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... Particular cases of higher order spectra are the third order spectrum, also known as the bispectrum, which is defined as the Fourier transform of the third order joint cumulant, and the fourth order spectrum, or trispectrum, which is defined in terms of the Fourier transform of the fourth order joint cumulant. The power spectrum, bispectrum and trispectrum are just particular examples of the generalised concept of polyspectra which were introduced by Tukey [78] and Brillinger [9,10,11] in the early ...
... The power spectrum, bispectrum and trispectrum are just particular examples of the generalised concept of polyspectra [78]. Just as the power spectrum is able to give a decomposition of power over frequency, it is possible to use higher order spectra to obtain a decomposition of skewness and kurtosis over frequency and so obtain more information about the higher order statistics of a signal. ...
Thesis
p>This thesis is concerned with the development of useful engineering techniques to detect and analyse non linearities in mechanical systems. The methods developed are based on the concepts of higher order spectra, in particular the bispectrum and trispectrum, and the Volterra series. The study of higher order statistics has been dominated by work on the bispectrum. The bispectrum can be viewed as a decomposition of the third moment (skewness) of a signal over frequency and as such is blind to symmetric non linearities. To study such phenomena one has to go a stage further and resort to the trispectrum, or decomposition of kurtosis over frequency. Techniques are presented here that enable one to estimate and display both auto and cross, bispectra and trispectra. Initially auto higher order spectra are studied in detail with particular attention being paid to normalisation methods. Two traditional methods based on the bicoherence and skewness function are studied and these are expanded to their fourth order equivalents, the tricoherence and kurtosis functions. Under certain conditions, notably narrow band signals, the above normalisation methods are shown to fail and so a new technique based on pre whitening the signal in the time domain is developed. Examples of these functions are given both for memoryless and dynamic systems. The Volterra series is presented and discussed in some detail. Techniques for calculating a system's Volterra kernals from cross higher order spectra are derived. New methods are presented for the estimation of higher order Volterra kernels which are shown to produce better results than traditional approaches. These are then applied to some simple analytic systems which include the Duffing oscillator.</p
... By assuming a significance level of 0.1 (i.e., a significance level of 0.1 shows a 10% risk of concluding that a difference exists when there is no actual difference), there is a significant difference between the results of these four methods (i.e., F > Sig). Tukey's analysis was used to determine the best method of WtWc (Tukey, 1984). The results of Tukey's analysis are depicted in Fig. 14. ...
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Identifying the location of lithological boundaries is one of the essential steps of reservoir characterizations. The manual well-to-well correlation is usually implemented to identify lithological boundaries. Various automated methods were introduced to accelerate this correlation; however, most of them use single well-log data. As each well-log contains specific information of rock and fluid properties, the simultaneous use of various well-logs can enhance the correlation accuracy. We extend an automatic well-to-well correlation approach from the literature to use the benefits of various well-logs by applying principal component analysis on multiple well-logs of a carbonate reservoir. The extracted features (i.e., mean, coefficient of variation, maximum to minimum ratio, trend angle, and fractal dimension) from a reference well are examined across observation wells. The energy of principal components is evaluated to determine the appropriate number of principal components. We examine three different scenarios of applying principal component analysis and determine the best methodology for well-to-well correlation. In the first scenario, the principal component analysis reduces the dependency of statistical attributes extracted from a single well-log. We then apply principal component analysis on multiple well-logs to extract their features (Scenario II). Finally, we check whether principal component analysis can be applied at multiple steps (Scenario III). The analysis of variance and Tukey are used to compare the accuracy of the scenarios. The results show that identifying lithological boundaries in different wells is significantly improved when the principal component analysis approach combines information from multiple well-logs. Generally, it is concluded that principal component analysis is an effective tool for increasing well-to-well correlation accuracy by reducing the dependency of well-to-well correlation parameters (Scenario I) and the feature extraction from log data (Scenario II & III).
... The first point to make in this respect is that no method exists that explicitly considers claims. The per family error rate (PFER) discussed in [5] defined there as number of erroneous rejections number of families or more formally described as E.V/ is a special case of our proposal. The fundamental difference between the PFER and the EFC is that for the former, any wrongly rejected hypothesis is counted while the EFC only considers cases where at least l i hypotheses in K i are rejected. ...
