Topic: non-linear dynamics

A fundamental problem in systems neuroscience is understanding how the brain learns the non-linear dynamics of the complex world and identifies the environment's state. Data-driven learning in such high-dimensional spaces requires lifting the curse of dimensionality. One way of reducing dimensionality relies on extracting from observed trajectories the underlying topological skeleton, i.e., fixed points connected by invariant manifolds. Thus, online extraction of fixed points from input trajectories is an important task. Whereas Dynamic Mode Decomposition (DMD) provides a framework to calculat

The brain needs to process high-dimensional sensory information in order to control the non-linear dynamics of body movements. One view posits that it does so modularly with different brain regions solving specific and distinct objectives that can be studied quasi-independently (e.g. visual classification in the ventral visual stream or path integration in entorhinal-hippocampal circuit). However, it is unclear how these modular abstract objectives would emerge and how they give rise to coherent behavior executed through concrete actions. An alternative paradigm proposes that the brain holisti