909 resultados para Interval analysis (Mathematics)
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This study explores the development of a coding system for analysing test questions in two context-based chemistry exams. We describe our unique analytical procedures before contrasting the data from both tests. Our findings indicate that when a new curriculum is developed such as a context-based curriculum, teachers are required to combine the previously separate domains of context and concept to develop contextualised assessment. We argue that constructing contextualised assessment items requires teachers to view concepts and context as interconnected rather than as separate entities that may polarise scientific endeavour. Implications for practice, curriculum and assessment-development in context-based courses are proposed.
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Two decades after its inception, Latent Semantic Analysis(LSA) has become part and parcel of every modern introduction to Information Retrieval. For any tool that matures so quickly, it is important to check its lore and limitations, or else stagnation will set in. We focus here on the three main aspects of LSA that are well accepted, and the gist of which can be summarized as follows: (1) that LSA recovers latent semantic factors underlying the document space, (2) that such can be accomplished through lossy compression of the document space by eliminating lexical noise, and (3) that the latter can best be achieved by Singular Value Decomposition. For each aspect we performed experiments analogous to those reported in the LSA literature and compared the evidence brought to bear in each case. On the negative side, we show that the above claims about LSA are much more limited than commonly believed. Even a simple example may show that LSA does not recover the optimal semantic factors as intended in the pedagogical example used in many LSA publications. Additionally, and remarkably deviating from LSA lore, LSA does not scale up well: the larger the document space, the more unlikely that LSA recovers an optimal set of semantic factors. On the positive side, we describe new algorithms to replace LSA (and more recent alternatives as pLSA, LDA, and kernel methods) by trading its l2 space for an l1 space, thereby guaranteeing an optimal set of semantic factors. These algorithms seem to salvage the spirit of LSA as we think it was initially conceived.
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Objective: To determine whether remote monitoring (structured telephone support or telemonitoring) without regular clinic or home visits improves outcomes for patients with chronic heart failure. Data sources: 15 electronic databases, hand searches of previous studies, and contact with authors and experts. Data extraction: Two investigators independently screened the results. Review methods: Published randomised controlled trials comparing remote monitoring programmes with usual care in patients with chronic heart failure managed within the community. Results: 14 randomised controlled trials (4264 patients) of remote monitoring met the inclusion criteria: four evaluated telemonitoring, nine evaluated structured telephone support, and one evaluated both. Remote monitoring programmes reduced the rates of admission to hospital for chronic heart failure by 21% (95% confidence interval 11% to 31%) and all cause mortality by 20% (8% to 31%); of the six trials evaluating health related quality of life three reported significant benefits with remote monitoring, and of the four studies examining healthcare costs with structured telephone support three reported reduced cost and one no effect. Conclusion: Programmes for chronic heart failure that include remote monitoring have a positive effect on clinical outcomes in community dwelling patients with chronic heart failure.
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The multifractal properties of two indices of geomagnetic activity, D st (representative of low latitudes) and a p (representative of the global geomagnetic activity), with the solar X-ray brightness, X l , during the period from 1 March 1995 to 17 June 2003 are examined using multifractal detrended fluctuation analysis (MF-DFA). The h(q) curves of D st and a p in the MF-DFA are similar to each other, but they are different from that of X l , indicating that the scaling properties of X l are different from those of D st and a p . Hence, one should not predict the magnitude of magnetic storms directly from solar X-ray observations. However, a strong relationship exists between the classes of the solar X-ray irradiance (the classes being chosen to separate solar flares of class X-M, class C, and class B or less, including no flares) in hourly measurements and the geomagnetic disturbances (large to moderate, small, or quiet) seen in D st and a p during the active period. Each time series was converted into a symbolic sequence using three classes. The frequency, yielding the measure representations, of the substrings in the symbolic sequences then characterizes the pattern of space weather events. Using the MF-DFA method and traditional multifractal analysis, we calculate the h(q), D(q), and τ (q) curves of the measure representations. The τ (q) curves indicate that the measure representations of these three indices are multifractal. On the basis of this three-class clustering, we find that the h(q), D(q), and τ (q) curves of the measure representations of these three indices are similar to each other for positive values of q. Hence, a positive flare storm class dependence is reflected in the scaling exponents h(q) in the MF-DFA and the multifractal exponents D(q) and τ (q). This finding indicates that the use of the solar flare classes could improve the prediction of the D st classes.
