Numerically Stable Approximate Bayesian Methods for Generalized Linear Mixed Models and Linear Model Selection

Approximate Bayesian inference methods offer methodology for fitting Bayesian models as fast alternatives to Markov Chain Monte Carlo methods that sometimes have only a slight loss of accuracy. In this thesis, we consider variable selection for linear models, and zero inflated mixed models. Variable selection for linear regression models are ubiquitous in applied statistics. We use the popular g-prior (Zellner, 1986) for model selection of linear models with normal priors where g is a prior hyperparameter. We derive exact expressions for the model selection Bayes Factors in terms of special functions depending on the sample size, number of covariates and R-squared of the model. We show that these expressions are accurate, fast to evaluate, and numerically stable. An R package blma for doing Bayesian linear model averaging using these exact expressions has been released on GitHub. We extend the Particle EM method of (Rockova, 2017) using Particle Variational Approximation and the exact posterior marginal likelihood expressions to derive a computationally efficient algorithm for model selection on data sets with many covariates. Our algorithm performs well relative to existing algorithms, completing in 8 seconds on a model selection problem with a sample size of 600 and 7200 covariates. We consider zero-inflated models that have many applications in areas such as manufacturing and public health, but pose numerical issues when fitting them to data. We apply a variational approximation to zero-inflated Poisson mixed models with Gaussian distributed random effects using a combination of VB and the Gaussian Variational Approximation (GVA). We also incorporate a novel parameterisation of the covariance of the GVA using the Cholesky factor of the precision matrix, similar to Tan and Nott (2018) to resolve associated numerical difficulties

Effects of classical stochastic webs on the quantum dynamics of cold atomic gases in a moving optical lattice

We introduce and investigate a system that uses temporal resonance-induced phase-space pathways to create strong coupling between an atomic Bose-Einstein condensate and a traveling optical lattice potential. We show that these pathways thread both the classical and quantum phase space of the atom cloud, even when the optical lattice potential is arbitrarily weak. The topology of the pathways, which form weblike patterns, can by controlled by changing the amplitude and period of the optical lattice. In turn, this control can be used to increase and limit the BEC’s center-of-mass kinetic energy to prespecified values. Surprisingly, the strength of the atom-lattice interaction and resulting BEC heating of the center-of-mass motion is enhanced by the repulsive interatomic interactions

Single particle and collective dynamics in periodic potentials

In this thesis, we describe, both semiclassically and quantum mechanically, the single-particle and collective dynamics of electrons and ultracold atoms moving through periodic potentials. Firstly, we explore collective electron dynamics in superlattices with an applied voltage and tilted magnetic field. Single electrons in this system exhibit non-KAM chaotic dynamics. Consequently, at critical field values, coupling between Bloch and cyclotron motion causes delocalisation of the electron orbits, resulting in strong resonant enhancement of the drift velocity. We show that this dramatically affects the collective electron behaviour by inducing multiple propagating charge domains and, consequently, GHz-THz current oscillations with frequencies ten times higher than with no tilted field. Secondly, we study the effect of applying an acoustic wave to the superlattice and find that we can induce high-frequency single electron dynamics that depend critically on the wave amplitude. There are two dynamical regimes depending on the wave amplitude and the electron's initial position in the acoustic wave. Either the electron can be dragged through the superlattice and is allowed to perform drifting periodic orbits with THz frequencies far above the GHz frequencies of the acoustic wave; or, by exerting a large enough potential amplitude, Bloch-like oscillations can be induced, which can cause ultra-high negative differential velocity. We also consider collective electron effects and find that, generally, the acoustic wave drags electrons through the lattice. Additionally, high negative differential drift velocity at the transition between these two single-electron dynamical regimes, induces charge domains in the superlattice that generates extra features in the current oscillations. Finally, we investigate cold atoms in optical lattices driven by a moving potential wave, directly analogous to acoustically-driven superlattices. In this case, we find the same dynamical regimes found in the acoustically driven superlattice. In addition, there are a number a sharp resonant features in the velocity of the atom at critical wave amplitudes and speeds. This could provide a flexible mechanism for transporting atoms to precise locations in a lattice

III-V semiconductor waveguides for photonic functionality at 780 nm

Photonic integrated circuits based on III-V semiconductor polarization-maintaining waveguides were designed and fabricated for the first time for application in a compact cold-atom gravimeter1,2 at an operational wavelength of 780 nm. Compared with optical fiber-based components, semiconductor waveguides achieve very compact guiding of optical signals for both passive functions, such as splitting and recombining, and for active functions, such as switching or modulation. Quantum sensors, which have enhanced sensitivity to a physical parameter as a result of their quantum nature, can be made from quantum gases of ultra-cold atoms. A cloud of ultra-cold atoms may start to exhibit quantum-mechanical properties when it is trapped and cooled using laser cooling in a magneto-optical trap, to reach milli-Kelvin temperatures. The work presented here focuses on the design and fabrication of optical devices for a quantum sensor to measure the acceleration of gravity precisely and accurately. In this case the cloud of ultra-cold atoms consists of rubidium (87Rb) atoms and the sensor exploits the hyperfine structure of the D1 transition, from an outer electronic state of 5 2S ½ to 5 2P3/2 which has an energy of 1.589 eV or 780.241 nm. The short wavelength of operation of the devices dictated stringent requirements on the Molecular Beam Epitaxy (MBE) and device fabrication in terms of anisotropy and smoothness of plasma etch processes, cross-wafer uniformities and alignment tolerances. Initial measurements of the optical loss of the polarization-maintaining waveguide, assuming Fresnel reflection losses only at the facets, suggested a loss of 8 dB cm-1, a loss coefficient, α, of 1.9 (±0.3) cm-1

