Browsing Mathematics (Faculty of) by Title
Now showing items 1557-1576 of 2985
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Mathematical Modeling of C elegans L1 aggregation
(University of Waterloo, 2020-01-16)First-stage larvae (L1s) of the nematode Caenorhabditis elegans aggregate after starvation. I develop a mathematical model of this behavior based on the classic Keller-Segel model. In the Keller-Segel model, organisms ... -
Mathematical Modeling of Kidney Function During Pregnancy
(University of Waterloo, 2022-05-16)During pregnancy major adaptations must occur in the maternal body to be able to support the rapidly developing fetus and placenta. Adaptations occur in almost all tissues and organs. These changes are dynamic, complex, ... -
Mathematical Modeling of Secondary Malignancies and Associated Treatment Strategies
(University of Waterloo, 2014-05-21)Several scientific and technological advancements in radiation oncology have resulted in dramatic improvements in dose conformity and delivery to the target volumes using external beam radiation therapy (EBRT). However, ... -
Mathematical Modeling of the Vaporization of Encapsulated Perfluorocarbon Nanodroplets using Chirp Ultrasound
(University of Waterloo, 2023-08-29)Ultrasound imaging is the use of sound waves beyond the human frequency range to construct images of human tissue. This is carried out through the measurement of reflected and scattered waves from the interfaces between ... -
Mathematical Modelling and Numerical Simulation of Marine Ecosystems With Applications to Ice Algae
(University of Waterloo, 2013-07-26)Sea-ice ecosystem modelling is a novel field of research. In this thesis, the main organism studied is sea-ice algae. A basic introduction to algae and its importance in the aquatic food web is given first. An introduction ... -
Mathematical Modelling of Cancer Stem Cells
(University of Waterloo, 2009-08-06)The traditional view of cancer asserts that a malignant tumour is composed of a population of cells, all of which share the ability to divide without limit. Within the last decade, however, this notion has lost ground ... -
Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs
(University of Waterloo, 2019-08-19)Cancer is one of the world's deadliest diseases despite immense investments into oncological research in recent years. Although great strides have been made in our understanding of cancer, much remains unknown regarding ... -
Mathematical Modelling of Social Factors in Decision Making Processes at the Individual and Population Levels
(University of Waterloo, 2016-08-11)In this thesis we apply mathematical modelling techniques to investigate the implications of social influence on decision making processes in two related contexts. The first problem concerns the mathematical modelling ... -
Mathematical modelling of supraglacial meltwater production and drainage
(University of Waterloo, 2021-08-30)Mountain glaciers and the polar ice sheets exert a critical control on water resource availability, drive sea level change, and impact global ocean circulation. These and other impacts are controlled by surface meltwater ... -
Mathematical Modelling of the Intrarenal Renin Angiotensin System in Hypertension
(University of Waterloo, 2023-04-24)Hypertension is the leading cause of cardiovascular disease and premature death world-wide. It is a highly multi-factorial disease associated with multiple risk factors and patho-physiological changes, including impaired ... -
Mathematical models for angiogenic, metabolic and apoptotic processes in tumours
(University of Waterloo, 2014-08-15)This doctoral thesis outlines a body of research within the field of mathematical oncology that focusses on the inclusion of microenvironmental factors in mathematical models for solid tumour behaviour. These models primarily ... -
Mathematical Models of Mitochondria in the Kidney and Liver
(University of Waterloo, 2022-03-24)Mitochondria are key players in several kinds of tissue injury, and are even the site of mechanism of certain diseases. In this work we introduce new models of mitochondrial ATP generation in multiple tissues, including ... -
Mathematical Programming Formulations of the Planar Facility Location Problem
(University of Waterloo, 2007-09-24)The facility location problem is the task of optimally placing a given number of facilities in a certain subset of the plane. In this thesis, we present various mathematical programming formulations of the planar ... -
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(Elsevier, 2021-07-15)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... -
Matrix analytic methods for computations in risk theory
(University of Waterloo, 2019-01-15)The introduction of matrix analytic methods in risk theory has marked a significant progress in computations in risk theory. Matrix analytic methods have proven to be powerful computational tools for numerically analyzing ... -
Matrix Formulations of Matching Problems
(University of Waterloo, 2000)Finding the maximum size of a matching in an undirected graph and finding the maximum size of branching in a directed graph can be formulated as matrix rank problems. The Tutte matrix, introduced by Tutte as a representation ... -
Matrix Polynomials and their Lower Rank Approximations
(University of Waterloo, 2019-08-07)This thesis is a wide ranging work on computing a “lower-rank” approximation of a matrix polynomial using second-order non-linear optimization techniques. Two notions of rank are investigated. The first is the rank as the ... -
Matrix-Variate Regression with Measurement Error
(University of Waterloo, 2020-09-28)Matrix-variate regression models are useful for featuring data with a matrix structure, such as brain imaging data. However, those methods do not apply to data with measurement error or misclassification. While mismeasurement ... -
Maximal ideal space techniques in non-selfadjoint operator algebras
(University of Waterloo, 2013-04-26)The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties. Specifically, we consider the restrictions M_V of the ... -
Maximal Operators in R^2
(University of Waterloo, 2007-08-13)A maximal operator over the bases $\mathcal{B}$ is defined as \[Mf(x) = \sup_{x \in B \in \mathcal{B}} \frac{1}{|B|}\int_B |f(y)|dy. \] The boundedness of this operator can be used in a number of applications including ...