ENHANCING NETWORK SYNCHRONIZATION BY SPARSE REPULSIVE COUPLINGS

2009 ◽  
Vol 19 (02) ◽  
pp. 711-717 ◽  
Author(s):  
J. A. ALMENDRAL ◽  
I. LEYVA ◽  
I. SENDIÑA-NADAL
Keyword(s):  
Spectral Analysis ◽  
Structural Properties ◽  
Long Range ◽  
Dynamical Behavior ◽  
Small World ◽  
Small World Network ◽  
Network Synchronization ◽  
Connection Probability ◽  
Link Strength

In a small-world network of mainly attractively coupled nonidentical neurons, we show that a small fraction of phase-repulsive couplings is able to strongly improve synchronization for certain values of the link strength, and long-range connection probability. By means of a spectral analysis we relate the observed dynamical behavior with the structural properties of the network.

scholarly journals Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

2008 ◽  
Vol 40 (4) ◽  
pp. 966-978
Author(s):  
Archis Ghate
Keyword(s):  
Markov Chains ◽  
Structural Properties ◽  
Long Range ◽  
World Literature ◽  
Relative Size ◽  
Small World ◽  
Hitting Time ◽  
Hitting Times ◽  
Message Delivery ◽  
Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

scholarly journals Decentralized search on spheres using small-world Markov chains: expected hitting times and structural properties

2008 ◽  
Vol 40 (04) ◽  
pp. 966-978
Author(s):  
Archis Ghate
Keyword(s):  
Markov Chains ◽  
Structural Properties ◽  
Long Range ◽  
World Literature ◽  
Relative Size ◽  
Small World ◽  
Hitting Time ◽  
Hitting Times ◽  
Message Delivery ◽  
Expected Hitting Time

We build a family of Markov chains on a sphere using distance-based long-range connection probabilities to model the decentralized message-passing problem that has recently gained significant attention in the small-world literature. Starting at an arbitrary source point on the sphere, the expected message delivery time to an arbitrary target on the sphere is characterized by a particular expected hitting time of our Markov chains. We prove that, within this family, there is a unique efficient Markov chain whose expected hitting time is polylogarithmic in the relative size of the sphere. For all other chains, this expected hitting time is at least polynomial. We conclude by defining two structural properties, called scale invariance and steady improvement, of the probability density function of long-range connections and prove that they are sufficient and necessary for efficient decentralized message delivery.

A Kind of Deterministic Small-World Network Derived from Polygonal Nesting

2014 ◽  
Vol 614 ◽  
pp. 543-549
Author(s):  
Hui Li ◽  
Liang Yuan
Keyword(s):  
Long Range ◽  
Outer Layer ◽  
Degree Distribution ◽  
Path Length ◽  
Small Diameter ◽  
Small World ◽  
Average Path Length ◽  
Node Degree ◽  
Small World Network ◽  
Central Node

A kind of deterministic small-world network is constructed based on polygonal nesting with discrete degree distribution. By adding contrapuntal edges and alternate-position edges between adjacent nests, the intra-nest edges and the long-range edges from the central node to certain outer layer nodes, the proposed polygonal nesting small-world (PNSW) networks have the property of large clustering coefficients. Also these kinds of PNSW networks have small diameter, average node degree and average path length, whose moments ofkorder are given.

A Surveillance and Spatiotemporal Visualization Model for Infectious Diseases Using Social Network

2019 ◽  
pp. 1027-1046
Author(s):  
Younsi Fatima-Zohra ◽  
Hamdadou Djamila ◽  
Boussaid Omar
Keyword(s):  
Risk Factors ◽  
Infectious Diseases ◽  
Human Population ◽  
Dynamical Behavior ◽  
Small World ◽  
Decision Makers ◽  
Small World Network ◽  
Seir Model ◽  
Visualization System ◽  
Spatiotemporal Visualization

In this paper, the authors propose a surveillance and spatiotemporal visualization system to simulate the infectious diseases spread which enables users to make decisions during a simulated pandemic. This system is based on compartment Susceptible, Exposed, Infected, and Removed (SEIR) model within a Small World network and Geographic Information System. The main advantage of this system is that it allows not only to understand how epidemic spreads in the human population and which risk factors promote this transmission but also to visualize epidemic outbreaks on the region's map. Experiments results reflect significantly the dynamical behavior of the influenza epidemic and the system can provide significant guidelines for decision makers when coping with epidemic diffusion controlling problems.

Geographical effect on small-world network synchronization

2008 ◽  
Vol 77 (2) ◽  
Author(s):  
Chuan-Yang Yin ◽  
Bing-Hong Wang ◽  
Wen-Xu Wang ◽  
Guan-Rong Chen
Keyword(s):  
Small World ◽  
Small World Network ◽  
Network Synchronization ◽  
Geographical Effect

A Surveillance and Spatiotemporal Visualization Model for Infectious Diseases using Social Network

2015 ◽  
Vol 7 (4) ◽  
pp. 1-19 ◽  
Author(s):  
Younsi Fatima-Zohra ◽  
Hamdadou Djamila ◽  
Boussaid Omar
Keyword(s):  
Infectious Diseases ◽  
Human Population ◽  
Dynamical Behavior ◽  
Small World ◽  
Decision Makers ◽  
Small World Network ◽  
Influenza Epidemic ◽  
Seir Model ◽  
Visualization System ◽  
Spatiotemporal Visualization

In this paper, the authors propose a surveillance and spatiotemporal visualization system to simulate the infectious diseases spread which enables users to make decisions during a simulated pandemic. This system is based on compartment Susceptible, Exposed, Infected, and Removed (SEIR) model within a Small World network and Geographic Information System. The main advantage of this system is that it allows not only to understand how epidemic spreads in the human population and which risk factors promote this transmission but also to visualize epidemic outbreaks on the region's map. Experiments results reflect significantly the dynamical behavior of the influenza epidemic and the system can provide significant guidelines for decision makers when coping with epidemic diffusion controlling problems.

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