Simulating Structural Plasticity of the Brain more Scalable than Expected

TL;DR

This paper refines the understanding of a scalable algorithm for simulating brain structural plasticity, demonstrating that its runtime complexity can be improved from $O(n \, \log^2 n)$ to $O(n \, \log n)$ with careful analysis.

Contribution

The paper provides a rigorous proof that the algorithm's runtime complexity is actually $O(n \, \log n)$, improving previous results.

Findings

Runtime complexity improved from $O(n \log^2 n)$ to $O(n \log n)$

Algorithm remains scalable for up to one billion neurons

Careful analysis and proof enhance understanding of the algorithm's efficiency

Abstract

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 $O(n \log n)$.