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Multiplicity is common in clinical studies and the current standard is to use the familywise error rate to ensure that the errors are kept at a prespecified level. In this paper, we will show that, in certain situations, familywise error rate control does not account for all errors made. To counteract this problem, we propose the use of the expected number of false claims (EFC). We will show that a (weighted) Bonferroni approach can be used to control the EFC, discuss how a study that uses the EFC can be powered for co-primary, exchangeable, and hierarchical endpoints, and show how the weight for the weighted Bonferroni test can be determined in this manner. ©2016 The Authors. Pharmaceutical Statistics Published by John Wiley & Sons Ltd.
... Theoretical basis for the study Dewey (1996) finds the core of existence in the process of human growth where experience is continually transformed into culture through communicative practice. People want to be active participants in the cultural life of their environment and identification with that cultural life helps young people to find their own way of experiencing and expressing arts. ...
... IGT overall net score and sensitivity to punishment frequency for control subjects and the euthymic patients with and without lithium were compared using a one-way ANOVA (3 groups: control subjects, euthymic patients with and without lithium). Post-hoc Tukey tests of Honestly Significant Differences (HSD) were performed to test for significant group differences and to control for type I error (Tukey, 1993). Sensitivity to punishment frequency scores were also compared to the value zero using single sample t-tests. ...
Article
Bipolar disorder is associated with impaired decision-making. Little is known about how treatment, especially lithium, influences decision-making abilities in bipolar patients when euthymic. We aimed at testing for an association between lithium medication and decision-making performance in remitted bipolar patients. Decision-making was measured using the Iowa Gambling Task in 3 groups of subjects: 34 and 56 euthymic outpatients with bipolar disorder, treated with lithium (monotherapy and lithium combined with anticonvulsant or antipsychotic) and without lithium (anticonvulsant, antipsychotic and combination treatment), respectively, and 152 matched healthy controls. Performance was compared between the 3 groups. In the 90 euthymic patients, the relationship between different sociodemographic and clinical variables and decision-making was assessed by stepwise multivariate regression analysis. Euthymic patients with lithium (p=0.007) and healthy controls (p=0.001) selected significantly more cards from the safe decks than euthymic patients without lithium, with no significant difference between euthymic patients with lithium and healthy controls (p=0.9). In the 90 euthymic patients, the stepwise linear multivariate regression revealed that decision-making was significantly predicted (p<0.001) by lithium dose, level of education and no family history of bipolar disorder (all p≤0.01). Because medication was not randomized, it was not possible to discriminate the effect of different medications. Lithium medication might be associated with better decision-making in remitted bipolar patients. A randomized trial is required to test for the hypothesis that lithium, but not other mood stabilizers, may specifically improve decision-making abilities in bipolar disorder. Copyright © 2015 Elsevier B.V. and ECNP. All rights reserved.
... Polyspectra are higher order time series analysis techniques analogous to the classical Fourier spectrum which take into account more than one Fourier frequency (Tukey 1984). The bispectrum is the first of a series of polyspectra which can be used to understand phase correlations in single time series at two independent Fourier frequencies. ...
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We explore the non-linear, high-frequency, aperiodic variability properties in the three cataclysmic variables MV Lyr, KIC 8751494 and V1504 Cyg observed with Kepler, as well as the X-ray binary Cyg X-1 observed with RXTE. This is done through the use of a high-order Fourier statistic called the bispectrum and its related biphase and bicoherence, as well as the time-skewness statistic. We show how all objects display qualitatively similar biphase trends. In particular all biphase amplitudes are found to be smaller than π/2\pi/2, suggesting that the flux distributions for all sources are positively skewed on all observed timescales, consistent with the log-normal distributions expected from the fluctuating accretion disk model. We also find that for all objects the biphases are positive at frequencies where the corresponding power spectral densities display their high frequency break. This suggests that the noise-like flaring observed is rising more slowly than it is falling, and thus not time-reversible. This observation is also consistent with the fluctuating accretion disk model. Furthermore, we observe the same qualitative biphase trends in all four objects, where the biphases display a distinct decrease at frequencies below the high-frequency break in their respective power spectral densities. This behaviour can also be observed in the time-skewness of all four objects. As far as we are aware, there is no immediate explanation for the observed biphase decreases. The biphase decreases may thus suggest that the fluctuating accretion disk model begins to break down at frequencies below the high frequency break.
