Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?

Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that `quantisation commutes with reduction' and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.Comment: 18 Page

Frailty as a Predictor of Alzheimer Disease, Vascular Dementia, and All Dementia Among Community-Dwelling Older People: A Systematic Review and Meta-Analysis

OBJECTIVE: To perform a systematic search of the literature for currently available evidence on frailty as a predictor of dementia and to conduct a meta-analysis to synthesize the pooled risk estimates among community-dwelling older people. DESIGN: A systematic review and meta-analysis. DATA SOURCES: Embase, MEDLINE, CINAHL Plus, PsycINFO, and the Cochrane Library from 2000 to January 2016, and reference lists of relevant articles. ELIGIBILITY CRITERIA: Any studies that prospectively examined the incident risks of dementia with frailty among community-dwelling older people without language restriction. RESULTS: Of 2565 studies identified through the systematic review, 7 studies were included in this review. Of these, 4 studies reported hazard ratios (HR) of incident dementia for physical frailty defined by Cardiovascular Health Study criteria and were included in a meta-analysis. Frailty was a significant predictor of incident Alzheimer disease (4 studies: pooled HR = 1.28, 95% confidence interval (95% CI) = 1.00-1.63, P = .05), vascular dementia (2 studies: pooled HR 2.70, 95% CI 1.40-5.23, P = .003), and all dementia (3 studies: pooled HR 1.33, 95% CI 1.07-1.67, P = .01). Heterogeneity across the studies was low to modest (I(2) = 0%-51%). A random-effects meta-regression analysis showed that the female proportion of the cohort primarily mediated the association of frailty with Alzheimer disease (female proportion coefficient = 0.04, 95%CI = 0.01-0.08, P = .01). CONCLUSION: This systematic review and meta-analysis suggests that frailty was a significant predictor of Alzheimer disease, vascular dementia, and all dementia among community-dwelling older people. Frail women may have a higher risk of incident Alzheimer disease than frail men

The Structure on Invariant Measures of C1C^1 generic diffeomorphisms

Let $\Lambda$ be an isolated non-trival transitive set of a $C^1$ generic diffeomorphism f\in\Diff(M). We show that the space of invariant measures supported on $\Lambda$ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in $\Lambda$ (which implies the set of irregular$^+$ points is also residual in $\Lambda$). As an application, we show that the non-uniform hyperbolicity of irregular$^+$ points in $\Lambda$ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in $\Lambda$) determines the uniform hyperbolicity of $\Lambda$

Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.Comment: 8 pages, 3 figure

Number of Pregnancies and Trajectory of Frailty Index: English Longitudinal Study of Ageing

OBJECTIVES: Women are frailer than men across different populations and age groups. However, the mechanisms are still not fully understood. One possible cause is pregnancy and motherhood. The objective of this study was to examine trajectories of Frailty Index over time according to the number of pregnancies. DESIGN: A prospective study with repeated measures over 14 years. SETTING AND PARTICIPANTS: A total of 2060 community-dwelling older women aged ≥60 years in England. METHODS: The number of pregnancies was calculated as a sum of the number of live births and the number of miscarriages, still-births, or abortions. The Frailty Index (FI) was constructed using 60 deficits and repeatedly calculated every 2 years over 14 years. Trajectories of FI according to the number of pregnancies were estimated by a mixed effects model. RESULTS: Mean FI was 0.15 at baseline. A mixed effects model adjusted for age, smoking, alcohol use, education, and wealth showed that FI increased over time. A higher number of pregnancies were significantly associated with a higher FI (estimate = 0.0047, 95% confidence interval = 0.0020, 0.0074). CONCLUSIONS AND IMPLICATIONS: The current study showed that a higher number of pregnancies were significantly associated with a higher degree of frailty at baseline and over time. Pregnancy and child rearing may explain some of the observed excess risk of frailty in women. Pregnancy-related factors, such as pregnancy loss, types of delivery, length of pregnancy, childbearing, and child rearing, should be examined in relation to frailty in future studies

Marital status and risk of physical frailty: A systematic review and meta-analysis

Objectives: Evidence on associations between marital status and frailty is limited. The objectives of this study were to perform a systematic review for associations between marital status and physical frailty and to perform a meta-analysis to combine findings. Design: Systematic review and meta-analysis. Setting and participants: Community-dwelling older people with mean age ≥60 years. Methods: Systematic literature search using 5 databases was conducted in February 2019 to identify longitudinal and cross-sectional studies examining associations between marital status and Fried's phenotype-based frailty status. Additional studies were searched for by reviewing the reference lists of relevant articles and conducting forward citation tracking of included articles. Odds ratio (OR) of marital status and frailty was pooled using a random-effects meta-analysis. Subgroup analysis and analyses stratified by gender and marital status (married, widowed, divorced or separated, and never married) were completed. Results: A total of 1565 studies were found, from which 3 studies with longitudinal data and 35 studies with cross-sectional data were included. Although longitudinal studies suggested that married men had lower frailty risks than unmarried men while married women had higher frailty risks than widowed women, meta-analysis was not possible because of different methodologies. Meta-analyses of cross-sectional data from 35 studies including 80,754 individuals showed that unmarried individuals were almost twice more likely to be frail than married individuals (pooled odds ratio = 1.88, 95% confidence interval = 1.70-2.07). A high degree of heterogeneity was observed (I2 = 69%) and was partially explained by reasons for not being married and study location. Stratified analyses showed that pooled risks of frailty in the unmarried compared with the married were not statistically different between women and women (P for difference = .62). Conclusions and Implications: Three and 35 studies, respectively, were found providing longitudinal and cross-sectional data regarding associations between marital status and frailty among community-dwelling older people. A meta-analysis of cross-sectional data showed almost twice higher frailty risk in unmarried individuals compared with married individuals. Marital status should be recognized as an important factor, and more longitudinal studies controlling for potential confounding factors are needed