The Mathematics of Neural Networks

Challenge

New technologies are greatly expanding our ability to map neural systems. Reconstructions of the synaptic connections between neurons and large-scale recordings of spikes are now able to map both the structure and function of hundreds to thousands of cells. For decades, it was only possible to study the activity of a handful of cells in a living, functional neural circuit, but now, it is rapidly becoming possible to study activity in massive ensembles of cells during active sensory perception and sleep. With these new technologies, neuroscientists can study how the collective activity of hundreds or thousands of cells creates sensory and cognitive computations. The challenges posed by these increasingly large and complex datasets requires new and rigorous mathematical approaches.

Aim

Led by Lyle Muller, PhD, Assistant Professor in the Department of Mathematics at Western University, the team aimed to develop new approaches in discrete mathematics to understand neural systems at a new theoretical level. These developments have promise to shed light on fundamental questions like the codes used by neurons in sensory and cognitive computations – where the team is using techniques from symmetries, algebraic geometry, and Galois theory to understand patterns in spike times – to important translational applications, where new techniques in processing discrete signals and analyzing neural activity patterns are providing insight into neural recordings collected at the Robarts Research Institute and London Health Sciences Centre.

Impact

Highlights of successes include:

  • Use of stem cell technologies
  • A new understanding of artificial intelligence
  • Fields Lab for Network Science
  • Building international partnerships

Read more about our progress here.