... Rewired genes were identified using Z-scores. derive statistical significance of pairwise mean differences (Tukey and Braun, 1994). In this study, a series of Tukey's HSD tests were performed for those genes determined to be differentially expressed by ANOVA after a Benjamini and Hochberg false discovery rate (FDR) correction (Benjamini and Hochberg, 1995). ...
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Background and Aims A key challenge in biology is to systematically investigate and integrate the different levels of information available at the global and single-cell level. Recent studies have elucidated spatiotemporal expression patterns of root cell types in Arabidopsis thaliana, and genome-wide quantification of polysome-associated mRNA levels, i.e. the translatome, has also been obtained for corresponding cell types. Translational control has been increasingly recognized as an important regulatory step in protein synthesis. The aim of this study was to investigate coupled transcription and translation by use of publicly available root datasets.
... In addition to the many applications of statistical graphics, there is also a large and rapidly growing research literature on statistical methods that use graphics. Recent years have seen statistical graphics discussed in complete books (for example, Chambers et al. 1983;Cleveland 1985Cleveland ,1991 and in collections of papers (Tukey 1988;Cleveland and McGill, 1988). An indication of the widespread interest in statistical graphics beyond the statistical community is that this subject was chosen for an article in an encyclopedia intended for a general technical audience (Landwehr, 1990). ...
... Sensitivity to punishment frequency scores were also compared with the value zero using single sample t tests. Post hoc Tukey tests of honestly significant differences (HSD) were performed to determine significant group differences and to control for Type I error (28). ...
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In bipolar disorder (BD), little is known about how deficits in neurocognitive functions such as decision-making are related to phase of illness. We predicted that manic, depressed, and euthymic bipolar patients (BPs) would display impaired decision-making, and we tested whether clinical characteristics could predict patients' decision-making performance. Subjects (N = 317; age range: 18-65 years) including 167 BPs (45 manic and 32 depressed inpatients, and 90 euthymic outpatients) and 150 age-, IQ-, and gender-matched healthy control (HC) participants, were included within three university psychiatric hospitals using a cross-sectional design. The relationship between predictor variables and decision-making was assessed by one-step multivariate analysis. The main outcome measures were overall decision-making ability on the Iowa Gambling Task (IGT) and an index of sensitivity to punishment frequency. Manic, depressed, and euthymic BPs selected significantly more cards from the risky decks than HCs (p < .001, p < .01, and p < .05, respectively), with no significant differences between the three BD groups. However, like HCs, BPs preferred decks that yielded infrequent penalties over those yielding frequent penalties. In multivariate analysis, decision-making impairment was significantly (p < .001) predicted by low level of education, high depressive scores, family history of BD, use of benzodiazepines, and nonuse of serotonin and norepinephrine reuptake inhibitor (SNRI) antidepressants. BPs have a trait-related impairment in decision-making that does not vary across illness phase. However, some subtle differences between the BD groups in the individual deck analyses may point to subtle state influences on reinforcement mechanisms, in addition to a more fundamental trait impairment in risk-sensitive decision making.
... No discussion of graphical displays would be complete without the mention of the seminal contributions of Tukey (1984), Tufte (1983), and Cleveland (1985). The works encompassed by these three authors probably have done more to define the art of a meaningful graph than any other authors. ...
Article
This paper explores some techniques which may help facility operators better understand complex hourly energy data by enhancing the display of data with animation (or timesequencing). Animated displays such as the ones presented in this paper enhance the usefulness of the graphic display because time and temperature dependent trends can be more easily seen. There is an increasing need for new display paradigms that can help facility operators efficiently scan and detect problems within the river of incoming data from control systems. This need becomes even more important during times of a shrinking labor pool. In this paper the use of animated displays are described as they apply to the measurement of chilled water where the animated display makes a faulty flow meter easier to diagnose.
