Quadtree representation and compression of spatial data

Spatial data representation and compression has become a focus issue in computer graphics and image processing applications. Quadtrees, as one of hierarchical data structures, basing on the principle of recursive decomposition of space, always offer a compact and efficient representation of an image. For a given image, the choice of quadtree root node plays an important role in its quadtree representation and final data compression. The goal of this thesis is to present a heuristic algorithm for finding a root node of a region quadtree, which is able to reduce the number of leaf nodes when compared with the standard quadtree decomposition. The empirical results indicate that, this proposed algorithm has quadtree representation and data compression improvement when in comparison with the traditional method.

Solid state NMR chemical shifts as an alternative to diffraction data in the determination of SIC polytypic structures

Silicon carbide, which has many polytypic modifications of a very simple and very symmetric structure, is an excellent model system for exploring, the relationship between chemical shift, long-range dipolar shielding, and crystal structure in network solids. A simple McConnell equation treatment of bond anisotropy effects in a poly type predicts chemical shifts for silicon and carbon sites which agree well with the experiment, provided that contributions from bonds up to 100 A are included in the calculation. The calculated chemical shifts depend on three factors: the layer stacking sequence, electrical centre of gravity, and the spacings between silicon and carbon layers. The assignment of peaks to lattice sites is proved possible for three polytypes (6H, 15R, and 3C). The fact that the calculated chemical shifts are very sensitive to layer spacings provides us a potential way to detennine and refine a crystal structure. In this work, the layer spacings of 6H SiC have been calculated and are within X-ray standard deviations. Under this premise, the layer spacings of 15R have been detennined. 29Si and 13C single crystal nmr studies of 6H SiC polytype indicate that all silicons and carbons are magnetically anisotropic. The relationship between a magnetic shielding tensor component and layer spacings has been derived. The comparisons between experimental and semi-empirical chemical shielding tensor components indicate that the paramagnetic shielding of silicon should be included in the single crystal chemical shift calculation.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

The relationship between stem-form, stand-closure and site -conditions : the influence of environmental conditions on tree allometry and forest structure in west-central Alberta

Changes in the configuration of a tree stern result insignificant differences in its total volume and in the proportion of that volume that is merchantable timber. Tree allometry, as represented by stem-fo~, is the result of the vertical force of gravity and the horizontal force of wind. The effect of wind force is demonstrated in the relationship between stem-form, standclosure and site-conditions. An increase in wind force on the individual tree due to a decrease in stand density should produce a more tapered tree. The density of the stand is determined by the conditions that the trees are growing under. The ability of the tree to respond to increased wind force may also be a function of these conditions . This stem-form/stand-closure/site-conditions relationship was examined using a pre-existing database from westcentral Alberta. This database consisted of environmental, vegetation, soils and timber data covering a wide range of sites. There were 653 sample trees with 82 variables that formed the basis of the analysis. There were eight tree species consisting of Pinus contorta, Picea mariana, Picea engelmannii x glauca, Abies lasiocarpa, Larix laricina, Populus tremuloides, Betula papyrifera and Populus balsamifera plus a comprehensive all-species data set. As the actual conformation of the stern is very individual, stem-fo~was represented by the diameter at breast height to total height r~tio. The four stand-closure variables, crown closure, total basal area, total volume and total number of stems were reduced to total basal area and total number of stems utilizing a bivariate correlation matrix by species. Site-conditions were subdivided into macro, meso and micro variables and reduced in number 3 using cross-tabulations, bivariate correlation and principal components analysis as screening tools. The stem-fo~/stand-closure relationship was examined using bivariate correlation coefficients for stem-fo~ with total number of stems and stem-fo~ with total basal area. The stem-fo~/site-conditions and the stand-closure/site- conditions relationships were examined using multiple correlation coefficients. The stem-form/stand-closure/site-conditions relationship was examined using multiple correlation coefficients in separate analyses for both total number of stems and total basal area. An increase in stand-closure produced a decrease in stem-form for both total number of stems and total basal area for most species. There was a significant relationship between stem-form and site-conditions and between stand-closure and site-conditions for both total number of stems and total basal area for most species. There was a significant relationship between the stemform and site-conditions, including the stand-closure, for most species; total number of stems was involved independently of the site-conditions in the prediction of stem-form and total basal area was not. Larix laricina and Betula papyrifera were the exceptions to the trends observed with most species. The influence of both stand-closure (total number of stems in particular) and site-conditions (elevation in particular) suggest that forest management practices should include these- ecological parameters in determining appropriate restocking levels.

