47 research outputs found
Greedy low-rank algorithm for spatial connectome regression
Recovering brain connectivity from tract tracing data is an important
computational problem in the neurosciences. Mesoscopic connectome
reconstruction was previously formulated as a structured matrix regression
problem (Harris et al., 2016), but existing techniques do not scale to the
whole-brain setting. The corresponding matrix equation is challenging to solve
due to large scale, ill-conditioning, and a general form that lacks a
convergent splitting. We propose a greedy low-rank algorithm for connectome
reconstruction problem in very high dimensions. The algorithm approximates the
solution by a sequence of rank-one updates which exploit the sparse and
positive definite problem structure. This algorithm was described previously
(Kressner and Sirkovi\'c, 2015) but never implemented for this connectome
problem, leading to a number of challenges. We have had to design judicious
stopping criteria and employ efficient solvers for the three main sub-problems
of the algorithm, including an efficient GPU implementation that alleviates the
main bottleneck for large datasets. The performance of the method is evaluated
on three examples: an artificial "toy" dataset and two whole-cortex instances
using data from the Allen Mouse Brain Connectivity Atlas. We find that the
method is significantly faster than previous methods and that moderate ranks
offer good approximation. This speedup allows for the estimation of
increasingly large-scale connectomes across taxa as these data become available
from tracing experiments. The data and code are available online
Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks
For a broad range single-seed contagion processes acting on generalized
random networks, we derive a unifying analytic expression for the possibility
of global spreading events in a straightforward, physically intuitive fashion.
Our reasoning lays bare a direct mechanical understanding of an archetypal
spreading phenomena that is not evident in circuitous extant mathematical
approaches.Comment: 4 pages, 1 figure, 1 tabl
Exact solutions for social and biological contagion models on mixed directed and undirected, degree-correlated random networks
We derive analytic expressions for the possibility, probability, and expected
size of global spreading events starting from a single infected seed for a
broad collection of contagion processes acting on random networks with both
directed and undirected edges and arbitrary degree-degree correlations. Our
work extends previous theoretical developments for the undirected case, and we
provide numerical support for our findings by investigating an example class of
networks for which we are able to obtain closed-form expressions.Comment: 10 pages, 3 figure