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Here, we propose to realise the sum-over-trips framework by a length-priority method.
The pyramidal cell's convergence shows very discontinuous behaviour (Fig. 5F), particularly in the length-priority method.
The savings in space already allow the length-priority method to scale better than the four-classes algorithm.
We then developed the length-priority method, in which trips are constructed purely in length order rather than in classes.
Fig. 5 Convergence of the four-classes and length-priority methods for a number of dendritic morphologies.
Then, a length-priority ordering of the trips using Eppstein's algorithm [23] for finding the k shortest trips on a graph is proposed.
This indicates that neither the length-priority or the four-classes methods are good heuristics for ordering terms in the Green's function.
Instead of a length-ordered series solution as provided by the length-priority approach, the Green's function (5) can be constructed using a stochastic algorithm.
The tangential cell's convergence, shown in Fig. 5G, shows almost identical errors for both the four-classes and the length-priority methods, indicating that trips are generated in a similar order regardless of method.
Our results clearly indicate that the convergence of the realisation of the sum-over-trips framework by either the four-classes or the length-priority method strongly depends on a dendritic geometry.
Two profiles of the response function obtained by the length-priority, the Monte-Carlo and the matrix methods are shown in Fig. 3 and compared to a numerical simulation computed by the software package NEURON [26].
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