Distribution of the angle of rotation plane random walks

We study the probability distribution of the angle by which the tangent to the trajectory rotates in the course of a plane random walk. It is shown that the determination of this distribution function can be reduced to an integral equation, which can be rigorously transformed into a differential equation of Hill's type. We derive the asymptotic distribution for very long walks.

Statistical analysis of the associations of hereditary factors with the risk of Type 1 diabetes and Diabetic Nephropathy based on the familial data collected through ascertaiment from population-based registers

In genetic epidemiology, population-based disease registries are commonly used to collect genotype or other risk factor information concerning affected subjects and their relatives. This work presents two new approaches for the statistical inference of ascertained data: a conditional and full likelihood approaches for the disease with variable age at onset phenotype using familial data obtained from population-based registry of incident cases. The aim is to obtain statistically reliable estimates of the general population parameters. The statistical analysis of familial data with variable age at onset becomes more complicated when some of the study subjects are non-susceptible, that is to say these subjects never get the disease. A statistical model for a variable age at onset with long-term survivors is proposed for studies of familial aggregation, using latent variable approach, as well as for prospective studies of genetic association studies with candidate genes. In addition, we explore the possibility of a genetic explanation of the observed increase in the incidence of Type 1 diabetes (T1D) in Finland in recent decades and the hypothesis of non-Mendelian transmission of T1D associated genes. Both classical and Bayesian statistical inference were used in the modelling and estimation. Despite the fact that this work contains five studies with different statistical models, they all concern data obtained from nationwide registries of T1D and genetics of T1D. In the analyses of T1D data, non-Mendelian transmission of T1D susceptibility alleles was not observed. In addition, non-Mendelian transmission of T1D susceptibility genes did not make a plausible explanation for the increase in T1D incidence in Finland. Instead, the Human Leucocyte Antigen associations with T1D were confirmed in the population-based analysis, which combines T1D registry information, reference sample of healthy subjects and birth cohort information of the Finnish population. Finally, a substantial familial variation in the susceptibility of T1D nephropathy was observed. The presented studies show the benefits of sophisticated statistical modelling to explore risk factors for complex diseases.

Plasma-enhanced synthesis of bioactive polymeric coatings from monoterpene alcohols: A combined experimental and theoretical study

This paper describes the synthesis and characterization of a novel organic polymer coating for the prevention of the growth of Pseudomonas aeruginosa on the solid surface of three-dimensional objects. Substrata were encapsulated with polyterpenol thin films prepared from terpinen-4-ol using radio frequency plasma enhanced chemical vapor deposition. Terpinen-4-ol is a constituent of tea tree oil with known antibacterial properties. The influence of deposition power on the chemical structure, surface composition, and ultimately the antibacterial inhibitory activity of the resulting polyterpenol thin films was studied using X-ray photoelectron spectroscopy (XPS), water contact angle measurement, atomic force microscopy (AFM), and 3-D interactive visualization and statistical approximation of the topographic profiles. The experimental results were consistent with those predicted by molecular simulations. The extent of bacterial attachment and extracellular polymeric substances (EPS) production was analyzed using scanning electron microscopy (SEM) and confocal scanning laser microscopy (CSLM). Polyterpenol films deposited at lower power were particularly effective against P. aeruginosa due to the preservation of original terpinen-4-ol molecules in the film structure. The proposed antimicrobial and antifouling coating can be potentially integrated into medical and other clinically relevant devices to prevent bacterial growth and to minimize bacteria-associated adverse host responses.

GENEHUNTER: your 'one-stop shop' for statistical genetic analysis?

The past decade has brought a proliferation of statistical genetic (linkage) analysis techniques, incorporating new methodology and/or improvement of existing methodology in gene mapping, specifically targeted towards the localization of genes underlying complex disorders. Most of these techniques have been implemented in user-friendly programs and made freely available to the genetics community. Although certain packages may be more 'popular' than others, a common question asked by genetic researchers is 'which program is best for me?'. To help researchers answer this question, the following software review aims to summarize the main advantages and disadvantages of the popular GENEHUNTER package.

