48 research outputs found
Point Processes Modeling of Time Series Exhibiting Power-Law Statistics
We consider stochastic point processes generating time series exhibiting
power laws of spectrum and distribution density (Phys. Rev. E 71, 051105
(2005)) and apply them for modeling the trading activity in the financial
markets and for the frequencies of word occurrences in the language.Comment: 4 pages, 2 figure
Modeling non-Gaussian 1/f Noise by the Stochastic Differential Equations
We consider stochastic model based on the linear stochastic differential
equation with the linear relaxation and with the diffusion-like fluctuations of
the relaxation rate. The model generates monofractal signals with the
non-Gaussian power-law distributions and 1/f^b noise.Comment: 4 pages, 3 figure
Point process model of 1/f noise versus a sum of Lorentzians
We present a simple point process model of noise, covering
different values of the exponent . 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 the 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 spectra in a wide
range of frequency. 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 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 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.Comment: 23 pages, 10 figures, to be published in Phys. Rev.
Intense Synaptic Activity Enhances Temporal Resolution in Spinal Motoneurons
In neurons, spike timing is determined by integration of synaptic potentials in delicate concert with intrinsic properties. Although the integration time is functionally crucial, it remains elusive during network activity. While mechanisms of rapid processing are well documented in sensory systems, agility in motor systems has received little attention. Here we analyze how intense synaptic activity affects integration time in spinal motoneurons during functional motor activity and report a 10-fold decrease. As a result, action potentials can only be predicted from the membrane potential within 10 ms of their occurrence and detected for less than 10 ms after their occurrence. Being shorter than the average inter-spike interval, the AHP has little effect on integration time and spike timing, which instead is entirely determined by fluctuations in membrane potential caused by the barrage of inhibitory and excitatory synaptic activity. By shortening the effective integration time, this intense synaptic input may serve to facilitate the generation of rapid changes in movements