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.

Scaling and percolation in the small-world network model

International Nuclear Information System (INIS)

Newman, M. E. J.; Watts, D. J.

1999-01-01

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 networks of fuzzy chaotic oscillators

CERN Document Server

Bucolo, M; Fortuna, L

2003-01-01

Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.

Epidemics in interconnected small-world networks

NARCIS (Netherlands)

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

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.

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...

Hierarchical regular small-world networks

International Nuclear Information System (INIS)

Boettcher, Stefan; Goncalves, Bruno; Guclu, Hasan

2008-01-01

Two new networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They possess a unique one-dimensional lattice backbone overlaid by a hierarchical sequence of long-distance links, mixing real-space and small-world features. Both networks, one 3-regular and the other 4-regular, lead to distinct behaviors, as revealed by renormalization group studies. The 3-regular network is planar, has a diameter growing as √N with system size N, and leads to super-diffusion with an exact, anomalous exponent d w = 1.306..., but possesses only a trivial fixed point T c = 0 for the Ising ferromagnet. In turn, the 4-regular network is non-planar, has a diameter growing as ∼2 √(log 2 N 2 ) , exhibits 'ballistic' diffusion (d w = 1), and a non-trivial ferromagnetic transition, T c > 0. It suggests that the 3-regular network is still quite 'geometric', while the 4-regular network qualifies as a true small world with mean-field properties. As an engineering application we discuss synchronization of processors on these networks. (fast track communication)

Critical behavior of the contact process on small-world networks

Science.gov (United States)

Ferreira, Ronan S.; Ferreira, Silvio C.

2013-11-01

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering ( p → 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

A small-world network model of facial emotion recognition.

Science.gov (United States)

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.

Network marketing on a small-world network

Science.gov (United States)

Kim, Beom Jun; Jun, Tackseung; Kim, Jeong-Yoo; Choi, M. Y.

2006-02-01

We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability α is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price p of the product and the referral fee r are used as free parameters to maximize the profit of the manufacturer. It is observed that at α=0 the maximized profit is constant independent of the network size N while at α≠0, it increases linearly with N. This is in parallel to the small-world transition. It is also revealed that while the optimal value of p stays at an almost constant level in a broad range of α, that of r is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.

The Topological Analysis of Urban Transit System as a Small-World Network

OpenAIRE

Zhaosheng Yang; Huxing Zhou; Peng Gao; Hong Chen; Nan Zhang

2011-01-01

This paper proposes a topological analysis of urban transit system based on a functional representation network constructed from the urban transit system in Beijing. The representation gives a functional view on nodes named a transit line. Statistical measures are computed and introduced in complex network analysis. It shows that the urban transit system forms small-world networks and exhibits properties different from random networks and regular networks. Furthermore, the topological propert...

Monte Carlo tests of small-world architecture for coarse-grained networks of the United States railroad and highway transportation systems

Science.gov (United States)

Aldrich, Preston R.; El-Zabet, Jermeen; Hassan, Seerat; Briguglio, Joseph; Aliaj, Enela; Radcliffe, Maria; Mirza, Taha; Comar, Timothy; Nadolski, Jeremy; Huebner, Cynthia D.

2015-11-01

Several studies have shown that human transportation networks exhibit small-world structure, meaning they have high local clustering and are easily traversed. However, some have concluded this without statistical evaluations, and others have compared observed structure to globally random rather than planar models. Here, we use Monte Carlo randomizations to test US transportation infrastructure data for small-worldness. Coarse-grained network models were generated from GIS data wherein nodes represent the 3105 contiguous US counties and weighted edges represent the number of highway or railroad links between counties; thus, we focus on linkage topologies and not geodesic distances. We compared railroad and highway transportation networks with a simple planar network based on county edge-sharing, and with networks that were globally randomized and those that were randomized while preserving their planarity. We conclude that terrestrial transportation networks have small-world architecture, as it is classically defined relative to global randomizations. However, this topological structure is sufficiently explained by the planarity of the graphs, and in fact the topological patterns established by the transportation links actually serve to reduce the amount of small-world structure.

Nonequilibrium phase transition in directed small-world-Voronoi-Delaunay random lattices

International Nuclear Information System (INIS)

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. (paper)

Stability of a neural network model with small-world connections

International Nuclear Information System (INIS)

Li Chunguang; Chen Guanrong

2003-01-01

Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connection. There are no special weightings in the connections of most existing small-world network models. However, this kind of simply connected model cannot characterize biological neural networks, in which there are different weights in synaptic connections. In this paper, we present a neural network model with weighted small-world connections and further investigate the stability of this model

Multiobjective Bak-Sneppen model on a small-world network

International Nuclear Information System (INIS)

Elettreby, M.F.

2005-01-01

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

Multiobjective Bak-Sneppen model on a small-world network

International Nuclear Information System (INIS)

Elettreby, M.

2004-09-01

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. (author)

Optimal network structure to induce the maximal small-world effect

International Nuclear Information System (INIS)

Zhang Zheng-Zhen; Xu Wen-Jun; Lin Jia-Ru; Zeng Shang-You

2014-01-01

In this paper, the general efficiency, which is the average of the global efficiency and the local efficiency, is defined to measure the communication efficiency of a network. The increasing ratio of the general efficiency of a small-world network relative to that of the corresponding regular network is used to measure the small-world effect quantitatively. The more considerable the small-world effect, the higher the general efficiency of a network with a certain cost is. It is shown that the small-world effect increases monotonically with the increase of the vertex number. The optimal rewiring probability to induce the best small-world effect is approximately 0.02 and the optimal average connection probability decreases monotonically with the increase of the vertex number. Therefore, the optimal network structure to induce the maximal small-world effect is the structure with the large vertex number (> 500), the small rewiring probability (≍ 0.02) and the small average connection probability (< 0.1). Many previous research results support our results. (interdisciplinary physics and related areas of science and technology)

Searching in small-world networks

International Nuclear Information System (INIS)

Moura, Alessandro P.S. de; Motter, Adilson E.; Grebogi, Celso

2003-01-01

We study the average time it takes to find a desired node in the Watts-Strogatz family of networks. We consider the case when the look-up time can be neglected and when it is important, where the look-up time is the time needed to choose one among all the neighboring nodes of a node at each step in the search. We show that in both cases, the search time is minimum in the small-world regime, when an appropriate distance between the nodes is defined. Through an analytical model, we show that the search time scales as N 1/D(D+1) for small-world networks, where N is the number of nodes and D is the dimension of the underlying lattice. This model is shown to be in agreement with numerical simulations

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.

Efficient network reconstruction from dynamical cascades identifies small-world topology of neuronal avalanches.

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.

An Investigation of the Differences and Similarities between Generated Small-World Networks for Right- and Left-Hand Motor Imageries.

Science.gov (United States)

Zhang, Jiang; Li, Yuyao; Chen, Huafu; Ding, Jurong; Yuan, Zhen

2016-11-04

In this study, small-world network analysis was performed to identify the similarities and differences between functional brain networks for right- and left-hand motor imageries (MIs). First, Pearson correlation coefficients among the nodes within the functional brain networks from healthy subjects were calculated. Then, small-world network indicators, including the clustering coefficient, the average path length, the global efficiency, the local efficiency, the average node degree, and the small-world index, were generated for the functional brain networks during both right- and left-hand MIs. We identified large differences in the small-world network indicators between the functional networks during MI and in the random networks. More importantly, the functional brain networks underlying the right- and left-hand MIs exhibited similar small-world properties in terms of the clustering coefficient, the average path length, the global efficiency, and the local efficiency. By contrast, the right- and left-hand MI brain networks showed differences in small-world characteristics, including indicators such as the average node degree and the small-world index. Interestingly, our findings also suggested that the differences in the activity intensity and range, the average node degree, and the small-world index of brain networks between the right- and left-hand MIs were associated with the asymmetry of brain functions.

Stochastic resonance in small-world neuronal networks with hybrid electrical–chemical synapses

International Nuclear Information System (INIS)

Wang, Jiang; Guo, Xinmeng; Yu, Haitao; Liu, Chen; Deng, Bin; Wei, Xile; Chen, Yingyuan

2014-01-01

Highlights: •We study stochastic resonance in small-world neural networks with hybrid synapses. •The resonance effect depends largely on the probability of chemical synapse. •An optimal chemical synapse probability exists to evoke network resonance. •Network topology affects the stochastic resonance in hybrid neuronal networks. - Abstract: The dependence of stochastic resonance in small-world neuronal networks with hybrid electrical–chemical synapses on the probability of chemical synapse and the rewiring probability is investigated. A subthreshold periodic signal is imposed on one single neuron within the neuronal network as a pacemaker. It is shown that, irrespective of the probability of chemical synapse, there exists a moderate intensity of external noise optimizing the response of neuronal networks to the pacemaker. Moreover, the effect of pacemaker driven stochastic resonance of the system depends largely on the probability of chemical synapse. A high probability of chemical synapse will need lower noise intensity to evoke the phenomenon of stochastic resonance in the networked neuronal systems. In addition, for fixed noise intensity, there is an optimal chemical synapse probability, which can promote the propagation of the localized subthreshold pacemaker across neural networks. And the optimal chemical synapses probability turns even larger as the coupling strength decreases. Furthermore, the small-world topology has a significant impact on the stochastic resonance in hybrid neuronal networks. It is found that increasing the rewiring probability can always enhance the stochastic resonance until it approaches the random network limit

A family of small-world network models built by complete graph and iteration-function

Science.gov (United States)

Ma, Fei; Yao, Bing

2018-02-01

Small-world networks are popular in real-life complex systems. In the past few decades, researchers presented amounts of small-world models, in which some are stochastic and the rest are deterministic. In comparison with random models, it is not only convenient but also interesting to study the topological properties of deterministic models in some fields, such as graph theory, theorem computer sciences and so on. As another concerned darling in current researches, community structure (modular topology) is referred to as an useful statistical parameter to uncover the operating functions of network. So, building and studying such models with community structure and small-world character will be a demanded task. Hence, in this article, we build a family of sparse network space N(t) which is different from those previous deterministic models. Even though, our models are established in the same way as them, iterative generation. By randomly connecting manner in each time step, every resulting member in N(t) has no absolutely self-similar feature widely shared in a large number of previous models. This makes our insight not into discussing a class certain model, but into investigating a group various ones spanning a network space. Somewhat surprisingly, our results prove all members of N(t) to possess some similar characters: (a) sparsity, (b) exponential-scale feature P(k) ∼α-k, and (c) small-world property. Here, we must stress a very screming, but intriguing, phenomenon that the difference of average path length (APL) between any two members in N(t) is quite small, which indicates this random connecting way among members has no great effect on APL. At the end of this article, as a new topological parameter correlated to reliability, synchronization capability and diffusion properties of networks, the number of spanning trees on a representative member NB(t) of N(t) is studied in detail, then an exact analytical solution for its spanning trees entropy is also

Local stability and Hopf bifurcation in small-world delayed networks

International Nuclear Information System (INIS)

Li Chunguang; Chen Guanrong

2004-01-01

The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis

Local stability and Hopf bifurcation in small-world delayed networks

Energy Technology Data Exchange (ETDEWEB)

Li Chunguang E-mail: cgli@uestc.edu.cn; Chen Guanrong E-mail: gchen@ee.cityu.edu.hk

2004-04-01

The notion of small-world networks, recently introduced by Watts and Strogatz, has attracted increasing interest in studying the interesting properties of complex networks. Notice that, a signal or influence travelling on a small-world network often is associated with time-delay features, which are very common in biological and physical networks. Also, the interactions within nodes in a small-world network are often nonlinear. In this paper, we consider a small-world networks model with nonlinear interactions and time delays, which was recently considered by Yang. By choosing the nonlinear interaction strength as a bifurcation parameter, we prove that Hopf bifurcation occurs. We determine the stability of the bifurcating periodic solutions and the direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, we show a numerical example to verify the theoretical analysis.

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...... rapidly and clustering coefficients increase greatly. A tree abstract, Cayley tree, is considered for the study of the navigation algorithm, which runs automatically in the small worlds of tree-based networks. In the further study, epidemics in the small worlds of tree-based wireless sensor networks...

Small-world human brain networks: Perspectives and challenges.

Science.gov (United States)

Liao, Xuhong; Vasilakos, Athanasios V; He, Yong

2017-06-01

Modelling the human brain as a complex network has provided a powerful mathematical framework to characterize the structural and functional architectures of the brain. In the past decade, the combination of non-invasive neuroimaging techniques and graph theoretical approaches enable us to map human structural and functional connectivity patterns (i.e., connectome) at the macroscopic level. One of the most influential findings is that human brain networks exhibit prominent small-world organization. Such a network architecture in the human brain facilitates efficient information segregation and integration at low wiring and energy costs, which presumably results from natural selection under the pressure of a cost-efficiency balance. Moreover, the small-world organization undergoes continuous changes during normal development and ageing and exhibits dramatic alterations in neurological and psychiatric disorders. In this review, we survey recent advances regarding the small-world architecture in human brain networks and highlight the potential implications and applications in multidisciplinary fields, including cognitive neuroscience, medicine and engineering. Finally, we highlight several challenging issues and areas for future research in this rapidly growing field. Copyright © 2017 Elsevier Ltd. All rights reserved.

Immunizations on small worlds of tree-based wireless sensor networks

International Nuclear Information System (INIS)

Li Qiao; Zhang Bai-Hai; Cui Ling-Guo; Fan Zhun; Vasilakos Athanasios, V.

2012-01-01

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, 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 when the spatial-temporal dynamics of the epidemic are considered. The oscillations come from the small-world structure and the temporary immunization. Mathematical analyses on the small world of the Cayley tree are presented to reveal the epidemic dynamics with the two immunization strategies. (general)

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...

Small-world network effects on innovation: evidences from nanotechnology patenting

Energy Technology Data Exchange (ETDEWEB)

Shi, Yuan [University of Maryland, Robert H. Smith School of Business (United States); Guan, JianCheng, E-mail: guanjianch@ucas.ac.cn [University of Chinese Academy of Sciences, School of Economics and Management (China)

2016-11-15

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.

Small-world network effects on innovation: evidences from nanotechnology patenting

International Nuclear Information System (INIS)

Shi, Yuan; Guan, JianCheng

2016-01-01

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.

An effective method to improve the robustness of small-world networks under attack

International Nuclear Information System (INIS)

Zhang Zheng-Zhen; Xu Wen-Jun; Lin Jia-Ru; Zeng Shang-You

2014-01-01

In this study, the robustness of small-world networks to three types of attack is investigated. Global efficiency is introduced as the network coefficient to measure the robustness of a small-world network. The simulation results prove that an increase in rewiring probability or average degree can enhance the robustness of the small-world network under all three types of attack. The effectiveness of simultaneously increasing both rewiring probability and average degree is also studied, and the combined increase is found to significantly improve the robustness of the small-world network. Furthermore, the combined effect of rewiring probability and average degree on network robustness is shown to be several times greater than that of rewiring probability or average degree individually. This means that small-world networks with a relatively high rewiring probability and average degree have advantages both in network communications and in good robustness to attacks. Therefore, simultaneously increasing rewiring probability and average degree is an effective method of constructing realistic networks. Consequently, the proposed method is useful to construct efficient and robust networks in a realistic scenario. (interdisciplinary physics and related areas of science and technology)

Constructing a Watts-Strogatz network from a small-world network with symmetric degree distribution.

Directory of Open Access Journals (Sweden)

Mozart B C Menezes

Full Text Available Though the small-world phenomenon is widespread in many real networks, it is still challenging to replicate a large network at the full scale for further study on its structure and dynamics when sufficient data are not readily available. We propose a method to construct a Watts-Strogatz network using a sample from a small-world network with symmetric degree distribution. Our method yields an estimated degree distribution which fits closely with that of a Watts-Strogatz network and leads into accurate estimates of network metrics such as clustering coefficient and degree of separation. We observe that the accuracy of our method increases as network size increases.

Constructing a Watts-Strogatz network from a small-world network with symmetric degree distribution.

Science.gov (United States)

Menezes, Mozart B C; Kim, Seokjin; Huang, Rongbing

2017-01-01

Though the small-world phenomenon is widespread in many real networks, it is still challenging to replicate a large network at the full scale for further study on its structure and dynamics when sufficient data are not readily available. We propose a method to construct a Watts-Strogatz network using a sample from a small-world network with symmetric degree distribution. Our method yields an estimated degree distribution which fits closely with that of a Watts-Strogatz network and leads into accurate estimates of network metrics such as clustering coefficient and degree of separation. We observe that the accuracy of our method increases as network size increases.

A game-theoretic approach to optimize ad hoc networks inspired by small-world network topology

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Tan, Mian; Yang, Tinghong; Chen, Xing; Yang, Gang; Zhu, Guoqing; Holme, Petter; Zhao, Jing

2018-03-01

Nodes in ad hoc networks are connected in a self-organized manner. Limited communication radius makes information transmit in multi-hop mode, and each forwarding needs to consume the energy of nodes. Insufficient communication radius or exhaustion of energy may cause the absence of some relay nodes and links, further breaking network connectivity. On the other hand, nodes in the network may refuse to cooperate due to objective faulty or personal selfish, hindering regular communication in the network. This paper proposes a model called Repeated Game in Small World Networks (RGSWN). In this model, we first construct ad hoc networks with small-world feature by forming "communication shortcuts" between multiple-radio nodes. Small characteristic path length reduces average forwarding times in networks; meanwhile high clustering coefficient enhances network robustness. Such networks still maintain relative low global power consumption, which is beneficial to extend the network survival time. Then we use MTTFT strategy (Mend-Tolerance Tit-for-Tat) for repeated game as a rule for the interactions between neighbors in the small-world networks. Compared with other five strategies of repeated game, this strategy not only punishes the nodes' selfishness more reasonably, but also has the best tolerance to the network failure. This work is insightful for designing an efficient and robust ad hoc network.

Graph analysis of structural brain networks in Alzheimer's disease: beyond small world properties.

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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

Broad-scale small-world network topology induces optimal synchronization of flexible oscillators

International Nuclear Information System (INIS)

Markovič, Rene; Gosak, Marko; Marhl, Marko

2014-01-01

The discovery of small-world and scale-free properties of many man-made and natural complex networks has attracted increasing attention. Of particular interest is how the structural properties of a network facilitate and constrain its dynamical behavior. In this paper we study the synchronization of weakly coupled limit-cycle oscillators in dependence on the network topology as well as the dynamical features of individual oscillators. We show that flexible oscillators, characterized by near zero values of divergence, express maximal correlation in broad-scale small-world networks, whereas the non-flexible (rigid) oscillators are best correlated in more heterogeneous scale-free networks. We found that the synchronization behavior is governed by the interplay between the networks global efficiency and the mutual frequency adaptation. The latter differs for flexible and rigid oscillators. The results are discussed in terms of evolutionary advantages of broad-scale small-world networks in biological systems

Potts Model in One-Dimension on Directed Small-World Networks

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Aquino, Édio O.; Lima, F. W. S.; Araújo, Ascânio D.; Costa Filho, Raimundo N.

2018-06-01

The critical properties of the Potts model with q=3 and 8 states in one-dimension on directed small-world networks are investigated. This disordered system is simulated by updating it with the Monte Carlo heat bath algorithm. The Potts model on these directed small-world networks presents in fact a second-order phase transition with a new set of critical exponents for q=3 considering a rewiring probability p=0.1. For q=8 the system exhibits only a first-order phase transition independent of p.

Complete and phase synchronization in a heterogeneous small-world neuronal network

International Nuclear Information System (INIS)

Fang, Han; Qi-Shao, Lu; Quan-Bao, Ji; Marian, Wiercigroch

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 networks 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 effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony. (general)

Large Scale Community Detection Using a Small World Model

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Ranjan Kumar Behera

2017-11-01

Full Text Available In a social network, small or large communities within the network play a major role in deciding the functionalities of the network. Despite of diverse definitions, communities in the network may be defined as the group of nodes that are more densely connected as compared to nodes outside the group. Revealing such hidden communities is one of the challenging research problems. A real world social network follows small world phenomena, which indicates that any two social entities can be reachable in a small number of steps. In this paper, nodes are mapped into communities based on the random walk in the network. However, uncovering communities in large-scale networks is a challenging task due to its unprecedented growth in the size of social networks. A good number of community detection algorithms based on random walk exist in literature. In addition, when large-scale social networks are being considered, these algorithms are observed to take considerably longer time. In this work, with an objective to improve the efficiency of algorithms, parallel programming framework like Map-Reduce has been considered for uncovering the hidden communities in social network. The proposed approach has been compared with some standard existing community detection algorithms for both synthetic and real-world datasets in order to examine its performance, and it is observed that the proposed algorithm is more efficient than the existing ones.

Two-dimensional small-world networks: Navigation with local information

International Nuclear Information System (INIS)

Chen Jianzhen; Liu Wei; Zhu Jianyang

2006-01-01

A navigation process is studied on a variant of the Watts-Strogatz small-world network model embedded on a square lattice. With probability p, each vertex sends out a long-range link, and the probability of the other end of this link falling on a vertex at lattice distance r away decays as r -α . Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For α 1, a dynamic small world effect is observed, and the behavior of the scaling function at large enough pL is obtained. At α=2 and 3, this kind of scaling breaks down, and different functions of the average actual path length are obtained. For α>3, the average actual path length is nearly linear with network size

Structure of Small World Innovation Network and Learning Performance

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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.

Small-world organization of self-similar modules in functional brain networks

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Sigman, Mariano; Gallos, Lazaros; Makse, Hernan

2012-02-01

The modular organization of the brain implies the parallel nature of brain computations. These modules have to remain functionally independent, but at the same time they need to be sufficiently connected to guarantee the unitary nature of brain perception. Small-world architectures have been suggested as probable structures explaining this behavior. However, there is intrinsic tension between shortcuts generating small-worlds and the persistence of modularity. In this talk, we study correlations between the activity in different brain areas. We suggest that the functional brain network formed by the 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 shown to follow a pattern that maximizes information transfer with minimal wiring costs. This architecture is reminiscent of the concept of weak-ties strength in social networks and provides a natural solution to the puzzle of efficient infomration flow in the highly modular structure of the brain.

Small-World and Scale-Free Network Models for IoT Systems

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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.

Finite Memory Walk and Its Application to Small-World Network

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Oshima, Hiraku; Odagaki, Takashi

2012-07-01

In order to investigate the effects of cycles on the dynamical process on both regular lattices and complex networks, we introduce a finite memory walk (FMW) as an extension of the simple random walk (SRW), in which a walker is prohibited from moving to sites visited during m steps just before the current position. This walk interpolates the simple random walk (SRW), which has no memory (m = 0), and the self-avoiding walk (SAW), which has an infinite memory (m = ∞). We investigate the FMW on regular lattices and clarify the fundamental characteristics of the walk. We find that (1) the mean-square displacement (MSD) of the FMW shows a crossover from the SAW at a short time step to the SRW at a long time step, and the crossover time is approximately equivalent to the number of steps remembered, and that the MSD can be rescaled in terms of the time step and the size of memory; (2) the mean first-return time (MFRT) of the FMW changes significantly at the number of remembered steps that corresponds to the size of the smallest cycle in the regular lattice, where ``smallest'' indicates that the size of the cycle is the smallest in the network; (3) the relaxation time of the first-return time distribution (FRTD) decreases as the number of cycles increases. We also investigate the FMW on the Watts--Strogatz networks that can generate small-world networks, and show that the clustering coefficient of the Watts--Strogatz network is strongly related to the MFRT of the FMW that can remember two steps.

The relations between network-operation and topological-property in a scale-free and small-world network with community structure

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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.

Complex Behavior in a Selective Aging Neuron Model Based on Small World Networks

International Nuclear Information System (INIS)

Zhang Guiqing; Chen Tianlun

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.

Dynamical mean-field approximation to small-world networks of spiking neurons: From local to global and/or from regular to random couplings

International Nuclear Information System (INIS)

Hasegawa, Hideo

2004-01-01

By extending a dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E 67, 041903 (2003)], we have developed a semianalytical theory which takes into account a wide range of couplings in a small-world network. Our network consists of noisy N-unit FitzHugh-Nagumo neurons with couplings whose average coordination number Z may change from local (Z<< N) to global couplings (Z=N-1) and/or whose concentration of random couplings p is allowed to vary from regular (p=0) to completely random (p=1). We have taken into account three kinds of spatial correlations: the on-site correlation, the correlation for a coupled pair, and that for a pair without direct couplings. The original 2N-dimensional stochastic differential equations are transformed to 13-dimensional deterministic differential equations expressed in terms of means, variances, and covariances of state variables. The synchronization ratio and the firing-time precision for an applied single spike have been discussed as functions of Z and p. Our calculations have shown that with increasing p, the synchronization is worse because of increased heterogeneous couplings, although the average network distance becomes shorter. Results calculated by our theory are in good agreement with those by direct simulations

Spiral Wave in Small-World Networks of Hodgkin-Huxley Neurons

International Nuclear Information System (INIS)

Ma Jun; Zhang Cairong; Yang Lijian; Wu Ying

2010-01-01

The effect of small-world connection and noise on the formation and transition of spiral wave in the networks of Hodgkin-Huxley neurons are investigated in detail. Some interesting results are found in our numerical studies. i) The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii) A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise. iii) Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv) Gaussian white noise is introduced on the membrane of neurons to study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Gaussian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave. (interdisciplinary physics and related areas of science and technology)

Synchronization of the small-world neuronal network with unreliable synapses

International Nuclear Information System (INIS)

Li, Chunguang; Zheng, Qunxian

2010-01-01

As is well known, synchronization phenomena are ubiquitous in neuronal systems. Recently a lot of work concerning the synchronization of the neuronal network has been accomplished. In these works, the synapses are usually considered reliable, but experimental results show that, in biological neuronal networks, synapses are usually unreliable. In our previous work, we have studied the synchronization of the neuronal network with unreliable synapses; however, we have not paid attention to the effect of topology on the synchronization of the neuronal network. Several recent studies have found that biological neuronal networks have typical properties of small-world networks, characterized by a short path length and high clustering coefficient. In this work, mainly based on the small-world neuronal network (SWNN) with inhibitory neurons, we study the effect of network topology on the synchronization of the neuronal network with unreliable synapses. Together with the network topology, the effects of the GABAergic reversal potential, time delay and noise are also considered. Interestingly, we found a counter-intuitive phenomenon for the SWNN with specific shortcut adding probability, that is, the less reliable the synapses, the better the synchronization performance of the SWNN. We also consider the effects of both local noise and global noise in this work. It is shown that these two different types of noise have distinct effects on the synchronization: one is negative and the other is positive

Extraction of network topology from multi-electrode recordings: Is there a small-world effect?

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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.

Interictal to Ictal Phase Transition in a Small-World Network

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Nemzer, Louis; Cravens, Gary; Worth, Robert

Real-time detection and prediction of seizures in patients with epilepsy is essential for rapid intervention. Here, we perform a full Hodgkin-Huxley calculation using n 50 in silico neurons configured in a small-world network topology to generate simulated EEG signals. The connectivity matrix, constructed using a Watts-Strogatz algorithm, admits randomized or deterministic entries. We find that situations corresponding to interictal (non-seizure) and ictal (seizure) states are separated by a phase transition that can be influenced by congenital channelopathies, anticonvulsant drugs, and connectome plasticity. The interictal phase exhibits scale-free phenomena, as characterized by a power law form of the spectral power density, while the ictal state suffers from pathological synchronization. We compare the results with intracranial EEG data and show how these findings may be used to detect or even predict seizure onset. Along with the balance of excitatory and inhibitory factors, the network topology plays a large role in determining the overall characteristics of brain activity. We have developed a new platform for testing the conditions that contribute to the phase transition between non-seizure and seizure states.

Evaluating the transport in small-world and scale-free networks

International Nuclear Information System (INIS)

Juárez-López, R.; Obregón-Quintana, B.; Hernández-Pérez, R.; Reyes-Ramírez, I.; Guzmán-Vargas, L.

2014-01-01

We present a study of some properties of transport in small-world and scale-free networks. Particularly, we compare two types of transport: subject to friction (electrical case) and in the absence of friction (maximum flow). We found that in clustered networks based on the Watts–Strogatz (WS) model, for both transport types the small-world configurations exhibit the best trade-off between local and global levels. For non-clustered WS networks the local transport is independent of the rewiring parameter, while the transport improves globally. Moreover, we analyzed both transport types in scale-free networks considering tendencies in the assortative or disassortative mixing of nodes. We construct the distribution of the conductance G and flow F to evaluate the effects of the assortative (disassortative) mixing, finding that for scale-free networks, as we introduce different levels of the degree–degree correlations, the power-law decay in the conductances is altered, while for the flow, the power-law tail remains unchanged. In addition, we analyze the effect on the conductance and the flow of the minimum degree and the shortest path between the source and destination nodes, finding notable differences between these two types of transport

Networks of neuroblastoma cells on porous silicon substrates reveal a small world topology

KAUST Repository

Marinaro, Giovanni; La Rocca, Rosanna; Toma, Andrea; Barberio, Marianna; Cancedda, Laura; Di Fabrizio, Enzo M.; Decuzzi, Paolo C W; Gentile, Francesco T.

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

Small-worldness characteristics and its gender relation in specific hemispheric networks.

Science.gov (United States)

Miraglia, F; Vecchio, F; Bramanti, P; Rossini, P M

2015-12-03

Aim of this study was to verify whether the topological organization of human brain functional networks is different for males and females in resting state EEGs. Undirected and weighted brain networks were computed by eLORETA lagged linear connectivity in 130 subjects (59 males and 71 females) within each hemisphere and in four resting state networks (Attentional Network (AN), Frontal Network (FN), Sensorimotor Network (SN), Default Mode Network (DMN)). We found that small-world (SW) architecture in the left hemisphere Frontal network presented differences in both delta and alpha band, in particular lower values in delta and higher in alpha 2 in males respect to females while in the right hemisphere differences were found in lower values of SW in males respect to females in gamma Attentional, delta Sensorimotor and delta and gamma DMNs. Gender small-worldness differences in some of resting state networks indicated that there are specific brain differences in the EEG rhythms when the brain is in the resting-state condition. These specific regions could be considered related to the functions of behavior and cognition and should be taken into account both for research on healthy and brain diseased subjects. Copyright © 2015 IBRO. Published by Elsevier Ltd. All rights reserved.

Dynamic Evolution with Limited Learning Information on a Small-World Network

International Nuclear Information System (INIS)

Dong Linrong

2010-01-01

This paper investigates the dynamic evolution with limited learning information on a small-world network. In the system, the information among the interaction players is not very lucid, and the players are not allowed to inspect the profit collected by its neighbors, thus the focal player cannot choose randomly a neighbor or the wealthiest one and compare its payoff to copy its strategy. It is assumed that the information acquainted by the player declines in the form of the exponential with the geographical distance between the players, and a parameter V is introduced to denote the inspect-ability about the players. It is found that under the hospitable conditions, cooperation increases with the randomness and is inhibited by the large connectivity for the prisoner's dilemma; however, cooperation is maximal at the moderate rewiring probability and is chaos with the connectivity for the snowdrift game. For the two games, the acuminous sight is in favor of the cooperation under the hospitable conditions; whereas, the myopic eyes are advantageous to cooperation and cooperation increases with the randomness under the hostile condition. (interdisciplinary physics and related areas of science and technology)

On the structural properties of small-world networks with range-limited shortcut links

Science.gov (United States)

Jia, Tao; Kulkarni, Rahul V.