Water-ethanol mixtures by molecular dynamics and x-ray Compton scattering

Water-ethanol mixtures are commonly used in industry and house holds. However, quite surprisingly their molecular-level structure is still not completely understood. In particular, there is evidence that the local intermolecular geometries depend significantly on the concentration. The aim of this study was to gain information on the molecular-level structures of water-ethanol mixtures by two computational methods. The methods are classical molecular dynamics (MD), where the movement of molecules can be studied, and x-ray Compton scattering, in which the scattering cross section is sensitive to the electron momentum density. Firstly, the water-ethanol mixtures were studied with MD simulations, with the mixture concentration ranging from 0 to 100%. For the simulations well-established force fields were used for the water and ethanol molecules (TIP4P and OPLS-AA, respectively). Moreover, two models were used for ethanol, rigid and non-rigid. In the rigid model the intramolecular bond lengths are fixed, whereas in the non-rigid model the lengths are determined by harmonic potentials. Secondly, mixtures with three different concentrations employing both ethanol models were studied by calculating the experimentally observable x-ray quantity, the Compton profile. In the MD simulations a slight underestimation in the density was observed as compared to experiment. Furthermore, a positive excess of hydrogen bonding with water molecules and a negative one with ethanol was quantified. Also, the mixture was found more structured when the ethanol concentration was higher. Negligible differences in the results were found between the two ethanol models. In contrast, in the Compton scattering results a notable difference between the ethanol models was observed. For the rigid model the Compton profiles were similar for all the concentrations, but for the non-rigid model they were distinct. This leads to two possibilities of how the mixing occurs. Either the mixing is similar in all concentrations (as suggested by the rigid model) or the mixing changes for different concentrations (as suggested by the non-rigid model). Either way, this study shows that the choice of the force field is essential in the microscopic structure formation in the MD simulations. When the sources of uncertainty in the calculated Compton profiles were analyzed, it was found that more statistics needs to be collected to reduce the statistical uncertainty in the final results. The obtained Compton scattering results can be considered somewhat preliminary, but clearly indicative of the behaviour of the water-ethanol mixtures when the force field is modified. The next step is to collect more statistics and compare the results with experimental data to decide which ethanol model describes the mixture better. This way, valuable information on the microscopic structure of water-ethanol mixtures can be found. In addition, information on the force fields in the MD simulations and on the ability of the MD simulations to reproduce the microscopic structure of binary liquids is obtained.

Crystal Physics, Diffraction, Theoretical and General Crystallography

A formula has been derived for the mean-square error in the phases of crystal reflections determined through the multiwavelength anomalous scattering method. The error is written in terms of a simple function of the positions in the complex plane of the 'centres' corresponding to the different wavelengths. For the case of three centres, the mean-square error is inversely proportional to the area of the triangle formed by them. The theoretical values are in good agreement with those obtained by earlier workers from computer simulations. The present method makes it easier to optimize the number and the actual wavelengths to be employed in the multiwavelength method. The maximum benefits of this method are expected in experiments employing synchrotron radiation or neutrons.

The puzzle of falling enrolments in physics and chemistry courses: Putting some pieces together

This paper reports and discusses the principal findings of an Australian study exploring the decisions of high achieving Year 10 students about taking physics and chemistry courses (Lyons, 2003). The study used a ‘multiple worlds’ framework to explore the diverse background characteristics that previous quantitative research had shown were implicated in these decisions. Based on analyses of questionnaire and interview data, the study found that the students’ decisions involved the complex negotiation of a number of cultural characteristics within their school science and family worlds. Many of the students regarded junior high school science as irrelevant, uninteresting and difficult, leaving them with few intrinsic reasons for enrolling in senior science courses. The study found that decisions about taking physical science courses were associated with the resources of cultural and social capital within their families, and the degree to which these resources were congruent with the advantages of choosing these courses. The paper concludes that the low intrinsic value of school science and the erosion of its strategic value contribute to the reluctance of students to choose physical science courses in the senior school.

Statistical significance of sequential firing patterns in multi-neuronal spike trains

Sequential firings with fixed time delays are frequently observed in simultaneous recordings from multiple neurons. Such temporal patterns are potentially indicative of underlying microcircuits and it is important to know when a repeatedly occurring pattern is statistically significant. These sequences are typically identified through correlation counts. In this paper we present a method for assessing the significance of such correlations. We specify the null hypothesis in terms of a bound on the conditional probabilities that characterize the influence of one neuron on another. This method of testing significance is more general than the currently available methods since under our null hypothesis we do not assume that the spiking processes of different neurons are independent. The structure of our null hypothesis also allows us to rank order the detected patterns. We demonstrate our method on simulated spike trains.

