Topic: Traveling waves

Predicting traveling waves: a new mathematical technique to link the structure of a network to the specific patterns of neural activity

Exact coherent structures and transition to turbulence in a confined active nematic

Active matter describes a class of systems that are maintained far from equilibrium by driving forces acting on the constituent particles. Here I will focus on confined active nematics, which exhibit especially rich flow behavior, ranging from structured patterns in space and time to disordered turbulent flows. To understand this behavior, I will take a deterministic dynamical systems approach, beginning with the hydrodynamic equations for the active nematic. This approach reveals that the infinite-dimensional phase space of all possible flow configurations is populated by Exact Coherent Structures (ECS), which are exact solutions of the hydrodynamic equations with distinct and regular spatiotemporal structure; examples include unstable equilibria, periodic orbits, and traveling waves. The ECS are connected by dynamical pathways called invariant manifolds. The main hypothesis in this approach is that turbulence corresponds to a trajectory meandering in the phase space, transitioning between ECS by traveling on the invariant manifolds. Similar approaches have been successful in characterizing high Reynolds number turbulence of passive fluids. Here, I will present the first systematic study of active nematic ECS and their invariant manifolds and discuss their role in characterizing the phenomenon of active turbulence.

Revealing the neural basis of human memory with direct recordings of place and grid cells and traveling waves

The ability to remember spatial environments is critical for everyday life. In this talk, I will discuss my lab’s findings on how the human brain supports spatial memory and navigation based on our experiments with direct brain recordings from neurosurgical patients performing virtual-reality spatial memory tasks. I will show that humans have a network of neurons that represent where we are located and trying to go. This network includes some cell types that are similar to those seen in animals, such as place and grid cells, as well as others that have not been seen before in animals, such as anchor and spatial-target cells. I also will explore the role of network oscillations in human memory, where humans again show several distinctive patterns compared to animals. Whereas rodents generally show a hippocampal oscillation at ~8Hz, humans have two separate hippocampal oscillations, at low and high frequencies, which support memory and navigation, respectively. Finally, I will show that neural oscillations in humans are traveling waves, propagating across the cortex, to coordinate the timing of neuronal activity across regions, which is another property not seen in animals. A theme from this work is that in terms of navigation and memory the human brain has novel characteristics compared with animals, which helps explain our rich behavioural abilities and has implications for treating disease and neurological disorders.