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This paper provides fundamental understanding for the use of cumulative plots for travel time estimation on signalized urban networks. Analytical modeling is performed to generate cumulative plots based on the availability of data: a) Case-D, for detector data only; b) Case-DS, for detector data and signal timings; and c) Case-DSS, for detector data, signal timings and saturation flow rate. The empirical study and sensitivity analysis based on simulation experiments have observed the consistency in performance for Case-DS and Case-DSS, whereas, for Case-D the performance is inconsistent. Case-D is sensitive to detection interval and signal timings within the interval. When detection interval is integral multiple of signal cycle then it has low accuracy and low reliability. Whereas, for detection interval around 1.5 times signal cycle both accuracy and reliability are high.
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The natural convection thermal boundary layer adjacent to an inclined flat plate and inclined walls of an attic space subject to instantaneous and ramp heating and cooling is investigated. A scaling analysis has been performed to describe the flow behaviour and heat transfer. Major scales quantifying the flow velocity, flow development time, heat transfer and the thermal and viscous boundary layer thicknesses at different stages of the flow development are established. Scaling relations of heating-up and cooling-down times and heat transfer rates have also been reported for the case of attic space. The scaling relations have been verified by numerical simulations over a wide range of parameters. Further, a periodic temperature boundary condition is also considered to show the flow features in the attic space over diurnal cycles.
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Purpose: Colorectal cancer patients diagnosed with stage I or II disease are not routinely offered adjuvant chemotherapy following resection of the primary tumor. However, up to 10% of stage I and 30% of stage II patients relapse within 5 years of surgery from recurrent or metastatic disease. The aim of this study was to determine if tumor-associated markers could detect disseminated malignant cells and so identify a subgroup of patients with early-stage colorectal cancer that were at risk of relapse. Experimental Design: We recruited consecutive patients undergoing curative resection for early-stage colorectal cancer. Immunobead reverse transcription-PCR of five tumor-associated markers (carcinoembryonic antigen, laminin γ2, ephrin B4, matrilysin, and cytokeratin 20) was used to detect the presence of colon tumor cells in peripheral blood and within the peritoneal cavity of colon cancer patients perioperatively. Clinicopathologic variables were tested for their effect on survival outcomes in univariate analyses using the Kaplan-Meier method. A multivariate Cox proportional hazards regression analysis was done to determine whether detection of tumor cells was an independent prognostic marker for disease relapse. Results: Overall, 41 of 125 (32.8%) early-stage patients were positive for disseminated tumor cells. Patients who were marker positive for disseminated cells in post-resection lavage samples showed a significantly poorer prognosis (hazard ratio, 6.2; 95% confidence interval, 1.9-19.6; P = 0.002), and this was independent of other risk factors. Conclusion: The markers used in this study identified a subgroup of early-stage patients at increased risk of relapse post-resection for primary colorectal cancer. This method may be considered as a new diagnostic tool to improve the staging and management of colorectal cancer. © 2006 American Association for Cancer Research.
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Modern technology now has the ability to generate large datasets over space and time. Such data typically exhibit high autocorrelations over all dimensions. The field trial data motivating the methods of this paper were collected to examine the behaviour of traditional cropping and to determine a cropping system which could maximise water use for grain production while minimising leakage below the crop root zone. They consist of moisture measurements made at 15 depths across 3 rows and 18 columns, in the lattice framework of an agricultural field. Bayesian conditional autoregressive (CAR) models are used to account for local site correlations. Conditional autoregressive models have not been widely used in analyses of agricultural data. This paper serves to illustrate the usefulness of these models in this field, along with the ease of implementation in WinBUGS, a freely available software package. The innovation is the fitting of separate conditional autoregressive models for each depth layer, the ‘layered CAR model’, while simultaneously estimating depth profile functions for each site treatment. Modelling interest also lay in how best to model the treatment effect depth profiles, and in the choice of neighbourhood structure for the spatial autocorrelation model. The favoured model fitted the treatment effects as splines over depth, and treated depth, the basis for the regression model, as measured with error, while fitting CAR neighbourhood models by depth layer. It is hierarchical, with separate onditional autoregressive spatial variance components at each depth, and the fixed terms which involve an errors-in-measurement model treat depth errors as interval-censored measurement error. The Bayesian framework permits transparent specification and easy comparison of the various complex models compared.
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With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.
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BACKGROUND: The effect of extreme temperature has become an increasing public health concern. Evaluating the impact of ambient temperature on morbidity has received less attention than its impact on mortality. METHODS: We performed a systematic literature review and extracted quantitative estimates of the effects of hot temperatures on cardiorespiratory morbidity. There were too few studies on effects of cold temperatures to warrant a summary. Pooled estimates of effects of heat were calculated using a Bayesian hierarchical approach that allowed multiple results to be included from the same study, particularly results at different latitudes and with varying lagged effects. RESULTS: Twenty-one studies were included in the final meta-analysis. The pooled results suggest an increase of 3.2% (95% posterior interval = -3.2% to 10.1%) in respiratory morbidity with 1°C increase on hot days. No apparent association was observed for cardiovascular morbidity (-0.5% [-3.0% to 2.1%]). The length of lags had inconsistent effects on the risk of respiratory and cardiovascular morbidity, whereas latitude had little effect on either. CONCLUSIONS: The effects of temperature on cardiorespiratory morbidity seemed to be smaller and more variable than previous findings related to mortality.
