QSpace Collection:http://hdl.handle.net/1974/7582014-10-01T20:25:17Z2014-10-01T20:25:17ZNonparametric and parametric methods for solar oscillation spectraHaley, Charlottehttp://hdl.handle.net/1974/125022014-09-28T05:15:16Z2014-09-27T04:00:00ZTitle: Nonparametric and parametric methods for solar oscillation spectra
Authors: Haley, Charlotte
Abstract: The study of the systematic oscillations of the Sun has led to better understanding
of the Sun’s inner structure and dynamics, and may help to resolve inconsistencies
between observations and the standard solar model. Recent studies have concluded
that solar modal structure remains coherent past turbulence in the convection zone
and imprints its signatures on the solar wind and the interplanetary magnetic field
fluctuations, and these structures are coherent with atmospheric pressure variations,
terrestrial seismic oscillations, and data from communications systems. Time series
containing modal structure can be expected to contain several thousands of resolved
and unresolved line components in very short bands in frequency, and the measure-
ment of these modes pushes spectrum estimation methods for time series to its limit.
This thesis presents two theoretical contributions for modeling solar oscillations in
power spectra (i) expressions for the expected number and shape of significant spuri-
ous peaks in spectrum estimates are given, in the absence of modal structure, and a
permutation test for the identification of spectra containing pathological numbers of
modal components. (ii) A model for maximum likelihood estimation of the solar os-
cillation parameters in composite spectra is given. The scientific contributions of this
thesis are (a) identification of highly significant modal artifacts in solar wind mea-
surements as seen by the Advanced Composition Explorer (ACE) on the 2 − 3mHz
band and (b) quantification of the presence of modal structure in secondary cosmic
rays (specifically neutrons) on Earth.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2014-09-25 19:20:15.2252014-09-27T04:00:00ZOn Malliavin Calculus and Concentration InequalitiesTreilhard, Johnhttp://hdl.handle.net/1974/122702014-07-07T20:54:52Z2014-07-07T04:00:00ZTitle: On Malliavin Calculus and Concentration Inequalities
Authors: Treilhard, John
Abstract: We prove new abstract results concerning concentration inequalities and density estimates for Malliavin differentiable random variables. The efficacy of these results are demonstrated by practical computations, such as the calculation of novel concentration inequalities for $Z = \max_{1 \leq i \leq n} N_i - E\left[ \max_{1 \leq i \leq n} N_i \right]$ where the $\{N_i\}_{i=1, ..., n}$ are Normal random variables, and $\int_0^1 B_s^4 ds - \frac{3}{4H+1}$ where $\{B_s, s \in [0,1] \}$ is a fractional Brownian motion with Hurst parameter $H$, as well as the derivation of non-asymptotic confidence intervals for the Hurst parameter of a fractional Brownian motion.
Description: Thesis (Master, Mathematics & Statistics) -- Queen's University, 2014-07-03 23:31:55.9672014-07-07T04:00:00ZArithmetic problems around the ABC conjecture and connections with logicPasten, Hectorhttp://hdl.handle.net/1974/121232014-04-29T05:10:00Z2014-04-28T04:00:00ZTitle: Arithmetic problems around the ABC conjecture and connections with logic
Authors: Pasten, Hector
Abstract: The main theme in this thesis is the ABC conjecture. We prove some partial results towards it and we find new applications of this conjecture, mainly in the context of B\"uchi's n squares problem (which has consequences in logic related to Hilbert's tenth problem) and squarefree values of polynomials. We also study related topics, such as arithmetic properties of additive subgroups of Hecke algebras, function field and meromorphic value distribution, and undecidability of the positive existential theories over languages of arithmetic interest.
Description: Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2014-04-28 10:47:54.0642014-04-28T04:00:00ZForecasting and Non-Stationarity of Surgical Demand Time SeriesMoore, Ianhttp://hdl.handle.net/1974/86192014-02-05T05:58:45Z2014-02-04T05:00:00ZTitle: 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 11:55:42.4942014-02-04T05:00:00Z