Representations for the extreme zeros of orthogonal polynomials

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed

Representations for the extreme zeros of orthogonal polynomials

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth death process (with killing) are displayed

Analysis of Numerical Errors in the DSMC Method

Abstract. The direct simulation Monte Carlo (DSMC) method is one of the most popular numerical methods used to model rarefied gas environment flows. In order to predict the accuracy of a solution obtained by the DSMC method we have to be able to estimate its accuracy. In the work presented here we have developed a technique to estimate the numerical accuracy of the DSMC method. This paper presents a derivation of expressions of the variance of the DSMC estimators of number density and translational temperature, and the corresponding comparison with the empirical variance. A discussion of the deterministic numerical errors corresponding to typical DSMC parameters such as the time step, cell volume, and total number of simulated particles is given. Moreover, a comparison of two different DSMC schemes, No Time Counter (NTC) and Majorant Frequency (MF), is made

Towards a new evolutionary subsampling technique for heuristic optimisation of load disaggregators

In this paper we present some preliminary work towards the development of a new evolutionary subsampling technique for solving the non-intrusive load monitoring (NILM) problem. The NILM problem concerns using predictive algorithms to analyse whole-house energy usage measurements, so that individual appliance energy usages can be disaggregated. The motivation is to educate home owners about their energy usage. However, by their very nature, the datasets used in this research are massively imbalanced in their target value distributions. Consequently standard machine learning techniques, which often rely on optimising for root mean squared error (RMSE), typically fail. We therefore propose the target-weighted RMSE (TW-RMSE) metric as an alternative fitness function for optimising load disaggregators, and show in a simple initial study in which random search is utilised that TW-RMSE is a metric that can be optimised, and therefore has the potential to be included in a larger evolutionary subsampling-based solution to this problem

Sex stereotypes influence adults' perception of babies' cries

Background: Despite widespread evidence that gender stereotypes influence human parental behavior, their potential effects on adults’ perception of babies’ cries have been overlooked. In particular, whether adult listeners overgeneralize the sex dimorphism that characterizes the voice of adult speakers (men are lower-pitched than women) to their perception of babies’ cries has not been investigated. Methods: We used playback experiments combining natural and re-synthesised cries of 3 month-old babies to investigate whether the interindividual variation in the fundamental frequency (pitch) of cries affected adult listeners’ identification of the baby’s sex, their perception the baby’s femininity and masculinity, and whether these biases interacted with their perception of the level of discomfort expressed by the cry. Results: We show that low-pitched cries are more likely to be attributed to boys and high-pitched cries to girls, despite the absence of sex differences in pitch. Moreover, low-pitched boys are perceived as more masculine and high-pitched girls are perceived as more feminine. Finally, adult men rate relatively low-pitched cries as expressing more discomfort when presented as belonging to boys than to girls. Conclusion: Such biases in caregivers’ responses to babies’ cries may have implications on children’s immediate welfare and on the development of their gender identity

Attachment and coping in psychosis in relation to spiritual figures

Background: Studies have found higher levels of insecure attachment in individuals with schizophrenia. Attachment theory provides a framework necessary for conceptualizing the development of interpersonal functioning. Some aspects of the attachment of the believer to his/her spiritual figure are similar to those between the child and his/her parents. The correspondence hypothesis suggests that early child-parent interactions correspond to a person's relation to a spiritual figure. The compensation hypothesis suggests that an insecure attachment history would lead to a strong religiousness/spirituality as a compensation for the lack of felt security. The aim of this study is to explore attachment models in psychosis vs. healthy controls, the relationships between attachment and psychopathology and the attachment processes related to spiritual figures. Methods: Attachment models were measured in 30 patients with psychosis and 18 controls with the AAI (Adult Attachment interview) in relationship with psychopathology. Beliefs and practices related to a spiritual figure were investigated by qualitative and quantitative analyses. Results: Patients with psychosis showed a high prevalence of insecure avoidant attachment. Spiritual entities functioned like attachment figures in two thirds of cases. Interviews revealed the transformation of internal working models within relation to a spiritual figure: a compensation process was found in 7 of the 32 subjects who showed a significant attachment to a spiritual figure. Conclusions: Attachment theory allows us to highlight one of the underlying dimensions of spiritual coping in patients with psychosis

Enzymatic oligomerization and polymerization of arylamines: state of the art and perspectives

The literature concerning the oxidative oligomerization and polymerization of various arylamines, e.g., aniline, substituted anilines, aminonaphthalene and its derivatives, catalyzed by oxidoreductases, such as laccases and peroxidases, in aqueous, organic, and mixed aqueous organic monophasic or biphasic media, is reviewed. An overview of template-free as well as template-assisted enzymatic syntheses of oligomers and polymers of arylamines is given. Special attention is paid to mechanistic aspects of these biocatalytic processes. Because of the nontoxicity of oxidoreductases and their high catalytic efficiency, as well as high selectivity of enzymatic oligomerizations/polymerizations under mild conditions-using mainly water as a solvent and often resulting in minimal byproduct formation-enzymatic oligomerizations and polymerizations of arylamines are environmentally friendly and significantly contribute to a "green'' chemistry of conducting and redox-active oligomers and polymers. Current and potential future applications of enzymatic polymerization processes and enzymatically synthesized oligo/polyarylamines are discussed

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We correct representations for the endpoints of the true interval of orthogonality of a sequence of orthogonal polynomials that were stated by us in the Journal of Computational and Applied Mathematics 233 (2009) 847–851