2013-12-01

We explore a new variant of Small-World Networks (SWNs), in which an additional parameter (r) sets the length scale over which shortcuts are uniformly distributed. When r=0 we have an ordered network, whereas r=1 corresponds to the original Watts-Strogatz SWN model. These limited range SWNs have a similar degree distribution and scaling properties as the original SWN model. We observe the small-world phenomenon for r≪1, indicating that global shortcuts are not necessary for the small-world effect. For limited range SWNs, the average path length changes nonmonotonically with system size, whereas for the original SWN model it increases monotonically. We propose an expression for the average path length for limited range SWNs based on numerical simulations and analytical approximations.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

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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.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks

International Nuclear Information System (INIS)

Yu, Haitao; Guo, Xinmeng; Wang, Jiang; Deng, Bin; Wei, Xile

2014-01-01

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

Growing Homophilic Networks Are Natural Navigable Small Worlds.

Science.gov (United States)

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.

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.

Phase Transitions of an Epidemic Spreading Model in Small-World Networks

Science.gov (United States)

Hua, Da-Yin; Gao, Ke

2011-06-01

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.

A fault-tolerant small world topology control model in ad hoc networks for search and rescue

Science.gov (United States)

Tan, Mian; Fang, Ling; Wu, Yue; Zhang, Bo; Chang, Bowen; Holme, Petter; Zhao, Jing

2018-02-01

Due to their self-organized, multi-hop and distributed characteristics, ad hoc networks are useful in search and rescue. Topology control models need to be designed for energy-efficient, robust and fast communication in ad hoc networks. This paper proposes a topology control model which specializes for search and rescue-Compensation Small World-Repeated Game (CSWRG)-which integrates mobility models, constructing small world networks and a game-theoretic approach to the allocation of resources. Simulation results show that our mobility models can enhance the communication performance of the constructed small-world networks. Our strategy, based on repeated game, can suppress selfish behavior and compensate agents that encounter selfish or faulty neighbors. This model could be useful for the design of ad hoc communication networks.

Statistical complexity is maximized in a small-world brain.

Directory of Open Access Journals (Sweden)

Teck Liang Tan

Full Text Available In this paper, we study a network of Izhikevich neurons to explore what it means for a brain to be at the edge of chaos. To do so, we first constructed the phase diagram of a single Izhikevich excitatory neuron, and identified a small region of the parameter space where we find a large number of phase boundaries to serve as our edge of chaos. We then couple the outputs of these neurons directly to the parameters of other neurons, so that the neuron dynamics can drive transitions from one phase to another on an artificial energy landscape. Finally, we measure the statistical complexity of the parameter time series, while the network is tuned from a regular network to a random network using the Watts-Strogatz rewiring algorithm. We find that the statistical complexity of the parameter dynamics is maximized when the neuron network is most small-world-like. Our results suggest that the small-world architecture of neuron connections in brains is not accidental, but may be related to the information processing that they do.

Cognition Is Related to Resting-State Small-World Network Topology: An Magnetoencephalographic Study

NARCIS (Netherlands)

Douw, L.; Schoonheim, M.M.; Landi, D.; van der Meer, M.L.; Geurts, J.J.G.; Reijneveld, J.C.; Klein, M.; Stam, C.J.

2011-01-01

Brain networks and cognition have recently begun to attract attention: studies suggest that more efficiently wired resting-state brain networks are indeed correlated with better cognitive performance. "Small-world" brain networks combine local segregation with global integration, hereby subserving

The lesioned brain: still a small world?

Directory of Open Access Journals (Sweden)

Linda Douw

2010-11-01

Full Text Available The intra-arterial amobarbital procedure (IAP or Wada test is used to determine language lateralization and contralateral memory functioning in patients eligible for neurosurgery because of pharmaco-resistant epilepsy. During unilateral sedation, functioning of the contralateral hemisphere is assessed by means of neuropsychological tests. We use the IAP as a reversible model for the effect of lesions on brain network topology. Three artifact free epochs (4096 samples were selected from each EEG record before and after amobarbital injection. Functional connectivity was assessed by means of the synchronization likelihood (SL. The resulting functional connectivity matrices were constructed for all six epochs per patient in four frequency bands, and weighted network analysis was performed. The clustering coefficient, average path length, small-world-index, and edge weight correlation were calculated. Recordings of 33 patients were available. Network topology changed significantly after amobarbital injection: clustering decreased in all frequency bands, while path length decreased in the theta and lower alpha band, indicating a shift towards a more random network topology. Likewise, the edge weight correlation decreased after injection of amobarbital in the theta and beta bands. Network characteristics after injection of amobarbital were correlated with memory score: higher theta band small-world-index and increased upper alpha path length were related to better memory score. The whole-brain network topology in patients eligible for epilepsy surgery becomes more random and less optimally organized after selective sedation of one hemisphere, as has been reported in studies with brain tumor patients. Furthermore, memory functioning after injection seems related to network topology, indicating that functional performance is related to topological network properties of the brain.

Stability of the spreading in small-world network with predictive controller

International Nuclear Information System (INIS)

Bao, Z.J.; Jiang, Q.Y.; Yan, W.J.; Cao, Y.J.

2010-01-01

In this Letter, we apply the predictive control strategy to suppress the propagation of diseases or viruses in small-world network. The stability of small-world spreading model with predictive controller is investigated. The sufficient and necessary stability condition is given, which is closely related to the controller parameters and small-world rewiring probability p. Our simulations discover a phenomenon that, with the fixed predictive controller parameters, the spreading dynamics become more and more stable when p decreases from a larger value to a smaller one, and the suitable controller parameters can effectively suppress the spreading behaviors even when p varies within the whole spectrum, and the unsuitable controller parameters can lead to oscillation when p lies within a certain range.

Topology of the Italian airport network: A scale-free small-world network with a fractal structure?

International Nuclear Information System (INIS)

Guida, Michele; Maria, Funaro

2007-01-01

In this paper, for the first time we analyze the structure of the Italian Airport Network (IAN) looking at it as a mathematical graph and investigate its topological properties. We find that it has very remarkable features, being like a scale-free network, since both the degree and the 'betweenness centrality' distributions follow a typical power-law known in literature as a Double Pareto Law. From a careful analysis of the data, the Italian Airport Network turns out to have a self-similar structure. In short, it is characterized by a fractal nature, whose typical dimensions can be easily determined from the values of the power-law scaling exponents. Moreover, we show that, according to the period examined, these distributions exhibit a number of interesting features, such as the existence of some 'hubs', i.e. in the graph theory's jargon, nodes with a very large number of links, and others most probably associated with geographical constraints. Also, we find that the IAN can be classified as a small-world network because the average distance between reachable pairs of airports grows at most as the logarithm of the number of airports. The IAN does not show evidence of 'communities' and this result could be the underlying reason behind the smallness of the value of the clustering coefficient, which is related to the probability that two nearest neighbors of a randomly chosen airport are connected

Small World Properties Generated by a New Algorithm Under Same Degree of All Nodes

International Nuclear Information System (INIS)

Li Yong; Fang Jinqing; 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.

Mapping Koch curves into scale-free small-world networks

International Nuclear Information System (INIS)

Zhang Zhongzhi; Gao Shuyang; Zhou Shuigeng; Chen Lichao; Zhang Hongjuan; Guan Jihong

2010-01-01

The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping technique converting Koch fractals into a family of deterministic networks called Koch networks. This novel class of networks incorporates some key properties characterizing a majority of real-life networked systems-a power-law distribution with exponent in the range between 2 and 3, a high clustering coefficient, a small diameter and average path length and degree correlations. Besides, we enumerate the exact numbers of spanning trees, spanning forests and connected spanning subgraphs in the networks. All these features are obtained exactly according to the proposed generation algorithm of the networks considered. The network representation approach could be used to investigate the complexity of some real-world systems from the perspective of complex networks.

Small-world topology of functional connectivity in randomly connected dynamical systems

Czech Academy of Sciences Publication Activity Database

Hlinka, Jaroslav; Hartman, David; Paluš, Milan

2012-01-01

Roč. 22, č. 3 (2012), art no 033107 ISSN 1054-1500 R&D Projects: GA ČR GCP103/11/J068 Institutional support: RVO:67985807 Keywords : graph theory * nonlinear dynamical systems * small-world networks Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.188, year: 2012

Impaired small-world network efficiency and dynamic functional distribution in patients with cirrhosis.

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

Phase synchronization on small-world networks with community structure

International Nuclear Information System (INIS)

Xiao-Hua, Wang; Li-Cheng, Jiao; Jian-She, Wu

2010-01-01

In this paper, we propose a simple model that can generate small-world network with community structure. The network is introduced as a tunable community organization with parameter r, which is directly measured by the ratio of inter- to intra-community connectivity, and a smaller r corresponds to a stronger community structure. The structure properties, including the degree distribution, clustering, the communication efficiency and modularity are also analysed for the network. In addition, by using the Kuramoto model, we investigated the phase synchronization on this network, and found that increasing the fuzziness of community structure will markedly enhance the network synchronizability; however, in an abnormal region (r ≤ 0.001), the network has even worse synchronizability than the case of isolated communities (r = 0). Furthermore, this network exhibits a remarkable synchronization behaviour in topological scales: the oscillators of high densely interconnected communities synchronize more easily, and more rapidly than the whole network. (general)

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

Current redistribution in resistor networks: Fat-tail statistics in regular and small-world networks.

Science.gov (United States)

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.

Suppression of anomalous synchronization and nonstationary behavior of neural network under small-world topology

Science.gov (United States)

Boaretto, B. R. R.; Budzinski, R. C.; Prado, T. L.; Kurths, J.; Lopes, S. R.

2018-05-01

It is known that neural networks under small-world topology can present anomalous synchronization and nonstationary behavior for weak coupling regimes. Here, we propose methods to suppress the anomalous synchronization and also to diminish the nonstationary behavior occurring in weakly coupled neural network under small-world topology. We consider a network of 2000 thermally sensitive identical neurons, based on the model of Hodgkin-Huxley in a small-world topology, with the probability of adding non local connection equal to p = 0 . 001. Based on experimental protocols to suppress anomalous synchronization, as well as nonstationary behavior of the neural network dynamics, we make use of (i) external stimulus (pulsed current); (ii) biologic parameters changing (neuron membrane conductance changes); and (iii) body temperature changes. Quantification analysis to evaluate phase synchronization makes use of the Kuramoto's order parameter, while recurrence quantification analysis, particularly the determinism, computed over the easily accessible mean field of network, the local field potential (LFP), is used to evaluate nonstationary states. We show that the methods proposed can control the anomalous synchronization and nonstationarity occurring for weak coupling parameter without any effect on the individual neuron dynamics, neither in the expected asymptotic synchronized states occurring for large values of the coupling parameter.

Stretched exponential dynamics of coupled logistic maps on a small-world network

Science.gov (United States)

Mahajan, Ashwini V.; Gade, Prashant M.

2018-02-01

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in a coarse grained sense acts as an excellent order parameter to study this transition. We investigate the phase diagram by varying coupling strength and small-world rewiring probability p of nonlocal connections. The persistent region is a compact region bounded by two critical lines where band-merging crisis occurs. On one critical line, the persistent sites shows a nonexponential (stretched exponential) decay for all p while for another one, it shows crossover from nonexponential to exponential behavior as p → 1 . With an effectively antiferromagnetic coupling, coupling to two neighbors on either side leads to exchange frustration. Apart from exchange frustration, non-bipartite topology and nonlocal couplings in a small-world network could be a reason for anomalous relaxation. The distribution of trap times in asymptotic regime has a long tail as well. The dependence of temporal evolution of persistence on initial conditions is studied and a scaling form for persistence after waiting time is proposed. We present a simple possible model for this behavior.

Small-world networks exhibit pronounced intermittent synchronization

Science.gov (United States)

Choudhary, Anshul; Mitra, Chiranjit; Kohar, Vivek; Sinha, Sudeshna; Kurths, Jürgen

2017-11-01

We report the phenomenon of temporally intermittently synchronized and desynchronized dynamics in Watts-Strogatz networks of chaotic Rössler oscillators. We consider topologies for which the master stability function (MSF) predicts stable synchronized behaviour, as the rewiring probability (p) is tuned from 0 to 1. MSF essentially utilizes the largest non-zero Lyapunov exponent transversal to the synchronization manifold in making stability considerations, thereby ignoring the other Lyapunov exponents. However, for an N-node networked dynamical system, we observe that the difference in its Lyapunov spectra (corresponding to the N - 1 directions transversal to the synchronization manifold) is crucial and serves as an indicator of the presence of intermittently synchronized behaviour. In addition to the linear stability-based (MSF) analysis, we further provide global stability estimate in terms of the fraction of state-space volume shared by the intermittently synchronized state, as p is varied from 0 to 1. This fraction becomes appreciably large in the small-world regime, which is surprising, since this limit has been otherwise considered optimal for synchronized dynamics. Finally, we characterize the nature of the observed intermittency and its dominance in state-space as network rewiring probability (p) is varied.

Critical behavior of the XY-rotor model on regular and small-world networks

Science.gov (United States)

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 Nlinks˜Nγ, 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 ɛ=E/N,ɛc=0.75. Moreover, for γc≃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 pSW∝1/Nγ. Then considering the XY-rotors model on these networks, we find that a second-order phase transition occurs at a critical energy ɛc which logarithmically depends on the topological parameters p and γ. We also define a critical probability pMF, corresponding to the probability beyond which the mean field is quantitatively recovered, and we analyze its dependence on γ.

Algebraic approach to small-world network models

Science.gov (United States)

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.

The small world yields the most effective information spreading

International Nuclear Information System (INIS)

Lü Linyuan; Chen Duanbing; Zhou Tao

2011-01-01

The spreading dynamics of information and diseases are usually analyzed by using a unified framework and analogous models. In this paper, we propose a model to emphasize the essential difference between information spreading and epidemic spreading, where the memory effects, the social reinforcement and the non-redundancy of contacts are taken into account. Under certain conditions, the information spreads faster and broader in regular networks than in random networks, which to some extent supports the recent experimental observation of spreading in online society (Centola D 2010 Science 329 1194). At the same time, the simulation result indicates that the random networks tend to be favorable for effective spreading when the network size increases. This challenges the validity of the above-mentioned experiment for large-scale systems. More importantly, we show that the spreading effectiveness can be sharply enhanced by introducing a little randomness into the regular structure, namely the small-world networks yield the most effective information spreading. This work provides insights into the role of local clustering in information spreading. (paper)

Robustness of cluster synchronous patterns in small-world networks with inter-cluster co-competition balance

International Nuclear Information System (INIS)

Zhang, Jianbao; Ma, Zhongjun; Chen, Guanrong

2014-01-01

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

Robustness of cluster synchronous patterns in small-world networks with inter-cluster co-competition balance

Science.gov (United States)

Zhang, Jianbao; Ma, Zhongjun; Chen, Guanrong

2014-06-01

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.

Robustness of cluster synchronous patterns in small-world networks with inter-cluster co-competition balance

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.

Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology

International Nuclear Information System (INIS)

Liu Qiang; Fang Jinqing; 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 SW topology, 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.

Abnormal small-world brain functional networks in obsessive-compulsive disorder patients with poor insight.

Science.gov (United States)

Lei, Hui; Cui, Yan; Fan, Jie; Zhang, Xiaocui; Zhong, Mingtian; Yi, Jinyao; Cai, Lin; Yao, Dezhong; Zhu, Xiongzhao

2017-09-01

There are limited data on neurobiological correlates of poor insight in obsessive-compulsive disorder (OCD). This study explored whether specific changes occur in small-world network (SWN) properties in the brain functional network of OCD patients with poor insight. Resting-state electroencephalograms (EEGs) were recorded for 12 medication-free OCD patients with poor insight, 50 medication-free OCD patients with good insight, and 36 healthy controls. Both of the OCD groups exhibited topological alterations in the brain functional network characterized by abnormal small-world parameters at the beta band. However, the alterations at the theta band only existed in the OCD patients with poor insight. A relatively small sample size. Subjects were naïve to medications and those with Axis I comorbidity were excluded, perhaps limiting generalizability. Disrupted functional integrity at the beta bands of the brain functional network may be related to OCD, while disrupted functional integrity at the theta band may be associated with poor insight in OCD patients, thus this study might provide novel insight into our understanding of the pathophysiology of OCD. Copyright © 2017 Elsevier B.V. All rights reserved.

Small Worlds and Cultural Polarization

NARCIS (Netherlands)

Flache, Andreas; Macy, Michael W.

2011-01-01

Building on Granovetter's theory of the "strength of weak ties,'' research on "small-world'' networks suggests that bridges between clusters in a social network (long-range ties) promote cultural diffusion, homogeneity, and integration. We show that this macro-level implication of network structure

Disease spreading with epidemic alert on small-world networks

International Nuclear Information System (INIS)

Han, Xiao-Pu

2007-01-01

Base on two-dimension small-world networks, a susceptible-infected model with epidemic alert is proposed in this Letter. In this model, if some parts of the network are alarmed as dangerous, a fraction of edges between the alarmed parts and others will be removed, and two cases of alerting rules that the degree and frequency of contacts kept unchanged are considered respectively. The numerical simulations show that the spreading velocity is reduced by the accurate and timely epidemic alert, and the more accurate and timely, the stronger the deceleration effect. This model indicates that to broadcast epidemic alert timely is helpful and necessary in the control of epidemic spreading, and in agreement with the general view of epidemic alert. This work is helpful to understand the effects of epidemic alert on disease spreading

Impact of small-world network topology on the conventional artificial neural network for the diagnosis of diabetes

International Nuclear Information System (INIS)

Erkaymaz, Okan; Ozer, Mahmut

2016-01-01

Artificial intelligent systems have been widely used for diagnosis of diseases. Due to their importance, new approaches are attempted consistently to increase the performance of these systems. In this study, we introduce a new approach for diagnosis of diabetes based on the Small-World Feed Forward Artificial Neural Network (SW- FFANN). We construct the small-world network by following the Watts–Strogatz approach, and use this architecture for classifying the diabetes, and compare its performance with that of the regular or the conventional FFANN. We show that the classification performance of the SW-FFANN is better than that of the conventional FFANN. The SW-FFANN approach also results in both the highest output correlation and the best output error parameters. We also perform the accuracy analysis and show that SW-FFANN approach exhibits the highest classifier performance.

Chaos in complex motor networks induced by Newman—Watts small-world connections

International Nuclear Information System (INIS)

Wei Du-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. (interdisciplinary physics and related areas of science and technology)

[Analysis of the Characteristics of Infantile Small World Neural Network Node Properties Correlated with the Influencing Factors].

Science.gov (United States)

Qu, Haibo; Lu, Su; Zhang, Wenjing; Xiao, Yuan; Ning, Gang; Sun, Huaiqiang

2016-10-01

We applied resting-state functional magnetic resonance imaging(rfMRI)combined with graph theory to analyze 90 regions of the infantile small world neural network of the whole brain.We tried to get the following two points clear:1 whether the parameters of the node property of the infantile small world neural network are correlated with the level of infantile intelligence development;2 whether the parameters of the infantile small world neural network are correlated with the children’s baseline parameters,i.e.,the demographic parameters such as gender,age,parents’ education level,etc.Twelve cases of healthy infants were included in the investigation(9males and 3females with the average age of 33.42±8.42 months.)We then evaluated the level of infantile intelligence of all the cases and graded by Gesell Development Scale Test.We used a Siemens 3.0T Trio imaging system to perform resting-state(rs)EPI scans,and collected the BOLD functional Magnetic Resonance Imaging(fMRI)data.We performed the data processing with Statistical Parametric Mapping 5(SPM5)based on Matlab environment.Furthermore,we got the attributes of the whole brain small world and node attributes of 90 encephalic regions of templates of Anatomatic Automatic Labeling(ALL).At last,we carried out correlation study between the above-mentioned attitudes,intelligence scale parameters and demographic data.The results showed that many node attributes of small world neural network were closely correlated with intelligence scale parameters.Betweeness was mainly centered in thalamus,superior frontal gyrus,and occipital lobe(negative correlation).The r value of superior occipital gyrus associated with the individual and social intelligent scale was-0.729(P=0.007);degree was mainly centered in amygdaloid nucleus,superior frontal gyrus,and inferior parietal gyrus(positive correlation).The r value of inferior parietal gyrus associated with the gross motor intelligent scale was 0.725(P=0.008);efficiency was mainly

Critical features of coupling parameter in synchronization of small world neural networks

International Nuclear Information System (INIS)

Li Yanlong; Ma Jun; Xu Wenke; Li Hongbo; Wu Min

2008-01-01

The critical features of a coupling parameter in the synchronization of small world neural networks are investigated. A power law decay form is observed in this spatially extended system, the larger linked degree becomes, the larger critical coupling intensity. There exists maximal and minimal critical coupling intensity for synchronization in the extended system. An approximate synchronization diagram has been constructed. In the case of partial coupling, a primary result is presented about the critical coupling fraction for various linked degree of networks

Phase synchronization of non-Abelian oscillators on small-world networks

Energy Technology Data Exchange (ETDEWEB)

Gu, Zhi-Ming [College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Zhao, Ming [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China); Zhou, Tao [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)]. E-mail: zhutou@ustc.edu; Zhu, Chen-Ping [College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China); Wang, Bing-Hong [Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)

2007-02-26

In this Letter, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems on Watts-Strogatz networks are given, including the n-dimensional torus, the identity component of 3-dimensional general linear group, the special unitary group, and the special orthogonal group. In all cases, the greater disorder of networks will predict better synchronizability, and the small-world effect ensures the global synchronization for sufficiently large coupling strength. The collective synchronized behaviors of many dynamical systems, such as the integrable systems, the two-state quantum systems and the top systems, can be described by the present phase synchronization frame. In addition, it is intuitive that the low-dimensional systems are more easily to synchronize, however, to our surprise, we found that the high-dimensional systems display obviously synchronized behaviors in regular networks, while these phenomena cannot be observed in low-dimensional systems.

Phase synchronization of non-Abelian oscillators on small-world networks

International Nuclear Information System (INIS)

Gu, Zhi-Ming; Zhao, Ming; Zhou, Tao; Zhu, Chen-Ping; Wang, Bing-Hong

2007-01-01

In this Letter, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems on Watts-Strogatz networks are given, including the n-dimensional torus, the identity component of 3-dimensional general linear group, the special unitary group, and the special orthogonal group. In all cases, the greater disorder of networks will predict better synchronizability, and the small-world effect ensures the global synchronization for sufficiently large coupling strength. The collective synchronized behaviors of many dynamical systems, such as the integrable systems, the two-state quantum systems and the top systems, can be described by the present phase synchronization frame. In addition, it is intuitive that the low-dimensional systems are more easily to synchronize, however, to our surprise, we found that the high-dimensional systems display obviously synchronized behaviors in regular networks, while these phenomena cannot be observed in low-dimensional systems

Time reversibility of quantum diffusion in small-world networks

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Han, Sung-Guk; Kim, Beom Jun

2012-02-01

We study the time-reversal dynamics of a tight-binding electron in the Watts-Strogatz (WS) small-world networks. The localized initial wave packet at time t = 0 diffuses as time proceeds until the time-reversal operation, together with the momentum perturbation of the strength η, is made at the reversal time T. The time irreversibility is measured by I = |Π( t = 2 T) - Π( t = 0)|, where Π is the participation ratio gauging the extendedness of the wavefunction and for convenience, t is measured forward even after the time reversal. When η = 0, the time evolution after T makes the wavefunction at t = 2 T identical to the one at t = 0, and we find I = 0, implying a null irreversibility or a complete reversibility. On the other hand, as η is increased from zero, the reversibility becomes weaker, and we observe enhancement of the irreversibility. We find that I linearly increases with increasing η in the weakly-perturbed region, and that the irreversibility is much stronger in the WS network than in the local regular network.

Impact of Partial Time Delay on Temporal Dynamics of Watts-Strogatz Small-World Neuronal Networks

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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.

Unraveling spurious properties of interaction networks with tailored random networks.

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Stephan Bialonski

Full Text Available We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erdös-Rényi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures--known for their complex spatial and temporal dynamics--we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.

A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks.

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Gallos, Lazaros K; Makse, Hernán A; Sigman, Mariano

2012-02-21

The human brain is organized in functional modules. Such an organization presents a basic 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 of short paths and large local clustering may solve this problem. However, there is intrinsic tension between shortcuts generating small worlds and the persistence of modularity, a global property unrelated to local clustering. Here, we present a possible solution to this puzzle. We first show that a modified percolation theory can define a set of hierarchically organized modules made of strong links in functional brain networks. These modules are "large-world" self-similar structures and, therefore, are far from being small-world. However, incorporating weaker ties to the network converts it into a small world preserving an underlying backbone of well-defined modules. Remarkably, weak ties are precisely organized as predicted by theory maximizing information transfer with minimal wiring cost. This trade-off architecture is reminiscent of the "strength of weak ties" crucial concept of social networks. Such a design suggests a natural solution to the paradox of efficient information flow in the highly modular structure of the brain.

Simple, distance-dependent formulation of the Watts-Strogatz model for directed and undirected small-world networks

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Song, H. Francis; Wang, Xiao-Jing

2014-12-01

Small-world networks—complex networks characterized by a combination of high clustering and short path lengths—are widely studied using the paradigmatic model of Watts and Strogatz (WS). Although the WS model is already quite minimal and intuitive, we describe an alternative formulation of the WS model in terms of a distance-dependent probability of connection that further simplifies, both practically and theoretically, the generation of directed and undirected WS-type small-world networks. In addition to highlighting an essential feature of the WS model that has previously been overlooked, namely the equivalence to a simple distance-dependent model, this alternative formulation makes it possible to derive exact expressions for quantities such as the degree and motif distributions and global clustering coefficient for both directed and undirected networks in terms of model parameters.

Transmission of severe acute respiratory syndrome in dynamical small-world networks

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Masuda, Naoki; Konno, Norio; Aihara, Kazuyuki

2004-03-01

The outbreak of severe acute respiratory syndrome (SARS) is still threatening the world because of a possible resurgence. In the current situation that effective medical treatments such as antiviral drugs are not discovered yet, dynamical features of the epidemics should be clarified for establishing strategies for tracing, quarantine, isolation, and regulating social behavior of the public at appropriate costs. Here we propose a network model for SARS epidemics and discuss why superspreaders emerged and why SARS spread especially in hospitals, which were key factors of the recent outbreak. We suggest that superspreaders are biologically contagious patients, and they may amplify the spreads by going to potentially contagious places such as hospitals. To avoid mass transmission in hospitals, it may be a good measure to treat suspected cases without hospitalizing them. Finally, we indicate that SARS probably propagates in small-world networks associated with human contacts and that the biological nature of individuals and social group properties are factors more important than the heterogeneous rates of social contacts among individuals. This is in marked contrast with epidemics of sexually transmitted diseases or computer viruses to which scale-free network models often apply.

Critical behavior and correlations on scale-free small-world networks: Application to network design

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Ostilli, M.; Ferreira, A. L.; Mendes, J. F. F.

2011-06-01

We analyze critical phenomena on networks generated as the union of hidden variable models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small worlds similar to those à la Watts and Strogatz, but with a heterogeneous degree distribution. We prove that the critical behavior (thermal or percolative) remains completely unchanged by the presence of finite loops (or finite clustering). Then, we show that, in large but finite networks, correlations of two given spins may be strong, i.e., approximately power-law-like, at any temperature. Quite interestingly, if γ is the exponent for the power-law distribution of the vertex degree, for γ⩽3 and with or without short-range couplings, such strong correlations persist even in the thermodynamic limit, contradicting the common opinion that, in mean-field models, correlations always disappear in this limit. Finally, we provide the optimal choice of rewiring under which percolation phenomena in the rewired network are best performed, a natural criterion to reach best communication features, at least in noncongested regimes.

Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings

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Hasegawa, Hideo

2005-01-01

By using a semianalytical dynamical mean-field approximation previously proposed by the author [H. Hasegawa, Phys. Rev. E 70, 066107 (2004)], we have studied the synchronization of stochastic, small-world (SW) networks of FitzHugh-Nagumo neurons with diffusive couplings. The difference and similarity between results for diffusive and sigmoid couplings have been discussed. It has been shown that with introducing the weak heterogeneity to regular networks, the synchronization may be slightly increased for diffusive couplings, while it is decreased for sigmoid couplings. This increase in the synchronization for diffusive couplings is shown to be due to their local, negative feedback contributions, but not due to the short average distance in SW networks. Synchronization of SW networks depends not only on their structure but also on the type of couplings

Heterogeneous delay-induced asynchrony and resonance in a small-world neuronal network system

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Yu, Wen-Ting; Tang, Jun; Ma, Jun; Yang, Xianqing

2016-06-01

A neuronal network often involves time delay caused by the finite signal propagation time in a given biological network. This time delay is not a homogenous fluctuation in a biological system. The heterogeneous delay-induced asynchrony and resonance in a noisy small-world neuronal network system are numerically studied in this work by calculating synchronization measure and spike interval distribution. We focus on three different delay conditions: double-values delay, triple-values delay, and Gaussian-distributed delay. Our results show the following: 1) the heterogeneity in delay results in asynchronous firing in the neuronal network, and 2) maximum synchronization could be achieved through resonance given that the delay values are integer or half-integer times of each other.

A dynamical characterization of the small world phase

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Araujo, Tanya; Vilela Mendes, R.; Seixas, Joao

2003-12-08

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the Watts-Strogatz {beta}-model, a coupled map dynamical system is defined on the network. Entrance to and exit from the SW phase are related to the behavior of the ergodic invariants of the dynamics.

A dynamical characterization of the small world phase

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Araujo, Tanya; Vilela Mendes, R.; Seixas, Joao

2003-01-01

Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these networks. Here a dynamical approach is used to characterize the small-world phenomenon. Using the Watts-Strogatz β-model, a coupled map dynamical system is defined on the network. Entrance to and exit from the SW phase are related to the behavior of the ergodic invariants of the dynamics

A review of structural and functional brain networks: small world and atlas.

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Yao, Zhijun; Hu, Bin; Xie, Yuanwei; Moore, Philip; Zheng, Jiaxiang

2015-03-01

Brain networks can be divided into two categories: structural and functional networks. Many studies of neuroscience have reported that the complex brain networks are characterized by small-world or scale-free properties. The identification of nodes is the key factor in studying the properties of networks on the macro-, micro- or mesoscale in both structural and functional networks. In the study of brain networks, nodes are always determined by atlases. Therefore, the selection of atlases is critical, and appropriate atlases are helpful to combine the analyses of structural and functional networks. Currently, some problems still exist in the establishment or usage of atlases, which are often caused by the segmentation or the parcellation of the brain. We suggest that quantification of brain networks might be affected by the selection of atlases to a large extent. In the process of building atlases, the influences of single subjects and groups should be balanced. In this article, we focused on the effects of atlases on the analysis of brain networks and the improved divisions based on the tractography or connectivity in the parcellation of atlases.

Altered small-world properties of gray matter networks in breast cancer

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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.

