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Neurons are spatially extended structures that receive and process inputs on their dendrites. It is generally accepted that neuronal computations arise from the active integration of synaptic inputs along a dendrite between the input location and the location of spike generation in the axon initial segment. However, many application such as simulations of… (More)

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs, and when the inputs are restricted to a spatially discrete set of points, the Green's function (GF) formalism can be rewritten to scale as O(n) with the number n of inputs locations, contrarily to the previously reported O(n 2)… (More)

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))… (More)

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