arXiv subjects

Hua Zhou

Publications and source records attributed to Hua Zhou.

At least 145 records · Page 8Linked to original sources

arXiv2015

Using coherent X-rays to directly measure the propagation velocity of defects during thin film deposition

The properties of artificially grown thin films are often strongly affected by the dynamic relationship between surface growth processes and subsurface structure. Coherent mixing of X-ray signals promises to provide an approach to better understand such processes. Here, we demonstrate the continuously variable mixing of surface and bulk scattering signals during real-time studies of sputter deposition of a-Si and a-WiS2 films by controlling the X-ray penetration and escape depths in coherent grazing incidence small angle X-ray scattering (Co-GISAXS). Under conditions where the X-ray signal comes from both the growth surface and the thin film bulk, oscillations in temporal correlations arise from coherent interference between scattering from stationary bulk features and from the advancing surface. We also observe evidence that elongated bulk features propagate upward at the same velocity as the surface. Additionally, a highly surface sensitive mode is demonstrated that can access the surface dynamics independently of the subsurface structure.

cond-mat.mtrl-sci↗

arXiv2015

MM Algorithms for Variance Components Models

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum likelihood estimation and restricted maximum likelihood estimation of variance component models remain numerically challenging. Building on the minorization-maximization (MM) principle, this paper presents a novel iterative algorithm for variance components estimation. MM algorithm is trivial to implement and competitive on large data problems. The algorithm readily extends to more complicated problems such as linear mixed models, multivariate response models possibly with missing data, maximum a posteriori estimation, penalized estimation, and generalized estimating equations (GEE). We establish the global convergence of the MM algorithm to a KKT point and demonstrate, both numerically and theoretically, that it converges faster than the classical EM algorithm when the number of variance components is greater than two and all covariance matrices are positive definite.

stat.CO↗

arXiv2015

Co-GISAXS as a New Technique to Investigate Surface Growth Dynamics

Detailed quantitative measurement of surface dynamics during thin film growth is a major experimental challenge. Here X-ray Photon Correlation Spectroscopy with coherent hard X-rays is used in a Grazing-Incidence Small-Angle X-ray Scattering (i.e. Co-GISAXS) geometry as a new tool to investigate nanoscale surface dynamics during sputter deposition of a-Si and a-WSi$_2$ thin films. For both films, kinetic roughening during surface growth reaches a dynamic steady state at late times in which the intensity autocorrelation function $g_2$(q,t) becomes stationary. The $g_2$(q,t) functions exhibit compressed exponential behavior at all wavenumbers studied. The overall dynamics are complex, but the most surface sensitive sections of the structure factor and correlation time exhibit power law behaviors consistent with dynamical scaling.

cond-mat.mtrl-sci↗

arXiv2014

Fast Genome-Wide QTL Association Mapping on Pedigree and Population Data

Since most analysis software for genome-wide association studies (GWAS) currently exploit only unrelated individuals, there is a need for efficient applications that can handle general pedigree data or mixtures of both population and pedigree data. Even data sets thought to consist of only unrelated individuals may include cryptic relationships that can lead to false positives if not discovered and controlled for. In addition, family designs possess compelling advantages. They are better equipped to detect rare variants, control for population stratification, and facilitate the study of parent-of-origin effects. Pedigrees selected for extreme trait values often segregate a single gene with strong effect. Finally, many pedigrees are available as an important legacy from the era of linkage analysis. Unfortunately, pedigree likelihoods are notoriously hard to compute. In this paper we re-examine the computational bottlenecks and implement ultra-fast pedigree-based GWAS analysis. Kinship coefficients can either be based on explicitly provided pedigrees or automatically estimated from dense markers. Our strategy (a) works for random sample data, pedigree data, or a mix of both; (b) entails no loss of power; (c) allows for any number of covariate adjustments, including correction for population stratification; (d) allows for testing SNPs under additive, dominant, and recessive models; and (e) accommodates both univariate and multivariate quantitative traits. On a typical personal computer (6 CPU cores at 2.67 GHz), analyzing a univariate HDL (high-density lipoprotein) trait from the San Antonio Family Heart Study (935,392 SNPs on 1357 individuals in 124 pedigrees) takes less than 2 minutes and 1.5 GB of memory. Complete multivariate QTL analysis of the three time-points of the longitudinal HDL multivariate trait takes less than 5 minutes and 1.5 GB of memory.

