Curvilinear Terms Research Articles

A numerical-tensorial "hybrid" nuclear motion Hamiltonian and dipole moment operator for spectra calculation of polyatomic nonrigid molecules.

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen-Bunker-Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from abinitio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems.

Adolescent Popularity as a Nonlinear, Two-Dimensional Construct: Convergent Results From Three Large Samples

The goal of this study was to advance the conceptualization and measurement of adolescent popularity by exploring the commonly used composite score (popularity minus unpopularity). We used standardized peer nominations from 4,414 early adolescents (ages ≈ 12-14 years) from three samples collected in two countries. Popularity and unpopularity were strongly related, but not linearly; scatterplots of the two variables resembled an L-shaped right angle. Subsequent analyses indicated that either including popularity as a curvilinear term or including both popularity and unpopularity as separate terms explained significantly more variance in social and behavioral correlates than linear, bivariate analyses using popularity, unpopularity, or composite popularity. These results suggest that researchers studying adolescent popularity should either separate popularity and unpopularity or treat composite popularity as curvilinear.

A simple immersed boundary forcing for flows over steep and complex orography

AbstractSimulation and parametrization of flow over the Earth's orographic features is an important element of any climate or weather model. With increasing resolution, especially in the limited‐area context, the orographic features are not only becoming better resolved but, importantly for numerical stability, the slopes are becoming ever steeper and the currently employed terrain‐following coordinates can cause convergence issues as the curvilinear terms become relatively large. This paper discusses this specific issue and suggests a possible solution based upon an immersed boundary forcing method for representing steep and complex terrain. The method is simple and straightforward to incorporate into any atmospheric model.

Does social thermal regulation constrain individual thermal tolerance in an ant species?

In ants, social thermal regulation is the collective maintenance of a nest temperature that is optimal for individual colony members. In the thermophilic ant Aphaenogaster iberica, two key behaviours regulate nest temperature: seasonal nest relocation and variable nest depth. Outside the nest, foragers must adapt their activity to avoid temperatures that exceed their thermal limits. It has been suggested that social thermal regulation constrains physiological and morphological thermal adaptations at the individual level. We tested this hypothesis by examining the foraging rhythms of six populations of A. iberica, which were found at different elevations (from 100 to 2,000m) in the Sierra Nevada mountain range of southern Spain. We tested the thermal resistance of individuals from these populations under controlled conditions. Janzen's climatic variability hypothesis (CVH) states that greater climatic variability should select for organisms with broader temperature tolerances. We found that the A. iberica population at 1,300m experienced the most extreme temperatures and that ants from this population had the highest heat tolerance (LT50=57.55°C). These results support CVH's validity at microclimatic scales, such as the one represented by the elevational gradient in this study. Aphaenogaster iberica maintains colony food intake levels across different elevations and mean daily temperatures by shifting its rhythm of activity. This efficient colony-level thermal regulation and the significant differences in individual heat tolerance that we observed among the populations suggest that behaviourally controlled thermal regulation does not constrain individual physiological adaptations for coping with extreme temperatures.

Identification of the trajectory of functional decline for advance care planning in a nursing home population.

To identify diagnostic groups and the form of the trajectory of functional decline that has the potential to enhance advance care planning (ACP) in a nursing home (NH) population. Retrospective, longitudinal study with dependent variable (function) derived from the Resident Classification Scale (RCS), 1997-2008. Trajectory modelling used linear and curvilinear terms. The organ failure or other residents have a linear average functional decline. The organ failure residents had an average decline of 6.5 points per year and average function score at death of 68.6, CI [62.4, 74.8]. The cancer and frailty residents had significant curvilinear terms. The frailty residents had a slower rate of decline at 9.54 points per year and were most care dependent at death, with an average function score of 77.1, CI [73.8, 80.9]. Functional change is a measurable variable for a predictive tool to enhance ACP for NH residents based on their diagnosis.

Low and High Birth Weight and the Risk of Child Attention Problems

To study the prospective association between birth weight and attention problems and to explore the role of maternal body mass index (BMI) in this association. In 6015 children of a population-based cohort (Rotterdam, The Netherlands, 2001-2005), information on birth weight was collected and gestational age-adjusted SDS were calculated. At age 6 years, parents assessed attention problems with the Child Behavior Checklist. We used linear regression to study the association of birth weight with attention problem score and examined the modification of this association by maternal early pregnancy BMI. The observed association between birth weight and attention problem score was curvilinear (adjusted β per birth weight SDS(2): 0.02, 95% CI 0.00; 0.03, P = .008); the turning point equals 3.6 kg at term. In analyses of the extreme tails of the birth weight distribution, the associations with attention problem score disappeared after adjustment for socioeconomic confounders. Maternal early pregnancy BMI moderated the association of child birth weight with attention problem score (P interaction = .007, with curvilinear term in model). Higher birth weight was related to less attention problems but from a birth weight of about 3.6 kg or more, a higher birth weight did not reduce the risk of attention problems any further. However, in children of obese mothers (BMI >30 kg/m(2)), high birth weight may increase the risk of attention problems.

A Bivariate Generalized Linear Item Response Theory Modeling Framework to the Analysis of Responses and Response Times

A generalized linear modeling framework to the analysis of responses and response times is outlined. In this framework, referred to as bivariate generalized linear item response theory (B-GLIRT), separate generalized linear measurement models are specified for the responses and the response times that are subsequently linked by cross-relations. The cross-relations can take various forms. Here, we focus on cross-relations with a linear or interaction term for ability tests, and cross-relations with a curvilinear term for personality tests. In addition, we discuss how popular existing models from the psychometric literature are special cases in the B-GLIRT framework depending on restrictions in the cross-relation. This allows us to compare existing models conceptually and empirically. We discuss various extensions of the traditional models motivated by practical problems. We also illustrate the applicability of our approach using various real data examples, including data on personality and cognitive ability.

Relation between geoidal undulation, deflection of the vertical and vertical gravity gradient revisited

The vertical gradients of gravity anomaly and gravity disturbance can be related to horizontal first derivatives of deflection of the vertical or second derivatives of geoidal undulations. These are simplified relations of which different variations have found application in satellite altimetry with the implicit assumption that the neglected terms—using remove-restore—are sufficiently small. In this paper, the different simplified relations are rigorously connected and the neglected terms are made explicit. The main neglected terms are a curvilinear term that accounts for the difference between second derivatives in a Cartesian system and on a spherical surface, and a small circle term that stems from the difference between second derivatives on a great and small circle. The neglected terms were compared with the dynamic ocean topography (DOT) and the requirements on the GOCE gravity gradients. In addition, the signal root-mean-square (RMS) of the neglected terms and vertical gravity gradient were compared, and the effect of a remove-restore procedure was studied. These analyses show that both neglected terms have the same order of magnitude as the DOT gradient signal and may be above the GOCE requirements, and should be accounted for when combining altimetry derived and GOCE measured gradients. The signal RMS of both neglected terms is in general small when compared with the signal RMS of the vertical gravity gradient, but they may introduce gradient errors above the spherical approximation error. Remove-restore with gravity field models reduces the errors in the vertical gravity gradient, but it appears that errors above the spherical approximation error cannot be avoided at individual locations. When computing the vertical gradient of gravity anomaly from satellite altimeter data using deflections of the vertical, the small circle term is readily available and can be included. The direct computation of the vertical gradient of gravity disturbance from satellite altimeter data is more difficult than the computation of the vertical gradient of gravity anomaly because in the former case the curvilinear term is needed, which is not readily available.

Simple Curvilinear Method for Numerical Methods of Open Channels

Three-dimensional finite-difference or finite-volume models of sinuous open channels (e.g., narrow rivers, estuaries, and reservoirs) generally require boundary-fitted grids and curvilinear flow solution. Cartesian models with square grid cells are simpler to apply, but require a larger number of cells, as the cell size is determined by cross-stream resolution. This paper presents a simplified curvilinear approach suitable for systems where the along-stream length scale is larger than the cross-stream scale. The curvilinear Navier-Stokes equations are manipulated so the left-hand side is identical to the Cartesian momentum equations. The right-hand side then consists of grid-stretching curvature terms. These terms are written as functions of a perturbation parameter, so the first-order curvilinear effects are obtained with the lowest-order perturbation terms. As the Cartesian equations' form is preserved, we can readily adapt a Cartesian model to this perturbation curvilinear approach by adding the small curvilinear terms as explicit momentum sources.

Misleading interaction and curvilinear terms.

