1988 DWC Membership and Mailing Lists

Membership list of DWC members, 198

Efficient Multidimensional Functional Data Analysis Using Marginal Product Basis Systems

In areas ranging from neuroimaging to climate science, advances in data storage and sensor technology have led to a proliferation in multidimensional functional datasets. A common approach to analyzing functional data is to first map the discretely observed functional samples into continuous representations, and then perform downstream statistical analysis on these smooth representations. It is well known that many of the traditional approaches used for 1D functional data representation are plagued by the curse of dimensionality and quickly become intractable as the dimension of the domain increases. In this paper, we propose a computational framework for learning continuous representations from a sample of multidimensional functional data that is immune to several manifestations of the curse. The representations are constructed using a set of separable basis functions that are defined to be optimally adapted to the data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition of a carefully defined reduction transformation of the observed data. Roughness-based regularization is incorporated using a class of differential operator-based penalties. Relevant theoretical properties are also discussed. The advantages of our method over competing methods are thoroughly demonstrated in simulations. We conclude with a real data application of our method to a clinical diffusion MRI dataset.</p

Number of detected DEGs as a function of sample size.

<p>(a): <b>TALL</b> versus <b>TEL</b>; (b) <b>HYPERDIP</b> versus <b>TEL</b>. Total number of genes is . <i>t</i>-test and Bonferroni procedure are applied. Adjusted -value threshold: 0.05.</p

Additional file 1 of Super-delta: a new differential gene expression analysis procedure with robust data normalization

Theoretical proofs and justifications. This file contains a series of theorem/lemma/proposition/corollary proofs that form the theoretical foundation of super-delta method. (PDF 236 kb

Number of true (a,c) and false (b,d) positives as functions of effect size (SIMU1).

<p>Total number of genes is . Total number of truly differentially expressed genes is , where and are the numbers of up- and down-regulated genes, respectively. The sample size is . <i>t</i>-test and Bonferroni procedure are applied. Adjusted -value threshold: 0.05.</p

Additional file 3 of Super-delta: a new differential gene expression analysis procedure with robust data normalization

Top 30 significant genes’ annotation. This file includes biological annotation of the 30 most significant genes, detected by each method, sorted by the magnitude of t-statistics. (XLSX 39 kb

Additional file 2 of Super-delta: a new differential gene expression analysis procedure with robust data normalization

Full significant gene lists. This file lists all the significant genes detected by all five methods, each list in a separate worksheet. (XLSX 223 kb

Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High-Dimensional Ordinary Differential Equations

<div><p>The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.</p></div

Parameter Estimation and Variable Selection for Big Systems of Linear Ordinary Differential Equations: A Matrix-Based Approach

<p>Ordinary differential equations (ODEs) are widely used to model the dynamic behavior of a complex system. Parameter estimation and variable selection for a “Big System” with linear ODEs are very challenging due to the need of nonlinear optimization in an ultra-high dimensional parameter space. In this article, we develop a parameter estimation and variable selection method based on the ideas of similarity transformation and separable least squares (SLS). Simulation studies demonstrate that the proposed matrix-based SLS method could be used to estimate the coefficient matrix more accurately and perform variable selection for a linear ODE system with thousands of dimensions and millions of parameters much better than the direct least squares method and the vector-based two-stage method that are currently available. We applied this new method to two real datasets—a yeast cell cycle gene expression dataset with 30 dimensions and 930 unknown parameters and the Standard & Poor 1500 index stock price data with 1250 dimensions and 1,563,750 unknown parameters—to illustrate the utility and numerical performance of the proposed parameter estimation and variable selection method for big systems in practice. Supplementary materials for this article are available online.</p

The inward and outward regulations in the module-based regulatory network.

<p>The negative sign indicates a negative coefficient in the linear ODE model; otherwise the coefficient is positive. The underlined modules are hub modules with the most outward regulations.</p