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Some remarks concerning finitely Subadditive outer measures with applications
John E. Knight
International Journal of Mathematics and Mathematical Sciences , 1998, DOI: 10.1155/s016117129800091x
Abstract: The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the relationship of their properties to those of an associated finitely subadditive outer measure. In particular, the interconnections between the measurable sets determined by both the outer measure and its associated inner measure are examined. Finally, several applications of the general theory are given, with special attention being paid to various lattice related set functions.
Applying the PDCA Cycle to the Complex Task of Teaching and Assessing Public Relations Writing
John E. Knight,Sandra Allen
International Journal of Higher Education , 2012, DOI: 10.5430/ijhe.v1n2p67
Abstract: Teaching skills, knowledge and abilities appropriate for career-ready graduates and assessing learning are complex issues. Developing a valid and reliable approach is often by trial and error. Instead, the authors employed Deming’s PDCA Cycle of continuous improvement as a systematic procedure to incrementally move closer to their goal. This paper outlines a multiyear project where academics and public relations professionals collaborated to answer 4 questions: What are the basic SKAs for a career-ready graduate?; How to orient the pedagogy?; How to evaluate and assess student learning?; and, How to insure validity of the measurements?. The authors used a variety of qualitative and quantitative procedures to (a) gather knowledge and information from public relations professionals; (b) facilitate consensus on career-specific pedagogy; and (c) develop a repeatable and reliable rubric to measure students’ news release writing skills.
A pragmatic suggestion for dealing with results for candidate genes obtained from genome wide association studies
David Curtis, Anna E Vine, Jo Knight
BMC Genetics , 2007, DOI: 10.1186/1471-2156-8-20
Abstract: An approach is proposed in which differential treatment is afforded to markers from candidate regions and from those that are routinely typed in the context of a genome wide scan. Different prior probabilities are assigned to the two types of marker. A likelihood ratio is derived from the reported p value for each marker, calculated as LR = echiinv(1,p)/2, and the posterior odds in favour of a true positive association are obtained. These odds can be used to rank the markers with a view to suggesting the regions in which further genotyping is indicated. We suggest that prior probabilities be specified such that a candidate marker significant at p = 0.01 and a routine marker significant at p = 0.00001 will yield similar values for the posterior odds. We show that this can be achieved by setting a value for prior probability of association to 0.1 for candidate markers and to 0.00018 for routine markers.It is essential that formal procedures be adopted in order to avoid modestly positively results from candidate regions being swamped by the huge number of nominally significant results which will be obtained when very many markers are genotyped. Software to carry out the conversion from p values to posterior odds is available from http://www.mds.qmul.ac.uk/statgen/grpsoft.html webcite.The ability to carry out so-called genome wide association studies using a standard panel of single nucleotide polymorphisms (SNPs) presents obvious difficulties. For many diseases it will be the case that particular genes have already been implicated as possibly or probably being involved. Typically, there will be some positive and some negative association studies, some groups will report positive results with particular markers or haplotypes while others will report negative results with those markers but positive results from some other markers nearby and a third set of groups will report positive results with a different, though related, phenotype. There may be general consensus that
A simple method for assessing the strength of evidence for association at the level of the whole gene
David Curtis, Anna E Vine, Jo Knight
Advances and Applications in Bioinformatics and Chemistry , 2008, DOI: http://dx.doi.org/10.2147/AABC.S4095
Abstract: simple method for assessing the strength of evidence for association at the level of the whole gene Original Research (5695) Total Article Views Authors: David Curtis, Anna E Vine, Jo Knight Published Date November 2008 Volume 2008:1 Pages 115 - 120 DOI: http://dx.doi.org/10.2147/AABC.S4095 David Curtis1, Anna E Vine1, Jo Knight2 1Centre for Psychiatry, Queen Mary’s School of Medicine and Dentistry, London E1 1BB, UK; 2Social Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, De Crespigny Park, London SE5 8AF, UK Introduction: It is expected that different markers may show different patterns of association with different pathogenic variants within a given gene. It would be helpful to combine the evidence implicating association at the level of the whole gene rather than just for individual markers or haplotypes. Doing this is complicated by the fact that different markers do not represent independent sources of information. Method: We propose combining the p values from all single locus and/or multilocus analyses of different markers according to the formula of Fisher, X = Σ( 2ln(pi)), and then assessing the empirical significance of this statistic using permutation testing. We present an example application to 19 markers around the HTRA2 gene in a case-control study of Parkinson’s disease. Results: Applying our approach shows that, although some individual tests produce low p values, overall association at the level of the gene is not supported. Discussion: Approaches such as this should be more widely used in assimilating the overall evidence supporting involvement of a gene in a particular disease. Information can be combined from biallelic and multiallelic markers and from single markers along with multimarker analyses. Single genes can be tested or results from groups of genes involved in the same pathway could be combined in order to test biologically relevant hypotheses. The approach has been implemented in a computer program called COMBASSOC which is made available for downloading.
