A Comparative Review of Computational Methods as Applied to Gold(I) Complexes and Mechanisms

In the last two decades, the field of homogeneous gold catalysis has been

extremely active, growing at a rapid pace. Another rapidly-growing field—that of

computational chemistry—has often been applied to the investigation of various gold-

catalyzed reaction mechanisms. Unfortunately, a number of recent mechanistic studies

have utilized computational methods that have been shown to be inappropriate and

inaccurate in their description of gold chemistry. This work presents an overview of

available computational methods with a focus on the approximations and limitations

inherent in each, and offers a review of experimentally-characterized gold(I) complexes

and proposed mechanisms as compared with their computationally-modeled

counterparts. No aim is made to identify a “recommended” computational method for

investigations of gold catalysis; rather, discrepancies between experimentally and

computationally obtained values are highlighted, and the systematic errors between

different computational methods are discussed.

A Bayesian Dirichlet-Multinomial Test for Cross-Group Differences

Testing for differences within data sets is an important issue across various applications. Our work is primarily motivated by the analysis of microbiomial composition, which has been increasingly relevant and important with the rise of DNA sequencing. We first review classical frequentist tests that are commonly used in tackling such problems. We then propose a Bayesian Dirichlet-multinomial framework for modeling the metagenomic data and for testing underlying differences between the samples. A parametric Dirichlet-multinomial model uses an intuitive hierarchical structure that allows for flexibility in characterizing both the within-group variation and the cross-group difference and provides very interpretable parameters. A computational method for evaluating the marginal likelihoods under the null and alternative hypotheses is also given. Through simulations, we show that our Bayesian model performs competitively against frequentist counterparts. We illustrate the method through analyzing metagenomic applications using the Human Microbiome Project data.

Path Optimization in Free Energy Calculations

Free energy calculations are a computational method for determining thermodynamic quantities, such as free energies of binding, via simulation.

Currently, due to computational and algorithmic limitations, free energy calculations are limited in scope.

In this work, we propose two methods for improving the efficiency of free energy calculations.

First, we expand the state space of alchemical intermediates, and show that this expansion enables us to calculate free energies along lower variance paths.

We use Q-learning, a reinforcement learning technique, to discover and optimize paths at low computational cost.

Second, we reduce the cost of sampling along a given path by using sequential Monte Carlo samplers.

We develop a new free energy estimator, pCrooks (pairwise Crooks), a variant on the Crooks fluctuation theorem (CFT), which enables decomposition of the variance of the free energy estimate for discrete paths, while retaining beneficial characteristics of CFT.

Combining these two advancements, we show that for some test models, optimal expanded-space paths have a nearly 80% reduction in variance relative to the standard path.

Additionally, our free energy estimator converges at a more consistent rate and on average 1.8 times faster when we enable path searching, even when the cost of path discovery and refinement is considered.

Computational inference of neural information flow networks.

Determining how information flows along anatomical brain pathways is a fundamental requirement for understanding how animals perceive their environments, learn, and behave. Attempts to reveal such neural information flow have been made using linear computational methods, but neural interactions are known to be nonlinear. Here, we demonstrate that a dynamic Bayesian network (DBN) inference algorithm we originally developed to infer nonlinear transcriptional regulatory networks from gene expression data collected with microarrays is also successful at inferring nonlinear neural information flow networks from electrophysiology data collected with microelectrode arrays. The inferred networks we recover from the songbird auditory pathway are correctly restricted to a subset of known anatomical paths, are consistent with timing of the system, and reveal both the importance of reciprocal feedback in auditory processing and greater information flow to higher-order auditory areas when birds hear natural as opposed to synthetic sounds. A linear method applied to the same data incorrectly produces networks with information flow to non-neural tissue and over paths known not to exist. To our knowledge, this study represents the first biologically validated demonstration of an algorithm to successfully infer neural information flow networks.

Computational Inference of Genome-Wide Protein-DNA Interactions Using High-Throughput Genomic Data

Transcriptional regulation has been studied intensively in recent decades. One important aspect of this regulation is the interaction between regulatory proteins, such as transcription factors (TF) and nucleosomes, and the genome. Different high-throughput techniques have been invented to map these interactions genome-wide, including ChIP-based methods (ChIP-chip, ChIP-seq, etc.), nuclease digestion methods (DNase-seq, MNase-seq, etc.), and others. However, a single experimental technique often only provides partial and noisy information about the whole picture of protein-DNA interactions. Therefore, the overarching goal of this dissertation is to provide computational developments for jointly modeling different experimental datasets to achieve a holistic inference on the protein-DNA interaction landscape.