Chapter
In many scientific investigations, the interest lies in the study of effects of two or more factors simultaneously. Factorial designs are most commonly used for this type of investigation. This chapter considers the important class of factorial designs for factors at two levels. It also considers the estimation and testing of factorial effects for location and dispersion models for replicated and unreplicated experiments. The chapter discusses optimal blocking schemes for full factorial designs. It describes how the factorial effects can be computed using regression analysis. The chapter also discusses three fundamental principles: effect hierarchy principle, effect sparsity principle, and effect heredity principle. These principles are often used to justify the development of factorial design theory and data analysis strategies. The chapter also describes a graphical method that uses the normal probability plot for assessing the normality assumption.
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Introduction. The relevance of the article is determined by the lack of scientific substantiation of existing methods of quantitative analysis of mass student questionnaires that can lead to erroneous conclusions about the quality of educational services they receive. Authors first applied the in-house probabilistic approach to the preparation of data for mass questioning of students to develop regression and factor models that adequately reflect their subjective judgments about learning quality. Our goal was to estimate the efficiency and possibility of the practical application of the authors, approach to the analysis of student questionnaire results by means of multivariate statistics by the example of the development of the quantitative estimation model of education quality and subjective well-being of student s of Orel State Agrarian University. Materials and Methods. The suggested approach is based on the methods of parametrical multivariate statistics. The empiric basis of modeling consists of the results of questioning students of the 2nd-4th years of learning. The analytic software SPSS Base was used. Results. At the example of the development of correlation-regressive and factor models of the subjective well-being of the students, we proved the efficiency of the suggested approach to the quantitative modeling of questionnaire results by means of multivariate statistical methods. It is shown that all the obtained correlation-regression models have high statistical characteristics of quality and adequately reflect the simulated phenomena. Of particular interest is the model structure of factors of subjective well-being of students, reflecting the process of their professional and cultural development and adaptation to the current socio-political environment. Discussion and Conclusion. The completed study expanded the understanding of possibilities of quantitative analysis of the results of mass student questioning by simulating various aspects of their subjective wellbeing. The advantage of this method is that at modeling it allows considering the status features influence on the degree of the higher educational institution satisfaction and the obtainable education quality. The approach suggested by the authors will be useful in quality education monitoring at higher schools as well as in the educational sphere in general and for various social and economic studies.
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Mixed data sets containing numerical and categorical attributes are nowadays ubiquitous. Converting them to one attribute type may lead to a loss of information. We present an approach for handling numerical and categorical attributes in a holistic view. For data sets with many attributes, dimensionality reduction (DR) methods can help to generate visual representations involving all attributes. While automatic DR for mixed data sets is possible using weighted combinations, the impact of each attribute on the resulting projection is difficult to measure. Interactive support allows the user to understand the impact of data dimensions in the formation of patterns. Star Coordinates is a well‐known interactive linear DR technique for multi‐dimensional numerical data sets. We propose to extend Star Coordinates and its initial configuration schemes to mixed data sets. In conjunction with analysing numerical attributes, our extension allows for exploring the impact of categorical dimensions and individual categories on the structure of the entire data set. The main challenge when interacting with Star Coordinates is typically to find a good configuration of the attribute axes. We propose a guided mixed data analysis based on maximizing projection quality measures by the use of recommended transformations, named hints, in order to find a proper configuration of the attribute axes. image
Chapter
This chapter starts by presenting some basic notions and characteristics of different types of data collection systems and types of sensors. Next, simple ways of validating and assessing the accuracy of the data collected are addressed. Subsequently, salient statistical measures to describe univariate and multivariate data are presented along with how to use them during basic exploratory data and graphical analyses. The two types of measurement uncertainty (bias and random) are discussed and the concept of confidence intervals is introduced and its usefulness illustrated. Finally, three different ways of determining uncertainty in a data reduction equation by propagating individual variable uncertainty are presented; namely, the analytical, numerical and Monte Carlo methods.