A hybrid small-world network/semi-physical model for predicting wildfire spread in heterogeneous landscapes

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Billaud, Y; Kaiss, A; Drissi, M; Pizzo, Y; Porterie, B; Zekri, N; Acem, Z; Collin, A; Boulet, P; Santoni, P-A; Bosseur, F

2012-01-01

This paper presents the latest developments and validation results of a hybrid model which combines a broad-scale stochastic small-world network model with a macroscopic deterministic approach, to simulate the effects of large fires burning in heterogeneous landscapes. In the extended version of the model, vegetation is depicted as an amorphous network of combustible cells, and both radiation and convection from the flaming zone are considered in the preheating process of unburned cells. Examples are given to illustrate small-world effects and fire behavior near the percolation threshold. The model is applied to a Mediterranean fire that occurred in Corsica in 2009 showing a good agreement in terms of rate of spread, and area and shape of the burn. A study, based on a fractional factorial plan, is conducted to evaluate the influence of variations of model parameters on fire propagation.

Focus-based filtering + clustering technique for power-law networks with small world phenomenon

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Boutin, François; Thièvre, Jérôme; Hascoët, Mountaz

2006-01-01

Realistic interaction networks usually present two main properties: a power-law degree distribution and a small world behavior. Few nodes are linked to many nodes and adjacent nodes are likely to share common neighbors. Moreover, graph structure usually presents a dense core that is difficult to explore with classical filtering and clustering techniques. In this paper, we propose a new filtering technique accounting for a user-focus. This technique extracts a tree-like graph with also power-law degree distribution and small world behavior. Resulting structure is easily drawn with classical force-directed drawing algorithms. It is also quickly clustered and displayed into a multi-level silhouette tree (MuSi-Tree) from any user-focus. We built a new graph filtering + clustering + drawing API and report a case study.

A small-world methodology of analysis of interchange energy-networks: The European behaviour in the economical crisis

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Dassisti, M.; Carnimeo, L.

2013-01-01

European energy policy pursues the objective of a sustainable, competitive and reliable supply of energy. In 2007, the European Commission adopted a proper energy policy for Europe supported by several documents and included an action plan to meet the major energy challenges Europe has to face. A farsighted diversified yearly mix of energies was suggested to countries, aiming at increasing security of supply and efficiency, but a wide and systemic view of energy interchanges between states was missing. In this paper, a Small-World methodology of analysis of Interchange Energy-Networks (IENs) is presented, with the aim of providing a useful tool for planning sustainable energy policies. A proof case is presented to validate the methodology by considering the European IEN behaviour in the period of economical crisis. This network is approached as a Small World Net from a modelling point of view, by supposing that connections between States are characterised by a probability value depending on economic/political relations between countries. - Highlights: • Different view of the imports and exports of electric energy flows between European for potential use in ruling exchanges. • Panel data from 1996 to 2010 as part of a network of exchanges was considered from Eurostat official database. • The European import/export energy flows modelled as a network with Small World phenomena, interpreting the evolution over the years. • Interesting systemic tool for ruling and governing energy flows between countries

Complex Behavior in an Integrate-and-Fire Neuron Model Based on Small World Networks

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Lin Min; Chen Tianlun

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.

Optimal convergence in naming game with geography-based negotiation on small-world networks

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Liu Runran, E-mail: runran@mail.ustc.edu.c [Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei Anhui 230026 (China); Wang Wenxu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Lai Yingcheng [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Chen Guanrong [Department of Electronic Engineering, City University of Hong Kong, Hong Kong (Hong Kong); Wang Binghong [Department of Modern Physics and Nonlinear Science Center, University of Science and Technology of China, Hefei Anhui 230026 (China); Research Center for Complex System Science, University of Shanghai for Science and Technology and Shanghai Academy of System Science, Shanghai 200093 (China)

2011-01-17

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.

Optimal convergence in naming game with geography-based negotiation on small-world networks

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Liu Runran; Wang Wenxu; Lai Yingcheng; Chen Guanrong; Wang Binghong

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.

Small-worldness and gender differences of large scale brain metabolic covariance networks in young adults: a FDG PET study of 400 subjects.

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Hu, Yuxiao; Xu, Qiang; Shen, Junkang; Li, Kai; Zhu, Hong; Zhang, Zhiqiang; Lu, Guangming

2015-02-01

Many studies have demonstrated the small-worldness of the human brain, and have revealed a sexual dimorphism in brain network properties. However, little is known about the gender effects on the topological organization of the brain metabolic covariance networks. To investigate the small-worldness and the gender differences in the topological architectures of human brain metabolic networks. FDG-PET data of 400 healthy right-handed subjects (200 women and 200 age-matched men) were involved in the present study. Metabolic networks of each gender were constructed by calculating the covariance of regional cerebral glucose metabolism (rCMglc) across subjects on the basis of AAL parcellation. Gender differences of network and nodal properties were investigated by using the graph theoretical approaches. Moreover, the gender-related difference of rCMglc in each brain region was tested for investigating the relationships between the hub regions and the brain regions showing significant gender-related differences in rCMglc. We found prominent small-world properties in the domain of metabolic networks in each gender. No significant gender difference in the global characteristics was found. Gender differences of nodal characteristic were observed in a few brain regions. We also found bilateral and lateralized distributions of network hubs in the females and males. Furthermore, we first reported that some hubs of a gender located in the brain regions showing weaker rCMglc in this gender than the other gender. The present study demonstrated that small-worldness was existed in metabolic networks, and revealed gender differences of organizational patterns in metabolic network. These results maybe provided insights into the understanding of the metabolic substrates underlying individual differences in cognition and behaviors. © The Foundation Acta Radiologica 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Vulnerability of complex networks

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Mishkovski, Igor; Biey, Mario; Kocarev, Ljupco

2011-01-01

We consider normalized average edge betweenness of a network as a metric of network vulnerability. We suggest that normalized average edge betweenness together with is relative difference when certain number of nodes and/or edges are removed from the network is a measure of network vulnerability, called vulnerability index. Vulnerability index is calculated for four synthetic networks: Erdős-Rényi (ER) random networks, Barabási-Albert (BA) model of scale-free networks, Watts-Strogatz (WS) model of small-world networks, and geometric random networks. Real-world networks for which vulnerability index is calculated include: two human brain networks, three urban networks, one collaboration network, and two power grid networks. We find that WS model of small-world networks and biological networks (human brain networks) are the most robust networks among all networks studied in the paper.

Effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks

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Sun, Xiaojuan; Perc, Matjaž; Kurths, Jürgen

2017-05-01

In this paper, we study effects of partial time delays on phase synchronization in Watts-Strogatz small-world neuronal networks. Our focus is on the impact of two parameters, namely the time delay τ and the probability of partial time delay pdelay, whereby the latter determines the probability with which a connection between two neurons is delayed. Our research reveals that partial time delays significantly affect phase synchronization in this system. In particular, partial time delays can either enhance or decrease phase synchronization and induce synchronization transitions with changes in the mean firing rate of neurons, as well as induce switching between synchronized neurons with period-1 firing to synchronized neurons with period-2 firing. Moreover, in comparison to a neuronal network where all connections are delayed, we show that small partial time delay probabilities have especially different influences on phase synchronization of neuronal networks.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Dynamic Evolution with Limited Learning Information on a Small-World Network

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Dong, Lin-Rong

2010-09-01

This paper investigates the dynamic evolution with limited learning information on a small-world network. In the system, the information among the interaction players is not very lucid, and the players are not allowed to inspect the profit collected by its neighbors, thus the focal player cannot choose randomly a neighbor or the wealthiest one and compare its payoff to copy its strategy. It is assumed that the information acquainted by the player declines in the form of the exponential with the geographical distance between the players, and a parameter V is introduced to denote the inspect-ability about the players. It is found that under the hospitable conditions, cooperation increases with the randomness and is inhibited by the large connectivity for the prisoner's dilemma; however, cooperation is maximal at the moderate rewiring probability and is chaos with the connectivity for the snowdrift game. For the two games, the acuminous sight is in favor of the cooperation under the hospitable conditions; whereas, the myopic eyes are advantageous to cooperation and cooperation increases with the randomness under the hostile condition.

Resilience of networks to environmental stress: From regular to random networks

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Eom, Young-Ho

2018-04-01

Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating their external conditions. We show that, when regular networks gradually disintegrate as environmental stress increases, disordered networks can suddenly collapse at critical stress with hysteresis and vulnerability to perturbations. We demonstrate that this difference results from a trade-off between node resilience and network resilience to environmental stress. The nodes in the disordered networks can suppress their collapses due to the small-world topology of the networks but eventually collapse all together in return. Our findings indicate that some real networks can be highly resilient against environmental stress to a threshold yet extremely vulnerable to the stress above the threshold because of their small-world topology.

Empirical Analysis on Evolution and Small World Effect of Chinese Enterprise-Enterprise Patent Cooperation Network: From the Perspective of Open Innovation

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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.

Modeling and Analysis of Epidemic Diffusion within Small-World Network

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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.

Research on Some Bus Transport Networks with Random Overlapping Clique Structure

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Yang Xuhua; Sun Youxian; Wang Bo; Wang Wanliang

2008-01-01

On the basis of investigating the statistical data of bus transport networks of three big cities in China, we propose that each bus route is a clique (maximal complete subgraph) and a bus transport network (BTN) consists of a lot of cliques, which intensively connect and overlap with each other. We study the network properties, which include the degree distribution, multiple edges' overlapping time distribution, distribution of the overlap size between any two overlapping cliques, distribution of the number of cliques that a node belongs to. Naturally, the cliques also constitute a network, with the overlapping nodes being their multiple links. We also research its network properties such as degree distribution, clustering, average path length, and so on. We propose that a BTN has the properties of random clique increment and random overlapping clique, at the same time, a BTN is a small-world network with highly clique-clustered and highly clique-overlapped. Finally, we introduce a BTN evolution model, whose simulation results agree well with the statistical laws that emerge in real BTNs

Complex networks generated by the Penna bit-string model: Emergence of small-world and assortative mixing

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Li, Chunguang; Maini, Philip K.

2005-10-01

The Penna bit-string model successfully encompasses many phenomena of population evolution, including inheritance, mutation, evolution, and aging. If we consider social interactions among individuals in the Penna model, the population will form a complex network. In this paper, we first modify the Verhulst factor to control only the birth rate, and introduce activity-based preferential reproduction of offspring in the Penna model. The social interactions among individuals are generated by both inheritance and activity-based preferential increase. Then we study the properties of the complex network generated by the modified Penna model. We find that the resulting complex network has a small-world effect and the assortative mixing property.

Effects of channel noise on firing coherence of small-world Hodgkin-Huxley neuronal networks

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Sun, X. J.; Lei, J. Z.; Perc, M.; Lu, Q. S.; Lv, S. J.

2011-01-01

We investigate the effects of channel noise on firing coherence of Watts-Strogatz small-world networks consisting of biophysically realistic HH neurons having a fraction of blocked voltage-gated sodium and potassium ion channels embedded in their neuronal membranes. The intensity of channel noise is determined by the number of non-blocked ion channels, which depends on the fraction of working ion channels and the membrane patch size with the assumption of homogeneous ion channel density. We find that firing coherence of the neuronal network can be either enhanced or reduced depending on the source of channel noise. As shown in this paper, sodium channel noise reduces firing coherence of neuronal networks; in contrast, potassium channel noise enhances it. Furthermore, compared with potassium channel noise, sodium channel noise plays a dominant role in affecting firing coherence of the neuronal network. Moreover, we declare that the observed phenomena are independent of the rewiring probability.

Infection dynamics on spatial small-world network models

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Iotti, Bryan; Antonioni, Alberto; Bullock, Seth; Darabos, Christian; Tomassini, Marco; Giacobini, Mario

2017-11-01

The study of complex networks, and in particular of social networks, has mostly concentrated on relational networks, abstracting the distance between nodes. Spatial networks are, however, extremely relevant in our daily lives, and a large body of research exists to show that the distances between nodes greatly influence the cost and probability of establishing and maintaining a link. A random geometric graph (RGG) is the main type of synthetic network model used to mimic the statistical properties and behavior of many social networks. We propose a model, called REDS, that extends energy-constrained RGGs to account for the synergic effect of sharing the cost of a link with our neighbors, as is observed in real relational networks. We apply both the standard Watts-Strogatz rewiring procedure and another method that conserves the degree distribution of the network. The second technique was developed to eliminate unwanted forms of spatial correlation between the degree of nodes that are affected by rewiring, limiting the effect on other properties such as clustering and assortativity. We analyze both the statistical properties of these two network types and their epidemiological behavior when used as a substrate for a standard susceptible-infected-susceptible compartmental model. We consider and discuss the differences in properties and behavior between RGGs and REDS as rewiring increases and as infection parameters are changed. We report considerable differences both between the network types and, in the case of REDS, between the two rewiring schemes. We conclude that REDS represent, with the application of these rewiring mechanisms, extremely useful and interesting tools in the study of social and epidemiological phenomena in synthetic complex networks.

Statistical properties of random clique networks

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Ding, Yi-Min; Meng, Jun; Fan, Jing-Fang; Ye, Fang-Fu; Chen, Xiao-Song

2017-10-01

In this paper, a random clique network model to mimic the large clustering coefficient and the modular structure that exist in many real complex networks, such as social networks, artificial networks, and protein interaction networks, is introduced by combining the random selection rule of the Erdös and Rényi (ER) model and the concept of cliques. We find that random clique networks having a small average degree differ from the ER network in that they have a large clustering coefficient and a power law clustering spectrum, while networks having a high average degree have similar properties as the ER model. In addition, we find that the relation between the clustering coefficient and the average degree shows a non-monotonic behavior and that the degree distributions can be fit by multiple Poisson curves; we explain the origin of such novel behaviors and degree distributions.

Exploring the story, science, and adventure of small worlds

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Swann, J. L.; Elkins-Tanton, L. T.; Anbar, A. D.; Klug Boonstra, S.; Tamer, A. J.; Mead, C.; Hunsley, D.

2017-12-01

Small worlds are a strategic focus at NASA, reflected by missions such as Osiris Rex and Psyche among others. The Infiniscope project, with funding from NASA SMD, is building on this scientific and public interest to teach formal and informal learners about asteroids and other small worlds. The digital learning experience, "Where are the small worlds?", and future Infiniscope experiences, incorporate a design theory that we describe as "education through exploration" (ETX) which is provided through an adaptive e-learning platform. This design ensures that learners actively engage in exploration and discovery, while receiving targeted feedback to push through challenges. To ensure that this and future experiences reach and meet the needs of as many educators as possible, Infiniscope includes a digital teaching network to host the experiences and support the reuse and adaptation of digital resources in new lessons. "Where are the small worlds?" puts learners in an interactive simulation of the solar system and provides a mission structure in which they hunt for "astrocaches" on near earth objects, main belt asteroids, and Kuiper-belt objects. These activities allow the learner to discover the locations of the small worlds in the solar system and develop an intuitive understanding for the relative motion of objects at various distances from the Sun. The experience is NGSS-aligned and accompanied by a lesson plan for integration into the classroom. In testing with more than 500 middle-school students, 83% of participants said they wanted to do more experiences like "Where are the small worlds?" They also found the experience both "fun" and "interesting" while being moderately difficult. "Where are the small worlds?" is one of many visualizations and lessons that is available within the Infiniscope teaching network. The network already has hundreds of members and is expected to grow in both numbers and engagement over time. Currently, educators can search and use pre

Disrupted small world networks in patients without overt hepatic encephalopathy: A resting state fMRI study

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.

Disrupted small world networks in patients without overt hepatic encephalopathy: A resting state fMRI study

International Nuclear Information System (INIS)

Zhang, Long Jiang; Zheng, Gang; Zhang, Liping; Zhong, Jianhui; Li, Qiang; Zhao, Tie Zhu; Lu, Guang Ming

2014-01-01

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

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.

A comprehensive multi-local-world model for complex networks

International Nuclear Information System (INIS)

Fan Zhengping; Chen Guanrong; Zhang Yunong

2009-01-01

The nodes in a community within a network are much more connected to each other than to the others outside the community in the same network. This phenomenon has been commonly observed from many real-world networks, ranging from social to biological even to technical networks. Meanwhile, the number of communities in some real-world networks, such as the Internet and most social networks, are evolving with time. To model this kind of networks, the present Letter proposes a multi-local-world (MLW) model to capture and describe their essential topological properties. Based on the mean-field theory, the degree distribution of this model is obtained analytically, showing that the generated network has a novel topological feature as being not completely random nor completely scale-free but behaving somewhere between them. As a typical application, the MLW model is applied to characterize the Internet against some other models such as the BA, GBA, Fitness and HOT models, demonstrating the superiority of the new model.

Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?

Science.gov (United States)

Varoquaux, G; Gramfort, A; Poline, J B; Thirion, B

2012-01-01

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems. Copyright © 2012 Elsevier Ltd. All rights reserved.

On the agreement between small-world-like OFC model and real earthquakes

International Nuclear Information System (INIS)

Ferreira, Douglas S.R.; Papa, Andrés R.R.; Menezes, Ronaldo

2015-01-01

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 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

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.

Testing the structure of earthquake networks from multivariate time series of successive main shocks in Greece

Science.gov (United States)

Chorozoglou, D.; Kugiumtzis, D.; Papadimitriou, E.

2018-06-01

The seismic hazard assessment in the area of Greece is attempted by studying the earthquake network structure, such as small-world and random. In this network, a node represents a seismic zone in the study area and a connection between two nodes is given by the correlation of the seismic activity of two zones. To investigate the network structure, and particularly the small-world property, the earthquake correlation network is compared with randomized ones. Simulations on multivariate time series of different length and number of variables show that for the construction of randomized networks the method randomizing the time series performs better than methods randomizing directly the original network connections. Based on the appropriate randomization method, the network approach is applied to time series of earthquakes that occurred between main shocks in the territory of Greece spanning the period 1999-2015. The characterization of networks on sliding time windows revealed that small-world structure emerges in the last time interval, shortly before the main shock.

SmallWorld Behavior of the Worldwide Active Volcanoes Network: Preliminary Results

Science.gov (United States)

Spata, A.; Bonforte, A.; Nunnari, G.; Puglisi, G.

2009-12-01

We propose a preliminary complex networks based approach in order to model and characterize volcanoes activity correlation observed on a planetary scale over the last two thousand years. Worldwide volcanic activity is in fact related to the general plate tectonics that locally drives the faults activity, that in turn controls the magma upraise beneath the volcanoes. To find correlations among different volcanoes could indicate a common underlying mechanism driving their activity and could help us interpreting the deeper common dynamics controlling their unrest. All the first evidences found testing the procedure, suggest the suitability of this analysis to investigate global volcanism related to plate tectonics. The first correlations found, in fact, indicate that an underlying common large-scale dynamics seems to drive volcanic activity at least around the Pacific plate, where it collides and subduces beneath American, Eurasian and Australian plates. From this still preliminary analysis, also more complex relationships among volcanoes lying on different tectonic margins have been found, suggesting some more complex interrelationships between different plates. The understanding of eventually detected correlations could be also used to further implement warning systems, relating the unrest probabilities of a specific volcano also to the ongoing activity to the correlated ones. Our preliminary results suggest that, as for other many physical and biological systems, an underlying organizing principle of planetary volcanoes activity might exist and it could be a small-world principle. In fact we found that, from a topological perspective, volcanoes correlations are characterized by the typical features of small-world network: a high clustering coefficient and a low characteristic path length. These features confirm that global volcanoes activity is characterized by both short and long-range correlations. We stress here the fact that numerical simulation carried out in

RMBNToolbox: random models for biochemical networks

Directory of Open Access Journals (Sweden)

Niemi Jari

2007-05-01

Full Text Available Abstract Background There is an increasing interest to model biochemical and cell biological networks, as well as to the computational analysis of these models. The development of analysis methodologies and related software is rapid in the field. However, the number of available models is still relatively small and the model sizes remain limited. The lack of kinetic information is usually the limiting factor for the construction of detailed simulation models. Results We present a computational toolbox for generating random biochemical network models which mimic real biochemical networks. The toolbox is called Random Models for Biochemical Networks. The toolbox works in the Matlab environment, and it makes it possible to generate various network structures, stoichiometries, kinetic laws for reactions, and parameters therein. The generation can be based on statistical rules and distributions, and more detailed information of real biochemical networks can be used in situations where it is known. The toolbox can be easily extended. The resulting network models can be exported in the format of Systems Biology Markup Language. Conclusion While more information is accumulating on biochemical networks, random networks can be used as an intermediate step towards their better understanding. Random networks make it possible to study the effects of various network characteristics to the overall behavior of the network. Moreover, the construction of artificial network models provides the ground truth data needed in the validation of various computational methods in the fields of parameter estimation and data analysis.

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

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.

Spatiotemporal dynamics on small-world neuronal networks: The roles of two types of time-delayed coupling

International Nuclear Information System (INIS)

Wu Hao; Jiang Huijun; Hou Zhonghuai

2011-01-01

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: {x j (t - τ) - x i (t)} and {x j (t - τ) - x i (t - τ)}. 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 τ 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.

Quality of Care as an Emergent Phenomenon out of a Small-World Network of Relational Actors.

Science.gov (United States)

Fiorini, Rodolfo; De Giacomo, Piero; Marconi, Pier Luigi; L'Abate, Luciano

2014-01-01

In Healthcare Decision Support System, the development and evaluation of effective "Quality of Care" (QOC) indicators, in simulation-based training, are key feature to develop resilient and antifragile organization scenarios. Is it possible to conceive of QOC not only as a result of a voluntary and rational decision, imposed or even not, but also as an overall system "emergent phenomenon" out of a small-world network of relational synthetic actors, endowed with their own personality profiles to simulate human behaviour (for short, called "subjects")? In order to answer this question and to observe the phenomena of real emergence we should use computational models of high complexity, with heavy computational load and extensive computational time. Nevertheless, De Giacomo's Elementary Pragmatic Model (EPM) intrinsic self-reflexive functional logical closure enables to run simulation examples to classify the outcomes grown out of a small-world network of relational subjects fast and effectively. Therefore, it is possible to take note and to learn of how much strategic systemic interventions can induce context conditions of QOC facilitation, which can improve the effectiveness of specific actions, which otherwise might be paradoxically counterproductive also. Early results are so encouraging to use EPM as basic block to start designing more powerful Evolutive Elementary Pragmatic Model (E2PM) for real emergence computational model, to cope with ontological uncertainty at system level.

Multifractal analysis of complex networks

International Nuclear Information System (INIS)

Wang Dan-Ling; Yu Zu-Guo; Anh V

2012-01-01

Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions D q of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein—protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein—protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of D q due to changes in the parameters of the theoretical network models is also discussed. (general)

Long-duration transcutaneous electric acupoint stimulation alters small-world brain functional networks.

Science.gov (United States)

Zhang, Yue; Jiang, Yin; Glielmi, Christopher B; Li, Longchuan; Hu, Xiaoping; Wang, Xiaoying; Han, Jisheng; Zhang, Jue; Cui, Cailian; Fang, Jing

2013-09-01

Acupuncture, which is recognized as an alternative and complementary treatment in Western medicine, has long shown efficiencies in chronic pain relief, drug addiction treatment, stroke rehabilitation and other clinical practices. The neural mechanism underlying acupuncture, however, is still unclear. Many studies have focused on the sustained effects of acupuncture on healthy subjects, yet there are very few on the topological organization of functional networks in the whole brain in response to long-duration acupuncture (longer than 20 min). This paper presents a novel study on the effects of long-duration transcutaneous electric acupoint stimulation (TEAS) on the small-world properties of brain functional networks. Functional magnetic resonance imaging was used to construct brain functional networks of 18 healthy subjects (9 males and 9 females) during the resting state. All subjects received both TEAS and minimal TEAS (MTEAS) and were scanned before and after each stimulation. An altered functional network was found with lower local efficiency and no significant change in global efficiency for healthy subjects after TEAS, while no significant difference was observed after MTEAS. The experiments also showed that the nodal efficiencies in several paralimbic/limbic regions were altered by TEAS, and those in middle frontal gyrus and other regions by MTEAS. To remove the psychological effects and the baseline, we compared the difference between diffTEAS (difference between after and before TEAS) and diffMTEAS (difference between after and before MTEAS). The results showed that the local efficiency was decreased and that the nodal efficiencies in frontal gyrus, orbitofrontal cortex, anterior cingulate gyrus and hippocampus gyrus were changed. Based on those observations, we conclude that long-duration TEAS may modulate the short-range connections of brain functional networks and also the limbic system. Copyright © 2013 Elsevier Inc. All rights reserved.

Doubly stochastic coherence in complex neuronal networks

Science.gov (United States)

Gao, Yang; Wang, Jianjun

2012-11-01

A system composed of coupled FitzHugh-Nagumo neurons with various topological structures is investigated under the co-presence of two independently additive and multiplicative Gaussian white noises, in which particular attention is paid to the neuronal networks spiking regularity. As the additive noise intensity and the multiplicative noise intensity are simultaneously adjusted to optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of doubly stochastic coherence. The network topology randomness exerts different influences on the temporal coherence of the spiking oscillation for dissimilar coupling strength regimes. At a small coupling strength, the spiking regularity shows nearly no difference in the regular, small-world, and completely random networks. At an intermediate coupling strength, the temporal periodicity in a small-world neuronal network can be improved slightly by adding a small fraction of long-range connections. At a large coupling strength, the dynamical behavior of the neurons completely loses the resonance property with regard to the additive noise intensity or the multiplicative noise intensity, and the spiking regularity decreases considerably with the increase of the network topology randomness. The network topology randomness plays more of a depressed role than a favorable role in improving the temporal coherence of the spiking oscillation in the neuronal network research study.

Study Under AC Stimulation on Excitement Properties of Weighted Small-World Biological Neural Networks with Side-Restrain Mechanism

International Nuclear Information System (INIS)

Yuan Wujie; Luo Xiaoshu; Jiang Pinqun

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 noise and coupling. The results of the study have reference worthiness for the brain nerve electrophysiology and epistemological science.

Network rewiring dynamics with convergence towards a star network.

Science.gov (United States)

Whigham, P A; Dick, G; Parry, M

2016-10-01

Network rewiring as a method for producing a range of structures was first introduced in 1998 by Watts & Strogatz ( Nature 393 , 440-442. (doi:10.1038/30918)). This approach allowed a transition from regular through small-world to a random network. The subsequent interest in scale-free networks motivated a number of methods for developing rewiring approaches that converged to scale-free networks. This paper presents a rewiring algorithm (RtoS) for undirected, non-degenerate, fixed size networks that transitions from regular, through small-world and scale-free to star-like networks. Applications of the approach to models for the spread of infectious disease and fixation time for a simple genetics model are used to demonstrate the efficacy and application of the approach.

Applications of Temporal Graph Metrics to Real-World Networks

Science.gov (United States)

Tang, John; Leontiadis, Ilias; Scellato, Salvatore; Nicosia, Vincenzo; Mascolo, Cecilia; Musolesi, Mirco; Latora, Vito

Real world networks exhibit rich temporal information: friends are added and removed over time in online social networks; the seasons dictate the predator-prey relationship in food webs; and the propagation of a virus depends on the network of human contacts throughout the day. Recent studies have demonstrated that static network analysis is perhaps unsuitable in the study of real world network since static paths ignore time order, which, in turn, results in static shortest paths overestimating available links and underestimating their true corresponding lengths. Temporal extensions to centrality and efficiency metrics based on temporal shortest paths have also been proposed. Firstly, we analyse the roles of key individuals of a corporate network ranked according to temporal centrality within the context of a bankruptcy scandal; secondly, we present how such temporal metrics can be used to study the robustness of temporal networks in presence of random errors and intelligent attacks; thirdly, we study containment schemes for mobile phone malware which can spread via short range radio, similar to biological viruses; finally, we study how the temporal network structure of human interactions can be exploited to effectively immunise human populations. Through these applications we demonstrate that temporal metrics provide a more accurate and effective analysis of real-world networks compared to their static counterparts.

Anomalous Anticipatory Responses in Networked Random Data

International Nuclear Information System (INIS)

Nelson, Roger D.; Bancel, Peter A.

2006-01-01

We examine an 8-year archive of synchronized, parallel time series of random data from a world spanning network of physical random event generators (REGs). The archive is a publicly accessible matrix of normally distributed 200-bit sums recorded at 1 Hz which extends from August 1998 to the present. The primary question is whether these data show non-random structure associated with major events such as natural or man-made disasters, terrible accidents, or grand celebrations. Secondarily, we examine the time course of apparently correlated responses. Statistical analyses of the data reveal consistent evidence that events which strongly affect people engender small but significant effects. These include suggestions of anticipatory responses in some cases, leading to a series of specialized analyses to assess possible non-random structure preceding precisely timed events. A focused examination of data collected around the time of earthquakes with Richter magnitude 6 and greater reveals non-random structure with a number of intriguing, potentially important features. Anomalous effects in the REG data are seen only when the corresponding earthquakes occur in populated areas. No structure is found if they occur in the oceans. We infer that an important contributor to the effect is the relevance of the earthquake to humans. Epoch averaging reveals evidence for changes in the data some hours prior to the main temblor, suggestive of reverse causation

Hemisphere- and gender-related differences in small-world brain networks: a resting-state functional MRI study.

Science.gov (United States)

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. Copyright © 2010 Elsevier Inc. All rights reserved.

Effect of the small-world structure on encoding performance in the primary visual cortex: an electrophysiological and modeling analysis.

Science.gov (United States)

Shi, Li; Niu, Xiaoke; Wan, Hong

2015-05-01

The biological networks have been widely reported to present small-world properties. However, the effects of small-world network structure on population's encoding performance remain poorly understood. To address this issue, we applied a small world-based framework to quantify and analyze the response dynamics of cell assemblies recorded from rat primary visual cortex, and further established a population encoding model based on small world-based generalized linear model (SW-GLM). The electrophysiological experimental results show that the small world-based population responses to different topological shapes present significant variation (t test, p 0.8), while no significant variation was found for control networks without considering their spatial connectivity (t test, p > 0.05; effect size: Hedge's g < 0.5). Furthermore, the numerical experimental results show that the predicted response under SW-GLM is more accurate and reliable compared to the control model without small-world structure, and the decoding performance is also improved about 10 % by taking the small-world structure into account. The above results suggest the important role of the small-world neural structure in encoding visual information for the neural population by providing electrophysiological and theoretical evidence, respectively. The study helps greatly to well understand the population encoding mechanisms of visual cortex.

Softening in Random Networks of Non-Identical Beams.

Science.gov (United States)

Ban, Ehsan; Barocas, Victor H; Shephard, Mark S; Picu, Catalin R

2016-02-01

Random fiber networks are assemblies of elastic elements connected in random configurations. They are used as models for a broad range of fibrous materials including biopolymer gels and synthetic nonwovens. Although the mechanics of networks made from the same type of fibers has been studied extensively, the behavior of composite systems of fibers with different properties has received less attention. In this work we numerically and theoretically study random networks of beams and springs of different mechanical properties. We observe that the overall network stiffness decreases on average as the variability of fiber stiffness increases, at constant mean fiber stiffness. Numerical results and analytical arguments show that for small variabilities in fiber stiffness the amount of network softening scales linearly with the variance of the fiber stiffness distribution. This result holds for any beam structure and is expected to apply to a broad range of materials including cellular solids.

