Extending stability through hierarchical clusters in Echo State Networks

Jarvis, Sarah; Rotter, Stefan; Egert, Ulrich

doi:10.3389/fninf.2010.00011

Cited by 17 publications

(10 citation statements)

References 20 publications

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“…Hierarchical modularity specifically also enhances dynamical reconnectability (Robinson et al, 2009), as marginally stable networks can be combined or divided while preserving stability. Other benefits of a hierarchically modular organization include an enhanced stability of echo state networks (Jarvis et al, 2010), and dynamical re-connectivity between different transient dynamic behaviors (Müller-Linow et al, 2008; Hütt and Lesne, 2009). …”

Section: Why Are Brain Network Expected To Be Modular?mentioning

confidence: 99%

Modular and Hierarchically Modular Organization of Brain Networks

Meunier¹,

Lambiotte²,

Bullmore³

2010

Front. Neurosci.

1,060

859

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Brain networks are increasingly understood as one of a large class of information processing systems that share important organizational principles in common, including the property of a modular community structure. A module is topologically defined as a subset of highly inter-connected nodes which are relatively sparsely connected to nodes in other modules. In brain networks, topological modules are often made up of anatomically neighboring and/or functionally related cortical regions, and inter-modular connections tend to be relatively long distance. Moreover, brain networks and many other complex systems demonstrate the property of hierarchical modularity, or modularity on several topological scales: within each module there will be a set of sub-modules, and within each sub-module a set of sub-sub-modules, etc. There are several general advantages to modular and hierarchically modular network organization, including greater robustness, adaptivity, and evolvability of network function. In this context, we review some of the mathematical concepts available for quantitative analysis of (hierarchical) modularity in brain networks and we summarize some of the recent work investigating modularity of structural and functional brain networks derived from analysis of human neuroimaging data.

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Section: Why Are Brain Network Expected To Be Modular?mentioning

confidence: 99%

Modular and Hierarchically Modular Organization of Brain Networks

Meunier¹,

Lambiotte²,

Bullmore³

2010

Front. Neurosci.

1,060

859

View full text Add to dashboard Cite

show abstract

“…As shown by the above simulations, the activity inside the modules is strongly correlated in modular networks. Such dynamical characteristics of modular networks would be beneficial in increasing the robustness against noise, as partial synchronization would be maintained even when reservoir responses fluctuate by noise [28].…”

Section: Resultsmentioning

confidence: 99%

Modular networks of spiking neurons for applications in time-series information processing

Moriya

Yamamoto

Hirano‐Iwata

et al. 2020

NOLTA

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Spiking neural networks with complex spatiotemporal dynamics support efficient information processing of time-series signals. Here, we investigate the relationship between complexity of network dynamics and modular topology of networks using numerical simulations and discuss their effect on the classification performance of spoken-digit recognition tasks. The results show that modular networks generate spatially complex dynamics in which partially and globally synchronous bursts coexist. The classification rate of the modular reservoir network was approximately 75%, a value of which was comparable to that of a random network. This was caused by the randomly-connection structure between the input-reservoir and reservoirreadout layers, thus appropriate inference methods and asymmetry of connections should be introduced to take advantage of the complex dynamics in modular networks.

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“…We have not considered the modularity of our networks (Leicht and Newman, 2008). The presence of hierarchical connectivity can also affect the dynamics (Müller-Linow et al, 2008; Jarvis et al, 2010; Kaiser and Hilgetag, 2010). As our networks are not embedded in space, no distance between neurons can be defined, and consequently effects of the distance dependence of neural connections which can lead to spatial patterns like propagating waves (Roxin, 2004; Voges and Perrinet, 2009, 2012), are not taken into account.…”

Section: Discussionmentioning

confidence: 99%

The relevance of network micro-structure for neural dynamics

Pernice¹,

Deger²,

Cardanobile³

et al. 2013

Front. Comput. Neurosci.

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The activity of cortical neurons is determined by the input they receive from presynaptic neurons. Many previous studies have investigated how specific aspects of the statistics of the input affect the spike trains of single neurons and neurons in recurrent networks. However, typically very simple random network models are considered in such studies. Here we use a recently developed algorithm to construct networks based on a quasi-fractal probability measure which are much more variable than commonly used network models, and which therefore promise to sample the space of recurrent networks in a more exhaustive fashion than previously possible. We use the generated graphs as the underlying network topology in simulations of networks of integrate-and-fire neurons in an asynchronous and irregular state. Based on an extensive dataset of networks and neuronal simulations we assess statistical relations between features of the network structure and the spiking activity. Our results highlight the strong influence that some details of the network structure have on the activity dynamics of both single neurons and populations, even if some global network parameters are kept fixed. We observe specific and consistent relations between activity characteristics like spike-train irregularity or correlations and network properties, for example the distributions of the numbers of in- and outgoing connections or clustering. Exploiting these relations, we demonstrate that it is possible to estimate structural characteristics of the network from activity data. We also assess higher order correlations of spiking activity in the various networks considered here, and find that their occurrence strongly depends on the network structure. These results provide directions for further theoretical studies on recurrent networks, as well as new ways to interpret spike train recordings from neural circuits.

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Extending stability through hierarchical clusters in Echo State Networks

Cited by 17 publications

References 20 publications

Modular and Hierarchically Modular Organization of Brain Networks

Modular and Hierarchically Modular Organization of Brain Networks

Modular networks of spiking neurons for applications in time-series information processing

The relevance of network micro-structure for neural dynamics

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