Regression modelling using priors depending on Fisher information covariance kernels (I-priors)

Regression analysis is undoubtedly an important tool to understand the relationship between one or more explanatory and independent variables of interest. In this thesis, we explore a novel methodology for fitting a wide range of parametric and nonparametric regression models, called the I-prior methodology (Bergsma, 2018). We assume that the regression function belongs to a reproducing kernel Hilbert or Kreĭn space of functions, and by doing so, allows us to utilise the convenient topologies of these vector spaces. This is important for the derivation of the Fisher information of the regression function, which might be infinite dimensional. Based on the principle of maximum entropy, an I-prior is an objective Gaussian process prior for the regression function with covariance function proportional to its Fisher information. Our work focusses on the statistical methodology and computational aspects of fitting I-priors models. We examine a likelihood-based approach (direct optimisation and EM algorithm) for fitting I-prior models with normally distributed errors. The culmination of this work is the R package iprior (Jamil, 2017) which has been made publicly available on CRAN. The normal I-prior methodology is subsequently extended to fit categorical response models, achieved by “squashing” the regression functions through a probit sigmoid function. Estimation of I-probit models, as we call it, proves challenging due to the intractable integral involved in computing the likelihood. We overcome this difficulty by way of variational approximations. Finally, we turn to a fully Bayesian approach of variable selection using I-priors for linear models to tackle multicollinearity. We illustrate the use of I-priors in various simulated and real-data examples. Our study advocates the I-prior methodology as being a simple, intuitive, and comparable alternative to similar leading state-of-the-art models

Stability of Topological States and Crystalline Solids

From the alignment of magnets to the melting of ice, the transition between different phases of matter underpins our exploitation of materials. Both a quantum and a classical phase can undergo an instability into another state. In this thesis, we study the stability of matter in both contexts: topological states and crystalline solids. We start with the stability of fractional quantum Hall states on a lattice, known as fractional Chern insulators. We investigate, using exact diagonalization, fractional Chern insulators in higher Chern bands of the Harper-Hofstadter model, and examine the robustness of their many-body energy gap in the effective continuum limit. We report evidence of stable states in this regime; comment on two cases associated with a bosonic integer quantum Hall effect; and find a modulation of the correlation function in higher Chern bands. We next examine the stability of molecules using variational and diffusion Monte Carlo. By incorporating the matrix of force constants directly into the algorithms, we find that we are able to improve the efficiency and accuracy of atomic relaxation and eigenfrequency calculation. We test the performance on a diverse selection of case studies, with varying symmetries and mass distributions, and show that the proposed formalism outperforms existing restricted Hartree-Fock and density functional theory methods. Finally, we analyze the stability of three-dimensional crystals. We note that for repulsive Coulomb crystals of point nuclei, cubic systems have a zero matrix of force constants at second order. We investigate this by constructing an analytical model in the tight-binding approximation, and present a phase diagram of the most stable crystal structures, as we tune core and valence orbital radii. We reconcile our results with calculations in the nearly free electron regime, as well as current research in condensed matter and plasma physics.Funded by the Engineering and Physical Sciences Research Council under grant no. EP/M506485/1

