Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Reproducing subgroups of Sp(2,R)Sp(2,\mathbb{R}). Part I: algebraic classification

We classify the connected Lie subgroups of the symplectic group $Sp(2,\mathbb{R})$ whose elements are matrices in block lower triangular form. The classification is up to conjugation within $Sp(2,\mathbb{R})$. Their study is motivated by the need of a unified approach to continuous 2D signal analyses, as those provided by wavelets and shearlets.Comment: 26 page

Children's humor types and psychosocial adjustment

Attempting to understand how humor styles relate to psychological adjustment by correlating these two constructs fails to address the emerging understanding that individuals use combinations of humor styles, and that different combinations may be differentially associated with psychosocial adjustment. Indeed humor types have been identified in adult samples (Galloway, 2010; Leist & Müller, 2013). The main aim of the study was to explore whether similar humor types are evident at a younger age and whether these types can be distinguished in terms of children's psychological and social well-being. Participants were 1234 adolescents (52% female) aged 11–13 years, drawn from six secondary schools in England. Self-reports of humor styles and psychosocial adjustment were collected at two time points, 6 months apart. A cluster analysis was performed using the child humor styles scores at Time 1. Four humor types were identified: ‘Interpersonal Humorists’ (high on aggressive and affiliative humor, low on self-defeating and self-enhancing humor), ‘Self-Defeaters’ (high self-defeating humor, low on the other three), ‘Humor Endorsers’ (high on all four humor styles), and ‘Adaptive Humorists’ (high on self-enhancing and affiliative humor, but low on aggressive and self-defeating humor). ‘Self-Defeaters’ scored highest in terms of maladjustment across all of the outcomes measured. Our analyses support the presence of distinctive humor types in childhood and indicate that these are related to psychosocial adjustment

The Essential Elements of a Risk Governance Framework for Current and Future Nanotechnologies

Societies worldwide are investing considerable resources into the safe development and use of nanomaterials. Although each of these protective efforts is crucial for governing the risks of nanomaterials, they are insufficient in isolation. What is missing is a more integrative governance approach that goes beyond legislation. Development of this approach must b