Mean-field approach to evolving spatial networks, with an application to osteocyte network formation
We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or some more abstract internal property that describes something like social tr...
| Main Authors: | , , , |
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| Format: | Journal article |
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American Physical Society
2017
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| _version_ | 1826277400510464000 |
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| author | Taylor-King, J Basanta, D Chapman, S Porter, M |
| author_facet | Taylor-King, J Basanta, D Chapman, S Porter, M |
| author_sort | Taylor-King, J |
| collection | OXFORD |
| description | We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or some more abstract internal property that describes something like social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a “local state degree distribution” (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple continuum model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes but with a lower number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis. |
| first_indexed | 2024-03-06T23:28:20Z |
| format | Journal article |
| id | oxford-uuid:6b2dcba8-49ad-4b46-9466-49fd772dd23c |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:28:20Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:6b2dcba8-49ad-4b46-9466-49fd772dd23c2022-03-26T19:02:03ZMean-field approach to evolving spatial networks, with an application to osteocyte network formationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6b2dcba8-49ad-4b46-9466-49fd772dd23cSymplectic Elements at OxfordAmerican Physical Society2017Taylor-King, JBasanta, DChapman, SPorter, MWe consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or some more abstract internal property that describes something like social trait. Edges between nodes are created and destroyed, and new nodes enter the system. We introduce a “local state degree distribution” (LSDD) as the degree distribution at a particular point in state space. We then make a mean-field assumption and thereby derive an integro-partial differential equation that is satisfied by the LSDD. We perform numerical experiments and find good agreement between solutions of the integro-differential equation and the LSDD from stochastic simulations of the full model. To illustrate our theory, we apply it to a simple continuum model for osteocyte network formation within bones, with a view to understanding changes that may take place during cancer. Our results suggest that increased rates of differentiation lead to higher densities of osteocytes but with a lower number of dendrites. To help provide biological context, we also include an introduction to osteocytes, the formation of osteocyte networks, and the role of osteocytes in bone metastasis. |
| spellingShingle | Taylor-King, J Basanta, D Chapman, S Porter, M Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title | Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title_full | Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title_fullStr | Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title_full_unstemmed | Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title_short | Mean-field approach to evolving spatial networks, with an application to osteocyte network formation |
| title_sort | mean field approach to evolving spatial networks with an application to osteocyte network formation |
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