QSpace Community: Queen's UniversityInformation
http://hdl.handle.net/1974/6
Queen's UniversityInformation2014-10-01T14:22:40ZNonparametric and parametric methods for solar oscillation spectra
http://hdl.handle.net/1974/12502
Title: 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 Inequalities
http://hdl.handle.net/1974/12270
Title: 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 Analysis
http://hdl.handle.net/1974/12234
Title: 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 logic
http://hdl.handle.net/1974/12123
Title: 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 10:47:54.0642014-04-28T04:00:00Z