Branching processes and computational collapse of discretized unimodal mappings

In computer simulations of smooth dynamical systems, the original phase space is replaced by machine arithmetic, which is a finite set. The resulting spatially discretized dynamical systems do not inherit all functional properties of the original systems, such as surjectivity and existence of absolutely continuous invariant measures. This can lead to computational collapse to fixed points or short cycles. The paper studies loss of such properties in spatial discretizations of dynamical systems induced by unimodal mappings of the unit interval. The problem reduces to studying set-valued negative semitrajectories of the discretized system. As the grid is refined, the asymptotic behavior of the cardinality structure of the semitrajectories follows probabilistic laws corresponding to a branching process. The transition probabilities of this process are explicitly calculated. These results are illustrated by the example of the discretized logistic mapping.

Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

Exact results for a tunnel-coupled pair of trapped Bose-Einstein condensates

A model describing coherent quantum tunnelling between two trapped Bose-Einstein condensates is discussed. It is not well known that the model admits an exact solution, obtained some time ago, with the energy spectrum derived through the algebraic Bethe ansatz. An asymptotic analysis of the Bethe ansatz equations leads us to explicit expressions for the energies of the ground and the first excited states in the limit of weak tunnelling and all energies for strong tunnelling. The results are used to extract the asymptotic limits of the quantum fluctuations of the boson number difference between the two Bose-Einstein condensates and to characterize the degree of coherence in the system.

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.

Optimal quantum trajectories for discrete measurements

Using the method of quantum trajectories we show that a known pure state can be optimally monitored through time when subject to a sequence of discrete measurements. By modifying the way that we extract information from the measurement apparatus we can minimize the average algorithmic information of the measurement record, without changing the unconditional evolution of the measured system. We define an optimal measurement scheme as one which has the lowest average algorithmic information allowed. We also show how it is possible to extract information about system operator averages from the measurement records and their probabilities. The optimal measurement scheme, in the limit of weak coupling, determines the statistics of the variance of the measured variable directly. We discuss the relevance of such measurements for recent experiments in quantum optics.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

A small disturbance in the strong vortex flow

A small disturbance in the axisymmetric, bathtub-like flow with strong vorticity is considered and the asymptotic representation of the solution is found. It is shown that if the disturbance is smaller than a certain critical scale, the conventional strong vortex approximation cannot describe the field generated by the disturbance not only in the vicinity of the disturbance but also at the distances much larger than the critical scale. (C) 2001 American Institute of Physics.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.