. Temporal data streams from socioeconomic interactions, social networking web sites, communication traffic, and scientific computing can be intuitively modeled as graphs. We present the first study of novel high-performance combinatorial techniques for analyzing large-scale information networks, encapsulating dynamic interaction data in the order of billions of entities. We present new data structures to represent dynamic interaction networks, and discuss algorithms for processing parallel insertions and deletions of edges in small-world networks. With these new approaches, we achieve an average performance rate of 25 million structural updates per second and a parallel speedup of nearly28 on a 64-way Sun UltraSPARC T2 multicore processor, for insertions and deletions to a small-world network of 33.5 million vertices and 268 million edges. We also design parallel implementations of fundamental dynamic graph kernels related to connectivity and centrality queries. Our implementations are freely distributed as part of the open-source SNAP (Small-world Network Analysis and Partitioning) complex network analysis framework.
Enhanced brain small-worldness after sleep deprivation: a compensatory effect.
Liu, Huan; Li, Hong; Wang, Yulin; Lei, Xu
2014-10-01
Sleep deprivation has a variable impact on extrinsic activities during multiple cognitive tasks, especially on mood and emotion processing. There is also a trait-like individual vulnerability or compensatory effect in cognition. Previous studies have elucidated the altered functional connectivity after sleep deprivation. However, it remains unclear whether the small-world properties of resting-state network are sensitive to sleep deprivation. A small-world network is a type of graph that combines a high local connectivity as well as a few long-range connections, which ensures a higher information-processing efficiency at a low cost. The complex network of the brain can be described as a small-world network, in which a node is a brain region and an edge is present when there is a functional correlation between two nodes. Here, we investigated the topological properties of the human brain networks of 22 healthy subjects under sufficient sleep and sleep-deprived conditions. Specifically, small-worldness is utilized to quantify the small-world property, by comparing the clustering coefficient and path length of a given network to an equivalent random network with same degree distribution. After sufficient sleep, the brain networks showed the property of small-worldness. Compared with the resting state under sufficient sleep, the small-world property was significantly enhanced in the sleep deprivation condition, suggesting a possible compensatory adaptation of the human brain. Specifically, the altered measurements were correlated with the neuroticism of subjects, indicating that individuals with low-levels of neuroticism are more resilient to sleep deprivation.
Simulating market dynamics: interactions between consumer psychology and social networks.
Janssen, Marco A; Jager, Wander
2003-01-01
Markets can show different types of dynamics, from quiet markets dominated by one or a few products, to markets with continual penetration of new and reintroduced products. In a previous article we explored the dynamics of markets from a psychological perspective using a multi-agent simulation model. The main results indicated that the behavioral rules dominating the artificial consumer's decision making determine the resulting market dynamics, such as fashions, lock-in, and unstable renewal. Results also show the importance of psychological variables like social networks, preferences, and the need for identity to explain the dynamics of markets. In this article we extend this work in two directions. First, we will focus on a more systematic investigation of the effects of different network structures. The previous article was based on Watts and Strogatz's approach, which describes the small-world and clustering characteristics in networks. More recent research demonstrated that many large networks display a scale-free power-law distribution for node connectivity. In terms of market dynamics this may imply that a small proportion of consumers may have an exceptional influence on the consumptive behavior of others (hubs, or early adapters). We show that market dynamics is a self-organized property depending on the interaction between the agents' decision-making process (heuristics), the product characteristics (degree of satisfaction of unit of consumption, visibility), and the structure of interactions between agents (size of network and hubs in a social network).
Dynamic Network Change Detection
2008-12-01
detection methods is presented; the cumulative sum ( CUSUM ), the exponentially weighted moving average (EWMA), and a scan statistic (SS). Statistical...minimizing the risk of false alarms. Three common SPC methods that we consider here are the CUSUM (Page, 1961), EWMA (Roberts, 1959), and the SS...successive dynamic network measures are then used to calculate the statistics for the CUSUM , the EWMA, and the SS. These are then compared to decision
Impact of informal networks on opinion dynamics in hierarchically formal organization
Song, Xiao; Shi, Wen; Ma, Yaofei; Yang, Chen
2015-10-01
Traditional opinion dynamics model focused mainly on the conditions under which a group of agents would reach a consensus. Conclusion has been gained that continuous opinion dynamics are subject to the constraint that convergent opinion adjustment only proceeds when opinion difference is below a given tolerance. This conclusion is useful but neglected the fact that an organization often consists of overlapped networks including formally hierarchical network and small-world/scale-free informal networks. To study the impact of different types of informal networks on converging speed or the number of opinion clusters, four typical types of informal networks (small-world, scale-free, tree and fully connected) are modeled and proposed as complements to formal communications. Experiments to compare formal network and hybrid networks are then carried out. It is observed that opinion dynamics with supplemented communications of informal networks can benefit convergence speed and reduce opinion clusters. More importantly, it is revealed that three key factors of informal networks affect their impact on formal network. These factors of informal network in descending orders are: agents' tolerances, scale and number of links.
Tracking the dynamic variations in a social network formed through shared interests
Directory of Open Access Journals (Sweden)
Gerold Pedemonte
2009-06-01
Full Text Available We tracked the dynamics of a social network formed by a shared interest in movies. Users-, movie ratings-, and rental date-data from the Netflix Prize dataset were used to construct a series of date-filtered social networks, wherein viewers were linked when they rented the same movie and gave the same rating. We obtained a nearly constant high clustering coefficient (0.60 – 0.85, and a low average path length (1.4 – 2.3 indicating a static 'small-world' network despite the dynamic behavior of the borrowers.
Directory of Open Access Journals (Sweden)
J. Reyes-Reyes
2000-01-01
Full Text Available In this paper, an adaptive technique is suggested to provide the passivity property for a class of partially known SISO nonlinear systems. A simple Dynamic Neural Network (DNN, containing only two neurons and without any hidden-layers, is used to identify the unknown nonlinear system. By means of a Lyapunov-like analysis the new learning law for this DNN, guarantying both successful identification and passivation effects, is derived. Based on this adaptive DNN model, an adaptive feedback controller, serving for wide class of nonlinear systems with an a priori incomplete model description, is designed. Two typical examples illustrate the effectiveness of the suggested approach.
The structure of borders in a small world
Thiemann, C; Grady, D; Brune, R; Brockmann, D
2010-01-01
Geographic borders are not only essential for the effective functioning of government, the distribution of administrative responsibilities and the allocation of public resources, they also influence the interregional flow of information, cross-border trade operations, the diffusion of innovation and technology, and the spatial spread of infectious diseases. However, as growing interactions and mobility across long distances, cultural, and political borders continue to amplify the small world effect and effectively decrease the relative importance of local interactions, it is difficult to assess the location and structure of effective borders that may play the most significant role in mobility-driven processes. The paradigm of spatially coherent communities may no longer be a plausible one, and it is unclear what structures emerge from the interplay of interactions and activities across spatial scales. Here we analyse a multi-scale proxy network for human mobility that incorporates travel across a few to a few...
Complex Dynamics in Communication Networks
Kocarev, Ljupco
2005-01-01
Computer and communication networks are among society's most important infrastructures. The internet, in particular, is a giant global network of networks without central control or administration. It is a paradigm of a complex system, where complexity may arise from different sources: topological structure, network evolution, connection and node diversity, or dynamical evolution. The present volume is the first book entirely devoted to the new and emerging field of nonlinear dynamics of TCP/IP networks. It addresses both scientists and engineers working in the general field of communication networks.
Topology and dynamics of attractor neural networks: The role of loopiness
Zhang, Pan; Chen, Yong
2008-07-01
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large loopiness coefficient means a high probability of finding loops in the networks. We develop recursive equations for the overlap parameters of neural networks in terms of their loopiness. It was found that a large loopiness increases the correlation among the network states at different times and eventually reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular and densely-connected small-world, where encouraging results are obtained.
Small World Model-Based Polylogarithmic Routing Using Mobile Nodes
Institute of Scientific and Technical Information of China (English)
Jie Wu; Shu-Hui Yang
2008-01-01
The use of mobile nodes to improve network system performance has drawn considerable attention recently.The movement-assisted model considers mobility as a desirable feature, where routing is based on the store-carry-forward paradigm with random or controlled movement of resource rich mobile nodes. The application of such a model has been used in several emerging networks, including mobile ad hoc networks (MANETs), wireless sensor networks (WSNs), and delay tolerant networks (DTNs). It is well known that mobility increases the capacity of MANETs by reducing the number of relays for routing, prolonging the lifespan of WSNs by using mobile nodes in place of bottleneck static sensors, and ensuring network connectivity in DTNs using mobile nodes to connect different parts of a disconnected network. Trajectory planning and the coordination of mobile nodes are two important design issues aiming to optimize or balance several measures,including delay, average number of relays, and moving distance. In this paper, we propose a new controlled mobility model with an expected polylogarithmic number of relays to achieve a good balance among several contradictory goals, including delay, the number of relays, and moving distance. The model is based on the small-world model where each static node has "short" link connections to its nearest neighbors and "long" link connections to other nodes following a certain probability distribution. Short links are regular wireless connections whereas long links are implemented using mobile nodes. Various issues are considered, including trade-offs between delay and average number of relays, selection of the number of mobilenodes, and selection of the number of long links. The effectiveness of the proposed model is evaluated analytically as well as through simulation.
Institute of Scientific and Technical Information of China (English)
史朋亮; 吴晨
2011-01-01
概括国际期刊业建设审稿专家数据库的动态，总结当前期刊编辑部所使用的审稿专家数据库的来源，分析中国期刊业在审稿专家数据库建设上面临的机遇。基于小世界网络模型的观点，提出在中国知网（CNKI）作者库基础上构建审稿专家网络系统的设想和方案，并对所能达到的目标作了展望。%We give an overview of trends on establishment of peer reviewer database for academic periodicals in the world, conclude various resources of it, and sharpen current picture of challenge and chance on construction of a new peer reviewer database. Based on conception of a small-world-network model, we promote to build a system of networks group for peer reviewer database on authors in Chinese National Knowledge Infrastructure （CNKI）, and give a prospection eventually.
Dynamic Evolution of Financial Network and its Relation to Economic Crises
Gao, Ya-Chun; Wei, Zong-Wen; Wang, Bing-Hong
2013-02-01
The static topology properties of financial networks have been widely investigated since the work done by Mantegna, yet their dynamic evolution with time is little considered. In this paper, we comprehensively study the dynamic evolution of financial network by a sliding window technique. The vertices and edges of financial network are represented by the stocks from S&P500 components and correlations between pairs of daily returns of price fluctuation, respectively. Furthermore, the duration of stock price fluctuation, spanning from January 4, 1985 to September 14, 2009, makes us to carefully observe the relation between the dynamic topological properties and big financial crashes. The empirical results suggest that the financial network has the robust small-world property when the time evolves, and the topological structure drastically changes when the big financial crashes occur. This correspondence between the dynamic evolution of financial network and big financial crashes may provide a novel view to understand the origin of economic crisis.
The interaction of intrinsic dynamics and network topology in determining network burst synchrony.
Gaiteri, Chris; Rubin, Jonathan E
2011-01-01
The pre-Bötzinger complex (pre-BötC), within the mammalian respiratory brainstem, represents an ideal system for investigating the synchronization properties of complex neuronal circuits via the interaction of cell-type heterogeneity and network connectivity. In isolation, individual respiratory neurons from the pre-BötC may be tonically active, rhythmically bursting, or quiescent. Despite this intrinsic heterogeneity, coupled networks of pre-BötC neurons en bloc engage in synchronized bursting that can drive inspiratory motor neuron activation. The region's connection topology has been recently characterized and features dense clusters of cells with occasional connections between clusters. We investigate how the dynamics of individual neurons (quiescent/bursting/tonic) and the betweenness centrality of neurons' positions within the network connectivity graph interact to govern network burst synchrony, by simulating heterogeneous networks of computational model pre-BötC neurons. Furthermore, we compare the prevalence and synchrony of bursting across networks constructed with a variety of connection topologies, analyzing the same collection of heterogeneous neurons in small-world, scale-free, random, and regularly structured networks. We find that several measures of network burst synchronization are determined by interactions of network topology with the intrinsic dynamics of neurons at central network positions and by the strengths of synaptic connections between neurons. Surprisingly, despite the functional role of synchronized bursting within the pre-BötC, we find that synchronized network bursting is generally weakest when we use its specific connection topology, which leads to synchrony within clusters but poor coordination across clusters. Overall, our results highlight the relevance of interactions between topology and intrinsic dynamics in shaping the activity of networks and the concerted effects of connectivity patterns and dynamic heterogeneities.
M.J. van der Leij (Marco); S. Goyal (Sanjeev)
2006-01-01
textabstractIn this paper we test the celebrated `Strength of weak ties' theory of Granovetter (1973). We test two hypotheses on the network structure in a data set of collaborating economists. While we find support for the hypothesis of transitivity of strong ties, we reject the hypothesis that wea
Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks
Institute of Scientific and Technical Information of China (English)
HUA Da-Yin
2009-01-01
We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion σ(t, L) = (∑i(mi - ρ0)2/L)1/2 is defined to describe the dynamical behaviour where ρ0 is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ(t, L) follows a power-law scaling σ(t, L) ～ tδ1 and σ(t, L) ～ tδ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ(t, L) ～ tδ2 when t＜T and a(t, L) ～ tδ3 when tT. Moreover, it is found numerically that δ2 is near to δ1 for small rewiring probability q, and δ3 hardly changes with varying q and it is almost the same as δ4. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when tT for the small-world networks. We also show that the relaxation time T follows a power-law scaling τ Lz and σ(t, L) in the stationary state follows a power-law σs(L) ～ Lσ for three different structures.
The classification and analysis of dynamic networks
Institute of Scientific and Technical Information of China (English)
Guo Jin-Li
2007-01-01
In this paper we, firstly, classify the complex networks in which the nodes are of the lifetime distribution. Secondly, in order to study complex networks in terms of queuing system and homogeneous Markov chain, we establish the relation between the complex networks and queuing system, providing a new way of studying complex networks. Thirdly, we prove that there exist stationary degree distributions of M-G-P network, and obtain the analytic expression of the distribution by means of Markov chain theory. We also obtain the average path length and clustering coefficient of the network. The results show that M-G-P network is not only scale-free but also of a small-world feature in proper conditions.
Rashvand, Habib
2013-01-01
Motivated by the exciting new application paradigm of using amalgamated technologies of the Internet and wireless, the next generation communication networks (also called 'ubiquitous', 'complex' and 'unstructured' networking) are changing the way we develop and apply our future systems and services at home and on local, national and global scales. Whatever the interconnection - a WiMAX enabled networked mobile vehicle, MEMS or nanotechnology enabled distributed sensor systems, Vehicular Ad hoc Networking (VANET) or Mobile Ad hoc Networking (MANET) - all can be classified under new networking s
Cognitive Dynamic Optical Networks
DEFF Research Database (Denmark)
de Miguel, Ignacio; Duran, Ramon J.; Lorenzo, Ruben M.
2013-01-01
Cognitive networks are a promising solution for the control of heterogeneous optical networks. We review their fundamentals as well as a number of applications developed in the framework of the EU FP7 CHRON project.......Cognitive networks are a promising solution for the control of heterogeneous optical networks. We review their fundamentals as well as a number of applications developed in the framework of the EU FP7 CHRON project....
Directed network discovery with dynamic network modelling.
Anzellotti, Stefano; Kliemann, Dorit; Jacoby, Nir; Saxe, Rebecca
2017-05-01
Cognitive tasks recruit multiple brain regions. Understanding how these regions influence each other (the network structure) is an important step to characterize the neural basis of cognitive processes. Often, limited evidence is available to restrict the range of hypotheses a priori, and techniques that sift efficiently through a large number of possible network structures are needed (network discovery). This article introduces a novel modelling technique for network discovery (Dynamic Network Modelling or DNM) that builds on ideas from Granger Causality and Dynamic Causal Modelling introducing three key changes: (1) efficient network discovery is implemented with statistical tests on the consistency of model parameters across participants, (2) the tests take into account the magnitude and sign of each influence, and (3) variance explained in independent data is used as an absolute (rather than relative) measure of the quality of the network model. In this article, we outline the functioning of DNM, we validate DNM in simulated data for which the ground truth is known, and we report an example of its application to the investigation of influences between regions during emotion recognition, revealing top-down influences from brain regions encoding abstract representations of emotions (medial prefrontal cortex and superior temporal sulcus) onto regions engaged in the perceptual analysis of facial expressions (occipital face area and fusiform face area) when participants are asked to switch between reporting the emotional valence and the age of a face. Copyright © 2017 Elsevier Ltd. All rights reserved.
Cognitive Dynamic Optical Networks
DEFF Research Database (Denmark)
de Miguel, Ignacio; Duran, Ramon J.; Jimenez, Tamara
2013-01-01
learning with the aim of improving performance. In this paper, we review the fundamentals of cognitive networks and focus on their application to the optical networking area. In particular, a number of cognitive network architectures proposed so far, as well as their associated supporting technologies......The use of cognition is a promising element for the control of heterogeneous optical networks. Not only are cognitive networks able to sense current network conditions and act according to them, but they also take into account the knowledge acquired through past experiences; that is, they include......, are reviewed. Moreover, several applications, mainly developed in the framework of the EU FP7 Cognitive Heterogeneous Reconfigurable Optical Network (CHRON) project, are also described....
Dynamical Response of Networks Under External Perturbations: Exact Results
Chinellato, David D.; Epstein, Irving R.; Braha, Dan; Bar-Yam, Yaneer; de Aguiar, Marcus A. M.
2015-04-01
We give exact statistical distributions for the dynamic response of influence networks subjected to external perturbations. We consider networks whose nodes have two internal states labeled 0 and 1. We let nodes be frozen in state 0, in state 1, and the remaining nodes change by adopting the state of a connected node with a fixed probability per time step. The frozen nodes can be interpreted as external perturbations to the subnetwork of free nodes. Analytically extending and to be smaller than 1 enables modeling the case of weak coupling. We solve the dynamical equations exactly for fully connected networks, obtaining the equilibrium distribution, transition probabilities between any two states and the characteristic time to equilibration. Our exact results are excellent approximations for other topologies, including random, regular lattice, scale-free and small world networks, when the numbers of fixed nodes are adjusted to take account of the effect of topology on coupling to the environment. This model can describe a variety of complex systems, from magnetic spins to social networks to population genetics, and was recently applied as a framework for early warning signals for real-world self-organized economic market crises.
Nonlinear Dynamics on Interconnected Networks
Arenas, Alex; De Domenico, Manlio
2016-06-01
Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).
Tensor networks for dynamic spacetimes
May, Alex
2016-01-01
Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary to give a new definition of length in the network, and propose a definition based on the mutual information. We show that by associating a set of networks with a single quantum state and making use of the mutual information based definition of length, a network analogue of the maximin formula can be used to calculate the entropy of boundary regions.
Dynamical Convergence Trajectory in Networks
Institute of Scientific and Technical Information of China (English)
TAN Ning; ZHANG Yun-Jun; OUYANG Qi; GENG Zhi
2005-01-01
@@ It is well known that topology and dynamics are two major aspects to determine the function of a network. We study one of the dynamic properties of a network: trajectory convergence, i.e. how a system converges to its steady state. Using numerical and analytical methods, we show that in a logical-like dynamical model, the occurrence of convergent trajectory in a network depends mainly on the type of the fixed point and the ratio between activation and inhibition links. We analytically proof that this property is induced by the competition between two types of state transition structures in phase space: tree-like transition structure and star-like transition structure. We show that the biological networks, such as the cell cycle network in budding yeast, prefers the tree-like transition structures and suggest that this type of convergence trajectories may be universal.
Studying Dynamics in Business Networks
DEFF Research Database (Denmark)
Andersen, Poul Houman; Anderson, Helen; Havila, Virpi;
1998-01-01
This paper develops a theory on network dynamics using the concepts of role and position from sociological theory. Moreover, the theory is further tested using case studies from Denmark and Finland...
