Gaussian processes:iterative sparse approximations

In recent years there has been an increased interest in applying non-parametric methods to real-world problems. Significant research has been devoted to Gaussian processes (GPs) due to their increased flexibility when compared with parametric models. These methods use Bayesian learning, which generally leads to analytically intractable posteriors. This thesis proposes a two-step solution to construct a probabilistic approximation to the posterior. In the first step we adapt the Bayesian online learning to GPs: the final approximation to the posterior is the result of propagating the first and second moments of intermediate posteriors obtained by combining a new example with the previous approximation. The propagation of em functional forms is solved by showing the existence of a parametrisation to posterior moments that uses combinations of the kernel function at the training points, transforming the Bayesian online learning of functions into a parametric formulation. The drawback is the prohibitive quadratic scaling of the number of parameters with the size of the data, making the method inapplicable to large datasets. The second step solves the problem of the exploding parameter size and makes GPs applicable to arbitrarily large datasets. The approximation is based on a measure of distance between two GPs, the KL-divergence between GPs. This second approximation is with a constrained GP in which only a small subset of the whole training dataset is used to represent the GP. This subset is called the em Basis Vector, or BV set and the resulting GP is a sparse approximation to the true posterior. As this sparsity is based on the KL-minimisation, it is probabilistic and independent of the way the posterior approximation from the first step is obtained. We combine the sparse approximation with an extension to the Bayesian online algorithm that allows multiple iterations for each input and thus approximating a batch solution. The resulting sparse learning algorithm is a generic one: for different problems we only change the likelihood. The algorithm is applied to a variety of problems and we examine its performance both on more classical regression and classification tasks and to the data-assimilation and a simple density estimation problems.

Functional and biophysical analysis of the C-terminus of the CGRP-receptor; a family B GPCR

G-protein coupled receptors (GPCRs) typically have a functionally important C-terminus which, in the largest subfamily (family A), includes a membrane-parallel eighth helix. Mutations of this region are associated with several diseases. There are few C-terminal studies on the family B GPCRs and no data supporting the existence of a similar eighth helix in this second major subfamily, which has little or no sequence homology to family A GPCRs. Here we show that the C-terminus of a family B GPCR (CLR) has a disparate region from N400 to C436 required for CGRP-mediated internalization, and a proximal region of twelve residues (from G388 to W399), in a similar position to the family A eighth helix, required for receptor localization at the cell surface. A combination of circular and linear dichroism, fluorescence and modified waterLOGSY NMR spectroscopy (SALMON) demonstrated that a peptide mimetic of this domain readily forms a membrane-parallel helix anchored to the liposome by an interfacial tryptophan residue. The study reveals two key functions held within the C-terminus of a family B GPCR and presents support for an eighth helical region with striking topological similarity to the nonhomologous family A receptor. This helix structure appears to be found in most other family B GPCRs.

Functional characterization of two human receptor activity-modifying protein 3 variants

Adrenomedullin (AM) and amylin are involved in angiogenesis/lymphangiogenesis and glucose homeostasis/food intake, respectively. They activate receptor activity-modifying protein (RAMP)/G protein-coupled receptor (GPCR) complexes. RAMP3 with the calcitonin receptor-like receptor (CLR) forms the AM(2) receptor, whereas when paired with the calcitonin receptor AMY(3) receptors are formed. RAMP3 interacts with other GPCRs although the consequences of these interactions are poorly understood. Therefore, variations in the RAMP3 sequence, such as single nucleotide polymorphisms or mutations could be relevant to human health. Variants of RAMP3 have been identified. In particular, analysis of AK222469 (Homo sapiens mRNA for receptor (calcitonin) activity-modifying protein 3 precursor variant) revealed several nucleotide differences, three of which encoded amino acid changes (Cys40Trp, Phe100Ser, Leu147Pro). Trp56Arg RAMP3 is a polymorphic variant of human RAMP3 at a conserved amino acid position. To determine their function we used wild-type (WT) human RAMP3 as a template for introducing amino acid mutations. Mutant or WT RAMP3 function was determined in Cos-7 cells with CLR or the calcitonin receptor (CT((a))). Cys40Trp/Phe100Ser/Leu147Pro RAMP3 was functionally compromised, with reduced AM and amylin potency at the respective AM(2) and AMY(3(a)) receptor complexes. Cys40Trp and Phe100Ser mutations contributed to this phenotype, unlike Leu147Pro. Reduced cell-surface expression of mutant receptor complexes probably explains the functional data. In contrast, Trp56Arg RAMP3 was WT in phenotype. This study provides insight into the role of these residues in RAMP3. The existence of AK222469 in the human population has implications for the function of RAMP3/GPCR complexes, particularly AM and amylin receptors.

Functional carbon nanotubes for photonic applications

Carbon nanomaterials are an active frontier of research in current nanotechnology. Single wall Carbon Nanotube (SWNT) is a unique material which has already found several applications in photonics, electronics, sensors and drug delivery. This thesis presents a summary of the author’s research on functionalisation of SWNTs, a study of their optical properties, and potential for an application in laser physics. The first significant result is a breakthrough in controlling the size of SWNT bundles by varying the salt concentrations in N-methyl 2-pyrrolidone (NMP) through a salting out effect. The addition of Sodium iodide leads to self-assembly of CNTs into recognizable bundles. Furthermore, a stable dispersion can be made via addition polyvinylpyrrolidone (PVP) polymer to SWNTs-NMP dispersion, which indicates a promising direction for SWNT bundle engineering in organic solvents. The second set of experiments are concerned with enhancement of photoluminescence (PL), through the formation of novel macromolecular complexes of SWNTs with polymethine dyes with emission from enhanced nanotubes in the range of dye excitation. The effect appears to originate from exciton energy transfer within the solution. Thirdly, SWNT base-saturable absorbers (SA) were developed and applied to mode locking of fibre lasers. SWNT-based SAs were applied in both composite and liquid dispersion forms and achieved stable ultrashort generation at 1000nm, 1550nm, and 1800 nm for Ytterbium, Erbium and Thulium-doped fibre laser respectively. The work presented here demonstrates several innovative approaches for development of rapid functionalised SWNT-based dispersions and composites with potential for application in various photonic devices at low cost.