Numerical analysis of particle-laden flows with the finite element method

In this work we study the numerical simulation of particle-laden fluids, with a focus on Newtonian fluids and spherical, rigid particles. We are thus dealing with a multi-phase (more precisely, a multi-component) problem, with two phases: the fluid (continuous phase) and the the particles (disperse phase). Our general strategy consists in using the discrete element method (DEM) to model the particles and the finite element method (FEM) to discretize the Navier-Stokes equations, which model the continuous phase. The interaction model between both phases is (must be) based on a multiscale concept, since the smallest scales resolved of the continuous phase are considered much bigger than the particles. In other words, the resolution of the numerical model for the particles is finer than that used for the fluid. Consequently, whether implicit or explicit, there must be a filtering or averaging operation involved in the interaction between both phases, where the details of their motions smaller than the smallest resolution scale of the fluid are soothed out, since the latter is the coarsest of the two different resolutions considered. The spatial discretization of the continuous phase is performed with the FEM, using equal-order spaces of shape functions for the velocity and for the pressure. It is a well-known fact that this type of combination involves the violation of the Ladyzenskaja-Babuška-Brezzi (LBB) condition, resulting in an unstable numerical method. Moreover, the presence of the convective term in Eulerian description of the flow also leads to numerical instabilities. Both effects are treated with the sub-grid scale stabilization methods here. About the disperse phase, the trajectory of each particle is calculated based both on the fluid-interaction forces and on the contact forces between them and the surrounding rigid boundaries. The differential equation that describes the motion of particles in between successive collisions, given the mean (averaged) far field and for particles much smaller than the smallest scales of the flow (the Kolmogorov scale in turbulence) is the Maxey-Riley equation (MRE). This equation is the subject of chapter 2. The objective of this theoretical study is to establish quantitative (up to order-of-magnitude accuracy) limits to its range of validity and to the relative importance of its various terms. The method employed is dimensional analysis, which is systematically applied to derive the 'first effects' of a series of phenomena that are neglected in the derivation of the MRE. Chapter 3 is dedicated to the numerical resolution of the MRE. Here we present improvements to the method of van Hinsberg et al. (2011) for the calculation of the history term and analyse the method thoroughly. We include several tests to show the efficiency and utility of the proposed approach. The MRE is directly applicable to flows where the particle-based Reynolds number is Re << 1. But its relevance reaches further, as its structure is the basis for the majority of extensions that model the movement of suspended particles outside the range of validity of the MRE. Chapter 4 is markedly more applied than the two preceding ones. It treats various industrial flux types with particles where we employ several extensions of the MRE of the type mentioned above. In the first part of this chapter we review the most important of these extensions and study the process of derivative recovery, necessary to calculate several terms in the equation of motion. The tests examples considered include bubble trapping in 'T'-junction tubes, the simulation of drilling systems of the oil industry based on the bombardment of steel particles and fluidized beds. For the latter we use a discrete filtering-based coupling approach, that mirrors the continuous theory sketched above. This set of three chapters (2, 3, 4) is the core of the Thesis, which is completed with an introduction (chapter 1) and the conclusions (chapter 5).En este trabajo se estudia la simulación numérica de fluidos con partículas en suspensión, con énfasis en fluidos newtonianos y partículas esféricas y rígidas. El problema es, pues, multi-fásico (o, más precisamente, multi-componente) en donde dos son las fases: el fluido (fase continua) y las partículas (fase dispersa). La estrategia general consiste en la modelización de las partículas mediante el método de los elementos discretos (DEM) y el método de los elementos finitos (FEM) para la discretización de las ecuaciones de Navier-Stokes, que modelan la fase continua. El modelo de interacción entre fases se basa (debe basarse) en una concepción multiescala del sistema, puesto que las escalas más pequeñas resueltas para el fluido se consideran mucho mayores a las partículas. Dicho de otro modo, ya sea implícita o explícitamente, en la interacción interviene un proceso de filtrado o promediado en que se suavizan los detalles del movimiento más pequeños que la escala de resolución del fluido. Par la fase continua la discretización del dominio se realiza con el FEM, con espacios de funciones de forma de igual orden para la velocidad y para la presión. Como es bien sabido, ello conlleva la violación de la condición de Ladyzenskaja-Babuška-Brezzi (LBB), dando un método numérico inestable. Además, la presencia del término convectivo en la descripción euleriana del flujo también resulta en inestabilidad. Ambos son tratados con métodos de estabilización basada en la modelización de 'escalas sub-malla'. En cuanto a la fase dispersa, se calcula la trayectoria de cada una de las partículas en función de fuerzas de contacto con las demás partículas y las superficies sólidas que limitan el dominio de cálculo por un lado, y de las fuerzas de interacción con el fluido por otro. La ecuación que describe el movimiento entre colisiones para partículas menores que las escalas más pequeñas del flujo (escala de Kolmogorov en flujos turbulentos), dado el campo lejano (promediado) de velocidades es la de Maxey-Riley (MRE). Esta ecuación es el objeto de estudio del capítulo 2. El objetivo de este estudio teórico es establecer de forma cuantitativa (en orden de magnitud) su rango de validez y la importancia relativa de sus distintos términos. El método empleado es el análisis dimensional aplicado sistemáticamente al estudio de los 'primeros efectos' de distintos fenómenos físicos que se desprecian en el planteamiento de la ecuación. El capítulo 3 se centra en la resolución numérica de la MRE. En él se presenta una mejora y estudio sistemático del método de van Hinsberg et al. (2011) para el cálculo del término histórico de la ecuación. Se incluyen distintos tests para demostrar la eficiencia del método y su aplicabilidad práctica. La MRE es de directa aplicación en flujos en los que el número de Reynolds relativo a la partícula es Re << 1. Sin embargo, su relevancia va más allá, pues en su estructura se basan la mayoría de modelos para el movimiento de partículas en suspensión, fuera del rango de aplicación de la MRE. El capítulo 4 es de índole más aplicada que los dos anteriores, y trata diversos ejemplos industriales de flujos con partículas en los que se emplean extensiones de la MRE de este tipo. En la primera parte se revisan las extensiones más importantes y la recuperación de derivadas, proceso necesario para el cálculo de varios términos de la ecuación de movimiento de las partículas. Las aplicaciones prácticas tratadas incluyen el aprisionamiento de burbujas en juntas en 'T', la simulación de sistemas de perforación petrolífera basados en el bombardeo con partículas de acero y los lechos fluidificados. Para esta última, se usa una técnica de filtrado discreto inspirada en la teoría esbozada más arriba. Estos tres capítulos (2, 3, 4) se completan con la introducción (capítulo 1) y las conclusiones (capítulo 5)

Abstracts on Radio Direction Finding (1899 - 1995)

The files on this record represent the various databases that originally composed the CD-ROM issue of "Abstracts on Radio Direction Finding" database, which is now part of the Dudley Knox Library's Abstracts and Selected Full Text Documents on Radio Direction Finding (1899 - 1995) Collection. (See Calhoun record https://calhoun.nps.edu/handle/10945/57364 for further information on this collection and the bibliography). Due to issues of technological obsolescence preventing current and future audiences from accessing the bibliography, DKL exported and converted into the three files on this record the various databases contained in the CD-ROM. The contents of these files are: 1) RDFA_CompleteBibliography_xls.zip [RDFA_CompleteBibliography.xls: Metadata for the complete bibliography, in Excel 97-2003 Workbook format; RDFA_Glossary.xls: Glossary of terms, in Excel 97-2003 Workbookformat; RDFA_Biographies.xls: Biographies of leading figures, in Excel 97-2003 Workbook format]; 2) RDFA_CompleteBibliography_csv.zip [RDFA_CompleteBibliography.TXT: Metadata for the complete bibliography, in CSV format; RDFA_Glossary.TXT: Glossary of terms, in CSV format; RDFA_Biographies.TXT: Biographies of leading figures, in CSV format]; 3) RDFA_CompleteBibliography.pdf: A human readable display of the bibliographic data, as a means of double-checking any possible deviations due to conversion

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency