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

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        NECO_04_15_2360_PDF.pdf (PDF, 1Mb)
        Author
        Wybo, Willem A. M.
        Boccalini, Daniele
        Torben-Nielsen, Ben
        Gewaltig, Marc-Oliver
        Attention
        2299/16767
        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.
        Publication date
        2015-12
        Published in
        Neural Computation
        Published version
        https://doi.org/10.1162/NECO_a_00788
        Other links
        http://hdl.handle.net/2299/16767
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