The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.htm

Stable vortex and dipole vector solitons in a saturable nonlinear medium

We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.Comment: To appear in Phys. Rev.

Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with Subtype and Stage Inference

The heterogeneity of neurodegenerative diseases is a key confound to disease understanding and treatment development, as study cohorts typically include multiple phenotypes on distinct disease trajectories. Here we introduce a machine-learning technique\u2014Subtype and Stage Inference (SuStaIn)\u2014able to uncover data-driven disease phenotypes with distinct temporal progression patterns, from widely available cross-sectional patient studies. Results from imaging studies in two neurodegenerative diseases reveal subgroups and their distinct trajectories of regional neurodegeneration. In genetic frontotemporal dementia, SuStaIn identifies genotypes from imaging alone, validating its ability to identify subtypes; further the technique reveals within-genotype heterogeneity. In Alzheimer\u2019s disease, SuStaIn uncovers three subtypes, uniquely characterising their temporal complexity. SuStaIn provides fine-grained patient stratification, which substantially enhances the ability to predict conversion between diagnostic categories over standard models that ignore subtype (p = 7.18 7 10 124 ) or temporal stage (p = 3.96 7 10 125 ). SuStaIn offers new promise for enabling disease subtype discovery and precision medicine

Towards improved empirical isobase models of Holocene land uplift for mainland Scotland, UK

A new approach to modelling patterns of glacio-isostatic land uplift during the Holocene in mainland Scotland, UK, is described. The approach is based upon altitude measurements at the inner margin or locally highest point of raised estuarine surfaces dated by radiocarbon assay supported by microfossil analyses. 2241 altitudes have been analysed by a technique new to studies of former sea-levels, Gaussian Trend Surface Analysis, and isobase models for four Holocene shorelines: the Holocene Storegga Slide tsunami shoreline, abandoned rapidly circa 7900 sidereal years BP; the Main Postglacial shoreline, abandoned during circa 6400–7700 sidereal years BP; the Blairdrummond shoreline, abandoned during circa 4500–5800 sidereal years BP, and a speculative fourth shoreline, the Wigtown shoreline, abandoned during circa 1520–3700 sidereal years BP, are shown in a series of maps. The implications of the shoreline patterns for glaicio-isostasy in the area are discussed. It is maintained that the statistical technique used enables broad estimates to be made of nearshore sea surface change

Raised shorelines and ice limits in the Inner Moray Firth and Loch Ness areas, Scotland

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