Analysis of hippocampal local field potentials by diffusion mapped delay coordinates

Spatial navigation through novel spaces and to known goal locations recruits multiple integrated structures in the mammalian brain. Within this extended network, the hippocampus enables formation and retrieval of cognitive spatial maps and contributes to decision making at choice points. Exploration and navigation to known goal locations produce synchronous activity of hippocampal neurons resulting in rhythmic oscillation events in local networks. Power of specific oscillatory frequencies and numbers of these events recorded in local field potentials correlate with distinct cognitive aspects of spatial navigation. Typically, oscillatory power in brain circuits is analyzed with Fourier transforms or short-time Fourier methods, which involve assumptions about the signal that are likely not true and fail to succinctly capture potentially informative features. To avoid such assumptions, we applied a method that combines manifold discovery techniques with dynamical systems theory, namely diffusion maps and Takens' time-delay embedding theory, that avoids limitations seen in traditional methods. This method, called diffusion mapped delay coordinates (DMDC), when applied to hippocampal signals recorded from juvenile rats freely navigating a Y-maze, replicates some outcomes seen with standard approaches and identifies age differences in dynamic states that traditional analyses are unable to detect. Thus, DMDC may serve as a suitable complement to more traditional analyses of LFPs recorded from behaving subjects that may enhance information yield.

Energy flux fluctuations in a finite volume of turbulent flow

The flux of turbulent kinetic energy from large to small spatial scales is measured in a small domain of varying size . The probability distribution function of the flux is obtained using a time-local version of Kolmogorov four-fifths law. The measurements, made at a moderate Reynolds number, show frequent events where the flux is backscattered from small to large scales, their frequency increasing as is decreased. The observations are corroborated by a numerical simulation based on the motion of many particles and on an explicit form of the eddy damping.

Where surface physics and fluid dynamics meet: Rupture of an amphiphile layer by fluid flow

We investigate the fluctuating pattern created by a jet of fluid impingent upon an amphiphile-covered surface. This microscopically thin layer is initially covered with 50 microm floating particles so that the layer can be visualized. A vertical jet of water located below the surface and directed upward drives a hole in this layer. The hole is particle-free and is surrounded by the particle-laden amphiphile region. The jet ruptures the amphiphile layer creating a particle-free region that is surrounded by the particle-covered surface. The aim of the experiment is to understand the (fluctuating) shape of the ramified interface between the particle-laden and particle-free regions.

Turbulence in a free surface

We report an experimental and numerical study of turbulent fluid motion in a free surface. The flow is realized experimentally on the surface of a tank filled with water stirred by a vertically oscillating grid positioned well below the surface. The effect of surface waves appears to be negligible so that the flow can numerically be realized with a flat surface and stress-free boundary conditions. The surface flow is unconventional in that it is not incompressible and neither energy nor enstrophy are conserved. Nevertheless, according to both experiment and numerical simulation, the second order structure function S2(R) scales essentially as for a three-dimensional system. However, the surface flow seems to be more intermittent.

Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding

Hysteresis has been observed in a study of the transition between laminar flow and vortex shedding in a quasi-two-dimensional system. The system is a vertical, rapidly flowing soap film which is penetrated by a rod oriented perpendicular to the film plane. Our experiments show that the transition from laminar flow to a periodic von Karman vortex street can be hysteretic, i.e., vortices can survive at velocities lower than the velocity needed to generate them.