Complete Sudoku - extra rules for more symmetry

We propose some extra rules to add to the well-known Sudoku puzzle and present an argument to justify their inclusion. The rules mean that puzzles can be created with fewer cells completed initially yet which still have only one solution. We have created a Web-based program which can be used to generate and solve both standard and extended (Complete) puzzles.

An ingress and a complete transit of HD80606 b

We have used four telescopes at different longitudes to obtain near-continuous light-curve coverage of the star HD80606 as it was transited by its ~4-MJup planet. The observations were performed during the predicted transit windows around 2008 October 25 and 2009 February 14. Our data set is unique in that it simultaneously constrains the duration of the transit and the planet's period. Our Markov Chain Monte Carlo analysis of the light curves, combined with constraints from radial-velocity data, yields system parameters consistent with previously reported values. We find a planet-to-star radius ratio marginally smaller than previously reported, corresponding to a planet radius of Rp = 0.921 +/- 0.036RJup.

Complete nonlinear theory of longitudinal-to-transverse dust lattice mode coupling in a single-layer dusty plasma crystal

A comprehensive nonlinear model is put forward for coupled longitudinal to transverse displacements in a horizontal dust mono-layer, levitated under the combined influence of gravity and an electric and/or magnetic sheath field. A set of coupled nonlinear evolution equations are obtained in a discrete description, and a pair of coupled (Boussinesq-like) PDEs are obtained in the continuum approximation. Finally, the amplitude modulation of the coupled modes is discussed, pointing out the importance of the coupling. All these results are generic, i.e. valid for any assumed form of the inter-grain interaction potential U and the sheath potential Phi.

Meta-analysis of 32 genome-wide linkage studies of schizophrenia

A genome scan meta-analysis (GSMA) was carried out on 32 independent genome-wide linkage scan analyses that included 3255 pedigrees with 7413 genotyped cases affected with schizophrenia (SCZ) or related disorders. The primary GSMA divided the autosomes into 120 bins, rank-ordered the bins within each study according to the most positive linkage result in each bin, summed these ranks (weighted for study size) for each bin across studies and determined the empirical probability of a given summed rank (P-SR) by simulation. Suggestive evidence for linkage was observed in two single bins, on chromosomes 5q (142-168 Mb) and 2q (103-134 Mb). Genome-wide evidence for linkage was detected on chromosome 2q (119-152 Mb) when bin boundaries were shifted to the middle of the previous bins. The primary analysis met empirical criteria for 'aggregate' genome-wide significance, indicating that some or all of 10 bins are likely to contain loci linked to SCZ, including regions of chromosomes 1, 2q, 3q, 4q, 5q, 8p and 10q. In a secondary analysis of 22 studies of European-ancestry samples, suggestive evidence for linkage was observed on chromosome 8p (16-33 Mb). Although the newer genome-wide association methodology has greater power to detect weak associations to single common DNA sequence variants, linkage analysis can detect diverse genetic effects that segregate in families, including multiple rare variants within one locus or several weakly associated loci in the same region. Therefore, the regions supported by this meta-analysis deserve close attention in future studies. Molecular Psychiatry (2009) 14, 774-785; doi:10.1038/mp.2008.135; published online 30 December 2008

Novel linkage to chromosome 20p using latent classes of psychotic illness in 270 Irish high-density families

Background: Several lines of evidence suggest that the clinical heterogeneity of schizophrenia is due to genetic heterogeneity. Genetic heterogeneity may decrease the signal-to-noise ratio in linkage and association studies. Therefore, linkage studies of clinically homogeneous classes of psychotic illness may result in greater power to detect at least some loci.