Local communities obstruct global consensus: Naming game on multi-local-world networks

Science.gov (United States)

Lou, Yang; Chen, Guanrong; Fan, Zhengping; Xiang, Luna

2018-02-01

Community structure is essential for social communications, where individuals belonging to the same community are much more actively interacting and communicating with each other than those in different communities within the human society. Naming game, on the other hand, is a social communication model that simulates the process of learning a name of an object within a community of humans, where the individuals can generally reach global consensus asymptotically through iterative pair-wise conversations. The underlying network indicates the relationships among the individuals. In this paper, three typical topologies, namely random-graph, small-world and scale-free networks, are employed, which are embedded with the multi-local-world community structure, to study the naming game. Simulations show that (1) the convergence process to global consensus is getting slower as the community structure becomes more prominent, and eventually might fail; (2) if the inter-community connections are sufficiently dense, neither the number nor the size of the communities affects the convergence process; and (3) for different topologies with the same (or similar) average node-degree, local clustering of individuals obstruct or prohibit global consensus to take place. The results reveal the role of local communities in a global naming game in social network studies.

Hyperbolicity measures democracy in real-world networks

Science.gov (United States)

Borassi, Michele; Chessa, Alessandro; Caldarelli, Guido

2015-09-01

In this work, we analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. We provide two improvements in our understanding of this quantity: first of all, in our interpretation, a hyperbolic network is "aristocratic", since few elements "connect" the system, while a non-hyperbolic network has a more "democratic" structure with a larger number of crucial elements. The second contribution is the introduction of the average hyperbolicity of the neighbors of a given node. Through this definition, we outline an "influence area" for the vertices in the graph. We show that in real networks the influence area of the highest degree vertex is small in what we define "local" networks (i.e., social or peer-to-peer networks), and large in "global" networks (i.e., power grid, metabolic networks, or autonomous system networks).

Pollination networks of oil-flowers: a tiny world within the smallest of all worlds.

Science.gov (United States)

Bezerra, Elisângela L S; Machado, Isabel C; Mello, Marco A R

2009-09-01

1. In the Neotropics, most plants depend on animals for pollination. Solitary bees are the most important vectors, and among them members of the tribe Centridini depend on oil from flowers (mainly Malpighiaceae) to feed their larvae. This specialized relationship within 'the smallest of all worlds' (a whole pollination network) could result in a 'tiny world' different from the whole system. This 'tiny world' would have higher nestedness, shorter path lengths, lower modularity and higher resilience if compared with the whole pollination network. 2. In the present study, we contrasted a network of oil-flowers and their visitors from a Brazilian steppe ('caatinga') to whole pollination networks from all over the world. 3. A network approach was used to measure network structure and, finally, to test fragility. The oil-flower network studied was more nested (NODF = 0.84, N = 0.96) than all of the whole pollination networks studied. Average path lengths in the two-mode network were shorter (one node, both for bee and plant one-mode network projections) and modularity was lower (M = 0.22 and four modules) than in all of the whole pollination networks. Extinctions had no or small effects on the network structure, with an average change in nestedness smaller than 2% in most of the cases studied; and only two species caused coextinctions. The higher the degree of the removed species, the stronger the effect and the higher the probability of a decrease in nestedness. 4. We conclude that the oil-flower subweb is more cohesive and resilient than whole pollination networks. Therefore, the Malpighiaceae have a robust pollination service in the Neotropics. Our findings reinforce the hypothesis that each ecological service is in fact a mosaic of different subservices with a hierarchical structure ('webs within webs').

Revealing the structure of the world airline network

Science.gov (United States)

Verma, T.; Araújo, N. A. M.; Herrmann, H. J.

2014-07-01

Resilience of most critical infrastructures against failure of elements that appear insignificant is usually taken for granted. The World Airline Network (WAN) is an infrastructure that reduces the geographical gap between societies, both small and large, and brings forth economic gains. With the extensive use of a publicly maintained data set that contains information about airports and alternative connections between these airports, we empirically reveal that the WAN is a redundant and resilient network for long distance air travel, but otherwise breaks down completely due to removal of short and apparently insignificant connections. These short range connections with moderate number of passengers and alternate flights are the connections that keep remote parts of the world accessible. It is surprising, insofar as there exists a highly resilient and strongly connected core consisting of a small fraction of airports (around 2.3%) together with an extremely fragile star-like periphery. Yet, in spite of their relevance, more than 90% of the world airports are still interconnected upon removal of this core. With standard and unconventional removal measures we compare both empirical and topological perceptions for the fragmentation of the world. We identify how the WAN is organized into different classes of clusters based on the physical proximity of airports and analyze the consequence of this fragmentation.

Vaccination intervention on epidemic dynamics in networks

Science.gov (United States)

Peng, Xiao-Long; Xu, Xin-Jian; Fu, Xinchu; Zhou, Tao

2013-02-01

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, Barabási-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.

Noise influence on spike activation in a Hindmarsh–Rose small-world neural network

International Nuclear Information System (INIS)

Zhe, Sun; Micheletto, Ruggero

2016-01-01

We studied the role of noise in neural networks, especially focusing on its relation to the propagation of spike activity in a small sized system. We set up a source of information using a single neuron that is constantly spiking. This element called initiator x o feeds spikes to the rest of the network that is initially quiescent and subsequently reacts with vigorous spiking after a transitional period of time. We found that noise quickly suppresses the initiator’s influence and favors spontaneous spike activity and, using a decibel representation of noise intensity, we established a linear relationship between noise amplitude and the interval from the initiator’s first spike and the rest of the network activation. We studied the same process with networks of different sizes (number of neurons) and found that the initiator x o has a measurable influence on small networks, but as the network grows in size, spontaneous spiking emerges disrupting its effects on networks of more than about N = 100 neurons. This suggests that the mechanism of internal noise generation allows information transmission within a small neural neighborhood, but decays for bigger network domains. We also analyzed the Fourier spectrum of the whole network membrane potential and verified that noise provokes the reduction of main θ and α peaks before transitioning into chaotic spiking. However, network size does not reproduce a similar phenomena; instead we recorded a reduction in peaks’ amplitude, a better sharpness and definition of Fourier peaks, but not the evident degeneration to chaos observed with increasing external noise. This work aims to contribute to the understanding of the fundamental mechanisms of propagation of spontaneous spiking in neural networks and gives a quantitative assessment of how noise can be used to control and modulate this phenomenon in Hindmarsh−Rose (H−R) neural networks. (paper)

Noise influence on spike activation in a Hindmarsh-Rose small-world neural network

Science.gov (United States)

Zhe, Sun; Micheletto, Ruggero

2016-07-01

We studied the role of noise in neural networks, especially focusing on its relation to the propagation of spike activity in a small sized system. We set up a source of information using a single neuron that is constantly spiking. This element called initiator x o feeds spikes to the rest of the network that is initially quiescent and subsequently reacts with vigorous spiking after a transitional period of time. We found that noise quickly suppresses the initiator’s influence and favors spontaneous spike activity and, using a decibel representation of noise intensity, we established a linear relationship between noise amplitude and the interval from the initiator’s first spike and the rest of the network activation. We studied the same process with networks of different sizes (number of neurons) and found that the initiator x o has a measurable influence on small networks, but as the network grows in size, spontaneous spiking emerges disrupting its effects on networks of more than about N = 100 neurons. This suggests that the mechanism of internal noise generation allows information transmission within a small neural neighborhood, but decays for bigger network domains. We also analyzed the Fourier spectrum of the whole network membrane potential and verified that noise provokes the reduction of main θ and α peaks before transitioning into chaotic spiking. However, network size does not reproduce a similar phenomena; instead we recorded a reduction in peaks’ amplitude, a better sharpness and definition of Fourier peaks, but not the evident degeneration to chaos observed with increasing external noise. This work aims to contribute to the understanding of the fundamental mechanisms of propagation of spontaneous spiking in neural networks and gives a quantitative assessment of how noise can be used to control and modulate this phenomenon in Hindmarsh-Rose (H-R) neural networks.

Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks

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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.

Effects of small-world connectivity on noise-induced temporal and spatial order in neural media

International Nuclear Information System (INIS)

Perc, Matjaz

2007-01-01

We present an overview of possible effects of small-world connectivity on noise-induced temporal and spatial order in a two-dimensional network of excitable neural media with FitzHugh-Nagumo local dynamics. Small-world networks are characterized by a given fraction of so-called long-range couplings or shortcut links that connect distant units of the system, while all other units are coupled in a diffusive-like manner. Interestingly, already a small fraction of these long-range couplings can have wide-ranging effects on the temporal as well as spatial noise-induced dynamics of the system. Here we present two main effects. First, we show that the temporal order, characterized by the autocorrelation of a firing-rate function, can be greatly enhanced by the introduction of small-world connectivity, whereby the effect increases with the increasing fraction of introduced shortcut links. Second, we show that the introduction of long-range couplings induces disorder of otherwise ordered, spiral-wave-like, noise-induced patterns that can be observed by exclusive diffusive connectivity of spatial units. Thereby, already a small fraction of shortcut links is sufficient to destroy coherent pattern formation in the media. Although the two results seem contradictive, we provide an explanation considering the inherent scale-free nature of small-world networks, which on one hand, facilitates signal transduction and thus temporal order in the system, whilst on the other hand, disrupts the internal spatial scale of the media thereby hindering the existence of coherent wave-like patterns. Additionally, the importance of spatially versus temporally ordered neural network functioning is discussed

Towards structural controllability of local-world networks

International Nuclear Information System (INIS)

Sun, Shiwen; Ma, Yilin; Wu, Yafang; Wang, Li; Xia, Chengyi

2016-01-01

Controlling complex networks is of vital importance in science and engineering. Meanwhile, local-world effect is an important ingredient which should be taken into consideration in the complete description of real-world complex systems. In this letter, structural controllability of a class of local-world networks is investigated. Through extensive numerical simulations, firstly, effects of local world size M and network size N on structural controllability are examined. For local-world networks with sparse topological configuration, compared to network size, local-world size can induce stronger influence on controllability, however, for dense networks, controllability is greatly affected by network size and local-world effect can be neglected. Secondly, relationships between controllability and topological properties are analyzed. Lastly, the robustness of local-world networks under targeted attacks regarding structural controllability is discussed. These results can help to deepen the understanding of structural complexity and connectivity patterns of complex systems. - Highlights: • Structural controllability of a class of local-world networks is investigated. • For sparse local-world networks, compared to network size, local-world size can bring stronger influence on controllability. • For dense networks, controllability is greatly affected by network size and the effect of local-world size can be neglected. • Structural controllability against targeted node attacks is discussed.

Towards structural controllability of local-world networks

Energy Technology Data Exchange (ETDEWEB)

Sun, Shiwen, E-mail: sunsw80@126.com [Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384 (China); Key Laboratory of Computer Vision and System (Tianjin University of Technology), Ministry of Education, Tianjin 300384 (China); Ma, Yilin; Wu, Yafang; Wang, Li; Xia, Chengyi [Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin 300384 (China); Key Laboratory of Computer Vision and System (Tianjin University of Technology), Ministry of Education, Tianjin 300384 (China)

2016-05-20

Controlling complex networks is of vital importance in science and engineering. Meanwhile, local-world effect is an important ingredient which should be taken into consideration in the complete description of real-world complex systems. In this letter, structural controllability of a class of local-world networks is investigated. Through extensive numerical simulations, firstly, effects of local world size M and network size N on structural controllability are examined. For local-world networks with sparse topological configuration, compared to network size, local-world size can induce stronger influence on controllability, however, for dense networks, controllability is greatly affected by network size and local-world effect can be neglected. Secondly, relationships between controllability and topological properties are analyzed. Lastly, the robustness of local-world networks under targeted attacks regarding structural controllability is discussed. These results can help to deepen the understanding of structural complexity and connectivity patterns of complex systems. - Highlights: • Structural controllability of a class of local-world networks is investigated. • For sparse local-world networks, compared to network size, local-world size can bring stronger influence on controllability. • For dense networks, controllability is greatly affected by network size and the effect of local-world size can be neglected. • Structural controllability against targeted node attacks is discussed.

Stability and complexity of small random linear systems

Science.gov (United States)

Hastings, Harold

2010-03-01

We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.

The Evolution of World Trade from 1995 to 2014: A Network Approach

OpenAIRE

Cepeda, Fredy; Gamboa, Freddy; Leon Rincon, Carlos; Rincon, Hernan

2017-01-01

This paper employs network analysis to study world trade from 1995 to 2014. We focus on the main connective features of the world trade network (WTN) and their dynamics. Results suggest that countries’ efforts to attain the benefits of trade have resulted in an intertwined network that is increasingly dense, reciprocal, and clustered. Trade linkages are distributed homogeneously among countries, but their intensity (i.e. their value) is highly concentrated in a small set of countries. The mai...

Plasticity-induced characteristic changes of pattern dynamics and the related phase transitions in small-world neuronal networks

International Nuclear Information System (INIS)

Huang Xu-Hui; Hu Gang

2014-01-01

Phase transitions widely exist in nature and occur when some control parameters are changed. In neural systems, their macroscopic states are represented by the activity states of neuron populations, and phase transitions between different activity states are closely related to corresponding functions in the brain. In particular, phase transitions to some rhythmic synchronous firing states play significant roles on diverse brain functions and disfunctions, such as encoding rhythmical external stimuli, epileptic seizure, etc. However, in previous studies, phase transitions in neuronal networks are almost driven by network parameters (e.g., external stimuli), and there has been no investigation about the transitions between typical activity states of neuronal networks in a self-organized way by applying plastic connection weights. In this paper, we discuss phase transitions in electrically coupled and lattice-based small-world neuronal networks (LBSW networks) under spike-timing-dependent plasticity (STDP). By applying STDP on all electrical synapses, various known and novel phase transitions could emerge in LBSW networks, particularly, the phenomenon of self-organized phase transitions (SOPTs): repeated transitions between synchronous and asynchronous firing states. We further explore the mechanics generating SOPTs on the basis of synaptic weight dynamics. (interdisciplinary physics and related areas of science and technology)

Robustness of Dengue Complex Network under Targeted versus Random Attack

Directory of Open Access Journals (Sweden)

Hafiz Abid Mahmood Malik

2017-01-01

Full Text Available Dengue virus infection is one of those epidemic diseases that require much consideration in order to save the humankind from its unsafe impacts. According to the World Health Organization (WHO, 3.6 billion individuals are at risk because of the dengue virus sickness. Researchers are striving to comprehend the dengue threat. This study is a little commitment to those endeavors. To observe the robustness of the dengue network, we uprooted the links between nodes randomly and targeted by utilizing different centrality measures. The outcomes demonstrated that 5% targeted attack is equivalent to the result of 65% random assault, which showed the topology of this complex network validated a scale-free network instead of random network. Four centrality measures (Degree, Closeness, Betweenness, and Eigenvector have been ascertained to look for focal hubs. It has been observed through the results in this study that robustness of a node and links depends on topology of the network. The dengue epidemic network presented robust behaviour under random attack, and this network turned out to be more vulnerable when the hubs of higher degree have higher probability to fail. Moreover, representation of this network has been projected, and hub removal impact has been shown on the real map of Gombak (Malaysia.

Searching for the most cost-effective strategy for controlling epidemics spreading on regular and small-world networks.

Science.gov (United States)

Kleczkowski, Adam; Oleś, Katarzyna; Gudowska-Nowak, Ewa; Gilligan, Christopher A

2012-01-07

We present a combined epidemiological and economic model for control of diseases spreading on local and small-world networks. The disease is characterized by a pre-symptomatic infectious stage that makes detection and control of cases more difficult. The effectiveness of local (ring-vaccination or culling) and global control strategies is analysed by comparing the net present values of the combined cost of preventive treatment and illness. The optimal strategy is then selected by minimizing the total cost of the epidemic. We show that three main strategies emerge, with treating a large number of individuals (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. If the disease spreads within the well-defined neighbourhood, the local strategy is optimal unless the cost of a single vaccine is much higher than the cost associated with hospitalization. In the latter case, it is most cost-effective to refrain from prevention. Destruction of local correlations, either by long-range (small-world) links or by inclusion of many initial foci, expands the range of costs for which the NS is most cost-effective. The GS emerges for the case when the cost of prevention is much lower than the cost of treatment and there is a substantial non-local component in the disease spread. We also show that local treatment is only desirable if the disease spreads on a small-world network with sufficiently few long-range links; otherwise it is optimal to treat globally. In the mean-field case, there are only two optimal solutions, to treat all if the cost of the vaccine is low and to treat nobody if it is high. The basic reproduction ratio, R(0), does not depend on the rate of responsive treatment in this case and the disease always invades

A Novel Memristive Multilayer Feedforward Small-World Neural Network with Its Applications in PID Control

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.

A novel memristive multilayer feedforward small-world neural network with its applications in PID control.

Science.gov (United States)

Dong, Zhekang; Duan, Shukai; Hu, Xiaofang; Wang, Lidan; Li, Hai

2014-01-01

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.

Carbon Reduction Strategies Based on an NW Small-World Network with a Progressive Carbon Tax

Directory of Open Access Journals (Sweden)

Bin Wu

2017-09-01

Full Text Available There is an increasingly urgent need to reduce carbon emissions. Devising effective carbon tax policies has become an important research topic. It is necessary to explore carbon reduction strategies based on the design of carbon tax elements. In this study, we explore the effect of a progressive carbon tax policy on carbon emission reductions using the logical deduction method. We apply experience-weighted attraction learning theory to construct an evolutionary game model for enterprises with different levels of energy consumption in an NW small-world network, and study their strategy choices when faced with a progressive carbon tax policy. The findings suggest that enterprises that adopt other energy consumption strategies gradually transform to a low energy consumption strategy, and that this trend eventually spreads to the entire system. With other conditions unchanged, the rate at which enterprises change to a low energy consumption strategy becomes faster as the discount coefficient, the network externality, and the expected adjustment factor increase. Conversely, the rate of change slows as the cost of converting to a low energy consumption strategy increases.

Exponential random graph models for networks with community structure.

Science.gov (United States)

Fronczak, Piotr; Fronczak, Agata; Bujok, Maksymilian

2013-09-01

Although the community structure organization is an important characteristic of real-world networks, most of the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for testing community detection algorithms. They are also inadequate to predict various properties of real networks. With this paper we intend to fill the gap. We develop an exponential random graph approach to networks with community structure. To this end we mainly built upon the idea of blockmodels. We consider both the classical blockmodel and its degree-corrected counterpart and study many of their properties analytically. We show that in the degree-corrected blockmodel, node degrees display an interesting scaling property, which is reminiscent of what is observed in real-world fractal networks. A short description of Monte Carlo simulations of the models is also given in the hope of being useful to others working in the field.

Time Delay and Long-Range Connection Induced Synchronization Transitions in Newman-Watts Small-World Neuronal Networks

Science.gov (United States)

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

World Input-Output Network.

Directory of Open Access Journals (Sweden)

Federica Cerina

Full Text Available Production systems, traditionally analyzed as almost independent national systems, are increasingly connected on a global scale. Only recently becoming available, the World Input-Output Database (WIOD is one of the first efforts to construct the global multi-regional input-output (GMRIO tables. By viewing the world input-output system as an interdependent network where the nodes are the individual industries in different economies and the edges are the monetary goods flows between industries, we analyze respectively the global, regional, and local network properties of the so-called world input-output network (WION and document its evolution over time. At global level, we find that the industries are highly but asymmetrically connected, which implies that micro shocks can lead to macro fluctuations. At regional level, we find that the world production is still operated nationally or at most regionally as the communities detected are either individual economies or geographically well defined regions. Finally, at local level, for each industry we compare the network-based measures with the traditional methods of backward linkages. We find that the network-based measures such as PageRank centrality and community coreness measure can give valuable insights into identifying the key industries.

Generic Properties of Random Gene Regulatory Networks.

Science.gov (United States)

Li, Zhiyuan; Bianco, Simone; Zhang, Zhaoyang; Tang, Chao

2013-12-01

Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In particular, it is not clear typically how attractors partition among the three types of orbits: steady state, periodic and chaotic, and how the dynamical properties change with network's topological characteristics. In this work, we first investigated these questions in random GRNs with different network sizes, connectivity, fraction of inhibitory links and transcription regulation rules. Then we searched for the core motifs that govern the dynamic behavior of large GRNs. We show that the stability of a random GRN is typically governed by a few embedding motifs of small sizes, and therefore can in general be understood in the context of these short motifs. Our results provide insights for the study and design of genetic networks.

Gradient networks on uncorrelated random scale-free networks

International Nuclear Information System (INIS)

Pan Guijun; Yan Xiaoqing; Huang Zhongbing; Ma Weichuan

2011-01-01

Uncorrelated random scale-free (URSF) networks are useful null models for checking the effects of scale-free topology on network-based dynamical processes. Here, we present a comparative study of the jamming level of gradient networks based on URSF networks and Erdos-Renyi (ER) random networks. We find that the URSF networks are less congested than ER random networks for the average degree (k)>k c (k c ∼ 2 denotes a critical connectivity). In addition, by investigating the topological properties of the two kinds of gradient networks, we discuss the relations between the topological structure and the transport efficiency of the gradient networks. These findings show that the uncorrelated scale-free structure might allow more efficient transport than the random structure.

The Academic Life: Small Worlds, Different Worlds

Science.gov (United States)

Locke, William

2010-01-01

"The Academic Life: Small Worlds, Different Worlds" represented an impressive investigation of the largest and most complex national academic community in the world, which seriously attempted a detailed representation of the variations in its form. Its ethnographic orientation to understanding the internal academic life through exploratory…

Creating, generating and comparing random network models with NetworkRandomizer.

Science.gov (United States)

Tosadori, Gabriele; Bestvina, Ivan; Spoto, Fausto; Laudanna, Carlo; Scardoni, Giovanni

2016-01-01

Biological networks are becoming a fundamental tool for the investigation of high-throughput data in several fields of biology and biotechnology. With the increasing amount of information, network-based models are gaining more and more interest and new techniques are required in order to mine the information and to validate the results. To fill the validation gap we present an app, for the Cytoscape platform, which aims at creating randomised networks and randomising existing, real networks. Since there is a lack of tools that allow performing such operations, our app aims at enabling researchers to exploit different, well known random network models that could be used as a benchmark for validating real, biological datasets. We also propose a novel methodology for creating random weighted networks, i.e. the multiplication algorithm, starting from real, quantitative data. Finally, the app provides a statistical tool that compares real versus randomly computed attributes, in order to validate the numerical findings. In summary, our app aims at creating a standardised methodology for the validation of the results in the context of the Cytoscape platform.

Emergence of cooperation in non-scale-free networks

International Nuclear Information System (INIS)

Zhang, Yichao; Aziz-Alaoui, M A; Bertelle, Cyrille; Zhou, Shi; Wang, Wenting

2014-01-01

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a framework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do not favor cooperation under this updating rule. However, a recent empirical result shows the heterogeneous networks do not promote cooperation when humans play a prisoner’s dilemma. In this paper, we propose a strategy updating rule with payoff memory. We observe that the random graphs and small-world networks can provide even better frameworks for cooperation than the scale-free networks in this scenario. Our observations suggest that the degree heterogeneity may be neither a sufficient condition nor a necessary condition for the widespread cooperation in complex networks. Also, the topological structures are not sufficed to determine the level of cooperation in complex networks. (paper)

Organization of signal flow in directed networks

International Nuclear Information System (INIS)

Bányai, M; Bazsó, F; Négyessy, L

2011-01-01

Confining an answer to the question of whether and how the coherent operation of network elements is determined by the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the degree of edge convergence and the overlap between the in- and output sets of an edge. Definitions of convergence degree and overlap are based on the shortest paths, thus they encapsulate global network properties. Using the defining notions of convergence degree and overlapping set we clarify the meaning of network causality and demonstrate the crucial role of chordless circles. In real-world networks the flow representation distinguishes nodes according to their signal transmitting, processing and control properties. The analysis of real-world networks in terms of flow representation was in accordance with the known functional properties of the network nodes. It is shown that nodes with different signal processing, transmitting and control properties are randomly connected at the global scale, while local connectivity patterns depart from randomness. The grouping of network nodes according to their signal flow properties was unrelated to the network's community structure. We present evidence that the signal flow properties of small-world-like, real-world networks cannot be reconstructed by algorithms used to generate small-world networks. Convergence degree values were calculated for regular oriented trees, and the probability density function for networks grown with the preferential attachment mechanism. For Erdos–Rényi graphs we calculated the probability density function of both convergence degrees and overlaps

Simulating synchronization in neuronal networks

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Fink, Christian G.

2016-06-01

We discuss several techniques used in simulating neuronal networks by exploring how a network's connectivity structure affects its propensity for synchronous spiking. Network connectivity is generated using the Watts-Strogatz small-world algorithm, and two key measures of network structure are described. These measures quantify structural characteristics that influence collective neuronal spiking, which is simulated using the leaky integrate-and-fire model. Simulations show that adding a small number of random connections to an otherwise lattice-like connectivity structure leads to a dramatic increase in neuronal synchronization.

Identifying Vulnerable Nodes of Complex Networks in Cascading Failures Induced by Node-Based Attacks

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Shudong Li

2013-01-01

Full Text Available In the research on network security, distinguishing the vulnerable components of networks is very important for protecting infrastructures systems. Here, we probe how to identify the vulnerable nodes of complex networks in cascading failures, which was ignored before. Concerned with random attack (RA and highest load attack (HL on nodes, we model cascading dynamics of complex networks. Then, we introduce four kinds of weighting methods to characterize the nodes of networks including Barabási-Albert scale-free networks (SF, Watts-Strogatz small-world networks (WS, Erdos-Renyi random networks (ER, and two real-world networks. The simulations show that, for SF networks under HL attack, the nodes with small value of the fourth kind of weight are the most vulnerable and the ones with small value of the third weight are also vulnerable. Also, the real-world autonomous system with power-law distribution verifies these findings. Moreover, for WS and ER networks under both RA and HL attack, when the nodes have low tolerant ability, the ones with small value of the fourth kind of weight are more vulnerable and also the ones with high degree are easier to break down. The results give us important theoretical basis for digging the potential safety loophole and making protection strategy.

Incremental Centrality Algorithms for Dynamic Network Analysis

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2013-08-01

literature.   7.1.3 Small World Networks In 1998, Watts and Strogatz introduced a model that starts with a regular lattice (ring) of n nodes and...and S. Strogatz , "Collective Dynamics of ‘Small-World’ Networks," Nature, vol. 393, pp. 440-442, 1998. [13] T. Opsahl, "Structure and Evolution of...34On Random Graphs," Publicationes Mathematicae, vol. 6, 1959. [167] D.J. Watts and S.H. Strogatz , "Collective Dynamics of ‘Small-World’ Networks

An evolving network model with modular growth

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Zou Zhi-Yun; Liu Peng; Lei Li; Gao Jian-Zhi

2012-01-01

In this paper, we propose an evolving network model growing fast in units of module, according to the analysis of the evolution characteristics in real complex networks. Each module is a small-world network containing several interconnected nodes and the nodes between the modules are linked by preferential attachment on degree of nodes. We study the modularity measure of the proposed model, which can be adjusted by changing the ratio of the number of inner-module edges and the number of inter-module edges. In view of the mean-field theory, we develop an analytical function of the degree distribution, which is verified by a numerical example and indicates that the degree distribution shows characteristics of the small-world network and the scale-free network distinctly at different segments. The clustering coefficient and the average path length of the network are simulated numerically, indicating that the network shows the small-world property and is affected little by the randomness of the new module. (interdisciplinary physics and related areas of science and technology)

Efficient sampling of complex network with modified random walk strategies

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Xie, Yunya; Chang, Shuhua; Zhang, Zhipeng; Zhang, Mi; Yang, Lei

2018-02-01

We present two novel random walk strategies, choosing seed node (CSN) random walk and no-retracing (NR) random walk. Different from the classical random walk sampling, the CSN and NR strategies focus on the influences of the seed node choice and path overlap, respectively. Three random walk samplings are applied in the Erdös-Rényi (ER), Barabási-Albert (BA), Watts-Strogatz (WS), and the weighted USAir networks, respectively. Then, the major properties of sampled subnets, such as sampling efficiency, degree distributions, average degree and average clustering coefficient, are studied. The similar conclusions can be reached with these three random walk strategies. Firstly, the networks with small scales and simple structures are conducive to the sampling. Secondly, the average degree and the average clustering coefficient of the sampled subnet tend to the corresponding values of original networks with limited steps. And thirdly, all the degree distributions of the subnets are slightly biased to the high degree side. However, the NR strategy performs better for the average clustering coefficient of the subnet. In the real weighted USAir networks, some obvious characters like the larger clustering coefficient and the fluctuation of degree distribution are reproduced well by these random walk strategies.

The capacity for multistability in small gene regulatory networks

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Grotewold Erich

2009-09-01

Full Text Available Abstract Background Recent years have seen a dramatic increase in the use of mathematical modeling to gain insight into gene regulatory network behavior across many different organisms. In particular, there has been considerable interest in using mathematical tools to understand how multistable regulatory networks may contribute to developmental processes such as cell fate determination. Indeed, such a network may subserve the formation of unicellular leaf hairs (trichomes in the model plant Arabidopsis thaliana. Results In order to investigate the capacity of small gene regulatory networks to generate multiple equilibria, we present a chemical reaction network (CRN-based modeling formalism and describe a number of methods for CRN analysis in a parameter-free context. These methods are compared and applied to a full set of one-component subnetworks, as well as a large random sample from 40,680 similarly constructed two-component subnetworks. We find that positive feedback and cooperativity mediated by transcription factor (TF dimerization is a requirement for one-component subnetwork bistability. For subnetworks with two components, the presence of these processes increases the probability that a randomly sampled subnetwork will exhibit multiple equilibria, although we find several examples of bistable two-component subnetworks that do not involve cooperative TF-promoter binding. In the specific case of epidermal differentiation in Arabidopsis, dimerization of the GL3-GL1 complex and cooperative sequential binding of GL3-GL1 to the CPC promoter are each independently sufficient for bistability. Conclusion Computational methods utilizing CRN-specific theorems to rule out bistability in small gene regulatory networks are far superior to techniques generally applicable to deterministic ODE systems. Using these methods to conduct an unbiased survey of parameter-free deterministic models of small networks, and the Arabidopsis epidermal cell

Analytical connection between thresholds and immunization strategies of SIS model in random networks

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Zhou, Ming-Yang; Xiong, Wen-Man; Liao, Hao; Wang, Tong; Wei, Zong-Wen; Fu, Zhong-Qian

2018-05-01

Devising effective strategies for hindering the propagation of viruses and protecting the population against epidemics is critical for public security and health. Despite a number of studies based on the susceptible-infected-susceptible (SIS) model devoted to this topic, we still lack a general framework to compare different immunization strategies in completely random networks. Here, we address this problem by suggesting a novel method based on heterogeneous mean-field theory for the SIS model. Our method builds the relationship between the thresholds and different immunization strategies in completely random networks. Besides, we provide an analytical argument that the targeted large-degree strategy achieves the best performance in random networks with arbitrary degree distribution. Moreover, the experimental results demonstrate the effectiveness of the proposed method in both artificial and real-world networks.

