On strongly connected networks with excitable-refractory dynamics and delayed coupling
<p>We consider a directed graph model for the human brain’s neural architecture that is based on small scale, directed, strongly connected sub-graphs (SCGs) of neurons, that are connected together by a sparser mesoscopic network.We assume transmission delays within neuron-to-neuron stimulation...
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| Format: | Journal article |
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Royal Society
2017
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| _version_ | 1797088500688879616 |
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| author | Lee, T Grindrod, P |
| author_facet | Lee, T Grindrod, P |
| author_sort | Lee, T |
| collection | OXFORD |
| description | <p>We consider a directed graph model for the human brain’s neural architecture that is based on small scale, directed, strongly connected sub-graphs (SCGs) of neurons, that are connected together by a sparser mesoscopic network.We assume transmission delays within neuron-to-neuron stimulation, and that individual neurons have an excitable-refractory dynamic, with single firing “spikes” occurring on a much faster time scale than that of the transmission delays. We demonstrate numerically that the SCGs typically have attractors that are equivalent to continual winding maps over relatively low dimensional tori, thus representing a limit on the range of distinct behaviour.</p> <br/> <p>For a discrete formulation, we conduct a large scale survey of SCGs of varying size, but with the same local structure. We demonstrate that there may be benefits (increased processing capacity and efficiency) in brains having evolved to have a larger number of small irreducible sub-graphs, rather than few, large irreducible sub-graphs.</p> <br/> <p>The network of SCGs could be thought of as an architecture that has evolved to create decisions in the light of partial or early incoming information. Hence the applicability of the proposed paradigm to underpinning human cognition.</p> |
| first_indexed | 2024-03-07T02:51:00Z |
| format | Journal article |
| id | oxford-uuid:adaccb25-151f-4bb3-aa1d-7dd9da161c39 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T02:51:00Z |
| publishDate | 2017 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:adaccb25-151f-4bb3-aa1d-7dd9da161c392022-03-27T03:37:20ZOn strongly connected networks with excitable-refractory dynamics and delayed couplingJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:adaccb25-151f-4bb3-aa1d-7dd9da161c39Irreducible networksbrain sciencediscrete dynamical systemsSymplectic Elements at OxfordRoyal Society2017Lee, TGrindrod, P<p>We consider a directed graph model for the human brain’s neural architecture that is based on small scale, directed, strongly connected sub-graphs (SCGs) of neurons, that are connected together by a sparser mesoscopic network.We assume transmission delays within neuron-to-neuron stimulation, and that individual neurons have an excitable-refractory dynamic, with single firing “spikes” occurring on a much faster time scale than that of the transmission delays. We demonstrate numerically that the SCGs typically have attractors that are equivalent to continual winding maps over relatively low dimensional tori, thus representing a limit on the range of distinct behaviour.</p> <br/> <p>For a discrete formulation, we conduct a large scale survey of SCGs of varying size, but with the same local structure. We demonstrate that there may be benefits (increased processing capacity and efficiency) in brains having evolved to have a larger number of small irreducible sub-graphs, rather than few, large irreducible sub-graphs.</p> <br/> <p>The network of SCGs could be thought of as an architecture that has evolved to create decisions in the light of partial or early incoming information. Hence the applicability of the proposed paradigm to underpinning human cognition.</p> |
| spellingShingle | Irreducible networks brain science discrete dynamical systems Lee, T Grindrod, P On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title | On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title_full | On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title_fullStr | On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title_full_unstemmed | On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title_short | On strongly connected networks with excitable-refractory dynamics and delayed coupling |
| title_sort | on strongly connected networks with excitable refractory dynamics and delayed coupling |
| topic | Irreducible networks brain science discrete dynamical systems |
| work_keys_str_mv | AT leet onstronglyconnectednetworkswithexcitablerefractorydynamicsanddelayedcoupling AT grindrodp onstronglyconnectednetworkswithexcitablerefractorydynamicsanddelayedcoupling |