MICROSCOPIC SELF-ORGANIZATION IN NETWORKS AND REGULAR LATTICE

2002 ◽  
Vol 16 (25) ◽  
pp. 923-935
Author(s):  
QI OUYANG ◽  
KAI SUN ◽  
HONGLI WANG
Keyword(s):  
Correlation Length ◽  
Random Network ◽  
Reaction System ◽  
Small World ◽  
Self Organization ◽  
Fast Diffusion ◽  
Small World Network ◽  
Regular Lattice ◽  
Numerical Studies ◽  
Regular Network

We report our numerical studies on the microscopic self-organizations of a reaction system in three types of networks: a regular network, a small-world network, and a random network as well as on a regular lattice. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in the regular network. As a result, it is much easier to obtain a microscopic self-organization in a small-world or a random network. A phase transition from a stochastic state to a synchronized state was observed when the randomness of a small-world network was increased. We also demonstrate that good synchronization activities of enzymatic turnover cycles can be developed on a regular lattice when the correlation length created by the fast diffusion of regulatory particles is large enough.

scholarly journals How Does the Heterogeneity of Members Affect the Evolution of Group Opinions?

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
An Lu ◽  
Haifeng Ling ◽  
Zhengping Ding
Keyword(s):  
Decision Making ◽  
Random Network ◽  
Small World ◽  
Important Influence ◽  
The Other ◽  
Network Structures ◽  
Small World Network ◽  
Average Amount ◽  
Regular Network ◽  
The Impact

Understanding the impact of heterogeneity on the evolution of group opinions can enlighten us on how to effectively organize, redesign, and improve decision-making efficiency. This article explores mainly the effects of heterogeneity on the evolution of group opinions. It is found that the heterogeneity of individuals’ openness has an important influence on the ability to aggregate group opinions. According to the average amount of clusters and Herfindahl–Hirschman Index (HHI) under different network structures, heterogeneity often improves the ability. In addition, for the small-world network and random network, there is little difference in the aggregation ability from both the average amount of clusters and the Herfindahl–Hirschman Index. While for the regular network, the ability is obviously weaker than that of the other two. This result also shows that the randomness of interaction between members will enhance the cohesion of a group.

scholarly journals Factor or Network Model? Predictions From Neural Networks

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Alexander P. Christensen ◽  
Keyword(s):  
Neural Networks ◽  
Network Model ◽  
Latent Variable ◽  
Random Network ◽  
Network Models ◽  
Small World ◽  
Small World Network ◽  
Monte Carlo Simulation Study ◽  
Psychological Phenomena ◽  
The Neural Networks

The nature of associations between variables is important for constructing theory about psychological phenomena. In the last decade, this topic has received renewed interest with the introduction of psychometric network models. In psychology, network models are often contrasted with latent variable (e.g., factor) models. Recent research has shown that differences between the two tend to be more substantive than statistical. One recently developed algorithm called the Loadings Comparison Test (LCT) was developed to predict whether data were generated from a factor or small-world network model. A significant limitation of the current LCT implementation is that it's based on heuristics that were derived from descriptive statistics. In the present study, we used artificial neural networks to replace these heuristics and develop a more robust and generalizable algorithm. We performed a Monte Carlo simulation study that compared neural networks to the original LCT algorithm as well as logistic regression models that were trained on the same data. We found that the neural networks performed as well as or better than both methods for predicting whether data were generated from a factor, small-world network, or random network model. Although the neural networks were trained on small-world networks, we show that they can reliably predict the data-generating model of random networks, demonstrating generalizability beyond the trained data. We echo the call for more formal theories about the relations between variables and discuss the role of the LCT in this process.

