Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

Positive Definite ℓ1\ell_1 Penalized Estimation of Large Covariance Matrices

The thresholding covariance estimator has nice asymptotic properties for estimating sparse large covariance matrices, but it often has negative eigenvalues when used in real data analysis. To simultaneously achieve sparsity and positive definiteness, we develop a positive definite $\ell_1$-penalized covariance estimator for estimating sparse large covariance matrices. An efficient alternating direction method is derived to solve the challenging optimization problem and its convergence properties are established. Under weak regularity conditions, non-asymptotic statistical theory is also established for the proposed estimator. The competitive finite-sample performance of our proposal is demonstrated by both simulation and real applications.Comment: accepted by JASA, August 201

Nonconcave penalized composite conditional likelihood estimation of sparse Ising models

The Ising model is a useful tool for studying complex interactions within a system. The estimation of such a model, however, is rather challenging, especially in the presence of high-dimensional parameters. In this work, we propose efficient procedures for learning a sparse Ising model based on a penalized composite conditional likelihood with nonconcave penalties. Nonconcave penalized likelihood estimation has received a lot of attention in recent years. However, such an approach is computationally prohibitive under high-dimensional Ising models. To overcome such difficulties, we extend the methodology and theory of nonconcave penalized likelihood to penalized composite conditional likelihood estimation. The proposed method can be efficiently implemented by taking advantage of coordinate-ascent and minorization--maximization principles. Asymptotic oracle properties of the proposed method are established with NP-dimensionality. Optimality of the computed local solution is discussed. We demonstrate its finite sample performance via simulation studies and further illustrate our proposal by studying the Human Immunodeficiency Virus type 1 protease structure based on data from the Stanford HIV drug resistance database. Our statistical learning results match the known biological findings very well, although no prior biological information is used in the data analysis procedure.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1017 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Alternating Direction Methods for Latent Variable Gaussian Graphical Model Selection

Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance matrix that can be decomposed into a sparse matrix minus a low-rank matrix from sample data. Solving this convex optimization problem is very challenging, especially for large problems. In this paper, we propose two alternating direction methods for solving this problem. The first method is to apply the classical alternating direction method of multipliers to solve the problem as a consensus problem. The second method is a proximal gradient based alternating direction method of multipliers. Our methods exploit and take advantage of the special structure of the problem and thus can solve large problems very efficiently. Global convergence result is established for the proposed methods. Numerical results on both synthetic data and gene expression data show that our methods usually solve problems with one million variables in one to two minutes, and are usually five to thirty five times faster than a state-of-the-art Newton-CG proximal point algorithm

Stress intensity factor in a tapered specimen

The general problem of a tapered specimen containing an edge crack is formulated in terms of a system of singular integral equations. The equations are solved and the stress intensity factor is calculated for a compact and for a slender tapered specimen, the latter simulating the double cantilever beam. The results are obtained primarily for a pair of concentrated forces and for crack surface wedge forces. The stress intensity factors are also obtained for a long strip under uniform tension which contains inclined edge cracks

Interaction between a crack and a soft inclusion

With the application to weld defects in mind, the interaction problem between a planar-crack and a flat inclusion in an elastic solid is considered. The elastic inclusion is assumed to be sufficiently thin so that the thickness distribution of the stresses in the inclusion may be neglected. The problem is reduced to a system of four integral equations having Cauchy-type dominant kernels. The stress intensity factors are calculated and tabulated for various crack-inclusion geometries and the inclusion to matrix modulus ratios, and for general homogeneous loadiong conditions away from the crack-inclusion region

Methods for enhanced learning using wearable technologies. A study of the maritime sector

Maritime safety is a critical concern due to the potential for serious consequences or accidents for the crew, passengers, environment, and assets resulting from navigation errors or unsafe acts. Traditional training methods face challenges in the rapidly evolving maritime industry, and innovative training methods are being explored. This study explores the use of wearable sensors with biosignal data collection to improve training performance in the maritime sector. Three experiments were conducted progressively to investigate the relationship between navigators' experience levels and biosignal data results, the effects of different training methods on cognitive workload, trainees' stress levels, and their decision-making skills, and the classification of scenario complexity and the biosignal data obtained by the trainees. questionnaire data on stress levels, workload, and user satisfaction of auxiliary training equipment; performance evaluation data on navigational abilities, decision-making skills, and ship-handling abilities; and biosignal data, including electrodermal activity (EDA), body temperature, blood volume pulse (BVP), inter-beat interval (IBI), and heart rate (HR). Several statistical methods and machine-learning algorithms were used in the data analysis. The present dissertation contributes to the advancement of the field of maritime education and training by exploring methods for enhancing learning in complex situations. The use of biosignal data provides insights into the interplay between stress levels and training outcomes in the maritime industry. The proposed conceptual training model underscores the relationship between trainees' stress and safety factors and offers a framework for the development and evaluation of advanced biosignal data-based training systems