Point process model of 1/f noise vs a sum of Lorentzians.

We present a simple point process model of 1/f(beta) noise, covering different values of the exponent beta . The signal of the model consists of pulses or events. The interpulse, interevent, interarrival, recurrence, or waiting times of the signal are described by the general Langevin equation with the multiplicative noise and stochastically diffuse in some interval resulting in a power-law distribution. Our model is free from the requirement of a wide distribution of relaxation times and from the power-law forms of the pulses. It contains only one relaxation rate and yields 1/f(beta) spectra in a wide range of frequencies. We obtain explicit expressions for the power spectra and present numerical illustrations of the model. Further we analyze the relation of the point process model of 1/f noise with the Bernamont-Surdin-McWhorter model, representing the signals as a sum of the uncorrelated components. We show that the point process model is complementary to the model based on the sum of signals with a wide-range distribution of the relaxation times. In contrast to the Gaussian distribution of the signal intensity of the sum of the uncorrelated components, the point process exhibits asymptotically a power-law distribution of the signal intensity. The developed multiplicative point process model of 1/f(beta)noise may be used for modeling and analysis of stochastic processes in different systems with the power-law distribution of the intensity of pulsing signals.

[Criteria of bistability of the cylindrical dendrite with the variable negative slope of the N-shaped current-voltage membrane characteristic]. / Uslovie bistabil'nosti tsilindricheskogo dendrita s peremennoi krutiznoi otritsatel'nogo naklona N-obraznoi vol't-ampernoi kharakteristiki membrany.

The criteria for hystheresis in the input current-voltage relation of a cylindrical dendrite, i.e. cable bistability, were studied earlier in case of the constant negative slope of the N-shaped membrane current-voltage characteristic. For a membrane with a variable negative slope of the current-voltage characteristic, only sufficient conditions of dendritic bistability were formulated: [equation: see text], where df/dV/h is the negative slope of the membrane current-voltage characteristic at zero current point, h; X is the electrotonic length of the dendrite. We propose to use as the necessary condition of bistability the above equation but with the maximal value of the negative slope df/dV/max instead of df/dV/h. Calculations illustrate that this necessary condition, with acceptable accuracy, can be used as the necessary and sufficient condition of the cable bistability when the N-shaped current-voltage characteristic of the membrane is arbitrary.