Institute of Scientific and Technical Information of China (English)
WANG; Xiaoguang; JIANG; Tingting; LI; Xiaoyu
2010-01-01
Co-word networks are constructed with author-provided keywords in academic publications and their relations of co-occurrence.As special form of scientific knowledge networks,they represent the cognitive structure of scientific literature.This paper analyzes the complex structure of a co-word network based on 8,190 author-provided keywords extracted from 3,651 papers in five Chinese core journals in the field of management science.Small-world and scale-free phenomena are found in this network.A large-scale co-word network graph,which consists of one major giant component and many small isolated components,has been generated with the GUESS software.The dynamic growth of keywords and keyword co-occurrence relationships are described with four new informetrics measures.The results indicate that existing concepts always serve as the intellectual base of new ideas as represented by keywords.
Spontaneous Functional Network Dynamics and Associated Structural Substrates in the Human Brain
Directory of Open Access Journals (Sweden)
Xuhong eLiao
2015-09-01
Full Text Available Recent imaging connectomics studies have demonstrated that the spontaneous human brain functional networks derived from resting-state functional MRI (R-fMRI include many non-trivial topological properties, such as highly efficient small-world architecture and densely connected hub regions. However, very little is known about dynamic functional connectivity (D-FC patterns of spontaneous human brain networks during rest and about how these spontaneous brain dynamics are constrained by the underlying structural connectivity. Here, we combined sub-second multiband R-fMRI data with graph-theoretical approaches to comprehensively investigate the dynamic characteristics of the topological organization of human whole-brain functional networks, and then employed diffusion imaging data in the same participants to further explore the associated structural substrates. At the connection level, we found that human whole-brain D-FC patterns spontaneously fluctuated over time, while homotopic D-FC exhibited high connectivity strength and low temporal variability. At the network level, dynamic functional networks exhibited time-varying but evident small-world and assortativity architecture, with several regions (e.g., insula, sensorimotor cortex and medial prefrontal cortex emerging as functionally persistent hubs (i.e., highly connected regions while possessing large temporal variability in their degree centrality. Finally, the temporal characteristics (i.e., strength and variability of the connectional and nodal properties of the dynamic brain networks were significantly associated with their structural counterparts. Collectively, we demonstrate the economical, efficient and flexible characteristics of dynamic functional coordination in large-scale human brain networks during rest, and highlight their relationship with underlying structural connectivity, which deepens our understandings of spontaneous brain network dynamics in humans.
Wright, Christopher K
2010-07-01
Although habitat networks show promise for conservation planning at regional scales, their spatiotemporal dynamics have not been well studied, especially in climate-sensitive landscapes. Here I use satellite remote sensing to compile wetland habitat networks from the Prairie Pothole Region (PPR) of North America. An ensemble of networks assembled across a hydrologic gradient from deluge to drought and a range of representative dispersal distances exhibits power-law scaling of important topological parameters. Prairie wetland networks are "meso-worlds" with mean topological distance increasing faster with network size than small-world networks, but slower than a regular lattice (or "large world"). This scaling implies rapid dispersal through wetland networks without some of the risks associated with "small worlds" (e.g., extremely rapid propagation of disease or disturbance). Retrospective analysis of wetland networks establishes a climatic envelope for landscape connectivity in the PPR, where I show that a changing climate might severely impact metapopulation viability and restrict long-distance dispersal and range shifts. More generally, this study demonstrates an efficient approach to conservation planning at a level of abstraction addressing key drivers of the global biodiversity crisis: habitat fragmentation and climatic change.
Exponentially asymptotical synchronization in uncertain complex dynamical networks with time delay
Energy Technology Data Exchange (ETDEWEB)
Luo Qun; Yang Han; Li Lixiang; Yang Yixian [Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876 (China); Han Jiangxue, E-mail: luoqun@bupt.edu.c [National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876 (China)
2010-12-10
Over the past decade, complex dynamical network synchronization has attracted more and more attention and important developments have been made. In this paper, we explore the scheme of globally exponentially asymptotical synchronization in complex dynamical networks with time delay. Based on Lyapunov stability theory and through defining the error function between adjacent nodes, four novel adaptive controllers are designed under four situations where the Lipschitz constants of the state function in nodes are known or unknown and the network structure is certain or uncertain, respectively. These controllers could not only globally asymptotically synchronize all nodes in networks, but also ensure that the error functions do not exceed the pre-scheduled exponential function. Finally, simulations of the synchronization among the chaotic system in the small-world and scale-free network structures are presented, which prove the effectiveness and feasibility of our controllers.
A small-world-based population encoding model of the primary visual cortex.
Shi, Li; Niu, Xiaoke; Wan, Hong; Shang, Zhigang; Wang, Zhizhong
2015-06-01
A wide range of evidence has shown that information encoding performed by the visual cortex involves complex activities of neuronal populations. However, the effects of the neuronal connectivity structure on the population's encoding performance remain poorly understood. In this paper, a small-world-based population encoding model of the primary visual cortex (V1) is established on the basis of the generalized linear model (GLM) to describe the computation of the neuronal population. The model mainly consists of three sets of filters, including a spatiotemporal stimulus filter, a post-spike history filter, and a set of coupled filters with the coupling neurons organizing as a small-world network. The parameters of the model were fitted with neuronal data of the rat V1 recorded with a micro-electrode array. Compared to the traditional GLM, without considering the small-world structure of the neuronal population, the proposed model was proved to produce more accurate spiking response to grating stimuli and enhance the capability of the neuronal population to carry information. The comparison results proved the validity of the proposed model and further suggest the role of small-world structure in the encoding performance of local populations in V1, which provides new insights for understanding encoding mechanisms of a small scale population in visual system.
Dynamical detection of network communities
Quiles, Marcos G.; Macau, Elbert E. N.; Rubido, Nicolás
2016-05-01
A prominent feature of complex networks is the appearance of communities, also known as modular structures. Specifically, communities are groups of nodes that are densely connected among each other but connect sparsely with others. However, detecting communities in networks is so far a major challenge, in particular, when networks evolve in time. Here, we propose a change in the community detection approach. It underlies in defining an intrinsic dynamic for the nodes of the network as interacting particles (based on diffusive equations of motion and on the topological properties of the network) that results in a fast convergence of the particle system into clustered patterns. The resulting patterns correspond to the communities of the network. Since our detection of communities is constructed from a dynamical process, it is able to analyse time-varying networks straightforwardly. Moreover, for static networks, our numerical experiments show that our approach achieves similar results as the methodologies currently recognized as the most efficient ones. Also, since our approach defines an N-body problem, it allows for efficient numerical implementations using parallel computations that increase its speed performance.
The Dynamics of Semilattice Networks
Veliz-Cuba, Alan
2010-01-01
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being intuitive and models can be easily simulated on a computer in most cases; however, few analytical tools beyond simulation are available. The motivation for this paper is to develop such tools for the analysis of models in biology. In this paper we have identified a broad class of discrete dynamical systems with a finite phase space for which one can derive strong results about their long-term dynamics in terms of properties of their dependency graphs. We classify completely the limit cycles of semilattice networks with strongly connected dependency graph and provide polynomial upper and lower bounds in the general case.
Spontaneous recovery in dynamical networks
Majdandzic, Antonio; Podobnik, Boris; Buldyrev, Sergey V.; Kenett, Dror Y.; Havlin, Shlomo; Eugene Stanley, H.
2014-01-01
Much research has been carried out to explore the structural properties and vulnerability of complex networks. Of particular interest are abrupt dynamic events that cause networks to irreversibly fail. However, in many real-world phenomena, such as brain seizures in neuroscience or sudden market crashes in finance, after an inactive period of time a significant part of the damaged network is capable of spontaneously becoming active again. The process often occurs repeatedly. To model this marked network recovery, we examine the effect of local node recoveries and stochastic contiguous spreading, and find that they can lead to the spontaneous emergence of macroscopic `phase-flipping' phenomena. As the network is of finite size and is stochastic, the fraction of active nodes z switches back and forth between the two network collective modes characterized by high network activity and low network activity. Furthermore, the system exhibits a strong hysteresis behaviour analogous to phase transitions near a critical point. We present real-world network data exhibiting phase switching behaviour in accord with the predictions of the model.
Dawn of small worlds dwarf planets, asteroids, comets
Moltenbrey, Michael
2016-01-01
This book gives a detailed introduction to the thousands and thousands of smaller bodies in the solar system. Written for interested laymen, amateur astronomers and students it describes the nature and origin of asteroids, dwarf planets and comets, and gives detailed information about their role in the solar system. The author nicely reviews the history of small-world-exploration and describes past, current and future space craft missions studying small worlds, and presents their results. Readers will learn that small solar system worlds have a dramatically different nature and appearance than the planets. Even though research activity on small worlds has increased in the recent past many of their properties are still in the dark and need further research.
Wealth dynamics on complex networks
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.
Decoding network dynamics in cancer
DEFF Research Database (Denmark)
Linding, Rune
2014-01-01
models through computational integration of systematic, large-scale, high-dimensional quantitative data sets. I will review our latest advances in methods for exploring phosphorylation networks. In particular I will discuss how the combination of quantitative mass-spectrometry, systems...... in comparative phospho-proteomics and network evolution [Tan et al. Science Signaling 2009, Tan et al. Science 2009, Tan et al. Science 2011]. Finally, I will discuss our most recent work in analyzing genomic sequencing data from NGS studies and how we have developed new powerful algorithms to predict the impact......Biological systems are composed of highly dynamic and interconnected molecular networks that drive biological decision processes. The goal of network biology is to describe, quantify and predict the information flow and functional behaviour of living systems in a formal language...
Tutte polynomial of a small-world Farey graph
Liao, Yunhua; Hou, Yaoping; Shen, Xiaoling
2013-11-01
In this paper, we find recursive formulas for the Tutte polynomials of a family of small-world Farey graphs, which are modular, and has an exponential degree hierarchy. As applications of the recursive formula, the exact expressions for the chromatic polynomial and the reliability polynomial of Fare graphs are derived and the number of connected spanning subgraphs is also obtained.
Modeling and dynamical topology properties of VANET based on complex networks theory
Directory of Open Access Journals (Sweden)
Hong Zhang
2015-01-01
Full Text Available Vehicular Ad hoc Network (VANET is a special subset of multi-hop Mobile Ad hoc Networks in which vehicles can not only communicate with each other but also with the fixed equipments along the roads through wireless interfaces. Recently, it has been discovered that essential systems in real world share similar properties. When they are regarded as networks, among which the dynamic topology structure of VANET system is an important issue. Many real world networks are actually growing with preferential attachment like Internet, transportation system and telephone network. Those phenomena have brought great possibility in finding a strategy to calibrate and control the topology parameters which can help find VANET topology change regulation to relieve traffic jam, prevent traffic accident and improve traffic safety. VANET is a typical complex network which has its basic characteristics. In this paper, we focus on the macroscopic Vehicle-to-Infrastructure (V2I and Vehicle-to-Vehicle (V2V inter-vehicle communication network with complex network theory. In particular, this paper is the first one to propose a method analyzing the topological structure and performance of VANET and present the communications in VANET from a new perspective. Accordingly, we propose degree distribution, clustering coefficient and the short path length of complex network to implement our strategy by numerical example and simulation. All the results demonstrate that VANET shows small world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The average path length of the network is simulated numerically, which indicates that the network shows small-world property and is rarely affected by the randomness. What’s more, we carry out extensive simulations of information propagation and mathematically prove the power law property when γ > 2. The results of this study provide useful information for VANET
Modeling and dynamical topology properties of VANET based on complex networks theory
Zhang, Hong; Li, Jie
2015-01-01
Vehicular Ad hoc Network (VANET) is a special subset of multi-hop Mobile Ad hoc Networks in which vehicles can not only communicate with each other but also with the fixed equipments along the roads through wireless interfaces. Recently, it has been discovered that essential systems in real world share similar properties. When they are regarded as networks, among which the dynamic topology structure of VANET system is an important issue. Many real world networks are actually growing with preferential attachment like Internet, transportation system and telephone network. Those phenomena have brought great possibility in finding a strategy to calibrate and control the topology parameters which can help find VANET topology change regulation to relieve traffic jam, prevent traffic accident and improve traffic safety. VANET is a typical complex network which has its basic characteristics. In this paper, we focus on the macroscopic Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) inter-vehicle communication network with complex network theory. In particular, this paper is the first one to propose a method analyzing the topological structure and performance of VANET and present the communications in VANET from a new perspective. Accordingly, we propose degree distribution, clustering coefficient and the short path length of complex network to implement our strategy by numerical example and simulation. All the results demonstrate that VANET shows small world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The average path length of the network is simulated numerically, which indicates that the network shows small-world property and is rarely affected by the randomness. What's more, we carry out extensive simulations of information propagation and mathematically prove the power law property when γ > 2. The results of this study provide useful information for VANET optimization from a
Modeling and dynamical topology properties of VANET based on complex networks theory
Energy Technology Data Exchange (ETDEWEB)
Zhang, Hong; Li, Jie, E-mail: prof.li@foxmail.com [School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, Wuhan, 430074 (China)
2015-01-15
Vehicular Ad hoc Network (VANET) is a special subset of multi-hop Mobile Ad hoc Networks in which vehicles can not only communicate with each other but also with the fixed equipments along the roads through wireless interfaces. Recently, it has been discovered that essential systems in real world share similar properties. When they are regarded as networks, among which the dynamic topology structure of VANET system is an important issue. Many real world networks are actually growing with preferential attachment like Internet, transportation system and telephone network. Those phenomena have brought great possibility in finding a strategy to calibrate and control the topology parameters which can help find VANET topology change regulation to relieve traffic jam, prevent traffic accident and improve traffic safety. VANET is a typical complex network which has its basic characteristics. In this paper, we focus on the macroscopic Vehicle-to-Infrastructure (V2I) and Vehicle-to-Vehicle (V2V) inter-vehicle communication network with complex network theory. In particular, this paper is the first one to propose a method analyzing the topological structure and performance of VANET and present the communications in VANET from a new perspective. Accordingly, we propose degree distribution, clustering coefficient and the short path length of complex network to implement our strategy by numerical example and simulation. All the results demonstrate that VANET shows small world network features and is characterized by a truncated scale-free degree distribution with power-law degree distribution. The average path length of the network is simulated numerically, which indicates that the network shows small-world property and is rarely affected by the randomness. What’s more, we carry out extensive simulations of information propagation and mathematically prove the power law property when γ > 2. The results of this study provide useful information for VANET optimization from a
Small Worlds Week: Raising Curiosity and Contributing to STEM
Ng, C.; Mayo, L.; Stephenson, B. E.; Keck, A.; Cline, T. D.; Lewis, E. M.
2015-12-01
Dwarf planets, comets, asteroids, and icy moons took center stage in the years 2014-2015 as multiple spacecraft (New Horizons, Dawn, Rosetta, Cassini) and ground-based observing campaigns observed these small and yet amazing celestial bodies. Just prior to the historic New Horizons encounter with the Pluto system, NASA celebrated Small Worlds Week (July 6-10) as a fully online program to highlight small worlds mission discoveries. Small Worlds Week leveraged the infrastructure of Sun-Earth Days that included a robust web design, exemplary education materials, hands-on fun activities, multimedia resources, science and career highlights, and a culminating event. Each day from July 6-9, a new class of solar system small worlds was featured on the website: Monday-comets, Tuesday-asteroids, Wednesday-icy moons, and Thursday-dwarf planets. Then on Friday, July 10, nine scientists from Goddard Space Flight Center, Jet Propulsion Laboratory, Naval Research Laboratory, and Lunar and Planetary Institute gathered online for four hours to answer questions from the public via Facebook and Twitter. Throughout the afternoon the scientists worked closely with a social media expert and several summer interns to reply to inquirers and to archive their chats. By all accounts, Small Worlds Week was a huge success. The group plans to improve and replicate the program during the school year with a more classroom focus, and then to build and extend the program to be held every year. For more information, visit http:// sunearthday.nasa.gov or catch us on Twitter, #nasasww.
Distributed Queuing in Dynamic Networks
Directory of Open Access Journals (Sweden)
Gokarna Sharma
2013-10-01
Full Text Available We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010 in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors are for the current round before they broadcast their messages. Queue requests may arrive over rounds at arbitrary nodes and the goal is to eventually enqueue them in a distributed queue. We present two algorithms that give a total distributed ordering of queue requests in this model. We measure the performance of our algorithms through round complexity, which is the total number of rounds needed to solve the distributed queuing problem. We show that in 1-interval connected graphs, where the communication links change arbitrarily between every round, it is possible to solve the distributed queueing problem in O(nk rounds using O(log n size messages, where n is the number of nodes in the network and k 0 is the concurrency level parameter that captures the minimum number of active queue requests in the system in any round. These results hold in any arbitrary (sequential, one-shot concurrent, or dynamic arrival of k queue requests in the system. Moreover, our algorithms ensure correctness in the sense that each queue request is eventually enqueued in the distributed queue after it is issued and each queue request is enqueued exactly once. We also provide an impossibility result for this distributed queuing problem in this model. To the best of our knowledge, these are the first solutions to the distributed queuing problem in adversarial dynamic networks.
Dynamics of network motifs in genetic regulatory networks
Institute of Scientific and Technical Information of China (English)
Li Ying; Liu Zeng-Rong; Zhang Jian-Bao
2007-01-01
Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.
DEAON: dynamically-evolving active overlay networks for scalable information retrieval
Institute of Scientific and Technical Information of China (English)
Huang Xinli; Ma Fanyuan
2007-01-01
In this paper,we propose the dynamically-evolving active overlay network(DEAON),which is an efficient,scalable yet simple protocol to facilitate applications of decentralized information retrieval in P2P networks.DEAON consists of three novel components:a Desirable Topology Construction and Adantation algorithm to guide the evolution of the overlay topology towards a small-world-like graph;a Semantic-based Neighbor Selection scheme to conduct an online neighbor ranking;a Topology-aware Intelligent Search mechanism to forward incoming queries to deliberately selected neighbors.We deploy and compare DEAON with other several existing distributed search techniques over static and dynamic environments.The results indicate that DEAON outperforms its competitors by achieving higher recall rate while using much less network resources,in both of the above environments.
Bialonski, S
2012-01-01
Understanding the dynamics of spatially extended systems represents a challenge in diverse scientific disciplines, ranging from physics and mathematics to the earth and climate sciences or the neurosciences. This challenge has stimulated the development of sophisticated data analysis approaches adopting concepts from network theory: systems are considered to be composed of subsystems (nodes) which interact with each other (represented by edges). In many studies, such complex networks of interactions have been derived from empirical time series for various spatially extended systems and have been repeatedly reported to possess the same, possibly desirable, properties (e.g. small-world characteristics and assortativity). In this thesis we study whether and how interaction networks are influenced by the analysis methodology, i.e. by the way how empirical data is acquired (the spatial and temporal sampling of the dynamics) and how nodes and edges are derived from multivariate time series. Our modeling and numeric...
Role of Clustering Coefficient on Cooperation Dynamics in Homogeneous Networks
Institute of Scientific and Technical Information of China (English)
WU Gang; GAO Kun; YANG Han-Xin; WANG Bing-Hong
2008-01-01
Based on previous works, we give further investigations on the Prisoners' Dilemma Game (PDG) on two different types of homogeneous networks, i.e. the homogeneous small-world network (HSWN) and the regular ring graph. We find that the so-called resonance-like character can occur on both the networks. Different from the viewpoint in previous publications, we think the small-world effect may be unnecessary to produce this character. Therefore, over these two types of networks, we suggest a common understanding in the viewpoint of clustering coefficient. Detailed simulation results can sustain our viewpoint quite well. Furthermore, we investigate the Snowdrift Game (SG) on the same networks. The difference between the outputs of the PDG and the SG can also sustain our viewpoint.
Asynchronous networks and event driven dynamics
Bick, Christian; Field, Michael
2017-02-01
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In this paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the following companion paper, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks.
Competitive Dynamics on Complex Networks
Zhao, Jiuhua; 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 much more likely to be the winner. These findings may shed new light on the role of n...
