Front propagation and arrival times in networks with application to neurodegenerative diseases
Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2023
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| _version_ | 1826309430928474112 |
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| author | Putra, P Oliveri, H Thompson, T Goriely, A |
| author_facet | Putra, P Oliveri, H Thompson, T Goriely, A |
| author_sort | Putra, P |
| collection | OXFORD |
| description | Many physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher–Kolmogorov–Petrovsky–Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions. |
| first_indexed | 2024-03-07T07:35:33Z |
| format | Journal article |
| id | oxford-uuid:d9491c03-3a82-4dce-ab50-bbe3941dcf55 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:35:33Z |
| publishDate | 2023 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:d9491c03-3a82-4dce-ab50-bbe3941dcf552023-02-28T11:43:17ZFront propagation and arrival times in networks with application to neurodegenerative diseasesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d9491c03-3a82-4dce-ab50-bbe3941dcf55EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2023Putra, POliveri, HThompson, TGoriely, AMany physical, epidemiological, or physiological dynamical processes on networks support front-like propagation, where an initial localized perturbation grows and systematically invades all nodes in the network. A key problem is then to extract estimates for the dynamics. In particular, if a single node is seeded at a small concentration, when will other nodes reach the same initial concentration? Here, motivated by the study of toxic protein propagation in neurodegenerative diseases, we present and compare three different estimates for the arrival time in order of increasing analytical complexity: the linear arrival time, obtained by linearizing the underlying dynamical system; the Lambert time, obtained by considering the interaction of pairs of nodes; and the nonlinear arrival time, obtained by asymptotic techniques. We use the classic Fisher–Kolmogorov–Petrovsky–Piskunov equation as a paradigm for the dynamics and show that each method provides different insights but consistent time estimates. Further, we show that the nonlinear asymptotic method also gives an approximate solution, valid in the entire domain, and the correct ordering of arrival regions over large regions of parameters and initial conditions. |
| spellingShingle | Putra, P Oliveri, H Thompson, T Goriely, A Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title | Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title_full | Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title_fullStr | Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title_full_unstemmed | Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title_short | Front propagation and arrival times in networks with application to neurodegenerative diseases |
| title_sort | front propagation and arrival times in networks with application to neurodegenerative diseases |
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