A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models

Willem A. M. Wybo, Daniele Boccalini, Ben Torben-Nielsen, Marc-Oliver Gewaltig

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
83 Downloads (Pure)

Abstract

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O (n) with the number n of inputs locations, contrary to the previously reported O (n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.

Original languageEnglish
Pages (from-to)2587-2622
JournalNeural Computation
Volume27
Issue number12
Early online date23 Oct 2015
DOIs
Publication statusPublished - Dec 2015

Fingerprint

Dive into the research topics of 'A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models'. Together they form a unique fingerprint.

Cite this