Coordination Games on Dynamical Networks
Directory of Open Access Journals (Sweden)
Enea Pestelacci
2010-07-01
Full Text Available We propose a model in which agents of a population interacting according to a network of contacts play games of coordination with each other and can also dynamically break and redirect links to neighbors if they are unsatisfied. As a result, there is co-evolution of strategies in the population and of the graph that represents the network of contacts. We apply the model to the class of pure and general coordination games. For pure coordination games, the networks co-evolve towards the polarization of different strategies. In the case of general coordination games our results show that the possibility of refusing neighbors and choosing different partners increases the success rate of the Pareto-dominant equilibrium.
Complex networks for streamflow dynamics
Directory of Open Access Journals (Sweden)
B. Sivakumar
2014-07-01
Full Text Available Streamflow modeling is an enormously challenging problem, due to the complex and nonlinear interactions between climate inputs and landscape characteristics over a wide range of spatial and temporal scales. A basic idea in streamflow studies is to establish connections that generally exist, but attempts to identify such connections are largely dictated by the problem at hand and the system components in place. While numerous approaches have been proposed in the literature, our understanding of these connections remains far from adequate. The present study introduces the theory of networks, and in particular complex networks, to examine the connections in streamflow dynamics, with a particular focus on spatial connections. Monthly streamflow data observed over a period of 52 years from a large network of 639 monitoring stations in the contiguous United States are studied. The connections in this streamflow network are examined using the concept of clustering coefficient, which is a measure of local density and quantifies the network's tendency to cluster. The clustering coefficient analysis is performed with several different threshold levels, which are based on correlations in streamflow data between the stations. The clustering coefficient values of the 639 stations are used to obtain important information about the connections in the network and their extent, similarity and differences between stations/regions, and the influence of thresholds. The relationship of the clustering coefficient with the number of links/actual links in the network and the number of neighbors is also addressed. The results clearly indicate the usefulness of the network-based approach for examining connections in streamflow, with important implications for interpolation and extrapolation, classification of catchments, and predictions in ungaged basins.
Network dynamics and systems biology
Norrell, Johannes A.
The physics of complex systems has grown considerably as a field in recent decades, largely due to improved computational technology and increased availability of systems level data. One area in which physics is of growing relevance is molecular biology. A new field, systems biology, investigates features of biological systems as a whole, a strategy of particular importance for understanding emergent properties that result from a complex network of interactions. Due to the complicated nature of the systems under study, the physics of complex systems has a significant role to play in elucidating the collective behavior. In this dissertation, we explore three problems in the physics of complex systems, motivated in part by systems biology. The first of these concerns the applicability of Boolean models as an approximation of continuous systems. Studies of gene regulatory networks have employed both continuous and Boolean models to analyze the system dynamics, and the two have been found produce similar results in the cases analyzed. We ask whether or not Boolean models can generically reproduce the qualitative attractor dynamics of networks of continuously valued elements. Using a combination of analytical techniques and numerical simulations, we find that continuous networks exhibit two effects---an asymmetry between on and off states, and a decaying memory of events in each element's inputs---that are absent from synchronously updated Boolean models. We show that in simple loops these effects produce exactly the attractors that one would predict with an analysis of the stability of Boolean attractors, but in slightly more complicated topologies, they can destabilize solutions that are stable in the Boolean approximation, and can stabilize new attractors. Second, we investigate ensembles of large, random networks. Of particular interest is the transition between ordered and disordered dynamics, which is well characterized in Boolean systems. Networks at the
On the agreement between small-world-like OFC model and real earthquakes
Energy Technology Data Exchange (ETDEWEB)
Ferreira, Douglas S.R., E-mail: douglas.ferreira@ifrj.edu.br [Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, Paracambi, RJ (Brazil); Geophysics Department, Observatório Nacional, Rio de Janeiro, RJ (Brazil); Papa, Andrés R.R., E-mail: papa@on.br [Geophysics Department, Observatório Nacional, Rio de Janeiro, RJ (Brazil); Instituto de Física, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ (Brazil); Menezes, Ronaldo, E-mail: rmenezes@cs.fit.edu [BioComplex Laboratory, Computer Sciences, Florida Institute of Technology, Melbourne (United States)
2015-03-20
In this article we implemented simulations of the OFC model for earthquakes for two different topologies: regular and small-world, where in the latter the links are randomly rewired with probability p. In both topologies, we have studied the distribution of time intervals between consecutive earthquakes and the border effects present in each one. In addition, we also have characterized the influence that the probability p produces in certain characteristics of the lattice and in the intensity of border effects. From the two topologies, networks of consecutive epicenters were constructed, that allowed us to analyze the distribution of connectivities of each one. In our results distributions arise belonging to a family of non-traditional distributions functions, which agrees with previous studies using data from actual earthquakes. Our results reinforce the idea that the Earth is in a critical self-organized state and furthermore point towards temporal and spatial correlations between earthquakes in different places. - Highlights: • OFC model simulations for regular and small-world topologies. • For small-world topology distributions agree remarkably well with actual earthquakes. • Reinforce the idea of a critical self-organized state for the Earth's crust. • Point towards temporal and spatial correlations between far earthquakes in far places.
Anomaly Detection in Dynamic Networks
Energy Technology Data Exchange (ETDEWEB)
Turcotte, Melissa [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-10-14
Anomaly detection in dynamic communication networks has many important security applications. These networks can be extremely large and so detecting any changes in their structure can be computationally challenging; hence, computationally fast, parallelisable methods for monitoring the network are paramount. For this reason the methods presented here use independent node and edge based models to detect locally anomalous substructures within communication networks. As a first stage, the aim is to detect changes in the data streams arising from node or edge communications. Throughout the thesis simple, conjugate Bayesian models for counting processes are used to model these data streams. A second stage of analysis can then be performed on a much reduced subset of the network comprising nodes and edges which have been identified as potentially anomalous in the first stage. The first method assumes communications in a network arise from an inhomogeneous Poisson process with piecewise constant intensity. Anomaly detection is then treated as a changepoint problem on the intensities. The changepoint model is extended to incorporate seasonal behavior inherent in communication networks. This seasonal behavior is also viewed as a changepoint problem acting on a piecewise constant Poisson process. In a static time frame, inference is made on this extended model via a Gibbs sampling strategy. In a sequential time frame, where the data arrive as a stream, a novel, fast Sequential Monte Carlo (SMC) algorithm is introduced to sample from the sequence of posterior distributions of the change points over time. A second method is considered for monitoring communications in a large scale computer network. The usage patterns in these types of networks are very bursty in nature and don’t fit a Poisson process model. For tractable inference, discrete time models are considered, where the data are aggregated into discrete time periods and probability models are fitted to the
van den Heuvel, M P; Stam, C J; Boersma, M; Hulshoff Pol, H E
2008-11-15
The brain is a complex dynamic system of functionally connected regions. Graph theory has been successfully used to describe the organization of such dynamic systems. Recent resting-state fMRI studies have suggested that inter-regional functional connectivity shows a small-world topology, indicating an organization of the brain in highly clustered sub-networks, combined with a high level of global connectivity. In addition, a few studies have investigated a possible scale-free topology of the human brain, but the results of these studies have been inconclusive. These studies have mainly focused on inter-regional connectivity, representing the brain as a network of brain regions, requiring an arbitrary definition of such regions. However, using a voxel-wise approach allows for the model-free examination of both inter-regional as well as intra-regional connectivity and might reveal new information on network organization. Especially, a voxel-based study could give information about a possible scale-free organization of functional connectivity in the human brain. Resting-state 3 Tesla fMRI recordings of 28 healthy subjects were acquired and individual connectivity graphs were formed out of all cortical and sub-cortical voxels with connections reflecting inter-voxel functional connectivity. Graph characteristics from these connectivity networks were computed. The clustering-coefficient of these networks turned out to be much higher than the clustering-coefficient of comparable random graphs, together with a short average path length, indicating a small-world organization. Furthermore, the connectivity distribution of the number of inter-voxel connections followed a power-law scaling with an exponent close to 2, suggesting a scale-free network topology. Our findings suggest a combined small-world and scale-free organization of the functionally connected human brain. The results are interpreted as evidence for a highly efficient organization of the functionally connected
Sensitive dependence of network dynamics on network structure
Nishikawa, Takashi; Motter, Adilson E
2016-01-01
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important longstanding problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. Here we show that such optimization can lead to sensitive dependence of the dynamics on the structure of the network. Specifically, we demonstrate that the stability of the dynamical state, as determined by the maximum Lyapunov exponent, can exhibit a cusp-like dependence on the number of nodes and links as well as on the size of perturbations applied to the network structure. As mechanisms underlying this sensitivity, we identify discontinuous transitions occurring in the complement of optimal networks and the prevalence of eigenvector degeneracy in these networks. These findings establish a unified characterization of networks optimized for dynamical stability in diffusively coupled systems, which we illustrate using Turing instability in act...
Dynamic properties of network motifs contribute to biological network organization.
Directory of Open Access Journals (Sweden)
Robert J Prill
2005-11-01
Full Text Available Biological networks, such as those describing gene regulation, signal transduction, and neural synapses, are representations of large-scale dynamic systems. Discovery of organizing principles of biological networks can be enhanced by embracing the notion that there is a deep interplay between network structure and system dynamics. Recently, many structural characteristics of these non-random networks have been identified, but dynamical implications of the features have not been explored comprehensively. We demonstrate by exhaustive computational analysis that a dynamical property--stability or robustness to small perturbations--is highly correlated with the relative abundance of small subnetworks (network motifs in several previously determined biological networks. We propose that robust dynamical stability is an influential property that can determine the non-random structure of biological networks.
Network dynamics in nanofilled polymers
Baeza, Guilhem P.; Dessi, Claudia; Costanzo, Salvatore; Zhao, Dan; Gong, Shushan; Alegria, Angel; Colby, Ralph H.; Rubinstein, Michael; Vlassopoulos, Dimitris; Kumar, Sanat K.
2016-04-01
It is well accepted that adding nanoparticles (NPs) to polymer melts can result in significant property improvements. Here we focus on the causes of mechanical reinforcement and present rheological measurements on favourably interacting mixtures of spherical silica NPs and poly(2-vinylpyridine), complemented by several dynamic and structural probes. While the system dynamics are polymer-like with increased friction for low silica loadings, they turn network-like when the mean face-to-face separation between NPs becomes smaller than the entanglement tube diameter. Gel-like dynamics with a Williams-Landel-Ferry temperature dependence then result. This dependence turns particle dominated, that is, Arrhenius-like, when the silica loading increases to ~31 vol%, namely, when the average nearest distance between NP faces becomes comparable to the polymer's Kuhn length. Our results demonstrate that the flow properties of nanocomposites are complex and can be tuned via changes in filler loading, that is, the character of polymer bridges which `tie' NPs together into a network.
Dynamic network management and service integration for airborne network
Pan, Wei; Li, Weihua
2009-12-01
The development of airborne network is conducive to resource sharing, flight management and interoperability in civilian and military aviation fields. To enhance the integrated ability of airborne network, the paper focuses on dynamic network management and service integration architecture for airborne network (DNMSIAN). Adaptive routing based on the mapping mechanism between connection identification and routing identification can provide diversified network access, and ensure the credibility and mobility of the aviation information exchange. Dynamic network management based on trustworthy cluster can ensure dynamic airborne network controllable and safe. Service integration based on semantic web and ontology can meet the customized and diversified needs for aviation information services. The DNMSIAN simulation platform demonstrates that our proposed methods can effectively perform dynamic network management and service integration.
Factorial graphical lasso for dynamic networks
Wit, E. C.; Abbruzzo, A.
2012-01-01
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this paper we focus on determining network structure. Estimating
The Analyses of Node Swapping Networks by New Graph Index
Toyota, N
2006-01-01
We have proposed two new dynamic networks where two node are swapped each other, and showed that the both networks behave as a small world like in the average path length but can not make any effective discussions on the clustering coefficient because of the topological invariant properties of the networks. In this article we introduce a new index, "hamming coefficient" or "multiplicity", that can act well for these dynamic networks. The hamming coefficient or multiplicity is shown essentially to behave as the clustering coefficient in the small world network proposed by Watts and Strogatz\\cite{Watt1}. By evaluating the new index, we uncover another properties of the two networks.
Factorial graphical lasso for dynamic networks
Wit, E C
2012-01-01
Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. There are many aspects of dynamical networks that require statistical considerations. In this paper we focus on determining network structure. Estimating dynamic networks is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is bigger than the number of observations. However, a characteristic of many networks is that they are sparse. For example, the molecular structure of genes make interactions with other components a highly-structured and therefore sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal constraints. We propose a structured Gaussian dynamical graphical model, where structures can consist of specific time dynamics, known presence or abse...
Tourism-planning network knowledge dynamics
DEFF Research Database (Denmark)
Dredge, Dianne
2014-01-01
, network agents, network boundaries and network resources. A case study of the development of the Next Generation Tourism Handbook (Queensland, Australia), a policy initiative that sought to bring tourism and land use planning knowledge closer together is presented. The case study illustrates...... that the tourism policy and land use planning networks operate in very different spheres and that context, network agents, network boundaries and network resources have a significant influence not only on knowledge dynamics but also on the capacity of network agents to overcome barriers to learning and to innovate.......This chapter explores the characteristics and functions of tourism networks as a first step in understanding how networks facilitate and reproduce knowledge. A framework to progress understandings of knowledge dynamics in tourism networks is presented that includes four key dimensions: context...
Electron Transport through Models for Small-World Nanomaterials
Solomon, Lazarus; Novotny, Mark
2008-03-01
We investigate the quantum transport of (spinless) electrons through simplified models related to small-world nanomaterials. We employ a tight-binding Hamiltonian, and obtain the transmission coefficient from a matrix solution of the associated time-independent Schrödinger Equation. The system studied corresponds to d=1 semi-infinite input and output leads, connected to a `blob' of N atoms. We first present exact results for N inter-connected atoms, a fully-connected graph. The exact solution, for any N, is given both for symmetric and non-symmetric connections between the `blob' and the input/output. We then present numerical results obtained by removing some of the connections within the N-site `blob', thereby approaching transport through a small-world nanomaterial [1-4]. [1] S. Caliskan, M.A. Novotny, and J.I. Cerd'a, J. Appl. Phys., 102, 013707 (2007). [2] M.A. Novotny et al., J. Appl. Phys., 97, 10B309 (2005). [3] M.A. Novotny and S.M. Wheeler, Braz. J. Physics 34, 395 (2004). [4] J. Yancey, M.A. Novotny, and S.R. Gwaltney, 2008 March Meeting presentation.
Strength dynamics of weighted evolving networks
Institute of Scientific and Technical Information of China (English)
Wu Jian-Jun; Gao Zi-You; Sun Hui-Jun
2007-01-01
In this paper, a simple model for the strength dynamics of weighted evolving networks is proposed to characterize the weighted networks. By considering the congestion effects, this approach can yield power law strength distribution appeared on the many real weighted networks, such as traffic networks, internet networks. Besides, the relationship between strength and degree is given. Numerical simulations indicate that the strength distribution is strongly related to the strength dynamics decline. The model also provides us with a better description of the real weighted networks.
Bayesian Overlapping Community Detection in Dynamic Networks
Ghorbani, Mahsa; Khodadadi, Ali
2016-01-01
Detecting community structures in social networks has gained considerable attention in recent years. However, lack of prior knowledge about the number of communities, and their overlapping nature have made community detection a challenging problem. Moreover, many of the existing methods only consider static networks, while most of real world networks are dynamic and evolve over time. Hence, finding consistent overlapping communities in dynamic networks without any prior knowledge about the number of communities is still an interesting open research problem. In this paper, we present an overlapping community detection method for dynamic networks called Dynamic Bayesian Overlapping Community Detector (DBOCD). DBOCD assumes that in every snapshot of network, overlapping parts of communities are dense areas and utilizes link communities instead of common node communities. Using Recurrent Chinese Restaurant Process and community structure of the network in the last snapshot, DBOCD simultaneously extracts the numbe...
Controlling edge dynamics in complex networks
Nepusz, Tamás
2011-01-01
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges of a network, and demonstrate that the controllability properties of this process significantly differ from simple nodal dynamics. Evaluation of real-world networks indicates that most of them are more controllable than their randomized counterparts. We also find that transcriptional regulatory networks are particularly easy to control. Analytic calculations show that networks with scale-free degree distributions have better controllability properties than uncorrelated networks, and positively correlated in- and out-degre...
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
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.
Hybrid Dynamic Network Data Envelopment Analysis
Directory of Open Access Journals (Sweden)
Ling Li
2015-01-01
Full Text Available Conventional DEA models make no hypothesis concerning the internal operations in a static situation. To open the “black box” and work with dynamic assessment issues synchronously, we put forward a hybrid model for evaluating the relative efficiencies of a set of DMUs over an observed time period with a composite of network DEA and dynamic DEA. We vertically deal with intermediate products between divisions with assignable inputs in the network structure and, horizontally, we extend network structure by means of a dynamic pattern with unrelated activities between two succeeding periods. The hybrid dynamic network DEA model proposed in this paper enables us to (i pry into the internal operations of DEA by another network structure, (ii obtain dynamic change of period efficiency, and (iii gain the overall dynamic efficiency of DMUs over the entire observed periods. We finally illustrate the calculation procedure of the proposed approach by a numerical example.
Capacity Analysis for Dynamic Space Networks
Institute of Scientific and Technical Information of China (English)
Yang Lu; Bo Li; Wenjing Kang; Gongliang Liu; Xueting Li
2015-01-01
To evaluate transmission rate of highly dynamic space networks, a new method for studying space network capacity is proposed in this paper. Using graph theory, network capacity is defined as the maximum amount of flows ground stations can receive per unit time. Combined with a hybrid constellation model, network capacity is calculated and further analyzed for practical cases. Simulation results show that network capacity will increase to different extents as link capacity, minimum ground elevation constraint and satellite onboard processing capability change. Considering the efficiency and reliability of communication networks, how to scientifically design satellite networks is also discussed.
Geographical threshold graphs with small-world and scale-free properties
Masuda, Naoki; Miwa, Hiroyoshi; Konno, Norio
2005-03-01
Many real networks are equipped with short diameters, high clustering, and power-law degree distributions. With preferential attachment and network growth, the model by Barabási and Albert simultaneously reproduces these properties, and geographical versions of growing networks have also been analyzed. However, nongrowing networks with intrinsic vertex weights often explain these features more plausibly, since not all networks are really growing. We propose a geographical nongrowing network model with vertex weights. Edges are assumed to form when a pair of vertices are spatially close and/or have large summed weights. Our model generalizes a variety of models as well as the original nongeographical counterpart, such as the unit disk graph, the Boolean model, and the gravity model, which appear in the contexts of percolation, wire communication, mechanical and solid physics, sociology, economy, and marketing. In appropriate configurations, our model produces small-world networks with power-law degree distributions. We also discuss the relation between geography, power laws in networks, and power laws in general quantities serving as vertex weights.
Revealing networks from dynamics: an introduction
Timme, Marc
2014-01-01
What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct interactions) from accessing the dynamics of the units. Potential applications range from interaction networks in physics, to chemical and metabolic reactions, protein and gene regulatory networks as well as neural circuits in biology and electric power grids or wireless sensor networks in engineering. Moreover, we briefly mention some standard ways of inferring effective or functional connectivity.
Learning dynamic Bayesian networks with mixed variables
DEFF Research Database (Denmark)
Bøttcher, Susanne Gammelgaard
This paper considers dynamic Bayesian networks for discrete and continuous variables. We only treat the case, where the distribution of the variables is conditional Gaussian. We show how to learn the parameters and structure of a dynamic Bayesian network and also how the Markov order can be learn....... An automated procedure for specifying prior distributions for the parameters in a dynamic Bayesian network is presented. It is a simple extension of the procedure for the ordinary Bayesian networks. Finally the W¨olfer?s sunspot numbers are analyzed....
