Saddlepoint approximation for moment generating functions of truncated random variables

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases ``to which it is suited.'' Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Portfolio assessment in primary school mathematics: a study of pedagogical implications

This thesis records a study of major change. The study was designed to reveal and address the implications for teachers of primary mathematics, of moving from test-based assessment to a base built upon a balanced blend of norm-referenced and criteria-based assessments. In developing embedded authentic assessment through a process portfolio model, the teachers looked to change from the assessment of learning to assessment for learning. Consequently, through the efforts of the teachers involved, their students and those students’ parents, the study traced a substantial pedagogical restructure. Based on an interpretative methodology, this study of significant assessment restructure used mainly qualitative approaches to data collection and analysis, supplemented by limited quantitative data. Interviews, participant observer interactions, surveys and joint teacher discussion and planning sessions were effective in mapping the change. Through frequent interaction, participating teachers shared their emerging understandings, along with difficulties and successes in the evolution and implementation of an effective, flexible process portfolio. From the beginning of the evolution, teachers working together to bring about improvements that would lead to students perceiving mathematics as meaningful, engendered a strong feeling of excitement, curiosity and ‘team’. As the change progressed the team identified and met a range of challenges, not the least of which was gaining an understanding of the nature and function of a process portfolio strategy as against the product portfolio which was in use at that time in the study school. The resultant change was not implemented without barriers.Of prime concern across the group of teachers involved was the perennial problem of finding development time in what were already busy teaching days. However, for the change to be meaningful and lasting, it was imperative that the teachers invested considerable time in assuming ownership through genuine engagement in the evolution of the new concept. The engagement saw teachers experience first-hand the application of constructivist learning theory. It was an approach to learning that was largely unfamiliar to them and one they needed to understand in developing a successful process portfolio model. The study of that learning and the resultant change illustrated that a well-designed process portfolio structure offers widely diverse opportunities for teachers and students to work meaningfully with authentic mathematics. The enthusiastic prolonged engagement on the part of the students, with notable parental support, was deemed by the participant teachers to be suitable reward for the time and effort that they invested over the two years of the study. Following the teachers’ prolonged commitment, the emergent portfolio was shared through an in-house booklet written to encourage other teachers to adopt authentic assessment, Process Portfolios in Primary Mathematics: A Guide. Within the booklet, explanation and illustration of the rationale, form and function of the unique process portfolio model offers starting points for others, should they embark on a similar course of assessment change in search of real student engagement in understanding mathematics. Subsequent sharing of the results of the study with the wider profession through journal articles and conference workshops is to be based on the contents of the guide booklet

Supersonic through-flow fan design

The NASA Lewis Research Center has embarked on a program to experimentally prove the concept of a supersonic through-flow fan which is to maintain supersonic velocities throughout the compression system with only weak shock-wave flow losses. The detailed design of a supersonic through-flow fan and estimated off-design performance with the use of advanced computational codes are described. A multistage compressor facility is being modified for the newly designed supersonic through-flow fan and the major aspects of this modification are briefly described

Rare isotope studies involving catalytic oxidation of CO over platinum-tin oxide

Results of studies utilizing normal and rare oxygen isotopes in the catalytic oxidation of carbon monoxide over a platinum-tin oxide catalyst substrate are presented. Chemisorption of labeled carbon monoxide on the catalyst followed by thermal desorption yielded a carbon dioxide product with an oxygen-18 composition consistent with the formation of a carbonate-like intermediate in the chemisorption process. The efficacy of a method developed for the oxygen-18 labeling of the platinum-tin oxide catalyst surface for use in closed cycle pulsed care isotope carbon dioxide lasers is demonstrated for the equivalent of 10 to the 6th power pulses at 10 pulses per second

Inpatient urine cultures are frequently performed without urinalysis or microscopy: Findings from a large academic medical center

OBJECTIVETo describe the frequency of urine cultures performed in inpatients without additional testing for pyuriaDESIGNRetrospective cohort studySETTINGA 1,250-bed academic tertiary referral centerPATIENTSHospitalized adultsMETHODSThis study included urine cultures drawn on 4 medical and 2 surgical wards from 2009 to 2013 and in the medical and surgical intensive care units (ICUs) from 2012 to 2013. Patient and laboratory data were abstracted from the hospital’s medical informatics database. We identified catheter-associated urinary tract infections (CAUTIs) in the ICUs by routine infection prevention surveillance. Cultures without urinalysis or urine microscopy were defined as “isolated.” The primary outcome was the proportion of isolated urine cultures obtained. We used multivariable logistic regression to assess predictors of isolated cultures.RESULTSDuring the study period, 14,743 urine cultures were obtained (63.5 cultures per 1,000 patient days) during 11,820 patient admissions. Of these, 2,973 cultures (20.2%) were isolated cultures. Of the 61 CAUTIs identified, 31 (50.8%) were identified by an isolated culture. Predictors for having an isolated culture included male gender (adjusted odds ratio [aOR], 1.22; 95%; confidence interval [CI], 1.11–1.35], urinary catheterization (aOR, 2.15; 95% CI, 1.89–2.46), ICU admission (medical ICU aOR, 1.72; 95% CI, 1.47–2.00; surgical ICU aOR, 1.82; 95% CI, 1.51–2.19), and obtaining the urine culture ≥1 calendar day after admission (1–7 days aOR, 1.91; 95% CI. 1.71–2.12; &gt;7 days after admission aOR, 2.81; 95% CI, 2.37–3.34).CONCLUSIONSIsolated urine cultures are common in hospitalized patients, particularly in patients with urinary catheters and those in ICUs. Interventions targeting inpatient culturing practices may improve the diagnosis of urinary tract infections.Infect Control Hosp Epidemiol2017;38:455–460</jats:sec

Application of advanced computational codes in the design of an experiment for a supersonic throughflow fan rotor

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes

Reliability of Semiautomated Kinetic Perimetry (SKP) and Goldmann Kinetic Perimetry in Children and Adults With Retinal Dystrophies.

PurposeTo investigate the precision of visual fields (VFs) from semiautomated kinetic perimetry (SKP) on Octopus 900 perimeters, for children and adults with inherited retinal degenerations (IRDs). Goldmann manual kinetic perimetry has long been used in the diagnosis and follow-up of these patients, but SKP is becoming increasingly common. Octopus VFs (OVFs) and Goldmann VFs (GVFs) were both mapped on two occasions.MethodsNineteen females and 10 males with IRDs were tested on OVFs and GVFs, with two targets per test (V4e and one smaller target). Tests were performed in the same (randomized) order at two visits about 1 week apart. The VFs were digitized to derive isopter solid angles. Comparisons, within and between visits, were performed with paired t-tests and Bland-Altman plots.ResultsMedian age was 20 years (range, 7-70; 10 participants aged ≤17 years old). There were no significant differences in solid angles between OVFs and GVFs (P ≥ 0.06) or between the two visits' solid angles on either perimeter (P ≥ 0.30). Between-visit test-retest variability for GVFs and OVFs was similar (P ≥ 0.73), with median values of approximately 9% to 13%. Overall variability was lower for children than adults (medians of 7.5% and 12.8%, respectively).ConclusionsOctopus SKP and Goldmann perimetry produced VFs of similar size and variability.Translational relevanceOur study indicates that SKP provides a viable alternative to traditional Goldmann perimetry in clinical trials or care involving both children and adults with IRDs