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Wavelet Coherence Analysis With An Application Of Brain Images, Yiqian Fang
Wavelet Coherence Analysis With An Application Of Brain Images, Yiqian Fang
Arts & Sciences Electronic Theses and Dissertations
Wavelet analysis has become an emerging method in a wide range of applications with non-stationary data. In this work, we apply wavelets to tackle the problem of estimating dynamic association in a collection of multivariate non-stationary time series. Coherence is a common metric for linear dependence across signals. However, it assumes static dependence and does not sufficiently model many biological processes with time-evolving dependence structures. We explore continuous wavelet analysis for modeling and estimating such dynamic dependence under the replicated multivariate time series settings. Wavelet transformation provides a decomposition of signals that localizes in both time and frequency domains, hence …
A Different Approach To Endpoint Weak-Type Estimates For Calder̟N-Zygmund Operators, Cody B. Stockdale
A Different Approach To Endpoint Weak-Type Estimates For Calder̟N-Zygmund Operators, Cody B. Stockdale
Arts & Sciences Electronic Theses and Dissertations
The aim of this thesis is to investigate weak-type inequalities for linear and multilinear Calderón-Zygmund operators in Euclidean and weighted settings using the Calderón- Zygmund decomposition and ideas inspired by Nazarov, Treil, and Volberg. In the linear setting, a new simple proof of the classical weak-type (1; 1) property is given with motivation For multilinear Calderón-Zygmund operators, the Nazarov-Treil-Volberg ideas lead to a new proof of the weak-type (1,. . . ,1; 1/m) estimate. Connecting the weighted and multilinear settings, a weighted weak-type estimate for multilinear Calderón-Zygmund operators is proved. Two proofs for the weighted multilinear inequality are presented – …
Computation Of Knudsen Diffusivity In Domains With Boundary Micro-Structure, Luis Alberto Garcia German
Computation Of Knudsen Diffusivity In Domains With Boundary Micro-Structure, Luis Alberto Garcia German
Arts & Sciences Electronic Theses and Dissertations
We develop an analytical framework and numerical methods for the determination of the coefficient of self-diffusivity for the transport of a rarefied gas in channels, in the limit of large Knudsen number. We provide an effective method for determining the influence of channel surface micro-structure on the value of diffusivity. We also show how characteristic numbers of the system, namely geometric parameters of the micro-structure, the spectral gap of a Markov transition operator defined for a given micro-structure, and the tangential momentum accommodation coefficient of a commonly used model of surface scattering, are related. Examples of micro-structures are investigated regarding …
A Study On Lexicographic Shellable Posets, Tiansi Li
A Study On Lexicographic Shellable Posets, Tiansi Li
Arts & Sciences Electronic Theses and Dissertations
In this thesis, I will discuss the relations and differences between EL-shellable and CL-shellable posets. I will present examples of EL-shellable posets that are previously known to be CL-shellable, including rank-selected subposets of EL- shellable posets such as the Smirnov words posets, and comodernistic lattices. I will show that EL-shellability is equivalent to root-independent recursive atom ordering, and present two examples of CL-shellable posets that are not EL- shellable, one of which is a graded poset and the other is ungraded. In the end, I will briefly discuss how I think might fully characterize CL-shellable posets that are not EL-shellable.
Operator Noncommutative Function Theory And Partial Matrix And Operator Convexity, Mark E. Mancuso
Operator Noncommutative Function Theory And Partial Matrix And Operator Convexity, Mark E. Mancuso
Arts & Sciences Electronic Theses and Dissertations
No abstract provided.