Order out of Randomness: Self-Organization Processes in Astrophysics
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Redesigned second-generation, tape-oriented computer system updates a data record, increases the capability to perform update runs, and produces a sequential report for every update run.
Maximum sample excursions of Kiefer-Wolfowitz stochastic approximation processes
Exact dynamical equation derived for conditional density mode representing stochastic process
Regarding new bipolar magnetic regions as sources of flux, the evolution of the photospheric magnetic field during 1976-1984 was computed and the corresponding evolution of the mean line-of-sight field as seen from earth was derived. A good, but imperfect, agreement was obtained between the observed mean field and the field computed for a nominal choice of flux transport parameters. The response of the computed mean field to variations in the transport parameters and the source properties was determined. The results suggest that the mean-field evolution is a random-walk process with dissipation. New eruptions of flux produce the random walk, and together differential rotation, meridional flow, and diffusion provide the dissipation. The net effect of each new source depends on its strength and orientation and on the time elapsed before the next eruption.
The first-excursion probability of a non-stationary Gaussian process with zero mean has been studied. Within the framework of the point process approach, a variety of analytical approximations applicable to stationary random processes is extended herein to non-stationary random processes. The extension is possible owing to a recent definition of non-stationary envelope processes proposed by the author. With the aid of numerical examples, merits of each approximation are examined by comparing with the results of simulation. It is found that under non-stationary excitations with short duration, the Markov approximation is the best among all the approximations discussed in this paper.
A method for measuring the time of arrival of very narrow laser pulses which have been reflected and randomly broadened by a target is examined. It is known that these return pulses from the target have very small rise times. A threshold detection algorithm that detects the rising edge of the pulse is used for obtaining the pulse arrival times. The errors of the scheme are evaluated numerically for different pulse shapes, and a loose bound on the errors of detecting a typical pulse is obtained. A gamma-density model is used to characterize the random gain processes of the optical receiver, and the effect of such random gains on the errors of threshold detection is analyzed.
Analysis of more than 36 years of time series of seven parameters measured in the NSO/AFRL/Sac Peak K-line monitoring program elucidates five elucidates five components of the variation: (1) the solar cycle (period approx. 11 years), (2) quasi-periodic variations (periods approx 100 days), (3) a broad band stochastic process (wide range of periods), (4) rotational modulation, and (5) random observational errors. Correlation and power spectrum analyses elucidate periodic and aperiodic variation of the chromospheric parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (1) and (2) at time scales in the range approx 0.1 - 10 years. These results using only full-disk data further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced by NASA's Kepler observatory. Component (3) consists of variations over a range of timescales, in the manner of a 1/f random noise process. A timedependent Wilson-Bappu effect appears to be present in the solar cycle variations (1), but not in the stochastic process (3). Component (4) characterizes differential rotation of the active regions, and (5) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The recent data suggest that the current cycle is starting late and may be relatively weak. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.
Flowgraph techniques for closed systems, discussing properties, approximation method, topology equation, frequency response, constraints, oscillatory and stochastic processes, etc
Error probabilities for partially coherent diversity reception, noting linearized receiver performance during random noise output
Sample continuous second order martingale process, determining existence of limit of stochastic processes using approximation theorems
Stochastic Liapunov function existence demonstrated for continuous strong Markov process with certain stochastic stability properties
Sufficient conditions for recurrence and positivity of diffusion process defined by stochastic differential equation, using Liapunov function
Generalization of binary processes, discussing time domain and frequency domain analysis
General theory describing discontinuous processes and application to hydrodynamic inhomogeneities such as combustion waves, combustion zone motion
Optimal control and stability for stochastic systems, viewing linear diffusion models based upon Gaussian-Markov process as finite dimensional linear system driven by white noise
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
Most existing deconvolution techniques are incapable of determining phase properties of wavelets from time series data; to assure a unique solution, minimum phase is usually assumed. It is demonstrated, for moving average processes of order one, that deconvolution filtering using the absolute value norm provides an estimate of the wavelet shape that has the correct phase character when the random driving process is nonnormal. Numerical tests show that this result probably applies to more general processes.