stat.AP↗

arXiv2014

Tensor Generalized Estimating Equations for Longitudinal Imaging Analysis

In an increasing number of neuroimaging studies, brain images, which are in the form of multidimensional arrays (tensors), have been collected on multiple subjects at multiple time points. Of scientific interest is to analyze such massive and complex longitudinal images to diagnose neurodegenerative disorders and to identify disease relevant brain regions. In this article, we treat those problems in a unifying regression framework with image predictors, and propose tensor generalized estimating equations (GEE) for longitudinal imaging analysis. The GEE approach takes into account intra-subject correlation of responses, whereas a low rank tensor decomposition of the coefficient array enables effective estimation and prediction with limited sample size. We propose an efficient estimation algorithm, study the asymptotics in both fixed $p$ and diverging $p$ regimes, and also investigate tensor GEE with regularization that is particularly useful for region selection. The efficacy of the proposed tensor GEE is demonstrated on both simulated data and a real data set from the Alzheimer's Disease Neuroimaging Initiative (ADNI).

stat.ME↗

arXiv2014

Interfacial Ionic Liquids: Connecting Static and Dynamic Structures

It is well-known that room temperature ionic liquids (RTILs) often adopt a charge-separated layered structure, i.e., with alternating cation- and anion-rich layers, at electrified interfaces. However, the dynamic response of the layered structure to temporal variations in applied potential is not well understood. We used in situ, real-time X-ray reflectivity (XR) to study the potential-dependent electric double layer (EDL) structure of an imidazolium-based RTIL on charged epitaxial graphene during potential cycling as a function of temperature. The results suggest that the graphene-RTIL interfacial structure is bistable in which the EDL structure at any intermediate potential can be described by the combination of two extreme-potential structures whose proportions vary depending on the polarity and magnitude of the applied potential. This picture is supported by the EDL structures obtained by fully atomistic molecular dynamics (MD) simulations at various static potentials. The potential-driven transition between the two structures is characterized by an increasing width but with an approximately fixed hysteresis magnitude as a function of temperature. The results are consistent with the coexistence of distinct anion and cation adsorbed structures separated by an energy barrier (~0.15 eV).

cond-mat.soft↗

arXiv2014

IsoDOT Detects Differential RNA-isoform Expression/Usage with respect to a Categorical or Continuous Covariate with High Sensitivity and Specificity

We have developed a statistical method named IsoDOT to assess differential isoform expression (DIE) and differential isoform usage (DIU) using RNA-seq data. Here isoform usage refers to relative isoform expression given the total expression of the corresponding gene. IsoDOT performs two tasks that cannot be accomplished by existing methods: to test DIE/DIU with respect to a continuous covariate, and to test DIE/DIU for one case versus one control. The latter task is not an uncommon situation in practice, e.g., comparing paternal and maternal allele of one individual or comparing tumor and normal sample of one cancer patient. Simulation studies demonstrate the high sensitivity and specificity of IsoDOT. We apply IsoDOT to study the effects of haloperidol treatment on mouse transcriptome and identify a group of genes whose isoform usages respond to haloperidol treatment.

stat.AP↗

arXiv2014

Fast Genome-Wide QTL Analysis Using Mendel

Pedigree GWAS (Option 29) in the current version of the Mendel software is an optimized subroutine for performing large scale genome-wide QTL analysis. This analysis (a) works for random sample data, pedigree data, or a mix of both, (b) is highly efficient in both run time and memory requirement, (c) accommodates both univariate and multivariate traits, (d) works for autosomal and x-linked loci, (e) correctly deals with missing data in traits, covariates, and genotypes, (f) allows for covariate adjustment and constraints among parameters, (g) uses either theoretical or SNP-based empirical kinship matrix for additive polygenic effects, (h) allows extra variance components such as dominant polygenic effects and household effects, (i) detects and reports outlier individuals and pedigrees, and (j) allows for robust estimation via the $t$-distribution. The current paper assesses these capabilities on the genetics analysis workshop 19 (GAW19) sequencing data. We analyzed simulated and real phenotypes for both family and random sample data sets. For instance, when jointly testing the 8 longitudinally measured systolic blood pressure (SBP) and diastolic blood pressure (DBP) traits, it takes Mendel 78 minutes on a standard laptop computer to read, quality check, and analyze a data set with 849 individuals and 8.3 million SNPs. Genome-wide eQTL analysis of 20,643 expression traits on 641 individuals with 8.3 million SNPs takes 30 hours using 20 parallel runs on a cluster. Mendel is freely available at \url{http://www.genetics.ucla.edu/software}.