Properties of four real world collaboration--competition networks

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Fu, Chun-Hua; Xu, Xiu-Lian; He, Da-Ren

2009-03-01

Our research group has empirically investigated 9 real world collaboration networks and 25 real world cooperation-competition networks. Among the 34 real world systems, all the 9 real world collaboration networks and 6 real world cooperation-competition networks show the unimodal act-size distribution and the shifted power law distribution of degree and act-degree. We have proposed a collaboration network evolution model for an explanation of the rules [1]. The other 14 real world cooperation-competition networks show that the act-size distributions are not unimodal; instead, they take qualitatively the same shifted power law forms as the degree and act-degree distributions. The properties of four systems (the main land movie film network, Beijing restaurant network, 2004 Olympic network, and Tao-Bao notebook computer sale network) are reported in detail as examples. Via a numerical simulation, we show that the new rule can still be explained by the above-mentioned model. [1] H. Chang, B. B. Su, et al. Phsica A, 2007, 383: 687-702.

Small Worldness in Dense and Weighted Connectomes

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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.

Spectra of random networks in the weak clustering regime

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Peron, Thomas K. DM.; Ji, Peng; Kurths, Jürgen; Rodrigues, Francisco A.

2018-03-01

The asymptotic behavior of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values of the clustering coefficient. Here we study effects of cycles of order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectral distribution of the network adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Implications to network dynamics are discussed. Our findings can shed light in the study of how particular kinds of subgraphs influence network dynamics.

Network formation determined by the diffusion process of random walkers

International Nuclear Information System (INIS)

Ikeda, Nobutoshi

2008-01-01

We studied the diffusion process of random walkers in networks formed by their traces. This model considers the rise and fall of links determined by the frequency of transports of random walkers. In order to examine the relation between the formed network and the diffusion process, a situation in which multiple random walkers start from the same vertex is investigated. The difference in diffusion rate of random walkers according to the difference in dimension of the initial lattice is very important for determining the time evolution of the networks. For example, complete subgraphs can be formed on a one-dimensional lattice while a graph with a power-law vertex degree distribution is formed on a two-dimensional lattice. We derived some formulae for predicting network changes for the 1D case, such as the time evolution of the size of nearly complete subgraphs and conditions for their collapse. The networks formed on the 2D lattice are characterized by the existence of clusters of highly connected vertices and their life time. As the life time of such clusters tends to be small, the exponent of the power-law distribution changes from γ ≅ 1-2 to γ ≅ 3

A class of vertex-edge-growth small-world network models having scale-free, self-similar and hierarchical characters

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Ma, Fei; Su, Jing; Hao, Yongxing; Yao, Bing; Yan, Guanghui

2018-02-01

The problem of uncovering the internal operating function of network models is intriguing, demanded and attractive in researches of complex networks. Notice that, in the past two decades, a great number of artificial models are built to try to answer the above mentioned task. Based on the different growth ways, these previous models can be divided into two categories, one type, possessing the preferential attachment, follows a power-law P(k) ∼k-γ, 2 motivated from a new attachment way, vertex-edge-growth network-operation, more precisely, the couple of both them. We report that this model is sparse, small world and hierarchical. And then, not only is scale-free feature in our model, but also lies the degree parameter γ(≈ 3 . 242) out the typical range. Note that, we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power-law parameter γ, and the preferential attachment plays a dominate role on the development of networks over time. At the end of this paper, we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements.

More randomized and resilient in the topological properties of functional brain networks in patients with major depressive disorder.

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Li, Huaizhou; Zhou, Haiyan; Yang, Yang; Wang, Haiyuan; Zhong, Ning

2017-10-01

Previous studies have reported the enhanced randomization of functional brain networks in patients with major depressive disorder (MDD). However, little is known about the changes of key nodal attributes for randomization, the resilience of network, and the clinical significance of the alterations. In this study, we collected the resting-state functional MRI data from 19 MDD patients and 19 healthy control (HC) individuals. Graph theory analysis showed that decreases were found in the small-worldness, clustering coefficient, local efficiency, and characteristic path length (i.e., increase of global efficiency) in the network of MDD group compared with HC group, which was consistent with previous findings and suggested the development toward randomization in the brain network in MDD. In addition, the greater resilience under the targeted attacks was also found in the network of patients with MDD. Furthermore, the abnormal nodal properties were found, including clustering coefficients and nodal efficiencies in the left orbital superior frontal gyrus, bilateral insula, left amygdala, right supramarginal gyrus, left putamen, left posterior cingulate cortex, left angular gyrus. Meanwhile, the correlation analysis showed that most of these abnormal areas were associated with the clinical status. The observed increased randomization and resilience in MDD might be related to the abnormal hub nodes in the brain networks, which were attacked by the disease pathology. Our findings provide new evidence to indicate that the weakening of specialized regions and the enhancement of whole brain integrity could be the potential endophenotype of the depressive pathology. Copyright © 2017 Elsevier Ltd. All rights reserved.

Handedness- and brain size-related efficiency differences in small-world brain networks: a resting-state functional magnetic resonance imaging study.

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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.

Unified Model for Generation Complex Networks with Utility Preferential Attachment

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Wu Jianjun; Gao Ziyou; Sun Huijun

2006-01-01

In this paper, based on the utility preferential attachment, we propose a new unified model to generate different network topologies such as scale-free, small-world and random networks. Moreover, a new network structure named super scale network is found, which has monopoly characteristic in our simulation experiments. Finally, the characteristics of this new network are given.

From Networks to Time Series

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Shimada, Yutaka; Ikeguchi, Tohru; Shigehara, Takaomi

2012-10-01

In this Letter, we propose a framework to transform a complex network to a time series. The transformation from complex networks to time series is realized by the classical multidimensional scaling. Applying the transformation method to a model proposed by Watts and Strogatz [Nature (London) 393, 440 (1998)], we show that ring lattices are transformed to periodic time series, small-world networks to noisy periodic time series, and random networks to random time series. We also show that these relationships are analytically held by using the circulant-matrix theory and the perturbation theory of linear operators. The results are generalized to several high-dimensional lattices.

Network resilience to real-world disasters: Eyjafjallajökull and 9/11

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Woolley, Olivia; Thiemann, Christian; Grady, Daniel; Brockmann, Dirk

2011-03-01

We investigate the resilience of the the world-wide air transportation network (WAN) to the 9/11 terrorist attacks and the recent eruption of the volcano Eyjafjallajökull. Although both disasters caused wide-spread disruption, the number of airports that were closed and the volume of interrupted traffic were well below the percolation threshold predicted by the classical theory. In order to quantify and visualize network deformation before breakdown, we introduce a framework based on the increase in shortest-path distance and homogenization of shortest-path structure. These real-world disasters are a new type of disruption because the removal of all vertices (airports) is geographically compact. Our framework incorporates the dual perspective of individual airports and geopolitical regions to capture how the impact interacts with the sub-network structure.We find that real-world events have an impact signature which is qualitatively different from that of random or high-centrality attacks. Furthermore, we find that the network is more resilient to the 9/11 disaster, although it removed more airports and traffic than the volcanic ash-cloud. This is due to the network roles of Europe and North America. We discuss how regional roles influence resilience to a region's removal.

Exploring biological network structure with clustered random networks

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Bansal Shweta

2009-12-01

Full Text Available Abstract Background Complex biological systems are often modeled as networks of interacting units. Networks of biochemical interactions among proteins, epidemiological contacts among hosts, and trophic interactions in ecosystems, to name a few, have provided useful insights into the dynamical processes that shape and traverse these systems. The degrees of nodes (numbers of interactions and the extent of clustering (the tendency for a set of three nodes to be interconnected are two of many well-studied network properties that can fundamentally shape a system. Disentangling the interdependent effects of the various network properties, however, can be difficult. Simple network models can help us quantify the structure of empirical networked systems and understand the impact of various topological properties on dynamics. Results Here we develop and implement a new Markov chain simulation algorithm to generate simple, connected random graphs that have a specified degree sequence and level of clustering, but are random in all other respects. The implementation of the algorithm (ClustRNet: Clustered Random Networks provides the generation of random graphs optimized according to a local or global, and relative or absolute measure of clustering. We compare our algorithm to other similar methods and show that ours more successfully produces desired network characteristics. Finding appropriate null models is crucial in bioinformatics research, and is often difficult, particularly for biological networks. As we demonstrate, the networks generated by ClustRNet can serve as random controls when investigating the impacts of complex network features beyond the byproduct of degree and clustering in empirical networks. Conclusion ClustRNet generates ensembles of graphs of specified edge structure and clustering. These graphs allow for systematic study of the impacts of connectivity and redundancies on network function and dynamics. This process is a key step in

Impact of network topology on synchrony of oscillatory power grids

Energy Technology Data Exchange (ETDEWEB)

Rohden, Martin; Sorge, Andreas; Witthaut, Dirk [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Faculty of Physics, Georg August Universität Göttingen, Göttingen (Germany)

2014-03-15

Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. In particular, power generation in the resulting grid will be far more decentralized, with a distinctly different topology. Here, we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random, and small-world topologies and focusing on the influence of decentralization. We model the consumers and sources of the power grid as second order oscillators. First, we analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage), and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular, star-like networks and regular grid motifs. For larger networks, we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in exhibiting a stable state for lower transmission line capacities. Decentralization may thus be beneficial for power grids, regardless of the details of their resulting topology. Regular grids show a specific sharper transition not found for random or small-world grids.

Network dynamics: The World Wide Web

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Adamic, Lada Ariana

Despite its rapidly growing and dynamic nature, the Web displays a number of strong regularities which can be understood by drawing on methods of statistical physics. This thesis finds power-law distributions in website sizes, traffic, and links, and more importantly, develops a stochastic theory which explains them. Power-law link distributions are shown to lead to network characteristics which are especially suitable for scalable localized search. It is also demonstrated that the Web is a "small world": to reach one site from any other takes an average of only 4 hops, while most related sites cluster together. Additional dynamical properties of the Web graph are extracted from diffusion processes.

Proposal of world network on material testing reactors

International Nuclear Information System (INIS)

Takemoto, Noriyuki; Izumo, Hironobu; Hori, Naohiko; Ishitsuka, Etsuo; Ishihara, Masahiro

2011-01-01

Establishment of an international cooperation system of worldwide testing reactor network (world network) is proposed in order to achieve efficient facility utilization and provide high quality irradiation data by role sharing of irradiation tests with materials testing reactors in the world. As for the first step, mutual understanding among materials testing reactors is thought to be necessary. From this point, an international symposium on materials testing reactors (ISMTR) was held to construct the world network from 2008, and a common understanding of world network has begun to be shared. (author)

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

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Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

Random walks and diffusion on networks

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Masuda, Naoki; Porter, Mason A.; Lambiotte, Renaud

2017-11-01

Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including diffusion, interactions, and opinions among humans and animals; and can be used to extract information about important entities or dense groups of entities in a network. Random walks have been studied for many decades on both regular lattices and (especially in the last couple of decades) on networks with a variety of structures. In the present article, we survey the theory and applications of random walks on networks, restricting ourselves to simple cases of single and non-adaptive random walkers. We distinguish three main types of random walks: discrete-time random walks, node-centric continuous-time random walks, and edge-centric continuous-time random walks. We first briefly survey random walks on a line, and then we consider random walks on various types of networks. We extensively discuss applications of random walks, including ranking of nodes (e.g., PageRank), community detection, respondent-driven sampling, and opinion models such as voter models.

The architecture of dynamic reservoir in the echo state network

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Cui, Hongyan; Liu, Xiang; Li, Lixiang

2012-09-01

Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.

Best Signal Quality in Cellular Networks: Asymptotic Properties and Applications to Mobility Management in Small Cell Networks

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Baccelli François

2010-01-01

Full Text Available The quickly increasing data traffic and the user demand for a full coverage of mobile services anywhere and anytime are leading mobile networking into a future of small cell networks. However, due to the high-density and randomness of small cell networks, there are several technical challenges. In this paper, we investigate two critical issues: best signal quality and mobility management. Under the assumptions that base stations are uniformly distributed in a ring-shaped region and that shadowings are lognormal, independent, and identically distributed, we prove that when the number of sites in the ring tends to infinity, then (i the maximum signal strength received at the center of the ring tends in distribution to a Gumbel distribution when properly renormalized, and (ii it is asymptotically independent of the interference. Using these properties, we derive the distribution of the best signal quality. Furthermore, an optimized random cell scanning scheme is proposed, based on the evaluation of the optimal number of sites to be scanned for maximizing the user data throughput.

Intermittent exploration on a scale-free network

International Nuclear Information System (INIS)

Ramezanpour, A

2007-02-01

We study an intermittent random walk on a random network of scale-free degree distribution. The walk is a combination of simple random walks of duration t w and random long-range jumps. While the time the walker needs to cover all the nodes increases with t w , the corresponding time for the edges displays a non monotonic behavior with a minimum for some nontrivial value of t w . This is a heterogeneity-induced effect that is not observed in homogeneous small-world networks. The optimal t w increases with the degree of assortativity in the network. Depending on the nature of degree correlations and the elapsed time the walker finds an over/underestimate of the degree distribution exponent. (author)

Order-based representation in random networks of cortical neurons.

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Goded Shahaf

2008-11-01

Full Text Available The wide range of time scales involved in neural excitability and synaptic transmission might lead to ongoing change in the temporal structure of responses to recurring stimulus presentations on a trial-to-trial basis. This is probably the most severe biophysical constraint on putative time-based primitives of stimulus representation in neuronal networks. Here we show that in spontaneously developing large-scale random networks of cortical neurons in vitro the order in which neurons are recruited following each stimulus is a naturally emerging representation primitive that is invariant to significant temporal changes in spike times. With a relatively small number of randomly sampled neurons, the information about stimulus position is fully retrievable from the recruitment order. The effective connectivity that makes order-based representation invariant to time warping is characterized by the existence of stations through which activity is required to pass in order to propagate further into the network. This study uncovers a simple invariant in a noisy biological network in vitro; its applicability under in vivo constraints remains to be seen.

Probabilistic generation of random networks taking into account information on motifs occurrence.

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Bois, Frederic Y; Gayraud, Ghislaine

2015-01-01

Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of some meaningful patterns (motifs) is also difficult. We show how to generate such random graphs according to a formal probabilistic representation, using fast Markov chain Monte Carlo methods to sample them. As an illustration, we generate realistic graphs with several hundred nodes mimicking a gene transcription interaction network in Escherichia coli.

Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network.

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Kim, Sang-Yoon; Lim, Woochang

2017-09-01

We consider an inhomogeneous small-world network (SWN) composed of inhibitory short-range (SR) and long-range (LR) interneurons, and investigate the effect of network architecture on emergence of synchronized brain rhythms by varying the fraction of LR interneurons p long . The betweenness centralities of the LR and SR interneurons (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 the same betweenness centralities. For small p long , the load of communication traffic is much concentrated on a few LR interneurons. However, as p long is increased, the number of LR connections (coming from LR interneurons) increases, and then the load of communication traffic is less concentrated on LR interneurons, which leads to better efficiency of global communication between interneurons. Sparsely synchronized rhythms are thus found to emerge when passing a small critical value p long (c) (≃0.16). The population frequency of the sparsely synchronized rhythm is ultrafast (higher than 100 Hz), while the mean firing rate of individual interneurons is much lower (∼30 Hz) due to stochastic and intermittent neural discharges. These dynamical behaviors in the inhomogeneous SWN are also compared with those in the homogeneous Watts-Strogatz SWN, in connection with their network topologies. Particularly, we note that the main difference between the two types of SWNs lies in the distribution of betweenness centralities. Unlike the case of the Watts-Strogatz SWN, dynamical responses to external stimuli vary depending on the type of stimulated interneurons in the inhomogeneous SWN. We consider two cases of external time-periodic stimuli applied to sub-populations of the LR and SR interneurons, respectively. Dynamical responses (such as synchronization suppression and enhancement) to these two cases of

Reducing financial avalanches by random investments

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Biondo, Alessio Emanuele; Pluchino, Alessandro; Rapisarda, Andrea; Helbing, Dirk

2013-12-01

Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets. We consider a community of interacting investors, distributed in a small-world network, who bet on the bullish (increasing) or bearish (decreasing) behavior of the market which has been specified according to the S&P 500 historical time series. Remarkably, we find that the size of herding-related avalanches in the community can be strongly reduced by the presence of a relatively small percentage of traders, randomly distributed inside the network, who adopt a random investment strategy. Our findings suggest a promising strategy to limit the size of financial bubbles and crashes. We also obtain that the resulting wealth distribution of all traders corresponds to the well-known Pareto power law, while that of random traders is exponential. In other words, for technical traders, the risk of losses is much greater than the probability of gains compared to those of random traders.

Random walk centrality for temporal networks

International Nuclear Information System (INIS)

Rocha, Luis E C; Masuda, Naoki

2014-01-01

Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included. (paper)

Random walk centrality for temporal networks

Science.gov (United States)

Rocha, Luis E. C.; Masuda, Naoki

2014-06-01

Nodes can be ranked according to their relative importance within a network. Ranking algorithms based on random walks are particularly useful because they connect topological and diffusive properties of the network. Previous methods based on random walks, for example the PageRank, have focused on static structures. However, several realistic networks are indeed dynamic, meaning that their structure changes in time. In this paper, we propose a centrality measure for temporal networks based on random walks under periodic boundary conditions that we call TempoRank. It is known that, in static networks, the stationary density of the random walk is proportional to the degree or the strength of a node. In contrast, we find that, in temporal networks, the stationary density is proportional to the in-strength of the so-called effective network, a weighted and directed network explicitly constructed from the original sequence of transition matrices. The stationary density also depends on the sojourn probability q, which regulates the tendency of the walker to stay in the node, and on the temporal resolution of the data. We apply our method to human interaction networks and show that although it is important for a node to be connected to another node with many random walkers (one of the principles of the PageRank) at the right moment, this effect is negligible in practice when the time order of link activation is included.

The complex network reliability and influential nodes

Science.gov (United States)

Li, Kai; He, Yongfeng

2017-08-01

In order to study the complex network node important degree and reliability, considering semi-local centrality, betweenness centrality and PageRank algorithm, through the simulation method to gradually remove nodes and recalculate the importance in the random network, small world network and scale-free network. Study the relationship between the largest connected component and node removed proportion, the research results show that betweenness centrality and PageRank algorithm based on the global information network are more effective for evaluating the importance of nodes, and the reliability of the network is related to the network topology.

Order parameters and synchronization of FitzHugh–Nagumo small-world networks

International Nuclear Information System (INIS)

Yan-Long, Li; Jun, Ma; Yan-Jun, Liu; Wei, Zhang

2009-01-01

This paper numerically investigates the order parameter and synchronisation in the small world connected FitzHugh–Nagumo excitable systems. The simulations show that the order parameter continuously decreases with increasing D, the quality of the synchronisation worsens for large noise intensity. As the coupling intensity goes up, the quality of the synchronisation worsens, and it finds that the larger rewiring probability becomes the larger order parameter. It obtains the complete phase diagram for a wide range of values of noise intensity D and control parameter g. (cross-disciplinary physics and related areas of science and technology)

Scale free effects in world currency exchange network

Science.gov (United States)

Górski, A. Z.; Drożdż, S.; Kwapień, J.

2008-11-01

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed - like the USD case - towards more compact MST topology can be observed when correlations increase.

Navigating the massive world of reddit: using backbone networks to map user interests in social media

Directory of Open Access Journals (Sweden)

Randal S. Olson

2015-05-01

Full Text Available In the massive online worlds of social media, users frequently rely on organizing themselves around specific topics of interest to find and engage with like-minded people. However, navigating these massive worlds and finding topics of specific interest often proves difficult because the worlds are mostly organized haphazardly, leaving users to find relevant interests by word of mouth or using a basic search feature. Here, we report on a method using the backbone of a network to create a map of the primary topics of interest in any social network. To demonstrate the method, we build an interest map for the social news web site reddit and show how such a map could be used to navigate a social media world. Moreover, we analyze the network properties of the reddit social network and find that it has a scale-free, small-world, and modular community structure, much like other online social networks such as Facebook and Twitter. We suggest that the integration of interest maps into popular social media platforms will assist users in organizing themselves into more specific interest groups, which will help alleviate the overcrowding effect often observed in large online communities.

Dawn of small worlds dwarf planets, asteroids, comets

CERN Document Server

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.

Entropy Characterization of Random Network Models

Directory of Open Access Journals (Sweden)

Pedro J. Zufiria

2017-06-01

Full Text Available This paper elaborates on the Random Network Model (RNM as a mathematical framework for modelling and analyzing the generation of complex networks. Such framework allows the analysis of the relationship between several network characterizing features (link density, clustering coefficient, degree distribution, connectivity, etc. and entropy-based complexity measures, providing new insight on the generation and characterization of random networks. Some theoretical and computational results illustrate the utility of the proposed framework.

Analysis of world terror networks from the reduced Google matrix of Wikipedia

Science.gov (United States)

El Zant, Samer; Frahm, Klaus M.; Jaffrès-Runser, Katia; Shepelyansky, Dima L.

2018-01-01

We apply the reduced Google matrix method to analyze interactions between 95 terrorist groups and determine their relationships and influence on 64 world countries. This is done on the basis of the Google matrix of the English Wikipedia (2017) composed of 5 416 537 articles which accumulate a great part of global human knowledge. The reduced Google matrix takes into account the direct and hidden links between a selection of 159 nodes (articles) appearing due to all paths of a random surfer moving over the whole network. As a result we obtain the network structure of terrorist groups and their relations with selected countries including hidden indirect links. Using the sensitivity of PageRank to a weight variation of specific links we determine the geopolitical sensitivity and influence of specific terrorist groups on world countries. The world maps of the sensitivity of various countries to influence of specific terrorist groups are obtained. We argue that this approach can find useful application for more extensive and detailed data bases analysis.

Modeling of contact tracing in social networks

Science.gov (United States)

Tsimring, Lev S.; Huerta, Ramón

2003-07-01

Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks which incorporates an additional (traced) state. We describe a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also discuss the role of contact tracing in epidemics control in small-world and scale-free networks. Effectiveness of contact tracing grows as the rewiring probability is reduced.

A random network based, node attraction facilitated network evolution method

Directory of Open Access Journals (Sweden)

WenJun Zhang

2016-03-01

Full Text Available In present study, I present a method of network evolution that based on random network, and facilitated by node attraction. In this method, I assume that the initial network is a random network, or a given initial network. When a node is ready to connect, it tends to link to the node already owning the most connections, which coincides with the general rule (Barabasi and Albert, 1999 of node connecting. In addition, a node may randomly disconnect a connection i.e., the addition of connections in the network is accompanied by the pruning of some connections. The dynamics of network evolution is determined of the attraction factor Lamda of nodes, the probability of node connection, the probability of node disconnection, and the expected initial connectance. The attraction factor of nodes, the probability of node connection, and the probability of node disconnection are time and node varying. Various dynamics can be achieved by adjusting these parameters. Effects of simplified parameters on network evolution are analyzed. The changes of attraction factor Lamda can reflect various effects of the node degree on connection mechanism. Even the changes of Lamda only will generate various networks from the random to the complex. Therefore, the present algorithm can be treated as a general model for network evolution. Modeling results show that to generate a power-law type of network, the likelihood of a node attracting connections is dependent upon the power function of the node's degree with a higher-order power. Matlab codes for simplified version of the method are provided.

Hello! Kids Network around the World.

Science.gov (United States)

Lynes, Kristine

1996-01-01

Describes Kids Network, an educational network available from the National Geographic Society that allows students in grades four through six to become part of research teams that include students from around the world. Computer hardware requirements and a list of Kids Network research questions are listed in a sidebar. (JMV)

Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

KAUST Repository

Yasin Yazicioǧlu, A.; Egerstedt, Magnus; Shamma, Jeff S.

2015-01-01

Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

Formation of Robust Multi-Agent Networks through Self-Organizing Random Regular Graphs

KAUST Repository

Yasin Yazicioǧlu, A.

2015-11-25

Multi-Agent networks are often modeled as interaction graphs, where the nodes represent the agents and the edges denote some direct interactions. The robustness of a multi-Agent network to perturbations such as failures, noise, or malicious attacks largely depends on the corresponding graph. In many applications, networks are desired to have well-connected interaction graphs with relatively small number of links. One family of such graphs is the random regular graphs. In this paper, we present a decentralized scheme for transforming any connected interaction graph with a possibly non-integer average degree of k into a connected random m-regular graph for some m ϵ [k+k ] 2. Accordingly, the agents improve the robustness of the network while maintaining a similar number of links as the initial configuration by locally adding or removing some edges. © 2015 IEEE.

Network Analysis of Resting State EEG in the Developing Young Brain: Structure Comes With Maturation

NARCIS (Netherlands)

Boersma, M.; Smit, D.J.A.; de Bie, H.M.A.; van Baal, G.C.M.; Boomsma, D.I.; de Geus, E.J.C.; Delemarre-van de Waal, H.A.; Stam, C.J.

2011-01-01

During childhood, brain structure and function changes substantially. Recently, graph theory has been introduced to model connectivity in the brain. Small-world networks, such as the brain, combine optimal properties of both ordered and random networks, i.e., high clustering and short path lengths.

The correlation of metrics in complex networks with applications in functional brain networks

International Nuclear Information System (INIS)

Li, C; Wang, H; Van Mieghem, P; De Haan, W; Stam, C J

2011-01-01

An increasing number of network metrics have been applied in network analysis. If metric relations were known better, we could more effectively characterize networks by a small set of metrics to discover the association between network properties/metrics and network functioning. In this paper, we investigate the linear correlation coefficients between widely studied network metrics in three network models (Bárabasi–Albert graphs, Erdös–Rényi random graphs and Watts–Strogatz small-world graphs) as well as in functional brain networks of healthy subjects. The metric correlations, which we have observed and theoretically explained, motivate us to propose a small representative set of metrics by including only one metric from each subset of mutually strongly dependent metrics. The following contributions are considered important. (a) A network with a given degree distribution can indeed be characterized by a small representative set of metrics. (b) Unweighted networks, which are obtained from weighted functional brain networks with a fixed threshold, and Erdös–Rényi random graphs follow a similar degree distribution. Moreover, their metric correlations and the resultant representative metrics are similar as well. This verifies the influence of degree distribution on metric correlations. (c) Most metric correlations can be explained analytically. (d) Interestingly, the most studied metrics so far, the average shortest path length and the clustering coefficient, are strongly correlated and, thus, redundant. Whereas spectral metrics, though only studied recently in the context of complex networks, seem to be essential in network characterizations. This representative set of metrics tends to both sufficiently and effectively characterize networks with a given degree distribution. In the study of a specific network, however, we have to at least consider the representative set so that important network properties will not be neglected

Modified Small Business Network Security

OpenAIRE

Md. Belayet Ali; Oveget Das; Md. Shamim Hossain

2012-01-01

This paper covers some likely threats and effectivesteps for a secure small business. It also involves a flowchart tocomprehend the overall small business network security easilyand we identify a set of security issues and applyappropriate techniques to satisfy the correspondingsecurity requirements. In respect of all, this document isstrong enough for any small business network security.

Random walks on generalized Koch networks

International Nuclear Information System (INIS)

Sun, Weigang

2013-01-01

For deterministically growing networks, it is a theoretical challenge to determine the topological properties and dynamical processes. In this paper, we study random walks on generalized Koch networks with features that include an initial state that is a globally connected network to r nodes. In each step, every existing node produces m complete graphs. We then obtain the analytical expressions for first passage time (FPT), average return time (ART), i.e. the average of FPTs for random walks from node i to return to the starting point i for the first time, and average sending time (AST), defined as the average of FPTs from a hub node to all other nodes, excluding the hub itself with regard to network parameters m and r. For this family of Koch networks, the ART of the new emerging nodes is identical and increases with the parameters m or r. In addition, the AST of our networks grows with network size N as N ln N and also increases with parameter m. The results obtained in this paper are the generalizations of random walks for the original Koch network. (paper)

Search for Directed Networks by Different Random Walk Strategies

Science.gov (United States)

Zhu, Zi-Qi; Jin, Xiao-Ling; Huang, Zhi-Long

2012-03-01

A comparative study is carried out on the efficiency of five different random walk strategies searching on directed networks constructed based on several typical complex networks. Due to the difference in search efficiency of the strategies rooted in network clustering, the clustering coefficient in a random walker's eye on directed networks is defined and computed to be half of the corresponding undirected networks. The search processes are performed on the directed networks based on Erdös—Rényi model, Watts—Strogatz model, Barabási—Albert model and clustered scale-free network model. It is found that self-avoiding random walk strategy is the best search strategy for such directed networks. Compared to unrestricted random walk strategy, path-iteration-avoiding random walks can also make the search process much more efficient. However, no-triangle-loop and no-quadrangle-loop random walks do not improve the search efficiency as expected, which is different from those on undirected networks since the clustering coefficient of directed networks are smaller than that of undirected networks.

Percolation and epidemics in random clustered networks

Science.gov (United States)

Miller, Joel C.

2009-08-01

The social networks that infectious diseases spread along are typically clustered. Because of the close relation between percolation and epidemic spread, the behavior of percolation in such networks gives insight into infectious disease dynamics. A number of authors have studied percolation or epidemics in clustered networks, but the networks often contain preferential contacts in high degree nodes. We introduce a class of random clustered networks and a class of random unclustered networks with the same preferential mixing. Percolation in the clustered networks reduces the component sizes and increases the epidemic threshold compared to the unclustered networks.

Generating random networks and graphs

CERN Document Server

Coolen, Ton; Roberts, Ekaterina

2017-01-01

This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...

A local-world node deleting evolving network model

International Nuclear Information System (INIS)

Gu Yuying; Sun Jitao

2008-01-01

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as p a decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient decreases as generally node deleting increases. Finally, trends up when the local-world size M increases, so as to k max . Hence, the expanding local-world can compensate the infection of the node deleting

A local-world node deleting evolving network model

Energy Technology Data Exchange (ETDEWEB)

Gu Yuying [Department of Mathematics, Tongji University, Shanghai 200092 (China); Sun Jitao [Department of Mathematics, Tongji University, Shanghai 200092 (China)], E-mail: sunjt@sh163.net

2008-06-16

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as p{sub a} decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient decreases as generally node deleting increases. Finally, trends up when the local-world size M increases, so as to k{sub max}. Hence, the expanding local-world can compensate the infection of the node deleting.

Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons.

Science.gov (United States)

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.

