Attention-deficit hyperactivity disorder shares copy number variant risk with schizophrenia and autism spectrum disorder

Publisher's version (útgefin grein).Attention-deficit/hyperactivity disorder (ADHD) is a highly heritable common childhood-onset neurodevelopmental disorder. Some rare copy number variations (CNVs) affect multiple neurodevelopmental disorders such as intellectual disability, autism spectrum disorders (ASD), schizophrenia and ADHD. The aim of this study is to determine to what extent ADHD shares high risk CNV alleles with schizophrenia and ASD. We compiled 19 neuropsychiatric CNVs and test 14, with sufficient power, for association with ADHD in Icelandic and Norwegian samples. Eight associate with ADHD; deletions at 2p16.3 (NRXN1), 15q11.2, 15q13.3 (BP4 & BP4.5–BP5) and 22q11.21, and duplications at 1q21.1 distal, 16p11.2 proximal, 16p13.11 and 22q11.21. Six of the CNVs have not been associated with ADHD before. As a group, the 19 CNVs associate with ADHD (OR = 2.43, P = 1.6 × 10−21), even when comorbid ASD and schizophrenia are excluded from the sample. These results highlight the pleiotropic effect of the neuropsychiatric CNVs and add evidence for ADHD, ASD and schizophrenia being related neurodevelopmental disorders rather than distinct entities.We are grateful to the participants and we thank the staff at the Research Recruitment Center. We also thank the staff at deCODE genetics core facilities and all our colleagues for their important contribution to this work. We are grateful to the Benefit Society for Children with Disabilities (Styrktarfélag Lamaðra og Fatlaðra; SLF) for their participation. The research leading to these results has received support from the Innovative Medicines Initiative Joint Undertaking under grant agreements’ no. 115008 (NEWMEDS) and no. 115300 (EUAIMS), of which resources are composed of EFPIA in-kind contribution and financial contribution from the European Union’s Seventh Framework Programme (EU-FP7/2007–2013), from EU-FP7 grants no. 602450 (IMAGEMEND) and no. 502805 (Aggressotype), EU-FP7-People-2011-IAPP grant no. 286213 (PsychDPC), and The Research Council of Norway (#226971, 229129, 223273, 213694, 248778), the KG Jebsen Stiftelsen (SKGJ-MED-002 and SKGJ-MED-008), and The South-East Norway Health Authority (#2012–132).Peer Reviewe

The Efficient Computation of Structured Gradients using Automatic Differentiation

The advent of robust automatic differentiation tools is an exciting and important development in scientific computing. It is particularily noteworthy that the gradient of a scalar-valued function of many variables can be computed with essentially the same time complexity as required to evaluate the function itself. This is true, in theory, when the "reverse mode" of automatic differentiation is used (whereas the "forward mode" introduces an additional factor corresponding to the problem dimension). However, in practise performance on large problems can be significantly (and unacceptably) worse than predicted. In this paper we illustrate that when natural structure is exploited fast gradient computation can be recovered, even for large dimensional problems

Accurate solution of polynomial equations using macaulay resultant matrices

We propose an algorithm for solving two polynomial equations in two variables. Our algorithm is based on the Macaulay resultant approach combined with new techniques, including randomization, to make the algorithm accurate in the presence of roundoff error. The ultimate computation is the solution of a generalized eigenvalue problem via the QZ method. We analyze the error due to roundoff of the method, showing that with high probability the roots are computed accurately, assuming that the input data (that is, the two polynomials) are well conditioned. Our analysis requires a novel combination of algebraic and numerical techniques