Following the classical theory of Baire category results for sets of measure-preserving transformations, this work develops a theory for Baire category results for sets of measure-preserving extensions. First the case is considered where a measure space and a sub-algebra are fixed, and extensions are considered to be any measure-preserving transformations which leave this sub-algebra invariant. In the latter case, extensions of a fixed measure-preserving transformation are considered. In both cases, it is shown that the set of weakly mixing extensions form a dense, G-delta set

Multiple-input-multiple-output (MIMO) wireless systems use multiple antenna elements at the transmitter and receiver to offer improved spectral efficiency over traditional single antenna systems. In these systems, properties of the transmit and receive antenna arrays play a key role in determining the overall performance of the system. This thesis derives an upper bound on ergodic (average) channel capacity which formally links good antenna diversity performance with good ergodic capacity. As a result of this derivation, antenna arrays with good ergodic capacity performance are designed in this thesis by designing antenna arrays with near-optimal diversity gain. Several approaches are developed to design antenna array elements which achieve near-optimal diversity. These design methods only require an array geometry and the power azimuth spectrum of the propagation environment. Examples and analysis are included that illustrate advantages and disadvantages of each design technique. Three different array geometries are also investigated. Diversity performance results for each design technique and array geometry, averaged over an ensemble of typical power azimuth spectrums, are presented and compared. This analysis shows that the diversity gain achieved by the best design approach is, on average, less than 1.5 dB below the optimal diversity gain.

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This paper describes the development process of an Interactive Fiction game focused on the theme oflanguage. The paper includes a brief description of the history of the genre and its definitions, a discussionabout its multiple variations and attributes, and an overview of some examples that handled similar subjects.Then it considers some of the unique properties of the written language and examines language as both ashared and subjective relationship with reality . This is followed by a description of tools and methodsadopted in the design process and how the development went — from initial research to the final concept.The results is then described, followed by the user test results and a critical evaluation. At the end, someconcluding remarks are included together with possible future developments.

<p>This thesis is centered around three infinite dimensional diffusion processes:</p> <p>(i). the infinitely-many-neutral-alleles diffusion model [Ethier and Kurtz, 1981],</p> <p>(ii). the two-parameter infinite dimensional diffusion model [Petrov, 2009] and [Feng and Sun, 2010],</p> <p>(iii). the infinitely-many-alleles diffusion with symmetric dominance [Ethier and Kurtz, 1998].</p> <p>The partition structures, the ergodic inequalities and the asymptotic theory of these three models are discussed. In particular, the asymptotic theory turns out to be the major contribution of this thesis.</p> <p>In Chapter 2, a slightly altered version of Kingman's one-to-one correspondence theorem on partition structures is provided, which in turn becomes a handy tool for obtaining the asymptotic result on the partition structures associated with models (i) and (ii).</p> <p>In Chapter 3, the three diffusion models are briefly introduced. New representations of the transition densities of models (i) and (ii) are obtained simply by rearranging the previous representations obtained in [Ethier, 1992] and [Feng et al., 2011] respectively. These two new representations have their own advantages, by making use of which the corresponding ergodic inequalities easily follow. Furthermore, thanks to the functional inequalities in [Feng et al., 2011], the ergodic inequality for model (iii) becomes available as well.</p> <p>In Chapter 4, the asymptotic properties of models (i) and (ii) are thoroughly studied. Various asymptotic results are obtained, such as the weak limits of models (i) and (ii) at different time scales when the mutation rate approaches infinity, and the large deviation principle for models (i) and (ii) at a fixed time, and that of the transient partition structures of models (i) and (ii). Of all these results, the weak limit and the large deviation principle of the transient partition structures are of particular interest.</p> <p>In Chapter 5, the asymptotic results on the stationary distribution and the transient distribution of model (iii) are both obtained. The weak limit of the infinitely-many- alleles diffusion with symmetric overdominance at fixed time t serves as an alternative answer to Gillespie's conjecture [Gillespie, 1999]. The weak limit of the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance provides a complete solution to the remaining problem in [Feng, 2009].</p> / Doctor of Philosophy (PhD)

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