Variational Markov Chain Monte Carlo for Bayesian smoothing of non-linear niffusions

In this paper we develop set of novel Markov chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. Flexible blocking strategies are introduced to further improve mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample, applications the algorithm is accurate except in the presence of large observation errors and low observation densities, which lead to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

Synthesis and biological evaluation of potential anti-cancer agents

The new technology of combinational chemistry has been introduced to pharmaceutical companies, improving and making more efficient the process of drug discovery. Automated combinatorial chemistry in the solution-phase has been used to prepare a large number of compounds of anti-cancer screening. A library of caffeic acid derivatives has been prepared by the Knoevenagel condensation of aldehyde and active methylene reagents. These products have been screened against two murine adenocarcinoma cell lines (MAC) which are generally refractive to standard cytotoxic agents. The target of anti-proliferative action was the 12- and 15-lipoxygenase enzymes upon which these tumour cell lines have been shown to be dependent for proliferation and metastasis. Compounds were compared to a standard lipoxygenase inhibitor and if found to be active anti-proliferative agents were tested for their general cytotoxicity and lipoxygenase inhibition. A solid-phase bound catalyst, piperazinomethyl polystyrene, was devised and prepared for the improved generation of Knoevenagel condensation products. This piperazinomethyl polystyrene was compared to the traditional liquid catalyst, piperidine, and was found to reduce the amount of by-products formed during reaction and had the advantage of easy removal from the reaction. 13C NMR has been used to determine the E/Z stereochemistry of Knoevenagel condensation products. Soluble polymers have been prepared containing different building blocks pendant to the polymer backbone. Aldehyde building blocks incorporated into the polymer structure have been subjected to the Knoevenagel condensation. Cleavage of the resultant pendant molecules has proved that soluble linear polymers have the potential to generate combinatorial mixtures of known composition for biological testing. Novel catechol derivatives have been prepared by traditional solution-phase chemistry with the intention of transferring their synthesis to a solid-phase support. Catechol derivatives prepared were found to be active inhibitors of lipoxygenase. Soluble linear supports for the preparation of these active compounds were designed and tested. The aim was to develop a support suitable for the automated synthesis of libraries of catechol derivatives for biological screening.

A novel dried blood spot-LCMS method for the quantification of methotrexate polyglutamates as a potential marker for methotrexate use in children

Objective: Development and validation of a selective and sensitive LCMS method for the determination of methotrexate polyglutamates in dried blood spots (DBS). Methods: DBS samples [spiked or patient samples] were prepared by applying blood to Guthrie cards which was then dried at room temperature. The method utilised 6-mm disks punched from the DBS samples (equivalent to approximately 12 μl of whole blood). The simple treatment procedure was based on protein precipitation using perchloric acid followed by solid phase extraction using MAX cartridges. The extracted sample was chromatographed using a reversed phase system involving an Atlantis T3-C18 column (3 μm, 2.1x150 mm) preceded by Atlantis guard column of matching chemistry. Analytes were subjected to LCMS analysis using positive electrospray ionization. Key Results: The method was linear over the range 5-400 nmol/L. The limits of detection and quantification were 1.6 and 5 nmol/L for individual polyglutamates and 1.5 and 4.5 nmol/L for total polyglutamates, respectively. The method has been applied successfully to the determination of DBS finger-prick samples from 47 paediatric patients and results confirmed with concentrations measured in matched RBC samples using conventional HPLC-UV technique. Conclusions and Clinical Relevance: The methodology has a potential for application in a range of clinical studies (e.g. pharmacokinetic evaluations or medication adherence assessment) since it is minimally invasive and easy to perform, potentially allowing parents to take blood samples at home. The feasibility of using DBS sampling can be of major value for future clinical trials or clinical care in paediatric rheumatology. © 2014 Hawwa et al.

Synthesis and screening of potential antimicrobial compounds

Tuberculosis (TB), an infection caused by human pathogen Mycobacterium tuberculosis, continues to kill millions each year and is as prevalent as it was in the pre-antimicrobial era. With the emergence of continuously-evolving multi-drug resistant strains (MDR) and the implications of the HIV epidemic, it is crucial that new drugs with better efficacy and affordable cost are developed to treat TB. With this in mind, the first part of this thesis discusses the synthesis of libraries of derivatives of pyridine carboxamidrazones, along with cyclised (1,2,4-triazole and 1,2,4-oxadiazole) and fluorinated analogues. Microbiological screening against M. tuberculosis was carried out at the TAACF, NIAID and IDRI (USA). This confirmed the earlier findings that 2-pyridyl-substituted carboxamidrazones were more active than the 4-pyridyl-substituted carboxamidrazones. Another important observation was that upon cyclisation of these carboxamidrazones, a small number of the triazoles retained their activity while in most of the remaining compounds the activity was diminished. This might be attributed to the significant increase in logP value caused by cyclisation of these linear carboxamidrazones, resulting in high lipophilicity and decreased permeability. Another reason might be that the rigidity conferred upon the compound due to cyclisation, results in failure of the compound to fit into the active site of the putative target enzyme. In order to investigate the potential change to the compounds’ metabolism in the organism and/or host, the most active compounds were selected and a fluorine atom was introduced in the pyridine ring. The microbiological results shows a drastic improvement in the activity of the fluorinated carboxamidrazone amides as compared to their non fluorinated counterpart. This improvement in the activity could possibly be the result of the increased cell permeability caused by the fluorine. In a subsidiary strand, a selection of long-chain , -unsaturated carboxylic esters, -keto, -hydroxy carboxylic esters and -keto, -hydroxy carboxylic esters, structurally similar to mycolic acids, were synthesised. The microbiological data revealed that one of the open chain compound was active against the Mycobacterium tuberculosis H37Rv strain and some resistant isolates. The possible compound activity could be its potential to disrupt mycobacterial cell wall synthesis by interfering with the FAS-II pathway.

Evaluation on a 60 GHz radio over fiber system employing photonic up conversion and optically beam formed linear array antenna for broadband indoor access

In this study, two linear coplanar array antennas based on Indium Phosphide (InP) substrate are designed, presented and compared in terms of bandwidth and gain. Slot introduction in combination with coplanar structure is investigated, providing enhanced antenna gain and bandwidth at the 60 GHz frequency band. In addition the proposed array antennas are evaluated in terms of integration with a high-speed photodiode and investigated in terms of matching, providing a bandwidth that reaches 2 GHz. Moreover a potential beam forming scenario combined with photonic up-conversion scheme has been proposed. © 2013 IEEE.

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

A linear relational DEA model to evaluate two-stage processes with shared inputs

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach.