Very fast automatic rejection algorithms were developed recently which allow to generate random variates from large classes of unimodal distributions. They require the choice of several design points which decompose the domain of the distribution into small sub-intervals. The optimal choice of these points is an important but unsolved problem. So we present an approach that allows to characterize optimal design points in the asymptotic case (when their number tends to infinity) under mild regularity conditions. We describe a short algorithm to calculate these asymptotically optimal points in practice. Numerical experiments indicate that they are very close to optimal even when only six or seven design points are calculated. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

The transformed rejection method, a combination of the inversion and the rejection method, which is used to generate non-uniform random numbers from a variety of continuous distributions can be applied to discrete distributions as well. For the Poisson distribution a short and simple algorithm is obtained which is well suited for large values of the Poisson parameter $\mu$, even when $\mu$ may vary from call to call. The average number of uniform deviates required is lower than for any of the known uniformly fast algorithms. Timings for a C implementation show that the algorithm needs only half of the code but is - for $\mu$ not too small - at least as fast as the current state-of-the-art algorithms. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is obtained by breadth-first search. This structure is uniquely determined up to isomorphism. We also show that the maximum eigenvalue in such classes of trees is strictly monotone with respect to majorization. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

We give an upper bound for the norm distance of (0,1) -valued Markov-exchangeable random variables to mixtures of distributions of Markov processes. A Markov-exchangeable random variable has a distribution that depends only on the starting value and the number of transitions 0-0, 0-1, 1-0 and 1-1. We show that if, for increasing length of variables, the norm distance to mixtures of Markov processes goes to 0, the rate of this convergence may be arbitrarily slow. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

We study the asymptotic behavior of the quantization error for general information functions and prove results for distributions P with regular support. We characterize the information functions for which the uniform distribution on the set of prototypes converges weakly to P. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

This short note discusses performance bounds for "Ahrens" algorithm, that can generate random variates from continuous distributions with monotonically decreasing density. This rejection algorithms uses constant hat-functions and constant squeezes over many small intervals. The choice of these intervals is important. Ahrens has demonstrated that the equal area rule that uses strips of constant area leads to a very simple algorithm. We present bounds on the rejection constant of this algorithm depending only on the number of intervals. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

We study the empirical quantization error in case the number of prototypes increases with the size of the sample. We present a proof of the consistency of the empirical quantization error and of corresponding estimators of the quantization dimensions of distributions. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

<p>Articular cartilage is the thin, load-bearing connective tissue that lines the ends of long bones in diarthroidal joints, providing predominantly a mechanical function. Because cartilage is avascular and aneural, it has little capacity for self-repair if damaged. One repair strategy is through a functional tissue engineering approach using adipose-derived stem cells (ASCs). ASCs are an abundant progenitor cell source easily obtained through a minimally invasive liposuction procedure. When appropriately stimulated, ASCs have demonstrated significant potential for chondrogenic differentiation. Though studies have demonstrated the ability of ASCs to synthesize cartilage-specific macromolecules, a more thorough understanding of factors that modulate ASC chondrogenesis is required. Accordingly, the central aim of this dissertation was to study the chondrogenic response of ASCs to biochemical, biomechanical, and biomaterial factors.</p><p>We hypothesized that factors, other than TGF-beta and dexamethasone, would improve ASC chondrogenesis. BMP-6 emerged as a potent regulator of ASC chondrogenesis, particularly in early culture, as noted by significant upregulation of cartilage-specific extracellular matrix (ECM) genes and downregulation of cartilage hypertrophy markers.</p><p>Hypothesizing that biomechanical factors would accelerate the formation of cartilage-specific macromolecules, we designed and manufactured an instrument to apply dynamic deformational loading to ASC seeded constructs. Dynamic loading significantly inhibited ASC metabolism and downregulated cartilage-specific ECM genes. However, 21 days of dynamic loading induced the production of type II collagen, a principal component of articular cartilage.</p><p>We hypothesized that a biomaterial derived from cartilage would serve as a bioactive scaffold and induce chondrogenic differentiation. The novel, ECM-derived scaffold promoted the most robust differentiation of ASCs relative to both biochemical and biomechanical factors, particularly noted by a type II collagen-rich matrix after 28 days of culture. After 42 days of culture, biphasic mechanical testing revealed an aggregate modulus of 150 kPa, approaching that of native cartilage. These data suggest that the ECM-derived scaffold may retain important signaling molecules to drive differentiation or that ASC differentiation is dependent on proper cell anchorage.</p><p>In summary, we have shown that biochemical, biomechanical, and biomaterial factors have strong influences on the chondrogenic potential of ASCs. Optimization of these factors will ultimately be required to successfully engineer a functional tissue.</p> / Dissertation

