Modern criticism and the preaching of the Old Testament : eight lectures on the Lyman Beecher foundation, Yale Uuniversity /

"The Eight Lectures in this volume . . . were delivered before Yale University in 1899." --Pref.

Lower bounds on the complexity of simulating quantum gates

We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates.

Solvability of singular second order m-point boundary value problems of Dirichlet type

Let f : [0, 1] x R2 -> R be a function satisfying the Caxatheodory conditions and t(1 - t)e(t) epsilon L-1 (0, 1). Let a(i) epsilon R and xi(i) (0, 1) for i = 1,..., m - 2 where 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1 - In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem [GRAPHICS] The proof of our main result is based on the Leray-Schauder continuation theorem.

Automated layout of small lattices using layer diagrams

Good quality concept lattice drawings are required to effectively communicate logical structure in Formal Concept Analysis. Data analysis frameworks such as the Toscana System use manually arranged concept lattices to avoid the problem of automatically producing high quality lattices. This limits Toscana systems to a finite number of concept lattices that have been prepared a priori. To extend the use of formal concept analysis, automated techniques are required that can produce high quality concept lattice drawings on demand. This paper proposes and evaluates an adaption of layer diagrams to improve automated lattice drawing. © Springer-Verlag Berlin Heidelberg 2006.

Flexible proof reuse for software verification

Proof reuse, or analogical reasoning, involves reusing the proof of a source theorem in the proof of a target conjecture. We have developed a method for proof reuse that is based on the generalisation replay paradigm described in the literature, in which a generalisation of the source proof is replayed to construct the target proof. In this paper, we describe the novel aspects of our method, which include a technique for producing more accurate source proof generalisations (using knowledge of the target goal), as well as a flexible replay strategy that allows the user to set various parameters to control the size and the shape of the search space. Finally, we report on the results of applying this method to a case study from the realm of software verification.

Axiomatisation of an Interval Calculus for Theorem Proving

We provide an axiomatisation of the Timed Interval Calculus, a set-theoretic notation for expressing properties of time intervals. We implement the axiomatisation in the Ergo theorem prover in order to allow the machine-checked proof of laws for reasoning about predicates expressed using interval operators. These laws can be then used in the machine-assisted verification of real-time applications.

Investigating Concept Mapping and Stimulated Recall to Reveal Academic Teacher Beliefs and how they are enacted through learning designs for the Web

Increasingly, academic teachers are designing their own web sites to add value to or replace other forms of university teaching. These web sites are tangible and dynamic constructions that represent the teachers thinking and decisions derived from an implicit belief system about teaching and learning. The emphasis of this study is to explore the potential of the research techniques of concept-mapping and stimulated recall to locate the implicit pedagogies of academic teachers and investigate how they are enacted through the learning designs of their web sites. The rationale behind such an investigation is that once these implicit belief systems are made visible, then conversations can commence about how these beliefs are transformed into practice, providing a potent departure point for academic development.

Management of type 2 diabetes:new and future developments in treatment

The increasing prevalence, variable pathogenesis, progressive natural history, and complications of type 2 diabetes emphasise the urgent need for new treatment strategies. Longacting (eg, once weekly) agonists of the glucagon-like-peptide-1 receptor are advanced in development, and they improve prandial insulin secretion, reduce excess glucagon production, and promote satiety. Trials of inhibitors of dipeptidyl peptidase 4, which enhance the effect of endogenous incretin hormones, are also nearing completion. Novel approaches to glycaemic regulation include use of inhibitors of the sodium-glucose cotransporter 2, which increase renal glucose elimination, and inhibitors of 11ß-hydroxysteroid dehydrogenase 1, which reduce the glucocorticoid effects in liver and fat. Insulin-releasing glucokinase activators and pancreatic-G-protein-coupled fatty-acid-receptor agonists, glucagon-receptor antagonists, and metabolic inhibitors of hepatic glucose output are being assessed. Early proof of principle has been shown for compounds that enhance and partly mimic insulin action and replicate some effects of bariatric surgery.