Bayesian statistical analysis of bacterial diversity

Bacteria play an important role in many ecological systems. The molecular characterization of bacteria using either cultivation-dependent or cultivation-independent methods reveals the large scale of bacterial diversity in natural communities, and the vastness of subpopulations within a species or genus. Understanding how bacterial diversity varies across different environments and also within populations should provide insights into many important questions of bacterial evolution and population dynamics. This thesis presents novel statistical methods for analyzing bacterial diversity using widely employed molecular fingerprinting techniques. The first objective of this thesis was to develop Bayesian clustering models to identify bacterial population structures. Bacterial isolates were identified using multilous sequence typing (MLST), and Bayesian clustering models were used to explore the evolutionary relationships among isolates. Our method involves the inference of genetic population structures via an unsupervised clustering framework where the dependence between loci is represented using graphical models. The population dynamics that generate such a population stratification were investigated using a stochastic model, in which homologous recombination between subpopulations can be quantified within a gene flow network. The second part of the thesis focuses on cluster analysis of community compositional data produced by two different cultivation-independent analyses: terminal restriction fragment length polymorphism (T-RFLP) analysis, and fatty acid methyl ester (FAME) analysis. The cluster analysis aims to group bacterial communities that are similar in composition, which is an important step for understanding the overall influences of environmental and ecological perturbations on bacterial diversity. A common feature of T-RFLP and FAME data is zero-inflation, which indicates that the observation of a zero value is much more frequent than would be expected, for example, from a Poisson distribution in the discrete case, or a Gaussian distribution in the continuous case. We provided two strategies for modeling zero-inflation in the clustering framework, which were validated by both synthetic and empirical complex data sets. We show in the thesis that our model that takes into account dependencies between loci in MLST data can produce better clustering results than those methods which assume independent loci. Furthermore, computer algorithms that are efficient in analyzing large scale data were adopted for meeting the increasing computational need. Our method that detects homologous recombination in subpopulations may provide a theoretical criterion for defining bacterial species. The clustering of bacterial community data include T-RFLP and FAME provides an initial effort for discovering the evolutionary dynamics that structure and maintain bacterial diversity in the natural environment.

Statistical and Information-Theoretic Methods for Data-Analysis

In this Thesis, we develop theory and methods for computational data analysis. The problems in data analysis are approached from three perspectives: statistical learning theory, the Bayesian framework, and the information-theoretic minimum description length (MDL) principle. Contributions in statistical learning theory address the possibility of generalization to unseen cases, and regression analysis with partially observed data with an application to mobile device positioning. In the second part of the Thesis, we discuss so called Bayesian network classifiers, and show that they are closely related to logistic regression models. In the final part, we apply the MDL principle to tracing the history of old manuscripts, and to noise reduction in digital signals.

Does the addition of Clonidine to lumbar nerve root blocks improve outcome? A randomised, prospective, single-blinded controlled pilot study

Purpose To evaluate if adding clonidine to a standard nerve root block containing local anaesthetic and steroid improved the outcome of patients with severe lumbar nerve root pain secondary to MRI proven lumbar disc prolapse. Methods We undertook a single blind, prospective, randomised controlled trial evaluating 100 consecutive patients with nerve root pain secondary to lumbar disc prolapse undergoing trans-foraminal epidural steroid injection either with or without the addition of clonidine. 50 patients were allocated to each arm of the study. The primary outcome measure was the avoidance of a second procedure- repeat injection or micro-discectomy surgery. Secondary outcome measures were also studied: pain scores for leg and back pain using a visual analogue scale (VAS), the Roland Morris Disability Questionnaire (RMDQ) and the Measure Your Own Medical Outcome Profile (MYMOP). Follow up was carried out at 6 weeks, 6 months and 1 year. Results No serious complications occurred. Of the 50 patients who received the addition of clonidine, 56% were classified as successful injections, with no further intervention required, as opposed to 40% who received the standard injection. This difference did not reach statistical significance (p=0.109, chi-squared test). All secondary measures showed no statistically significant differences between the groups except curiously, the standard group who had been classified as successful had better leg pain relief than the clonidine group (p=0.026) at 1 year. Conclusions This pilot study has shown a 16% treatment effect with adding clonidine to lumbar nerve root blocks and that it is a safe injectate for this purpose.

