Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Trends in mean and extreme precipitation in the Mount Kenya region from observations and reanalyses

Land and water management in semi-arid regions requires detailed information on precipitation distribution, including extremes, and changes therein. Such information is often lacking. This paper describes statistics of mean and extreme precipitation in a unique data set from the Mount Kenya region, encompassing around 50 stations with at least 30 years of data. We describe the data set, including quality control procedures and statistical break detection. Trends in mean precipitation and extreme indices calculated from these data for individual rainy seasons are compared with corresponding trends in reanalysis products. From 1979 to 2011, mean precipitation decreased at 75% of the stations during the ‘long rains’ (March to May) and increased at 70% of the stations during the ‘short rains’ (October to December). Corresponding trends are found in the number of heavy precipitation days, and maximum of consecutive 5-day precipitation. Conversely, an increase in consecutive dry days within both main rainy seasons is found. However, trends are only statistically significant in very few cases. Reanalysis data sets agree with observations with respect to interannual variability, while correlations are considerably lower for monthly deviations (ratios) from the mean annual cycle. While some products well reproduce the rainfall climatology and some the spatial trend pattern, no product reproduces both.

Regional-Scale Mean Copepod Concentration Indicates Relative Abundance of North Atlantic Right Whales

Management plans to reduce human-caused deaths of North Atlantic right whales Eubalaena glacialis depend, in part, on knowing when and where right whales are likely to be found. Local environmental conditions that influence movements of feeding right whales, such as ultra-dense copepod patches, are unpredictable and ephemeral. We examined the utility of using the regional-scale mean copepod concentration as an indicator of the abundance of right whales in 2 critical habitats off the northeastern coast of the United States: Cape Cod Bay and Great South Channel. Right whales are usually found in Cape Cod Bay during the late winter and early spring, and in the Great South Channel during the late spring and early summer. We found a significant positive relationship between mean concentration of the copepod Calanus finmarchicus in the western Gulf of Maine and the frequency of right whale sightings in the Great South Channel. In Cape Cod Bay we found a significant positive relationship between the mean concentration of other copepods (largely Pseudocalanus spp. and Centropages spp.) and the frequency of right whale sightings. This information could be used to further our understanding of the environmental factors that drive seasonal movement and aggregation of right whales in the Gulf of Maine, and it offers a tool to resource managers and modelers who seek to predict the movements of right whales based upon the concentration of copepods.

What Does Height Really Mean? Part III: Height Systems

This is the third paper in a four-part series considering the fundamental question, “what does the word “height” really mean?” The first paper reviewed reference ellipsoids and mean sea level datums. The second paper reviewed the physics of heights culminating in a simple development of the geoid and explained why mean sea level stations are not all at the same orthometric height. This third paper develops the principle notions of height, namely measured, differentially deduced changes in elevation, orthometric heights, Helmert orthometric heights, normal orthometric heights, dynamic heights, and geopotential numbers. We conclude with a more in-depth discussion of current thoughts regarding the geoid.

Mean corpuscular volume as a marker for adherence to antiretroviral therapy among HIV infected children and adolescents in Uganda