This article examines the relationships between interaction (product) terms and curvilinear (quadratic) terms in regression models in which the independent variables are correlated. The author uses 2 substantive examples to demonstrate the following outcomes: (a) If the appropriate quadratic terms are not added to the estimated model, then the observed interaction may indicate a synergistic (offsetting) relationship between the independent variables, whereas the true relationship is, in fact, offsetting (synergistic). (b) If the appropriate product terms are not added to the equation, then the estimated model may indicate concave (convex) relationships between the independent variables and the dependent variable, whereas the true relationship is, in fact, convex (concave). (c) If the appropriate product and quadratic terms are not examined simultaneously, then the observed interactive or curvilinear relationships may be nonsignificant when such relationships exist. The implications of these results for the examination of interaction and quadratic effects in multiple regression analysis are discussed.

Misleading interaction and curvilinear terms.

Misleading interaction and curvilinear terms.

The association of body fat distribution with lifestyle and reproductive factors in a population study of postmenopausal women : Int. J. Obesity 1990 14/7 (583–591)

We examined the cross-sectional association of fat distribution with a number of lifestyle and reproductive factors in a random sample of 40,980 postmenopausal women, aged 55 to 69 years. The relationship of weight history with current fat distribution was also explored. Body fat distribution, defined by the ratio of waist-to-hip circumferences (WHR), was most strongly related to body mass index (BMI). WHR was also significantly and negatively associated with physical activity, alcohol consumption, and education, and was significantly positively associated with age, cigarette smoking, and a number of reproductive factors, such as history of infertility, number of live births, age at first live birth, and replacement estrogen use. WHR was not related to past BMIs, after adjusting for current body mass. The best-fit final regression model included (beta +/- s.e.) age (0.003 +/- 0.0001), BMI (0.02 +/- 0.0005), a curvilinear term for BMI (-0.0002 +/- 0.00001), greater than high school education (-0.007 +/- 0.001), cigarette smoking (0.02 +/- 0.001), alcohol drinker (-0.005 +/- 0.001), and number of live births (0.001 +/- 0.0002). The model R2 was 0.21. BMI (R2 = 0.18) and age (R2 = 0.02) accounted for most of the variation in WHR. The association of these lifestyle and reproductive factors with WHR suggests that the deposition of fat in the abdominal versus the gluteal region may be influenced somewhat by factors other than overall adiposity and genetics.

On the motivational effects of positive verbal reinforcement on performance: Toward an inverted-U relationship

The purpose of this study was to ascertain the motivational effects of positive verbal reinforcement on the performance of a qualitative task. Male subjects performed on a task consisting of 24 slides that allowed them to test their decision-making abilities in simulated situations. Subjects performed under one of five noncontingent verbal reinforcement ratios (.00, .25, .50, .75, or 1.00). Subjects' accuracy and reaction times to each of the 24 slide stimuli were recorded and transformed into a total performance index. In line with an inverted-U hypothesis, it was hypothesized that if motivational effects of positive verbal reinforcement exist, they should induce a curvilinear relationship between reinforcement ratio and performance. This hypothesis was supported by the results of a trend analysis that showed that only the quadratic curvilinear term was significant. Inspection of means revealed the presence of an inverted-U curve such that performance gradually increased from ratio 0 and reached a maximum at ratio .50, following which a decrease in performance was obtained for ratios .75 and 1.00. Results support a motivational interpretation of the effects of positive verbal reinforcement on performance. Findings are discussed in light of the interaction between motivational and attentional processes.

Multivariate analysis of tree height increment on meteorological variables, near the altitudinal tree limit in northern England

The relationships between height increment of Scots pine (PINUS SYLVESTRIS L.), birch (BETULA PUBESCENS Ehrh.) and rowan (SORBUS AUCUPARIA L.) during one growing season to meteorological variables at 580 m above sea level in the northern Pennines were previously examined using orthogonalized regression analysis. The paper describes methods made to improve the efficiency of the models. Values of principal components of the meteorological variables of the current and preceding sets were associated with 76.5, 60.4 and 75.9 percentage of variability respectively, showing an improvement by allowing for lag effects in this way. Efficiency of using values of the original variables, with those of the preceding set, or with curvilinear terms, was generally less. Variation of response during the season was examined and was discussed in terms of plant behaviour.

Erodibility of some California wildland soils related to their metallic cation exchange capacity

The inherent erodibility of twenty soils was indexed using Middleton's dispersion ratio and Anderson's surface-aggregation ratio. These indices were then used as dependent variables for several regression analyses. The milliequivalents per 100 grams of oven-dried soil for the four most plentiful soil cations (Ca, Mg, K, and Na) were determined and then used as independent variables in the regressions. The best fit to the data was found to be an equation of the type: Both the linear and the curvilinear terms were significant at the arbitrarily selected 5 per cent level.