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#### Martingale Property and Pricing for Time-homogeneous Diffusion Models in Finance

(University of Waterloo, 2013-08-09)

The thesis studies the martingale properties, probabilistic methods and efficient unbiased Monte Carlo simulation methods for various time-homogeneous diffusion models commonly used in mathematical finance. Some of the ...

#### Software Architecture Recovery based on Pattern Matching

(University of Waterloo, 2003)

Pattern matching approaches in reverse engineering aim to incorporate domain knowledge and system documentation in the software architecture extraction process, hence provide a user/tool collaborative environment for ...

#### Classification of Nilpotent Lie Algebras of Dimension 7 (over Algebraically Closed Field and R)

(University of Waterloo, 1998)

This thesis is concerned with the classification of 7-dimensional nilpotent Lie algebras. Skjelbred and Sund have published in 1977 their method of constructing all nilpotent Lie algebras of dimension <i>n</i> given those ...

#### Answering Object Queries over Knowledge Bases with Expressive Underlying Description Logics

(University of Waterloo, 2013-10-25)

Many information sources can be viewed as collections of objects and descriptions about objects. The relationship between objects is often characterized by a set of constraints that semantically encode background knowledge ...

#### Nonlinear Dimensionality Reduction with Side Information

(University of Waterloo, 2006)

In this thesis, I look at three problems with important applications in data processing. Incorporating side information, provided by the user or derived from data, is a main theme of each of these problems. <br /><br ...

#### The Continuum Architecture: Towards Enabling Chaotic Ubiquitous Computing

(University of Waterloo, 2005)

Interactions in the style of the ubiquitous computing paradigm are possible today, but only in handcrafted environments within one administrative and technological realm. This thesis describes an architecture (called ...

#### Reconstruction and Visualization of Polyhedra Using Projections

(University of Waterloo, 2005)

Two types of problems are studied in this thesis: reconstruction and visualization of polygons and polyhedra. <br /><br /> Three problems are considered in reconstruction of polygons and polyhedra, given a set of projection characteristics. The first problem is to reconstruct a closed convex polygon (polyhedron) given the number of visible edges (faces) from each of a set of directions

**S**. The main results for this problem include the necessary and sufficient conditions for the existence of a polygon that realizes the projections. This characterization gives an algorithm to construct a feasible polygon when it exists. The other main result is an algorithm to find the maximum and minimum size of a feasible polygon for the given set**S**. Some special cases for non-convex polygons and for perspective projections are also studied. <br /><br /> For reconstruction of polyhedra, it is shown that when the projection directions are co-planar, a feasible polyhedron (i. e. a polyhedron satisfying the projection properties) can be constructed from a feasible polygon and vice versa. When the directions are covered by two planes, if the number of visible faces from each of the directions is at least four, then an algorithm is presented to decide the existence of a feasible polyhedron and to construct one, when it exists. When the directions see arbitrary number of faces, the same algorithm works, except for a particular sub-case. <br /><br /> A polyhedron is, in general, called equiprojective, if from any direction the size of the projection or the projection boundary is fixed, where the "size" means the number of vertices, edge, or faces. A special problem on reconstruction of polyhedra is to find all equiprojective polyhedra. For the case when the size is the number of vertices in the projection boundary, main results include the characterization of all equiprojective polyhedra and an algorithm to recognize them, and finding the minimum equiprojective polyhedra. Other measures of equiprojectivity are also studied. <br /><br /> Finally, the problem of efficient visualization of polyhedra under given constraints is considered. A user might wish to find a projection that highlights certain properties of a polyhedron. In particular, the problem considered is given a set of vertices, edges, and/or faces of a convex polyhedron, how to determine all projections of the polyhedron such that the elements of the given set are on the projection boundary. The results include efficient algorithms for both perspective and orthogonal projections, and improved adaptive algorithm when only edges are given and they form disjoint paths. A related problem of finding all projections where the given edges, faces, and/or vertices are not on the projection boundary is also studied....#### Analysis of Longitudinal Surveys with Missing Responses

(University of Waterloo, 2008-09-12)

Longitudinal surveys have emerged in recent years as an important data collection tool for population studies where the primary interest is to examine population changes over time at the individual level. The National ...

#### Multi-User File System Search

(University of Waterloo, 2007-08-03)

Information retrieval research usually deals with globally visible, static document collections. Practical applications, in contrast, like file system search and enterprise search, have to cope with highly dynamic text ...

#### Rough Set Based Rule Evaluations and Their Applications

(University of Waterloo, 2007-03-06)

Knowledge discovery is an important process in data analysis, data
mining and machine learning. Typically knowledge is presented in the
form of rules. However, knowledge discovery systems often generate a
huge amount ...