Topology influences performance in the associative memory neural networks

International Nuclear Information System (INIS)

Lu Jianquan; He Juan; Cao Jinde; Gao Zhiqiang

2006-01-01

To explore how topology affects performance within Hopfield-type associative memory neural networks (AMNNs), we studied the computational performance of the neural networks with regular lattice, random, small-world, and scale-free structures. In this Letter, we found that the memory performance of neural networks obtained through asynchronous updating from 'larger' nodes to 'smaller' nodes are better than asynchronous updating in random order, especially for the scale-free topology. The computational performance of associative memory neural networks linked by the above-mentioned network topologies with the same amounts of nodes (neurons) and edges (synapses) were studied respectively. Along with topologies becoming more random and less locally disordered, we will see that the performance of associative memory neural network is quite improved. By comparing, we show that the regular lattice and random network form two extremes in terms of patterns stability and retrievability. For a network, its patterns stability and retrievability can be largely enhanced by adding a random component or some shortcuts to its structured component. According to the conclusions of this Letter, we can design the associative memory neural networks with high performance and minimal interconnect requirements

Dynamic defense and network randomization for computer systems

Science.gov (United States)

Chavez, Adrian R.; Stout, William M. S.; Hamlet, Jason R.; Lee, Erik James; Martin, Mitchell Tyler

2018-05-29

The various technologies presented herein relate to determining a network attack is taking place, and further to adjust one or more network parameters such that the network becomes dynamically configured. A plurality of machine learning algorithms are configured to recognize an active attack pattern. Notification of the attack can be generated, and knowledge gained from the detected attack pattern can be utilized to improve the knowledge of the algorithms to detect a subsequent attack vector(s). Further, network settings and application communications can be dynamically randomized, wherein artificial diversity converts control systems into moving targets that help mitigate the early reconnaissance stages of an attack. An attack(s) based upon a known static address(es) of a critical infrastructure network device(s) can be mitigated by the dynamic randomization. Network parameters that can be randomized include IP addresses, application port numbers, paths data packets navigate through the network, application randomization, etc.

Topological properties of random wireless networks

Indian Academy of Sciences (India)

Wireless networks in which the node locations are random are best modelled as random geometric graphs (RGGs). In addition to their extensive application in the modelling of wireless networks, RGGs find many new applications and are being studied in their own right. In this paper we first provide a brief introduction to the ...

Consumers don’t play dice, influence of social networks and advertisements

Science.gov (United States)

Groot, Robert D.

2006-05-01

Empirical data of supermarket sales show stylised facts that are similar to stock markets, with a broad (truncated) Lévy distribution of weekly sales differences in the baseline sales [R.D. Groot, Physica A 353 (2005) 501]. To investigate the cause of this, the influence of social interactions and advertisements are studied in an agent-based model of consumers in a social network. The influence of network topology was varied by using a small-world network, a random network and a Barabási-Albert network. The degree to which consumers value the opinion of their peers was also varied. On a small-world and random network we find a phase transition between an open market and a locked-in market that is similar to condensation in liquids. At the critical point, fluctuations become large and buying behaviour is strongly correlated. However, on the small world network the noise distribution at the critical point is Gaussian, and critical slowing down occurs which is not observed in supermarket sales. On a scale-free network, the model shows a transition between a gas-like phase and a glassy state, but at the transition point the noise amplitude is much larger than what is seen in supermarket sales. To explore the role of advertisements, a model is studied where imprints are placed on the minds of consumers that ripen when a decision for a product is made. The correct distribution of weekly sales returns follows naturally from this model, as well as the noise amplitude, the correlation time and cross-correlation of sales fluctuations. For particular parameter values, simulated sales correlation shows power-law decay in time. The model predicts that social interaction helps to prevent aversion, and that products are viewed more positively when their consumption rate is higher.

Market-oriented Programming Using Small-world Networks for Controlling Building Environments

Science.gov (United States)

Shigei, Noritaka; Miyajima, Hiromi; Osako, Tsukasa

The market model, which is one of the economic activity models, is modeled as an agent system, and applying the model to the resource allocation problem has been studied. For air conditioning control of building, which is one of the resource allocation problems, an effective method based on the agent system using auction has been proposed for traditional PID controller. On the other hand, it has been considered that this method is performed by decentralized control. However, its decentralization is not perfect, and its performace is not enough. In this paper, firstly, we propose a perfectly decentralized agent model and show its performance. Secondly, in order to improve the model, we propose the agent model based on small-world model. The effectiveness of the proposed model is shown by simulation.

A Single Session of rTMS Enhances Small-Worldness in Writer’s Cramp: Evidence from Simultaneous EEG-fMRI Multi-Modal Brain Graph

Directory of Open Access Journals (Sweden)

Rose D. Bharath

2017-09-01

Full Text Available Background and Purpose: Repetitive transcranial magnetic stimulation (rTMS induces widespread changes in brain connectivity. As the network topology differences induced by a single session of rTMS are less known we undertook this study to ascertain whether the network alterations had a small-world morphology using multi-modal graph theory analysis of simultaneous EEG-fMRI.Method: Simultaneous EEG-fMRI was acquired in duplicate before (R1 and after (R2 a single session of rTMS in 14 patients with Writer’s Cramp (WC. Whole brain neuronal and hemodynamic network connectivity were explored using the graph theory measures and clustering coefficient, path length and small-world index were calculated for EEG and resting state fMRI (rsfMRI. Multi-modal graph theory analysis was used to evaluate the correlation of EEG and fMRI clustering coefficients.Result: A single session of rTMS was found to increase the clustering coefficient and small-worldness significantly in both EEG and fMRI (p < 0.05. Multi-modal graph theory analysis revealed significant modulations in the fronto-parietal regions immediately after rTMS. The rsfMRI revealed additional modulations in several deep brain regions including cerebellum, insula and medial frontal lobe.Conclusion: Multi-modal graph theory analysis of simultaneous EEG-fMRI can supplement motor physiology methods in understanding the neurobiology of rTMS in vivo. Coinciding evidence from EEG and rsfMRI reports small-world morphology for the acute phase network hyper-connectivity indicating changes ensuing low-frequency rTMS is probably not “noise”.

Topology and computational performance of attractor neural networks

International Nuclear Information System (INIS)

McGraw, Patrick N.; Menzinger, Michael

2003-01-01

To explore the relation between network structure and function, we studied the computational performance of Hopfield-type attractor neural nets with regular lattice, random, small-world, and scale-free topologies. The random configuration is the most efficient for storage and retrieval of patterns by the network as a whole. However, in the scale-free case retrieval errors are not distributed uniformly among the nodes. The portion of a pattern encoded by the subset of highly connected nodes is more robust and efficiently recognized than the rest of the pattern. The scale-free network thus achieves a very strong partial recognition. The implications of these findings for brain function and social dynamics are suggestive

World Small Hydropower Development Report

Energy Technology Data Exchange (ETDEWEB)

Liu, Heng; Esser, Lara [ICSGP (China); Masera, Diego [UNIDO, Vienna (Austria)

2013-07-01

Currently, small hydropower plants with a capacity of 10 MW, exist in 148 countries or territories worldwide. Four other countries have been identified with resource potential. This report aims to identify the development status and resource potential of small hydro in various countries, territories and regions throughout the world. Working with experts at the ground level to compile and share existing information, experiences and challenges, one comprehensive report was created. Decision-makers, stakeholders and potential investors clearly need this comprehensive information to more effectively promote small hydropower as a renewable and rural energy source for sustainable development and to overcome the existing development barriers. The findings of this report show that small hydropower potential globally is approximated at almost 173 GW. The figure is arrived by totaling data from a wide range of sources with potential compromise of data integrity to varying degrees. For example, research data on economically feasible potential were more readily available in developed countries than those in the least developed or developing countries. More than half of the world's known hydropower potential is located in Asia, around one third can be found in Europe and the Americas. It is possible in the future that more small hydropower potential might be identified both on the African and American continents. The installed small hydropower capacity (up to 10 MW) is estimated to be 75 GW in 2011/2012. The report provides detailed data for each country/region, including recommendations on the national, regional and international level.

World Small Hydropower Development Report

Energy Technology Data Exchange (ETDEWEB)

Liu, Heng; Esser, Lara (ICSGP (China)); Masera, Diego (UNIDO, Vienna (Austria))

2013-07-01

Currently, small hydropower plants with a capacity of 10 MW, exist in 148 countries or territories worldwide. Four other countries have been identified with resource potential. This report aims to identify the development status and resource potential of small hydro in various countries, territories and regions throughout the world. Working with experts at the ground level to compile and share existing information, experiences and challenges, one comprehensive report was created. Decision-makers, stakeholders and potential investors clearly need this comprehensive information to more effectively promote small hydropower as a renewable and rural energy source for sustainable development and to overcome the existing development barriers. The findings of this report show that small hydropower potential globally is approximated at almost 173 GW. The figure is arrived by totaling data from a wide range of sources with potential compromise of data integrity to varying degrees. For example, research data on economically feasible potential were more readily available in developed countries than those in the least developed or developing countries. More than half of the world's known hydropower potential is located in Asia, around one third can be found in Europe and the Americas. It is possible in the future that more small hydropower potential might be identified both on the African and American continents. The installed small hydropower capacity (up to 10 MW) is estimated to be 75 GW in 2011/2012. The report provides detailed data for each country/region, including recommendations on the national, regional and international level.

Generating Realistic Labelled, Weighted Random Graphs

Directory of Open Access Journals (Sweden)

Michael Charles Davis

2015-12-01

Full Text Available Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs. Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

Random catalytic reaction networks

Science.gov (United States)

Stadler, Peter F.; Fontana, Walter; Miller, John H.

1993-03-01

We study networks that are a generalization of replicator (or Lotka-Volterra) equations. They model the dynamics of a population of object types whose binary interactions determine the specific type of interaction product. Such a system always reduces its dimension to a subset that contains production pathways for all of its members. The network equation can be rewritten at a level of collectives in terms of two basic interaction patterns: replicator sets and cyclic transformation pathways among sets. Although the system contains well-known cases that exhibit very complicated dynamics, the generic behavior of randomly generated systems is found (numerically) to be extremely robust: convergence to a globally stable rest point. It is easy to tailor networks that display replicator interactions where the replicators are entire self-sustaining subsystems, rather than structureless units. A numerical scan of random systems highlights the special properties of elementary replicators: they reduce the effective interconnectedness of the system, resulting in enhanced competition, and strong correlations between the concentrations.

A Markov random walk under constraint for discovering overlapping communities in complex networks

International Nuclear Information System (INIS)

Jin, Di; Yang, Bo; Liu, Dayou; He, Dongxiao; Liu, Jie; Baquero, Carlos

2011-01-01

The detection of overlapping communities in complex networks has motivated recent research in relevant fields. Aiming to address this problem, we propose a Markov-dynamics-based algorithm, called UEOC, which means 'unfold and extract overlapping communities'. In UEOC, when identifying each natural community that overlaps, a Markov random walk method combined with a constraint strategy, which is based on the corresponding annealed network (degree conserving random network), is performed to unfold the community. Then, a cutoff criterion with the aid of a local community function, called conductance, which can be thought of as the ratio between the number of edges inside the community and those leaving it, is presented to extract this emerged community from the entire network. The UEOC algorithm depends on only one parameter whose value can be easily set, and it requires no prior knowledge of the hidden community structures. The proposed UEOC has been evaluated both on synthetic benchmarks and on some real-world networks, and has been compared with a set of competing algorithms. The experimental result has shown that UEOC is highly effective and efficient for discovering overlapping communities

Impact of mobility on call block, call drops and optimal cell size in small cell networks

OpenAIRE

Ramanath , Sreenath; Voleti , Veeraruna Kavitha; Altman , Eitan

2011-01-01

We consider small cell networks and study the impact of user mobility. Assuming Poisson call arrivals at random positions with random velocities, we discuss the characterization of handovers at the boundaries. We derive explicit expressions for call block and call drop probabilities using tools from spatial queuing theory. We also derive expressions for the average virtual server held up time. These expressions are used to derive optimal cell sizes for various profile of velocities in small c...

A model of coauthorship networks

Science.gov (United States)

Zhou, Guochang; Li, Jianping; Xie, Zonglin

2017-10-01

A natural way of representing the coauthorship of authors is to use a generalization of graphs known as hypergraphs. A random geometric hypergraph model is proposed here to model coauthorship networks, which is generated by placing nodes on a region of Euclidean space randomly and uniformly, and connecting some nodes if the nodes satisfy particular geometric conditions. Two kinds of geometric conditions are designed to model the collaboration patterns of academic authorities and basic researches respectively. The conditions give geometric expressions of two causes of coauthorship: the authority and similarity of authors. By simulation and calculus, we show that the forepart of the degree distribution of the network generated by the model is mixture Poissonian, and the tail is power-law, which are similar to these of some coauthorship networks. Further, we show more similarities between the generated network and real coauthorship networks: the distribution of cardinalities of hyperedges, high clustering coefficient, assortativity, and small-world property

Statistical investigation of avalanches of three-dimensional small-world networks and their boundary and bulk cross-sections

Science.gov (United States)

Najafi, M. N.; Dashti-Naserabadi, H.

2018-03-01

In many situations we are interested in the propagation of energy in some portions of a three-dimensional system with dilute long-range links. In this paper, a sandpile model is defined on the three-dimensional small-world network with real dissipative boundaries and the energy propagation is studied in three dimensions as well as the two-dimensional cross-sections. Two types of cross-sections are defined in the system, one in the bulk and another in the system boundary. The motivation of this is to make clear how the statistics of the avalanches in the bulk cross-section tend to the statistics of the dissipative avalanches, defined in the boundaries as the concentration of long-range links (α ) increases. This trend is numerically shown to be a power law in a manner described in the paper. Two regimes of α are considered in this work. For sufficiently small α s the dominant behavior of the system is just like that of the regular BTW, whereas for the intermediate values the behavior is nontrivial with some exponents that are reported in the paper. It is shown that the spatial extent up to which the statistics is similar to the regular BTW model scales with α just like the dissipative BTW model with the dissipation factor (mass in the corresponding ghost model) m2˜α for the three-dimensional system as well as its two-dimensional cross-sections.

Transcranial direct current stimulation generates a transient increase of small-world in brain connectivity: an EEG graph theoretical analysis.

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Vecchio, Fabrizio; Di Iorio, Riccardo; Miraglia, Francesca; Granata, Giuseppe; Romanello, Roberto; Bramanti, Placido; Rossini, Paolo Maria

2018-04-01

Transcranial direct current stimulation (tDCS) is a non-invasive technique able to modulate cortical excitability in a polarity-dependent way. At present, only few studies investigated the effects of tDCS on the modulation of functional connectivity between remote cortical areas. The aim of this study was to investigate-through graph theory analysis-how bipolar tDCS modulate cortical networks high-density EEG recordings were acquired before and after bipolar cathodal, anodal and sham tDCS involving the primary motor and pre-motor cortices of the dominant hemispherein 14 healthy subjects. Results showed that, after bipolar anodal tDCS stimulation, brain networks presented a less evident "small world" organization with a global tendency to be more random in its functional connections with respect to prestimulus condition in both hemispheres. Results suggest that tDCS globally modulates the cortical connectivity of the brain, modifying the underlying functional organization of the stimulated networks, which might be related to changes in synaptic efficiency of the motor network and related brain areas. This study demonstrated that graph analysis approach to EEG recordings is able to intercept changes in cortical functions mediated by bipolar anodal tDCS mainly involving the dominant M1 and related motor areas. Concluding, tDCS could be an useful technique to help understanding brain rhythms and their topographic functional organization and specificity.

A random spatial network model based on elementary postulates

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Karlinger, Michael R.; Troutman, Brent M.

1989-01-01

A model for generating random spatial networks that is based on elementary postulates comparable to those of the random topology model is proposed. In contrast to the random topology model, this model ascribes a unique spatial specification to generated drainage networks, a distinguishing property of some network growth models. The simplicity of the postulates creates an opportunity for potential analytic investigations of the probabilistic structure of the drainage networks, while the spatial specification enables analyses of spatially dependent network properties. In the random topology model all drainage networks, conditioned on magnitude (number of first-order streams), are equally likely, whereas in this model all spanning trees of a grid, conditioned on area and drainage density, are equally likely. As a result, link lengths in the generated networks are not independent, as usually assumed in the random topology model. For a preliminary model evaluation, scale-dependent network characteristics, such as geometric diameter and link length properties, and topologic characteristics, such as bifurcation ratio, are computed for sets of drainage networks generated on square and rectangular grids. Statistics of the bifurcation and length ratios fall within the range of values reported for natural drainage networks, but geometric diameters tend to be relatively longer than those for natural networks.

Altered Cerebral Blood Flow Covariance Network in Schizophrenia.

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Liu, Feng; Zhuo, Chuanjun; Yu, Chunshui

2016-01-01

Many studies have shown abnormal cerebral blood flow (CBF) in schizophrenia; however, it remains unclear how topological properties of CBF network are altered in this disorder. Here, arterial spin labeling (ASL) MRI was employed to measure resting-state CBF in 96 schizophrenia patients and 91 healthy controls. CBF covariance network of each group was constructed by calculating across-subject CBF covariance between 90 brain regions. Graph theory was used to compare intergroup differences in global and nodal topological measures of the network. Both schizophrenia patients and healthy controls had small-world topology in CBF covariance networks, implying an optimal balance between functional segregation and integration. Compared with healthy controls, schizophrenia patients showed reduced small-worldness, normalized clustering coefficient and local efficiency of the network, suggesting a shift toward randomized network topology in schizophrenia. Furthermore, schizophrenia patients exhibited altered nodal centrality in the perceptual-, affective-, language-, and spatial-related regions, indicating functional disturbance of these systems in schizophrenia. This study demonstrated for the first time that schizophrenia patients have disrupted topological properties in CBF covariance network, which provides a new perspective (efficiency of blood flow distribution between brain regions) for understanding neural mechanisms of schizophrenia.

Cluster-size entropy in the Axelrod model of social influence: Small-world networks and mass media

Science.gov (United States)

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 Sc, 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 Sc(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 qc 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.

5th International Workshop on Real-World Wireless Sensor Networks

CERN Document Server

Hu, Wen; Ferrari, Federico; Zimmerling, Marco; Mottola, Luca

2014-01-01

This edited book presents the results of the 5th Workshop on Real-world Wireless Sensor Networks (REALWSN). The purpose of this workshop  was to bring together researchers and practitioners working in the area of sensor networks, with focus on real-world experiments or deployments of wireless sensor networks. Included were, nonetheless, emerging forms of sensing such as those that leverage smart phones, Internet of Things, RFIDs, and robots. Indeed, when working with real-world experiments or deployments, many new or unforeseen issues may arise: the network environment may be composed of a variety of different technologies, leading to very heterogeneous network structures; software development for large scale networks poses new types of problems; the performance of prototype networks may differ significantly from the deployed system; whereas actual sensor network deployments may need a complex combination of autonomous and manual configuration. Furthermore, results obtained through simulation are typically n...

Continuous-time random walks on networks with vertex- and time-dependent forcing.

Science.gov (United States)

Angstmann, C N; Donnelly, I C; Henry, B I; Langlands, T A M

2013-08-01

We have investigated the transport of particles moving as random walks on the vertices of a network, subject to vertex- and time-dependent forcing. We have derived the generalized master equations for this transport using continuous time random walks, characterized by jump and waiting time densities, as the underlying stochastic process. The forcing is incorporated through a vertex- and time-dependent bias in the jump densities governing the random walking particles. As a particular case, we consider particle forcing proportional to the concentration of particles on adjacent vertices, analogous to self-chemotactic attraction in a spatial continuum. Our algebraic and numerical studies of this system reveal an interesting pair-aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices. The steady states do not exhibit this pair aggregation if the transport is random on the vertices, i.e., without forcing. The manifestation of pair aggregation on a transport network may thus be a signature of self-chemotactic-like forcing.

Cross over of recurrence networks to random graphs and random ...

Indian Academy of Sciences (India)

2017-01-27

Jan 27, 2017 ... that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to .... municative [19] or social [20], deviate from the random ..... He has shown that the spatial effects become.

Brain Network Analysis from High-Resolution EEG Signals

Science.gov (United States)

de Vico Fallani, Fabrizio; Babiloni, Fabio

lattice and a random structure. Such a model has been designated as "small-world" network in analogy with the concept of the small-world phenomenon observed more than 30 years ago in social systems. In a similar way, many types of functional brain networks have been analyzed according to this mathematical approach. In particular, several studies based on different imaging techniques (fMRI, MEG and EEG) have found that the estimated functional networks showed small-world characteristics. In the functional brain connectivity context, these properties have been demonstrated to reflect an optimal architecture for the information processing and propagation among the involved cerebral structures. However, the performance of cognitive and motor tasks as well as the presence of neural diseases has been demonstrated to affect such a small-world topology, as revealed by the significant changes of L and C. Moreover, some functional brain networks have been mostly found to be very unlike the random graphs in their degree-distribution, which gives information about the allocation of the functional links within the connectivity pattern. It was demonstrated that the degree distributions of these networks follow a power-law trend. For this reason those networks are called "scale-free". They still exhibit the small-world phenomenon but tend to contain few nodes that act as highly connected "hubs". Scale-free networks are known to show resistance to failure, facility of synchronization and fast signal processing. Hence, it would be important to see whether the scaling properties of the functional brain networks are altered under various pathologies or experimental tasks. The present Chapter proposes a theoretical graph approach in order to evaluate the functional connectivity patterns obtained from high-resolution EEG signals. In this way, the "Brain Network Analysis" (in analogy with the Social Network Analysis that has emerged as a key technique in modern sociology) represents an

Small cell networks deployment, management, and optimization

CERN Document Server

Claussen, Holger; Ho, Lester; Razavi, Rouzbeh; Kucera, Stepan

2018-01-01

Small Cell Networks: Deployment, Management, and Optimization addresses key problems of the cellular network evolution towards HetNets. It focuses on the latest developments in heterogeneous and small cell networks, as well as their deployment, operation, and maintenance. It also covers the full spectrum of the topic, from academic, research, and business to the practice of HetNets in a coherent manner. Additionally, it provides complete and practical guidelines to vendors and operators interested in deploying small cells. The first comprehensive book written by well-known researchers and engineers from Nokia Bell Labs, Small Cell Networks begins with an introduction to the subject--offering chapters on capacity scaling and key requirements of future networks. It then moves on to sections on coverage and capacity optimization, and interference management. From there, the book covers mobility management, energy efficiency, and small cell deployment, ending with a section devoted to future trends and applicat...

Multidimensional Risk Management for Underground Electricity Networks

Directory of Open Access Journals (Sweden)

Garcez Thalles V.

2014-08-01

Full Text Available In the paper we consider an electricity provider company that makes decision on allocating resources on electric network maintenance. The investments decrease malfunction rate of network nodes. An accidental event (explosion, fire, etc. or a malfunctioning on underground system can have various consequences and in different perspectives, such as deaths and injuries of pedestrians, fires in nearby locations, disturbances in the flow of vehicular traffic, loss to the company image, operating and financial losses, etc. For this reason it is necessary to apply an approach of the risk management that considers the multidimensional view of the consequences. Furthermore an analysis of decision making should consider network dependencies between the nodes of the electricity distribution system. In the paper we propose the use of the simulation to assess the network effects (such as the increase of the probability of other accidental event and the occurrence of blackouts of the dependent nodes in the multidimensional risk assessment in electricity grid. The analyzed effects include node overloading due to malfunction of adjacent nodes and blackouts that take place where there is temporarily no path in the grid between the power plant and a node. The simulation results show that network effects have crucial role for decisions in the network maintenance – outcomes of decisions to repair a particular node in the network can have significant influence on performance of other nodes. However, those dependencies are non-linear. The effects of network connectivity (number of connections between nodes on its multidimensional performance assessment depend heavily on the overloading effect level. The simulation results do not depend on network type structure (random or small world – however simulation outcomes for random networks have shown higher variance compared to small-world networks.

Random vs. Combinatorial Methods for Discrete Event Simulation of a Grid Computer Network

Science.gov (United States)

Kuhn, D. Richard; Kacker, Raghu; Lei, Yu

2010-01-01

This study compared random and t-way combinatorial inputs of a network simulator, to determine if these two approaches produce significantly different deadlock detection for varying network configurations. Modeling deadlock detection is important for analyzing configuration changes that could inadvertently degrade network operations, or to determine modifications that could be made by attackers to deliberately induce deadlock. Discrete event simulation of a network may be conducted using random generation, of inputs. In this study, we compare random with combinatorial generation of inputs. Combinatorial (or t-way) testing requires every combination of any t parameter values to be covered by at least one test. Combinatorial methods can be highly effective because empirical data suggest that nearly all failures involve the interaction of a small number of parameters (1 to 6). Thus, for example, if all deadlocks involve at most 5-way interactions between n parameters, then exhaustive testing of all n-way interactions adds no additional information that would not be obtained by testing all 5-way interactions. While the maximum degree of interaction between parameters involved in the deadlocks clearly cannot be known in advance, covering all t-way interactions may be more efficient than using random generation of inputs. In this study we tested this hypothesis for t = 2, 3, and 4 for deadlock detection in a network simulation. Achieving the same degree of coverage provided by 4-way tests would have required approximately 3.2 times as many random tests; thus combinatorial methods were more efficient for detecting deadlocks involving a higher degree of interactions. The paper reviews explanations for these results and implications for modeling and simulation.

Detecting the influence of spreading in social networks with excitable sensor networks.

Directory of Open Access Journals (Sweden)

Sen Pei

Full Text Available Detecting spreading outbreaks in social networks with sensors is of great significance in applications. Inspired by the formation mechanism of humans' physical sensations to external stimuli, we propose a new method to detect the influence of spreading by constructing excitable sensor networks. Exploiting the amplifying effect of excitable sensor networks, our method can better detect small-scale spreading processes. At the same time, it can also distinguish large-scale diffusion instances due to the self-inhibition effect of excitable elements. Through simulations of diverse spreading dynamics on typical real-world social networks (Facebook, coauthor, and email social networks, we find that the excitable sensor networks are capable of detecting and ranking spreading processes in a much wider range of influence than other commonly used sensor placement methods, such as random, targeted, acquaintance and distance strategies. In addition, we validate the efficacy of our method with diffusion data from a real-world online social system, Twitter. We find that our method can detect more spreading topics in practice. Our approach provides a new direction in spreading detection and should be useful for designing effective detection methods.

Cooperative and networking strategies in small business

CERN Document Server

Ferreira, João

2017-01-01

The book aims to collect the most recent research and best practices in the cooperative and networking small business field identifying new theoretical models and describing the relationship between cooperation and networks in the small business strategy context. It examines different concepts and analytical techniques better understand the links between cooperative strategies and networks in small business. It also studies the existing economic conditions of network and strategic implications to small business from the point of view of their internal and external consistency. Cooperation and networks is a fashionable topic. It is receiving increasing attention in popular management publications, as well as specialized academic journals. Cooperation between firms and industries is a means of leveraging and aggregating knowledge also generating direct benefits in terms of innovation, productivity and competitiveness. Various options and decisions made within the framework of strategic alliances may be identifi...

Detection of high-grade small bowel obstruction on conventional radiography with convolutional neural networks.

Science.gov (United States)

Cheng, Phillip M; Tejura, Tapas K; Tran, Khoa N; Whang, Gilbert

2018-05-01

The purpose of this pilot study is to determine whether a deep convolutional neural network can be trained with limited image data to detect high-grade small bowel obstruction patterns on supine abdominal radiographs. Grayscale images from 3663 clinical supine abdominal radiographs were categorized into obstructive and non-obstructive categories independently by three abdominal radiologists, and the majority classification was used as ground truth; 74 images were found to be consistent with small bowel obstruction. Images were rescaled and randomized, with 2210 images constituting the training set (39 with small bowel obstruction) and 1453 images constituting the test set (35 with small bowel obstruction). Weight parameters for the final classification layer of the Inception v3 convolutional neural network, previously trained on the 2014 Large Scale Visual Recognition Challenge dataset, were retrained on the training set. After training, the neural network achieved an AUC of 0.84 on the test set (95% CI 0.78-0.89). At the maximum Youden index (sensitivity + specificity-1), the sensitivity of the system for small bowel obstruction is 83.8%, with a specificity of 68.1%. The results demonstrate that transfer learning with convolutional neural networks, even with limited training data, may be used to train a detector for high-grade small bowel obstruction gas patterns on supine radiographs.

Network meta-analysis of disconnected networks: How dangerous are random baseline treatment effects?

Science.gov (United States)

Béliveau, Audrey; Goring, Sarah; Platt, Robert W; Gustafson, Paul

2017-12-01

In network meta-analysis, the use of fixed baseline treatment effects (a priori independent) in a contrast-based approach is regularly preferred to the use of random baseline treatment effects (a priori dependent). That is because, often, there is not a need to model baseline treatment effects, which carry the risk of model misspecification. However, in disconnected networks, fixed baseline treatment effects do not work (unless extra assumptions are made), as there is not enough information in the data to update the prior distribution on the contrasts between disconnected treatments. In this paper, we investigate to what extent the use of random baseline treatment effects is dangerous in disconnected networks. We take 2 publicly available datasets of connected networks and disconnect them in multiple ways. We then compare the results of treatment comparisons obtained from a Bayesian contrast-based analysis of each disconnected network using random normally distributed and exchangeable baseline treatment effects to those obtained from a Bayesian contrast-based analysis of their initial connected network using fixed baseline treatment effects. For the 2 datasets considered, we found that the use of random baseline treatment effects in disconnected networks was appropriate. Because those datasets were not cherry-picked, there should be other disconnected networks that would benefit from being analyzed using random baseline treatment effects. However, there is also a risk for the normality and exchangeability assumption to be inappropriate in other datasets even though we have not observed this situation in our case study. We provide code, so other datasets can be investigated. Copyright © 2017 John Wiley & Sons, Ltd.

The effect of the neural activity on topological properties of growing neural networks.

Science.gov (United States)

Gafarov, F M; Gafarova, V R

2016-09-01

The connectivity structure in cortical networks defines how information is transmitted and processed, and it is a source of the complex spatiotemporal patterns of network's development, and the process of creation and deletion of connections is continuous in the whole life of the organism. In this paper, we study how neural activity influences the growth process in neural networks. By using a two-dimensional activity-dependent growth model we demonstrated the neural network growth process from disconnected neurons to fully connected networks. For making quantitative investigation of the network's activity influence on its topological properties we compared it with the random growth network not depending on network's activity. By using the random graphs theory methods for the analysis of the network's connections structure it is shown that the growth in neural networks results in the formation of a well-known "small-world" network.

Small Worlds Week: Raising Curiosity and Contributing to STEM

Science.gov (United States)

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.

Reduced small world brain connectivity in probands with a family history of epilepsy.

Science.gov (United States)

Bharath, R D; Chaitanya, G; Panda, R; Raghavendra, K; Sinha, S; Sahoo, A; Gohel, S; Biswal, B B; Satishchandra, P

2016-12-01

The role of inheritance in ascertaining susceptibility to epilepsy is well established, although the pathogenetic mechanisms are still not very clear. Interviewing for a positive family history is a popular epidemiological tool in the understanding of this susceptibility. Our aim was to visualize and localize network abnormalities that could be associated with a positive family history in a group of patients with hot water epilepsy (HWE) using resting-state functional magnetic resonance imaging (rsfMRI). Graph theory analysis of rsfMRI (clustering coefficient γ; path length λ; small worldness σ) in probands with a positive family history of epilepsy (FHE+, 25) were compared with probands without FHE (FHE-, 33). Whether a closer biological relationship was associated with a higher likelihood of network abnormalities was also ascertained. A positive family history of epilepsy had decreased γ, increased λ and decreased σ in bilateral temporofrontal regions compared to FHE- (false discovery rate corrected P ≤ 0.0062). These changes were more pronounced in probands having first degree relatives and siblings with epilepsy. Probands with multiple types of epilepsy in the family showed decreased σ in comparison to only HWE in the family. Graph theory analysis of the rsfMRI can be used to understand the neurobiology of diseases like genetic susceptibility in HWE. Reduced small worldness, proportional to the degree of relationship, is consistent with the current understanding that disease severity is higher in closer biological relations. © 2016 EAN.