stat.AP↗

arXiv2014

Evolution Process of Wurtzite ZnO Films on Cubic MgO (001) Substrates: a Structural, Optical and Electronic Investigation of the Misfit Structures

The interface between hexagonal ZnO films and cubic MgO (001) substrates, fabricated through molecular beam epitaxy, are thoroughly investigated. X-ray diffraction and (scanning) transmission electron microscopy reveal that, at the substrate temperature above 200 degree C, the growth follows the single [0001] direction; while at the substrate below 150 degree C, the growth is initially along [0001] and then mainly changes to [0-332] variants beyond the thickness of about 10 nm. Interestingly, a double-domain feature with a rotational angle of 30 degree appears for the growth along [0001] regardless of the growth temperature, experimentally demonstrated the theoretical predictions for occurrence of double rotational domains in such a heteroepitaxy [Grundmann et al, Phys. Rev. Lett. 105, 146102 (2010)]. It is also found that, the optical transmissivity of the ZnO film is greatly influenced by the mutation of growth directions, stimulated by the bond-length modulations, as further determined by X-ray absorption Spectra (XAS) at Zn K edge. The XAS results also show the evolution of 4pxy and 4pz states in the conduction band as the growth temperature increases. The results obtained from this work can hopefully promote the applications of ZnO in advanced optoelectronics for which its integration with other materials of different phases is desirable.

cond-mat.mtrl-sci↗

arXiv2013

Distance Majorization and Its Applications

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization (MM) principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

math.OC↗

arXiv2013

Tucker Tensor Regression and Neuroimaging Analysis

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a long vector causes extremely high dimensionality that compromises classical regression methods, and, more seriously, destroys the inherent spatial structure of array data that possesses wealth of information. In this article, we propose a family of generalized linear tensor regression models based upon the Tucker decomposition of regression coefficient arrays. Effectively exploiting the low rank structure of tensor covariates brings the ultrahigh dimensionality to a manageable level that leads to efficient estimation. We demonstrate, both numerically that the new model could provide a sound recovery of even high rank signals, and asymptotically that the model is consistently estimating the best Tucker structure approximation to the full array model in the sense of Kullback-Liebler distance. The new model is also compared to a recently proposed tensor regression model that relies upon an alternative CANDECOMP/PARAFAC (CP) decomposition.

stat.ME↗

arXiv2012

Atomic layer engineering of perovskite oxides for chemically sharp heterointerfaces

Advances in synthesis techniques and materials understanding have given rise to oxide heterostructures with intriguing physical phenomena that cannot be found in their constituents. In these structures, precise control of interface quality, including oxygen stoichiometry, is critical for unambiguous tailoring of the interfacial properties, with deposition of the first monolayer being the most important step in shaping a well-defined functional interface. Here, we studied interface formation and strain evolution during the initial growth of LaAlO3 on SrTiO3 by pulsed laser deposition, in search of a means for controlling the atomic-sharpness of the interfaces. Our experimental results show that growth of LaAlO3 at a high oxygen pressure dramatically enhances interface abruptness. As a consequence, the critical thickness for strain relaxation was increased, facilitating coherent epitaxy of perovskite oxides. This provides a clear understanding of the role of oxygen pressure during the interface formation, and enables the synthesis of oxide heterostructures with chemically-sharper interfaces.

cond-mat.mtrl-sci↗

arXiv2012

Regularized Matrix Regression

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained for each combination of two underlying variables. To address scientific questions arising from those data, new regression methods that take matrices as covariates are needed, and sparsity or other forms of regularization are crucial due to the ultrahigh dimensionality and complex structure of the matrix data. The popular lasso and related regularization methods hinge upon the sparsity of the true signal in terms of the number of its nonzero coefficients. However, for the matrix data, the true signal is often of, or can be well approximated by, a low rank structure. As such, the sparsity is frequently in the form of low rank of the matrix parameters, which may seriously violate the assumption of the classical lasso. In this article, we propose a class of regularized matrix regression methods based on spectral regularization. Highly efficient and scalable estimation algorithm is developed, and a degrees of freedom formula is derived to facilitate model selection along the regularization path. Superior performance of the proposed method is demonstrated on both synthetic and real examples.

stat.ME↗

arXiv2012

Tensor Regression with Applications in Neuroimaging Data Analysis

Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (tensors). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of tensor regression models that efficiently exploit the special structure of tensor covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data.

