Robust emergence of small-world structure in networks of spiking neurons

Kwok, Hoi Fei; Jurica, Peter; Raffone, Antonino; Leeuwen, Cees van

doi:10.1007/s11571-006-9006-5

Cited by 59 publications

(57 citation statements)

References 55 publications

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“…There is a wealth of studies showing how the structure of a network is a strong determinant of its dynamics (see e.g. Nishikawa et al, 2003;Kwok et al, 2007;Galan, 2008), and that the typical fall-back of completely regular or random networks give false impressions about both synchronisation and stability (see especially Watts & Strogatz, 1998;Lago-Fernandez et al, 2000). It is thus imperative that we begin from as accurate a network structure as possible.…”

Section: Creating the Striatal Microcircuitmentioning

confidence: 99%

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

2009

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The striatum, principal input structure of the basal ganglia, is crucial to both motor control and learning. It receives convergent input from all over neocortex, hippocampal formation, amygdala and thalamus, and is the primary recipient of dopamine in the brain. Within the striatum is a GABAergic microcircuit that acts upon these inputs, formed by the dominant medium-spiny projection neurons (MSNs) and fast-spiking interneurons (FSIs). There has been little progress in understanding the computations it performs, hampered by the non-laminar structure that prevents identification of a repeating canonical microcircuit. We here begin the identification of potential dynamically-defined computational elements within the striatum. We construct a new three-dimensional model of the striatal microcircuit's connectivity, and instantiate this with our dopamine-modulated neuron models of the MSNs and FSIs. A new model of gap junctions between the FSIs is introduced and tuned to experimental data. We introduce a novel multiple spiketrain analysis method, and apply this to the outputs of the model to find groups of synchronised neurons at multiple time-scales. We find that, with realistic in vivo background input, small assemblies of synchronised MSNs spontaneously appear, consistent with experimental observations, and that the number of assemblies and the time-scale of synchronisation is strongly dependent on the simulated concentration of dopamine. We also show that feed-forward inhibition from the FSIs counter-intuitively increases the firing rate of the MSNs. Such small cell assemblies forming spontaneously only in the absence of dopamine may contribute to motor control problems seen in humans and animals following loss of dopamine cells.

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Section: Creating the Striatal Microcircuitmentioning

confidence: 99%

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

2009

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“…These developments in CI have occurred simultaneously with some very interesting theoretical and empirical results in random graph theory -the introduction of small-world [4] and scale-free [5], [6] models, and investigation of their properties. Based on results already published by other authors [7], [8] we believe that the edge of these two dynamically growing disciplines might be an interesting field for research. In this paper we introduce a simplified model of spike flow network which in some details resembles a recurrent neural network with stochastic dynamics.…”

Section: R a F T D R A F T D R A F T D R A F T D R A F T D R A F T mentioning

confidence: 75%

“…, [8] we believe that the edge of these two dynamically growing disciplines might be an interesting field for research. In this paper we introduce a simplified model of spike flow network which in some details resembles a recurrent neural network with stochastic dynamics.…”

Section: R a F T D R A F T D R A F T D R A F T D R A F T D R A F T mentioning

confidence: 94%

Emergence of Scale-free Spike Flow Graphs in Recurrent Neural Networks

Piekniewski

Schreiber

2007

2007 IEEE Symposium on Foundations of Computational Intelligence

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D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t D r a f t [7], [8] we believe that the edge of these two dynamically growing disciplines might be an interesting field for research. In this paper we introduce a simplified model of spike flow network which in some details resembles a recurrent neural network with stochastic dynamics. We argue that within this setup a scale-free network structure emerges as a natural consequence of model structuring principles and we provide numerical evidence supporting this claim. Further in the paper we investigate a number of interesting properties of this network and discuss some consequences of this result.

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“…The concept of small-world networks by Watts and Strogatz was also included [1,6]. The recent innovation is the introduction of time delays to network models [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] which allows to study the influence of the limited speed of information processing on the network dynamics.…”

Section: Introductionmentioning

confidence: 99%

Spatial evolution of Hindmarsh–Rose neural network with time delays

Łepek¹,

Fronczak²

2018

Nonlinear Dyn

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Spatial relations between neurons in the network with time delays play a crucial role in determining dynamics of the system. During the development of the nervous system, different types of neurons group together to enable specific functions of the network. Right spatial distances, thus right time delays between cells are crucial for an appropriate functioning of the system. To model the process of neural migration, we proposed simple but effective model of network spatial evolution based on Hindmarsh-Rose neurons and Metropolis-Hastings Monte Carlo algorithm. Under the specific assumptions and using appropriate parameters of the neural evolution, the network can converge to the desirable state giving the opportunity of achieving large variety of spectra. We show that there is a specific range of network size in space which allows it to generate assumed output. A network or generally speaking a system with time delays (corresponding to the arrangement in the physical space) of specific output properties has a specific spatial dimension that allows it to function properly.

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Robust emergence of small-world structure in networks of spiking neurons

Cited by 59 publications

References 55 publications

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

Emergence of Scale-free Spike Flow Graphs in Recurrent Neural Networks

Spatial evolution of Hindmarsh–Rose neural network with time delays

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