Small-world phenomena in physics: the Ising model
Energy Technology Data Exchange (ETDEWEB)
Gitterman, M. [Department of Physics, Bar-Ilan University, Ramat-Gan (Israel)
2000-12-01
The Ising system with a small fraction of random long-range interactions is the simplest example of small-world phenomena in physics. Considering the latter both in an annealed and in a quenched state we conclude that: (a) the existence of random long-range interactions leads to a phase transition in the one-dimensional case and (b) there is a minimal average number p of these interactions per site (p<1 in the annealed state, and p{approx_equal}1 in the quenched state) needed for the appearance of the phase transition. Note that the average number of these bonds, pN/2, is much smaller than the total number of bonds, N{sup 2}/2. (author)
Dynamic information routing in complex networks
Kirst, Christoph; Battaglia, Demian
2015-01-01
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 generic mechanism specifically for oscillatory dynamics and analyze how individual unit properties, the network topology and external inputs coact 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 non-local network-wide communication. These results help...
Dynamic Analysis of Structures Using Neural Networks
Directory of Open Access Journals (Sweden)
N. Ahmadi
2008-01-01
Full Text Available In the recent years, neural networks are considered as the best candidate for fast approximation with arbitrary accuracy in the time consuming problems. Dynamic analysis of structures against earthquake has the time consuming process. We employed two kinds of neural networks: Generalized Regression neural network (GR and Back-Propagation Wavenet neural network (BPW, for approximating of dynamic time history response of frame structures. GR is a traditional radial basis function neural network while BPW categorized as a wavelet neural network. In BPW, sigmoid activation functions of hidden layer neurons are substituted with wavelets and weights training are achieved using Scaled Conjugate Gradient (SCG algorithm. Comparison the results of BPW with those of GR in the dynamic analysis of eight story steel frame indicates that accuracy of the properly trained BPW was better than that of GR and therefore, BPW can be efficiently used for approximate dynamic analysis of structures.
Synchronization of Intermittently Coupled Dynamical Networks
Directory of Open Access Journals (Sweden)
Gang Zhang
2013-01-01
Full Text Available This paper investigates the synchronization phenomenon of an intermittently coupled dynamical network in which the coupling among nodes can occur only at discrete instants and the coupling configuration of the network is time varying. A model of intermittently coupled dynamical network consisting of identical nodes is introduced. Based on the stability theory for impulsive differential equations, some synchronization criteria for intermittently coupled dynamical networks are derived. The network synchronizability is shown to be related to the second largest and the smallest eigenvalues of the coupling matrix, the coupling strength, and the impulsive intervals. Using the chaotic Chua system and Lorenz system as nodes of a dynamical network for simulation, respectively, the theoretical results are verified and illustrated.
MODELS FOR NETWORK DYNAMICS - A MARKOVIAN FRAMEWORK
LEENDERS, RTAJ
1995-01-01
A question not very often addressed in social network analysis relates to network dynamics and focuses on how networks arise and change. It alludes to the idea that ties do not arise or vanish randomly, but (partly) as a consequence of human behavior and preferences. Statistical models for modeling
A system dynamics model for communications networks
Awcock, A. J.; King, T. E. G.
1985-09-01
An abstract model of a communications network in system dynamics terminology is developed as implementation of this model by a FORTRAN program package developed at RSRE is discussed. The result of this work is a high-level simulation package in which the performance of adaptive routing algorithms and other network controls may be assessed for a network of arbitrary topology.
Using Network Dynamical Influence to Drive Consensus
Punzo, Giuliano; Young, George F.; MacDonald, Malcolm; Leonard, Naomi E.
2016-05-01
Consensus and decision-making are often analysed in the context of networks, with many studies focusing attention on ranking the nodes of a network depending on their relative importance to information routing. Dynamical influence ranks the nodes with respect to their ability to influence the evolution of the associated network dynamical system. In this study it is shown that dynamical influence not only ranks the nodes, but also provides a naturally optimised distribution of effort to steer a network from one state to another. An example is provided where the “steering” refers to the physical change in velocity of self-propelled agents interacting through a network. Distinct from other works on this subject, this study looks at directed and hence more general graphs. The findings are presented with a theoretical angle, without targeting particular applications or networked systems; however, the framework and results offer parallels with biological flocks and swarms and opportunities for design of technological networks.
Forced synchronization of autonomous dynamical Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Rivera-Durón, R. R., E-mail: roberto.rivera@ipicyt.edu.mx; Campos-Cantón, E., E-mail: eric.campos@ipicyt.edu.mx [División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P. (Mexico); Campos-Cantón, I. [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, C.P. 78000, San Luis Potosí, S.L.P. (Mexico); Gauthier, Daniel J. [Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708 (United States)
2015-08-15
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
Forced synchronization of autonomous dynamical Boolean networks.
Rivera-Durón, R R; Campos-Cantón, E; Campos-Cantón, I; Gauthier, Daniel J
2015-08-01
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
Dynamic Multi-class Network Loading Problem
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The dynamic network loading problem (DNLP) consists in determining on a congested network, timedependent arc volumes, together with arc and path travel times, given the time varying path flow departure rates over a finite time horizon. The objective of this paper is to present the formulation of an analytical dynamic multiclass network loading model. The model does not require the assumption of the FIFO condition. The existence of a solution to the model is shown.
Charge transport network dynamics in molecular aggregates
Energy Technology Data Exchange (ETDEWEB)
Jackson, Nicholas E. [Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry; Chen, Lin X. [Argonne National Lab. (ANL), Argonne, IL (United States). Chemical Science and Engineering Division; Ratner, Mark A. [Northwestern Univ., Evanston, IL (United States). Dept. of Chemistry
2016-07-20
Due to the nonperiodic nature of charge transport in disordered systems, generating insight into static charge transport networks, as well as analyzing the network dynamics, can be challenging. Here, we apply time-dependent network analysis to scrutinize the charge transport networks of two representative molecular semiconductors: a rigid n-type molecule, perylenediimide, and a flexible p-type molecule, bBDT(TDPP)2. Simulations reveal the relevant timescale for local transfer integral decorrelation to be ~100 fs, which is shown to be faster than that of a crystalline morphology of the same molecule. Using a simple graph metric, global network changes are observed over timescales competitive with charge carrier lifetimes. These insights demonstrate that static charge transport networks are qualitatively inadequate, whereas average networks often overestimate network connectivity. Finally, a simple methodology for tracking dynamic charge transport properties is proposed.
Cabral, Joana; Fernandes, Henrique M.; Van Hartevelt, Tim J.; James, Anthony C.; Kringelbach, Morten L.; Deco, Gustavo
2013-12-01
The neuropathology of schizophrenia remains unclear. Some insight has come from modern neuroimaging techniques, which offer an unparalleled opportunity to explore in vivo the structure and function of the brain. Using functional magnetic resonance imaging, it has been found that the large-scale resting-state functional connectivity (rsFC) in schizophrenia — measured as the temporal correlations of the blood-oxygen-level-dependent (BOLD) signal — exhibit altered network topology, with lower small-world index. The origin of these rsFC alterations and link with the underlying structural connectivity remain unclear. In this work, we used a computational model of spontaneous large-scale brain activity to explore the role of the structural connectivity in the large-scale dynamics of the brain in health and schizophrenia. The structural connectomes from 15 adolescent patients with early-onset schizophrenia and 15 age- and gender-matched controls were built from diffusion tensor imaging data to detect the white matter tracts between 90 brain areas. Brain areas, simulated using a reduced dynamic mean-field model, receive excitatory input from other areas in proportion to the number of fibre tracts between them. The simulated mean field activity was transformed into BOLD signal, and the properties of the simulated functional networks were analyzed. Our results suggest that the functional alterations observed in schizophrenia are not directly linked to alterations in the structural topology. Instead, subtly randomized and less small-world functional networks appear when the brain operates with lower global coupling, which shifts the dynamics from the optimal healthy regime.
Energy Technology Data Exchange (ETDEWEB)
Cabral, Joana [Theoretical and Computational Neuroscience Group, Center of Brain and Cognition, Universitat Pompeu Fabra, Barcelona 08018 (Spain); Department of Psychiatry, University of Oxford, Oxford OX3 7JX (United Kingdom); Fernandes, Henrique M.; Van Hartevelt, Tim J.; Kringelbach, Morten L. [Department of Psychiatry, University of Oxford, Oxford OX3 7JX (United Kingdom); Center of Functionally Integrative Neuroscience (CFIN), Aarhus University, Aarhus (Denmark); James, Anthony C. [Department of Psychiatry, University of Oxford, Oxford OX3 7JX (United Kingdom); Highfield Unit, Warneford Hospital, Oxford OX3 7JX (United Kingdom); Deco, Gustavo [Theoretical and Computational Neuroscience Group, Center of Brain and Cognition, Universitat Pompeu Fabra, Barcelona 08018 (Spain); Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona 08010 (Spain)
2013-12-15
The neuropathology of schizophrenia remains unclear. Some insight has come from modern neuroimaging techniques, which offer an unparalleled opportunity to explore in vivo the structure and function of the brain. Using functional magnetic resonance imaging, it has been found that the large-scale resting-state functional connectivity (rsFC) in schizophrenia — measured as the temporal correlations of the blood-oxygen-level-dependent (BOLD) signal — exhibit altered network topology, with lower small-world index. The origin of these rsFC alterations and link with the underlying structural connectivity remain unclear. In this work, we used a computational model of spontaneous large-scale brain activity to explore the role of the structural connectivity in the large-scale dynamics of the brain in health and schizophrenia. The structural connectomes from 15 adolescent patients with early-onset schizophrenia and 15 age- and gender-matched controls were built from diffusion tensor imaging data to detect the white matter tracts between 90 brain areas. Brain areas, simulated using a reduced dynamic mean-field model, receive excitatory input from other areas in proportion to the number of fibre tracts between them. The simulated mean field activity was transformed into BOLD signal, and the properties of the simulated functional networks were analyzed. Our results suggest that the functional alterations observed in schizophrenia are not directly linked to alterations in the structural topology. Instead, subtly randomized and less small-world functional networks appear when the brain operates with lower global coupling, which shifts the dynamics from the optimal healthy regime.
Controlling edge dynamics in complex networks
Nepusz, Tamás; Vicsek, Tamás
2012-01-01
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Here we introduce and evaluate a dynamical process defined on the edges ...
Müller, Viktor; Perdikis, Dionysios; von Oertzen, Timo; Sleimen-Malkoun, Rita; Jirsa, Viktor; Lindenberger, Ulman
2016-01-01
Resting-state and task-related recordings are characterized by oscillatory brain activity and widely distributed networks of synchronized oscillatory circuits. Electroencephalographic recordings (EEG) were used to assess network structure and network dynamics during resting state with eyes open and closed, and auditory oddball performance through phase synchronization between EEG channels. For this assessment, we constructed a hyper-frequency network (HFN) based on within- and cross-frequency coupling (WFC and CFC, respectively) at 10 oscillation frequencies ranging between 2 and 20 Hz. We found that CFC generally differentiates between task conditions better than WFC. CFC was the highest during resting state with eyes open. Using a graph-theoretical approach (GTA), we found that HFNs possess small-world network (SWN) topology with a slight tendency to random network characteristics. Moreover, analysis of the temporal fluctuations of HFNs revealed specific network topology dynamics (NTD), i.e., temporal changes of different graph-theoretical measures such as strength, clustering coefficient, characteristic path length (CPL), local, and global efficiency determined for HFNs at different time windows. The different topology metrics showed significant differences between conditions in the mean and standard deviation of these metrics both across time and nodes. In addition, using an artificial neural network approach, we found stimulus-related dynamics that varied across the different network topology metrics. We conclude that functional connectivity dynamics (FCD), or NTD, which was found using the HFN approach during rest and stimulus processing, reflects temporal and topological changes in the functional organization and reorganization of neuronal cell assemblies.
Smallest-Small-World Cellular Harmony Search for Optimization of Unconstrained Benchmark Problems
Directory of Open Access Journals (Sweden)
Sung Soo Im
2013-01-01
Full Text Available We presented a new hybrid method that combines cellular harmony search algorithms with the Smallest-Small-World theory. A harmony search (HS algorithm is based on musical performance processes that occur when a musician searches for a better state of harmony. Harmony search has successfully been applied to a wide variety of practical optimization problems. Most of the previous researches have sought to improve the performance of the HS algorithm by changing the pitch adjusting rate and harmony memory considering rate. However, there has been a lack of studies to improve the performance of the algorithm by the formation of population structures. Therefore, we proposed an improved HS algorithm that uses the cellular automata formation and the topological structure of Smallest-Small-World network. The improved HS algorithm has a high clustering coefficient and a short characteristic path length, having good exploration and exploitation efficiencies. Nine benchmark functions were applied to evaluate the performance of the proposed algorithm. Unlike the existing improved HS algorithm, the proposed algorithm is expected to have improved algorithmic efficiency from the formation of the population structure.
Temporal fidelity in dynamic social networks
DEFF Research Database (Denmark)
Stopczynski, Arkadiusz; Sapiezynski, Piotr; Pentland, Alex ‘Sandy’
2015-01-01
of the network dynamics can be used to inform the process of measuring social networks. The details of measurement are of particular importance when considering dynamic processes where minute-to-minute details are important, because collection of physical proximity interactions with high temporal resolution......It has recently become possible to record detailed social interactions in large social systems with high resolution. As we study these datasets, human social interactions display patterns that emerge at multiple time scales, from minutes to months. On a fundamental level, understanding...... is difficult and expensive. Here, we consider the dynamic network of proximity-interactions between approximately 500 individuals participating in the Copenhagen Networks Study. We show that in order to accurately model spreading processes in the network, the dynamic processes that occur on the order...
Pinning Synchronization of Switched Complex Dynamical Networks
Directory of Open Access Journals (Sweden)
Liming Du
2015-01-01
Full Text Available Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.
Psychology and social networks: a dynamic network theory perspective.
Westaby, James D; Pfaff, Danielle L; Redding, Nicholas
2014-04-01
Research on social networks has grown exponentially in recent years. However, despite its relevance, the field of psychology has been relatively slow to explain the underlying goal pursuit and resistance processes influencing social networks in the first place. In this vein, this article aims to demonstrate how a dynamic network theory perspective explains the way in which social networks influence these processes and related outcomes, such as goal achievement, performance, learning, and emotional contagion at the interpersonal level of analysis. The theory integrates goal pursuit, motivation, and conflict conceptualizations from psychology with social network concepts from sociology and organizational science to provide a taxonomy of social network role behaviors, such as goal striving, system supporting, goal preventing, system negating, and observing. This theoretical perspective provides psychologists with new tools to map social networks (e.g., dynamic network charts), which can help inform the development of change interventions. Implications for social, industrial-organizational, and counseling psychology as well as conflict resolution are discussed, and new opportunities for research are highlighted, such as those related to dynamic network intelligence (also known as cognitive accuracy), levels of analysis, methodological/ethical issues, and the need to theoretically broaden the study of social networking and social media behavior. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
Quasispecies dynamics with network constraints.
Barbosa, Valmir C; Donangelo, Raul; Souza, Sergio R
2012-11-07
A quasispecies is a set of interrelated genotypes that have reached a stationary state while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible for any genotype to mutate into any other, but recent finds indicate that this assumption is not necessarily true. Here we revisit the traditional quasispecies theory by adopting a network structure to constrain the occurrence of mutations. Such structure is governed by a random-graph model, whose single parameter (a probability p) controls both the graph's density and the dynamics of mutation. We contribute two further modifications to the theory, one to account for the fact that different loci in a genotype may be differently susceptible to the occurrence of mutations, the other to allow for a more plausible description of the transition from adaptation to degeneracy of the quasispecies as p is increased. We give analytical and simulation results for the usual case of binary genotypes, assuming the fitness landscape in which a genotype's fitness decays exponentially with its Hamming distance to the wild type. These results support the theory's assertions regarding the adaptation of the quasispecies to the fitness landscape and also its possible demise as a function of p.
Emergent Opinion Dynamics on Endogenous Networks
Gulyás, L; Dugundji, Elenna R.
2006-01-01
In recent years networks have gained unprecedented attention in studying a broad range of topics, among them in complex systems research. In particular, multi-agent systems have seen an increased recognition of the importance of the interaction topology. It is now widely recognized that emergent phenomena can be highly sensitive to the structure of the interaction network connecting the system's components, and there is a growing body of abstract network classes, whose contributions to emergent dynamics are well-understood. However, much less understanding have yet been gained about the effects of network dynamics, especially in cases when the emergent phenomena feeds back to and changes the underlying network topology. Our work starts with the application of the network approach to discrete choice analysis, a standard method in econometric estimation, where the classic approach is grounded in individual choice and lacks social network influences. In this paper, we extend our earlier results by considering th...
Global Synchronization of General Delayed Dynamical Networks
Institute of Scientific and Technical Information of China (English)
LI Zhi
2007-01-01
Global synchronization of general delayed dynamical networks with linear coupling are investigated. A sufficient condition for the global synchronization is obtained by using the linear matrix inequality and introducing a reference state. This condition is simply given based on the maximum nonzero eigenvalue of the network coupling matrix. Moreover, we show how to construct the coupling matrix to guarantee global synchronization of network,which is very convenient to use. A two-dimension system with delay as a dynamical node in network with global coupling is finally presented to verify the theoretical results of the proposed global synchronization scheme.
Mori, Hiroki; Okuyama, Yuji; Asada, Minoru
2017-01-01
Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797
Maximum entropy reconstructions of dynamic signaling networks from quantitative proteomics data.
Locasale, Jason W; Wolf-Yadlin, Alejandro
2009-08-26
Advances in mass spectrometry among other technologies have allowed for quantitative, reproducible, proteome-wide measurements of levels of phosphorylation as signals propagate through complex networks in response to external stimuli under different conditions. However, computational approaches to infer elements of the signaling network strictly from the quantitative aspects of proteomics data are not well established. We considered a method using the principle of maximum entropy to infer a network of interacting phosphotyrosine sites from pairwise correlations in a mass spectrometry data set and derive a phosphorylation-dependent interaction network solely from quantitative proteomics data. We first investigated the applicability of this approach by using a simulation of a model biochemical signaling network whose dynamics are governed by a large set of coupled differential equations. We found that in a simulated signaling system, the method detects interactions with significant accuracy. We then analyzed a growth factor mediated signaling network in a human mammary epithelial cell line that we inferred from mass spectrometry data and observe a biologically interpretable, small-world structure of signaling nodes, as well as a catalog of predictions regarding the interactions among previously uncharacterized phosphotyrosine sites. For example, the calculation places a recently identified tumor suppressor pathway through ARHGEF7 and Scribble, in the context of growth factor signaling. Our findings suggest that maximum entropy derived network models are an important tool for interpreting quantitative proteomics data.
Complex Network Characteristics and Invulnerability Simulating Analysis of Supply Chain
Hui-Huang Chen; Ai-Min Lin
2012-01-01
To study the characteristics of the complex supply chain, a invulnerability analysis method based on the complex network theory is proposed. The topological structure and dynamic characteristics of the complex supply chain network were analyzed. The fact was found that the network is with general characteristics of the complex network, and with the characteristics of small-world network and scale-free network. A simulation experiment was made on the invulnerability of the supply chain network...
Symmetry in Critical Random Boolean Networks Dynamics
Bassler, Kevin E.; Hossein, Shabnam
2014-03-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.
Coevolutionary dynamics of networks and games under birth-death and birth mechanisms
Huang, Z.-G.; Wu, Z.-X.; Xu, X.-J.; Guan, J.-Y.; Wang, Y.-H.
2007-08-01
There is much interest in studying evolutionary games in structured populations, in order to understand how cooperation emerges in communities of egoistic agents. In this paper, we consider a new mechanism for cooperation to survive on networks. Agents are designed to reproduce offspring in proportion to their fitness, i.e., the aggregate payoffs they collected in the previous Prisoner's Dilemma game with neighbours. The population then evolves either by an individual giving birth to an offspring that takes over a random neighbour (birth-death process dynamics as the competition for resources already occupied by others) or by an individual constructing one new site from unexploited resources for its offspring (birth process dynamics as the competition for the unexploited resources which induces the extension of system). The underlying interaction network thus evolves and expands simultaneously with the population dynamics. The birth process dynamics is proved to be one new route that favours cooperators, under which cooperators can successfully resist the invasion of defectors in spite of large cost. Furthermore, under this “birth-death & birth” mechanism, the resulting network has a scale-free degree distribution, a small-world property, and hierarchical topology.
Complex networks repair strategies: Dynamic models
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 and enhances network invulnerability.
