Studies on the signal amplification in weighted and unweighted small-world networks

Weighted and unweighted networks composed of coupled bistable oscillators with small-world topology are investigated under the co-presence of a weak signal and multiplicative Gaussian white noise. As the noise intensity is adjusted to one or two optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of stochastic resonance (SR) or stochastic bi-resonance (SBR). The resonance behavior is strongly-dependent on the coupling strength in both networks. At a weak coupling, SR more likely takes place; whereas at a strong coupling, SBR is prone to occur. Compared with unweighted networks, the span of coupling strength for SBR is narrower in weighted networks. In addition, the weak signal cannot be amplified so effectively in the weighted networks as in the unweighted networks, attributing to the weakening effect of the link weight on the coupling between oscillators and the heterogeneity of the whole network connectivity caused by the weight distribution.

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Small-World Outer Synchronization of Small-World Chaotic Networks

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4041032 ◽

2018 ◽

Vol 13 (10) ◽

Cited By ~ 5

Author(s):

A. Arellano-Delgado ◽

R. M. López-Gutiérrez ◽

R. Martínez-Clark ◽

C. Cruz-Hernández

Keyword(s):

Numerical Simulations ◽

Coupling Strength ◽

Small World ◽

Small World Networks ◽

Outer Synchronization

In this work, small-world outer synchronization of coupled small-world networks is presented. In particular, we use Newman and Watts model to achieve small-world outer synchronization of small-world chaotic networks with Chua's oscillators like chaotic nodes. By means of extensive numerical simulations, we show that the new outer connections between existing networks decrease the necessary coupling strength to achieve outer synchronization. Two scenarios of interest are studied, (i) small-world outer synchronization with unidirectional outer connections (with chaotic master network), and (ii) small-world outer synchronization with bidirectional outer connections (without chaotic master network). In both scenarios, the isolated networks are bidirectionally coupled using Chua's oscillators like chaotic nodes.

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An Extended Correlation Dimension of Complex Networks

Entropy ◽

10.3390/e23060710 ◽

2021 ◽

Vol 23 (6) ◽

pp. 710

Author(s):

Sheng Zhang ◽

Wenxiang Lan ◽

Weikai Dai ◽

Feng Wu ◽

Caisen Chen

Keyword(s):

Complex Networks ◽

Correlation Dimension ◽

Fractal Dimensions ◽

Small World ◽

Scaling Analysis ◽

Fractal Nature ◽

Small World Networks ◽

Self Similarity ◽

Weighted Networks ◽

Fractal Properties

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman–Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.

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State-Dependent Synchrony and Functional Connectivity in the Primary and Secondary Whisker Somatosensory Cortices

Frontiers in Systems Neuroscience ◽

10.3389/fnsys.2021.713397 ◽

2021 ◽

Vol 15 ◽

Author(s):

Mohamed Khateb ◽

Jackie Schiller ◽

Yitzhak Schiller

Keyword(s):

Functional Connectivity ◽

Network Connectivity ◽

Small World ◽

Sensory Coding ◽

Small World Networks ◽

Cell Level ◽

State Dependent ◽

Somatosensory Cortices ◽

Whisker Stimulation ◽

Sensory Activation

Synchronized activity plays an important role in sensory coding and memory and is a hallmark of functional network connectivity. However, the effect of sensory activation on synchronization and cortical functional connectivity is largely unknown. In this study, we investigated the effect of whisker activation on synchronization and functional connectivity of the primary (wS1) and secondary (wS2) whisker somatosensory cortices at the single-cell level. The results showed that during the spontaneous pre-stimulus state, neurons tended to be functionally connected with nearby neurons which shared similar tuning characteristics. Whisker activation using either ramp-and-hold stimulation or artificial whisking against sandpaper has significantly reduced the average overall pairwise synchronization and functional connectivity within the wS1 barrel and wS2 cortices. Whisker stimulation disconnected approximately a third of neuronal pairs that were functionally connected during the unstimulated state. Nearby neurons with congruent tuning properties were more likely to remain functionally connected during whisker activation. The findings of this study indicated that cortical somatosensory networks are organized in non-random small world networks composed of neurons sharing relatively similar tuning properties. Sensory whisker activation intensifies these properties and further subdivides the cortical network into smaller more functionally uniform subnetworks, which possibly serve to increase the computational capacity of the network.

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On the Distributions of Subgraph Centralities in Complex Networks

Discrete Dynamics in Nature and Society ◽

10.1155/2013/473248 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Faxu Li ◽

Liang Wei ◽

Haixing Zhao ◽

Feng Hu

Keyword(s):

Complex Networks ◽

Probability Distributions ◽

Network Connectivity ◽

Network Models ◽

Small World ◽

Small World Networks ◽

Power Law Distribution ◽

Scale Free ◽

Scale Free Networks ◽

Complex Network Models

Subgraph centrality measure characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than large ones, which makes this measure appropriate for characterizing network motifs. This measure is better in being able to discriminate the nodes of a network than alternate measures. In this paper, the important issue of subgraph centrality distributions is investigated through theory-guided extensive numerical simulations, for three typical complex network models, namely, the ER random-graph networks, WS small-world networks, and BA scale-free networks. It is found that these three very different types of complex networks share some common features, particularly that the subgraph centrality distributions in increasing order are all insensitive to the network connectivity characteristics, and also found that the probability distributions of subgraph centrality of the ER and of the WS models both follow the gamma distribution, and the BA scale-free networks exhibit a power-law distribution with an exponential cutoff.

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Large Scale-Free Network Organization is Likely Key for Biofilm Phase Transition

10.1101/630103 ◽

2019 ◽

Cited By ~ 1

Author(s):

Kumar Selvarajoo

Keyword(s):

Coupling Strength ◽

Biological Networks ◽

Large Scale ◽

Network Connectivity ◽

Small World ◽

Current Data ◽

Kuramoto Model ◽

Small Scale ◽

Scale Free ◽

Basic Model

AbstractNon-linear Kuramoto model has been used to study synchronized or sync behavior in numerous fields, however, its application in biology is scare. Here, I introduce the basic model and provide examples where large scale small-world or scale-free networks are crucial for spontaneous sync even for low coupling strength. This information was next checked for relevance in living systems where it is now well-known that biological networks are scale-free. Our recent transcriptome-wide data analysis of Saccharomyces cerevisiae biofilm showed that low to middle expressed genes are key for scale invariance in biology. Together, the current data indicate that biological network connectivity structure with low coupling strength, or expression levels, is sufficient for sync behavior. For biofilm regulation, it may, therefore, be necessary to investigate large scale low expression genes rather than small scale high expression genes.

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Networks

10.1093/oso/9780198821939.003.0004 ◽

2018 ◽

Author(s):

Stefan Thurner ◽

Rudolf Hanel ◽

Peter Klimekl

Keyword(s):

Complex Systems ◽

Complex Networks ◽

Phase Diagrams ◽

Community Detection ◽

Network Science ◽

Small World ◽

Small World Networks ◽

Multilayer Networks ◽

Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

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