We first present a computational framework that can incorporate the protein binding information in MNase-seq data into a thermodynamic model of protein-DNA interaction. We use a correlation-based objective function to model the MNase-seq data and a Markov chain Monte Carlo method to maximize the function. Our results show that the inferred protein-DNA interaction landscape is concordant with the MNase-seq data and provides a mechanistic explanation for the experimentally collected MNase-seq fragments. Our framework is flexible and can easily incorporate other data sources. To demonstrate this flexibility, we use prior distributions to integrate experimentally measured protein concentrations.

We also study the ability of DNase-seq data to position nucleosomes. Traditionally, DNase-seq has only been widely used to identify DNase hypersensitive sites, which tend to be open chromatin regulatory regions devoid of nucleosomes. We reveal for the first time that DNase-seq datasets also contain substantial information about nucleosome translational positioning, and that existing DNase-seq data can be used to infer nucleosome positions with high accuracy. We develop a Bayes-factor-based nucleosome scoring method to position nucleosomes using DNase-seq data. Our approach utilizes several effective strategies to extract nucleosome positioning signals from the noisy DNase-seq data, including jointly modeling data points across the nucleosome body and explicitly modeling the quadratic and oscillatory DNase I digestion pattern on nucleosomes. We show that our DNase-seq-based nucleosome map is highly consistent with previous high-resolution maps. We also show that the oscillatory DNase I digestion pattern is useful in revealing the nucleosome rotational context around TF binding sites.

Finally, we present a state-space model (SSM) for jointly modeling different kinds of genomic data to provide an accurate view of the protein-DNA interaction landscape. We also provide an efficient expectation-maximization algorithm to learn model parameters from data. We first show in simulation studies that the SSM can effectively recover underlying true protein binding configurations. We then apply the SSM to model real genomic data (both DNase-seq and MNase-seq data). Through incrementally increasing the types of genomic data in the SSM, we show that different data types can contribute complementary information for the inference of protein binding landscape and that the most accurate inference comes from modeling all available datasets.

This dissertation provides a foundation for future research by taking a step toward the genome-wide inference of protein-DNA interaction landscape through data integration.

Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Learning and Exploiting Camera Geometry for Computer Vision

This work explores the use of statistical methods in describing and estimating camera poses, as well as the information feedback loop between camera pose and object detection. Surging development in robotics and computer vision has pushed the need for algorithms that infer, understand, and utilize information about the position and orientation of the sensor platforms when observing and/or interacting with their environment.

The first contribution of this thesis is the development of a set of statistical tools for representing and estimating the uncertainty in object poses. A distribution for representing the joint uncertainty over multiple object positions and orientations is described, called the mirrored normal-Bingham distribution. This distribution generalizes both the normal distribution in Euclidean space, and the Bingham distribution on the unit hypersphere. It is shown to inherit many of the convenient properties of these special cases: it is the maximum-entropy distribution with fixed second moment, and there is a generalized Laplace approximation whose result is the mirrored normal-Bingham distribution. This distribution and approximation method are demonstrated by deriving the analytical approximation to the wrapped-normal distribution. Further, it is shown how these tools can be used to represent the uncertainty in the result of a bundle adjustment problem.

Another application of these methods is illustrated as part of a novel camera pose estimation algorithm based on object detections. The autocalibration task is formulated as a bundle adjustment problem using prior distributions over the 3D points to enforce the objects' structure and their relationship with the scene geometry. This framework is very flexible and enables the use of off-the-shelf computational tools to solve specialized autocalibration problems. Its performance is evaluated using a pedestrian detector to provide head and foot location observations, and it proves much faster and potentially more accurate than existing methods.

Finally, the information feedback loop between object detection and camera pose estimation is closed by utilizing camera pose information to improve object detection in scenarios with significant perspective warping. Methods are presented that allow the inverse perspective mapping traditionally applied to images to be applied instead to features computed from those images. For the special case of HOG-like features, which are used by many modern object detection systems, these methods are shown to provide substantial performance benefits over unadapted detectors while achieving real-time frame rates, orders of magnitude faster than comparable image warping methods.

The statistical tools and algorithms presented here are especially promising for mobile cameras, providing the ability to autocalibrate and adapt to the camera pose in real time. In addition, these methods have wide-ranging potential applications in diverse areas of computer vision, robotics, and imaging.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.