Network games theory, models, and dynamics
Ozdaglar, Asu
2011-01-01
Traditional network optimization focuses on a single control objective in a network populated by obedient users and limited dispersion of information. However, most of today's networks are large-scale with lack of access to centralized information, consist of users with diverse requirements, and are subject to dynamic changes. These factors naturally motivate a new distributed control paradigm, where the network infrastructure is kept simple and the network control functions are delegated to individual agents which make their decisions independently (""selfishly""). The interaction of multiple
Dynamics of comb-of-comb networks
Liu, Hongxiao; Lin, Yuan; Dolgushev, Maxim; Zhang, Zhongzhi
2016-03-01
The dynamics of complex networks, a current hot topic in many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we consider the deterministic networks which can be viewed as "comb-of-comb" iterative structures. For their Laplacian spectra we find analytical equations involving Chebyshev polynomials whose properties allow one to analyze the spectra in deep. Here, in particular, we find that in the infinite size limit the corresponding spectral dimension goes as ds→2 . The ds leaves its fingerprint on many dynamical processes, as we exemplarily show by considering the dynamical properties of polymer networks, including single monomer displacement under a constant force, mechanical relaxation, and fluorescence depolarization.
Identifying Community Structures in Dynamic Networks
Alvari, Hamidreza; Sukthankar, Gita; Lakkaraju, Kiran
2016-01-01
Most real-world social networks are inherently dynamic, composed of communities that are constantly changing in membership. To track these evolving communities, we need dynamic community detection techniques. This article evaluates the performance of a set of game theoretic approaches for identifying communities in dynamic networks. Our method, D-GT (Dynamic Game Theoretic community detection), models each network node as a rational agent who periodically plays a community membership game with its neighbors. During game play, nodes seek to maximize their local utility by joining or leaving the communities of network neighbors. The community structure emerges after the game reaches a Nash equilibrium. Compared to the benchmark community detection methods, D-GT more accurately predicts the number of communities and finds community assignments with a higher normalized mutual information, while retaining a good modularity.
Boolean networks with reliable dynamics
Peixoto, Tiago P
2009-01-01
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks, and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occur, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen...
Diffusion Dynamics with Changing Network Composition
Baños, Raquel A; Wang, Ning; Moreno, Yamir; González-Bailón, Sandra
2013-01-01
We analyze information diffusion using empirical data that tracks online communication around two instances of mass political mobilization, including the year that lapsed in-between the protests. We compare the global properties of the topological and dynamic networks through which communication took place as well as local changes in network composition. We show that changes in network structure underlie aggregated differences on how information diffused: an increase in network hierarchy is accompanied by a reduction in the average size of cascades. The increasing hierarchy affects not only the underlying communication topology but also the more dynamic structure of information exchange; the increase is especially noticeable amongst certain categories of nodes (or users). This suggests that the relationship between the structure of networks and their function in diffusing information is not as straightforward as some theoretical models of diffusion in networks imply.
On the agreement between small-world-like OFC model and real earthquakes
Ferreira, Douglas S R; Menezes, Ronaldo
2014-01-01
In this article we implemented simulations of the OFC model for earthquakes for two different topologies: regular and small-world, where in the latter the links are randomly rewired with probability $p$ . In both topologies, we have studied the distribution of time intervals between consecutive earthquakes and the border effects present in each one. In addition, we also have characterized the influence that the probability $p$ produces in certain characteristics of the lattice and in the intensity of border effects. From the two topologies, networks of consecutive epicenters were constructed, that allowed us to analyze the distribution of connectivities of each one. In our results distributions arise belonging to a family of non-traditional distributions functions, which agrees with previous studies using data from actual earthquakes. Our results reinforce the idea that the Earth is in a critical self-organized state and furthermore point towards temporal and spatial correlations between earthquakes in differ...
Mapping small-world properties through development in the human brain: disruption in schizophrenia.
Directory of Open Access Journals (Sweden)
Dardo Tomasi
Full Text Available Evidence from imaging studies suggests that the human brain has a small-world network topology that might be disrupted in certain brain disorders. However, current methodology is based on global graph theory measures, such as clustering, C, characteristic path length, L, and small-worldness, S, that lack spatial specificity and are insufficient to identify regional brain abnormalities. Here we propose novel ultra-fast methodology for mapping local properties of brain network topology such as local C, L and S (lC, lL and lS in the human brain at 3-mm isotropic resolution from 'resting-state' magnetic resonance imaging data. Test-retest datasets from 40 healthy children/adolescents were used to demonstrate the overall good reliability of the measures across sessions and computational parameters (intraclass correlation > 0.5 for lC and lL and their low variability across subjects (< 29%. Whereas regions with high local functional connectivity density (lFCD; local degree in posterior parietal and occipital cortices demonstrated high lC and short lL, subcortical regions (globus pallidus, thalamus, hippocampus and amygdala, cerebellum (lobes and vermis, cingulum and temporal cortex also had high, lS, demonstrating stronger small-world topology than other hubs. Children/adolescents had stronger lFCD, higher lC and longer lL in most cortical regions and thalamus than 74 healthy adults, consistent with pruning of functional connectivity during maturation. In contrast, lFCD, lC and lL were weaker in thalamus and midbrain, and lL was shorter in frontal cortical regions and cerebellum for 69 schizophrenia patients than for 74 healthy controls, suggesting exaggerated pruning of connectivity in schizophrenia. Follow up correlation analyses for seeds in thalamus and midbrain uncovered lower positive connectivity of these regions in thalamus, putamen, cerebellum and frontal cortex (cingulum, orbitofrontal, inferior frontal and lower negative connectivity in
Dynamical Adaptation in Terrorist Cells/Networks
DEFF Research Database (Denmark)
Hussain, Dil Muhammad Akbar; Ahmed, Zaki
2010-01-01
Typical terrorist cells/networks have dynamical structure as they evolve or adapt to changes which may occur due to capturing or killing of a member of the cell/network. Analytical measures in graph theory like degree centrality, betweenness and closeness centralities are very common and have long...
Collective dynamics of active cytoskeletal networks
Köhler, Simone; Bausch, Andreas R
2011-01-01
Self organization mechanisms are essential for the cytoskeleton to adapt to the requirements of living cells. They rely on the intricate interplay of cytoskeletal filaments, crosslinking proteins and molecular motors. Here we present an in vitro minimal model system consisting of actin filaments, fascin and myosin-II filaments exhibiting pulsative collective long range dynamics. The reorganizations in the highly dynamic steady state of the active gel are characterized by alternating periods of runs and stalls resulting in a superdiffusive dynamics of the network's constituents. They are dominated by the complex competition of crosslinking molecules and motor filaments in the network: Collective dynamics are only observed if the relative strength of the binding of myosin-II filaments to the actin network allows exerting high enough forces to unbind actin/fascin crosslinks. The feedback between structure formation and dynamics can be resolved by combining these experiments with phenomenological simulations base...
Symmetry in critical random Boolean network dynamics
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Network Physiology: How Organ Systems Dynamically Interact.
Bartsch, Ronny P; Liu, Kang K L; Bashan, Amir; Ivanov, Plamen Ch
2015-01-01
We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems.
Network Physiology: How Organ Systems Dynamically Interact.
Directory of Open Access Journals (Sweden)
Ronny P Bartsch
Full Text Available We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS, we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems.
Local Checkability in Dynamic Networks
DEFF Research Database (Denmark)
Förster, Klaus-Tycho; Richter, Oliver; Seidel, Jochen
2017-01-01
In this work we study local checkability of network properties considering inconsistency throughout the verification process. We use disappearing and appearing edges to model inconsistency and prover-verifier-pairs (PVPs) for verification. We say that a network property N is locally checkable und...
Metric projection for dynamic multiplex networks
Jurman, Giuseppe
2016-01-01
Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time series is still an open problem. Here we propose a two-steps strategy to tackle this problem based on the concept of distance (metric) between networks. Given a multiplex graph, first a network of networks is built for each time steps, and then a real valued time series is obtained by the sequence of (simple) networks by evaluating the distance from the first element of the series. The effectiveness of this approach in detecting the occurring changes along the original time series is shown on a synthetic example first, and then on the Gulf dataset of political events.
Dynamic bandwidth allocation in GPON networks
DEFF Research Database (Denmark)
Ozimkiewiez, J.; Ruepp, Sarah Renée; Dittmann, Lars
2009-01-01
Two Dynamic Bandwidth Allocation algorithms used for coordination of the available bandwidth between end users in a GPON network have been simulated using OPNET to determine and compare the performance, scalability and efficiency of status reporting and non status reporting dynamic bandwidth allo...
Yang, Xianxia; Yan, Meichen; Sharafat, Rajput Ramiz; Yang, Jian
2016-01-01
For many power-limited networks, such as wireless sensor networks and mobile ad hoc networks, maximizing the network lifetime is the first concern in the related designing and maintaining activities. We study the network lifetime from the perspective of network science. In our dynamic network, nodes are assigned a fixed amount of energy initially and consume the energy in the delivery of packets. We divided the network traffic flow into four states: no, slow, fast, and absolute congestion states. We derive the network lifetime by considering the state of the traffic flow. We find that the network lifetime is generally opposite to traffic congestion in that the more congested traffic, the less network lifetime. We also find the impacts of factors such as packet generation rate, communication radius, node moving speed, etc., on network lifetime and traffic congestion.
Markovian dynamics on complex reaction networks
Energy Technology Data Exchange (ETDEWEB)
Goutsias, J., E-mail: goutsias@jhu.edu; Jenkinson, G., E-mail: jenkinson@jhu.edu
2013-08-10
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.
Markovian Dynamics on Complex Reaction Networks
Goutsias, John
2012-01-01
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 underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the 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...
Using relaxational dynamics to reduce network congestion
Piontti, Ana L. Pastore y.; La Rocca, Cristian E.; Toroczkai, Zoltán; Braunstein, Lidia A.; Macri, Pablo A.; López, Eduardo
2008-09-01
We study the effects of relaxational dynamics on congestion pressure in scale-free (SF) networks by analyzing the properties of the corresponding gradient networks (Toroczkai and Bassler 2004 Nature 428 716). Using the Family model (Family and Bassler 1986 J. Phys. A: Math. Gen. 19 L441) from surface-growth physics as single-step load-balancing dynamics, we show that the congestion pressure considerably drops on SF networks when compared with the same dynamics on random graphs. This is due to a structural transition of the corresponding gradient network clusters, which self-organize so as to reduce the congestion pressure. This reduction is enhanced when lowering the value of the connectivity exponent λ towards 2.
Cognitive radio networks dynamic resource allocation schemes
Wang, Shaowei
2014-01-01
This SpringerBrief presents a survey of dynamic resource allocation schemes in Cognitive Radio (CR) Systems, focusing on the spectral-efficiency and energy-efficiency in wireless networks. It also introduces a variety of dynamic resource allocation schemes for CR networks and provides a concise introduction of the landscape of CR technology. The author covers in detail the dynamic resource allocation problem for the motivations and challenges in CR systems. The Spectral- and Energy-Efficient resource allocation schemes are comprehensively investigated, including new insights into the trade-off
Evolution of cooperation on stochastic dynamical networks.
Directory of Open Access Journals (Sweden)
Bin Wu
Full Text Available Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are, the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.
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.
Competing dynamic phases of active polymer networks
Freedman, Simon; Banerjee, Shiladitya; Dinner, Aaron R.
Recent experiments on in-vitro reconstituted assemblies of F-actin, myosin-II motors, and cross-linking proteins show that tuning local network properties can changes the fundamental biomechanical behavior of the system. For example, by varying cross-linker density and actin bundle rigidity, one can switch between contractile networks useful for reshaping cells, polarity sorted networks ideal for directed molecular transport, and frustrated networks with robust structural properties. To efficiently investigate the dynamic phases of actomyosin networks, we developed a coarse grained non-equilibrium molecular dynamics simulation of model semiflexible filaments, molecular motors, and cross-linkers with phenomenologically defined interactions. The simulation's accuracy was verified by benchmarking the mechanical properties of its individual components and collective behavior against experimental results at the molecular and network scales. By adjusting the model's parameters, we can reproduce the qualitative phases observed in experiment and predict the protein characteristics where phase crossovers could occur in collective network dynamics. Our model provides a framework for understanding cells' multiple uses of actomyosin networks and their applicability in materials research. Supported by the Department of Defense (DoD) through the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.
Dynamics of deceptive interactions in social networks
Barrio, Rafael A; Dunbar, Robin; Iñiguez, Gerardo; Kaski, Kimmo
2015-01-01
In this paper we examine the role of lies in human social relations by implementing some salient characteristics of deceptive interactions into an opinion formation model, so as to describe the dynamical behaviour of a social network more realistically. In this model we take into account such basic properties of social networks as the dynamics of the intensity of interactions, the influence of public opinion, and the fact that in every human interaction it might be convenient to deceive or withhold information depending on the instantaneous situation of each individual in the network. We find that lies shape the topology of social networks, especially the formation of tightly linked, small communities with loose connections between them. We also find that agents with a larger proportion of deceptive interactions are the ones that connect communities of different opinion, and in this sense they have substantial centrality in the network. We then discuss the consequences of these results for the social behaviou...
Control theory of digitally networked dynamic systems
Lunze, Jan
2013-01-01
The book gives an introduction to networked control systems and describes new modeling paradigms, analysis methods for event-driven, digitally networked systems, and design methods for distributed estimation and control. Networked model predictive control is developed as a means to tolerate time delays and packet loss brought about by the communication network. In event-based control the traditional periodic sampling is replaced by state-dependent triggering schemes. Novel methods for multi-agent systems ensure complete or clustered synchrony of agents with identical or with individual dynamic
Dynamical networks reconstructed from time series
Levnajić, Zoran
2012-01-01
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By statistically examining the correlations between motions displayed by network nodes, we derive a simple equation that directly yields the adjacency matrix, assuming the intra-network interaction functions to be known. We illustrate the method's implementation on a simple example and discuss the dependence of the reconstruction precision on the properties of time series. Our method is applicable to any network, allowing for reconstruction precision to be maximized, and errors to be estimated.
Synchronization of fractional order complex dynamical networks
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.
Evolutionary dynamics of prokaryotic transcriptional regulatory networks.
Madan Babu, M; Teichmann, Sarah A; Aravind, L
2006-04-28
The structure of complex transcriptional regulatory networks has been studied extensively in certain model organisms. However, the evolutionary dynamics of these networks across organisms, which would reveal important principles of adaptive regulatory changes, are poorly understood. We use the known transcriptional regulatory network of Escherichia coli to analyse the conservation patterns of this network across 175 prokaryotic genomes, and predict components of the regulatory networks for these organisms. We observe that transcription factors are typically less conserved than their target genes and evolve independently of them, with different organisms evolving distinct repertoires of transcription factors responding to specific signals. We show that prokaryotic transcriptional regulatory networks have evolved principally through widespread tinkering of transcriptional interactions at the local level by embedding orthologous genes in different types of regulatory motifs. Different transcription factors have emerged independently as dominant regulatory hubs in various organisms, suggesting that they have convergently acquired similar network structures approximating a scale-free topology. We note that organisms with similar lifestyles across a wide phylogenetic range tend to conserve equivalent interactions and network motifs. Thus, organism-specific optimal network designs appear to have evolved due to selection for specific transcription factors and transcriptional interactions, allowing responses to prevalent environmental stimuli. The methods for biological network analysis introduced here can be applied generally to study other networks, and these predictions can be used to guide specific experiments.
Dynamic simulation of regulatory networks using SQUAD
Directory of Open Access Journals (Sweden)
Xenarios Ioannis
2007-11-01
Full Text Available Abstract Background The ambition of most molecular biologists is the understanding of the intricate network of molecular interactions that control biological systems. As scientists uncover the components and the connectivity of these networks, it becomes possible to study their dynamical behavior as a whole and discover what is the specific role of each of their components. Since the behavior of a network is by no means intuitive, it becomes necessary to use computational models to understand its behavior and to be able to make predictions about it. Unfortunately, most current computational models describe small networks due to the scarcity of kinetic data available. To overcome this problem, we previously published a methodology to convert a signaling network into a dynamical system, even in the total absence of kinetic information. In this paper we present a software implementation of such methodology. Results We developed SQUAD, a software for the dynamic simulation of signaling networks using the standardized qualitative dynamical systems approach. SQUAD converts the network into a discrete dynamical system, and it uses a binary decision diagram algorithm to identify all the steady states of the system. Then, the software creates a continuous dynamical system and localizes its steady states which are located near the steady states of the discrete system. The software permits to make simulations on the continuous system, allowing for the modification of several parameters. Importantly, SQUAD includes a framework for perturbing networks in a manner similar to what is performed in experimental laboratory protocols, for example by activating receptors or knocking out molecular components. Using this software we have been able to successfully reproduce the behavior of the regulatory network implicated in T-helper cell differentiation. Conclusion The simulation of regulatory networks aims at predicting the behavior of a whole system when subject
Dynamical evolution of the community structure of complex earthquake network
Abe, Sumiyoshi
2012-01-01
Earthquake network is known to be complex in the sense that it is scale-free, small-world, hierarchically organized and assortatively mixed. Here, the time evolution of earthquake networks is analyzed around main shocks in the context of the community structure. It is found that the maximum of the modularity measure quantifying existence of communities exhibits a peculiar behavior: its maximum value stays at a large value before a main shock, suddenly drops to a small values at the main shock, and then increases to relax to a large value again relatively slowly. In this way, a main shock is characterized in the language of theory of complex networks. The result is also interpreted in terms of the clustering structure of the earthquake network.
Failure dynamics of the global risk network
Szymanski, Boleslaw K; Asztalos, Andrea; Sreenivasan, Sameet
2013-01-01
The risks faced by modern societies form an intricately interconnected network that often underlies crisis situations. Yet, little is known about the ways in which risks materializing across different domains influence each other. Here we present an approach in which experts' assessment of network dynamics is mapped into state transition probabilities in the model of network evolution. This approach enables us to analyze difficult to quantify risks, such as geo-political or social. The model is optimized using historical data on risk materialization. We apply this approach to the World Economic Forum Global Risk Network to quantify the adverse effects of risk interdependency. The optimized model can predict how changes in risk characteristics impact future states of the risk network. Thus, our approach facilitates actionable insights for mitigating globally networked risks.
Random graph models for dynamic networks
Zhang, Xiao; Newman, M E J
2016-01-01
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.
Altered functional connectivity and small-world in mesial temporal lobe epilepsy.
Directory of Open Access Journals (Sweden)
Wei Liao
Full Text Available BACKGROUND: The functional architecture of the human brain has been extensively described in terms of functional connectivity networks, detected from the low-frequency coherent neuronal fluctuations that can be observed in a resting state condition. Little is known, so far, about the changes in functional connectivity and in the topological properties of functional networks, associated with different brain diseases. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we investigated alterations related to mesial temporal lobe epilepsy (mTLE, using resting state functional magnetic resonance imaging on 18 mTLE patients and 27 healthy controls. Functional connectivity among 90 cortical and subcortical regions was measured by temporal correlation. The related values were analyzed to construct a set of undirected graphs. Compared to controls, mTLE patients showed significantly increased connectivity within the medial temporal lobes, but also significantly decreased connectivity within the frontal and parietal lobes, and between frontal and parietal lobes. Our findings demonstrated that a large number of areas in the default-mode network of mTLE patients showed a significantly decreased number of connections to other regions. Furthermore, we observed altered small-world properties in patients, along with smaller degree of connectivity, increased n-to-1 connectivity, smaller absolute clustering coefficients and shorter absolute path length. CONCLUSIONS/SIGNIFICANCE: We suggest that the mTLE alterations observed in functional connectivity and topological properties may be used to define tentative disease markers.
Relevance of Dynamic Clustering to Biological Networks
Kaneko, K
1993-01-01
Abstract Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered states with chaotic itinerancy. First, clustering with bit structures in a hypercubic lattice is studied. Spontaneous formation and destruction of relevant bits are found, which give self-organizing, and chaotic genetic algorithms. When spontaneous changes of effective couplings are introduced, chaotic itinerancy of clusterings is widely seen through a feedback mechanism, which supports dynamic stability allowing for complexity and diversity, known as homeochaos. Second, synaptic dynamics of couplings is studied in relation with neural dynamics. The clustering structure is formed with a balance between external inputs and internal dynamics. Last, an extension allowing for the growth of the number of elements is given, in connection with cell differentiation. Effecti...
