Browsing by Author "Wang, Hao"

Molecular dynamics (MD) simulations is an invaluable tool to investigate chemical and biological processes in atomic details. The accuracy of MD simulations strongly depends on underlying force fields. In conventional molecular mechanics (MM) force fields, the total energy is divided into bond energy, angle energy, dihedral energy, electrostatic interactions and van der Waals interactions. Each of these energy terms is parameterized by fitting to either experimental data or quantum mechanical (QM) calculations. In this dissertation, our aim is to develop accurate force fields for small molecules, water and proteins fully from QM calculations of small fragments. In the framework of conventional MM force fields, we calculated both transferable and molecule-specific atomic polarizabilities of small molecules by electrostatic potential fitting. Atomic polarizabilities are the key physical quantities in induced dipole polarization model. Molecular polarizabilities recovered from our atomic polarizabilities show good agreement with those obtained from QM calculations. We believe the main limitation of conventional MM force fields is the limited form of its Hamiltonian. Going beyond conventional MM force fields, we adopt the many-body expansion method and residue-based systematic molecular fragmentation (rSMF) method to start afresh building force fields for water and proteins, respectively. We used electrostatically embedded two-body expansion as the Hamiltonian of bulk water. QM reference of electrostatically embedded water monomer and dimer at the level of CCSD/aug-cc-pVDZ are parameterized by neural network (NN). Compared with experimental results, our water force fields show good structural and dynamical properties of bulk water. We developed rSMF to partition general proteins into twenty amino acid dipeptides and one peptide bond. The total energy of proteins is the combination of the energy of these small fragments. The QM reference energy of each fragment is parameterized by NN. Our protein force fields compare favorably with full QM calculations for both homogeneous and heterogeneous polypeptides in terms of energy and force errors.

Modelling and inference with higher-dimensional variables, including studies in multivariate time series analysis, raise challenges to our ability to ``scale-up'' statistical approaches that involve both modelling and computational issues. Modelling issues relate to the interest in parsimony of parametrisation and control over proliferation of parameters; computational issues relate to the basic challenges to the efficiency of statistical computation (simulation and optimisation) with increasingly high-dimensional and structured models. This thesis addresses these questions and explores Bayesian approaches inducing relevant sparsity and structure into parameter spaces, with a particular focus on time series and dynamic modelling.

Chapter 1 introduces the challenge of estimating covariance matrices in multivariate time series problems, and reviews Bayesian treatments of Gaussian graphical models that are useful for estimating covariance matrices. Chapter 2 and 3 introduce the development and application of matrix-variate graphical models and time series models. Chapter 4 develops dynamic graphical models for multivariate financial time series. Chapter 5 and 6 propose an integrated approach for dynamic multivariate regression modelling with simultaneous selection of variables and graphical-model structured covariance matrices. Finally, Chapter 7 summarises the dissertation and discusses a number of new and open research directions.