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Full-Text Articles in Physical Sciences and Mathematics
Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu
Nonparametric Variable Selection And Dimension Reduction Methods And Their Applications In Pharmacogenomics, Jingyi Zhu
Open Access Dissertations
Nowadays it is common to collect large volumes of data in many fields with an extensive amount of variables, but often a small or moderate number of samples. For example, in the analysis of genomic data, the number of genes can be very large, varying from tens of thousands to several millions, whereas the number of samples is several hundreds to thousands. Pharmacogenomics is an example of genomics data analysis that we are considering here. Pharmacogenomics research uses whole-genome genetic information to predict individuals' drug response. Because whole-genome data are high dimensional and their relationships to drug response are complicated, …
Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh
Probabilistic Uncertainty Quantification And Experiment Design For Nonlinear Models: Applications In Systems Biology, Vu Cao Duy Thien Dinh
Open Access Dissertations
Despite the ever-increasing interest in understanding biology at the system level, there are several factors that hinder studies and analyses of biological systems. First, unlike systems from other applied fields whose parameters can be effectively identified, biological systems are usually unidentifiable, even in the ideal case when all possible system outputs are known with high accuracy. Second, the presence of multivariate bifurcations often leads the system to behaviors that are completely different in nature. In such cases, system outputs (as function of parameters/inputs) are usually discontinuous or have sharp transitions across domains with different behaviors. Finally, models from systems biology …
On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan
On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan
Open Access Dissertations
In this dissertation we study three problems related to motifs and recursive trees. In the first problem we consider a collection of uncorrelated motifs and their occurrences on the fringe of random recursive trees. We compute the exact mean and variance of the multivariate random vector of the counts of occurrences of the motifs. We further use the Cramér-Wold device and the contraction method to show an asymptotic convergence in distribution to a multivariate normal random variable with this mean and variance. ^ The second problem we study is that of the probability that a collection of motifs (of the …