Determining rotational direction of rotation structures using prolate shaped grains within till

Micromorphology is used to analyze a wide range of sediments. Many microstructures have, as yet, not been analyzed. Rotation structures are the least understood of microstructures: their origin and development forms the basis of this thesis. Direction of rotational movement helps understand formative deformational and depositional processes. Twenty-eight rotation structures were analyzed through two methods of data extraction: (a) angle of grain rotation measured from Nikon NIS software, and (b) visual analyses of grain orientation, neighbouring grainstacks, lineations, and obstructions. Data indicates antithetic rotation is promoted by lubrication, accounting for 79% of counter-clockwise rotation structures while 21 % had clockwise rotation. Rotation structures are formed due to velocity gradients in sediment. Subglacial sediments are sheared due to overlying ice mass stresses. The grains in the sediment are differentially deformed. Research suggests rotation structures are formed under ductile conditions under low shear, low water content, and grain numbers inducing grain-to-grain interaction.

Dynamic Performance Evaluation of Canadian Fixed-Income Funds using Markov Regime Switching Models

This thesis examines the performance of Canadian fixed-income mutual funds in the context of an unobservable market factor that affects mutual fund returns. We use various selection and timing models augmented with univariate and multivariate regime-switching structures. These models assume a joint distribution of an unobservable latent variable and fund returns. The fund sample comprises six Canadian value-weighted portfolios with different investing objectives from 1980 to 2011. These are the Canadian fixed-income funds, the Canadian inflation protected fixed-income funds, the Canadian long-term fixed-income funds, the Canadian money market funds, the Canadian short-term fixed-income funds and the high yield fixed-income funds. We find strong evidence that more than one state variable is necessary to explain the dynamics of the returns on Canadian fixed-income funds. For instance, Canadian fixed-income funds clearly show that there are two regimes that can be identified with a turning point during the mid-eighties. This structural break corresponds to an increase in the Canadian bond index from its low values in the early 1980s to its current high values. Other fixed-income funds results show latent state variables that mimic the behaviour of the general economic activity. Generally, we report that Canadian bond fund alphas are negative. In other words, fund managers do not add value through their selection abilities. We find evidence that Canadian fixed-income fund portfolio managers are successful market timers who shift portfolio weights between risky and riskless financial assets according to expected market conditions. Conversely, Canadian inflation protected funds, Canadian long-term fixed-income funds and Canadian money market funds have no market timing ability. We conclude that these managers generally do not have positive performance by actively managing their portfolios. We also report that the Canadian fixed-income fund portfolios perform asymmetrically under different economic regimes. In particular, these portfolio managers demonstrate poorer selection skills during recessions. Finally, we demonstrate that the multivariate regime-switching model is superior to univariate models given the dynamic market conditions and the correlation between fund portfolios.

A DYNAMIC FRAMEWORK FOR THE RELATIONS BETWEEN FOREIGN EXCHANGE RATES, SAVINGS AND INVESTMENTS

The Meese-Rogoff forecasting puzzle states that foreign exchange (FX) rates are unpredictable. Since one country’s macroeconomic conditions could affect the price of its national currency, we study the dynamic relations between the FX rates and some macroeconomic accounts. Our research tests whether the predictability of the FX rates could be improved through the advanced econometrics. Improving the predictability of the FX rates has important implications for various groups including investors, business entities and the government. The present thesis examines the dynamic relations between the FX rates, savings and investments for a sample of 25 countries from the Organization for Economic Cooperation and Development. We apply quarterly data of FX rates, macroeconomic indices and accounts including the savings and the investments over three decades. Through preliminary Augmented Dickey-Fuller unit root tests and Johansen cointegration tests, we found that the savings rate and the investment rate are cointegrated with the vector (1,-1). This result is consistent with many previous studies on the savings-investment relations and therefore confirms the validity of the Feldstein-Horioka puzzle. Because of the special cointegrating relation between the savings rate and investment rate, we introduce the savings-investment rate differential (SID). Investigating each country through a vector autoregression (VAR) model, we observe extremely insignificant coefficient estimates of the historical SIDs upon the present FX rates. We also report similar findings through the panel VAR approach. We thus conclude that the historical SIDs are useless in forecasting the FX rate. Nonetheless, the coefficients of the past FX rates upon the current SIDs for both the country-specific and the panel VAR models are statistically significant. Therefore, we conclude that the historical FX rates can conversely predict the SID to some degree. Specifically, depreciation in the domestic currency would cause the increase in the SID.

Dynamics in large scale networks

In this thesis we study the properties of two large dynamic networks, the competition network of advertisers on the Google and Bing search engines and the dynamic network of friend relationships among avatars in the massively multiplayer online game (MMOG) Planetside 2. We are particularly interested in removal patterns in these networks. Our main finding is that in both of these networks the nodes which are most commonly removed are minor near isolated nodes. We also investigate the process of merging of two large networks using data captured during the merger of servers of Planetside 2. We found that the original network structures do not really merge but rather they get gradually replaced by newcomers not associated with the original structures. In the final part of the thesis we investigate the concept of motifs in the Barabási-Albert random graph. We establish some bounds on the number of motifs in this graph.