Abstract 17426: Pulmonary Vein Isolation ‘Rewires’ Electrical Communications to Enhance Small-world Network Topology During Atrial Fibrillation

Circulation ◽  
2015 ◽  
Vol 132 (suppl_3) ◽  
Author(s):  
Hiroshi Ashikaga ◽  
Jonathan Chrispin ◽  
Degang Wu ◽  
Joshua Garland
Keyword(s):  
Atrial Fibrillation ◽  
Communication Network ◽  
Mutual Information ◽  
Path Length ◽  
Random Network ◽  
Small World ◽  
Clustering Coefficient ◽  
Small World Network ◽  
Z Score ◽  
Network Properties

Recent evidence suggests that pulmonary vein isolation (PVI) may perturb the electrophysiological substrate for maintenance of atrial fibrillation (AF). Our previous work indicates that information theory metrics can quantify electrical communications during arrhythmia. We hypothesized that PVI ‘rewires’ the electrical communication network during AF such that the topology exhibits higher levels of small-world network properties, with higher clustering coefficient and lower path length, than would be expected by chance. Thirteen consecutive patients (n=6 with prior PVI and n=7 without) underwent AF ablation using a 64-electrode basket catheter in the left atrium. Multielectrode recording was performed during AF for 60 seconds, followed by PVI. Mutual information was calculated from the time series between each pair of electrodes using the Kraskov-Stögbauer-Grassberger estimator. The all-to-all mutual information matrix (64x64; Figure, upper panels) was thresholded by the median and standard deviations of mutual information to build a binary adjacency matrix for electrical communication networks. The properties of small-world network ( swn ; ‘small-world-ness’) were quantified by the ratio of the observed average clustering coefficient to that of a random network over the ratio of the observed average path length to that of a random network. swn was expressed in normal Z standard deviation units. As the binarizing threshold increased, the Z-score of swn decreased (Figure, lower panel). However, the Z-score at each threshold value was consistently higher with prior PVI than those without (p<0.05). In conclusion, electrical communication network during AF with prior PVI is associated with higher levels of small-world network properties than those without. This finding supports the concept that PVI perturbs the underlying substrate. In addition, swn of electrical communication network may be a promising metric to quantify substrate modification.

How to Quantify 'Small-World Networks'?

Fractals ◽  
1998 ◽  
Vol 06 (04) ◽  
pp. 301-303 ◽  
Author(s):  
Hanspeter Herzel
Keyword(s):  
Small World ◽  
Small World Network ◽  
Small Worlds ◽  
Small World Networks ◽  
Complete Regularity ◽  
Local Clustering ◽  
Regular Network ◽  
Analytical Expressions ◽  
Global Connection

Recently Watts and Strogatz emphasized the widespread relevance of 'small worlds' and studied numerically networks between complete regularity and complete randomness. In this letter, I derive simple analytical expressions which can reproduce the empirical observations. It is shown how a few random connections can turn a regular network into a 'small-world network' with a short global connection but persisting local clustering.

scholarly journals Revisiting the Small-World Phenomenon

2016 ◽  
Vol 20 (1) ◽  
pp. 149-173 ◽  
Author(s):  
Tore Opsahl ◽  
Antoine Vernet ◽  
Tufool Alnuaimi ◽  
Gerard George
Keyword(s):  
Significant Variation ◽  
Random Network ◽  
Small World ◽  
Random Networks ◽  
Significant Heterogeneity ◽  
Small World Network ◽  
Small World Networks ◽  
Firm Outcomes ◽  
Baseline Levels

Research has explored how embeddedness in small-world networks influences individual and firm outcomes. We show that there remains significant heterogeneity among networks classified as small-world networks. We develop measures of the efficiency of a network, which allow us to refine predictions associated with small-world networks. A network is classified as a small-world network if it exhibits a distance between nodes that is comparable to the distance found in random networks of similar sizes—with ties randomly allocated among nodes—in addition to containing dense clusters. To assess how efficient a network is, there are two questions worth asking: (a) What is a compelling random network for baseline levels of distance and clustering? and (b) How proximal should an observed value be to the baseline to be deemed comparable? Our framework tests properties of networks, using simulation, to further classify small-world networks according to their efficiency. Our results suggest that small-world networks exhibit significant variation in efficiency. We explore implications for the field of management and organization.

