QSpace Community: Queen's UniversityInformation
http://hdl.handle.net/1974/6
Queen's UniversityInformation2016-09-27T13:56:25ZAn impulsive differential equation model for Marek's disease
http://hdl.handle.net/1974/14944
Title: An impulsive differential equation model for Marek's disease
Authors: Rozins, CARLY
Abstract: Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are referred to as impulsive differential equations, systems of differential equations coupled with discrete mappings in state space. In this thesis we employ impulsive differential equations to model disease transmission within an industrial livestock barn.
In particular we focus on the poultry industry and a viral disease of poultry called Marek's disease. This system lends itself well to impulsive differential equations. Entire cohorts of poultry are introduced and removed from a barn concurrently. Additionally, Marek's disease is transmitted indirectly and the viral particles can survive outside the host for weeks. Therefore, depopulating, cleaning, and restocking of the barn are integral factors in modelling disease transmission and can be completely captured by the impulsive component of the model.
Our model allows us to investigate how modern broiler farm practices can make disease elimination difficult or impossible to achieve. It also enables us to investigate factors that may contribute to virulence evolution.
Our model suggests that by decrease the cohort duration or by decreasing the flock density, Marek's disease can be eliminated from a barn with no increase in cleaning effort. Unfortunately our model also suggests that these practices will lead to disease evolution towards greater virulence. Additionally, our model suggests that if intensive cleaning between cohorts does not rid the barn of disease, it may drive evolution and cause the disease to become more virulent.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2016-09-22 10:30:23.3422016-09-22T04:00:00ZElliptic Functions and Elliptic Interpolation
http://hdl.handle.net/1974/14922
Title: Elliptic Functions and Elliptic Interpolation
Authors: Ciupeanu, Adriana-Stefania2016-09-21T04:00:00ZIrreducibility of Random Hilbert Schemes
http://hdl.handle.net/1974/14882
Title: Irreducibility of Random Hilbert Schemes
Authors: Staal, Andrew P
Abstract: We prove that a random Hilbert scheme that parametrizes the closed
subschemes with a fixed Hilbert polynomial in some projective space is
irreducible and nonsingular with probability greater than $0.5$. To
consider the set of nonempty Hilbert schemes as a probability space,
we transform this set into a disjoint union of infinite binary trees,
reinterpreting Macaulay's classification of admissible Hilbert
polynomials. Choosing discrete probability distributions with
infinite support on the trees establishes our notion of random Hilbert
schemes. To bound the probability that random Hilbert schemes are
irreducible and nonsingular, we show that at least half of the
vertices in the binary trees correspond to Hilbert schemes with unique
Borel-fixed points.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2016-09-11 13:52:03.7712016-09-13T04:00:00ZEstimation of Sample Size and Power For Quantile Regression
http://hdl.handle.net/1974/14739
Title: Estimation of Sample Size and Power For Quantile Regression
Authors: Gong, Zhenxian
Abstract: Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences.
Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects.
Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation.
The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.2016-08-24T04:00:00Z