Adaptive rewiring in chaotic networks renders small-world connectivity with consistent clusters

Berg, Daan van den; Leeuwen, Cees van

doi:10.1209/epl/i2003-10116-1

Cited by 45 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar division of labour was subsequently observed in a number of related systems which can be interpreted as simple models of neural networks (Bornholdt & Rohlf 2000;Gong & van Leeuwen 2004;van den Berg & van Leeuwen 2004). As a common theme, in all these models the topological change arises through a strengthening of connections between elements in a similar state-a rule that is for neural networks well motivated by empirical results (Paulsen & Sejnowski 2000).…”

Section: Leadership In Coupled Oscillator Networkmentioning

confidence: 54%

Adaptive coevolutionary networks: a review

Groß

Blasius²

2007

J. R. Soc. Interface.

898

778

View full text Add to dashboard Cite

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

show abstract

Section: Leadership In Coupled Oscillator Networkmentioning

confidence: 54%

Adaptive coevolutionary networks: a review

Groß

Blasius²

2007

J. R. Soc. Interface.

898

778

View full text Add to dashboard Cite

show abstract

“…In previous adaptive rewiring models, functional connectivity was represented as synchronous activity 9,10,12,13,21,44,45 of linearly coupled nonlinear oscillators 46 or, somewhat more realistically, by spiking model neuron synchrony 47,48 . While these representations more closely resemble artificial neural networks than the current graph diffusion model, their shortcomings are twofold.…”

Section: Discussionmentioning

confidence: 99%

Adaptive rewiring evolves brain-like structure in weighted networks

Rentzeperis

Leeuwen

2020

Sci Rep

View full text Add to dashboard Cite

Activity-dependent plasticity refers to a range of mechanisms for adaptively reshaping neuronal connections. We model their common principle in terms of adaptive rewiring of network connectivity, while representing neural activity by diffusion on the network: Where diffusion is intensive, shortcut connections are established, while underused connections are pruned. In binary networks, this process is known to steer initially random networks robustly to high levels of structural complexity, reflecting the global characteristics of brain anatomy: modular or centralized small world topologies. We investigate whether this result extends to more realistic, weighted networks. Both normally-and lognormally-distributed weighted networks evolve either modular or centralized topologies. Which of these prevails depends on a single control parameter, representing global homeostatic or normalizing regulation mechanisms. intermediate control parameter values exhibit the greatest levels of network complexity, incorporating both modular and centralized tendencies. The simulation results allow us to propose diffusion based adaptive rewiring as a parsimonious model for activity-dependent reshaping of brain connectivity structure.From neuronal synapses to white matter tracts 1 , brain anatomical networks are characterized by the structural properties of small-worldness 2,3 , modularity 4,5 and rich club organization 6,7 . The pervasiveness of these properties raises the question whether they result from a common principle 5,8 . We proposed that these properties are the product of adaptive rewiring 9-13, for a review14 . Adaptive rewiring captures a crucial property of how the brain's anatomical network is shaped over time. Whereas the mechanisms that shape the brain network show great variety, as they encompass brain growth 15 , development, as well as learning 16,for a review , they are alike in their common dependency on the network's functional connectivity, i.e. the statistical dependencies between the nodes' activities 12,17 . Adaptive rewiring formalizes this dependency in terms of graph theory, as it encompasses adding shortcut links to network regions with intense functional connectivity while pruning underused ones. These dynamical rewirings could be regarded as adaptive network optimization to function 18 .Whereas adaptive rewiring represents the dependency of structural connectivity on network activity, the reverse, viz. the dependency of activity on structural connectivity, has been the focus of intense investigation. Recently, it was proposed that a simple, linear equation can predict brain activity from anatomical connectivity 19 . The proposal describes traffic on a fixed anatomical network in terms of random walks. This allows the amount of traffic to be stochastically approximated in terms of diffusion on the graph. Jarman and colleagues 11 adopted a similar principle in an adaptive rewiring model. They represented the amount of flow transferred between nodes by a heat kernel. During each rewiring step, an edge wit...

show abstract

“…However, the details of this simple model are hard to translate into possible neurobiological mechanisms of module formation. In a series of studies it has been shown that synchronization dependent rewiring of networks of coupled logistic functions can give rise to modular structure (van den Berg and van Leeuwen, 2004; Zhou et al, 2007; Rubinov et al, 2009b). While this is an elegant minimal scenario, it requires chaotic dynamics of the units, which may not be a realistic scenario for the dynamics of neural masses.…”

Section: Discussionmentioning

confidence: 99%

“…In vitro studies confirm the self-organizing properties of developing neural networks, but do not allow direct identification of the causal mechanisms. In a computational model of interconnected units consisting of logistic functions, activity dependent rewiring such that synchronous units become increasingly connected, results in an evolution from a random topology toward a small-world network with modular features (van den Berg and van Leeuwen, 2004; Rubinov et al, 2009b). In this model, chaotic dynamics of the individual units and weak connectivity were essential in giving rise to a modular functional organization that subsequently drove the structure of the underlying network.…”

Section: Introductionmentioning

confidence: 99%

Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity

Stam

Hillebrand

Wang

et al. 2010

Front. Comput. Neurosci.

View full text Add to dashboard Cite

A network of 32 or 64 connected neural masses, each representing a large population of interacting excitatory and inhibitory neurons and generating an electroencephalography/magnetoencephalography like output signal, was used to demonstrate how an interaction between dynamics and connectivity might explain the emergence of complex network features, in particular modularity. Network evolution was modeled by two processes: (i) synchronization dependent plasticity (SDP) and (ii) growth dependent plasticity (GDP). In the case of SDP, connections between neural masses were strengthened when they were strongly synchronized, and were weakened when they were not. GDP was modeled as a homeostatic process with random, distance dependent outgrowth of new connections between neural masses. GDP alone resulted in stable networks with distance dependent connection strengths, typical small-world features, but no degree correlations and only weak modularity. SDP applied to random networks induced clustering, but no clear modules. Stronger modularity evolved only through an interaction of SDP and GDP, with the number and size of the modules depending on the relative strength of both processes, as well as on the size of the network. Lesioning part of the network, after a stable state was achieved, resulted in a temporary disruption of the network structure. The model gives a possible scenario to explain how modularity can arise in developing brain networks, and makes predictions about the time course of network changes during development and following acute lesions.

show abstract

Adaptive rewiring in chaotic networks renders small-world connectivity with consistent clusters

Cited by 45 publications

References 22 publications

Adaptive coevolutionary networks: a review

Adaptive coevolutionary networks: a review

Adaptive rewiring evolves brain-like structure in weighted networks

Emergence of modular structure in a large-scale brain network with interactions between dynamics and connectivity

Contact Info

Product

Resources

About