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.

Utilizing Maximal Independent Sets as Dominating Sets in Scale-Free Networks

Science.gov (United States)

Derzsy, N.; Molnar, F., Jr.; Szymanski, B. K.; Korniss, G.

Dominating sets provide key solution to various critical problems in networked systems, such as detecting, monitoring, or controlling the behavior of nodes. Motivated by graph theory literature [Erdos, Israel J. Math. 4, 233 (1966)], we studied maximal independent sets (MIS) as dominating sets in scale-free networks. We investigated the scaling behavior of the size of MIS in artificial scale-free networks with respect to multiple topological properties (size, average degree, power-law exponent, assortativity), evaluated its resilience to network damage resulting from random failure or targeted attack [Molnar et al., Sci. Rep. 5, 8321 (2015)], and compared its efficiency to previously proposed dominating set selection strategies. We showed that, despite its small set size, MIS provides very high resilience against network damage. Using extensive numerical analysis on both synthetic and real-world (social, biological, technological) network samples, we demonstrate that our method effectively satisfies four essential requirements of dominating sets for their practical applicability on large-scale real-world systems: 1.) small set size, 2.) minimal network information required for their construction scheme, 3.) fast and easy computational implementation, and 4.) resiliency to network damage. Supported by DARPA, DTRA, and NSF.

Experimental multistable states for small network of coupled pendula

Science.gov (United States)

Dudkowski, Dawid; Grabski, Juliusz; Wojewoda, Jerzy; Perlikowski, Przemyslaw; Maistrenko, Yuri; Kapitaniak, Tomasz

2016-07-01

Chimera states are dynamical patterns emerging in populations of coupled identical oscillators where different groups of oscillators exhibit coexisting synchronous and incoherent behaviors despite homogeneous coupling. Although these states are typically observed in the large ensembles of oscillators, recently it has been shown that so-called weak chimera states may occur in the systems with small numbers of oscillators. Here, we show that similar multistable states demonstrating partial frequency synchronization, can be observed in simple experiments with identical mechanical oscillators, namely pendula. The mathematical model of our experiment shows that the observed multistable states are controlled by elementary dynamical equations, derived from Newton’s laws that are ubiquitous in many physical and engineering systems. Our finding suggests that multistable chimera-like states are observable in small networks relevant to various real-world systems.

Selectivity and sparseness in randomly connected balanced networks.

Directory of Open Access Journals (Sweden)

Cengiz Pehlevan

Full Text Available Neurons in sensory cortex show stimulus selectivity and sparse population response, even in cases where no strong functionally specific structure in connectivity can be detected. This raises the question whether selectivity and sparseness can be generated and maintained in randomly connected networks. We consider a recurrent network of excitatory and inhibitory spiking neurons with random connectivity, driven by random projections from an input layer of stimulus selective neurons. In this architecture, the stimulus-to-stimulus and neuron-to-neuron modulation of total synaptic input is weak compared to the mean input. Surprisingly, we show that in the balanced state the network can still support high stimulus selectivity and sparse population response. In the balanced state, strong synapses amplify the variation in synaptic input and recurrent inhibition cancels the mean. Functional specificity in connectivity emerges due to the inhomogeneity caused by the generative statistical rule used to build the network. We further elucidate the mechanism behind and evaluate the effects of model parameters on population sparseness and stimulus selectivity. Network response to mixtures of stimuli is investigated. It is shown that a balanced state with unselective inhibition can be achieved with densely connected input to inhibitory population. Balanced networks exhibit the "paradoxical" effect: an increase in excitatory drive to inhibition leads to decreased inhibitory population firing rate. We compare and contrast selectivity and sparseness generated by the balanced network to randomly connected unbalanced networks. Finally, we discuss our results in light of experiments.

Multi-agent coordination in directed moving neighbourhood random networks

International Nuclear Information System (INIS)

Yi-Lun, Shang

2010-01-01

This paper considers the consensus problem of dynamical multiple agents that communicate via a directed moving neighbourhood random network. Each agent performs random walk on a weighted directed network. Agents interact with each other through random unidirectional information flow when they coincide in the underlying network at a given instant. For such a framework, we present sufficient conditions for almost sure asymptotic consensus. Numerical examples are taken to show the effectiveness of the obtained results. (general)

The complex network of the Brazilian Popular Music

Science.gov (United States)

de Lima e Silva, D.; Medeiros Soares, M.; Henriques, M. V. C.; Schivani Alves, M. T.; de Aguiar, S. G.; de Carvalho, T. P.; Corso, G.; Lucena, L. S.

2004-02-01

We study the Brazilian Popular Music in a network perspective. We call the Brazilian Popular Music Network, BPMN, the graph where the vertices are the song writers and the links are determined by the existence of at least a common singer. The linking degree distribution of such graph shows power law and exponential regions. The exponent of the power law is compatible with the values obtained by the evolving network algorithms seen in the literature. The average path length of the BPMN is similar to the correspondent random graph, its clustering coefficient, however, is significantly larger. These results indicate that the BPMN forms a small-world network.

Randomizing world trade. II. A weighted network analysis

Science.gov (United States)

Squartini, Tiziano; Fagiolo, Giorgio; Garlaschelli, Diego

2011-10-01

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed and undirected, aggregated and disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.

Generating clustered scale-free networks using Poisson based localization of edges

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Türker, İlker

2018-05-01

We introduce a variety of network models using a Poisson-based edge localization strategy, which result in clustered scale-free topologies. We first verify the success of our localization strategy by realizing a variant of the well-known Watts-Strogatz model with an inverse approach, implying a small-world regime of rewiring from a random network through a regular one. We then apply the rewiring strategy to a pure Barabasi-Albert model and successfully achieve a small-world regime, with a limited capacity of scale-free property. To imitate the high clustering property of scale-free networks with higher accuracy, we adapted the Poisson-based wiring strategy to a growing network with the ingredients of both preferential attachment and local connectivity. To achieve the collocation of these properties, we used a routine of flattening the edges array, sorting it, and applying a mixing procedure to assemble both global connections with preferential attachment and local clusters. As a result, we achieved clustered scale-free networks with a computational fashion, diverging from the recent studies by following a simple but efficient approach.

Gossip in Random Networks

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Malarz, K.; Szvetelszky, Z.; Szekf, B.; Kulakowski, K.

2006-11-01

We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erd{õ}s and Rényi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value pc, for which half of agents are informed, scales with the system size as N-gamma with gamma approx 0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient C, X decreases.

Designing neural networks that process mean values of random variables

International Nuclear Information System (INIS)

Barber, Michael J.; Clark, John W.

2014-01-01

We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence. - Highlights: • High-level neural computations are specified by Bayesian belief networks of random variables. • Probability densities of random variables are encoded in activities of populations of neurons. • Top-down algorithm generates specific neural network implementation of given computation. • Resulting “neural belief networks” process mean values of random variables. • Such networks pool multiple sources of evidence and deal properly with inconsistent evidence

Designing neural networks that process mean values of random variables

Energy Technology Data Exchange (ETDEWEB)

Barber, Michael J. [AIT Austrian Institute of Technology, Innovation Systems Department, 1220 Vienna (Austria); Clark, John W. [Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, MO 63130 (United States); Centro de Ciências Matemáticas, Universidade de Madeira, 9000-390 Funchal (Portugal)

2014-06-13

We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence. - Highlights: • High-level neural computations are specified by Bayesian belief networks of random variables. • Probability densities of random variables are encoded in activities of populations of neurons. • Top-down algorithm generates specific neural network implementation of given computation. • Resulting “neural belief networks” process mean values of random variables. • Such networks pool multiple sources of evidence and deal properly with inconsistent evidence.

Rock-scissors-paper game on regular small-world networks

International Nuclear Information System (INIS)

Szabo, Gyoergy; Szolnoki, Attila; Izsak, Rudolf

2004-01-01

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

Throughput vs. Delay in Lossy Wireless Mesh Networks with Random Linear Network Coding

OpenAIRE

Hundebøll, Martin; Pahlevani, Peyman; Roetter, Daniel Enrique Lucani; Fitzek, Frank

2014-01-01

This work proposes a new protocol applying on–the–fly random linear network coding in wireless mesh net-works. The protocol provides increased reliability, low delay,and high throughput to the upper layers, while being obliviousto their specific requirements. This seemingly conflicting goalsare achieved by design, using an on–the–fly network codingstrategy. Our protocol also exploits relay nodes to increasethe overall performance of individual links. Since our protocolnaturally masks random p...

Random matrix approach to plasmon resonances in the random impedance network model of disordered nanocomposites

Science.gov (United States)

Olekhno, N. A.; Beltukov, Y. M.

2018-05-01

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions 0

Weighted Scaling in Non-growth Random Networks

International Nuclear Information System (INIS)

Chen Guang; Yang Xuhua; Xu Xinli

2012-01-01

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.

Altered network communication following a neuroprotective drug treatment.

Directory of Open Access Journals (Sweden)

Kathleen Vincent

Full Text Available Preconditioning is defined as a range of stimuli that allow cells to withstand subsequent anaerobic and other deleterious conditions. While cell protection under preconditioning is well established, this paper investigates the influence of neuroprotective preconditioning drugs, 4-aminopyridine and bicuculline (4-AP/bic, on synaptic communication across a broad network of in vitro rat cortical neurons. Using a permutation test, we evaluated cross-correlations of extracellular spiking activity across all pairs of recording electrodes on a 64-channel multielectrode array. The resulting functional connectivity maps were analyzed in terms of their graph-theoretic properties. A small-world effect was found, characterized by a functional network with high clustering coefficient and short average path length. Twenty-four hours after exposure to 4-AP/bic, small-world properties were comparable to control cultures that were not treated with the drug. Four hours following drug washout, however, the density of functional connections increased, while path length decreased and clustering coefficient increased. These alterations in functional connectivity were maintained at four days post-washout, suggesting that 4-AP/bic preconditioning leads to long-term effects on functional networks of cortical neurons. Because of their influence on communication efficiency in neuronal networks, alterations in small-world properties hold implications for information processing in brain systems. The observed relationship between density, path length, and clustering coefficient is captured by a phenomenological model where connections are added randomly within a spatially-embedded network. Taken together, results provide information regarding functional consequences of drug therapies that are overlooked in traditional viability studies and present the first investigation of functional networks under neuroprotective preconditioning.

Symmetry in Complex Networks

Directory of Open Access Journals (Sweden)

Angel Garrido

2011-01-01

Full Text Available In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features—such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.

Third-World Astronomy Network

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Narlikar, Jayant V.

Several developing countries of the Third World have been actively interested in astronomy, as is evidenced by the membership of the IAU. The enthusiasm of individual astronomers from these countries is, however, not matched by the resources available to them to pursue their interest in astronomy, in teaching as well as research, at an above-threshold level. Major problems requiring solutions are (I) isolation from the mainstream work, which leads to research work which is not quite relevant or realistic, and to teaching based on outdated knowledge; (II) lack of financial resources, leading to shortage of books and journals in the library, insufficient computing power, out-of-date instruments, as well as inability to participate in essential activities like schools, workshops, and major international conferences and symposia; and (III) lack of handson experience with state-of-the-art instrumentation that often leads to good scientists being turned away from astronomical observations towards abstract theories. Experience of the International Centre for Theoretical Physics at Trieste, Italy and of the inter-university centres in India, like the IUCAA at Pune, has shown that limited resources can be made to go a long way by sharing, networking and intelligent use of communications technology. Based on the above experience, this proposal envisages setting up a Third World Astronomy Network (TWAN) under the auspices of the IAU, within the wider ICSU-umbrella with support from the UNESCO as well as participating nations. The TWAN will operate with a few key institutions as local nodal points of a wide network. The objectives of the proposed TWAN and the role of the Nodal Institutions (NIs) are spelled out in this proposal, along with the budgetary support required.

Spectral dimensionality of random superconducting networks

International Nuclear Information System (INIS)

Day, A.R.; Xia, W.; Thorpe, M.F.

1988-01-01

We compute the spectral dimensionality d of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d = 4.1 +- 0.2 and 5.8 +- 0.3 in two and three dimensions, respectively, which confirms the scaling relation d = 2d/(2-s/ν), where s is the superconducting exponent and ν the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d = 0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special case. We comment on the connection between our calculations and the ''termite'' problem of a random walker on a random superconducting-normal network and point out difficulties in inferring d from simulations of the termite problem

A scaling law for random walks on networks

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Perkins, Theodore J.; Foxall, Eric; Glass, Leon; Edwards, Roderick

2014-10-01

The dynamics of many natural and artificial systems are well described as random walks on a network: the stochastic behaviour of molecules, traffic patterns on the internet, fluctuations in stock prices and so on. The vast literature on random walks provides many tools for computing properties such as steady-state probabilities or expected hitting times. Previously, however, there has been no general theory describing the distribution of possible paths followed by a random walk. Here, we show that for any random walk on a finite network, there are precisely three mutually exclusive possibilities for the form of the path distribution: finite, stretched exponential and power law. The form of the distribution depends only on the structure of the network, while the stepping probabilities control the parameters of the distribution. We use our theory to explain path distributions in domains such as sports, music, nonlinear dynamics and stochastic chemical kinetics.

Translocality, Network Structure, and Music Worlds: Underground Metal in the United Kingdom.

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Emms, Rachel; Crossley, Nick

2018-02-01

Translocal music worlds are often defined as networks of local music worlds. However, their networked character and more especially their network structure is generally assumed rather than concretely mapped and explored. Formal social network analysis (SNA) is beginning to attract interest in music sociology but it has not previously been used to explore a translocal music world. In this paper, drawing upon a survey of the participation of 474 enthusiasts in 148 live music events, spread across 6 localities, we use SNA to explore a significant "slice" of the network structure of the U.K.'s translocal underground heavy metal world. Translocality is generated in a number of ways, we suggest, but one way, the way we focus upon, involves audiences traveling between localities to attend gigs and festivals. Our analysis of this network uncovers a core-periphery structure which, we further find, maps onto locality. Not all live events enjoy equal standing in our music world and some localities are better placed to capture more prestigious events, encouraging inward travel. The identification of such structures, and the inequality they point to, is, we believe, one of several benefits of using SNA to analyze translocal music worlds. © 2018 Canadian Sociological Association/La Société canadienne de sociologie.

Routing in Networks with Random Topologies

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Bambos, Nicholas

1997-01-01

We examine the problems of routing and server assignment in networks with random connectivities. In such a network the basic topology is fixed, but during each time slot and for each of tis input queues, each server (node) is either connected to or disconnected from each of its queues with some probability.

Bipartite quantum states and random complex networks

International Nuclear Information System (INIS)

Garnerone, Silvano; Zanardi, Paolo; Giorda, Paolo

2012-01-01

We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of random graphs known as complex networks. In the case of classical random graphs, we derive an analytic expression for the averaged entanglement entropy S-bar while for general complex networks we rely on numerics. For a large number of nodes n we find a scaling S-bar ∼c log n +g e where both the prefactor c and the sub-leading O(1) term g e are characteristic of the different classes of complex networks. In particular, g e encodes topological features of the graphs and is named network topological entropy. Our results suggest that quantum entanglement may provide a powerful tool for the analysis of large complex networks with non-trivial topological properties. (paper)

Analyzing self-similar and fractal properties of the C. elegans neural network.

Directory of Open Access Journals (Sweden)

Tyler M Reese

Full Text Available The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons. A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.

The Evolution of World Trade from 1995 to 2014 : A Network Approach

NARCIS (Netherlands)

Cepeda, Fredy; Gamboa, Freddy; Leon Rincon, Carlos; Rincon, Hernan

2017-01-01

This paper employs network analysis to study world trade from 1995 to 2014. We focus on the main connective features of the world trade network (WTN) and their dynamics. Results suggest that countries’ efforts to attain the benefits of trade have resulted in an intertwined network that is

A Complex Network Approach to Distributional Semantic Models.

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Akira Utsumi

Full Text Available A number of studies on network analysis have focused on language networks based on free word association, which reflects human lexical knowledge, and have demonstrated the small-world and scale-free properties in the word association network. Nevertheless, there have been very few attempts at applying network analysis to distributional semantic models, despite the fact that these models have been studied extensively as computational or cognitive models of human lexical knowledge. In this paper, we analyze three network properties, namely, small-world, scale-free, and hierarchical properties, of semantic networks created by distributional semantic models. We demonstrate that the created networks generally exhibit the same properties as word association networks. In particular, we show that the distribution of the number of connections in these networks follows the truncated power law, which is also observed in an association network. This indicates that distributional semantic models can provide a plausible model of lexical knowledge. Additionally, the observed differences in the network properties of various implementations of distributional semantic models are consistently explained or predicted by considering the intrinsic semantic features of a word-context matrix and the functions of matrix weighting and smoothing. Furthermore, to simulate a semantic network with the observed network properties, we propose a new growing network model based on the model of Steyvers and Tenenbaum. The idea underlying the proposed model is that both preferential and random attachments are required to reflect different types of semantic relations in network growth process. We demonstrate that this model provides a better explanation of network behaviors generated by distributional semantic models.

Walking and Talking Geography: A Small-World Approach

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Fertig, Gary; Silverman, Rick

2007-01-01

When teaching geography to students in the primary grades, teachers should provide firsthand experiences that young children need to make meaningful sense of their world. David Sobel, author of "Mapmaking with Children: Sense of Place Education for the Elementary Years," suggests that teachers in the early grades adopt a small-world approach to…

Recurrence of random walks with long-range steps generated by fractional Laplacian matrices on regular networks and simple cubic lattices

Science.gov (United States)

Michelitsch, T. M.; Collet, B. A.; Riascos, A. P.; Nowakowski, A. F.; Nicolleau, F. C. G. A.

2017-12-01

We analyze a Markovian random walk strategy on undirected regular networks involving power matrix functions of the type L\\frac{α{2}} where L indicates a ‘simple’ Laplacian matrix. We refer to such walks as ‘fractional random walks’ with admissible interval 0walk. From these analytical results we establish a generalization of Polya’s recurrence theorem for fractional random walks on d-dimensional infinite lattices: The fractional random walk is transient for dimensions d > α (recurrent for d≤slantα ) of the lattice. As a consequence, for 0walk is transient for all lattice dimensions d=1, 2, .. and in the range 1≤slantα walk is transient only for lattice dimensions d≥slant 3 . The generalization of Polya’s recurrence theorem remains valid for the class of random walks with Lévy flight asymptotics for long-range steps. We also analyze the mean first passage probabilities, mean residence times, mean first passage times and global mean first passage times (Kemeny constant) for the fractional random walk. For an infinite 1D lattice (infinite ring) we obtain for the transient regime 0walk is generated by the non-diagonality of the fractional Laplacian matrix with Lévy-type heavy tailed inverse power law decay for the probability of long-range moves. This non-local and asymptotic behavior of the fractional random walk introduces small-world properties with the emergence of Lévy flights on large (infinite) lattices.

Scale-free models for the structure of business firm networks.

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Kitsak, Maksim; Riccaboni, Massimo; Havlin, Shlomo; Pammolli, Fabio; Stanley, H Eugene

2010-03-01

We study firm collaborations in the life sciences and the information and communication technology sectors. We propose an approach to characterize industrial leadership using k -shell decomposition, with top-ranking firms in terms of market value in higher k -shell layers. We find that the life sciences industry network consists of three distinct components: a "nucleus," which is a small well-connected subgraph, "tendrils," which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a "bulk body," which consists of the majority of nodes. Industrial leaders, i.e., the largest companies in terms of market value, are in the highest k -shells of both networks. The nucleus of the life sciences sector is very stable: once a firm enters the nucleus, it is likely to stay there for a long time. At the same time we do not observe the above three components in the information and communication technology sector. We also conduct a systematic study of these three components in random scale-free networks. Our results suggest that the sizes of the nucleus and the tendrils in scale-free networks decrease as the exponent of the power-law degree distribution lambda increases, and disappear for lambda>or=3 . We compare the k -shell structure of random scale-free model networks with two real-world business firm networks in the life sciences and in the information and communication technology sectors. We argue that the observed behavior of the k -shell structure in the two industries is consistent with the coexistence of both preferential and random agreements in the evolution of industrial networks.

A recursive method for calculating the total number of spanning trees and its applications in self-similar small-world scale-free network models

Science.gov (United States)

Ma, Fei; Su, Jing; Yao, Bing

2018-05-01

The problem of determining and calculating the number of spanning trees of any finite graph (model) is a great challenge, and has been studied in various fields, such as discrete applied mathematics, theoretical computer science, physics, chemistry and the like. In this paper, firstly, thank to lots of real-life systems and artificial networks built by all kinds of functions and combinations among some simpler and smaller elements (components), we discuss some helpful network-operation, including link-operation and merge-operation, to design more realistic and complicated network models. Secondly, we present a method for computing the total number of spanning trees. As an accessible example, we apply this method to space of trees and cycles respectively, and our results suggest that it is indeed a better one for such models. In order to reflect more widely practical applications and potentially theoretical significance, we study the enumerating method in some existing scale-free network models. On the other hand, we set up a class of new models displaying scale-free feature, that is to say, following P(k) k-γ, where γ is the degree exponent. Based on detailed calculation, the degree exponent γ of our deterministic scale-free models satisfies γ > 3. In the rest of our discussions, we not only calculate analytically the solutions of average path length, which indicates our models have small-world property being prevailing in amounts of complex systems, but also derive the number of spanning trees by means of the recursive method described in this paper, which clarifies our method is convenient to research these models.

Optimal Quantum Spatial Search on Random Temporal Networks

Science.gov (United States)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G (n ,p ), where p is the probability that any two given nodes are connected: After every time interval τ , a new graph G (n ,p ) replaces the previous one. We prove analytically that, for any given p , there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O (√{n }), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Optimal Quantum Spatial Search on Random Temporal Networks.

Science.gov (United States)

Chakraborty, Shantanav; Novo, Leonardo; Di Giorgio, Serena; Omar, Yasser

2017-12-01

To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of n nodes constituted by a time-ordered sequence of Erdös-Rényi random graphs G(n,p), where p is the probability that any two given nodes are connected: After every time interval τ, a new graph G(n,p) replaces the previous one. We prove analytically that, for any given p, there is always a range of values of τ for which the running time of the algorithm is optimal, i.e., O(sqrt[n]), even when search on the individual static graphs constituting the temporal network is suboptimal. On the other hand, there are regimes of τ where the algorithm is suboptimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the nontrivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.

Pheromone Static Routing Strategy for Complex Networks

Science.gov (United States)

Hu, Mao-Bin; Henry, Y. K. Lau; Ling, Xiang; Jiang, Rui

2012-12-01

We adopt the concept of using pheromones to generate a set of static paths that can reach the performance of global dynamic routing strategy [Phys. Rev. E 81 (2010) 016113]. The path generation method consists of two stages. In the first stage, a pheromone is dropped to the nodes by packets forwarded according to the global dynamic routing strategy. In the second stage, pheromone static paths are generated according to the pheromone density. The output paths can greatly improve traffic systems' overall capacity on different network structures, including scale-free networks, small-world networks and random graphs. Because the paths are static, the system needs much less computational resources than the global dynamic routing strategy.

Spatial Epidemic Modelling in Social Networks

Science.gov (United States)

Simoes, Joana Margarida

2005-06-01

The spread of infectious diseases is highly influenced by the structure of the underlying social network. The target of this study is not the network of acquaintances, but the social mobility network: the daily movement of people between locations, in regions. It was already shown that this kind of network exhibits small world characteristics. The model developed is agent based (ABM) and comprehends a movement model and a infection model. In the movement model, some assumptions are made about its structure and the daily movement is decomposed into four types: neighborhood, intra region, inter region and random. The model is Geographical Information Systems (GIS) based, and uses real data to define its geometry. Because it is a vector model, some optimization techniques were used to increase its efficiency.

Navigation by anomalous random walks on complex networks.

Science.gov (United States)

Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan

2016-11-23

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.

Navigation by anomalous random walks on complex networks

Science.gov (United States)

Weng, Tongfeng; Zhang, Jie; Khajehnejad, Moein; Small, Michael; Zheng, Rui; Hui, Pan

2016-11-01

Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.

Green heterogeneous small-cell networks: Toward reducing the CO2 emissions of mobile communications industry using uplink power adaptation

KAUST Repository

Shakir, Muhammad Zeeshan; Qaraqe, Khalid A.; Tabassum, Hina; Alouini, Mohamed-Slim; Serpedin, Erchin; Imran, Muhammad Ali

2013-01-01

Heterogeneous small cell networks, or Het- SNets, are considered as a standard part of future mobile networks in which multiple lowpower low-cost user deployed base stations complement the existing macrocell infrastructure. This article proposes an energy-efficient deployment of the cells where the small cell base stations are arranged around the edge of the reference macrocell, and the deployment is referred to as cell-on-edge (COE) deployment. The proposed deployment ensures an increase in the network spectral and energy efficiency by facilitating cell edge mobile users with small cells. Moreover, COE deployment guarantees reduction of the carbon footprint of mobile operations by employing adaptive uplink power control. In order to calibrate the reduction in CO2 emissions, this article quantifies the ecological and associated economical impacts of energy savings in the proposed deployment. Simulation results quantify the improvements in CO2 emissions and spectral and energy gains of the proposed COE deployment compared to macro-only networks and typical small cell deployment strategies where small cells are randomly deployed within a given macrocell. © 2013 IEEE.

Green heterogeneous small-cell networks: Toward reducing the CO2 emissions of mobile communications industry using uplink power adaptation

KAUST Repository

Shakir, Muhammad Zeeshan

2013-06-01

Heterogeneous small cell networks, or Het- SNets, are considered as a standard part of future mobile networks in which multiple lowpower low-cost user deployed base stations complement the existing macrocell infrastructure. This article proposes an energy-efficient deployment of the cells where the small cell base stations are arranged around the edge of the reference macrocell, and the deployment is referred to as cell-on-edge (COE) deployment. The proposed deployment ensures an increase in the network spectral and energy efficiency by facilitating cell edge mobile users with small cells. Moreover, COE deployment guarantees reduction of the carbon footprint of mobile operations by employing adaptive uplink power control. In order to calibrate the reduction in CO2 emissions, this article quantifies the ecological and associated economical impacts of energy savings in the proposed deployment. Simulation results quantify the improvements in CO2 emissions and spectral and energy gains of the proposed COE deployment compared to macro-only networks and typical small cell deployment strategies where small cells are randomly deployed within a given macrocell. © 2013 IEEE.

Distribution of shortest path lengths in a class of node duplication network models

Science.gov (United States)

Steinbock, Chanania; Biham, Ofer; Katzav, Eytan

2017-09-01

We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social networks, acquaintance networks, and scientific citation networks, where duplication mechanisms play a major role. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network, forming a link to the mother node, and with probability p to each one of its neighbors. The degree distribution of the resulting network turns out to follow a power-law distribution, thus the ND network is a scale-free network. To calculate the DSPL we derive a master equation for the time evolution of the probability Pt(L =ℓ ) , ℓ =1 ,2 ,⋯ , where L is the distance between a pair of nodes and t is the time. Finding an exact analytical solution of the master equation, we obtain a closed form expression for Pt(L =ℓ ) . The mean distance 〈L〉 t and the diameter Δt are found to scale like lnt , namely, the ND network is a small-world network. The variance of the DSPL is also found to scale like lnt . Interestingly, the mean distance and the diameter exhibit properties of a small-world network, rather than the ultrasmall-world network behavior observed in other scale-free networks, in which 〈L〉 t˜lnlnt .

Upgrading Wood-Based Industries: Harnessing the Social Network of Small-Scale Furniture Producers and Their Institutions

Directory of Open Access Journals (Sweden)

Melati ,

2011-05-01

Full Text Available Furniture is a major export commodity in Indonesia with a total value of USD 1.96 million in 2007.  Jepara District is one of the key location for wood furniture production with 15,271 furniture related business units employing 176,469 workers.  However, inefficiencies and power imbalances throughout the furniture value chain have resulted in overharvesting and uneven distribution of gains among the industry’s actors.  In contrast to price-setting international furniture retailers, small-scale producers enjoy the least value from their products.  In order to increase added value and competitiveness, small-scale furniture producers have made efforts to upgrade by harnessing their social network and institutions.  This paper describes small-scale furniture producers’ efforts to upgrade by utilising their social network and institutions in Jepara.  Data was collected through in-depth interviews with members of the small-scale furniture producers’ association.  The research provides insight into the nature of social networks and information flow and develops future scenarios to upgrade.  The scenarios will not only benefit the furniture industry in Jepara, but may also be adopted for similar industries throughout Indonesia and the world, and potentially improve many people’s economies and livelihoods.Keywords: wood-based industry, furniture, small-scale, social network, institution

A simple model of global cascades on random networks

Science.gov (United States)

Watts, Duncan J.

2002-04-01

The origin of large but rare cascades that are triggered by small initial shocks is a phenomenon that manifests itself as diversely as cultural fads, collective action, the diffusion of norms and innovations, and cascading failures in infrastructure and organizational networks. This paper presents a possible explanation of this phenomenon in terms of a sparse, random network of interacting agents whose decisions are determined by the actions of their neighbors according to a simple threshold rule. Two regimes are identified in which the network is susceptible to very large cascadesherein called global cascadesthat occur very rarely. When cascade propagation is limited by the connectivity of the network, a power law distribution of cascade sizes is observed, analogous to the cluster size distribution in standard percolation theory and avalanches in self-organized criticality. But when the network is highly connected, cascade propagation is limited instead by the local stability of the nodes themselves, and the size distribution of cascades is bimodal, implying a more extreme kind of instability that is correspondingly harder to anticipate. In the first regime, where the distribution of network neighbors is highly skewed, it is found that the most connected nodes are far more likely than average nodes to trigger cascades, but not in the second regime. Finally, it is shown that heterogeneity plays an ambiguous role in determining a system's stability: increasingly heterogeneous thresholds make the system more vulnerable to global cascades; but an increasingly heterogeneous degree distribution makes it less vulnerable.

Structure of a randomly grown 2-d network

DEFF Research Database (Denmark)

Ajazi, Fioralba; Napolitano, George M.; Turova, Tatyana

2015-01-01

We introduce a growing random network on a plane as a model of a growing neuronal network. The properties of the structure of the induced graph are derived. We compare our results with available data. In particular, it is shown that depending on the parameters of the model the system undergoes in...... in time different phases of the structure. We conclude with a possible explanation of some empirical data on the connections between neurons.......We introduce a growing random network on a plane as a model of a growing neuronal network. The properties of the structure of the induced graph are derived. We compare our results with available data. In particular, it is shown that depending on the parameters of the model the system undergoes...

Experimental percolation studies of random networks

Science.gov (United States)

Feinerman, A.; Weddell, J.

2017-06-01

This report establishes an experimental method of studying electrically percolating networks at a higher resolution than previously implemented. This method measures the current across a conductive sheet as a function of time as elliptical pores are cut into the sheet. This is done utilizing a Universal Laser System X2-600 100 W CO2 laser system with a 76 × 46 cm2 field and 394 dpc (dots/cm) resolution. This laser can cut a random system of elliptical pores into a conductive sheet with a potential voltage applied across it and measures the current versus time. This allows for experimental verification of a percolation threshold as a function of the ellipse's aspect ratio (minor/major diameter). We show that as an ellipse's aspect ratio approaches zero, the percolation threshold approaches one. The benefit of this method is that it can experimentally measure the effect of removing small pores, as well as pores with complex geometries, such as an asterisk from a conductive sheet.