A simple method for assessing the strength of evidence for association at the level of the whole gene
David Curtis,Anna E Vine,Jo Knight
Advances and Applications in Bioinformatics and Chemistry , 2008,
Abstract: David Curtis1, Anna E Vine1, Jo Knight21Centre for Psychiatry, Queen Mary’s School of Medicine and Dentistry, London E1 1BB, UK; 2Social Genetic and Developmental Psychiatry Centre, Institute of Psychiatry, De Crespigny Park, London SE5 8AF, UKIntroduction: It is expected that different markers may show different patterns of association with different pathogenic variants within a given gene. It would be helpful to combine the evidence implicating association at the level of the whole gene rather than just for individual markers or haplotypes. Doing this is complicated by the fact that different markers do not represent independent sources of information.Method: We propose combining the p values from all single locus and/or multilocus analyses of different markers according to the formula of Fisher, X = Σ( 2ln(pi)), and then assessing the empirical significance of this statistic using permutation testing. We present an example application to 19 markers around the HTRA2 gene in a case-control study of Parkinson’s disease.Results: Applying our approach shows that, although some individual tests produce low p values, overall association at the level of the gene is not supported.Discussion: Approaches such as this should be more widely used in assimilating the overall evidence supporting involvement of a gene in a particular disease. Information can be combined from biallelic and multiallelic markers and from single markers along with multimarker analyses. Single genes can be tested or results from groups of genes involved in the same pathway could be combined in order to test biologically relevant hypotheses. The approach has been implemented in a computer program called COMBASSOC which is made available for downloading.Keywords: Fisher, significance, genetic marker
Higher Spin Alternating Sign Matrices
Roger E. Behrend,Vincent A. Knight
Mathematics , 2007,
Abstract: We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The case r=1 gives standard alternating sign matrices, while the case in which all matrix entries are nonnegative gives semimagic squares. We show that the higher spin alternating sign matrices of size n are the integer points of the r-th dilate of an integral convex polytope of dimension (n-1)^2 whose vertices are the standard alternating sign matrices of size n. It then follows that, for fixed n, these matrices are enumerated by an Ehrhart polynomial in r.
Slow relaxation in granular compaction
E. Ben-Naim,J. B. Knight,E. R. Nowak
Physics , 1996, DOI: 10.1016/S0167-2789(98)00136-5
Abstract: Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density value follows an inverse logarithmic law. We propose a simple stochastic adsorption-desorption process which captures the essential mechanism underlying this remarkably slow relaxation. As the system approaches its final state, a growing number of beads have to be rearranged to enable a local density increase. In one dimension, this number grows as $N=\rho/(1-\rho)$, and the density increase rate is drastically reduced by a factor $e^{-N}$. Consequently, a logarithmically slow approach to the final state is found $\rho_{\infty}-\rho(t)\cong 1/\ln t$.
Propagating Quantum Walks: the origin of interference structures
P. L. Knight,E. Roldan,J. E. Sipe
Physics , 2003, DOI: 10.1080/09500340408232489
Abstract: We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The particular way of deriving the solution allows a rigorous derivation of a long wavelength approximation. This long wavelength approximation is useful as it provides an approximate analytical expression that captures the basics of the quantum walk and allows us to gain insight into the physics of the process.
Using Functional Annotation for the Empirical Determination of Bayes Factors for Genome-Wide Association Study Analysis
Jo Knight,Michael R. Barnes,Gerome Breen,Michael E. Weale
PLOS ONE , 2012, DOI: 10.1371/journal.pone.0014808
Abstract: A genome wide association study (GWAS) typically results in a few highly significant ‘hits’ and a much larger set of suggestive signals (‘near-hits’). The latter group are expected to be a mixture of true and false associations. One promising strategy to help separate these is to use functional annotations for prioritisation of variants for follow-up. A key task is to determine which annotations might prove most valuable. We address this question by examining the functional annotations of previously published GWAS hits. We explore three annotation categories: non-synonymous SNPs (nsSNPs), promoter SNPs and cis expression quantitative trait loci (eQTLs) in open chromatin regions. We demonstrate that GWAS hit SNPs are enriched for these three functional categories, and that it would be appropriate to provide a higher weighting for such SNPs when performing Bayesian association analyses. For GWAS studies, our analyses suggest the use of a Bayes Factor of about 4 for cis eQTL SNPs within regions of open chromatin, 3 for nsSNPs and 2 for promoter SNPs.
DNA Methylation in Circulating Tumour DNA as a Biomarker for Cancer
Ruth E Board,Lucy Knight,Alastair Greystoke,Fiona H Blackhall
Biomarker Insights , 2007,
Abstract: Free circulating DNA, which is thought to be derived from the primary tumour, can be detected in the blood of patients with cancer. Detection of genetic and epigenetic alteration in this tumour DNA offers a potential source of development of prognostic and predictive biomarkers for cancer. One such change is DNA methylation of the promotor region of tumour suppressor genes. This causes down regulation of tumour suppressor gene expression, a frequent event in carcinogenesis. Hypermethylation of the promotor region of a number of genes has been detected in many tumour types and more recently these changes have been detected in circulating tumour DNA. This review will summarise the literature detailing DNA methylation in circulating tumour DNA and discuss some of the current controversies and technical challenges facing its use as a potential biomarker for cancer.
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