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Determining distributed parameters in a neuronal cable model on a tree graph
Author(s) -
Avdonin Sergei,
Bell Jonathan,
Nurtazina Karlygash
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4277
Subject(s) - mathematics , graph , cable theory , tree (set theory) , inverse , boundary value problem , topology (electrical circuits) , mathematical analysis , combinatorics , discrete mathematics , geometry , computer science , telecommunications , cable gland , cable harness
For graph domains without cycles, we show how unknown coefficients and source terms for a parabolic equation can be recovered from the dynamical Neumann‐to‐Dirichlet map associated with the boundary vertices. Through use of a companion wave equation problem, the topology of the tree graph, degree of the vertices, and edge lengths can also be recovered. The motivation for this work comes from a neuronal cable equation defined on the neuron's dendritic tree, and the inverse problem concerns parameter identification of k unknown distributed conductance parameters. Copyright © 2017 John Wiley & Sons, Ltd.