by Tang Hing Sing. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1989. / Bibliography: leaves 92-96.

Markov chain Monte Carlo (MCMC) is one of the most popular statistical inference methods in machine learning. Recent work shows that a significant improvement of the statistical efficiency of MCMC on complex distributions can be achieved by exploiting geometric properties of the target distribution. This is known as geometric MCMC. However, many such methods, like Riemannian manifold Hamiltonian Monte Carlo (RMHMC), are computationally challenging to scale up to high dimensional distributions. The primary goal of this thesis is to develop novel geometric MCMC methods applicable to large-scale problems. To overcome the computational bottleneck of computing second order derivatives in geometric MCMC, I propose an adaptive MCMC algorithm using an efficient approximation based on Limited memory BFGS. I also propose a simplified variant of RMHMC that is able to work effectively on larger scale than the previous methods. Finally, I address an important limitation of geometric MCMC, namely that is only available for continuous distributions. I investigate a relaxation of discrete variables to continuous variables that allows us to apply the geometric methods. This is a new direction of MCMC research which is of potential interest to many applications. The effectiveness of the proposed methods is demonstrated on a wide range of popular models, including generalised linear models, conditional random fields (CRFs), hierarchical models and Boltzmann machines.

A turbomolecular pump (TMP) with good performance must have higher compress ratio and higher pumping speed. At the same time, the performance of turbomolecular pump depends on blade geometries and the rotational speed. When design the blade of Turbomolecular Pump, the blade geometries including, the blade angle, the blade spacing, the blade chord, the spacing-chord ratio, the tip diameter, the root diameter, and the number of blades and as well as the rotational speed of the rotor must be considered. In this paper the simulation for gas molecular behavior is obtained by the Monte Carlo method. Therefore, a Maxwellian distribution of particles at the inlet and outlet of the flow region and diffuse reflection for the particles that collide with the walls are assumed. Models of this type have been applied to the two-dimensional case. The most important result is to compare the performance between turbomolecular pumps with curve style and plane style of blades. Furthermore, that direct multi-stage simulation (DMS) by Monte Carlo method is used in this paper. The compression ratio multiplication (CRM) method is the improved due to the considering the change of velocity distribution of molecular at the adjacent stages. From results of the simulation, the effect upon the geometric parameters of the blades and the arrangement in the multi-stage are concluded, that are very useful in designing the turbomolecular.

published_or_final_version / Physics / Master / Master of Philosophy

Thesis (M.S. - Hydrology and Water Resources) - University of Arizona. / Includes bibliographical references (leaves 87-93).

Thesis (M.S.)--State University of New York at Binghamton, Watson School of Engineering and Applied Science (Systems Science), 2007. / Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 68-69).

Thesis (M.Ing.)--University of Stellenbosch, 1999. / Bibliography. Also available via the Internet.

Thesis (M.S.)--University of Wisconsin--Madison, 1981. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 55-56).

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