Browsing Theses by Subject "geometry"
Now showing items 1-7 of 7
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Average Cell Orientation, Eccentricity and Size Estimated from Tissue Images
(University of Waterloo, 2005)Five image processing algorithms are proposed to measure the average orientation, eccentricity and size of cells in images of biological tissue. These properties, which can be embodied by an elliptical 'composite cell', ... -
A Geometric Approach to Pattern Matching in Polyphonic Music
(University of Waterloo, 2005)The music pattern matching problem involves finding matches of a small fragment of music called the "pattern" into a larger body of music called the "score". We represent music as a series of horizontal line segments in ... -
Geometry of Quantum States from Symmetric Informationally Complete Probabilities
(University of Waterloo, 2013-08-06)It is usually taken for granted that the natural mathematical framework for quantum mechanics is the theory of Hilbert spaces, where pure states of a quantum system correspond to complex vectors of unit length. These vectors ... -
Hurwitz Trees and Tropical Geometry
(University of Waterloo, 2016-01-21)The lifting problem in algebraic geometry asks when a finite group G acting on a curve defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of this problem is the Hurwitz tree, which ... -
Mediation: Resonating between the Organic and Inorganic
(University of Waterloo, 2020-05-29)This thesis emerges from the desire of unity between the intuitive and empirical expressions of nature. It argues for a greater understanding of 'patterns' inherent in nature and advocates for the need to see things as a ... -
On the Representation Theory of Semisimple Lie Groups
(University of Waterloo, 2010-08-30)This thesis is an expository account of three central theorems in the representation theory of semisimple Lie groups, namely the theorems of Borel-Weil-Bott, Casselman-Osborne and Kostant. The first of these realizes all ... -
Tensors: Entanglement, Geometry, and Combinatorics
(University of Waterloo, 2022-04-26)In this thesis, we use algebraic-geometric and combinatorial techniques to study tensor decompositions, with applications in quantum information theory, algebraic complexity theory, and algebraic statistics. A tensor is a ...