1,612 research outputs found
Cascades of energy and helicity in the GOY shell model of turbulence
The effect of extreme hyperviscous damping, is studied
numerically in the GOY shell model of turbulence. It has resently been
demonstrated [Leveque and She, Phys. Rev. Lett, 75,2690 (1995)] that the
inertial range scaling in the GOY model is non-universal and depending on the
viscous damping. The present study shows that the deviation from Kolmogorov
scaling is due to the cascade of the second inviscid invariant. This invariant
is non-positive definite and in this sense analogous to the helicity of 3D
turbulent flow.Comment: 4 pages, 2 figure
A note on dissipation in helical turbulence
In helical turbulence a linear cascade of helicity accompanying the energy
cascade has been suggested. Since energy and helicity have different
dimensionality we suggest the existence of a characteristic inner scale,
, for helicity dissipation in a regime of hydrodynamic fully
developed turbulence and estimate it on dimensional grounds. This scale is
always larger than the Kolmogorov scale, , and their ratio vanishes in the high Reynolds number limit, so the flow will always be
helicity free in the small scales.Comment: 2 pages, submitted to Phys. Fluid
Multi-class oscillating systems of interacting neurons
We consider multi-class systems of interacting nonlinear Hawkes processes
modeling several large families of neurons and study their mean field limits.
As the total number of neurons goes to infinity we prove that the evolution
within each class can be described by a nonlinear limit differential equation
driven by a Poisson random measure, and state associated central limit
theorems. We study situations in which the limit system exhibits oscillatory
behavior, and relate the results to certain piecewise deterministic Markov
processes and their diffusion approximations.Comment: 6 figure
Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods
Parameter estimation in multidimensional diffusion models with only one
coordinate observed is highly relevant in many biological applications, but a
statistically difficult problem. In neuroscience, the membrane potential
evolution in single neurons can be measured at high frequency, but biophysical
realistic models have to include the unobserved dynamics of ion channels. One
such model is the stochastic Morris-Lecar model, defined by a nonlinear
two-dimensional stochastic differential equation. The coordinates are coupled,
that is, the unobserved coordinate is nonautonomous, the model exhibits
oscillations to mimic the spiking behavior, which means it is not of
gradient-type, and the measurement noise from intracellular recordings is
typically negligible. Therefore, the hidden Markov model framework is
degenerate, and available methods break down. The main contributions of this
paper are an approach to estimate in this ill-posed situation and nonasymptotic
convergence results for the method. Specifically, we propose a sequential Monte
Carlo particle filter algorithm to impute the unobserved coordinate, and then
estimate parameters maximizing a pseudo-likelihood through a stochastic version
of the Expectation-Maximization algorithm. It turns out that even the rate
scaling parameter governing the opening and closing of ion channels of the
unobserved coordinate can be reasonably estimated. An experimental data set of
intracellular recordings of the membrane potential of a spinal motoneuron of a
red-eared turtle is analyzed, and the performance is further evaluated in a
simulation study.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS729 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics
Here we present a simple stochastic threshold model consisting of a
deterministic slowly decaying term and a fast stochastic noise term. The
process shows a pseudo-resonance, in the sense that for small and large
intensities of the noise the signal is irregular and the distribution of
threshold crossings is broad, while for a tuned intermediate value of noise
intensity the signal becomes quasi-periodic and the distribution of threshold
crossings is narrow. The mechanism captured by the model might be relevant for
explaining apparent quasi-periodicity of observed climatic variations where no
internal or external periodicities can be identified.Comment: 8 pages, 4 figures, to appear in Stochastics and Dynamic
The space-clamped Hodgkin-Huxley system with random synaptic input: inhibition of spiking by weak noise and analysis with moment equations
We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated
by synaptic excitation and inhibition with conductances represented by
Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model
system obtained by an Euler method, it is found that with excitation only there
is a critical value of the steady state excitatory conductance for repetitive
spiking without noise and for values of the conductance near the critical value
small noise has a powerfully inhibitory effect. For a given level of inhibition
there is also a critical value of the steady state excitatory conductance for
repetitive firing and it is demonstrated that noise either in the excitatory or
inhibitory processes or both can powerfully inhibit spiking. Furthermore, near
the critical value, inverse stochastic resonance was observed when noise was
present only in the inhibitory input process.
The system of 27 coupled deterministic differential equations for the
approximate first and second order moments of the 6-dimensional model is
derived. The moment differential equations are solved using Runge-Kutta methods
and the solutions are compared with the results obtained by simulation for
various sets of parameters including some with conductances obtained by
experiment on pyramidal cells of rat prefrontal cortex. The mean and variance
obtained from simulation are in good agreement when there is spiking induced by
strong stimulation and relatively small noise or when the voltage is
fluctuating at subthreshold levels. In the occasional spike mode sometimes
exhibited by spinal motoneurons and cortical pyramidal cells the assunptions
underlying the moment equation approach are not satisfied
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