A time-domain test for some types of nonlinearity

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third-order moment. An advantage of the bispectrum is that its estimator comprises terms that are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third-order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third-order moment is required to construct the Fourier transform. In this paper, we propose a test for nonlinearity based upon the estimated third-order moment. We use the phase scrambling bootstrap method to give a nonparametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study, we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of nonlinearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of nonstationarity.

A generalisation of the Delogne-Kasa method for fitting hyperspheres

In this paper, we examine the problem of fitting a hypersphere to a set of noisy measurements of points on its surface. Our work generalises an estimator of Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972,117-123) which he proposed for circles and which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. We also generalise Chan's 'circular functional relationship' to describe the distribution of points. We derive the Cramer-Rao lower bound (CRLB) under this model and we derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We perform a statistical analysis of the estimate of the hypersphere's centre. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than M + 1, where M is the dimension of the hypersphere. The variance exists when the number of sample points is greater than M + 2. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRLB. We provide simulation results to support our findings.

Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Cosegregation analysis of natriuretic peptide genes and blood pressure in the spontaneously hypertensive rat

1. The natriuretic peptide precursor A (Nppa) and B (Nppb) genes are candidate genes for hypertension and cardiac hypertrophy in the spontaneously hypertensive rat (SHR). The purpose of the present study was to determine the role of the Nppa and Nppb genes in the development of hypertension in the SHR. 2. A cohort (n = 162) of F2 segregating intercross animals was established between strains of hypertensive SHR and normotensive Wistar-Kyoto rats. Blood pressure and heart weight were measured in each rat at 12-16 weeks of age. Rats were genotyped using 11 informative microsatellite markers, distributed in the vicinity of the Nppa marker on rat chromosome 5 including an Nppb marker. The phenotype values were compared with genotype using the computer package MAP-MAKER 3.0 (Whitehead Institute, Boston, MA, USA) to determine whether there was a link between the genetic variants of the natriuretic peptide family and blood pressure or cardiac hypertrophy. 3. A strong correlation was observed between the Nppa marker and blood pressure. A quantitative trait locus (QTL) for blood pressure on chromosome 5 was identified between the Nppa locus and the D5Mgh15 marker, less than 2 cM from the Nppa locus. The linkage score for the blood pressure QTL on chromosome 5 was 3.8 and the QTL accounted for 43% of the total variance of systolic blood pressure, 54% of diastolic blood pressure and 59% of mean blood pressure. No association was found between the Nppb gene and blood pressure. This is the first report of linkage between the Nppa marker and blood pressure in the rat. There was no correlation between the Nppa or Nppb genes or other markers in this region and either heart weight or left ventricular weight in F2 rats. 4. These findings suggest the existence of a blood pressure-dependent Nppa marker variant or a gene close to Nppa predisposing to spontaneous hypertension in the rat. It provides a strong foundation for further detailed genetic studies in congenic strains, which may help to narrow down the location of this gene and lead to positional cloning.

Use of pulse transit time to distinguish respiratory events from tidal breathing in sleeping children

Study objectives: Currently, esophageal pressure monitoring is the "gold standard" measure for inspiratory efforts, hut its invasive nature necessitates a better tolerated and noninvasive method to be used on children. Pulse transit time (PTT) has demonstrated its potential as a noninvasive surrogate marker for inspiratory efforts. The principle velocity determinant of PTT is the change in stiffness of the arterial wall and is inversely correlated to BP. Moreover, PTT has been shown to identify changes in inspiratory effort via the BP fluctuations induced by negative pleural pressure swings. In this study, the capability of PTT to classify respiratory, events during sleep as either central or obstructive in nature was investigated. Setting and participants: PTT measure was used in adjunct to routine overnight polysomnographic studies performed on 33 children (26 boys and 7 girls; mean +/- SD age, 6.7 +/- 3.9 years). The accuracy of PTT measurements was then evaluated against scored corresponding respiratory events in the polysomnography recordings. Results: Three hundred thirty-four valid respiratory events occurred and were analyzed. One hundred twelve obstructive events (OEs) showed a decrease in mean PTT over a 10-sample window that had a probability of being correctly ranked below the baseline PTT during tidal breathing of 0.92 (p < 0.005); 222 central events (CEs) showed a decrease in the variance of PTT over a 10-sample window that had a probability of being ranked below the baseline PTT of 0.94 (p < 0.005). This indicates that, at a sensitivity of 0.90, OEs can be detected with a specificity of 0.82 and CEs can be detected with a specificity of 0.80. Conclusions: PTT is able to categorize CEs and OEs accordingly in the absence of motion artifacts, including hypopneas. Hence, PTT shows promise to differentiate respiratory, events accordingly and can be an important diagnostic tool in pediatric respiratory sleep studies.< 0.005); 222 central events (CEs) showed a decrease in the variance of PTT over a 10-sample window that had a probability of being ranked below the baseline PTT of 0.94 (p < 0.005). This indicates that, at a sensitivity of 0.90, OEs can be detected with a specificity of 0.82 and CEs can be detected with a specificity of 0.80. Conclusions: PTT is able to categorize CEs and OEs accordingly in the absence of motion artifacts, including hypopneas. Hence, PTT shows promise to differentiate respiratory, events accordingly and can be an important diagnostic tool in pediatric respiratory sleep studies.');"

