QSpace Community: Queen's UniversityInformationQueen's UniversityInformationhttp://hdl.handle.net/1974/62014-09-21T10:09:54Z2014-09-21T10:09:54ZOn 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 23:31:55.9672014-07-07T04:00:00ZLocalization of Brain Activity Using Permutation AnalysisAlikhanian, Hoomanhttp://hdl.handle.net/1974/122342014-06-22T12:10:48Z2014-06-19T04:00:00ZTitle: Localization of Brain Activity Using Permutation Analysis
Authors: Alikhanian, Hooman
Abstract: In this report we study bootstrap theory and permutation analysis as a hypothesis testing method using bootstrap procedure. We investigate asymptotic properties of the bootstrap procedure as well as bootstrap estimate accuracy using Edgeworth and Cornish-Fisher expansions. We show that resampling with replacement from data provides a theoretically sound method that outperforms Normal approximation of data distribution in terms of convergence error and accuracy of estimates. We conclude the report by applying permutation analysis on Magentoencephalography (MEG) brain signals to localize human brain activity in pointing/reaching tasks and find regions that are significantly active.2014-06-19T04:00:00ZArithmetic 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