Application of regression in algorithm of nonlinear stochastic adaptation of unstable multidimensional objects

The results of a study of applicability of kernel estimation in the synergetic control systems for the objects unstable in an open-loop state (without a stabilizing control) have been presented. The effectiveness of kernel estimates has been shown for four nonlinear objects with unstable limiting states. The estimate the effectiveness of embedding the kernel predictive estimate of the state variables of a nonlinear object, subjected to disturbances of an unknown nature, into the system of synergetic control is demonstrated.

Stochastic slowly adapting ionic currents may provide a decorrelation mechanism for neural oscillators by causing wander in the intrinsic period

Oscillatory neurons integrate their synaptic inputs in fundamentally different ways than normally quiescent neurons. We show that the oscillation period of invertebrate endogenous pacemaker neurons wanders, producing random fluctuations in the interspike intervals (ISI) on a time scale of seconds to minutes, which decorrelates pairs of neurons in hybrid circuits constructed using the dynamic clamp. The autocorrelation of the ISI sequence remained high for many ISIs, but the autocorrelation of the ΔISI series had on average a single nonzero value, which was negative at a lag of one interval. We reproduced these results using a simple integrate and fire (IF) model with a stochastic population of channels carrying an adaptation current with a stochastic component that was integrated with a slow time scale, suggesting that a similar population of channels underlies the observed wander in the period. Using autoregressive integrated moving average (ARIMA) models, we found that a single integrator and a single moving average with a negative coefficient could simulate both the experimental data and the IF model. Feeding white noise into an integrator with a slow time constant is sufficient to produce the autocorrelation structure of the ISI series. Moreover, the moving average clearly accounted for the autocorrelation structure of the ΔISI series and is biophysically implemented in the IF model using slow stochastic adaptation. The observed autocorrelation structure may be a neural signature of slow stochastic adaptation, and wander generated in this manner may be a general mechanism for limiting episodes of synchronized activity in the nervous system.