Chapter
This chapter starts by introducing the benefits of applied data analysis and modeling methods through a case study example pertinent to energy use in buildings. Next, it reviews fundamental notions of mathematical models illustrates them in terms of sensor response, and differentiates between forward or simulation models and inverse models. Subsequently, various issues pertinent to data analysis and associated uncertainty are described, and the different analysis tools which fall within its purview are discussed. Basic concepts relating to white-box, black-box and grey-box models are then presented. An attempt is made to identify the different types of problems one faces with forward modeling as distinct from inverse modeling and analysis. Notions germane to the disciplines of decision analysis, data mining and intelligent data analysis are also covered. Finally, the various topics covered in each chapter of this book are described.
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Chapter
There are two phenomena, which can result from interaction of a shock wave (SW) with a solid surface. A SWreflects off a surface if the angle of incidence is less than 90°. If the angle of incidence is more than 90°, the shock wave diffracts over a surface. At once it is necessary to note that the diffraction phenomenon does not exist in steady flows. Moreover, for steady flows the term “head-on reflection of a SW” loses any meaning and there is no possibility to propose the elementary 5-shock model of the irregular intersection of two arbitrary SWs [1]. These facts reveal the principal differences between the processes of shock wave interaction in the steady and unsteady flows. In the case of shock wave reflection in the steady flows, we deal with a result of reflection in a shock-wave configuration form. Only two configurations — regular 2-shock (RR) and Mach 3-shock (MR) structures — are observed in steady flows and not any parameter of the configuration, including geometrical one, does not change in time. Von Neumann [2] proposed the analytical models of two. and three-shock waves configurations and formulated the local theories, which are valid for describing the flow field in the small vicinity of the intersection point regardless of the conditions of configurations origins.
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In clinical practice, red blood cells (RBCs) have a maximal shelf life (MSL) of 42 days. Recent studies suggest managing RBC inventory with a more restrictive MSL. To this end, a new simulation optimization (SO) framework is proposed for blood supply chain inventory management with ABO blood group compatibility. The inventory objective is to minimize the expected system outdate rate under a predetermined maximally allowable shortage level. The proposed SO framework is incorporated with a new metaheuristic optimization algorithm, TA-TS, to identify near-optimal inventory policies in reasonably acceptable computational time. The new SO framework is shown to offer a better tradeoff between solution accuracy and computational expense. The efficiency of the proposed framework is evaluated in detail for a single-hospital single-blood center supply chain system, in which the MSL of RBC units are shortened to 7, 14 and 21 days. A recently-developed replenishment policy based on old inventory ratio (the OIR policy developed by Duan and Liao (2013b)) is used to control the freshness of the entire inventory. Three different scenarios are investigated: (1) no ABO compatible substitution; (2) ABO compatible substitution at hospital only; (3) ABO compatible substitution at both hospital and blood center. Using the proposed SO framework, we are able to identify a near-optimal solution for each of these scenarios and quantify the potential savings offered by ABO compatible substitution. In the ABO compatible substitution scenarios, there is a clear trend of the increased use of group O blood. As the MSL decreases, group O blood are needed more frequently to substitute for other ABO/Rh(D) compatible blood types. Allowing ABO/Rh(D)-compatible blood substitution helps reduce the system-wide outdate at least by 16% even under the most restrictive MSL For more relax MSL of 14 days and 21 days, the proposed framework is capable of keeping the highest system-wide outdate rate at as little as 2%.
