Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

Walker Brothers Quarries Limited fonds, 1975, 1980-1981, 1984, 1987-1989

Serving the Niagara and surrounding areas for over 120 years, Walker Industries has made its impact not only commercially, but also culturally. Beginning in 1875 with the erection of a stone sawing mill on a property John Walker purchased from the Welland Canal Loan Company. One of the first projects Walker cut stone for was the Merritton Town Hall. In 1882 the business expanded to include Walkers children, changing the name to Walker & Sons. Eventually in 1887 the two eldest sons took control of the business operation and their partnership changed the company’s name to Walker Brothers, the same year the company began operating its first quarry. The quarry was conveniently located alongside the 3rd Welland canal, offering easy access to Toronto and Hamilton. It was also close to the railway system which allowed immediate access to Thorold and Niagara Falls and later access to parts of Ontario and Quebec. The quarry supplied stone to build numerous halls and armouries across Ontario. A use was also found for the ‘waste products’ of cutting the limestone. Leftover stone chips were sent to paper mills, where stone was needed as part of the sulphite pulp process for making paper. Beginning to supply the Ontario Paper Company with stone in 1913, meant not only long, hard, work, but also more profit for the company. Before mechanization, most of the loading and unloading of the stone was done by hand, taking 19 man-hours to load an 18 yard railway car. Mechanization followed in 1947 when the plant became fully mechanized making the work easier and increasing production rates. In 1957 the company moved from its original location and opened the St. Catharines Crushed Stone Plant.

A stochastic dynamic programming approach for pricing options on stock-index futures

The aim of this thesis is to price options on equity index futures with an application to standard options on S&P 500 futures traded on the Chicago Mercantile Exchange. Our methodology is based on stochastic dynamic programming, which can accommodate European as well as American options. The model accommodates dividends from the underlying asset. It also captures the optimal exercise strategy and the fair value of the option. This approach is an alternative to available numerical pricing methods such as binomial trees, finite differences, and ad-hoc numerical approximation techniques. Our numerical and empirical investigations demonstrate convergence, robustness, and efficiency. We use this methodology to value exchange-listed options. The European option premiums thus obtained are compared to Black's closed-form formula. They are accurate to four digits. The American option premiums also have a similar level of accuracy compared to premiums obtained using finite differences and binomial trees with a large number of time steps. The proposed model accounts for deterministic, seasonally varying dividend yield. In pricing futures options, we discover that what matters is the sum of the dividend yields over the life of the futures contract and not their distribution.

A. C. Thorburn Prescription Ledger

The gift plate in the front of the book indicates that the book is from Walker’s Drug Store, Niagara Falls, Ontario. Walker’s Drug Company was founded in 1925 by Ivan T. Walker. The dates of this book indicate that it is more likely to have come from A.C. Thorburn, Chemist and Druggist. A.C. Thorburn purchased Smith’s Pharmacy and Pursel and Company Dry Goods Store at the corner of Main Street and Lundy’s Lane in Niagara Falls, Ontario. In 1900, Pursel moved out and Thorburn’s Drug Store came into being. Ivan T. Walker, founder of Walker’s Drugs was employed by Thorburn Drugs in his teen years. The local doctors whose prescriptions are in the book include: J. H. McGarry; F.W.E. Wilson; C. F. Abraham; W.E. Olmsted; W.W. Thompson; Dr. Robb, dentist; Horace R. Elliot, physician and surgeon and Dr. Sutherland, eye, ear nose and throat specialist

Feature Selection and Classification Using Age Layered Population Structure Genetic Programming

The curse of dimensionality is a major problem in the fields of machine learning, data mining and knowledge discovery. Exhaustive search for the most optimal subset of relevant features from a high dimensional dataset is NP hard. Sub–optimal population based stochastic algorithms such as GP and GA are good choices for searching through large search spaces, and are usually more feasible than exhaustive and deterministic search algorithms. On the other hand, population based stochastic algorithms often suffer from premature convergence on mediocre sub–optimal solutions. The Age Layered Population Structure (ALPS) is a novel metaheuristic for overcoming the problem of premature convergence in evolutionary algorithms, and for improving search in the fitness landscape. The ALPS paradigm uses an age–measure to control breeding and competition between individuals in the population. This thesis uses a modification of the ALPS GP strategy called Feature Selection ALPS (FSALPS) for feature subset selection and classification of varied supervised learning tasks. FSALPS uses a novel frequency count system to rank features in the GP population based on evolved feature frequencies. The ranked features are translated into probabilities, which are used to control evolutionary processes such as terminal–symbol selection for the construction of GP trees/sub-trees. The FSALPS metaheuristic continuously refines the feature subset selection process whiles simultaneously evolving efficient classifiers through a non–converging evolutionary process that favors selection of features with high discrimination of class labels. We investigated and compared the performance of canonical GP, ALPS and FSALPS on high–dimensional benchmark classification datasets, including a hyperspectral image. Using Tukey’s HSD ANOVA test at a 95% confidence interval, ALPS and FSALPS dominated canonical GP in evolving smaller but efficient trees with less bloat expressions. FSALPS significantly outperformed canonical GP and ALPS and some reported feature selection strategies in related literature on dimensionality reduction.

Modeling short-range ballistic missile defense and Israel's Iron Dome system

This paper develops a model of short-range ballistic missile defense and uses it to study the performance of Israel’s Iron Dome system. The deterministic base model allows for inaccurate missiles, unsuccessful interceptions, and civil defense. Model enhancements consider the trade-offs in attacking the interception system, the difficulties faced by militants in assembling large salvos, and the effects of imperfect missile classification by the defender. A stochastic model is also developed. Analysis shows that system performance can be highly sensitive to the missile salvo size, and that systems with higher interception rates are more “fragile” when overloaded. The model is calibrated using publically available data about Iron Dome’s use during Operation Pillar of Defense in November 2012. If the systems performed as claimed, they saved Israel an estimated 1778 casualties and $80 million in property damage, and thereby made preemptive strikes on Gaza about 8 times less valuable to Israel. Gaza militants could have inflicted far more damage by grouping their rockets into large salvos, but this may have been difficult given Israel’s suppression efforts. Counter-battery fire by the militants is unlikely to be worthwhile unless they can obtain much more accurate missiles.