3 research outputs found
Self Tuned Criticality: Controlling a neuron near its bifurcation point via temporal correlations
Previous work showed that the collective activity of large neuronal networks
can be tamed to remain near its critical point by a feedback control that
maximizes the temporal correlations of the mean-field fluctuations. Since such
correlations behave similarly near instabilities across nonlinear dynamical
systems, it is expected that the principle should control also low dimensional
dynamical systems exhibiting continuous or discontinuous bifurcations from
fixed points to limit cycles. Here we present numerical evidence that the
dynamics of a single neuron can be controlled in the vicinity of its
bifurcation point. The approach is tested in two models: a 2D generic excitable
map and the paradigmatic FitzHugh-Nagumo neuron model. The results show that in
both cases, the system can be self-tuned to its bifurcation point by modifying
the control parameter according to the first coefficient of the autocorrelation
function
Scale-free correlations in the dynamics of a small (N ~ 10000) cortical network
The advent of novel opto-genetics technology allows the recording of brain
activity with a resolution never seen before. The characterisation of these
very large data sets offers new challenges as well as unique theory-testing
opportunities. Here we discuss whether the spatial and temporal correlation of
the collective activity of thousands of neurons are tangled as predicted by the
theory of critical phenomena. The analysis shows that both, the correlation
length and the correlation time scale as predicted as a function
of the system size. With some peculiarities that we discuss, the analysis
uncovers new evidence consistent with the view that the large scale brain
cortical dynamics corresponds to critical phenomena.Comment: 8 pages, 6 figure
Finite-size correlation behavior near a critical point: a simple metric for monitoring the state of a neural network
In this note, a correlation metric is proposed which is based on
the universal behavior of the linear/logarithmic growth of the correlation
length near/far the critical point of a continuous phase transition. The
problem is studied on a previously described neuronal network model for which
is known the scaling of the correlation length with the size of the observation
region. It is verified that the metric is maximized for the
conditions at which a power law distribution of neuronal avalanches sizes is
observed, thus characterizing well the critical state of the network. Potential
applications and limitations for its use with currently available optical
imaging techniques are discussed.Comment: 5 pages, 5 figure