Thesis (Ph.D.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 129-141). Also available in electronic version.

Thesis (Ph. D.)--Oregon State University, 1968. / Typescript (photocopy). Includes bibliographical references (leaf 101). Also available on the World Wide Web.

Thesis (Ph. D.)--Oregon State University, 1968. / Typescript (photocopy). Includes bibliographical references (leaves 87-88). Also available on the World Wide Web.

No description available.

The zero-crossing problem is the determination of the probability density function of the intervals between the successive axis crossings of a stochastic process. This thesis studies the properties of the zero-crossings of stationary processes belonging to the symmetric-stable class of Gaussian and non-Gaussian type, corresponding to the stability index nu=2 and 0 < nu < 2 respectively.

No description available.

Continuous random processes are used to model a huge variety of real world phenomena. In particular, the zero-crossings of such processes find application in modelling processes of diffusion, meteorology, genetics, finance and applied probability. Understanding the zero-crossings behaviour improves prediction of phenomena initiated by a threshold crossing, as well as extremal problems where the turning points of the process are of interest. To identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process is a challenging problem with a rich history. This thesis considers the effect of an oscillatory auto-correlation function on the zero-crossings of a Gaussian process. Examining statistical properties of the number of zeros in a fixed time period, it is found that increasing the rate of oscillations in the auto-correlation function results in more ‘deterministic’ realisations of the process. The random interval times between successive zeros become more regular, and the variance is reduced. Accurate calculation of the variance is achieved through analysing the correlation between intervals,which numerical simulations show can be anti-correlated or correlated, depending on the rate of oscillations in the auto-correlation function. The persistence exponent describes the tail of the inter-event PDF, which is steeper where zero-crossings occur more regularly. It exhibits a complex phenomenology, strongly influenced by the oscillatory nature of the auto-correlation function. The interplay between random and deterministic components of a system governs its complexity. In an ever-more complex world, the potential applications for this scale of ‘regularity’ in a random process are far reaching and powerful.

Please read the abstract/summary in the section 00back of this document. / Thesis (PhD (Applied Mathematics))--University of Pretoria, 2006. / Mathematics and Applied Mathematics / unrestricted

The absolute transition probabilities between the 3p⁵4s and 3p⁵4p configurations of neutral argon have been measured in a three part experiment. In the first experiment, a technique of absorption spectroscopy was used to obtain relative transition probabilities for spectral lines with a common lower level. Secondly, relative transition probabilities were obtained for spectral lines with a common upper level by measuring the relative intensities of suitable pairs of lines in an emission experiment. In the third experiment, the relative values were converted to absolute transition probabilities by obtaining the lifetime of the P₁-S2 transition at ʎ7503Å. The experimental techniques used in this experiment were developed by Robinson (1966) and van Andel (1966). / Science, Faculty of / Physics and Astronomy, Department of / Graduate

Given the complexity of the domains for which we would like to use computers as reasoning engines, an automated reasoning process will often be required to perform under some state of uncertainty. Probability provides a normative theory with which uncertainty can be modelled. Without assumptions of independence from the domain, naive computations of probability are intractible. If probability theory is to be used effectively in AI applications, the independence assumptions from the domain should be represented explicitly, and used to greatest possible advantage. One such representation is a class of mathematical structures called Bayesian networks. This thesis presents a framework for dynamically constructing and evaluating Bayesian networks. In particular, this thesis investigates the issue of representing probabilistic knowledge which has been abstracted from particular individuals to which this knowledge may apply, resulting in a simple representation language. This language makes the independence assumptions for a domain explicit. A simple procedure is provided for building networks from knowledge expressed in this language. The mapping between the knowledge base and network created is precisely defined, so that the network always represents a consistent probability distribution. Finally, this thesis investigates the issue of modifying the network after some evaluation has taken place, and several techniques for correcting the state of the resulting model are derived. / Science, Faculty of / Computer Science, Department of / Graduate