Enhancing optoelectronic properties of SiC-grown graphene by a surface layer of colloidal quantum dots

We report a simultaneous increase of carrier concentration, mobility and photoresponsivity when SiC-grown graphene is decorated with a surface layer of colloidal PbS quantum dots, which act as electron donors. The charge on the ionised dots is spatially correlated with defect charges on the SiC-graphene interface, thus enhancing both electron carrier density and mobility. This charge-correlation model is supported by Monte Carlo simulations of electron transport and used to explain the unexpected 3-fold increase of mobility with increasing electron density. The enhanced carrier concentration and mobility give rise to Shubnikov-de Haas oscillations in the magnetoresistance, which provide an estimate of the electron cyclotron mass in graphene at high densities and Fermi energies up to 1.2 × 1013 cm-2 and 400 meV, respectively

Using acoustic waves to induce high-frequency current oscillations in superlattices

We show that gigahertz acoustic waves in semiconductor superlattices can induce terahertz (THz) electron dynamics that depend critically on the wave amplitude. Below the threshold amplitude, the acoustic wave drags electrons through the superlattice with a peak drift velocity overshooting that produced by a static electric field. In this regime, single electrons perform drifting orbits with THz frequency components. When the wave amplitude exceeds the critical threshold, an abrupt onset of Bloch-type oscillations causes negative differential velocity. The acoustic wave also affects the collective behavior of the electrons by causing the formation of localized electron accumulation and depletion regions, which propagate through the superlattice, thereby producing self-sustained current oscillations even for very small wave amplitudes. We show that the underlying single-electron dynamics, in particular, the transition between the acoustic wave dragging and Bloch oscillation regimes, strongly influence the spatial distribution of the electrons and the form of the current oscillations. In particular, the amplitude of the current oscillations depends nonmonotonically on the strength of the acoustic wave, reflecting the variation in the single-electron drift velocity

Reactions of Dimethylether in Single Crystals of the Silicoaluminophosphate STA-7 Studied via Operando Synchrotron Infrared Microspectroscopy

Open access via the Springer Compact Agreement. We thank the Diamond Light Source for provision of beam time and support facilities at the MIRIAM beamline B22 (Experiments SM11766-1 and SM13725-1). Financial support from the EPSRC Catalysis Hub (Suwardiyanto) and an Industrial CASE Award (EPSRC/BP Chemicals) (Price) are also acknowledged.Peer reviewedPublisher PD

Semiconductor charge transport driven by a picosecond strain pulse

We demonstrate that a picosecond strain pulse can be used to drive an electric current through both thin-film epilayer and heterostructure semiconductor crystals in the absence of an external electric field. By measuring the transient current pulses, we are able to clearly distinguish the effects of the coherent and incoherent components of the acoustic packet. The properties of the strain induced signal suggest a technique for exciting picosecond current pulses, which may be used to probe semiconductor devices

Effects of crystal size on methanol to hydrocarbon conversion over single crystals of ZSM-5 studied by synchrotron infrared microspectroscopy

IBM and PAW would like to thank the EPSRC and CRITICAT Centre for Doctoral Training for Financial Support [PhD studentship to IBM, and supplementary equipment grant EP/L016419/1]. The UK Catalysis Hub is thanked for resources and support provided via membership of the UK Catalysis Hub Consortium and funded by EPSRC (grants EP/I038748/1, EP/I019693/1, EP/K014706/1, EP/K014668/1, EP/K014854/1, EP/K014714/1 and EP/M013219/1). We thank the Diamond Light Source for provision of beam time and support facilities at the MIRIAM beamline B22 (Experiments SM13725-1, SM16257-1, SM18680-1, SM20906-1). IBM and PAW thank EPSRC and CRTICAT Centre for Doctoral Training for a PhD Studentship (grant EP/IO17008/1) and Supplementary Equipment Grant (EP/L016419/1). We thank Pit Losch and Hans J. Bongard, Max-Planck-Institut fur Kohlenforschung for cross-sectional SEM-EDX analysis, Daniel M. Dawson, University of St Andrews, for solid state NMR, and Juan M.Gonzalez-Carballo, University of St Andrews, for assistance with ammonia TPD. The research data supporting this publication can be accessed at https://doi.org/10.17630/306bd3c3-014b-466f-9538-b107628c847d.Peer reviewedPostprin