269 research outputs found
Neural activity classification with machine learning models trained on interspike interval series data
The flow of information through the brain is reflected by the activity
patterns of neural cells. Indeed, these firing patterns are widely used as
input data to predictive models that relate stimuli and animal behavior to the
activity of a population of neurons. However, relatively little attention was
paid to single neuron spike trains as predictors of cell or network properties
in the brain. In this work, we introduce an approach to neuronal spike train
data mining which enables effective classification and clustering of neuron
types and network activity states based on single-cell spiking patterns. This
approach is centered around applying state-of-the-art time series
classification/clustering methods to sequences of interspike intervals recorded
from single neurons. We demonstrate good performance of these methods in tasks
involving classification of neuron type (e.g. excitatory vs. inhibitory cells)
and/or neural circuit activity state (e.g. awake vs. REM sleep vs. nonREM sleep
states) on an open-access cortical spiking activity dataset
Hyperbolic Magnetic Billiards on Surfaces of Constant Curvature
We consider classical billiards on surfaces of constant curvature, where the
charged billiard ball is exposed to a homogeneous, stationary magnetic field
perpendicular to the surface.
We establish sufficient conditions for hyperbolicity of the billiard
dynamics, and give lower estimation for the Lyapunov exponent. This extends our
recent results for non-magnetic billiards on surfaces of constant curvature.
Using these conditions, we construct large classes of magnetic billiard tables
with positive Lyapunov exponents on the plane, on the sphere and on the
hyperbolic plane.Comment: 25 pages, 12 ps figure
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