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Coordinated motion of active filaments on spherical surfaces
Filaments (slender, microscopic elastic bodies) are prevalent in biological and industrial settings. In the biological case, the filaments are often active, in that they are driven internally by motor proteins, with the prime examples being cilia and flagella. For cilia in particular, which can appear in dense arrays, their resulting motions are coupled through the surrounding fluid, as well as through surfaces to which they are attached. In this talk, I present numerical simulations exploring the coordinated motion of active filaments and how it depends on the driving force, density of filaments, as well as the attached surface. In particular, we find that when the surface is spherical, its topology introduces local defects in coordinated motion which can then feedback and alter the global state. This is particularly true when the surface is not held fixed and is free to move in the surrounding fluid. These simulations take advantage of a computational framework we developed for fully 3D filament motion that combines unit quaternions, implicit geometric time integration, quasi-Newton methods, and fast, matrix-free methods for hydrodynamic interactions and it will also be presented.
Reading out responses of large neural population with minimal information loss
Classic studies show that in many species – from leech and cricket to primate – responses of neural populations can be quite successfully read out using a measure neural population activity termed the population vector. However, despite its successes, detailed analyses have shown that the standard population vector discards substantial amounts of information contained in the responses of a neural population, and so is unlikely to accurately describe how signal communication between parts of the nervous system. I will describe recent theoretical results showing how to modify the population vector expression in order to read out neural responses without information loss, ideally. These results make it possible to quantify the contribution of weakly tuned neurons to perception. I will also discuss numerical methods that can be used to minimize information loss when reading out responses of large neural populations.