Directory of Open Access Journals (Sweden)
Cornelis Jan Stam
2010-09-01
Full Text Available A network of 32 or 64 connected neural masses, each representing a large population of interacting excitatory and inhibitory neurons and generating an EEG / MEG like output signal, was used to demonstrate how an interaction between dynamics and connectivity might explain the emergence of complex network features, in particular modularity. Network evolution was modeled by two processes: (i synchronization dependent plasticity (SDP and (ii growth dependent plasticity (GDP. In the case of SDP, connections between neural masses were strengthened when they were strongly synchronized, and were weakened when they were not. GDP was modeled as a homeostatic process with random, distance dependent outgrowth of new connections between neural masses. GDP alone resulted in stable networks with distance dependent connection strengths, typical small-world features, but no degree correlations and only weak modularity. SDP applied to random networks induced clustering, but no clear modules. Stronger modularity evolved only through an interaction of SDP and GDP, with the number and size of the modules depending on the relative strength of both processes, as well as on the size of the network. Lesioning part of the network, after a stable state was achieved, resulted in a temporary disruption of the network structure. The model gives a possible scenario to explain how modularity can arise in developing brain networks, and makes predictions about the time course of network changes during development and following acute lesions.
Dynamics-based centrality for directed networks
Masuda, Naoki; Kori, Hiroshi
2010-11-01
Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.
The dynamics of transmission and the dynamics of networks.
Farine, Damien
2017-05-01
A toy example depicted here highlighting the results of a study in this issue of the Journal of Animal Ecology that investigates the impact of network dynamics on potential disease outbreaks. Infections (stars) that spread by contact only (left) reduce the predicted outbreak size compared to situations where individuals can become infected by moving through areas that previously contained infected individuals (right). This is potentially important in species where individuals, or in this case groups, have overlapping ranges (as depicted on the top right). Incorporating network dynamics that maintain information about the ordering of contacts (central blocks; including the ordering of spatial overlap as noted by the arrows that highlight the blue group arriving after the red group in top-right of the figure) is important for capturing how a disease might not have the opportunity to spread to all individuals. By contrast, a static or 'average' network (lower blocks) does not capture any of these dynamics. Interestingly, although static networks generally predict larger outbreak sizes, the authors find that in cases when transmission probability is low, this prediction can switch as a result of changes in the estimated intensity of contacts among individuals. [Colour figure can be viewed at wileyonlinelibrary.com]. Springer, A., Kappeler, P.M. & Nunn, C.L. (2017) Dynamic vs. static social networks in models of parasite transmission: Predicting Cryptosporidium spread in wild lemurs. Journal of Animal Ecology, 86, 419-433. The spread of disease or information through networks can be affected by several factors. Whether and how these factors are accounted for can fundamentally change the predicted impact of a spreading epidemic. Springer, Kappeler & Nunn () investigate the role of different modes of transmission and network dynamics on the predicted size of a disease outbreak across several groups of Verreaux's sifakas, a group-living species of lemur. While some factors
Transportation dynamics on networks of mobile agents
Yang, Han-Xin; Xie, Yan-Bo; Lai, Ying-Cheng; Wang, Bing-Hong
2011-01-01
Most existing works on transportation dynamics focus on networks of a fixed structure, but networks whose nodes are mobile have become widespread, such as cell-phone networks. We introduce a model to explore the basic physics of transportation on mobile networks. Of particular interest are the dependence of the throughput on the speed of agent movement and communication range. Our computations reveal a hierarchical dependence for the former while, for the latter, we find an algebraic power law between the throughput and the communication range with an exponent determined by the speed. We develop a physical theory based on the Fokker-Planck equation to explain these phenomena. Our findings provide insights into complex transportation dynamics arising commonly in natural and engineering systems.
Cascading Edge Failures: A Dynamic Network Process
Zhang, June
2016-01-01
This paper considers the dynamics of edges in a network. The Dynamic Bond Percolation (DBP) process models, through stochastic local rules, the dependence of an edge $(a,b)$ in a network on the states of its neighboring edges. Unlike previous models, DBP does not assume statistical independence between different edges. In applications, this means for example that failures of transmission lines in a power grid are not statistically independent, or alternatively, relationships between individuals (dyads) can lead to changes in other dyads in a social network. We consider the time evolution of the probability distribution of the network state, the collective states of all the edges (bonds), and show that it converges to a stationary distribution. We use this distribution to study the emergence of global behaviors like consensus (i.e., catastrophic failure or full recovery of the entire grid) or coexistence (i.e., some failed and some operating substructures in the grid). In particular, we show that, depending on...
Competition and cooperation in dynamic replication networks.
Dadon, Zehavit; Wagner, Nathaniel; Alasibi, Samaa; Samiappan, Manickasundaram; Mukherjee, Rakesh; Ashkenasy, Gonen
2015-01-07
The simultaneous replication of six coiled-coil peptide mutants by reversible thiol-thioester exchange reactions is described. Experimental analysis of the time dependent evolution of networks formed by the peptides under different conditions reveals a complex web of molecular interactions and consequent mutant replication, governed by competition for resources and by autocatalytic and/or cross-catalytic template-assisted reactions. A kinetic model, first of its kind, is then introduced, allowing simulation of varied network behaviour as a consequence of changing competition and cooperation scenarios. We suggest that by clarifying the kinetic description of these relatively complex dynamic networks, both at early stages of the reaction far from equilibrium and at later stages approaching equilibrium, one lays the foundation for studying dynamic networks out-of-equilibrium in the near future.
Dynamical and bursty interactions in social networks
Stehle, Juliette; Bianconi, Ginestra
2010-01-01
We present a modeling framework for dynamical and bursty contact networks made of agents in social interaction. We consider agents' behavior at short time scales, in which the contact network is formed by disconnected cliques of different sizes. At each time a random agent can make a transition from being isolated to being part of a group, or vice-versa. Different distributions of contact times and inter-contact times between individuals are obtained by considering transition probabilities with memory effects, i.e. the transition probabilities for each agent depend both on its state (isolated or interacting) and on the time elapsed since the last change of state. The model lends itself to analytical and numerical investigations. The modeling framework can be easily extended, and paves the way for systematic investigations of dynamical processes occurring on rapidly evolving dynamical networks, such as the propagation of an information, or spreading of diseases.
Dynamic queuing transmission model for dynamic network loading
DEFF Research Database (Denmark)
Raovic, Nevena; Nielsen, Otto Anker; Prato, Carlo Giacomo
2017-01-01
This paper presents a new macroscopic multi-class dynamic network loading model called Dynamic Queuing Transmission Model (DQTM). The model utilizes ‘good’ properties of the Dynamic Queuing Model (DQM) and the Link Transmission Model (LTM) by offering a DQM consistent with the kinematic wave theory...... and allowing for the representation of multiple vehicle classes, queue spillbacks and shock waves. The model assumes that a link is split into a moving part plus a queuing part, and p that traffic dynamics are given by a triangular fundamental diagram. A case-study is investigated and the DQTM is compared...
Mapping the structure and dynamics of genomics-related MeSH terms complex networks.
Siqueiros-García, Jesús M; Hernández-Lemus, Enrique; García-Herrera, Rodrigo; Robina-Galatas, Andrea
2014-01-01
It has been proposed that the history and evolution of scientific ideas may reflect certain aspects of the underlying socio-cognitive frameworks in which science itself is developing. Systematic analyses of the development of scientific knowledge may help us to construct models of the collective dynamics of science. Aiming at scientific rigor, these models should be built upon solid empirical evidence, analyzed with formal tools leading to ever-improving results that support the related conclusions. Along these lines we studied the dynamics and structure of the development of research in genomics as represented by the entire collection of genomics-related scientific papers contained in the PubMed database. The analyzed corpus consisted in more than 49,000 articles published in the years 1987 (first appearance of the term Genomics) to 2011, categorized by means of the Medical Subheadings (MeSH) content-descriptors. Complex networks were built where two MeSH terms were connected if they are descriptors of the same article(s). The analysis of such networks revealed a complex structure and dynamics that to certain extent resembled small-world networks. The evolution of such networks in time reflected interesting phenomena in the historical development of genomic research, including what seems to be a phase-transition in a period marked by the completion of the first draft of the Human Genome Project. We also found that different disciplinary areas have different dynamic evolution patterns in their MeSH connectivity networks. In the case of areas related to science, changes in topology were somewhat fast while retaining a certain core-structure, whereas in the humanities, the evolution was pretty slow and the structure resulted highly redundant and in the case of technology related issues, the evolution was very fast and the structure remained tree-like with almost no overlapping terms.
Mapping the structure and dynamics of genomics-related MeSH terms complex networks.
Directory of Open Access Journals (Sweden)
Jesús M Siqueiros-García
Full Text Available It has been proposed that the history and evolution of scientific ideas may reflect certain aspects of the underlying socio-cognitive frameworks in which science itself is developing. Systematic analyses of the development of scientific knowledge may help us to construct models of the collective dynamics of science. Aiming at scientific rigor, these models should be built upon solid empirical evidence, analyzed with formal tools leading to ever-improving results that support the related conclusions. Along these lines we studied the dynamics and structure of the development of research in genomics as represented by the entire collection of genomics-related scientific papers contained in the PubMed database. The analyzed corpus consisted in more than 49,000 articles published in the years 1987 (first appearance of the term Genomics to 2011, categorized by means of the Medical Subheadings (MeSH content-descriptors. Complex networks were built where two MeSH terms were connected if they are descriptors of the same article(s. The analysis of such networks revealed a complex structure and dynamics that to certain extent resembled small-world networks. The evolution of such networks in time reflected interesting phenomena in the historical development of genomic research, including what seems to be a phase-transition in a period marked by the completion of the first draft of the Human Genome Project. We also found that different disciplinary areas have different dynamic evolution patterns in their MeSH connectivity networks. In the case of areas related to science, changes in topology were somewhat fast while retaining a certain core-structure, whereas in the humanities, the evolution was pretty slow and the structure resulted highly redundant and in the case of technology related issues, the evolution was very fast and the structure remained tree-like with almost no overlapping terms.
Dynamical behavior of disordered spring networks
Yucht, M. G.; Sheinman, M.; Broedersz, C. P.
2013-01-01
We study the dynamical rheology of spring networks with a percolation model constructed by bond dilution in a two-dimensional triangular lattice. Hydrodynamic interactions are implemented by a Stokesian viscous coupling between the network nodes and a uniformly deforming liquid. Our simulations show that in a critical connectivity regime, these systems display weak power law rheology in which the complex shear modulus scales with frequency as G^* ~ (i * omega)^Delta where Delta = 0.41, in dis...
Dynamics of Abusive IPv6 Networks
2014-09-01
NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DYNAMICS OF ABUSIVE IPV6 NETWORKS by Mark J. Turner September 2014 Thesis Advisor: Robert... IPV6 NETWORKS 5. FUNDING NUMBERS CNS-1111445 6. AUTHOR(S) Mark J. Turner 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Postgraduate School... IPv6 . As IPv6 becomes more commonplace, it permits abusive and malicious parties to exploit both new and existing vulnerabilities. Among such
Dynamic Protection of Optical Networks
DEFF Research Database (Denmark)
Ruepp, Sarah Renée
2008-01-01
This thesis deals with making optical networks resilient to failures. The recovery performance of path, segment and span restoration is evaluated in a network with limited wavelength conversion capability using both standard and enhanced wavelength assignment schemes. The enhanced wavelength...... assignment scheme is based on the Suggested Vector (SV), which is a Generalized Multi-Protocol Label Switching (GMPLS) compliant signalling extension aiming at wavelength conversion minimization. To increase the recovery percentage, two modifcations of the signalling session are proposed and evaluated...... through simulation. By resolving wavelength contention, the blocking reduction scheme reduces the number of necessary recovery retries and thereby the restoration time and control plane load. The stub-awareness schemes avoids wavelength conversions when merging the restoration segment to the connection...
Spreading dynamics in complex networks
Pei, Sen
2013-01-01
Searching for influential spreaders in complex networks is an issue of great significance for applications across various domains, ranging from the epidemic control, innovation diffusion, viral marketing, 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 LiveJournal social network, only a small fraction of them involve in spreading. For the spreading processes in Li...
Hydrogen application dynamics and networks
Energy Technology Data Exchange (ETDEWEB)
Schmidt, E. [Air Liquide Large Industries, Champigny-sur-Marne (France)
2010-12-30
The Chemical Industry consumes large volumes of hydrogen as raw material for the manufacture of numerous products (e.g. polyamides and polyurethanes account for 60% of hydrogen demand). The hydrogen demand was in the recent past and will continue to be driven by the polyurethane family. China will host about 60% of new hydrogen needs over the period 2010-2015 becoming the first hydrogen market next year and reaching 25% of market share by 2015 (vs. only 4% in 2001). Air Liquide supplies large volumes of Hydrogen (and other Industrial Gases) to customers by on-site plants and through pipeline networks which offer significant benefits such as higher safety, reliability and flexibility of supply. Thanks to its long term strategy and heavy investment in large units and pipeline networks, Air Liquide is the Industrial Gas leader in most of the world class Petrochemical basins (Rotterdam, Antwerp, US Gulf Coast, Yosu, Caojing,..) (orig.)
Dynamics in online social networks
Grabowicz, Przemyslaw A; Eguiluz, Victor M
2012-01-01
An increasing number of today's social interactions occurs using online social media as communication channels. Some online social networks have become extremely popular in the last decade. They differ among themselves in the character of the service they provide to online users. For instance, Facebook can be seen mainly as a platform for keeping in touch with close friends and relatives, Twitter is used to propagate and receive news, LinkedIn facilitates the maintenance of professional contacts, Flickr gathers amateurs and professionals of photography, etc. Albeit different, all these online platforms share an ingredient that pervades all their applications. There exists an underlying social network that allows their users to keep in touch with each other and helps to engage them in common activities or interactions leading to a better fulfillment of the service's purposes. This is the reason why these platforms share a good number of functionalities, e.g., personal communication channels, broadcasted status...
Network-Configurations of Dynamic Friction Patterns
Ghaffari, H O
2012-01-01
The complex configurations of dynamic friction patterns-regarding real time contact areas- are transformed into appropriate networks. With this transformation of a system to network space, many properties can be inferred about the structure and dynamics of the system. Here, we analyze the dynamics of static friction, i.e. nucleation processes, with respect to "friction networks". We show that networks can successfully capture the crack-like shear ruptures and possible corresponding acoustic features. We found that the fraction of triangles remarkably scales with the detachment fronts. There is a universal power law between nodes' degree and motifs frequency (for triangles, it reads T(k)\\proptok{\\beta} ({\\beta} \\approx2\\pm0.4)). We confirmed the obtained universality in aperture-based friction networks. Based on the achieved results, we extracted a possible friction law in terms of network parameters and compared it with the rate and state friction laws. In particular, the evolutions of loops are scaled with p...
Failure and recovery in dynamical networks
Böttcher, L.; Luković, M.; Nagler, J.; Havlin, S.; Herrmann, H. J.
2017-01-01
Failure, damage spread and recovery crucially underlie many spatially embedded networked systems ranging from transportation structures to the human body. Here we study the interplay between spontaneous damage, induced failure and recovery in both embedded and non-embedded networks. In our model the network’s components follow three realistic processes that capture these features: (i) spontaneous failure of a component independent of the neighborhood (internal failure), (ii) failure induced by failed neighboring nodes (external failure) and (iii) spontaneous recovery of a component. We identify a metastable domain in the global network phase diagram spanned by the model’s control parameters where dramatic hysteresis effects and random switching between two coexisting states are observed. This dynamics depends on the characteristic link length of the embedded system. For the Euclidean lattice in particular, hysteresis and switching only occur in an extremely narrow region of the parameter space compared to random networks. We develop a unifying theory which links the dynamics of our model to contact processes. Our unifying framework may help to better understand controllability in spatially embedded and random networks where spontaneous recovery of components can mitigate spontaneous failure and damage spread in dynamical networks. PMID:28155876
Six Degrees of Information Seeking: Stanley Milgram and the Small World of the Library
James, Kathryn
2006-01-01
Stanley Milgram's 1967 "small world" social connectivity study is used to analyze information connectivity, or patron information-seeking behavior. The "small world" study, upon examination, offers a clear example of the failure of social connectivity. This failure is used to highlight the importance of the subjectivities of patron experience of…
Dynamic Dilution Effects in Polymeric Networks
DEFF Research Database (Denmark)
Skov, Anne Ladegaard; Sommer-Larsen, Peter; Hassager, Ole
2006-01-01
processes, namely the reptation of linear species within the network and the arm withdrawal process of star arms in the sol fraction and of dangling single-chain ends attached to the network. The relaxation spectra are influenced by the stoichiometry to a large extent due to dynamic dilution effects caused...... by the change in the amount of dangling arms and solubles with stoichiometry. The star arm relaxation is suppressed by washing out the sol fraction which is seen as a clear example of the dynamic dilution effect arising from the small amount of non-reactive PDMS....
Dynamics of High-Resolution Networks
DEFF Research Database (Denmark)
Sekara, Vedran
NETWORKS are everywhere. From the smallest confines of the cells within our bodies to the webs of social relations across the globe. Networks are not static, they constantly change, adapt, and evolve to suit new conditions. In order to understand the fundamental laws that govern networks we need...... the unprecedented amounts of information collected by mobile phones to gain detailed insight into the dynamics of social systems. This dissertation presents an unparalleled data collection campaign, collecting highly detailed traces for approximately 1000 people over the course of multiple years. The availability...
Eigenvector dynamics under perturbation of modular networks
Sarkar, Somwrita; Robinson, Peter A; Fortunato, Santo
2015-01-01
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a "community" eigenspace and rotate together, but separately from that of the "bulk" eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general derivation for the theoretical detectability limit for sparse modular networks with $q$ communities is presented, beyond which modularity persists in the system but cannot be detected, and estimation results are shown to hold right to this limit.
Structural and dynamical properties of complex networks
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
Fundamental structures of dynamic social networks.
Sekara, Vedran; Stopczynski, Arkadiusz; Lehmann, Sune
2016-09-06
Social systems are in a constant state of flux, with dynamics spanning from minute-by-minute changes to patterns present on the timescale of years. Accurate models of social dynamics are important for understanding the spreading of influence or diseases, formation of friendships, and the productivity of teams. Although there has been much progress on understanding complex networks over the past decade, little is known about the regularities governing the microdynamics of social networks. Here, we explore the dynamic social network of a densely-connected population of ∼1,000 individuals and their interactions in the network of real-world person-to-person proximity measured via Bluetooth, as well as their telecommunication networks, online social media contacts, geolocation, and demographic data. These high-resolution data allow us to observe social groups directly, rendering community detection unnecessary. Starting from 5-min time slices, we uncover dynamic social structures expressed on multiple timescales. On the hourly timescale, we find that gatherings are fluid, with members coming and going, but organized via a stable core of individuals. Each core represents a social context. Cores exhibit a pattern of recurring meetings across weeks and months, each with varying degrees of regularity. Taken together, these findings provide a powerful simplification of the social network, where cores represent fundamental structures expressed with strong temporal and spatial regularity. Using this framework, we explore the complex interplay between social and geospatial behavior, documenting how the formation of cores is preceded by coordination behavior in the communication networks and demonstrating that social behavior can be predicted with high precision.
The effect of network structure on innovation initiation process: an evolutionary dynamics approach
Jafari, Afshin; Zolfagharzadeh, Mohammad Mahdi; Mohammadi, Mehdi
2016-01-01
In this paper we have proposed a basic agent-based model based on evolutionary dynamics for investigating innovation initiation process. In our model we suppose each agent will represent a firm which is interacting with other firms through a given network structure. We consider a two-hit process for presenting a potentially successful innovation in this model and therefore at each time step each firm can be in on of three different stages which are respectively, Ordinary, Innovative, and Successful. We design different experiments in order to investigate how different interaction networks may affect the process of presenting a successful innovation to the market. In this experiments, we use five different network structures, i.e. Erd\\H{o}s and R\\'enyi, Ring Lattice, Small World, Scale-Free and Distance-Based networks. According to the results of the simulations, for less frequent innovations like radical innovation, local structures are showing a better performance comparing to Scale-Free and Erd\\H{o}s and R\\...
