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Thesis (Ph.D.)--University of Melbourne, Dept. of Computer Science and Software Engineering, 2009. / Typescript. Includes bibliographical references (p. 131-146)

Today, the use of embedded Dynamic Random Access Memory (eDRAM) is increasing in our electronics that require large memories, such as gaming consoles and computer network routers. Unlike external DRAMs, eDRAMs are embedded inside ASICs for faster read and write operations. Until recently, eDRAMs required high manufacturing cost. Present process technology developments enabled the manufacturing of eDRAM at competitive costs. Unlike SRAM, eDRAM exhibits retention time bit fails from defects and capacitor leakage current. This retention time fail causes memory bits to lose stored values before refresh. Also, a small portion of the memory bits are known to fail at a random retention time. At test conditions, more stringent than use conditions, if all possible retention time fail bits are detected and replaced, there will be no additional fail bits during use. However, detecting all the retention time fails requires long time and also rejects bits that do not fail at the use condition. This research seeks to maximize the detection of eDRAM fail bits during test by determining effective test conditions and model the failure rate of eDRAM retention time during use conditions.

Persistence problem of compact invariant manifold under random perturbation is considered in this dissertation. Under uniformly small random perturbation and the condition of normal hyperbolicity, the original invariant manifold persists and becomes a random invariant manifold. The random counterpart has random local stable and unstable manifolds. They could be invariantly foliated thanks to the normal hyperbolicity. Those underlie an extension of the geometric singular perturbation theory to the random case which means the slow manifold persists and becomes a random manifold so that the local global structure near the slow manifold persists under singular perturbation. A normal form for a random differential equation is obtained and this helps to prove a random version of the exchange lemma.

There has been a lot of work done in recent decades in the field of symbolic dynamics. Much attention has been paid to the so-called "complexity" function, which gives a sense of the rate at which the number of words in the system grow. In this paper, we explore this and several notions of complexity of specific symbolic dynamical systems. In particular, we compute positive entropy and state some k-balancedness properties of a few specific (random) substitutions. We also view certain sequences as subsets of Z², stating several properties and computing bounds on entropy in a specific example. / Graduation date: 2011

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Random planar graphs have been the subject of much recent work. Many basic properties of the standard uniform random planar graph $P_{n}$, by which we mean a graph chosen uniformly at random from the set of all planar graphs with vertex set $ { 1,2, ldots, n }$, are now known, and variations on this standard random graph are also attracting interest. Prominent among the work on $P_{n}$ have been asymptotic results for the probability that $P_{n}$ will be connected or contain given components/ subgraphs. Such progress has been achieved through a combination of counting arguments cite{mcd} and a generating function approach cite{gim}. More recently, attention has turned to $P_{n,m}$, the graph taken uniformly at random from the set of all planar graphs on ${ 1,2, ldots, n }$ with exactly $m(n)$ edges (this can be thought of as a uniform random planar graph with a constraint on the average degree). In cite{ger} and cite{gim}, the case when $m(n) =~!lfloor qn floor$ for fixed $q in (1,3)$ has been investigated, and results obtained for the events that $P_{n, lfloor qn floor}$ will be connected and that $P_{n, lfloor qn floor}$ will contain given subgraphs. In Part I of this thesis, we use elementary counting arguments to extend the current knowledge of $P_{n,m}$. We investigate the probability that $P_{n,m}$ will contain given components, the probability that $P_{n,m}$ will contain given subgraphs, and the probability that $P_{n,m}$ will be connected, all for general $m(n)$, and show that there is different behaviour depending on which `region' the ratio $rac{m(n)}{n}$ falls into. In Part II, we investigate the same three topics for a uniform random planar graph with constraints on the maximum and minimum degrees.

Understanding protein-protein interaction (PPI) is important in order to understand cellular processes. X-ray crystallography and mutagenesis, expensive methods both in time and resources, are the most reliable methods for detecting PPI. Computational approaches could, therefore, reduce resources and time spent on detecting PPIs. During this master thesis a method, cProQPred, was created for scoring how realistic coarse PPI models are. cProQPred use the machine learning method Random Forest trained on previously calculated features from the programs ProQDock and InterPred. By combining some of ProQDock’s features and the InterPred score from InterPred the cProQPred method generated a higher performance than both ProQDock and InterPred. This work also tried to predict the quality of the PPI model after refinement and the chance for a coarse PPI model to succeed at refinement. The result illustrated that the predicted quality of a coarse PPI model also was a relatively good prediction of the quality the coarse PPI model would get after refinement. Prediction of the chance for a coarse PPI model to succeed at refinement was, however, without success.