QSpace Collection:
http://hdl.handle.net/1974/758
Mon, 21 Apr 2014 02:43:26 GMT2014-04-21T02:43:26ZForecasting and Non-Stationarity of Surgical Demand Time Series
http://hdl.handle.net/1974/8619
Title: Forecasting and Non-Stationarity of Surgical Demand Time Series
Authors: Moore, Ian
Abstract: Surgical scheduling is complicated by naturally occurring, and human-induced variability in the demand for surgical services. We used time series methods to detect, model and forecast these behaviors in surgical demand time series to help improve the scheduling of scarce surgical resources.
With institutional approval, we studied 47,752 surgeries undertaken at a large academic medical center over a six-year time frame. Each daily sample in this time series represented the aggregate total hours of surgeries worked on a given day. Linear terms such as periodic cycles, trends, and serial correlations explained approximately 80 percent of the variance in the raw data. We used a moving variance filter to help explain away a large share of the heteroscedastic behavior mainly attributable to surgical activities on specific US holidays, which we defined as holiday variance.
In the course of this research, we made a thoughtful attempt to understand the time series structure within our surgical demand data. We also laid a foundation, for further development, of two time series techniques, the multiwindow variance filter and cyclostatogram that can be applied not only to surgical demand time series, but also to other time series problems from other disciplines. We believe that understanding the non-stationarity, in surgical demand time series, may be an important initial step in helping health care managers save critical health care dollars.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2009-02-09 11:55:42.494Tue, 04 Feb 2014 05:00:00 GMThttp://hdl.handle.net/1974/86192014-02-04T05:00:00ZON THE CONVERGENCE AND APPLICATIONS OF MEAN SHIFT TYPE ALGORITHMS
http://hdl.handle.net/1974/8365
Title: ON THE CONVERGENCE AND APPLICATIONS OF MEAN SHIFT TYPE ALGORITHMS
Authors: Aliyari Ghassabeh, Youness
Abstract: Mean shift (MS) and subspace constrained mean shift (SCMS) algorithms are non-parametric, iterative methods to find a representation of a high dimensional data set on a principal curve or surface embedded in a high dimensional space. The representation of high dimensional data on a principal curve or surface, the class of mean shift type algorithms and their properties, and applications of these algorithms are the main focus of this dissertation. Although MS and SCMS algorithms have been used in many applications, a rigorous study of their convergence is still missing. This dissertation aims to fill some of the gaps between theory and practice by investigating some convergence properties of these algorithms. In particular, we propose a sufficient condition for a kernel density estimate with a Gaussian kernel to have isolated stationary points to guarantee the convergence of the MS algorithm. We also show that the SCMS algorithm inherits some of the important convergence properties of the MS algorithm. In particular, the monotonicity and convergence of the density estimate values along the sequence of output values of the algorithm are shown. We also show that the distance between consecutive points of the output sequence converges to zero, as does the projection of the gradient vector onto the subspace spanned by the D-d eigenvectors corresponding to the D-d largest eigenvalues of the local inverse covariance matrix. Furthermore, three new variations of the SCMS algorithm are proposed and the running times and performance of the resulting algorithms are compared with original SCMS algorithm. We also propose an adaptive version of the SCMS algorithm to consider the effect of new incoming samples without running the algorithm on the whole data set. As well, we develop some new potential applications of the MS and SCMS algorithm. These applications involve finding straight lines in digital images; pre-processing data before applying locally linear embedding (LLE) and ISOMAP for dimensionality reduction; noisy source vector quantization where the clean data need to be estimated before the quanization step; improving the performance of kernel regression in certain situations; and skeletonization of digitally stored handwritten characters.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-30 18:01:12.959Tue, 01 Oct 2013 04:00:00 GMThttp://hdl.handle.net/1974/83652013-10-01T04:00:00ZUnstable Brake Orbits in Symmetric Hamiltonian Systems
http://hdl.handle.net/1974/8313
Title: Unstable Brake Orbits in Symmetric Hamiltonian Systems
Authors: Lewis, Mark
Abstract: In this thesis we investigate the existence and stability of periodic solutions of Hamiltonian systems with a discrete symmetry. The global existence of periodic motions can be proven using the classical techniques of the calculus of variations; our particular interest is in how the stability type of the solutions thus obtained can be determined analytically using solely the variational problem and the symmetries of the system -- we make no use of numerical or perturbation techniques. Instead, we use a method introduced in [41] in the context of a special case of the three-body problem. Using techniques from symplectic geometry, and specifically the Maslov index for curves of Lagrangian subspaces along the minimizing trajectories, we verify conditions which preclude the existence of eigenvalues of the monodromy matrix on the unit circle.
We study the applicability of this method in two specific cases. Firstly, we consider another special case from celestial mechanics: the hip-hop solutions of the 2N-body problem. This is a family of Z_2-symmetric, periodic orbits which arise as collision-free minimizers of the Lagrangian action on a space of symmetric loops [14, 53]. Following a symplectic reduction, it is shown that the hip-hop solutions are brake orbits which are generically hyperbolic on the reduced energy-momentum surface.
Secondly we consider a class of natural Hamiltonian systems of two degrees of freedom with a homogeneous potential function. The associated action functional is unbounded above and below on the function space of symmetric curves, but saddle points can be located by minimization subject to a certain natural constraint of a type first considered by Nehari [37, 38]. Using the direct method of the calculus of variations, we prove the existence of symmetric solutions of both prescribed period and prescribed energy. In the latter case, we employ a variational principle of van Groesen [55] based upon a modification of the Jacobi functional, which has not been widely used in the literature. We then demonstrate that the (constrained) minimizers are again hyperbolic brake orbits; this is the first time the method has been applied to solutions which are not globally minimizing.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-25 10:47:53.257Wed, 25 Sep 2013 04:00:00 GMThttp://hdl.handle.net/1974/83132013-09-25T04:00:00ZTHE TATE CONJECTURES FOR PRODUCT AND QUOTIENT VARIETIES
http://hdl.handle.net/1974/8307
Title: THE TATE CONJECTURES FOR PRODUCT AND QUOTIENT VARIETIES
Authors: Ejouamai, Rachid
Abstract: This thesis extends Tate’s conjectures from the smooth case to quotient varieties. It
shows that two of those conjectures hold for quotient varieties if they hold for smooth
projective varieties. We also consider arbitrary product of modular curves and show
that the three conjectures of Tate (in codimension 1) hold for this product. Finally we
look at quotients of the surface V = X1(N)×X1(N) and prove that Tate’s conjectures
are satisfied for those quotients.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2013-09-21 09:43:47.789Tue, 24 Sep 2013 04:00:00 GMThttp://hdl.handle.net/1974/83072013-09-24T04:00:00Z