Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

Modified statistical methods to calculate rare gas interaction potentials

New density functionals representing the exchange and correlation energies (per electron) are employed, based on the electron gas model, to calculate interaction potentials of noble gas systems X2 and XY, where X (and Y) are He,Ne,Ar and Kr, and of hydrogen atomrare gas systems H-X. The exchange energy density functional is that recommended by Handler and the correlation energy density functional is a rational function involving two parameters which were optimized to reproduce the correlation energy of He atom. Application of the two parameter function to other rare gas atoms shows that it is "universal"; i. e. ,accurate for the systems considered. The potentials obtained in this work compare well with recent experimental results and are a significant improvement over those from competing statistical modelS.

On the path integral formulation and the evaluation of quantum statistical averages

Four problems of physical interest have been solved in this thesis using the path integral formalism. Using the trigonometric expansion method of Burton and de Borde (1955), we found the kernel for two interacting one dimensional oscillators• The result is the same as one would obtain using a normal coordinate transformation, We next introduced the method of Papadopolous (1969), which is a systematic perturbation type method specifically geared to finding the partition function Z, or equivalently, the Helmholtz free energy F, of a system of interacting oscillators. We applied this method to the next three problems considered• First, by summing the perturbation expansion, we found F for a system of N interacting Einstein oscillators^ The result obtained is the same as the usual result obtained by Shukla and Muller (1972) • Next, we found F to 0(Xi)f where A is the usual Tan Hove ordering parameter* The results obtained are the same as those of Shukla and Oowley (1971), who have used a diagrammatic procedure, and did the necessary sums in Fourier space* We performed the work in temperature space• Finally, slightly modifying the method of Papadopolous, we found the finite temperature expressions for the Debyecaller factor in Bravais lattices, to 0(AZ) and u(/K/ j,where K is the scattering vector* The high temperature limit of the expressions obtained here, are in complete agreement with the classical results of Maradudin and Flinn (1963) .

Optimization of the valence energy variance of the CuH molecule

We developed the concept of split-'t to deal with the large molecules (in terms of the number of electrons and nuclear charge Z). This naturally leads to partitioning the local energy into components due to each electron shell. The minimization of the variation of the valence shell local energy is used to optimize a simple two parameter CuH wave function. Molecular properties (spectroscopic constants and the dipole moment) are calculated for the optimized and nearly optimized wave functions using the Variational Quantum Monte Carlo method. Our best results are comparable to those from the single and double configuration interaction (SDCI) method.

The investigation of edge effects within ragmented forest islands in Short Hills Provincial Park

It has been well documented, within the field of landscape ecology, that terrestrial fragmentation contributes to increased heterogeneity at the landscape level. It has also been observed that elevated areas of edge habitat occur within fragmented landscapes. Spatial and temporal edge effects were investigated in four areas designated as Nature Reserve Zones within Short Hills Provincial Park, near St. Catharines, Ontario. Random sampling along exposed edges was performed on trees and saplings, at 5 and 25 ill edge depths, using the point-centred quarter method. Diameter at breast height (dbh) and distance from point measurements were used to establish relative density, dominance, frequency and importance value. One-way analyses of variance were used on dbh measurements of tree species and Chi-Square contingency tables were used on size class distributions of saplings species to determine significant differences between 5 and 25 metres. Qualitative comparisons of importance values were also used to determine differences between 5 and 25 metres as well as between trees and saplings. These statistical and qualitative comparisons suggest that a significant overall spatial edge effect is currently exhibited by fragmented wooded islands within the park. The major species of the park, Acersaccharuln, may be exhibiting a temporal edge effect. The heterogeneous nature of the park may be of importance in understanding this area as a complex, ecological system. It is possible that the remaining forest tracts of the park have been affected, and continue to be affected by previous disturbances. Based on these findings, recommendations are made to the Ontario Ministry of Natural Resources concerning the management of Short Hills Provincial Park in accordance with their 1990 proposed Management Plan.

Investigating Player Salaries and Performance in the National Hockey League

This thesis examines salary structure types (hierarchical or compressed) as predictors of team performance in the National Hockey League (NHL). Additionally, an analysis of goalie statistics is completed in order to determine what, if any, performance measures relate to salary. Data in this research were collected from the 2005-06 season up to the 2010-11 season. Salary inequality/equality (Gini coefficient) was used in a regression analysis to determine if it was an effective predictor of team performance (n = 178) (winning percentage). The results indicated that a hierarchical salary structure increased team performance, although the amount of variability explained was very small. Another regression analysis was completed to determine if any goalie performance measures (n = 245) were effective predictors of individual salary. A regression analysis was employed and indicated that goalie performance measures predicted 19.8% of variance to salary. The only statistical significant variable was games played.

SAVOURING ABILITIES SCALE (SAS): THE DEVELOPMENT OF A STRENGTHS - BASED ASSESSMENT FOR THERAPEUTIC RECREATION PROFESSIONALS

The purpose of this study was to develop and evaluate an assessment that measured savouring leisure. The assessment items developed were reviewed for content validity by eight international therapeutic recreation (TR) educators and administrators as well as eleven TR practitioners. An exploratory factor analysis was conducted to determine the most suitable items for the assessment. The results suggest that the original three subscale design needed to be modified to five. The reliability of the total assessment is α=.84. Statistical analysis for construct validity reveal 58.52% of the variance explained, and a moderate correlation was found between this study and other savouring assessments. The implications of the shift in conceptualization are reviewed through discussing factor analysis issues, the lived experience of savouring leisure, and the impact of the content validity process. This study contributes to the ongoing dialog of savouring leisure. Recommendations for future research are discussed.