261 research outputs found
Phase locking below rate threshold in noisy model neurons
The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
Neuron dynamics in the presence of 1/f noise
Interest in understanding the interplay between noise and the response of a
non-linear device cuts across disciplinary boundaries. It is as relevant for
unmasking the dynamics of neurons in noisy environments as it is for designing
reliable nanoscale logic circuit elements and sensors. Most studies of noise in
non-linear devices are limited to either time-correlated noise with a
Lorentzian spectrum (of which the white noise is a limiting case) or just white
noise. We use analytical theory and numerical simulations to study the impact
of the more ubiquitous "natural" noise with a 1/f frequency spectrum.
Specifically, we study the impact of the 1/f noise on a leaky integrate and
fire model of a neuron. The impact of noise is considered on two quantities of
interest to neuron function: The spike count Fano factor and the speed of
neuron response to a small step-like stimulus. For the perfect (non-leaky)
integrate and fire model, we show that the Fano factor can be expressed as an
integral over noise spectrum weighted by a (low pass) filter function. This
result elucidates the connection between low frequency noise and disorder in
neuron dynamics. We compare our results to experimental data of single neurons
in vivo, and show how the 1/f noise model provides much better agreement than
the usual approximations based on Lorentzian noise. The low frequency noise,
however, complicates the case for information coding scheme based on interspike
intervals by introducing variability in the neuron response time. On a positive
note, the neuron response time to a step stimulus is, remarkably, nearly
optimal in the presence of 1/f noise. An explanation of this effect elucidates
how the brain can take advantage of noise to prime a subset of the neurons to
respond almost instantly to sudden stimuli.Comment: Phys. Rev. E in pres
On the simulation of nonlinear bidimensional spiking neuron models
Bidimensional spiking models currently gather a lot of attention for their
simplicity and their ability to reproduce various spiking patterns of cortical
neurons, and are particularly used for large network simulations. These models
describe the dynamics of the membrane potential by a nonlinear differential
equation that blows up in finite time, coupled to a second equation for
adaptation. Spikes are emitted when the membrane potential blows up or reaches
a cutoff value. The precise simulation of the spike times and of the adaptation
variable is critical for it governs the spike pattern produced, and is hard to
compute accurately because of the exploding nature of the system at the spike
times. We thoroughly study the precision of fixed time-step integration schemes
for this type of models and demonstrate that these methods produce systematic
errors that are unbounded, as the cutoff value is increased, in the evaluation
of the two crucial quantities: the spike time and the value of the adaptation
variable at this time. Precise evaluation of these quantities therefore involve
very small time steps and long simulation times. In order to achieve a fixed
absolute precision in a reasonable computational time, we propose here a new
algorithm to simulate these systems based on a variable integration step method
that either integrates the original ordinary differential equation or the
equation of the orbits in the phase plane, and compare this algorithm with
fixed time-step Euler scheme and other more accurate simulation algorithms
An analytical approach to initiation of propagating fronts
We consider the problem of initiation of a propagating wave in a
one-dimensional excitable fibre. In the Zeldovich-Frank-Kamenetsky equation,
a.k.a. Nagumo equation, the key role is played by the "critical nucleus''
solution whose stable manifold is the threshold surface separating initial
conditions leading to initiation of propagation and to decay. Approximation of
this manifold by its tangent linear space yields an analytical criterion of
initiation which is in a good agreement with direct numerical simulations.Comment: 4 pages, 2 figures, submitted to Phys Rev Letter
Numerical Solution of Differential Equations by the Parker-Sochacki Method
A tutorial is presented which demonstrates the theory and usage of the
Parker-Sochacki method of numerically solving systems of differential
equations. Solutions are demonstrated for the case of projectile motion in air,
and for the classical Newtonian N-body problem with mutual gravitational
attraction.Comment: Added in July 2010: This tutorial has been posted since 1998 on a
university web site, but has now been cited and praised in one or more
refereed journals. I am therefore submitting it to the Cornell arXiv so that
it may be read in response to its citations. See "Spiking neural network
simulation: numerical integration with the Parker-Sochacki method:" J. Comput
Neurosci, Robert D. Stewart & Wyeth Bair and
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2717378
A simple self-organized swimmer driven by molecular motors
We investigate a self-organized swimmer at low Reynolds numbers. The
microscopic swimmer is composed of three spheres that are connected by two
identical active linker arms. Each linker arm contains molecular motors and
elastic elements and can oscillate spontaneously. We find that such a system
immersed in a viscous fluid can self-organize into a state of directed
swimming. The swimmer provides a simple system to study important aspects of
the swimming of micro-organisms.Comment: 6 pages, 4 figure
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Modelling and Formal Verification of Neuronal Archetypes Coupling
International audienceIn the literature, neuronal networks are often represented as graphs where each node symbolizes a neuron and each arc stands for a synaptic connection. Some specific neuronal graphs have biologically relevant structures and behaviors and we call them archetypes. Six of them have already been characterized and validated using formal methods. In this work, we tackle the next logical step and proceed to the study of the properties of their couplings. For this purpose, we rely on Leaky Integrate and Fire neuron modeling and we use the synchronous programming language Lustre to implement the neuronal archetypes and to formalize their expected properties. Then, we exploit an associated model checker called kind2 to automatically validate these behaviors. We show that, when the archetypes are coupled, either these behaviors are slightly modulated or they give way to a brand new behavior. We can also observe that different archetype couplings can give rise to strictly identical behaviors. Our results show that time coding modeling is more suited than rate coding modeling for this kind of studies
- …