CONTAGION AND THE SPEED OF ADJUSTMENT IN SMALL WORLDS

2007 ◽  
Vol 09 (04) ◽  
pp. 689-704 ◽  
Author(s):  
EDWARD J. CARTWRIGHT
Keyword(s):  
Dynamic Process ◽  
Random Network ◽  
Small World ◽  
Coordination Game ◽  
Small Worlds ◽  
Small World Networks ◽  
Regular Lattice ◽  
Speed Of Adjustment ◽  
Equilibrium Shift

We model a simple dynamic process in which myopic agents are matched amongst each other to play a coordination game. The network of player interaction is varied between a regular lattice and a random network allowing us to model contagion in small world networks. Weighting times for an equilibrium shift from the risk dominated to risk dominant equilibrium are shown to be smallest in small world networks.

STOCHASTIC RESONANCE IN HINDMARSH–ROSE NEURAL NETWORK WITH SMALL-WORLD CONNECTIONS

2008 ◽  
Vol 22 (30) ◽  
pp. 5365-5373 ◽  
Author(s):  
RENHUAN YANG ◽  
AIGUO SONG
Keyword(s):  
Neural Network ◽  
Stochastic Resonance ◽  
Random Network ◽  
Small World ◽  
Resonance Curve ◽  
Resonance Phenomenon ◽  
Node Degree ◽  
Regular Network ◽  
Stochastic Resonance Phenomenon ◽  
Peak Value

We study stochastic resonance (SR) in Hindmarsh–Rose (HR) neural network with small-world (SW) connections driven by external periodic stimulus, focusing on the dependence of properties of SR on the network structure parameters. It is found that, the SW neural network enhances SR compared with single neuron. By turning coupling strength c, two categories of SR were gained. With the connection-rewiring probability p increasing, the resonance curve becomes more and more sharp and the peak value increases gradually and then reaches saturation. The SW network enhances the SR peak value compared with regular network and widens resonance in ascending range compared with random network. When decreasing node degree k, the resonance range is enlarged, and the signal noise ratio (SNR) curve becomes a two peak one from a classic single peak SR curve, and then the stochastic resonance phenomenon almost disappears.

THE KEY ROLE OF SHORTCUTS OF SMALL-WORLD NETWORK IN OPINION FORMATION

2008 ◽  
Vol 19 (06) ◽  
pp. 867-873 ◽  
Author(s):  
LONG GUO ◽  
XU CAI
Keyword(s):  
Spatial Correlation ◽  
Hurst Exponent ◽  
Small World ◽  
Small World Network ◽  
Opinion Formation ◽  
Regular Lattice ◽  
Average Magnetization ◽  
Initial Opinion ◽  
Evolution Trend

In this paper, we analyze the average magnetization and spatial correlation of opinion formation in small-world network and in the regular lattice. We construct NW small-world network through adding shortcuts on the regular lattice. With computer simulation, we find that there exists short- and long-range spatial correlation of the average magnetization m(t) in NW small-world network and the evolution trend of opinion is dependent on the initial opinion condition by comparing with that in regular lattice. On the other hand, we analyze the average magnetization m(t) using the time series analysis, and find the Hurst exponent H ≃ 0.5 in NW small-world network and H = 0 in regular lattice. All the results show the important role of shortcuts in the NW small-world network, which reflects some interesting aspects in our real society indirectly.

scholarly journals Self-Organization of Small-World Network and Polychronous Neuronal Groups by Adaptive Rewiring

2015 ◽  
Vol 9 ◽  
Author(s):  
Jarman Nick ◽  
Trengove Chris ◽  
Steur Erik ◽  
Tyukin Ivan ◽  
Van Leeuwen Cees
Keyword(s):  
Small World ◽  
Self Organization ◽  
Small World Network ◽  
Neuronal Groups

scholarly journals Enhancing Controllability Robustness of q-Snapback Networks through Redirecting Edges

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Yang Lou ◽  
Lin Wang ◽  
Guanrong Chen
Keyword(s):  
Numerical Simulations ◽  
Network Model ◽  
Nearest Neighbor ◽  
Small World ◽  
Small World Network ◽  
Edge Removal ◽  
Regular Network ◽  
Node Removal ◽  
Network Controllability

The well-known small-world network model was established by randomly rewiring edges, aiming to enhance the synchronizability of an undirected nearest-neighbor regular network. This paper demonstrates via extensive numerical simulations that randomly redirecting edges could enhance the robustness of the network controllability for directed snapback networks against both random and intentional node-removal and edge-removal attacks.

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