From synaptic interactions to collective dynamics in random neuronal networks models: critical role of eigenvectors and transient behavior

Understand

The study of neuronal interactions is currently at the center of several big collaborative neuroscience projects (including the Human Connectome Project, the Blue Brain Project, the Brainome, etc.) which attempt to obtain a detailed map of the entire brain.

• Under certain constraints, mathematical theory can advance predictions of the expected neural dynamics based solely on the statistical properties of the synaptic interaction matrix.
• This work explores the application of free random variables to the study of large synaptic interaction matrices.
• Besides recovering in a straightforward way known results on eigenspectra in types of models of neural networks proposed by Rajan and Abbott, we extend them to heavy-tailed distributions of interactions.