The neural network in the brain is not hard-wired. Even in the mature brain, new connections between neurons are formed and existing ones are deleted, which is called structural plasticity. The dynamics of the connectome is key to understanding how learning, memory, and healing after lesions such as stroke work. However, with current experimental techniques even the creation of an exact static connectivity map, which is required for various brain simulations, is very difficult. One alternative is to use simulation based on network models to predict the evolution of synapses between neurons, based on their specified activity targets. This is particularly useful as experimental measurements of the spiking frequency of neurons are more easily accessible and reliable than biological connectivity data. The Model of Structural Plasticity (MSP) by Butz et al. is an example of this approach. However, to predict which neurons connect to each other, the current MSP model computes probabilities for all pairs of neurons, resulting in a complexity O(n2). To enable large-scale simulations with millions of neurons and beyond, this quadratic term is prohibitive. Inspired by hierarchical methods for solving n-body problems in particle physics, we propose a scalable approximation algorithm for MSP that reduces the complexity to O(n log2 n) without any notable impact on the quality of the results. An MPI-based parallel implementation of our scalable algorithm can simulate neuron counts that exceed the state of the art by two orders of magnitude.
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