Mean corpuscular volume, which is an inexpensive and widely available measure to assess, increases in HIV infected individuals receiving zidovudine and stavudine raising the hypothesis that it could be used as a surrogate for adherence.^ The aim of this study was to examine the association between mean corpuscular volume and adherence to antiretroviral therapy among HIV infected children and adolescents aged 0–19 years in Uganda as well as the extent to which changes in mean corpuscular volume predict adherence as determined by virologic suppression.^ The investigator retrospectively reviewed and analyzed secondary data of 158 HIV infected children and adolescents aged 0–19 years who initiated antiretroviral therapy under an observational cohort at the Baylor College of Medicine Children's Foundation - Uganda. Viral suppression was used as the gold standard for monitoring adherence and defined as viral load of < 400 copies/ml at 24 and 48 weeks. ^ Patients were at least 48 weeks on therapy, age 0.2–18.4 years, 54.4% female, 82.3% on zidovudine based regimen, 92% WHO stage III at initiation of therapy, median pre therapy MCV 80.6 fl (70.3–98.3 fl), median CD4% 10.2% (0.3%–28.0%), and mean pre therapy viral load 407,712.9 ± 270,413.9 copies/ml. For both 24 and 48 weeks of antiretroviral therapy, patients with viral suppression had a greater mean percentage change in mean corpuscular volume (15.1% ± 8.4 vs. 11.1% ± 7.8 and 2.3% ± 13.2 vs. -2.7% ± 10.5 respectively). The mean percentage change in mean corpuscular volume was greater in the first 24 weeks of therapy for patients with and without viral suppression (15.1% ± 8.4 vs. 2.3% ± 13.2 and 11.1% ± 7.8 vs. -2.7% ± 10.5 respectively). In the multivariate logistic regression model, percentage change in mean corpuscular volume ≥ 20% was significantly associated with viral suppression (adjusted OR 4.0; CI 1.2–13.3; p value 0.02). The ability of percentage changes in MCV to correctly identify children and adolescents with viral suppression was higher at a cut off of ≥ 20% (90.7%; sensitivity, 31.7%) than at ≥ 9% (82.9%; sensitivity, 78.9%). Negative predictive value was lower at ≥ 20% change (25%; specificity, 84.8%) than at ≥ 9% change (33.3%; specificity, 39.4%).^ Mean corpuscular volume is a useful marker of adherence among children and adolescents with viral suppression. ^

Intensive care noise and mean arterial blood pressure in ELBW neonates

Objective. Loud noises in neonatal intensive care units (NICUs) may impede growth and development for extremely low birthweight (ELBW, < 1000 grams) newborns. The objective of this study was to measure the association between NICU sound levels and ELBW neonates' arterial blood pressure to determine whether these newborns experience noise-induced stress. ^ Methods. Noise and arterial blood pressure recordings were collected for 9 ELBW neonates during the first week of life. Sound levels were measured inside the incubator, and each subject's arterial blood pressures were simultaneously recorded for 15 minutes (at 1 sec intervals). Time series cross-correlation functions were calculated for NICU noise and mean arterial blood pressure (MABP) recordings for each subject. The grand mean noise-MABP cross-correlation was calculated for all subjects and for lower and higher birthweight groups for comparison. ^ Results. The grand mean noise-MABP cross-correlation for all subjects was mostly negative (through 300 sec lag time) and nearly reached significance at the 95% level at 111 sec lag (mean r = -0.062). Lower birthweight newborns (454-709 g) experienced significant decreases in blood pressure with increasing NICU noise after 145 sec lag (peak r = -0.074). Higher birthweight newborns had an immediate negative correlation with NICU sound levels (at 3 sec lag, r = -0.071), but arterial blood pressures increased to a positive correlation with noise levels at 197 sec lag (r = 0.075). ^ Conclusions. ELBW newborns' arterial blood pressure was influenced by NICU noise levels during the first week of life. Lower birthweight newborns may have experienced an orienting reflex to NICU sounds. Higher birthweight newborns experienced an immediate orienting reflex to increasing sound levels, but arterial blood pressure increased approximately 3 minutes after increases in noise levels. Increases in arterial blood pressure following increased NICU sound levels may result from a stress response to noise. ^

DISTRIBUTION FUNCTIONS, MEAN SQUARED ERRORS, AND CONFIDENCE LIMITS FOR RIDGE REGRESSION ESTIMATORS

A large number of ridge regression estimators have been proposed and used with little knowledge of their true distributions. Because of this lack of knowledge, these estimators cannot be used to test hypotheses or to form confidence intervals.^ This paper presents a basic technique for deriving the exact distribution functions for a class of generalized ridge estimators. The technique is applied to five prominent generalized ridge estimators. Graphs of the resulting distribution functions are presented. The actual behavior of these estimators is found to be considerably different than the behavior which is generally assumed for ridge estimators.^ This paper also uses the derived distributions to examine the mean squared error properties of the estimators. A technique for developing confidence intervals based on the generalized ridge estimators is also presented. ^