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Structural plasticity of the brain describes the creation of new and the deletion of old synapses over time. Rinke et al. (JPDC 2018) introduced a scalable algorithm that simulates structural plasticity for up to one billion neurons on current hardware using a variant of the Barnes–Hut algorithm. They demonstrate good scalability and prove a runtime complexity of O (n log 2 ⁡ n). In this comment paper, we show that with careful consideration of the algorithm and a rigorous proof, the theoretical runtime can even be classified as O (n log ⁡ n). • Improved serial runtime bound for the adapted Barnes–Hut algorithm to Θ(n*log(n)). • Improved the parallel runtime bound to Θ(n/p*log(n)+p). • Mathematical justification that the given runtime bound is sharp. [ABSTRACT FROM AUTHOR]

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 network models to simulate 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 and van Ooyen 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 ( n 2 ) . 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 log 2 n ) without any notable impact on the quality of the results. We show that an MPI-based parallel implementation of our scalable algorithm can simulate the structural plasticity of up to 1 0 9 neurons—four orders of magnitude more than the naïve O ( n 2 ) version. [ABSTRACT FROM AUTHOR]