Institute of Scientific and Technical Information of China (English)
孙晓娟; 李国芳
2016-01-01
In a neuronal system, propagation speed of neuronal information is mainly determined by the length, the diameter, and the kind of the axons between the neurons. Thus, some communications between neurons are not instantaneous, and others are instantaneous or with some negligible delay. In the past years, effects of time delay on neuronal dynamics, such as synchronization, stochastic resonance, firing regularity, etc., have been investigated. For stochastic resonance, it has been reported recently that stochastic multi-resonance in a neuronal system can be induced by time delay. However, in these studies, time delay has been introduced to every connection of the neuronal system. As mentioned in the beginning, in a real neuronal system, communication between some neurons can be instantaneous or with some negligible delays. Thus, considering the effect of partial time delay (time delay is called as partial time delay if only part of connections are delayed) on neuronal dynamics could be more meaningful. In this paper, we focus on discussing effect of partial time delay on response amplitude of a Watts-Strogatz neuronal network which is locally modeled by Rulkov map. With the numerically obtained results, we can see that partial time delay can induce a stochastic multi-resonance which is indicated by the multi-peak characteristics in the variation of response amplitude with partial time delay. Namely, partial time delay could also induce stochastic multi-resonance in a neuronal system. Moreover, we also find that optimal response amplitude can be reached in much wider range of the partial time delay value when delayed connections are less (i.e., the partial time delay probability is small). This is different from the case in which all connections are delayed, where response amplitude become optimal only when time delay is nearly the multiples of external signal’s period. But the range of the partial time delay value becomes narrower and narrower with the increasing of
Excitation waves on a minimal small-world model
Isele, Thomas; Hartung, Benedikt; Hövel, Philipp; Schöll, Eckehard
2015-04-01
We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of spatio-temporal behavior that is not present without it. We describe the underlying mechanisms for different types of patterns: propagation failure, period decreasing, bistability, shortcut blocking and period multiplication. For this purpose, we investigate the dependence on d, the network size, the coupling range in the original ring and the global coupling strength and present a phase diagram summarizing the different scenarios. Furthermore, we discuss the scaling behavior of the critical distance by analytical means and address the connection to spatially continuous excitable media.
Spreading dynamics in complex networks
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.
Dynamic Shortest Path Monitoring in Spatial Networks
Institute of Scientific and Technical Information of China (English)
Shuo Shang; Lisi Chen; Zhe-Wei Wei; Dan-Huai Guo; Ji-Rong Wen
2016-01-01
With the increasing availability of real-time traﬃc information, dynamic spatial networks are pervasive nowa-days and path planning in dynamic spatial networks becomes an important issue. In this light, we propose and investigate a novel problem of dynamically monitoring shortest paths in spatial networks (DSPM query). When a traveler aims to a des-tination, his/her shortest path to the destination may change due to two reasons: 1) the travel costs of some edges have been updated and 2) the traveler deviates from the pre-planned path. Our target is to accelerate the shortest path computing in dynamic spatial networks, and we believe that this study may be useful in many mobile applications, such as route planning and recommendation, car navigation and tracking, and location-based services in general. This problem is challenging due to two reasons: 1) how to maintain and reuse the existing computation results to accelerate the following computations, and 2) how to prune the search space effectively. To overcome these challenges, filter-and-refinement paradigm is adopted. We maintain an expansion tree and define a pair of upper and lower bounds to prune the search space. A series of optimization techniques are developed to accelerate the shortest path computing. The performance of the developed methods is studied in extensive experiments based on real spatial data.
The fundamental structures of dynamic social networks
Sekara, Vedran; Lehmann, Sune
2015-01-01
Networks provide a powerful mathematical framework for analyzing the structure and dynamics of complex systems (1-3). The study of group behavior has deep roots in the social science literature (4,5) and community detection is a central part of modern network science. Network communities have been found to be highly overlapping and organized in a hierarchical structure (6-9). Recent technological advances have provided a toolset for measuring the detailed social dynamics at scale (10,11). In spite of great progress, a quantitative description of the complex temporal behavior of social groups-with dynamics spanning from minute-by-minute changes to patterns expressed on the timescale of years-is still absent. Here we uncover a class of fundamental structures embedded within highly dynamic social networks. On the shortest time-scale, we find that social gatherings are fluid, with members coming and going, but organized via a stable core of individuals. We show that cores represent social contexts (9), with recur...
Dynamical networks with topological self-organization
Zak, M.
2001-01-01
Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.
Distributed dynamic load balancing in wireless networks
S.C. Borst (Sem); I. Saniee; P.A. Whiting
2007-01-01
htmlabstractSpatial and temporal load variations, e.g. flash overloads and traffic hot spots that persist for minutes to hours, are intrinsic features of wireless networks, and give rise to potentially huge performance repercussions. Dynamic load balancing strategies provide a natural mechanism for
Wireless sensor networks dynamic runtime configuration
Dulman, S.O.; Hofmeijer, T.J.; Havinga, Paul J.M.
2004-01-01
Current Wireless Sensor Networks (WSN) use fixed layered architectures, that can be modified only at compile time. Using a non-layered architecture, which allows dynamic loading of modules and automatic reconfiguration to adapt to the surrounding environment was believed to be too resource consuming
Filtering in hybrid dynamic Bayesian networks
DEFF Research Database (Denmark)
Andersen, Morten Nonboe; Andersen, Rasmus Ørum; Wheeler, Kevin
2004-01-01
We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the 2-Time Slice DBN (2T-DBN) from (Koller & Lerner, 2000) to model fault detection in a watertank system. In (Koller & Lerner, 2000) a generic Particle Filter (PF) is used for infere...
Filtering in hybrid dynamic Bayesian networks (left)
DEFF Research Database (Denmark)
Andersen, Morten Nonboe; Andersen, Rasmus Ørum; Wheeler, Kevin
We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the 2-Time Slice DBN (2T-DBN) from (Koller & Lerner, 2000) to model fault detection in a watertank system. In (Koller & Lerner, 2000) a generic Particle Filter (PF) is used for infere...
Filtering in hybrid dynamic Bayesian networks (center)
DEFF Research Database (Denmark)
Andersen, Morten Nonboe; Andersen, Rasmus Ørum; Wheeler, Kevin
We demonstrate experimentally that inference in a complex hybrid Dynamic Bayesian Network (DBN) is possible using the 2-Time Slice DBN (2T-DBN) from (Koller & Lerner, 2000) to model fault detection in a watertank system. In (Koller & Lerner, 2000) a generic Particle Filter (PF) is used for infere...
Dynamical networks with topological self-organization
Zak, M.
2001-01-01
Coupled evolution of state and topology of dynamical networks is introduced. Due to the well organized tensor structure, the governing equations are presented in a canonical form, and required attractors as well as their basins can be easily implanted and controlled.
Small-world Characteristics of EEG Patterns in Post-Anoxic Encephalopathy
Directory of Open Access Journals (Sweden)
Martijn eBeudel
2014-06-01
Full Text Available Post-Anoxic Encephalopathy (PAE has a heterogenous outcome which is difficult to predict. At present, it is possible to predict poor outcome using somatosensory evoked potentials (SSEP in only a minority of the patients at an early stage. In addition, it remains difficult to predict good outcome at an early stage. Network architecture, as can be quantified with continuous electroencephalography (cEEG, may serve as a candidate measure for predicting neurological outcome. Here we explore whether cEEG monitoring can be used to detect the integrity of neural network architecture in patients with PAE after cardiac arrest. From 56 patients with PAE treated with mild therapeutic hypothermia (MTH, 19-channel cEEG data was recorded starting as soon as possible after cardiac arrest. Adjacency matrices of shared frequencies between 1 and 25 Hz of the EEG channels were obtained using Fourier transformations. Number of network nodes and connections, clustering coefficient (C, average path length (L and small-world index (SWI were derived. Outcome was quantified by the best Cerebral Performance Category (CPC-score within 6 months. Compared to non-survivors, survivors showed significantly more nodes and connections. L was significantly higher and C and SWI were significantly lower in the survivor group than in the non-survivor group. The number of nodes, connections and the L negatively correlated with the CPC-score. C and SWI correlated positively with the CPC-score. The combination of number of nodes, connections, C and L showed the most significant difference and correlation between survivors and non-survivors and CPC-score. Our data might implicate that non-survivors have insufficient distribution and differentiation of neural activity for regaining normal brain function. These network differences, already present during hypothermia, might be further developed as early prognostic markers. The predictive values are however still inferior to current practice
Dynamic multicast traffic grooming in WDM networks
Institute of Scientific and Technical Information of China (English)
CHENG Xiao-jun; GE Ning; FENG Chong-xi
2006-01-01
Dynamic multicast traffic grooming in wavelength division multiplexing (WDM) networks was analyzed to minimize networkwide costs and to increase the network resource utilization.A network model was developed for dynamic multicast traffic grooming with resource constraints and an algorithm that can provide quality of service (QoS)was proposed.The QoS is measured by the maximum number of lightpaths passing between the source and the destinations.The blocking probability of the algorithm was assessed in simulations.The results show that a higher QoS requirement results in higher blocking probability,and when the QoS requirement is low,changes in the QoS requirements have only small effects on the blocking probability.
Dynamical systems on networks a tutorial
Porter, Mason A
2016-01-01
This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Appli...
Power Aware Dynamic Provisioning of HPC Networks
Energy Technology Data Exchange (ETDEWEB)
Groves, Taylor [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Grant, Ryan [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-10-01
Future exascale systems are under increased pressure to find power savings. The network, while it consumes a considerable amount of power is often left out of the picture when discussing total system power. Even when network power is being considered, the references are frequently a decade or older and rely on models that lack validation on modern inter- connects. In this work we explore how dynamic mechanisms of an Infiniband network save power and at what granularity we can engage these features. We explore this within the context of the host controller adapter (HCA) on the node and for the fabric, i.e. switches, using three different mechanisms of dynamic link width, frequency and disabling of links for QLogic and Mellanox systems. Our results show that while there is some potential for modest power savings, real world systems need to improved responsiveness to adjustments in order to fully leverage these savings. This page intentionally left blank.
Modeling epidemics dynamics on heterogenous networks.
Ben-Zion, Yossi; Cohen, Yahel; Shnerb, Nadav M
2010-05-21
The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.
Dynamic analysis of biochemical network using complex network method
Directory of Open Access Journals (Sweden)
Wang Shuqiang
2015-01-01
Full Text Available In this study, the stochastic biochemical reaction model is proposed based on the law of mass action and complex network theory. The dynamics of biochemical reaction system is presented as a set of non-linear differential equations and analyzed at the molecular-scale. Given the initial state and the evolution rules of the biochemical reaction system, the system can achieve homeostasis. Compared with random graph, the biochemical reaction network has larger information capacity and is more efficient in information transmission. This is consistent with theory of evolution.
Water dynamics in rigid ionomer networks
Osti, N. C.; Etampawala, T. N.; Shrestha, U. M.; Aryal, D.; Tyagi, M.; Diallo, S. O.; Mamontov, E.; Cornelius, C. J.; Perahia, D.
2016-12-01
The dynamics of water within ionic polymer networks formed by sulfonated poly(phenylene) (SPP), as revealed by quasi-elastic neutron scattering (QENS), is presented. These polymers are distinguished from other ionic macromolecules by their rigidity and therefore in their network structure. QENS measurements as a function of temperature as the fraction of ionic groups and humidity were varied have shown that the polymer molecules are immobile while absorbed water molecules remain dynamic. The water molecules occupy multiple sites, either bound or loosely constrained, and bounce between the two. With increasing temperature and hydration levels, the system becomes more dynamic. Water molecules remain mobile even at subzero temperatures, illustrating the applicability of the SPP membrane for selective transport over a broad temperature range.
DYNAMIC CONGESTION CONTROL IN WDM OPTICAL NETWORK
Directory of Open Access Journals (Sweden)
Sangita Samajpati
2013-02-01
Full Text Available This paper is based on Wavelength Division Multiplexing (WDM optical networking. In this optical networking, prior to data transfer, lightpath establishment between source and destination nodes is usually carried out through a wavelength reservation protocol. This wavelength is reserved corresponding to a route between the source and destination and the route is chosen following any standard routing protocol based on shortest path. The backward reservation protocol is implemented initially. A fixed connected and weighted network is considered. The inputs of this implementation are the fixed network itself and its corresponding shortest path matrix. After this initial level of implementation, the average node usage over a time period is calculated and various thresholds for node usage are considered. Above threshold value, request arriving at that path selects its next shortest path. This concept is implemented on various wavelengths. The output represents the performance issues of dynamic congestion control.
Complex Dynamics in Information Sharing Networks
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.
Dynamics on modular networks with heterogeneous correlations
Melnik, Sergey; Porter, Mason A.; Mucha, Peter J.; Gleeson, James P.
2014-06-01
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.
Innovation networking between stability and political dynamics
DEFF Research Database (Denmark)
Koch, Christian
2004-01-01
of the contribution is to challenge and transcend these notions and develop an understanding of innovation networks as an interplay between stable and dynamic elements, where political processes in innovation are much more than a disruptive and even a counterproductive feature. It reviews the growing number......This contribution views innovation as a social activity of building networks, using software product development in multicompany alliances and networks as example. Innovation networks are frequently understood as quite stable arrangements characterised by high trust among the participants. The aim...... of studies that highlight the political aspect of innovation. The paper reports on a study of innovation processes conducted within the EU—TSER-programme and a study made under the banner of management of technology. Intensive field studies in two constellations of enterprises were carried out. One...
Traffic Dynamics of Computer Networks
Fekete, Attila
2008-01-01
Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I studied the stochastic behavior of TCP, the primary algorithm governing traffic in the current Internet, in an elementary network scenario consisting of a standalone infinite-sized buffer and an access link. The effect of the fast recovery and fast retransmission (FR/FR) algorithms is also considered. I showed that my model can be extended further to involve the effect of link propagation delay, characteristic of WAN. I continued my thesis with the investigation of finite-sized semi-bottleneck buffers, where packets can be dropped not only at the link, but also at the buffer. I demonstrated that the behavior of the system depends only on a certain combination of the parameters. Moreover, an analytic formula was derived that gives the ratio of packet loss rate at the buffer ...
Nonparametric inference of network structure and dynamics
Peixoto, Tiago P.
The network structure of complex systems determine their function and serve as evidence for the evolutionary mechanisms that lie behind them. Despite considerable effort in recent years, it remains an open challenge to formulate general descriptions of the large-scale structure of network systems, and how to reliably extract such information from data. Although many approaches have been proposed, few methods attempt to gauge the statistical significance of the uncovered structures, and hence the majority cannot reliably separate actual structure from stochastic fluctuations. Due to the sheer size and high-dimensionality of many networks, this represents a major limitation that prevents meaningful interpretations of the results obtained with such nonstatistical methods. In this talk, I will show how these issues can be tackled in a principled and efficient fashion by formulating appropriate generative models of network structure that can have their parameters inferred from data. By employing a Bayesian description of such models, the inference can be performed in a nonparametric fashion, that does not require any a priori knowledge or ad hoc assumptions about the data. I will show how this approach can be used to perform model comparison, and how hierarchical models yield the most appropriate trade-off between model complexity and quality of fit based on the statistical evidence present in the data. I will also show how this general approach can be elegantly extended to networks with edge attributes, that are embedded in latent spaces, and that change in time. The latter is obtained via a fully dynamic generative network model, based on arbitrary-order Markov chains, that can also be inferred in a nonparametric fashion. Throughout the talk I will illustrate the application of the methods with many empirical networks such as the internet at the autonomous systems level, the global airport network, the network of actors and films, social networks, citations among
Dynamic pricing by hopfield neural network
Institute of Scientific and Technical Information of China (English)
Lusajo M Minga; FENG Yu-qiang(冯玉强); LI Yi-jun(李一军); LU Yang(路杨); Kimutai Kimeli
2004-01-01
The increase in the number of shopbots users in e-commerce has triggered flexibility of sellers in their pricing strategies. Sellers see the importance of automated price setting which provides efficient services to a large number of buyers who are using shopbots. This paper studies the characteristic of decreasing energy with time in a continuous model of a Hopfield neural network that is the decreasing of errors in the network with respect to time. The characteristic shows that it is possible to use Hopfield neural network to get the main factor of dynamic pricing; the least variable cost, from production function principles. The least variable cost is obtained by reducing or increasing the input combination factors, and then making the comparison of the network output with the desired output, where the difference between the network output and desired output will be decreasing in the same manner as in the Hopfield neural network energy. Hopfield neural network will simplify the rapid change of prices in e-commerce during transaction that depends on the demand quantity for demand sensitive model of pricing.
Advances in dynamic network modeling in complex transportation systems
Ukkusuri, Satish V
2013-01-01
This book focuses on the latest in dynamic network modeling, including route guidance and traffic control in transportation systems and other complex infrastructure networks. Covers dynamic traffic assignment, flow modeling, mobile sensor deployment and more.
Koziol, Leonard F; Barker, Lauren A; Joyce, Arthur W; Hrin, Skip
2014-01-01
Brain structure and function is characterized by large-scale brain systems. However, each system has its own "small-world" organization, with sub-regions, or "hubs," that have varying degrees of specialization for certain cognitive and behavioral processes. This article describes this small-world organization, and the concepts of functional specialization and functional integration are defined and explained through practical examples. We also describe the development of large-scale brain systems and this small-world organization as a sensitive, protracted process, vulnerable to a variety of influences that generate neurodevelopmental disorders.
Population Dynamics of Genetic Regulatory Networks
Braun, Erez
2005-03-01
Unlike common objects in physics, a biological cell processes information. The cell interprets its genome and transforms the genomic information content, through the action of genetic regulatory networks, into proteins which in turn dictate its metabolism, functionality and morphology. Understanding the dynamics of a population of biological cells presents a unique challenge. It requires to link the intracellular dynamics of gene regulation, through the mechanism of cell division, to the level of the population. We present experiments studying adaptive dynamics of populations of genetically homogeneous microorganisms (yeast), grown for long durations under steady conditions. We focus on population dynamics that do not involve random genetic mutations. Our experiments follow the long-term dynamics of the population distributions and allow to quantify the correlations among generations. We focus on three interconnected issues: adaptation of genetically homogeneous populations following environmental changes, selection processes on the population and population variability and expression distributions. We show that while the population exhibits specific short-term responses to environmental inputs, it eventually adapts to a robust steady-state, largely independent of external conditions. Cycles of medium-switch show that the adapted state is imprinted in the population and that this memory is maintained for many generations. To further study population adaptation, we utilize the process of gene recruitment whereby a gene naturally regulated by a specific promoter is placed under a different regulatory system. This naturally occurring process has been recognized as a major driving force in evolution. We have recruited an essential gene to a foreign regulatory network and followed the population long-term dynamics. Rewiring of the regulatory network allows us to expose their complex dynamics and phase space structure.
Dynamic motifs in socio-economic networks
Zhang, Xin; Shao, Shuai; Stanley, H. Eugene; Havlin, Shlomo
2014-12-01
Socio-economic networks are of central importance in economic life. We develop a method of identifying and studying motifs in socio-economic networks by focusing on “dynamic motifs,” i.e., evolutionary connection patterns that, because of “node acquaintances” in the network, occur much more frequently than random patterns. We examine two evolving bi-partite networks: i) the world-wide commercial ship chartering market and ii) the ship build-to-order market. We find similar dynamic motifs in both bipartite networks, even though they describe different economic activities. We also find that “influence” and “persistence” are strong factors in the interaction behavior of organizations. When two companies are doing business with the same customer, it is highly probable that another customer who currently only has business relationship with one of these two companies, will become customer of the second in the future. This is the effect of influence. Persistence means that companies with close business ties to customers tend to maintain their relationships over a long period of time.
