Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering

Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. The proposed methods have been implemented in an R-package HDtest and is available on CRAN.Comment: The original title dated back to May 2015 is "Bootstrap Tests on High Dimensional Covariance Matrices with Applications to Understanding Gene Clustering

Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.Comment: 5+9 pages, 3 figures, updated references, fixed typos and refinements, added proof for equivalence to Lagrangian subgroups in Abelian case

Monte Carlo computations of hypersonic interacting flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76094/1/AIAA-2001-1029-411.pd

Hybrid DSMC-CFD Simulations of Hypersonic Flow over Sharp and Blunted Bodies

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77221/1/AIAA-2003-3644-430.pd

Understanding Repeat Purchase Intentions And Uncertainty In The Context Of Online Shopping

The distant and impersonal nature of e-commerce (EC) and the unpredictability of the Internet infrastructure generate an implicit uncertainty around online transactions. Moreover, customer repeat purchasing is critical to the e-commerce vendor’s survival and success. However, few studies explain online repeat purchase from an uncertainty perspective. The purpose of this study is to propose a conceptual model to examine the sources of uncertainty and types of uncertainty in an online transaction, which affect online repeat purchase intentions. We drew on uncertainty and online repeat purchase literature to formulate a conceptual model that identifies the sources of uncertainty, and three types of uncertainty (seller uncertainty, product uncertainty and environmental uncertainty) are respectively proposed as formative second-order constructs. The proposed structural model is empirically tested with data from 554 experienced online shoppers, and then analyzed using Structure Equation Model (SEM). The results show that seller uncertainty and environmental uncertainty have a negative effect on repeat purchase intentions. Implications for theory and practice and suggestions for future research are discussed

An Empirical Study Of Flow Experiences In Social Network Sites

Social network sites (SNS) have simplified and amplified social interaction between online users. The unique hedonic-oriented features provide experiential motives for SNS users. Although SNS is growing popularity, a number of questions remain to be addressed concerning the usage of SNS: What are experiential motives for SNS users? What is the relationship between flow experiences and behavioural intentions within the SNS context? Given the novelty of SNS phenomenon and its unexplored potential in many fields, this study develops a conceptual model derived from reference studies on online services and social psychology. The present study proposes four flow experiences of SNS users such as perceived enjoyment, concentration, escape and social interaction to represent the multidimensional aspect of flow instead of a single dimension. To investigate the research model, this study apply structural equation mode(SEM) analysis with 342 valid replies. As a result, this empirical study indicated that perceived enjoyment was the most important flow experience with SNS, followed by escape and social interaction. Concentration was not a significant predictor of behavioral intentions toward SNS

A New Energy Flux Model in the DSMC-IP Method for Nonequilibrium Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76742/1/AIAA-2003-3774-159.pd

Predicting continuum breakdown in hypersonic viscous flows

This paper presents a study of the breakdown of the Navier–Stokes equations in hypersonic viscous flows over a sharp cone tip and a hollow cylinder/flare geometry. Investigations are performed through detailed comparisons of the numerical results obtained with continuum and particle techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. A modified breakdown parameter is proposed that can predict the failure of the continuum approach accurately for the simple cone flow and fairly well for the more complex cylinder/flare flow. The study of continuum breakdown is the first step toward development of a hybrid numerical code. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69696/2/PHFLE6-15-1-91-1.pd