stat.ME↗

arXiv2012

Path Following and Empirical Bayes Model Selection for Sparse Regression

In recent years, a rich variety of regularization procedures have been proposed for high dimensional regression problems. However, tuning parameter choice and computational efficiency in ultra-high dimensional problems remain vexing issues. The routine use of $\ell_1$ regularization is largely attributable to the computational efficiency of the LARS algorithm, but similar efficiency for better behaved penalties has remained elusive. In this article, we propose a highly efficient path following procedure for combination of any convex loss function and a broad class of penalties. From a Bayesian perspective, this algorithm rapidly yields maximum a posteriori estimates at different hyper-parameter values. To bypass the inefficiency and potential instability of cross validation, we propose an empirical Bayes procedure for rapidly choosing the optimal model and corresponding hyper-parameter value. This approach applies to any penalty that corresponds to a proper prior distribution on the regression coefficients. While we mainly focus on sparse estimation of generalized linear models, the method extends to more general regularizations such as polynomial trend filtering after reparameterization. The proposed algorithm scales efficiently to large $p$ and/or $n$. Solution paths of 10,000 dimensional examples are computed within one minute on a laptop for various generalized linear models (GLM). Operating characteristics are assessed through simulation studies and the methods are applied to several real data sets.

stat.CO↗

arXiv2012

A Generic Path Algorithm for Regularized Statistical Estimation

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The penalty term is usually weighted by a tuning parameter and encourages certain constraints on the parameters to be estimated. Particular choices of constraints lead to the popular lasso, fused-lasso, and other generalized $l_1$ penalized regression methods. Although there has been a lot of research in this area, developing efficient optimization methods for many nonseparable penalties remains a challenge. In this article we propose an exact path solver based on ordinary differential equations (EPSODE) that works for any convex loss function and can deal with generalized $l_1$ penalties as well as more complicated regularization such as inequality constraints encountered in shape-restricted regressions and nonparametric density estimation. In the path following process, the solution path hits, exits, and slides along the various constraints and vividly illustrates the tradeoffs between goodness of fit and model parsimony. In practice, the EPSODE can be coupled with AIC, BIC, $C_p$ or cross-validation to select an optimal tuning parameter. Our applications to generalized $l_1$ regularized generalized linear models, shape-restricted regressions, Gaussian graphical models, and nonparametric density estimation showcase the potential of the EPSODE algorithm.

stat.CO↗

arXiv2012

Path Following in the Exact Penalty Method of Convex Programming

Classical penalty methods solve a sequence of unconstrained problems that put greater and greater stress on meeting the constraints. In the limit as the penalty constant tends to $\infty$, one recovers the constrained solution. In the exact penalty method, squared penalties are replaced by absolute value penalties, and the solution is recovered for a finite value of the penalty constant. In practice, the kinks in the penalty and the unknown magnitude of the penalty constant prevent wide application of the exact penalty method in nonlinear programming. In this article, we examine a strategy of path following consistent with the exact penalty method. Instead of performing optimization at a single penalty constant, we trace the solution as a continuous function of the penalty constant. Thus, path following starts at the unconstrained solution and follows the solution path as the penalty constant increases. In the process, the solution path hits, slides along, and exits from the various constraints. For quadratic programming, the solution path is piecewise linear and takes large jumps from constraint to constraint. For a general convex program, the solution path is piecewise smooth, and path following operates by numerically solving an ordinary differential equation segment by segment. Our diverse applications to a) projection onto a convex set, b) nonnegative least squares, c) quadratically constrained quadratic programming, d) geometric programming, and e) semidefinite programming illustrate the mechanics and potential of path following. The final detour to image denoising demonstrates the relevance of path following to regularized estimation in inverse problems. In regularized estimation, one follows the solution path as the penalty constant decreases from a large value.

math.NA↗

arXiv2012

Understanding Controls on Interfacial Wetting at Epitaxial Graphene: Experiment and Theory

The interaction of interfacial water with graphitic carbon at the atomic scale is studied as a function of the hydrophobicity of epitaxial graphene. High resolution X-ray reflectivity shows that the graphene-water contact angle is controlled by the average graphene thickness, due to the fraction of the film surface expressed as the epitaxial buffer layer whose contact angle (contact angle θ_c = 73°) is substantially smaller than that of multilayer graphene (θ_c = 93°). Classical and ab initio molecular dynamics simulations show that the reduced contact angle of the buffer layer is due to both its epitaxy with the SiC substrate and the presence of interfacial defects. This insight clarifies the relationship between interfacial water structure and hydrophobicity, in general, and suggests new routes to control interface properties of epitaxial graphene.

cond-mat.mtrl-sci↗