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Physicians' attitudes towards end-of-life decisions: a comparison between seven countries

In the context of an European collaborative research project (EURELD), a study on attitudes towards medical end-of-life decisions was conducted among physicians in Belgium, Denmark, Italy, the Netherlands, Sweden and Switzerland. Australia also joined the consortium. A written questionnaire with structured questions was sent to practising physicians from specialties frequently involved in the care of dying patients. 10,139 questionnaires were studied. Response rate was equal to or larger than 50% in all countries except Italy (39%). Apart from general agreement with respect to the alleviation of pain and symptoms with possible life-shortening effect, there was large variation in support-between and within countries-for medical decision that may result in the hastening of death. A principal component factor analysis found that 58% of the variance of the responses is explained by four factors. 'Country' explained the largest part of the variation of the standardized factor scores. (c) 2004 Elsevier Ltd. All rights reserved.

Quantum dynamics of a model for two Josephson-coupled Bose-Einstein condensates

In this work, we investigate the quantum dynamics of a model for two singlemode Bose-Einstein condensates which are coupled via Josephson tunnelling. Using direct numerical diagonalization of the Hamiltonian, we compute the time evolution of the expectation value for the relative particle number across a wide range of couplings. Our analysis shows that the system exhibits rich and complex behaviours varying between harmonic and non-harmonic oscillations, particularly around the threshold coupling between the delocalized and selftrapping phases. We show that these behaviours are dependent on both the initial state of the system and regime of the coupling. In addition, a study of the dynamics for the variance of the relative particle number expectation and the entanglement for different initial states is presented in detail.

Features of nitrogen adsorption on nonporous carbon and silica surfaces in the framework of classical density functional theory

Equilibrium adsorption data of nitrogen on a series of nongraphitized carbon blacks and nonporous silica at 77 K were analyzed by means of classical density functional theory to determine the solid-fluid potential. The behavior of this potential profile at large distance is particularly considered. The analysis of nitrogen adsorption isotherms seems to indicate that the adsorption in the first molecular layer is localized and controlled mainly by short-range forces due to the surface roughness, crystalline defects, and functional groups. At distances larger than approximately 1.3-1.5 molecular diameters, the adsorption is nonlocalized and appears as a thickening of the adsorbed film with increasing bulk pressure in a relatively weak adsorption potential field. It has been found that the asymptotic decay of the potential obeys the power law with the exponent being -3 for carbon blacks and -4 for silica surface, which signifies that in the latter case the adsorption potential is mainly exerted by surface oxygen atoms. In all cases, the absolute value of the solid-fluid potential is much smaller than that predicted by the Lennard-Jones pair potential with commonly used solid-fluid molecular parameters. The effect of surface heterogeneity on the heat of adsorption is also discussed.

Social cognitive predictors of sun protection intention and behavior

The authors investigated sunbathing behavior and intention prospectively using the Theory of Planned Behavior (TPB). Before summer, 85 young adults who intended to sunbathe completed a TPB questionnaire. After summer, 46 of them completed a second questionnaire about their summertime sunbathing behavior The proposed model was successful in predicting both behavior and intention to use sun protection, with 45% of the variance of self-reported sunscreen use and 32% of the variance in intention explained by the TPB. Items designed to measure self-efficacy and perceived control loaded onto different factors and demonstrated discriminant validity. Self-efficacy predicted both intention and behavior (after controlling for all other TPB variables), but perceived behavioral control did not. The authors discuss the implications of the findings for potential interventions to improve sun protection behavior.