Developing structural constraints on connectivity for biologically embedded neural networks

Partzsch, Johannes; Schüffny, René

doi:10.1007/s00422-012-0489-3

Cited by 7 publications

(19 citation statements)

References 30 publications

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“…However, few models have taken the small-world structure of neural ensembles into consideration. The recently developed methods have provided powerful tools for studying the functional connectivity property of brain networks (Sporns and Zwi 2004;Eldawlatly et al 2009;Partzsch and Schüffny 2012;Leergaard et al 2012). Most of them demonstrated that biological networks presented small-world properties, observed not only in large neural networks with each node representing a cortical area (Sporns and Zwi 2004;Bassett and Bullmore 2006;Kaiser 2008), but also in the local neural networks recorded with microelectrode arrays (Yu et al 2008;Gerhard et al 2011).…”

Section: Introductionmentioning

confidence: 99%

A small-world-based population encoding model of the primary visual cortex

et al. 2015

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A wide range of evidence has shown that information encoding performed by the visual cortex involves complex activities of neuronal populations. However, the effects of the neuronal connectivity structure on the population's encoding performance remain poorly understood. In this paper, a small-world-based population encoding model of the primary visual cortex (V1) is established on the basis of the generalized linear model (GLM) to describe the computation of the neuronal population. The model mainly consists of three sets of filters, including a spatiotemporal stimulus filter, a post-spike history filter, and a set of coupled filters with the coupling neurons organizing as a small-world network. The parameters of the model were fitted with neuronal data of the rat V1 recorded with a micro-electrode array. Compared to the traditional GLM, without considering the small-world structure of the neuronal population, the proposed model was proved to produce more accurate spiking response to grating stimuli and enhance the capability of the neuronal population to carry information. The comparison results proved the validity of the proposed model and further suggest the role of small-world structure in the encoding performance of local populations in V1, which provides new insights for understanding encoding mechanisms of a small scale population in visual system.

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Section: Introductionmentioning

confidence: 99%

A small-world-based population encoding model of the primary visual cortex

et al. 2015

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“…For each network, there is an empirical discrete function P = P c ( B ), called Rent characteristic 6, 7 , which directly relates the average number of nodes B for a topological partition of the network to the average number of edges P connecting different modules of the partition. We are interested in determining Region I where Rent characteristic fits well to Rent’s rule.…”

Section: Validating Rent’s Rulementioning

confidence: 99%

“…It relates the average number of external connections or pins on a module and the average number of blocks within the module for partitions of computer logic graphs 2 . Besides its extensive application in Circuit Design at all scales, from SSI to GSI passing through VLSI, Rent’s rule has been used to study the interconnection complexity of biological networks 3–6 , as well some benchmark models and technological networks 7–9 . At origin, given a logic circuit, the relationship between the average number of blocks or cells B in a module in a given partition and the average number of pins P connecting each module with the others iswhere k is the average number of pins per logic block (also called Rent coefficient ) and p is the Rent exponent describing proportionality in a log-log scale.…”

Section: Introductionmentioning

confidence: 99%

“…General models for VLSI circuits and neural networks actually consist of hypergraphs where an edge can connect more than two nodes 6, 24 . Special versions of partitioning-based algorithms, such as those used in the partitioning tool hMetis 25 , have been developed for hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

“…However, even if the considerations by Partzsch et al . 6 should be taken into account, we transformed hypergraphs into graphs in order to unify the framework. The scaling curves obtained via hMetis show a very different behavior of those obtained via box counting since Regions II and III are very small if present.…”

Section: Introductionmentioning

confidence: 99%

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A method for validating Rent’s rule for technological and biological networks

Cuesta

Sequeiros

Rojo

2017

Sci Rep

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Rent’s rule is empirical power law introduced in an effort to describe and optimize the wiring complexity of computer logic graphs. It is known that brain and neuronal networks also obey Rent’s rule, which is consistent with the idea that wiring costs play a fundamental role in brain evolution and development. Here we propose a method to validate this power law for a certain range of network partitions. This method is based on the bifurcation phenomenon that appears when the network is subjected to random alterations preserving its degree distribution. It has been tested on a set of VLSI circuits and real networks, including biological and technological ones. We also analyzed the effect of different types of random alterations on the Rentian scaling in order to test the influence of the degree distribution. There are network architectures quite sensitive to these randomization procedures with significant increases in the values of the Rent exponents.

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Effect of the small-world structure on encoding performance in the primary visual cortex: an electrophysiological and modeling analysis

2015

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The biological networks have been widely reported to present small-world properties. However, the effects of small-world network structure on population's encoding performance remain poorly understood. To address this issue, we applied a small world-based framework to quantify and analyze the response dynamics of cell assemblies recorded from rat primary visual cortex, and further established a population encoding model based on small world-based generalized linear model (SW-GLM). The electrophysiological experimental results show that the small world-based population responses to different topological shapes present significant variation (t test, p < 0.01; effect size: Hedge's g > 0.8), while no significant variation was found for control networks without considering their spatial connectivity (t test, p > 0.05; effect size: Hedge's g < 0.5). Furthermore, the numerical experimental results show that the predicted response under SW-GLM is more accurate and reliable compared to the control model without small-world structure, and the decoding performance is also improved about 10 % by taking the small-world structure into account. The above results suggest the important role of the small-world neural structure in encoding visual information for the neural population by providing electrophysiological and theoretical evidence, respectively. The study helps greatly to well understand the population encoding mechanisms of visual cortex.

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Developing structural constraints on connectivity for biologically embedded neural networks

Cited by 7 publications

References 30 publications

A small-world-based population encoding model of the primary visual cortex

A small-world-based population encoding model of the primary visual cortex

A method for validating Rent’s rule for technological and biological networks

Effect of the small-world structure on encoding performance in the primary visual cortex: an electrophysiological and modeling analysis

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