210 research outputs found

    The Writer in the Book: Four Narratives on Writing

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    Some applications of mathematics to coding theory

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    This thesis deals with the transmission of data over a channel that is subject to noise, or interference. There are many different methods of trying to achieve reliable communication of data in the presence of noise. This thesis considers some of these methods, in particular, those aspects involving the use of error-correcting codes. A number of specific applications are considered, as well as some more general theory. One general class of codes is that of cyclic codes (where every cyclic shift of a codeword is also a codeword). Chapter 2 of this thesis reviews a decoding scheme for cyclic codes proposed by Professor P.M. Cohn. The scheme is a modification of standard array syndrome decoding. It is shown that Cohn's scheme does not perform as well as the original version of syndrome decoding. Chapter 3 considers Cyclotomically Shortened Reed Solomon codes (a class of codes introduced by J.L. Dornstetter) and their relationship with the Chinese Remainder Theorem codes of J.J. Stone. The blocklength and dimension of these codes is established, together with the best possible lower bound on the minimum distance. The notion of cyclotomic shortening is then extended to Alternant codes. Chapter 4 deals with the subject of interleaving for channels that are subject to bursts of errors. An optimal solution is given to a problem posed by Inmarsat when interleaving is used with a convolutional code. It is shown how to improve the method of interleaving which feeds data column-wise into an array and then transmits row-wise, by careful selection of the order in which the rows are transmitted. The final chapter discusses the concept of an error-correcting code with two different codeword lengths. Some general results about such codes are presented. A method of forming these codes is given for the case when one word length is twice the other. A specific example of this type of code is considered. Both theoretical and simulated performance results are presented for the example.<p

    Learning health systems need to bridge the ‘two cultures’ of clinical informatics and data science

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    Background UK health research policy and plans for population health management are predicated upon transformative knowledge discovery from operational 'Big Data'. Learning health systems require not only data, but feedback loops of knowledge into changed practice. This depends on knowledge management and application, which in turn depends upon effective system design and implementation. Biomedical informatics is the interdisciplinary field at the intersection of health science, social science and information science and technology that spans this entire scope. Issues In the UK, the separate worlds of health data science (bioinformatics, 'Big Data') and effective healthcare system design and implementation (clinical informatics, 'Digital Health') have operated as 'two cultures'. Much National Health Service and social care data is of very poor quality. Substantial research funding is wasted on 'data cleansing' or by producing very weak evidence. There is not yet a sufficiently powerful professional community or evidence base of best practice to influence the practitioner community or the digital health industry. Recommendation The UK needs increased clinical informatics research and education capacity and capability at much greater scale and ambition to be able to meet policy expectations, address the fundamental gaps in the discipline's evidence base and mitigate the absence of regulation. Independent evaluation of digital health interventions should be the norm, not the exception. Conclusions Policy makers and research funders need to acknowledge the existing gap between the 'two cultures' and recognise that the full social and economic benefits of digital health and data science can only be realised by accepting the interdisciplinary nature of biomedical informatics and supporting a significant expansion of clinical informatics capacity and capability.</p
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