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In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.
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Graphical tasks have become a prominent aspect of mathematics assessment. From a conceptual stance, the purpose of this study was to better understand the composition of graphical tasks commonly used to assess students’ mathematics understandings. Through an iterative design, the investigation described the sense making of 11–12-year-olds as they decoded mathematics tasks which contained a graphic. An ongoing analysis of two phases of data collection was undertaken as we analysed the extent to which various elements of text, graphics, and symbols influenced student sense making. Specifically, the study outlined the changed behaviour (and performance) of the participants as they solved graphical tasks that had been modified with respect to these elements. We propose a theoretical framework for understanding the composition of a graphical task and identify three specific elements which are dependently and independently related to each other, namely: the graphic; the text; and the symbols. Results indicated that although changes to the graphical tasks were minimal, a change in student success and understanding was most evident when the graphic element was modified. Implications include the need for test designers to carefully consider the graphics embedded within mathematics tasks since the elements within graphical tasks greatly influence student understanding.
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Objectives: To investigate the efficacy of progestin treatment to achieve pathological complete response (pCR) in patients with complex atypical endometrial hyperplasia (CAH) or early endometrial adenocarcinoma (EC). Methods: A systematic search identified 3245 potentially relevant citations. Studies containing less than ten eligible CAH or EC patients in either oral or intrauterine treatment arm were excluded. Only information from patients receiving six or more months of treatment and not receiving other treatments was included. Weighted proportions of patients achieving pCR were calculated using R software. Results: Twelve studies met the selection criteria. Eleven studies reported treatment of patients with oral (219 patients, 117 with CAH, 102 with grade 1 Stage I EC) and one reported treatment of patients with intrauterine progestin (11 patients with grade 1 Stage IEC). Overall, 74% (95% confidence interval [CI] 65-81%) of patients with CAH and 72% (95% CI 62-80%) of patients with grade 1 Stage I EC achieved a pCR to oral progestin. Disease progression while on oral treatment was reported for 6/219 (2.7%), and relapse after initial complete response for 32/159 (20.1%) patients. The weighted mean pCR rate of patients with grade 1 Stage I EC treated with intrauterine progestin from one prospective pilot study and an unpublished retrospective case series from the Queensland Centre of Gynaecologic Oncology (QCGC) was 68% (95% CI 45- 86%). Conclusions: There is a lack of high quality evidence for the efficacy of progestin in CAH or EC. The available evidence however suggests that treatment with oral or intrauterine progestin is similarly effective. The risk of progression during treatment is small but longer follow-up is required. Evidence from prospective controlled clinical trials is warranted to establish how the efficacy of progestin for the treatment of CAH and EC can be improved further.
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Genome-wide association studies (GWAS) have identified multiple common genetic variants associated with an increased risk of prostate cancer (PrCa), but these explain less than one-third of the heritability. To identify further susceptibility alleles, we conducted a meta-analysis of four GWAS including 5953 cases of aggressive PrCa and 11 463 controls (men without PrCa). We computed association tests for approximately 2.6 million SNPs and followed up the most significant SNPs by genotyping 49 121 samples in 29 studies through the international PRACTICAL and BPC3 consortia. We not only confirmed the association of a PrCa susceptibility locus, rs11672691 on chromosome 19, but also showed an association with aggressive PrCa [odds ratio = 1.12 (95% confidence interval 1.03-1.21), P = 1.4 × 10(-8)]. This report describes a genetic variant which is associated with aggressive PrCa, which is a type of PrCa associated with a poorer prognosis.
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Natural convection thermal boundary layer adjacent to the heated inclined wall of a right angled triangle with an adiabatic fin attached to that surface is investigated by numerical simulations. The finite volume based unsteady numerical model is adopted for the simulation. It is revealed from the numerical results that the development of the boundary layer along the inclined surface is characterized by three distinct stages, i.e. a start-up stage, a transitional stage and a steady stage. These three stages can be clearly identified from the numerical simulations. Moreover, in presence of adiabatic fin, the thermal boundary layer adjacent to the inclined wall breaks initially. However, it is reattached with the downstream boundary layer next to the fin. More attention has been given to the boundary layer development near the fin area.