926 resultados para Elementary Methods In Number Theory


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"UNC-5014 (Volume A) Final Report covering the period 20 March 1961 - 31 May 1962."

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The desire to know the future is as old as humanity. For the tourism industry the demand for accurate foretelling of the future course of events is a task that consumes considerable energy and is of great significance to investors. This paper examines the issue of forecasting by comparing forecasts of inbound tourism made prior to the political and economic crises that engulfed Indonesia from 1997 onwards with actual arrival figures. The paper finds that current methods of forecasting are not able to cope with unexpected crises and other disasters and that alternative methods need to be examined including scenarios, political risk and application of chaos theory. The paper outlines a framework for classifying shocks according to a scale of severity, probability, type of event, level of certainty and suggested forecasting tools for each scale of shock. (C) 2003 Elsevier Science Ltd. All rights reserved.

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1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

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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.

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PCA/FA is a method of analyzing complex data sets in which there are no clearly defined X or Y variables. It has multiple uses including the study of the pattern of variation between individual entities such as patients with particular disorders and the detailed study of descriptive variables. In most applications, variables are related to a smaller number of ‘factors’ or PCs that account for the maximum variance in the data and hence, may explain important trends among the variables. An increasingly important application of the method is in the ‘validation’ of questionnaires that attempt to relate subjective aspects of a patients experience with more objective measures of vision.

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The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

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Healthcare providers and policy makers are faced with an ever-increasing number of medical publications. Searching for relevant information and keeping up to date with new research findings remains a constant challenge. It has been widely acknowledged that narrative reviews of the literature are susceptible to several types of bias and a systematic approach may protect against these biases. The aim of this thesis was to apply quantitative methods in the assessment of outcomes of topical therapies for psoriasis. In particular, to systematically examine the comparative efficacy, tolerability and cost-effectiveness of topical calcipotriol in the treatment of mild-to-moderate psoriasis. Over the years, a wide range of techniques have been used to evaluate the severity of psoriasis and the outcomes from treatment. This lack of standardisation complicates the direct comparison of results and ultimately the pooling of outcomes from different clinical trials. There is a clear requirement for more comprehensive tools for measuring drug efficacy and disease severity in psoriasis. Ideally, the outcome measures need to be simple, relevant, practical, and widely applicable, and the instruments should be reliable, valid and responsive. The results of the meta-analysis reported herein show that calcipotriol is an effective antipsoriatic agent. In the short-tenn, the pooled data found calcipotriol to be more effective than calcitriol, tacalcitol, coal tar and short-contact dithranol. Only potent corticosteroids appeared to have comparable efficacy, with less short-term side-effects. Potent corticosteroids also added to the antipsoriatic effect of calcipotriol, and appeared to suppress the occurrence of calcipotriol-induced irritation. There was insufficient evidence to support any large effects in favour of improvements in efficacy when calcipotriol is used in combination with systemic therapies in patients with severe psoriasis. However, there was a total absence of long-term morbidity data on the effectiveness of any of the interventions studied. Decision analysis showed that, from the perspective of the NHS as payer, the relatively small differences in efficacy between calcipotriol and short-contact dithranol lead to large differences in the direct cost of treating patients with mildto-moderate plaque psoriasis. Further research is needed to examine the clinical and economic issues affecting patients under treatment for psoriasis in the UK. In particular, the maintenance value and cost/benefit ratio for the various treatment strategies, and the assessment of patient's preferences has not yet been adequately addressed for this chronic recurring disease.

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This is a review of methodology for the algorithmic study of some useful models in point process and queueing theory, as discussed in three lectures at the Summer Institute at Sozopol, Bulgaria. We provide references to sources where the extensive details of this work are found. For future investigation, some open problems and new methodological approaches are proposed.

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The purpose of this research study was to investigate if the determination of school readiness as it was evaluated by Broward County kindergarten teachers on the Florida's Expectations of School Readiness checklist can be attributed to the effects of gender, chronological age on school entry, racial or ethnic background, attending public preschool, native language other than English, or socioeconomic status.^ This is a descriptive study in which the number of expectations passed or failed for each of the identifier categories was compared. The Chi-squared distribution was used to evaluate the null hypothesis that "chronological age at entry to school, gender, race or ethnicity, native language other than English, public preschool experience, and socioeconomic status have no effect on the determination of readiness for school". Results were confirmed using t-tests, ANOVA, and linear regression models. The cohort of 1555 Broward County students in the study were evaluated using the Florida's Expectations for School Readiness checklist and were determined not ready for school during the initial data collection year 1996-1997.^ The determination of school readiness was significantly dependent on the gender, and racial or ethnic background of the students in the cohort. The socioeconomic status and native language other than English designations were significant for students only in the areas of preacademic, academic and literacy development. Chronological age on entry to school or attendance in public preschool prior to entry in kindergarten for the cohort was not significant in the determination of readiness for school.^ Given the fact that this study followed only students that were determined not ready for school, it is recommended that a second cohort of both "ready" and "not ready" students be studied. ^

