1,196 research outputs found
Nonnormal amplification in random balanced neuronal networks
In dynamical models of cortical networks, the recurrent connectivity can
amplify the input given to the network in two distinct ways. One is induced by
the presence of near-critical eigenvalues in the connectivity matrix W,
producing large but slow activity fluctuations along the corresponding
eigenvectors (dynamical slowing). The other relies on W being nonnormal, which
allows the network activity to make large but fast excursions along specific
directions. Here we investigate the tradeoff between nonnormal amplification
and dynamical slowing in the spontaneous activity of large random neuronal
networks composed of excitatory and inhibitory neurons. We use a Schur
decomposition of W to separate the two amplification mechanisms. Assuming
linear stochastic dynamics, we derive an exact expression for the expected
amount of purely nonnormal amplification. We find that amplification is very
limited if dynamical slowing must be kept weak. We conclude that, to achieve
strong transient amplification with little slowing, the connectivity must be
structured. We show that unidirectional connections between neurons of the same
type together with reciprocal connections between neurons of different types,
allow for amplification already in the fast dynamical regime. Finally, our
results also shed light on the differences between balanced networks in which
inhibition exactly cancels excitation, and those where inhibition dominates.Comment: 13 pages, 7 figure
Extracting non-linear integrate-and-fire models from experimental data using dynamic IâV curves
The dynamic IâV curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional currentâvoltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron modelsâof the refractory exponential integrate-and-fire typeâprovide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons
Adaptation Reduces Variability of the Neuronal Population Code
Sequences of events in noise-driven excitable systems with slow variables
often show serial correlations among their intervals of events. Here, we employ
a master equation for general non-renewal processes to calculate the interval
and count statistics of superimposed processes governed by a slow adaptation
variable. For an ensemble of spike-frequency adapting neurons this results in
the regularization of the population activity and an enhanced post-synaptic
signal decoding. We confirm our theoretical results in a population of cortical
neurons.Comment: 4 pages, 2 figure
Crossover between Levy and Gaussian regimes in first passage processes
We propose a new approach to the problem of the first passage time. Our
method is applicable not only to the Wiener process but also to the
non--Gaussian Lvy flights or to more complicated stochastic
processes whose distributions are stable. To show the usefulness of the method,
we particularly focus on the first passage time problems in the truncated
Lvy flights (the so-called KoBoL processes), in which the
arbitrarily large tail of the Lvy distribution is cut off. We
find that the asymptotic scaling law of the first passage time distribution
changes from -law (non-Gaussian Lvy
regime) to -law (Gaussian regime) at the crossover point. This result
means that an ultra-slow convergence from the non-Gaussian Lvy
regime to the Gaussian regime is observed not only in the distribution of the
real time step for the truncated Lvy flight but also in the
first passage time distribution of the flight. The nature of the crossover in
the scaling laws and the scaling relation on the crossover point with respect
to the effective cut-off length of the Lvy distribution are
discussed.Comment: 18pages, 7figures, using revtex4, to appear in Phys.Rev.
Dynamical response of the Hodgkin-Huxley model in the high-input regime
The response of the Hodgkin-Huxley neuronal model subjected to stochastic
uncorrelated spike trains originating from a large number of inhibitory and
excitatory post-synaptic potentials is analyzed in detail. The model is
examined in its three fundamental dynamical regimes: silence, bistability and
repetitive firing. Its response is characterized in terms of statistical
indicators (interspike-interval distributions and their first moments) as well
as of dynamical indicators (autocorrelation functions and conditional
entropies). In the silent regime, the coexistence of two different coherence
resonances is revealed: one occurs at quite low noise and is related to the
stimulation of subthreshold oscillations around the rest state; the second one
(at intermediate noise variance) is associated with the regularization of the
sequence of spikes emitted by the neuron. Bistability in the low noise limit
can be interpreted in terms of jumping processes across barriers activated by
stochastic fluctuations. In the repetitive firing regime a maximization of
incoherence is observed at finite noise variance. Finally, the mechanisms
responsible for spike triggering in the various regimes are clearly identified.Comment: 14 pages, 24 figures in eps, submitted to Physical Review
The spike train statistics for consonant and dissonant musical accords
The simple system composed of three neural-like noisy elements is considered.
Two of them (sensory neurons or sensors) are stimulated by noise and periodic
signals with different ratio of frequencies, and the third one (interneuron)
receives the output of these two sensors and noise. We propose the analytical
approach to analysis of Interspike Intervals (ISI) statistics of the spike
train generated by the interneuron. The ISI distributions of the sensory
neurons are considered to be known. The frequencies of the input sinusoidal
signals are in ratios, which are usual for music. We show that in the case of
small integer ratios (musical consonance) the input pair of sinusoids results
in the ISI distribution appropriate for more regular output spike train than in
a case of large integer ratios (musical dissonance) of input frequencies. These
effects are explained from the viewpoint of the proposed theory.Comment: 22 pages, 6 figure
- âŠ