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Structural features associated with forearc basins appear to strongly influence the rupture processes of large subduction zone earthquakes. Recent studies demonstrated that a significant percentage of the global seismic moment release on subduction zone thrust faults is concentrated beneath the gravity lows resulting from forearc basins. To better determine the nature of this correlation and examine its effect on rupture directivity and termination, we estimated the rupture areas of a set of Mw 7.5-8.7 earthquakes that occurred in circum-Pacific subduction zones. We compare synthetic and observed seismograms by measuring frequency- dependent amplitude and arrival time differences of the first orbit Rayleigh waves. At low frequencies, the amplitude anomalies primarily result from the spatial and temporal extent of the rupture. We then invert the amplitude and arrival time measurements to estimate the second moments of the slip distribution which describe the rupture length, width, duration and propagation velocity of each earthquake. Comparing the rupture areas to the trench-parallel gravity anomaly (TPGA, Song and Simons 2003) above each rupture, we find that in 12 of the 14 events considered in this study the TPGA increases between the centroid and the limits of the rupture. Thus, local increases in TPGA appear to be related to the physical conditions along the plate interface that favor rupture termination. Owing to the inherently long time scales required for forearc basin formation, the correlation between the TPGA field and rupture termination regions indicates that long-lived material heterogeneity rather than short time-scale stress heterogeneities are responsible for arresting most great subduction zone ruptures.
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Graphs are an effective way of displaying quantitative and statistical information. Unfortunately, only a few studies have systematically looked at presenting building energy data in forms which are both informative, visually efficient, and easy to comprehend. Recent advancements in computing, including the development of sophisticated graphing packages and powerful indices more timely than ever before. In this two part paper, graphical displays or indices are reviewed and discussed that can be used to analyze several years of hourly data (20,000 to 30,000 data points). The purpose of these papers is to show how graphical indices can be used to help a building energy analyst view large amounts of hourly building energy consumption data in order to quickly and efficiently analyze the data, check for errors, or establish time and temperature related trends over a large period of time. Data from case study buildings in Texas are used to demonstrate the indices. Part 1 reviews the literature on graphical presentations of building energy use data and graphical perception and presents two graphical indices. Part 2 provides four additional graphical indices in use in the data review process for the Texas LoanSTAR program.
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The practice of history is under siege today from two armies: one made up of theorists, whose writings have called into question the truth claims of traditional historical discourse; another made up of filmmakers, who have stolen the audience for historical stories. Yet it is precisely the attacks from the former army that open the way for us to accept the latter as a new kind of historian - that is, of people who attempt to make meaning out of the traces of the past. This new 'history' on the screen has different rules of engagement with the past than does our traditional written history. It also raises new questions about why we study the past or what we really want to learn from that study. Before the Rain is a historical film that hints at a new kind of history, one set not in the past but in the very near future, a history that has as its burden not to explain what has happened but a history that uses trace elements of the past to serve as both witness of and warning against a potentially destructuve future.
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Ozone-sensitive (S156) and -tolerant (R123 and R331) genotypes of snap bean (Phaseolus vulgaris L.) were tested as a plant bioindicator system for detecting O(3) effects at current and projected future levels of tropospheric O(3) and atmospheric CO(2) under field conditions. Plants were treated with ambient air, 1.4× ambient O(3) and 550 ppm CO(2) separately and in combination using Free Air Concentration Enrichment technology. Under ambient O(3) concentrations pod yields were not significantly different among genotypes. Elevated O(3) reduced pod yield for S156 (63%) but did not significantly affect yields for R123 and R331. Elevated CO(2) at 550 ppm alone did not have a significant impact on yield for any genotype. Amelioration of the O(3) effect occurred in the O(3) + CO(2) treatment. Ratios of sensitive to tolerant genotype pod yields were identified as a useful measurement for assessing O(3) impacts with potential applications in diverse settings including agricultural fields.
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On the premise of discrete simulation technology, the study developed a simulation approach to quantify firms’ business operations and performances in a multi-tier supply chain. By careful simulation scenario design and statistical validation, the simulation model was applied to understand one practical business problem, i.e., how to evaluate the business model and its trade-off of implementing demand information sharing strategy. The results showed that with high demand variance, low demand correlation, and/or high demand covariance, the supply chain without the intermediate tier performed better than that with the intermediary. However, bypassing the intermediate tier in the chain might cause companies less responsive to demand variability. The simulation and analytical approaches presented in the paper can help firms make better decision on business model design and inter-organizational collaboration in supply chains.