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In quantitative risk analysis, the problem of estimating small threshold exceedance probabilities and extreme quantiles arise ubiquitously in bio-surveillance, economics, natural disaster insurance actuary, quality control schemes, etc. A useful way to make an assessment of extreme events is to estimate the probabilities of exceeding large threshold values and extreme quantiles judged by interested authorities. Such information regarding extremes serves as essential guidance to interested authorities in decision making processes. However, in such a context, data are usually skewed in nature, and the rarity of exceedance of large threshold implies large fluctuations in the distribution's upper tail, precisely where the accuracy is desired mostly. Extreme Value Theory (EVT) is a branch of statistics that characterizes the behavior of upper or lower tails of probability distributions. However, existing methods in EVT for the estimation of small threshold exceedance probabilities and extreme quantiles often lead to poor predictive performance in cases where the underlying sample is not large enough or does not contain values in the distribution's tail. In this dissertation, we shall be concerned with an out of sample semiparametric (SP) method for the estimation of small threshold probabilities and extreme quantiles. The proposed SP method for interval estimation calls for the fusion or integration of a given data sample with external computer generated independent samples. Since more data are used, real as well as artificial, under certain conditions the method produces relatively short yet reliable confidence intervals for small exceedance probabilities and extreme quantiles.

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Research in human computer interaction (HCI) covers both technological and human behavioural concerns. As a consequence, the contributions made in HCI research tend to be aware to either engineering or the social sciences. In HCI the purpose of practical research contributions is to reveal unknown insights about human behaviour and its relationship to technology. Practical research methods normally used in HCI include formal experiments, field experiments, field studies, interviews, focus groups, surveys, usability tests, case studies, diary studies, ethnography, contextual inquiry, experience sampling, and automated data collection. In this paper, we report on our experience using the evaluation methods focus groups, surveys and interviews and how we adopted these methods to develop artefacts: either interface’s design or information and technological systems. Four projects are examples of the different methods application to gather information about user’s wants, habits, practices, concerns and preferences. The goal was to build an understanding of the attitudes and satisfaction of the people who might interact with a technological artefact or information system. Conversely, we intended to design for information systems and technological applications, to promote resilience in organisations (a set of routines that allow to recover from obstacles) and user’s experiences. Organisations can here also be viewed within a system approach, which means that the system perturbations even failures could be characterized and improved. The term resilience has been applied to everything from the real estate, to the economy, sports, events, business, psychology, and more. In this study, we highlight that resilience is also made up of a number of different skills and abilities (self-awareness, creating meaning from other experiences, self-efficacy, optimism, and building strong relationships) that are a few foundational ingredients, which people should use along with the process of enhancing an organisation’s resilience. Resilience enhances knowledge of resources available to people confronting existing problems.

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Three long-line methods have been studied in the Algarve: 1) small-hook long-line for inshore (less than 30 m) ‘white’ sea breams (Sparidae); 2) small-hook long-line for deeper water (40-60 m) ‘red’ sea breams; and 3) deep water (500-700 m) semi-pelagic long-line for hake Merluccius merluccius (Linnaeus, 1758). Selectivity studies were carried out with three hook sizes in the first two cases: Mustad round-bent Quality 2369 hooks, numbers 15, 13, and 11, baited with a standardsized razor-shell Ensis siliqua (Linnaeus, 1758). Four hook sizes (numbers 10, 9, 7, and 5) of Stell round-bent, eyed hooks were used in the semi-pelagic long-line selectivity study, baited with a half of a standard-sized sardine. Some factors affecting catch composition and catch rates of the small hook long-lines were also evaluated: bait, gangion length, setting time, fishing ground, and depth. Species diversity was relatively high, with 40, 36 and 27 species, respectively, in the three studies. However, the catches were dominated by a limited number of species. Catch rates (number of fish per 100 hooks) were variable (< 5 %; > 20 %), with a general decrease in catch rate with increasing hook size in all the studies. In general, the catch size distributions for the different hook sizes for each species were highly overlapping, with little or no evidence of differences in size selectivity. Hooks caught a wide size-range for each species, with few or no illegal-sized fish, in most cases. Some implications of these results for the management of multi-species, multi-gear fisheries are discussed.