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Full-Text Articles in Physical Sciences and Mathematics
Local Holomorphic Extension Of Cauchy Riemann Functions, Brijitta Antony
Local Holomorphic Extension Of Cauchy Riemann Functions, Brijitta Antony
Doctoral Dissertations
"The purpose of this dissertation is to give an analytic disc approach to the CR extension problem. Analytic discs give a very convenient tool for holomorphic extension of CR functions. The type function is introduced and showed how these type functions have direct application to important questions about CR extension. In this dissertation the CR extension theorem is proved for a rigid hypersurface M in C2 given by y = (Re ω)m(Im ω)n where m and n are non-negative integers. If the type function is identically zero at the origin, then there is no CR extension. …
A Functional Data Analytic Approach For Region Level Differential Dna Methylation Detection, Mohamed Salem F. Milad
A Functional Data Analytic Approach For Region Level Differential Dna Methylation Detection, Mohamed Salem F. Milad
Doctoral Dissertations
"DNA methylation is an epigenetic modification that can alter gene expression without a DNA sequence change. The role of DNA methylation in biological processes and human health is important to understand, with many studies identifying associations between specific methylation patterns and diseases such as cancer. In mammals, DNA methylation almost always occurs when a methyl group attaches to a cytosine followed by a guanine (i.e. CpG dinucleotides) on the DNA sequence. Many statistical methods have been developed to test for a difference in DNA methylation levels between groups (e.g. healthy vs disease) at individual cytosines. Site level testing is often …