Synthesis and evaluation of novel ligands for quantum dot stabilisation and polymerisation studies

This thesis describes the design and synthesis of a variety of functionalised phosphine oxides and sulfides, based on the structure of trioctylphosphine oxide, synthesised for the purpose of surface modification of quantum dots. The ability of the ligands to modify the surface chemistry via displacement of the original hexadecylamine capping layer of quantum dots was evaluated. Finally the surface modified quantum dots were investigated for enhancement in their inherent properties and improved compatibility with the various applications for which they were initially designed. Upon the commencement of research involving quantum dots it became apparent that more information on their behaviour and interaction with the environment was required. The limits of the inherent stability of hexadecylamine capped quantum dots were investigated by exposure to a number of different environments. The effect upon the stability of the quantum dots was monitored by changes in the photoluminescence ability of their cores. Subtle differences between different batches of quantum dots were observed and the necessity to account for these in future applications noted. Lastly the displacement of the original hexadecylamine coating with the "designer" functionalised ligands was evaluated to produce a set of conditions that would result in the best possible surface modification. A general procedure was elucidated however it was discovered that each displacement still required slight adjustment by consideration of the other factors such as the difference in ligand structure and the individuality of the various batches of quantum dots. This thesis also describes a procedure for the addition of a protective layer to the surface of quantum dots by cross-linking the functionalised ligands bound to the surface via an acyclic diene metathesis polymerisation. A detailed description of the problems encountered in the analysis of these materials combined with the use of novel techniques such as diffusion ordered spectroscopy is provided as a means to overcome the limitations encountered. Finally a demonstration of the superior stability, upon exposure to a range of aggressive environments of these protected materials compared with those before cross-linking provided physical proof of the cross-linking process and the advantages of the cross-linking modification. Finally this thesis includes the presentation of initial work into the production of luminescent nanocrystal encoded resin beads for the specific use in solid phase combinatorial chemistry. Demonstration of the successful covalent incorporation of quantum dots into the polymeric matrices of non-functionalised and functionalised resin beads is described. Finally by preliminary work to address and overcome the possible limitations that may be encountered in the production and general employment of these materials in combinatorial techniques is given.

Immuno-potentiating activity of surfactant vesicles in DNA and subunit vaccination

Enhanced immune responses for DNA and subunit vaccines potentiated by surfactant vesicle based delivery systems outlined in the present study, provides proof of principle for the beneficial aspects of vesicle mediated vaccination. The dehydration-rehydration technique was used to entrap plasmid DNA or subunit antigens into lipid-based (liposomes) or non-ionic surfactant-based (niosomes) dehydration-rehydration vesicles (DRV). Using this procedure, it was shown that both these types of antigens can be effectively entrapped in DRV liposomes and DRV niosomes. The vesicle size of DRV niosomes was shown to be twice the diameter (~2µm) of that of their liposome counterparts. Incorporation of cryoprotectants such as sucrose in the DRV procedure resulted in reduced vesicle sizes while retaining high DNA incorporation efficiency (~95%). Transfection studies in COS 7 cells demonstrated that the choice of cationic lipid, the helper lipid, and the method of preparation, all influenced transfection efficiency indicating a strong interdependency of these factors. This phenomenon has been further reinforced when 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE): cholesteryl 3b- [N-(N’ ,N’ -dimethylaminoethane)-carbamoyl] cholesterol (DC-Chol)/DNA complexes were supplemented with non-ionic surfactants. Morphological analysis of these complexes using transmission electron microscopy and environmental scanning electron microscopy (ESEM) revealed the presence of heterogeneous structures which may be essential for an efficient transfection in addition to the fusogenic properties of DOPE. In vivo evaluation of these DNA incorporated vesicle systems in BALB/c mice showed weak antibody and cell-mediated immune (CMI) responses. Subsequent mock challenge with hepatitis B antigen demonstrated that, 1-monopalmitoyl glycerol (MP) based DRV, is a more promising DNA vaccine adjuvant. Studying these DRV systems as adjuvants for the Hepatitis B subunit antigen (HBsAg) revealed a balanced antibody/CMI response profile on the basis of the HBsAg specific antibody and cytokine responses which were higher than unadjuvated antigen. The effect of addition of MP, cholesterol and trehalose 6,6’-dibehenate (TDB) on the stability and immuno-efficacy of dimethyldioctadecylammonium bromide (DDA) vesicles was investigated. Differential scanning calorimetry showed a reduction in transition temperature of DDA vesicles by ~12°C when incorporated with surfactants. ESEM of MP based DRV system indicated an increased vesicle stability upon incorporation of antigen. Adjuvant activity of these systems tested in C57BL/6j mice against three subunit antigens i.e., mycobacterial fusion protein- Ag85B-ESAT-6, and two malarial antigens - merozoite surface protein-1, (MSP1), and glutamate rich protein, (GLURP) revealed that while MP and DDA based systems induced comparable antibody responses, DDA based systems induced powerful CMI responses.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.

