Curve of growth analysis, applied to the Lyman series absorption ratios deduced in our previous paper, yields a measurement of the logarithmic slope of distribution of Lyman α clouds in column density N. The observed exponential distribution of the clouds ’ equivalent widths W is then shown to require a broad distribution of velocity parameters b, extending up to 80 km s −1. We show how the exponential itself emerges in a natural way. An absolute normalization for the differential distribution of cloud numbers in z, N, and b is obtained. By detailed analysis of absorption fluctuations along the line of sight (including correlations among neighboring spectral frequency bins) we are able to put upper limits on the cloud-cloud correlation function ξ on several megaparsec length scales. We show that observed b values, if thermal, are incompatible, in several different ways, with the hypothesis of equilibrium heating and ionization by a background UV flux. Either a significant component of b is due to bulk motion (which we argue against on several grounds), or else the clouds are out of equilibrium, and hotter than is implied by their ionization state, a situation which could be indicative of recent adiabatic collapse. Subject headings: cosmology: observations – quasars – intergalactic medium – 2 – 1.

This dissertation is approved, and it is acceptable in quality and form for publication on microfilm: Approved by the Dissertation Committee: Accepted:

We argue that equilibrium unemployment has varies in the UK over the last twenty years, and that time series econometric methods have not always been suited to uncovering its evolution. Recent changes in the UK labour market seem to have had a significant impact on equilibrium unemployment, partly through a reduction in prime age participation. We calculate equilibrium unemployment using flows between employment, unemployment and inactivity for prime age members of the work-force. Labour market transitions do appear to have been eased by the acquisition of skills amongst the unemployed in the 1980s and 1990s, offsetting some of the potential effects of skill biased technical progress. Equilibrium unemployment may have fallen by up to two pints in the 1990s as compared to the late 1980s. We would judge that the UK has been close to equilibrium employment since late 1996.

A new scaling for the standard discrete Luria-Delbruck distribution is provided which leads to a weak convergence result as the parameter of the distribution tends to in nity. We show that the stable limiting probability measure has the Fourier transform t 7! exp( jtj=2 it log jtj).

The problem of structure from motion is often decomposed into two steps: feature correspondence and three-dimensional reconstruction. This separation often causes gross errors when establishing correspondence fails. Therefore, we advocate the necessity to integrate visual information not only in time (i.e. across different views), but also in space, by matching regions -- rather than points -- using explicit photometric deformation models. We present an algorithm that integrates image feature tracking and three-dimensional motion estimation into a closed loop, while detecting and rejecting outlier regions that do not fit the model. Due to occlusions and the causal nature of our algorithm, a drift in the estimates accumulates over time. We describe a method to perform global registration of local estimates of motion and structure by matching the appearance of feature regions stored over long time periods. We use image intensities to construct a score function that takes into account changes in brightness and contrast. Our algorithm is recursive and suitable for real-time implementation.

A new scaling for the standard discrete Luria-Delbrück distribution is provided which leads to a weak convergence result as the parameter of the distribution tends to infinity. We show that the stable limiting probability measure has the Fourier transform t ↦ → exp(−π|t|/2−it log |t|). For the corresponding density an integral representation is derived, which differs from that found in a closely related paper of Kepler and Oprea [4]. In addition, we indicate how the approach is connected to more general compound Poisson distributions.

In order to perform many signal processing tasks such as classification, pattern recognition and coding, it is helpful to specify a signal model in terms of meaningful signal structures. In general, designing such a model is complicated and for many signals it is not feasible to specify the appropriate structure. Adaptive models overcome this problem by learning structures from a set of signals. Such adaptive models need to be general enough, so that they can represent relevant structures. However, more general models often require additional constraints to guide the learning procedure. In this thesis

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