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A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models. / Wybo, Willem A. M.; Boccalini, Daniele; Torben-Nielsen, Ben; Gewaltig, Marc-Oliver.

In: Neural Computation, Vol. 27, No. 12, 12.2015, p. 2587-2622.

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Author

Wybo, Willem A. M. ; Boccalini, Daniele ; Torben-Nielsen, Ben ; Gewaltig, Marc-Oliver. / A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models. In: Neural Computation. 2015 ; Vol. 27, No. 12. pp. 2587-2622.

Bibtex

@article{c7351316fd1940efb8609093b3fa13a2,
title = "A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models",
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.",
author = "Wybo, {Willem A. M.} and Daniele Boccalini and Ben Torben-Nielsen and Marc-Oliver Gewaltig",
year = "2015",
month = dec,
doi = "10.1162/NECO_a_00788",
language = "English",
volume = "27",
pages = "2587--2622",
journal = "Neural Computation",
issn = "0899-7667",
publisher = "MIT Press Journals",
number = "12",

}

RIS

TY - JOUR

T1 - A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models

AU - Wybo, Willem A. M.

AU - Boccalini, Daniele

AU - Torben-Nielsen, Ben

AU - Gewaltig, Marc-Oliver

PY - 2015/12

Y1 - 2015/12

N2 - 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.

AB - 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.

U2 - 10.1162/NECO_a_00788

DO - 10.1162/NECO_a_00788

M3 - Article

C2 - 26496043

VL - 27

SP - 2587

EP - 2622

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 12

ER -