Probabilistic Arguments in Mathematics

This thesis addresses a question that emerges naturally from some observations about contemporary mathematical practice. Firstly, mathematicians always demand proof for the acceptance of new results. Secondly, the ability of mathematicians to tell if a discourse gives expression to a proof is less than perfect, and the computers they use are subject to a variety of hardware and software failures. So false results are sometimes accepted, despite insistence on proof. Thirdly, over the past few decades, researchers have also developed a variety of methods that are probabilistic in nature. Even if carried out perfectly, these procedures only yield a conclusion that is very likely to be true. In some cases, these chances of error are precisely specifiable and can be made as small as desired. The likelihood of an error arising from the inherently uncertain nature of these probabilistic algorithms can therefore be made vanishingly small in comparison to the chances of an error arising when implementing an equivalent deductive algorithm. Moreover, the structure of probabilistic algorithms tends to minimise these Implementation Errors too. So overall, probabilistic methods are sometimes more reliable than deductive ones. This invites the question: ‘Are mathematicians rational in continuing to reject these probabilistic methods as a means of establishing mathematical claims?

‘It’s too late’. Is it really? Considerations for amblyopia treatment in older children

In recent years, media coverage has demonstrated instances in which families of children aged 7 and older, newly diagnosed with strabismic and/or anisometropic amblyopia through community eyecare services, were told it was ‘too late’ for their child to effectively respond to conventional amblyopia treatment (occlusion or atropine penalisation). Formal guidance pertaining to binocular vision anomalies from eyecare professional bodies does not specifically make reference to a child’s age, beyond stating the importance of early diagnosis and treatment of strabismus/amblyopia. However, there have been many changes in the way we view the recovery period for amblyopia, and it is well demonstrated both within literature and clinical practice that conventional treatment can improve amblyopic eye visual acuity in children beyond the age of 7 years. The occurrence of these media described cases within the community eyecare sphere would suggest it is worthwhile revisiting the literature on the subject of amblyopia treatment in older children (aged 7+ years), to address misconceptions and place in the spotlight current considerations facing clinicians when treating newly diagnosed amblyopia within this age group. This perspective review provides an evidence-based update covering the various considerations associated with treatment of amblyopia in older children, along with recent amblyopia treatment advances that could have an impact on treatment prospects for this patient group. Considerations include the risks, benefits and efficacy of treating newly diagnosed amblyopia in older children, monitoring density of suppression to mitigate intractable diplopia risk, and recent findings regarding binocular treatments for amblyopia

A critique of neo-mercantilist analyses of Icelandic political economy and crisis

Iceland’s journey from rags to riches in the 20th century is related, in the dominant discourse, to its gaining independence in 1944. This discourse played a significant role in both the legitimation of the finance-dominated growth model in the 1990s and 2000s and in the latter’s defence as it came under scrutiny before its collapse in October 2008. It is therefore ironic – or perhaps, in some sense, logical – to find dominant analyses of the crisis arising from the neo-mercantilist tradition. Drawing on Marxist critiques of neo-mercantilism, we challenge these interventions and thus seek to redress the neglect of social struggle in the dominant discourse

Semantic distillation: a method for clustering objects by their contextual specificity

Techniques for data-mining, latent semantic analysis, contextual search of databases, etc. have long ago been developed by computer scientists working on information retrieval (IR). Experimental scientists, from all disciplines, having to analyse large collections of raw experimental data (astronomical, physical, biological, etc.) have developed powerful methods for their statistical analysis and for clustering, categorising, and classifying objects. Finally, physicists have developed a theory of quantum measurement, unifying the logical, algebraic, and probabilistic aspects of queries into a single formalism. The purpose of this paper is twofold: first to show that when formulated at an abstract level, problems from IR, from statistical data analysis, and from physical measurement theories are very similar and hence can profitably be cross-fertilised, and, secondly, to propose a novel method of fuzzy hierarchical clustering, termed \textit{semantic distillation} -- strongly inspired from the theory of quantum measurement --, we developed to analyse raw data coming from various types of experiments on DNA arrays. We illustrate the method by analysing DNA arrays experiments and clustering the genes of the array according to their specificity.Comment: Accepted for publication in Studies in Computational Intelligence, Springer-Verla

Acceptability of novel lifelogging technology to determine context of sedentary behaviour in older adults

<strong>Objective:</strong> Lifelogging, using body worn sensors (activity monitors and time lapse photography) has the potential to shed light on the context of sedentary behaviour. The objectives of this study were to examine the acceptability, to older adults, of using lifelogging technology and indicate its usefulness for understanding behaviour.<strong> </strong><strong>Method:</strong> 6 older adults (4 males, mean age: 68yrs) wore the equipment (ActivPAL^TM and Vicon Revue^TM/SenseCam^TM) for 7 consecutive days during free-living activity. The older adults’ perception of the lifelogging technology was assessed through semi-structured interviews, including a brief questionnaire (Likert scale), and reference to the researcher&#39;s diary. <strong>Results:</strong> Older adults in this study found the equipment acceptable to wear and it did not interfere with privacy, safety or create reactivity, but they reported problems with the actual technical functioning of the camera. <strong>Conclusion:</strong> This combination of sensors has good potential to provide lifelogging information on the context of sedentary behaviour