The purpose of this work is to extend the functionality of the Master Sintering Curve (MSC) such that it can be used as a practical tool for predicting sintering schemes that combine both a constant heating rate and an isothermal hold. Rather than just being able to predict a final density for the object of interest, the extension to the MSC will actually be able to model a sintering run from start to finish. Because the Johnson model does not incorporate this capability, the work presented is an extension of what has already been shown in literature to be a valuable resource in many sintering situations. A predicted sintering curve that incorporates a combination of constant heating rate and an isothermal hold is more indicative of what is found in real-life sintering operations. This research offers the possibility of predicting the sintering schedule for a material, thereby having advanced information about the extent of sintering, the time schedule for sintering, and the sintering temperature with a high degree of accuracy and repeatability. The research conducted in this thesis focuses on the development of a working model for predicting the sintering schedules of several stabilized zirconia powders having the compositions YSZ (HSY8), 10Sc1CeSZ, 10Sc1YSZ, and 11ScSZ1A. The compositions of the four powders are first verified using x-ray diffraction (XRD) and the particle size and surface area are verified using a particle size analyzer and BET analysis, respectively. The sintering studies were conducted on powder compacts using a double pushrod dilatometer. Density measurements are obtained both geometrically and using the Archimedes method. Each of the four powders is pressed into 1/4 inch diameter pellets using a manual press with no additives, such as a binder or lubricant. Using a double push-rod dilatometer, shrinkage data for the pellets is obtained over several different heating rates. The shrinkage data is then converted to reflect the change in relative density of the pellets based on the green density and the theoretical density of each of the compositions. The Master Sintering Curve (MSC) model is then utilized to generate data that can be utilized to predict the final density of the respective powder over a range of heating rates. The Elton Master Sintering Curve Extension (EMSCE) is developed to extend the functionality of the MSC tool. The parameters generated from the original MSC are used in tandem with the solution to a specific closed integral (discussed in document) over a set range of temperatures. The EMSCE is used to generate a set of sintering curves having both constant heating rate and isothermal hold portions. The EMSCE extends the usefulness of the MSC by allowing this generation of a complete sintering schedule rather than just being able to predict the final relative density of a given material. The EMSCE is verified by generating a set of curves having both constant heating rate and an isothermal hold for the heat-treatment. The modeled curves are verified experimentally and a comparison of the model and experimental results are given for a selected composition. Porosity within the final product can hinder the product from sintering to full density. It is shown that some of the compositions studied did not sinter to full density because of the presence of large porosity that could not be eliminated in a reasonable amount of time. A statistical analysis of the volume fraction of porosity is completed to show the significance of the presence in the final product. The reason this is relevant to the MSC is that the model does not take into account the presence of porosity and assumes that the samples sinter to full density. When this does not happen, the model actually under-predicts the final density of the material.

<p>Multinational companies (MNCs) often choose to locate near other MNCs in order to gain advantages from each other. This is one ingredient in creating a cluster, an area composed of companies, institutions and/or organisations, sharing a similar technology or knowledge base with mutual benefits for the cluster participants. Market forces have created the majority of the clusters in the world. Still, governments frequently aim at creating clusters in order to promote regional development and growth. This is the case with the Multimedia Super Corridor (MSC) in Malaysia that was launched in 1996. My purpose with this thesis is to examine if the creation and running of the MSC has had economical benefits for Malaysia and to examine the MSC’s potential to become profitable and productive. The MSC is a new technological area and it is still under construction. The return on investment seems to be negative and the area is dependent on the Malaysian government for its development. The infrastructure, political and economical factors seem, according to my analysis, to be sufficient for creating the MSC. However, the low level of human resource is a problem for the cluster. Furthermore, Malaysia’s comparative advantage does not seem to be in high-technology production but rather in high-quality manufacturing. Even though the MSC is unlikely to develop into a world leading high-technology cluster, it can help to transfer Malaysia into a new phase of development.</p>