Conference Paper
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Large-scale session log analysis typically includes statistical methods and detailed log examinations. While both methods have merits, statistical methods can miss previously unknown sub- populations in the data and detailed analyses may have selection biases. We therefore built Session Viewer, a visualization tool to facilitate and bridge between statistical and detailed analyses. Taking a multiple-coordinated view approach, Session Viewer shows multiple session populations at the Aggregate, Multiple, and Detail data levels to support different analysis styles. To bridge between the statistical and the detailed analysis levels, Session Viewer provides fluid traversal between data levels and side-by-side comparison at all data levels. We describe an analysis of a large-scale web usage study to demonstrate the use of Session Viewer, where we quantified the importance of grouping sessions based on task type.
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Data collected on benchmark soils from experimental sites in the Pianura Padano-Veneta, Northern Italy, stored in local soil data bases were used to test the reliability of existing pedotransfer functions to derive soil water retention properties, required as input to simulation models of pollutant transport in soils. Eight different algorithms were selected according to their principle of calculation, input variable requirements and in agreement with the different information currently existing in local soil databases. Results were validated against an experimental set of 139 retention curves. In order to assess the validity of the selected pedotransfer functions and to provide operative guidelines for their selection, quantitative error indices mean difference, and square root of the mean squared difference, were calculated and the results evaluated for the whole data set and for subsets of observations classed in terms of soil textural composition, bulk density, organic carbon content and matric potential. Non-parametric significance tests for unbalanced data were applied to assess the significance of the differences among classes. According to the kind of soil on which they were tested, the selected pedotransfer functions showed significantly different responses in terms of accuracy, providing therefore useful indications for their optimal applicability for different levels of available information.
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Augmented order statistics are defined as the order statistics in a sample of n consisting of n - k random observations and k fixed values. Some distribution theory is developed and applied to a study, for k = 1, of the biasing effect of an observation at x on estimators, such as trimmed means, that are linear functions of the order statistics.
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To describe the type, quantity, and quality of graphics used to present original research in Annals of Emergency Medicine. We performed a blinded, retrospective review of all graphics published in Annals of Emergency Medicine's original research articles from January 1998 through June 1999. We assessed the types of graphics, the use of special features to display detail, the clarity of each graphic, discrepancies within the graphic or between the graphic and text, and the efficiency of data presentation. Forty-six percent (68/147) of original research communications contained at least 1 graphic. Of the 128 graphics in these 68 articles, simple univariate displays predominated (53%). Only one third of graphics displayed by-subject data through the use of one-way plots, scatter plots, or other formats. Graphics generally defined all symbols and abbreviations (99%) and were self-explanatory (88%). Techniques for conveying the richness of a data set were seldom used (11% of all graphics). Forty percent (51/128) of the graphics contained internal contradictions (15%), muddled displays (19%), numeric distortion (5%), nonstandard graphing conventions (7%), and other lapses in design or execution. Inefficiencies of data presentation included internal redundancy (16%), extraneous decoration (10%), and redundancy of graphic data with other text/tables (15%). The majority of graphics in Annals of Emergency Medicine, although internally valid, failed to take full advantage of the graphic's potential and often depicted summary data when portrayal of subject-specific data was possible. To help readers fully understand research findings, authors and editors should take care to ensure that graphics efficiently and effectively portray the optimal amount of information.
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Copy toner samples were analyzed using reflection-absorption infrared microscopy (R-A IR). The grouping of copy toners into distinguishable classes achieved by visual comparison and computer-assisted spectral matching was compared to that achieved by multivariate discriminant analysis. For a data set containing spectra of 430 copy toners, 90% (388/430) of the spectra were initially correctly grouped into the classifications previously established by spectral matching. Three groups of samples that did not classify well contained too few samples to allow reliable classification. Samples from two other pairs of groups were similar and often misclassified. Closer examination of spectra from these groups revealed discriminating features that could be used in separate discriminant analyses to improve classification. For one pair of groups, the classification accuracy improved to 91% (81/89) and 97% (28/29), for the two groups, respectively. The other pair of groups were completely distinguishable from one another. With these additional tests, multivariate discriminant analysis correctly classified 96% of the 430 R-A IR toner spectra into the toner groups found previously by spectral matching.
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