2019 Joint Mathematics Meetings

Rainer Engelken

Artists

Rainer Engelken

Postdoc in Theoretical Neuroscience

Center for Theoretical Neuroscience, Columbia University

New York, USA

re2365@columbia.edu

https://ctn.zuckermaninstitute.columbia.edu/people/rainer-engelken

Statement

It is fascinating to me how information in the brain is processed by the coordinated interplay of many neurons. In particular, how neural activity patterns are shaped by the wiring diagram known as the connectome, and how changes at this level explain the reorganization of the collective dynamics during learning, triggered my curiosity. I am exploring the chaotic dynamics of neural tissue from a dynamical system perspective. This is rooted in the mathematical field of ergodic theory. As it is hard to visualize and imagine a 1000D entangled attractor living in a 10000D phase space, we sometimes use small networks for illustration and as a more intuitive approach to our scientific questions.

Artworks

Image for entry 'saudade'

saudade

23 x 45 cm

gentrified electrons

2018

Here is a two-dimensional projection of a strange chaotic attractor of the network activity of fifty randomly connected firing-rate neurons. Every state of the network is a point in the fifty-dimensional state space. The two axes are spanning the direction of the largest variance of the chaotic attractor. Grey-values encode the density of states on this two-dimensional slice through the fifty-dimensional state space. The attractor dimensionality indicates that the network activity explores only a small portion of the available fifty-dimensional phase space. Each rate unit has a sigmoidal input-output function and has simple relaxation dynamics. Only through the network interaction complex patterns and chaos can emerge.