A relaxation method of an alternating iterative algorithm for the Cauchy problem in linear isotropic elasticity

We propose two algorithms involving the relaxation of either the given Dirichlet data (boundary displacements) or the prescribed Neumann data (boundary tractions) on the over-specified boundary in the case of the alternating iterative algorithm of Kozlov et al. [16] applied to Cauchy problems in linear elasticity. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed method.

The formulation of artificial reference standards for use within the ELISPOT assay

Whether to assess the functionality of equipment or as a determinate for the accuracy of assays, reference standards are essential for the purposes of standardisation and validation. The ELISPOT assay, developed over thirty years ago, has emerged as a leading immunological assay in the development of novel vaccines for the assessment of efficacy. However, with its widespread use, there is a growing demand for a greater level of standardisation across different laboratories. One of the major difficulties in achieving this goal has been the lack of definitive reference standards. This is partly due to the ex vivo nature of the assay, which relies on cells being placed directly into the wells. Thus, the aim of this thesis was to produce an artificial reference standard using liposomes, for use within the assay. Liposomes are spherical bilayer vesicles with an enclosed aqueous compartment and therefore are models for biological membranes. Initial work examined pre-design considerations in order to produce an optimal formulation that would closely mimic the action of the cells ordinarily placed on the assay. Recognition of the structural differences between liposomes and cells led to the formulation of liposomes with increased density. This was achieved by using a synthesised cholesterol analogue. By incorporating this cholesterol analogue in liposomes, increased sedimentation rates were observed within the first few hours. The optimal liposome formulation from these studies was composed of 2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), cholesterol (Chol) and brominated cholesterol (Brchol) at a 16:4:12 µMol ratio, based on a significantly higher (p<0.01) sedimentation (as determined by a percentage transmission of 59 ± 5.9 % compared to the control formulation at 29 ± 12 % after four hours). By considering a range of liposome formulations ‘proof of principle’ for using liposomes as ELISPOT reference standards was shown; recombinant IFN? cytokine was successfully entrapped within vesicles of different lipid compositions, which were able to promote spot formation within the ELISPOT assay. Using optimised liposome formulations composed of phosphatidylcholine with or without cholesterol (16 µMol total lipid) further development was undertaken to produce an optimised, scalable protocol for the production of liposomes as reference standards. A linear increase in spot number by the manipulation of cytokine concentration and/or lipid concentrations was not possible, potentially due to the saturation that occurred within the base of wells. Investigations into storage of the formulations demonstrated the feasibility of freezing and lyophilisation with disaccharide cryoprotectants, but also highlighted the need for further protocol optimisation to achieve a robust reference standard upon storage. Finally, the transfer of small-scale production to a medium lab-scale batch (40 mL) demonstrated this was feasible within the laboratory using the optimised protocol.

An iterative method for the reconstruction of a stationary flow

In this article, an iterative algorithm based on the Landweber-Fridman method in combination with the boundary element method is developed for solving a Cauchy problem in linear hydrostatics Stokes flow of a slow viscous fluid. This is an iteration scheme where mixed well-posed problems for the stationary generalized Stokes system and its adjoint are solved in an alternating way. A convergence proof of this procedure is included and an efficient stopping criterion is employed. The numerical results confirm that the iterative method produces a convergent and stable numerical solution. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007