Edgeworth expansions for semiparametric Whittle estimation of long memory.

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order m-1/2 (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

Modified Whittle estimation of multilateral models on a lattice.

In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d≥2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the “edge effect”, which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in “multilateral” models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for “unilateral” models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.Spatial data; Multilateral modelling; Whittle estimation; Edge effect; Consistent variance estimation;

Embracing polygenicity: a review of methods and tools for psychiatric genetics research.

The availability of genome-wide genetic data on hundreds of thousands of people has led to an equally rapid growth in methodologies available to analyse these data. While the motivation for undertaking genome-wide association studies (GWAS) is identification of genetic markers associated with complex traits, once generated these data can be used for many other analyses. GWAS have demonstrated that complex traits exhibit a highly polygenic genetic architecture, often with shared genetic risk factors across traits. New methods to analyse data from GWAS are increasingly being used to address a diverse set of questions about the aetiology of complex traits and diseases, including psychiatric disorders. Here, we give an overview of some of these methods and present examples of how they have contributed to our understanding of psychiatric disorders. We consider: (i) estimation of the extent of genetic influence on traits, (ii) uncovering of shared genetic control between traits, (iii) predictions of genetic risk for individuals, (iv) uncovering of causal relationships between traits, (v) identifying causal single-nucleotide polymorphisms and genes or (vi) the detection of genetic heterogeneity. This classification helps organise the large number of recently developed methods, although some could be placed in more than one category. While some methods require GWAS data on individual people, others simply use GWAS summary statistics data, allowing novel well-powered analyses to be conducted at a low computational burden

Solution Structures of a Cyanobacterial Metallochaperone: INSIGHT INTO AN ATYPICAL COPPER-BINDING MOTIF *

The Atx1 copper metallochaperone from Synechocystis PCC 6803, ScAtx1, interacts with two P(1)-type copper ATPases to supply copper proteins within intracellular compartments, avoiding ATPases for other metals en route. Here we report NMR-derived solution structures for ScAtx1. The monomeric apo form has a betaalphabetabetaalpha fold with backbone motions largely restricted to loop 1 containing Cys-12 and Cys-15. The tumbling rate of Cu(I)ScAtx1 (0.1-0.8 mm) implies dimers. Experimental restraints are satisfied by symmetrical dimers with Cys-12 or His-61, but not Cys-15, invading the copper site of the opposing subunit. A full sequence of copper ligands from the cell surface to thylakoid compartments is proposed, considering in vitro homodimer liganding to mimic in vivo liganding in ScAtx1-ATPase heterodimers. A monomeric high resolution structure for Cu(I)ScAtx1, with Cys-12, Cys-15, and His-61 as ligands, is calculated without violations despite the rotational correlation time. (2)J(NH) couplings in the imidazole ring of His-61 establish coordination of N(epsilon2) to copper. His-61 is analogous to Lys-65 in eukaryotic metallochaperones, stabilizing Cu(I)S(2) complexes but by binding Cu(I) rather than compensating charge. Cys-Cys-His ligand sets are an emergent theme in some copper metallochaperones, although not in related Atx1, CopZ, or Hah1. Surface charge (Glu-13) close to the metal-binding site of ScAtx1 is likely to support interaction with complementary surfaces of copper-transporting ATPases (PacS-Arg-11 and CtaA-Lys-14) but to discourage interaction with zinc ATPase ZiaA and so inhibit aberrant formation of copper-ZiaA complexes

Perturbed angular correlations for Gd in gadolinium: in-beam comparisons of relative magnetizations

Perturbed angular correlations were measured for Gd ions implanted into gadolinium foils following Coulomb excitation with 40 MeV O-16 beams. A technique for measuring the relative magnetizations of ferromagnetic gadolinium hosts under in-beam conditions is described and discussed. The combined electric-quadrupole and magnetic-dipole interaction is evaluated. The effect of nuclei implanted onto damaged or non-substitutional sites is assessed, as is the effect of misalignment between the internal hyperfine field and the external polarizing field. Thermal effects due to beam heating are discussed.Comment: 37 pages, 15 figures, accepted for publication in NIM

Genome editing poses ethical problems that we cannot ignore

The ability to precisely and accurately change almost any part of any genome, even in complex species such as humans, may soon become a reality through genome editing. But with great power comes great responsibility – and few subjects elicit such heated debates about moral rights and wrongs. Although genetic engineering techniques have been around for some time, genome editing can achieve this with lower error rates, more simply and cheaply than ever – although the technology is certainly not yet perfect. Genome editing offers a greater degree of control and precision in how specific DNA sequences are changed. It could be used in basic science, for human health, or improvements to crops. There are a variety of techniques but clustered regularly inter-spaced short palindromic repeats, or CRISPR, is perhaps the foremost. CRISPR has prompted recent calls for a genome editing moratorium from a group of concerned US academics. Because it is the easiest technique to set up and so could be quickly and widely adopted, the fear is that it may be put into use far too soon – outstripping our understanding of its safety implications and preventing any opportunity to think about how such powerful tools should be controlled. Ethical concerns over genetic modification are not new, particularly when it comes to humans. While we don’t think genome editing gives rise to any completely new ethical concerns, there is more to gene editing than just genetic modification..

The telomerase reverse transcriptase is limiting and necessary for telomerase function in vivo

Mammalian telomerase is essential for the maintenance of telomere length [1–5]. Its catalytic core comprises a reverse transcriptase component (TERT) and an RNA component. While the biochemical role of mammalian TERT is well established [6–11], it is unknown whether it is sufficient for telomere-length maintenance, chromosome stability or other cellular processes. Cells from mice in which the mTert gene had been disrupted showed progressive loss of telomere DNA, a phenotype similar to cells in which the gene encoding the telomerase RNA component (mTR) has been disrupted [1,12]. On prolonged growth, mTert-deficient embryonic stem (ES) cells exhibited genomic instability, aneuploidy and telomeric fusions. ES cells heterozygous for the mTert disruption also showed telomere attrition, a phenotype that differs from heterozygous mTR cells [12]. Thus, telomere maintenance in mammals is carried out by a single, limiting TERT

Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions

We find all the higher dimensional solutions of the Einstein-Maxwell theory that are the topological product of two manifolds of constant curvature. These solutions include the higher dimensional Nariai, Bertotti-Robinson and anti-Nariai solutions, and the anti-de Sitter Bertotti-Robinson solutions with toroidal and hyperbolic topology (Plebanski-Hacyan solutions). We give explicit results for any dimension D>3. These solutions are generated from the appropriate extremal limits of the higher dimensional near-extreme black holes in a de Sitter, and anti-de Sitter backgrounds. Thus, we also find the mass and the charge parameters of the higher dimensional extreme black holes as a function of the radius of the degenerate horizon.Comment: 10 pages, 11 figures, RevTeX4. References added. Published versio