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases...... with the strength of the synapses in the network and with the value to which the membrane potential is reset after a spike. Generalizing the model to include conductance-based synapses gives insight into the connection between the firing statistics and the high- conductance state observed experimentally in visual...
Personality traits and ego-network dynamics
Centellegher, Simone; López, Eduardo; Saramäki, Jari; Lepri, Bruno
2017-01-01
Strong and supportive social relationships are fundamental to our well-being. However, there are costs to their maintenance, resulting in a trade-off between quality and quantity, a typical strategy being to put a lot of effort on a few high-intensity relationships while maintaining larger numbers of less close relationships. It has also been shown that there are persistent individual differences in this pattern; some individuals allocate their efforts more uniformly across their networks, while others strongly focus on their closest relationships. Furthermore, some individuals maintain more stable networks than others. Here, we focus on how personality traits of individuals affect this picture, using mobile phone calls records and survey data from the Mobile Territorial Lab (MTL) study. In particular, we look at the relationship between personality traits and the (i) persistence of social signatures, namely the similarity of the social signature shape of an individual measured in different time intervals; (ii) the turnover in egocentric networks, that is, differences in the set of alters present at two consecutive temporal intervals; and (iii) the rank dynamics defined as the variation of alter rankings in egocentric networks in consecutive intervals. We observe that some traits have effects on the stability of the social signatures as well as network turnover and rank dynamics. As an example, individuals who score highly in the Openness to Experience trait tend to have higher levels of network turnover and larger alter rank variations. On broader terms, our study shows that personality traits clearly affect the ways in which individuals maintain their personal networks. PMID:28253333
Personality traits and ego-network dynamics.
Centellegher, Simone; López, Eduardo; Saramäki, Jari; Lepri, Bruno
2017-01-01
Strong and supportive social relationships are fundamental to our well-being. However, there are costs to their maintenance, resulting in a trade-off between quality and quantity, a typical strategy being to put a lot of effort on a few high-intensity relationships while maintaining larger numbers of less close relationships. It has also been shown that there are persistent individual differences in this pattern; some individuals allocate their efforts more uniformly across their networks, while others strongly focus on their closest relationships. Furthermore, some individuals maintain more stable networks than others. Here, we focus on how personality traits of individuals affect this picture, using mobile phone calls records and survey data from the Mobile Territorial Lab (MTL) study. In particular, we look at the relationship between personality traits and the (i) persistence of social signatures, namely the similarity of the social signature shape of an individual measured in different time intervals; (ii) the turnover in egocentric networks, that is, differences in the set of alters present at two consecutive temporal intervals; and (iii) the rank dynamics defined as the variation of alter rankings in egocentric networks in consecutive intervals. We observe that some traits have effects on the stability of the social signatures as well as network turnover and rank dynamics. As an example, individuals who score highly in the Openness to Experience trait tend to have higher levels of network turnover and larger alter rank variations. On broader terms, our study shows that personality traits clearly affect the ways in which individuals maintain their personal networks.
Traffic chaotic dynamics modeling and analysis of deterministic network
Wu, Weiqiang; Huang, Ning; Wu, Zhitao
2016-07-01
Network traffic is an important and direct acting factor of network reliability and performance. To understand the behaviors of network traffic, chaotic dynamics models were proposed and helped to analyze nondeterministic network a lot. The previous research thought that the chaotic dynamics behavior was caused by random factors, and the deterministic networks would not exhibit chaotic dynamics behavior because of lacking of random factors. In this paper, we first adopted chaos theory to analyze traffic data collected from a typical deterministic network testbed — avionics full duplex switched Ethernet (AFDX, a typical deterministic network) testbed, and found that the chaotic dynamics behavior also existed in deterministic network. Then in order to explore the chaos generating mechanism, we applied the mean field theory to construct the traffic dynamics equation (TDE) for deterministic network traffic modeling without any network random factors. Through studying the derived TDE, we proposed that chaotic dynamics was one of the nature properties of network traffic, and it also could be looked as the action effect of TDE control parameters. A network simulation was performed and the results verified that the network congestion resulted in the chaotic dynamics for a deterministic network, which was identical with expectation of TDE. Our research will be helpful to analyze the traffic complicated dynamics behavior for deterministic network and contribute to network reliability designing and analysis.
Dynamic Trust Management for Mobile Networks and Its Applications
Bao, Fenye
2013-01-01
Trust management in mobile networks is challenging due to dynamically changing network environments and the lack of a centralized trusted authority. In this dissertation research, we "design" and "validate" a class of dynamic trust management protocols for mobile networks, and demonstrate the utility of dynamic trust management…
Activating and inhibiting connections in biological network dynamics
Directory of Open Access Journals (Sweden)
Knight Rob
2008-12-01
Full Text Available Abstract Background Many studies of biochemical networks have analyzed network topology. Such work has suggested that specific types of network wiring may increase network robustness and therefore confer a selective advantage. However, knowledge of network topology does not allow one to predict network dynamical behavior – for example, whether deleting a protein from a signaling network would maintain the network's dynamical behavior, or induce oscillations or chaos. Results Here we report that the balance between activating and inhibiting connections is important in determining whether network dynamics reach steady state or oscillate. We use a simple dynamical model of a network of interacting genes or proteins. Using the model, we study random networks, networks selected for robust dynamics, and examples of biological network topologies. The fraction of activating connections influences whether the network dynamics reach steady state or oscillate. Conclusion The activating fraction may predispose a network to oscillate or reach steady state, and neutral evolution or selection of this parameter may affect the behavior of biological networks. This principle may unify the dynamics of a wide range of cellular networks. Reviewers Reviewed by Sergei Maslov, Eugene Koonin, and Yu (Brandon Xia (nominated by Mark Gerstein. For the full reviews, please go to the Reviewers' comments section.
Study of the structure and dynamics of complex biological networks
Samal, Areejit
2008-12-01
In this thesis, we have studied the large scale structure and system level dynamics of certain biological networks using tools from graph theory, computational biology and dynamical systems. We study the structure and dynamics of large scale metabolic networks inside three organisms, Escherichia coli, Saccharomyces cerevisiae and Staphylococcus aureus. We also study the dynamics of the large scale genetic network controlling E. coli metabolism. We have tried to explain the observed system level dynamical properties of these networks in terms of their underlying structure. Our studies of the system level dynamics of these large scale biological networks provide a different perspective on their functioning compared to that obtained from purely structural studies. Our study also leads to some new insights on features such as robustness, fragility and modularity of these large scale biological networks. We also shed light on how different networks inside the cell such as metabolic networks and genetic networks are interrelated to each other.
A network-based dynamical ranking system
Motegi, Shun
2012-01-01
Ranking players or teams in sports is of practical interests. From the viewpoint of networks, a ranking system is equivalent a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based ranking systems are derived from static networks, i.e., aggregation of the results of games over time. However, the score (i.e., strength) of a player, for example, depends on time. Defeating a renowned player in the peak performance is intuitively more rewarding than defeating the same player in other periods. To account for this factor, we propose a dynamic variant of such a network-based ranking system and apply it to professional men's tennis data. Our ranking system, also interpreted as a centrality measure for directed temporal networks, has two parameters. One parameter represents the exponential decay rate of the past score, and the other parameter controls the effect of indirect wins on the score. We derive a set of linear online update equ...
Avoiding the "It's a Small World" Effect: A Lesson Plan to Explore Diversity
Endacott, Jason L.; Bowles, Freddie A.
2013-01-01
Classroom instruction about other cultures all too often resembles the Disney version of "It's a Small World" with Fantasyland-like cultural stereotypes, ceremonial activities, and traditional dress that can lead to serious
Physical Proximity and Spreading in Dynamic Social Networks
Stopczynski, Arkadiusz; Lehmann, Sune
2015-01-01
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have recorded every single interaction within a large population, mapping out---for the first time at scale---the complete proximity network for a densely-connected system. Here we show the striking impact of interaction-distance on the network structure and dynamics of spreading processes. We create networks supporting close (intimate network, up to ~1m) and longer distance (ambient network, up to ~10m) modes of transmission. The intimate network is fragmented, with weak ties bridging densely-connected neighborhoods, whereas the ambient network supports spread driven by random contacts between strangers. While there is no trivial mapping from the micro-dynamics of proximity networks to empirical epidemics, these networks provide a telling approximation of droplet and airborne modes o...
Programming the dynamics of biochemical reaction networks.
Simmel, Friedrich C
2013-01-22
The development of complex self-organizing molecular systems for future nanotechnology requires not only robust formation of molecular structures by self-assembly but also precise control over their temporal dynamics. As an exquisite example of such control, in this issue of ACS Nano, Fujii and Rondelez demonstrate a particularly compact realization of a molecular "predator-prey" ecosystem consisting of only three DNA species and three enzymes. The system displays pronounced oscillatory dynamics, in good agreement with the predictions of a simple theoretical model. Moreover, its considerable modularity also allows for ecological studies of competition and cooperation within molecular networks.
Energy Technology Data Exchange (ETDEWEB)
Liu, Hui; Song, Yongduan; Xue, Fangzheng; Li, Xiumin, E-mail: xmli@cqu.edu.cn [Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education, Chongqing University, Chongqing 400044 (China); College of Automation, Chongqing University, Chongqing 400044 (China)
2015-11-15
In this paper, the generation of multi-clustered structure of self-organized neural network with different neuronal firing patterns, i.e., bursting or spiking, has been investigated. The initially all-to-all-connected spiking neural network or bursting neural network can be self-organized into clustered structure through the symmetric spike-timing-dependent plasticity learning for both bursting and spiking neurons. However, the time consumption of this clustering procedure of the burst-based self-organized neural network (BSON) is much shorter than the spike-based self-organized neural network (SSON). Our results show that the BSON network has more obvious small-world properties, i.e., higher clustering coefficient and smaller shortest path length than the SSON network. Also, the results of larger structure entropy and activity entropy of the BSON network demonstrate that this network has higher topological complexity and dynamical diversity, which benefits for enhancing information transmission of neural circuits. Hence, we conclude that the burst firing can significantly enhance the efficiency of clustering procedure and the emergent clustered structure renders the whole network more synchronous and therefore more sensitive to weak input. This result is further confirmed from its improved performance on stochastic resonance. Therefore, we believe that the multi-clustered neural network which self-organized from the bursting dynamics has high efficiency in information processing.
Liu, Hui; Song, Yongduan; Xue, Fangzheng; Li, Xiumin
2015-11-01
In this paper, the generation of multi-clustered structure of self-organized neural network with different neuronal firing patterns, i.e., bursting or spiking, has been investigated. The initially all-to-all-connected spiking neural network or bursting neural network can be self-organized into clustered structure through the symmetric spike-timing-dependent plasticity learning for both bursting and spiking neurons. However, the time consumption of this clustering procedure of the burst-based self-organized neural network (BSON) is much shorter than the spike-based self-organized neural network (SSON). Our results show that the BSON network has more obvious small-world properties, i.e., higher clustering coefficient and smaller shortest path length than the SSON network. Also, the results of larger structure entropy and activity entropy of the BSON network demonstrate that this network has higher topological complexity and dynamical diversity, which benefits for enhancing information transmission of neural circuits. Hence, we conclude that the burst firing can significantly enhance the efficiency of clustering procedure and the emergent clustered structure renders the whole network more synchronous and therefore more sensitive to weak input. This result is further confirmed from its improved performance on stochastic resonance. Therefore, we believe that the multi-clustered neural network which self-organized from the bursting dynamics has high efficiency in information processing.
Evolutionary epistemology and dynamical virtual learning networks.
Giani, Umberto
2004-01-01
This paper is an attempt to define the main features of a new educational model aimed at satisfying the needs of a rapidly changing society. The evolutionary epistemology paradigm of culture diffusion in human groups could be the conceptual ground for the development of this model. Multidimensionality, multi-disciplinarity, complexity, connectivity, critical thinking, creative thinking, constructivism, flexible learning, contextual learning, are the dimensions that should characterize distance learning models aimed at increasing the epistemological variability of learning communities. Two multimedia educational software, Dynamic Knowledge Networks (DKN) and Dynamic Virtual Learning Networks (DVLN) are described. These two complementary tools instantiate these dimensions, and were tested in almost 150 online courses. Even if the examples are framed in the medical context, the analysis of the shortcomings of the traditional educational systems and the proposed solutions can be applied to the vast majority of the educational contexts.
Enhancing the network synchronizability
Institute of Scientific and Technical Information of China (English)
ZHAO Ming; ZHOU Tao; CHEN Guan-rong; WANG Bing-hong
2007-01-01
The structural and dynamical properties, partic-ularly the small-world effect and scale-free feature, of com-plex networks have attracted tremendous interest and atten-tion in recent years. This article offers a brief review of one focal issue concerning the structural and dynamical behav-iors of complex network synchronization. In the presenta-tion, the notions of synchronization of dynamical systems on networks, stability of dynamical networks, and relationships between network structure and synchronizability, will be first introduced. Then, various technical methods for enhancing the network synchronizability will be discussed, which are roughly divided into two classes: Structural Modification and Coupling-Pattern Regulation, where the former includes three typical methods-dividing hub nodes, shortening average dis-tances, and deleting overload edges, while the latter mainly is a method of strengthening the hub-nodes' influence on the network.
Message Passing for Dynamic Network Energy Management
Kraning, Matt; Lavaei, Javad; Boyd, Stephen
2012-01-01
We consider a network of devices, such as generators, fixed loads, deferrable loads, and storage devices, each with its own dynamic constraints and objective, connected by lossy capacitated lines. The problem is to minimize the total network objective subject to the device and line constraints, over a given time horizon. This is a large optimization problem, with variables for consumption or generation in each time period for each device. In this paper we develop a decentralized method for solving this problem. The method is iterative: At each step, each device exchanges simple messages with its neighbors in the network and then solves its own optimization problem, minimizing its own objective function, augmented by a term determined by the messages it has received. We show that this message passing method converges to a solution when the device objective and constraints are convex. The method is completely decentralized, and needs no global coordination other than synchronizing iterations; the problems to be...
Dynamic Spectrum Leasing to Cooperating Secondary Networks
Li, Cuilian
2008-01-01
We propose and analyze a dynamic implementation of the property-rights model of cognitive radio, whereby a primary link has the possibility to lease the owned spectrum to a MAC network of secondary nodes in exchange for cooperation in the form of distributed space-time coding. On one hand, the primary link attempts to maximize its quality of service in terms of Signal-to-interference-plus-noise ratio (SINR), accounting for the possible contribution from cooperation. On the other hand, nodes in the secondary network compete among themselves for transmission within the leased time-slot following a distributed heterogeneous opportunistic power control mechanism. The cooperation and competition between the primary and secondary network are cast in the framework of sequential game. We give consider both a baseline model with complete information and a more practical version with incomplete information, Using the backward induction approach for the former and providing approximating algorithm for the latter. Analys...
Eigenvector dynamics under perturbation of modular networks
Sarkar, Somwrita; Chawla, Sanjay; Robinson, P. A.; Fortunato, Santo
2016-06-01
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of q communities, the number of eigenvectors corresponding to the q largest eigenvalues form a "community" eigenspace and rotate together, but separately from that of the "bulk" eigenspace spanned by all the other eigenvectors. Using this property, the number of modules or clusters in a network can be estimated in an algorithm-independent way. A general argument and derivation for the theoretical detectability limit for sparse modular networks with q communities is presented, beyond which modularity persists in the system but cannot be detected. It is shown that for detecting the clusters or modules using the adjacency matrix, there is a "band" in which it is hard to detect the clusters even before the theoretical detectability limit is reached, and for which the theoretically predicted detectability limit forms the sufficient upper bound. Analytic estimations of these bounds are presented and empirically demonstrated.
Information spreading on dynamic social networks
Liu, Chuang
2012-01-01
Nowadays, information spreading on social networks has triggered an explosive attention in various disciplines. Most of previous related works in this area mainly focus on discussing the effects of spreading probability or immunization strategy on static networks. However, in real systems, the peer-to-peer network structure changes constantly according to frequently social activities of users. In order to capture this dynamical property and study its impact on information spreading, in this Letter, a link rewiring strategy based on the Fermi function is introduced. In the present model, the informed individuals tend to break old links and reconnect to ones with more uninformed neighbors. Simulation results on the susceptible-infected (\\textit{SI}) model with non-redundancy contacts indicate that the information spread more faster and broader with the rewiring strategy. Extensive analyses of the information cascading show that the spreading process of the initial steps plays a very important role, that is to s...
Time-Varying Graphs and Dynamic Networks
Casteigts, Arnaud; Quattrociocchi, Walter; Santoro, Nicola
2010-01-01
The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts can be viewed as fragments of a larger formal description of this universe. The main contribution of this paper is to integrate the existing partial models proposed in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. As part of the framework definition, we identify a hierarchy of classes of TVGs, defined with respects to basic properties to which correspond necessary conditions and impossibi...
Mean field methods for cortical network dynamics
DEFF Research Database (Denmark)
Hertz, J.; Lerchner, Alexander; Ahmadi, M.
2004-01-01
We review the use of mean field theory for describing the dynamics of dense, randomly connected cortical circuits. For a simple network of excitatory and inhibitory leaky integrate- and-fire neurons, we can show how the firing irregularity, as measured by the Fano factor, increases with the stren...... cortex. Finally, an extension of the model to describe an orientation hypercolumn provides understanding of how cortical interactions sharpen orientation tuning, in a way that is consistent with observed firing statistics...
Synchronization of coupled chaotic dynamics on networks
Indian Academy of Sciences (India)
R E Amritkar; Sarika Jalan
2005-03-01
We review some recent work on the synchronization of coupled dynamical systems on a variety of networks. When nodes show synchronized behaviour, two interesting phenomena can be observed. First, there are some nodes of the floating type that show intermittent behaviour between getting attached to some clusters and evolving independently. Secondly, two different ways of cluster formation can be identified, namely self-organized clusters which have mostly intra-cluster couplings and driven clusters which have mostly inter-cluster couplings.
Neural Networks in Chemical Reaction Dynamics
Raff, Lionel; Hagan, Martin
2011-01-01
This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic
Advances in theoretical models of network science
Institute of Scientific and Technical Information of China (English)
FANG Jin-qing; BI Qiao; LI Yong
2007-01-01
In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.
Dynamic congestion control mechanisms for MPLS networks
Holness, Felicia; Phillips, Chris I.
2001-02-01
Considerable interest has arisen in congestion control through traffic engineering from the knowledge that although sensible provisioning of the network infrastructure is needed, together with sufficient underlying capacity, these are not sufficient to deliver the Quality of Service required for new applications. This is due to dynamic variations in load. In operational Internet Protocol (IP) networks, it has been difficult to incorporate effective traffic engineering due to the limited capabilities of the IP technology. In principle, Multiprotocol Label Switching (MPLS), which is a connection-oriented label swapping technology, offers new possibilities in addressing the limitations by allowing the operator to use sophisticated traffic control mechanisms. This paper presents a novel scheme to dynamically manage traffic flows through the network by re-balancing streams during periods of congestion. It proposes management-based algorithms that will allow label switched routers within the network to utilize mechanisms within MPLS to indicate when flows are starting to experience frame/packet loss and then to react accordingly. Based upon knowledge of the customer's Service Level Agreement, together with instantaneous flow information, the label edge routers can then instigate changes to the LSP route and circumvent congestion that would hitherto violate the customer contacts.
The Global Carbon Cycle: It's a Small World
Ineson, Philip; Milcu, Alexander; Subke, Jens-Arne; Wildman, Dennis; Anderson, Robert; Manning, Peter; Heinemeyer, Andreas
2010-05-01
temperatures, or cessation of CO2 additions, showed rapid and proportionate decreases in atmospheric CO2 concentrations. The results indicate that short term terrestrial feedbacks are not sufficient to induce a CO2-temperature runaway scenario and suggest that predictions of atmospheric CO2 by current GCMs may under-estimate the CO2 fertilisation effect on plants and, hence, over-estimate future atmospheric CO2 increases. Perhaps, more importantly, the experiments show that the impacts of imposed elevated CO2 and temperature increase can be reversed. Whilst clearly representing a simplified version of terrestrial CO2 dynamics, it is proposed that closed system research represents a new form of test-bed for validation of processes represented within digital global CO2 models.