Multi-Equilibria Regulation Agent-Based Model of Opinion Dynamics in Social Networks

Directory of Open Access Journals (Sweden)

Andreas Koulouris

2013-01-01

Full Text Available This article investigates the Multiple Equilibria Regulation (MER model, i.e., an agent-based simulation model, to represent opinion dynamics in social networks. It relies on a small set of micro-prerequisites (intra-individual balance and confidence bound, leading to emergence of (nonstationary macro-outcomes. These outcomes may refer to consensus, polarization or fragmentation of opinions about taxation (e.g., congestion pricing or other policy measures, according to the way communication is structured. In contrast with other models of opinion dynamics, it allows for the impact of both the regulation of intra-personal discrepancy and the interpersonal variability of opinions on social learning and network dynamics. Several simulation experiments are presented to demonstrate, through the MER model, the role of different network structures (complete, star, cellular automata, small-world and random graphs on opinion formation dynamics and the overall evolution of the system. The findings can help to identify specific topological characteristics, such as density, number of neighbourhoods and critical nodes-agents, that affect the stability and system dynamics. This knowledge can be used to better organize the information diffusion and learning in the community, enhance the predictability of outcomes and manage possible conflicts. It is shown that a small-world organization, which depicts more realistic aspects of real-life and virtual social systems, provides increased predictability and stability towards a less fragmented and more manageable grouping of opinions, compared to random networks. Such macro-level organizations may be enhanced with use of web-based technologies to increase the density of communication and public acceptability of policy measures.

Pramipexole Modulates Interregional Connectivity Within the Sensorimotor Network.

Science.gov (United States)

Ye, Zheng; Hammer, Anke; Münte, Thomas F

2017-05-01

Pramipexole is widely prescribed to treat Parkinson's disease but has been reported to cause impulse control disorders such as pathological gambling. Recent neurocomputational models suggested that D2 agonists may distort functional connections between the striatum and the motor cortex, resulting in impaired reinforcement learning and pathological gambling. To examine how D2 agonists modulate the striatal-motor connectivity, we carried out a pharmacological resting-state functional magnetic resonance imaging study with a double-blind randomized within-subject crossover design. We analyzed the medication-induced changes of network connectivity and topology with two approaches, an independent component analysis (ICA) and a graph theoretical analysis (GTA). The ICA identified the sensorimotor network (SMN) as well as other classical resting-state networks. Within the SMN, the connectivity between the right caudate nucleus and other cortical regions was weaker under pramipexole than under placebo. The GTA measured the topological properties of the whole-brain network at global and regional levels. Both the whole-brain network under placebo and that under pramipexole were identified as small-world networks. The two whole-brain networks were similar in global efficiency, clustering coefficient, small-world index, and modularity. However, the degree of the right caudate nucleus decreased under pramipexole mainly due to the loss of the connectivity with the supplementary motor area, paracentral lobule, and precentral and postcentral gyrus of the SMN. The two network analyses consistently revealed that pramipexole weakened the functional connectivity between the caudate nucleus and the SMN regions.

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 Distributed Renewable Energy Generation for Low Voltage Distribution Networks

Directory of Open Access Journals (Sweden)

Chindris M.

2016-08-01

Full Text Available Driven by the existing energy policies, the use of renewable energy has increased considerably all over the world in order to respond to the increasing energy consumption and to reduce the environmental impact of the electricity generation. Although most policy makers and companies are focusing on large applications, the use of cheap small generation units, based on local renewable resources, has become increasingly attractive for the general public, small farms and remote communities. The paper presents several results of a research project aiming to identify the power quality issues and the impact of RES based distributed generation (DG or other non-linear loads on low voltage (LV distribution networks in Romania; the final goal is to develop a Universal Power Quality Conditioner (UPQC able to diminish the existing disturbances. Basically, the work analyses the existing DG technologies and identifies possible solutions for their integration in Romania; taking into account the existent state of the art, the attention was paid on small systems, using wind and solar energy, and on possibility to integrate them into suburban and rural LV distribution networks. The presence of DG units at distribution voltage level means the transition from traditional passive to active distribution networks. In general, the relatively low penetration levels of DG does not produce problems; however, the nowadays massive increase of local power generation have led to new integration challenges in order to ensure the reliability and quality of the power supply. Power quality issues are identified and their assessment is the key element in the design of measures aiming to diminish all existing disturbances.

The investigation of social networks based on multi-component random graphs

Science.gov (United States)

Zadorozhnyi, V. N.; Yudin, E. B.

2018-01-01

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed by the theory of random graphs with the nonlinear preferential attachment rule and the theory of Erdôs-Rényi random graphs. In fact, well-calibrated network graph models and computer experiments with these models would help developers (owners) of the networks to predict their development correctly and to choose effective strategies for controlling network projects.

Functional Disorganization of Small-World Brain Networks in mild Alzheimer’s Disease and amnestic Mild Cognitive Impairment: An EEG Study using Relative Wavelet Entropy (RWE

Directory of Open Access Journals (Sweden)

Christos A. Frantzidis

2014-08-01

Full Text Available Previous neuroscientific findings have linked Alzheimer’s disease (AD with less efficient information processing and brain network disorganization. However, pathological alterations of the brain networks during the preclinical phase of amnestic Mild Cognitive Impairment (aMCI remain largely unknown. The present study aimed at comparing patterns of the detection of functional disorganization in MCI relative to Mild Dementia (MD. Participants consisted of 23 cognitively healthy adults, 17 aMCI and 24 mild AD patients who underwent electroencephalographic (EEG data acquisition during a resting-state condition. Synchronization analysis through the Orthogonal Discrete Wavelet Transform (ODWT, and directional brain network analysis were applied on the EEG data. This computational model was performed for networks that have the same number of edges (N=500, 600, 700, 800 edges across all participants and groups (fixed density values. All groups exhibited a small-world (SW brain architecture. However, we found a significant reduction in the SW brain architecture in both aMCI and MD patients relative to the group of Healthy controls. This functional disorganization was also correlated with the participant’s generic cognitive status. The deterioration of the network’s organization was caused mainly by deficient local information processing as quantified by the mean cluster coefficient value. Functional hubs were identified through the normalized betweenness centrality metric. Analysis of the local characteristics showed relative hub preservation even with statistically significant reduced strength. Compensatory phenomena were also evident through the formation of additional hubs on left frontal and parietal regions. Our results indicate a declined functional network organization even during the prodromal phase. Degeneration is evident even in the preclinical phase and coexists with transient network reorganization due to compensation.

Intraoperative and postoperative feasibility and safety of total tubeless, tubeless, small-bore tube, and standard percutaneous nephrolithotomy: a systematic review and network meta-analysis of 16 randomized controlled trials.

Science.gov (United States)

Lee, Joo Yong; Jeh, Seong Uk; Kim, Man Deuk; Kang, Dong Hyuk; Kwon, Jong Kyou; Ham, Won Sik; Choi, Young Deuk; Cho, Kang Su

2017-06-27

Percutaneous nephrolithotomy (PCNL) is performed to treat relatively large renal stones. Recent publications indicate that tubeless and total tubeless (stentless) PCNL is safe in selected patients. We performed a systematic review and network meta-analysis to evaluate the feasibility and safety of different PCNL procedures, including total tubeless, tubeless with stent, small-bore tube, and large-bore tube PCNLs. PubMed, Cochrane Central Register of Controlled Trials, and EMBASE™ databases were searched to identify randomized controlled trials published before December 30, 2013. One researcher examined all titles and abstracts found by the searches. Two investigators independently evaluated the full-text articles to determine whether those met the inclusion criteria. Qualities of included studies were rated with Cochrane's risk-of-bias assessment tool. Sixteen studies were included in the final syntheses including pairwise and network meta-analyses. Operation time, pain scores, and transfusion rates were not significantly different between PCNL procedures. Network meta-analyses demonstrated that for hemoglobin changes, total tubeless PCNL may be superior to standard PCNL (mean difference [MD] 0.65, 95% CI 0.14-1.13) and tubeless PCNLs with stent (MD -1.14, 95% CI -1.65--0.62), and small-bore PCNL may be superior to tubeless PCNL with stent (MD 1.30, 95% CI 0.27-2.26). Network meta-analyses also showed that for length of hospital stay, total tubeless (MD 1.33, 95% CI 0.23-2.43) and tubeless PCNLs with stent (MD 0.99, 95% CI 0.19-1.79) may be superior to standard PCNL. In rank probability tests, small-bore tube and total tubeless PCNLs were superior for operation time, pain scores, and hemoglobin changes. For hemoglobin changes, total tubeless and small-bore PCNLs may be superior to other methods. For hospital stay, total tubeless and tubeless PCNLs with stent may be superior to other procedures.

A Markovian model of evolving world input-output network.

Directory of Open Access Journals (Sweden)

Vahid Moosavi

Full Text Available The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money.

A Markovian model of evolving world input-output network.

Science.gov (United States)

Moosavi, Vahid; Isacchini, Giulio

2017-01-01

The initial theoretical connections between Leontief input-output models and Markov chains were established back in 1950s. However, considering the wide variety of mathematical properties of Markov chains, so far there has not been a full investigation of evolving world economic networks with Markov chain formalism. In this work, using the recently available world input-output database, we investigated the evolution of the world economic network from 1995 to 2011 through analysis of a time series of finite Markov chains. We assessed different aspects of this evolving system via different known properties of the Markov chains such as mixing time, Kemeny constant, steady state probabilities and perturbation analysis of the transition matrices. First, we showed how the time series of mixing times and Kemeny constants could be used as an aggregate index of globalization. Next, we focused on the steady state probabilities as a measure of structural power of the economies that are comparable to GDP shares of economies as the traditional index of economies welfare. Further, we introduced two measures of systemic risk, called systemic influence and systemic fragility, where the former is the ratio of number of influenced nodes to the total number of nodes, caused by a shock in the activity of a node, and the latter is based on the number of times a specific economic node is affected by a shock in the activity of any of the other nodes. Finally, focusing on Kemeny constant as a global indicator of monetary flow across the network, we showed that there is a paradoxical effect of a change in activity levels of economic nodes on the overall flow of the world economic network. While the economic slowdown of the majority of nodes with high structural power results to a slower average monetary flow over the network, there are some nodes, where their slowdowns improve the overall quality of the network in terms of connectivity and the average flow of the money.

Equity venture capital platform model based on complex network

Science.gov (United States)

Guo, Dongwei; Zhang, Lanshu; Liu, Miao

2018-05-01

This paper uses the small-world network and the random-network to simulate the relationship among the investors, construct the network model of the equity venture capital platform to explore the impact of the fraud rate and the bankruptcy rate on the robustness of the network model while observing the impact of the average path length and the average agglomeration coefficient of the investor relationship network on the income of the network model. The study found that the fraud rate and bankruptcy rate exceeded a certain threshold will lead to network collapse; The bankruptcy rate has a great influence on the income of the platform; The risk premium exists, and the average return is better under a certain range of bankruptcy risk; The structure of the investor relationship network has no effect on the income of the investment model.

Model for the growth of the world airline network

Science.gov (United States)

Verma, T.; Araújo, N. A. M.; Nagler, J.; Andrade, J. S.; Herrmann, H. J.

2016-06-01

We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the World Airline Network (WAN), we observe that the difference between the two is minimized for α≈2. Interestingly, this is the value obtained for the node-node correlation function in the WAN. This suggests that our model explains quite well the growth of airline networks.

Heuristic algorithm for determination of local properties of scale-free networks

CERN Document Server

Mitrovic, M

2006-01-01

Complex networks are everywhere. Many phenomena in nature can be modeled as networks: - brain structures - protein-protein interaction networks - social interactions - the Internet and WWW. They can be represented in terms of nodes and edges connecting them. Important characteristics: - these networks are not random; they have a structured architecture. Structure of different networks are similar: - all have power law degree distribution (scale-free property) - despite large size there is usually relatively short path between any two nodes (small world property). Global characteristics: - degree distribution, clustering coefficient and the diameter. Local structure: - frequency of subgraphs of given type (subgraph of order k is a part of the network consisting of k nodes and edges between them). There are different types of subgraphs of the same order.

Coherence Resonance and Noise-Induced Synchronization in Hindmarsh-Rose Neural Network with Different Topologies

International Nuclear Information System (INIS)

Wei Duqu; Luo Xiaoshu

2007-01-01

In this paper, we investigate coherence resonance (CR) and noise-induced synchronization in Hindmarsh-Rose (HR) neural network with three different types of topologies: regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.

A model of gene expression based on random dynamical systems reveals modularity properties of gene regulatory networks.

Science.gov (United States)

Antoneli, Fernando; Ferreira, Renata C; Briones, Marcelo R S

2016-06-01

Here we propose a new approach to modeling gene expression based on the theory of random dynamical systems (RDS) that provides a general coupling prescription between the nodes of any given regulatory network given the dynamics of each node is modeled by a RDS. The main virtues of this approach are the following: (i) it provides a natural way to obtain arbitrarily large networks by coupling together simple basic pieces, thus revealing the modularity of regulatory networks; (ii) the assumptions about the stochastic processes used in the modeling are fairly general, in the sense that the only requirement is stationarity; (iii) there is a well developed mathematical theory, which is a blend of smooth dynamical systems theory, ergodic theory and stochastic analysis that allows one to extract relevant dynamical and statistical information without solving the system; (iv) one may obtain the classical rate equations form the corresponding stochastic version by averaging the dynamic random variables (small noise limit). It is important to emphasize that unlike the deterministic case, where coupling two equations is a trivial matter, coupling two RDS is non-trivial, specially in our case, where the coupling is performed between a state variable of one gene and the switching stochastic process of another gene and, hence, it is not a priori true that the resulting coupled system will satisfy the definition of a random dynamical system. We shall provide the necessary arguments that ensure that our coupling prescription does indeed furnish a coupled regulatory network of random dynamical systems. Finally, the fact that classical rate equations are the small noise limit of our stochastic model ensures that any validation or prediction made on the basis of the classical theory is also a validation or prediction of our model. We illustrate our framework with some simple examples of single-gene system and network motifs. Copyright © 2016 Elsevier Inc. All rights reserved.

Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks

Directory of Open Access Journals (Sweden)

Lindsay eRutter

2013-07-01

Full Text Available Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.

Brain anatomical networks in early human brain development.

Science.gov (United States)

Fan, Yong; Shi, Feng; Smith, Jeffrey Keith; Lin, Weili; Gilmore, John H; Shen, Dinggang

2011-02-01

Recent neuroimaging studies have demonstrated that human brain networks have economic small-world topology and modular organization, enabling efficient information transfer among brain regions. However, it remains largely unknown how the small-world topology and modular organization of human brain networks emerge and develop. Using longitudinal MRI data of 28 healthy pediatric subjects, collected at their ages of 1 month, 1 year, and 2 years, we analyzed development patterns of brain anatomical networks derived from morphological correlations of brain regional volumes. The results show that the brain network of 1-month-olds has the characteristically economic small-world topology and nonrandom modular organization. The network's cost efficiency increases with the brain development to 1 year and 2 years, so does the modularity, providing supportive evidence for the hypothesis that the small-world topology and the modular organization of brain networks are established during early brain development to support rapid synchronization and information transfer with minimal rewiring cost, as well as to balance between local processing and global integration of information. Copyright © 2010. Published by Elsevier Inc.

Natural Language Processing with Small Feed-Forward Networks

OpenAIRE

Botha, Jan A.; Pitler, Emily; Ma, Ji; Bakalov, Anton; Salcianu, Alex; Weiss, David; McDonald, Ryan; Petrov, Slav

2017-01-01

We show that small and shallow feed-forward neural networks can achieve near state-of-the-art results on a range of unstructured and structured language processing tasks while being considerably cheaper in memory and computational requirements than deep recurrent models. Motivated by resource-constrained environments like mobile phones, we showcase simple techniques for obtaining such small neural network models, and investigate different tradeoffs when deciding how to allocate a small memory...

Networks, Micro Small Enterprises (MSE'S) and Performance: the ...

African Journals Online (AJOL)

Networks, Micro Small Enterprises (MSE'S) and Performance: the Case of Kenya. ... It adopts the network perspective theoretical approach. Empirically, the ... entrepreneurial personal network as a copying strategy in the process of global

Random networks of Boolean cellular automata

Energy Technology Data Exchange (ETDEWEB)

Miranda, Enrique [Comision Nacional de Energia Atomica, San Carlos de Bariloche (Argentina). Centro Atomico Bariloche

1990-01-01

Some recent results about random networks of Boolean automata -the Kauffman model- are reviewed. The structure of configuration space is explored. Ultrametricity between cycles is analyzed and the effects of noise in the dynamics are studied. (Author).

Random networks of Boolean cellular automata

International Nuclear Information System (INIS)

Miranda, Enrique

1990-01-01

Some recent results about random networks of Boolean automata -the Kauffman model- are reviewed. The structure of configuration space is explored. Ultrametricity between cycles is analyzed and the effects of noise in the dynamics are studied. (Author)

The influence of single neuron dynamics and network topology on time delay-induced multiple synchronous behaviors in inhibitory coupled network

International Nuclear Information System (INIS)

Zhao, Zhiguo; Gu, Huaguang

2015-01-01

Highlights: • Time delay-induced multiple synchronous behaviors was simulated in neuronal networks. • Multiple behaviors appear at time delays shorter than a bursting period of neurons. • The more spikes per burst of bursting, the more synchronous regions of time delay. • From regular to random via small-world networks, synchronous degree becomes weak. • An interpretation of the multiple behaviors and the influence of network are provided. - Abstract: Time delay induced-multiple synchronous behaviors are simulated in neuronal network composed of many inhibitory neurons and appear at different time delays shorter than a period of endogenous bursting of individual neurons. It is different from previous investigations wherein only one of multiple synchronous behaviors appears at time delay shorter than a period of endogenous firing and others appear at time delay longer than the period duration. The bursting patterns of the synchronous behaviors are identified based on the dynamics of an individual neuron stimulated by a signal similar to the inhibitory coupling current, which is applied at the decaying branch of a spike and suitable phase within the quiescent state of the endogenous bursting. If a burst of endogenous bursting contains more spikes, the synchronous behaviors appear at more regions of time delay. As the coupling strength increases, the multiple synchronous behaviors appear in a sequence because the different threshold of coupling current or strength is needed to achieve synchronous behaviors. From regular, to small-world, and to random networks, synchronous degree of the multiple synchronous behaviors becomes weak, and synchronous bursting patterns with lower spikes per burst disappear, which is properly interpreted by the difference of coupling current between neurons induced by different degree and the high threshold of coupling current to achieve synchronization for the absent synchronous bursting patterns. The results of the influence of

Epidemic transmission on random mobile network with diverse infection periods

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Li, Kezan; Yu, Hong; Zeng, Zhaorong; Ding, Yong; Ma, Zhongjun

2015-05-01

The heterogeneity of individual susceptibility and infectivity and time-varying topological structure are two realistic factors when we study epidemics on complex networks. Current research results have shown that the heterogeneity of individual susceptibility and infectivity can increase the epidemic threshold in a random mobile dynamical network with the same infection period. In this paper, we will focus on random mobile dynamical networks with diverse infection periods due to people's different constitutions and external circumstances. Theoretical results indicate that the epidemic threshold of the random mobile network with diverse infection periods is larger than the counterpart with the same infection period. Moreover, the heterogeneity of individual susceptibility and infectivity can play a significant impact on disease transmission. In particular, the homogeneity of individuals will avail to the spreading of epidemics. Numerical examples verify further our theoretical results very well.

Real-world experimentation of distributed DSA network algorithms

DEFF Research Database (Denmark)

Tonelli, Oscar; Berardinelli, Gilberto; Tavares, Fernando Menezes Leitão

2013-01-01

such as a dynamic propagation environment, human presence impact and terminals mobility. This chapter focuses on the practical aspects related to the real world-experimentation with distributed DSA network algorithms over a testbed network. Challenges and solutions are extensively discussed, from the testbed design......The problem of spectrum scarcity in uncoordinated and/or heterogeneous wireless networks is the key aspect driving the research in the field of flexible management of frequency resources. In particular, distributed dynamic spectrum access (DSA) algorithms enable an efficient sharing...... to the setup of experiments. A practical example of experimentation process with a DSA algorithm is also provided....

Holographic duality from random tensor networks

Energy Technology Data Exchange (ETDEWEB)

Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao [Stanford Institute for Theoretical Physics, Department of Physics, Stanford University,382 Via Pueblo, Stanford, CA 94305 (United States)

2016-11-02

Tensor networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random tensors. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the tensors is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random tensors as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main

Disordered configurations of the Glauber model in two-dimensional networks

Science.gov (United States)

Bačić, Iva; Franović, Igor; Perc, Matjaž

2017-12-01

We analyze the ordering efficiency and the structure of disordered configurations for the zero-temperature Glauber model on Watts-Strogatz networks obtained by rewiring 2D regular square lattices. In the small-world regime, the dynamics fails to reach the ordered state in the thermodynamic limit. Due to the interplay of the perturbed regular topology and the energy neutral stochastic state transitions, the stationary state consists of two intertwined domains, manifested as multiclustered states on the original lattice. Moreover, for intermediate rewiring probabilities, one finds an additional source of disorder due to the low connectivity degree, which gives rise to small isolated droplets of spins. We also examine the ordering process in paradigmatic two-layer networks with heterogeneous rewiring probabilities. Comparing the cases of a multiplex network and the corresponding network with random inter-layer connectivity, we demonstrate that the character of the final state qualitatively depends on the type of inter-layer connections.

Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity

Directory of Open Access Journals (Sweden)

Silvia Scarpetta

2010-08-01

Full Text Available We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate-and-fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre- and post-synaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully-connected networks, we study sparse networks, where each neuron is connected only to a small number $zll N$ of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry.

Topological Effects and Performance Optimization in Transportation Continuous Network Design

Directory of Open Access Journals (Sweden)

Jianjun Wu

2014-01-01

Full Text Available Because of the limitation of budget, in the planning of road works, increased efforts should be made on links that are more critical to the whole traffic system. Therefore, it would be helpful to model and evaluate the vulnerability and reliability of the transportation network when the network design is processing. This paper proposes a bilevel transportation network design model, in which the upper level is to minimize the performance of the network under the given budgets, while the lower level is a typical user equilibrium assignment problem. A new solution approach based on particle swarm optimization (PSO method is presented. The topological effects on the performance of transportation networks are studied with the consideration of three typical networks, regular lattice, random graph, and small-world network. Numerical examples and simulations are presented to demonstrate the proposed model.

Spiking sychronization regulated by noise in three types of Hodgkin—Huxley neuronal networks

International Nuclear Information System (INIS)

Zhang Zheng-Zhen; Zeng Shang-You; Tang Wen-Yan; Hu Jin-Lin; Zeng Shao-Wen; Ning Wei-Lian; Qiu Yi; Wu Hui-Si

2012-01-01

In this paper, we study spiking synchronization in three different types of Hodgkin—Huxley neuronal networks, which are the small-world, regular, and random neuronal networks. All the neurons are subjected to subthreshold stimulus and external noise. It is found that in each of all the neuronal networks there is an optimal strength of noise to induce the maximal spiking synchronization. We further demonstrate that in each of the neuronal networks there is a range of synaptic conductance to induce the effect that an optimal strength of noise maximizes the spiking synchronization. Only when the magnitude of the synaptic conductance is moderate, will the effect be considerable. However, if the synaptic conductance is small or large, the effect vanishes. As the connections between neurons increase, the synaptic conductance to maximize the effect decreases. Therefore, we show quantitatively that the noise-induced maximal synchronization in the Hodgkin—Huxley neuronal network is a general effect, regardless of the specific type of neuronal network

Importance of small-degree nodes in assortative networks with degree-weight correlations

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Ma, Sijuan; Feng, Ling; Monterola, Christopher Pineda; Lai, Choy Heng

2017-10-01

It has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks. Yet its influence on weighted networks is not clear, in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in Twitter. Here we use the self-consistent probability method and revised nonperturbative heterogenous mean-field theory method to investigate this influence on both susceptible-infective-recovered (SIR) and susceptible-infective-susceptible (SIS) spreading dynamics. Both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity, the prevalence in the supercritical regime shows a crossover under different degree-weight correlations. In particular, unlike the case of random mixing networks, in assortative networks, the negative degree-weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity than that of the positively correlated. In addition, the previously observed inhibition effect on spreading velocity by assortative structure is not apparent in negatively degree-weight correlated networks, while it is enhanced for that of the positively correlated. Detailed investigation into the degree distribution of the infected nodes reveals that small-degree nodes play essential roles in the supercritical phase of both SIR and SIS spreadings. Our results have direct implications in understanding viral information spreading over online social networks and epidemic spreading over contact networks.

Organization of growing random networks

International Nuclear Information System (INIS)

Krapivsky, P. L.; Redner, S.

2001-01-01

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively, and linking each to an earlier node of degree k with an attachment probability A k . When A k grows more slowly than linearly with k, the number of nodes with k links, N k (t), decays faster than a power law in k, while for A k growing faster than linearly in k, a single node emerges which connects to nearly all other nodes. When A k is asymptotically linear, N k (t)∼tk -ν , with ν dependent on details of the attachment probability, but in the range 2 -2 power-law tail, where s is the component size. The out component has a typical size of order lnt, and it provides basic insights into the genealogy of the network

Distributed clone detection in static wireless sensor networks: random walk with network division.

Science.gov (United States)

Khan, Wazir Zada; Aalsalem, Mohammed Y; Saad, N M

2015-01-01

Wireless Sensor Networks (WSNs) are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND) for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s) by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.

Distributed clone detection in static wireless sensor networks: random walk with network division.

Directory of Open Access Journals (Sweden)

Wazir Zada Khan

Full Text Available Wireless Sensor Networks (WSNs are vulnerable to clone attacks or node replication attacks as they are deployed in hostile and unattended environments where they are deprived of physical protection, lacking physical tamper-resistance of sensor nodes. As a result, an adversary can easily capture and compromise sensor nodes and after replicating them, he inserts arbitrary number of clones/replicas into the network. If these clones are not efficiently detected, an adversary can be further capable to mount a wide variety of internal attacks which can emasculate the various protocols and sensor applications. Several solutions have been proposed in the literature to address the crucial problem of clone detection, which are not satisfactory as they suffer from some serious drawbacks. In this paper we propose a novel distributed solution called Random Walk with Network Division (RWND for the detection of node replication attack in static WSNs which is based on claimer-reporter-witness framework and combines a simple random walk with network division. RWND detects clone(s by following a claimer-reporter-witness framework and a random walk is employed within each area for the selection of witness nodes. Splitting the network into levels and areas makes clone detection more efficient and the high security of witness nodes is ensured with moderate communication and memory overheads. Our simulation results show that RWND outperforms the existing witness node based strategies with moderate communication and memory overheads.

Statistical mechanics of the fashion game on random networks

International Nuclear Information System (INIS)

Sun, YiFan

2016-01-01

A model of fashion on networks is studied. This model consists of two groups of agents that are located on a network and have opposite viewpoints towards being fashionable: behaving consistently with either the majority or the minority of adjacent agents. Checking whether the fashion game has a pure Nash equilibrium (pure NE) is a non-deterministic polynomial complete problem. Using replica-symmetric mean field theory, the largest proportion of satisfied agents and the region where at least one pure NE should exist are determined for several types of random networks. Furthermore, a quantitive analysis of the asynchronous best response dynamics yields the phase diagram of existence and detectability of pure NE in the fashion game on some random networks. (paper: classical statistical mechanics, equilibrium and non-equilibrium).

Dynamic Load Balanced Clustering using Elitism based Random Immigrant Genetic Approach for Wireless Sensor Networks

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K. Mohaideen Pitchai

2017-07-01

Full Text Available Wireless Sensor Network (WSN consists of a large number of small sensors with restricted energy. Prolonged network lifespan, scalability, node mobility and load balancing are important needs for several WSN applications. Clustering the sensor nodes is an efficient technique to reach these goals. WSN have the characteristics of topology dynamics because of factors like energy conservation and node movement that leads to Dynamic Load Balanced Clustering Problem (DLBCP. In this paper, Elitism based Random Immigrant Genetic Approach (ERIGA is proposed to solve DLBCP which adapts to topology dynamics. ERIGA uses the dynamic Genetic Algorithm (GA components for solving the DLBCP. The performance of load balanced clustering process is enhanced with the help of this dynamic GA. As a result, the ERIGA achieves to elect suitable cluster heads which balances the network load and increases the lifespan of the network.

Making big communities small: using network science to understand the ecological and behavioral requirements for community social capital.

Science.gov (United States)

Neal, Zachary

2015-06-01

The concept of social capital is becoming increasingly common in community psychology and elsewhere. However, the multiple conceptual and operational definitions of social capital challenge its utility as a theoretical tool. The goals of this paper are to clarify two forms of social capital (bridging and bonding), explicitly link them to the structural characteristics of small world networks, and explore the behavioral and ecological prerequisites of its formation. First, I use the tools of network science and specifically the concept of small-world networks to clarify what patterns of social relationships are likely to facilitate social capital formation. Second, I use an agent-based model to explore how different ecological characteristics (diversity and segregation) and behavioral tendencies (homophily and proximity) impact communities' potential for developing social capital. The results suggest diverse communities have the greatest potential to develop community social capital, and that segregation moderates the effects that the behavioral tendencies of homophily and proximity have on community social capital. The discussion highlights how these findings provide community-based researchers with both a deeper understanding of the contextual constraints with which they must contend, and a useful tool for targeting their efforts in communities with the greatest need or greatest potential.

Computer simulation of randomly cross-linked polymer networks

International Nuclear Information System (INIS)

Williams, Timothy Philip

2002-01-01

In this work, Monte Carlo and Stochastic Dynamics computer simulations of mesoscale model randomly cross-linked networks were undertaken. Task parallel implementations of the lattice Monte Carlo Bond Fluctuation model and Kremer-Grest Stochastic Dynamics bead-spring continuum model were designed and used for this purpose. Lattice and continuum precursor melt systems were prepared and then cross-linked to varying degrees. The resultant networks were used to study structural changes during deformation and relaxation dynamics. The effects of a random network topology featuring a polydisperse distribution of strand lengths and an abundance of pendant chain ends, were qualitatively compared to recent published work. A preliminary investigation into the effects of temperature on the structural and dynamical properties was also undertaken. Structural changes during isotropic swelling and uniaxial deformation, revealed a pronounced non-affine deformation dependant on the degree of cross-linking. Fractal heterogeneities were observed in the swollen model networks and were analysed by considering constituent substructures of varying size. The network connectivity determined the length scales at which the majority of the substructure unfolding process occurred. Simulated stress-strain curves and diffraction patterns for uniaxially deformed swollen networks, were found to be consistent with experimental findings. Analysis of the relaxation dynamics of various network components revealed a dramatic slowdown due to the network connectivity. The cross-link junction spatial fluctuations for networks close to the sol-gel threshold, were observed to be at least comparable with the phantom network prediction. The dangling chain ends were found to display the largest characteristic relaxation time. (author)