Synthetic opioids: a review and clinical update

The term ‘opioids’ refers to both the natural compounds (‘opiates’) which are extracted from the opium poppy plant ( Papaver somniferum) and their semi-synthetic and synthetic derivatives. They all possess relatively similar biochemical profiles and interact with the opioid receptors within the human body to produce a wide range of physiological effects. They have historically been used for medicinal purposes, their analgesic and sedative effects, and in the management of chronic and severe pain. They have also been used for non-medicinal and recreational purposes to produce feelings of relaxation, euphoria and well-being. Over the last decade, the emergence of an illegal market in new synthetic opioids has become a major global public health issue, associated with a substantial increase in unintentional overdoses and drug-related deaths. Synthetic opioids include fentanyl, its analogues and emerging non-fentanyl opioids. Their popularity relates to changes in criminal markets, pricing, potency, availability compared to classic opioids, ease of transport and use, rapid effect and lack of detection by conventional testing technologies. This article expands on our previous review on new psychoactive substances. We now provide a more in-depth review on synthetic opioids and explore the current challenges faced by people who use drugs, healthcare professionals, and global public health systems

Incremental dimension reduction of tensors with random index

We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low and predictable. Component encoding and decoding are performed on-line without computationally expensive re-analysis of the data set. The range of tensor indices can be extended dynamically without modifying the component representation. This idea originates from a mathematical model of semantic memory and a method known as random indexing in natural language processing. We generalize the random-indexing algorithm to tensors and present signal-to-noise-ratio simulations for representations of vectors and matrices. We present also a mathematical analysis of the approximate orthogonality of high-dimensional ternary vectors, which is a property that underpins this and other similar random-coding approaches to dimension reduction. To further demonstrate the properties of random indexing we present results of a synonym identification task. The method presented here has some similarities with random projection and Tucker decomposition, but it performs well at high dimensionality only (n>10^3). Random indexing is useful for a range of complex practical problems, e.g., in natural language processing, data mining, pattern recognition, event detection, graph searching and search engines. Prototype software is provided. It supports encoding and decoding of tensors of order >= 1 in a unified framework, i.e., vectors, matrices and higher order tensors.Comment: 36 pages, 9 figure

Effect of pre-milking teat preparation procedures on the microbial count on teats prior to cluster application

A study was carried out to investigate the effect of six pre-milking teat preparation procedures on lowering the staphylococal, streptococcal and coliform microbial count on teat skin prior to cluster application. The teat preparations included 'Iodine', 'Chlorhexidine' teat foam, 'Washing and drying' with paper, 'No preparation', 'Chlorine' teat foam, and disinfectant 'Wipes'. Teat preparations were applied for five days to 10 cows for each treatment during two herd management periods (indoors and outdoors). Teats were swabbed on day four and five before teat preparation and repeated after teat preparation. The swabs were plated on three selective agars: Baird Parker (Staphylococcus spp.), Edwards (Streptococcus spp.), and MacConkey (coliform). Following incubation, microbial counts for each pathogen type were manually counted and assigned to one of six categories depending on the microbial counts measured. The results were analysed by logistic regression using SAS [28]. The main analysis was conducted on binary improvement scores for the swabbing outcomes. There were no differences for staphylococcal, streptococcal and coliform bacterial counts between treatments, measured 'before' teat preparation. Treatments containing 'Chlorhexidine' teat foam (OR = 4.46) and 'Wipes' (OR = 4.46) resulted in a significant reduction (P < 0.01) in the staphylococcal count on teats compared to 'Washing and drying' or 'No preparation'. 'Chlorine' teat foam (OR = 3.45) and 'Wipes' (3.45) had the highest probability (P < 0.01) of reducing streptococcal counts compared to 'Washing and drying' or 'No preparation'. There was no statistical difference between any of the disinfectant treatments applied in reducing coliforms. Thus, the use of some disinfectant products for pre-milking teat preparation can have beneficial effects on reducing the levels of staphylococcal and streptococcal pathogens on teat skin

A family history of breast cancer will not predict female early onset breast cancer in a population-based setting

ABSTRACT: BACKGROUND: An increased risk of breast cancer for relatives of breast cancer patients has been demonstrated in many studies, and having a relative diagnosed with breast cancer at an early age is an indication for breast cancer screening. This indication has been derived from estimates based on data from cancer-prone families or from BRCA1/2 mutation families, and might be biased because BRCA1/2 mutations explain only a small proportion of the familial clustering of breast cancer. The aim of the current study was to determine the predictive value of a family history of cancer with regard to early onset of female breast cancer in a population based setting. METHODS: An unselected sample of 1,987 women with and without breast cancer was studied with regard to the age of diagnosis of breast cancer. RESULTS: The risk of early-onset breast cancer was increased when there were: (1) at least 2 cases of female breast cancer in first-degree relatives (yes/no; HR at age 30: 3.09; 95% CI: 128-7.44), (2) at least 2 cases of female breast cancer in first or second-degree relatives under the age of 50 (yes/no; HR at age 30: 3.36; 95% CI: 1.12-10.08), (3) at least 1 case of female breast cancer under the age of 40 in a first- or second-degree relative (yes/no; HR at age 30: 2.06; 95% CI: 0.83-5.12) and (4) any case of bilateral breast cancer (yes/no; HR at age 30: 3.47; 95%: 1.33-9.05). The positive predictive value of having 2 or more of these characteristics was 13% for breast cancer before the age of 70, 11% for breast cancer before the age of 50, and 1% for breast cancer before the age of 30. CONCLUSION: Applying family history related criteria in an unselected population could result in the screening of many women who will not develop breast cancer at an early age