Global surfaces of section in the planar restricted 3-body problem

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.Comment: 11 pages, 1 figur

Decay and Fission Hindrance of Two- and Four-Quasiparticle K Isomers in Rf 254

Two isomers decaying by electromagnetic transitions with half-lives of 4.7(1.1) and 247(73)μs have been discovered in the heavy Rf254 nucleus. The observation of the shorter-lived isomer was made possible by a novel application of a digital data acquisition system. The isomers were interpreted as the Kπ=8-, ν2(7/2+[624],9/2-[734]) two-quasineutron and the Kπ=16+, 8-ν2(7/2+[624],9/2-[734])⊗ - 8-π2(7/2-[514],9/2+[624]) four-quasiparticle configurations, respectively. Surprisingly, the lifetime of the two-quasiparticle isomer is more than 4 orders of magnitude shorter than what has been observed for analogous isomers in the lighter N=150 isotones. The four-quasiparticle isomer is longer lived than the Rf254 ground state that decays exclusively by spontaneous fission with a half-life of 23.2(1.1)μs. The absence of sizable fission branches from either of the isomers implies unprecedented fission hindrance relative to the ground state

Comprehensive analysis of epigenetic clocks reveals associations between disproportionate biological ageing and hippocampal volume

The concept of age acceleration, the difference between biological age and chronological age, is of growing interest, particularly with respect to age-related disorders, such as Alzheimer’s Disease (AD). Whilst studies have reported associations with AD risk and related phenotypes, there remains a lack of consensus on these associations. Here we aimed to comprehensively investigate the relationship between five recognised measures of age acceleration, based on DNA methylation patterns (DNAm age), and cross-sectional and longitudinal cognition and AD-related neuroimaging phenotypes (volumetric MRI and Amyloid-β PET) in the Australian Imaging, Biomarkers and Lifestyle (AIBL) and the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Significant associations were observed between age acceleration using the Hannum epigenetic clock and cross-sectional hippocampal volume in AIBL and replicated in ADNI. In AIBL, several other findings were observed cross-sectionally, including a significant association between hippocampal volume and the Hannum and Phenoage epigenetic clocks. Further, significant associations were also observed between hippocampal volume and the Zhang and Phenoage epigenetic clocks within Amyloid-β positive individuals. However, these were not validated within the ADNI cohort. No associations between age acceleration and other Alzheimer’s disease-related phenotypes, including measures of cognition or brain Amyloid-β burden, were observed, and there was no association with longitudinal change in any phenotype. This study presents a link between age acceleration, as determined using DNA methylation, and hippocampal volume that was statistically significant across two highly characterised cohorts. The results presented in this study contribute to a growing literature that supports the role of epigenetic modifications in ageing and AD-related phenotypes

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

A comparison between Rosenblatt's estimator and parametric density estimators for determining test limits

Because of measurement errors, test limits instead of specification limits are used for inspection to realize a prescribed bound on the consumer loss. Test limits based on the assumption of normality lead to severe violation of the prescribed bound when normality fails. While relaxing the assumption of normality, it is important to estimate the density of the inspected characteristic at the specification limit correctly. It is investigated whether larger parametric models provide a useful improvement. Simulations are carried out for several such models. It turns out that for estimating a density at a fixed point, the parametric estimators give improvements compared to application of the normal density. However, for small or moderate sample sizes Rosenblatt’s estimator is, in general, more accurate than the parametric density estimators

Accurate test limits under nonnormal measurement error

When screening a production process for nonconforming items the objective is to improve the average outgoing quality level. Due to measurement errors specification limits cannot be checked directly and hence test limits are required, which meet some given requirement, here given by a prescribed bound on the consumer loss. Classical test limits are based on normality, both for the product characteristic and for the measurement error. In practice, often nonnormality occurs for the product characteristic as well as for the measurement error. Recently, nonnormality of the product characteristic has been investigated. In this paper attention is focussed on the measurement error. Firstly, it is shown that nonnormality can lead to serious failure of the test limit. New test limits are therefore derived, which have the desired robustness property: a small loss under normality and a large gain in case of nonnormality when compared to the normal test limit. Monte Carlo results illustrate that the asymptotic theory is in agreement with moderate sample behaviour