Browsing by Subject "Functional analysis"

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Open Access
Development of a shiny application for comparative transcriptomics and differential gene expression analysis
(2022-09) Leka, Ronaldo
RNA sequencing has proven to be an effective technique for divulging information about the transcriptome in molecular biology research. Compared to microarrays and early methods of cDNA sequencing, high-throughput RNA sequencing has better resolution, low background noise, a higher range to quantify gene expression, and relatively lower cost. The development of sequencing technique has led to the development of tools for analyzing the high volume of data that is generated. Statistical methods for normalizing, filtering, performing exploratory and differential analysis, and other functional analyses based on RNA sequencing count data have made RNA sequencing one of the most popular techniques in genomics. To help facilitate the use of such statistical tools, web applications developed in R using the shiny package offer an advantageous environment where researchers can use a graphical interface to give inputs and instructions to the underlying server-side libraries that analyze and generate results in tables and plots. This thesis presents a new tool that has been developed for exploratory analysis, data normalization and filtering, differential gene expression analysis (DGEA), correlation analysis, principal component analysis, and functional analysis such as over-representation analysis and gene set enrichment analysis. When compared to other available applications, this new application offers the ability to run multiple methods for DGEA and compare results between them, leading to the output of gene sets that are discovered as DEGs in multiple tests. Here I present the features of this application in detail where I aim to improve upon the applications that are available in the literature. An example dataset from our lab was also investigated by this RNA-seq tool leading to a better understanding of Mineralocorticoid Receptor (MR) signaling in breast cancer.
Open Access
On the analyticity of functions approximated by their q-Bernstein polynomials when q > 1
(2010) Ostrovskii I.; Ostrovska, S.
Since in the case q > 1 the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties for q > 1 turns out to be much harder than the one for 0 < q < 1. What is more, the fast increase of the norms ∥Bn,q∥ as n → ∞, along with the sign oscillations of the q-Bernstein basic polynomials when q > 1, create a serious obstacle for the numerical experiments with the q-Bernstein polynomials. Despite the intensive research conducted in the area lately, the class of functions which are uniformly approximated by their q-Bernstein polynomials on [0, 1] is yet to be described. In this paper, we prove that if f:[0,1]→C is analytic at 0 and can be uniformly approximated by its q-Bernstein polynomials (q > 1) on [0, 1], then f admits an analytic continuation from [0, 1] into {z: z < 1}. © 2010 Elsevier Inc. All rights reserved.