Statistical methods for analysis of multi-harvest data from perennial pasture variety selection trials

Variety selection in perennial pasture crops involves identifying best varieties from data collected from multiple harvest times in field trials. For accurate selection, the statistical methods for analysing such data need to account for the spatial and temporal correlation typically present. This paper provides an approach for analysing multi-harvest data from variety selection trials in which there may be a large number of harvest times. Methods are presented for modelling the variety by harvest effects while accounting for the spatial and temporal correlation between observations. These methods provide an improvement in model fit compared to separate analyses for each harvest, and provide insight into variety by harvest interactions. The approach is illustrated using two traits from a lucerne variety selection trial. The proposed method provides variety predictions allowing for the natural sources of variation and correlation in multi-harvest data.

Electronic Building Passport - Final Report: Project 2 National Energy Efficient Building Project Phase 2

The National Energy Efficient Building Project (NEEBP) Phase One report, published in December 2014, investigated “process issues and systemic failures” in the administration of the energy performance requirements in the National Construction Code. It found that most stakeholders believed that under-compliance with these requirements is widespread across Australia, with similar issues being reported in all states and territories. The report found that many different factors were contributing to this outcome and, as a result, many recommendations were offered that together would be expected to remedy the systemic issues reported. To follow up on this Phase 1 report, three additional projects were commissioned as part of Phase 2 of the overall NEEBP project. This Report deals with the development and piloting of an Electronic Building Passport (EBP) tool – a project undertaken jointly by pitt&sherry and a team at the Queensland University of Technology (QUT) led by Dr Wendy Miller. The other Phase 2 projects cover audits of Class 1 buildings and issues relating to building alterations and additions. The passport concept aims to provide all stakeholders with (controlled) access to the key documentation and information that they need to verify the energy performance of buildings. This trial project deals with residential buildings but in principle could apply to any building type. Nine councils were recruited to help develop and test a pilot electronic building passport tool. The participation of these councils – across all states – enabled an assessment of the extent to which these councils are currently utilising documentation; to track the compliance of residential buildings with the energy performance requirements in the National Construction Code (NCC). Overall we found that none of the participating councils are currently compiling all of the energy performance-related documentation that would demonstrate code compliance. The key reasons for this include: a major lack of clarity on precisely what documentation should be collected; cost and budget pressures; low public/stakeholder demand for the documentation; and a pragmatic judgement that non-compliance with any regulated documentation requirements represents a relatively low risk for them. Some councils reported producing documentation, such as certificates of final completion, only on demand, for example. Only three of the nine council participants reported regularly conducting compliance assessments or audits utilising this documentation and/or inspections. Overall we formed the view that documentation and information tracking processes operating within the building standards and compliance system are not working to assure compliance with the Code’s energy performance requirements. In other words the Code, and its implementation under state and territory regulatory processes, is falling short as a ‘quality assurance’ system for consumers. As a result it is likely that the new housing stock is under-performing relative to policy expectations, consuming unnecessary amounts of energy, imposing unnecessarily high energy bills on occupants, and generating unnecessary greenhouse gas emissions. At the same time, Councils noted that the demand for documentation relating to building energy performance was low. All the participant councils in the EBP pilot agreed that documentation and information processes need to work more effectively if the potential regulatory and market drivers towards energy efficient homes are to be harnessed. These findings are fully consistent with the Phase 1 NEEBP report. It was also agreed that an EBP system could potentially play an important role in improving documentation and information processes. However, only one of the participant councils indicated that they might adopt such a system on a voluntary basis. The majority felt that such a system would only be taken up if it were: - A nationally agreed system, imposed as a mandatory requirement under state or national regulation; - Capable of being used by multiple parties including councils, private certifiers, building regulators, builders and energy assessors in particular; and - Fully integrated into their existing document management systems, or at least seamlessly compatible rather than a separate, unlinked tool. Further, we note that the value of an EBP in capturing statistical information relating to the energy performance of buildings would be much greater if an EBP were adopted on a nationally consistent basis. Councils were clear that a key impediment to the take up of an EBP system is that they are facing very considerable budget and staffing challenges. They report that they are often unable to meet all community demands from the resources available to them. Therefore they are unlikely to provide resources to support the roll out of an EBP system on a voluntary basis. Overall, we conclude from this pilot that the public good would be well served if the Australian, state and territory governments continued to develop and implement an Electronic Building Passport system in a cost-efficient and effective manner. This development should occur with detailed input from building regulators, the Australian Building Codes Board (ABCB), councils and private certifiers in the first instance. This report provides a suite of recommendations (Section 7.2) designed to advance the development and guide the implementation of a national EBP system.