Parametric Manifolds II: Intrinsic Approach

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) 1-form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a new geometric object, called the deficiency, which behaves much like torsion, and which measures whether a parametric manifold can be viewed as a 1-parameter family of orthogonal hypersurfaces.Comment: Plain TeX, 13 pages, no figure

Parametric Manifolds I: Extrinsic Approach

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the 1-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss-Codazzi formalism. We generalize this formalism to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface-forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed.Comment: Plain TeX, 21 pages, no figure

Parametric manifolds

A standard tool in general relativity is the 3+1 or ADM point of view, namely slicing spacetime into spacelike hypersurfaces of constant time and then describing physics in terms of time-dependent quantities on a typical such hypersurface. Much less well-known is the 1+3 point of view, in which one foliates spacetime with timelike curves, then describes physics in terms of the surfaces "locally orthogonal" to the given foliation. This is precisely the description of physics as seen by a single observer. However, in many instances there do not exist such orthogonal hypersurfaces. One may instead attempt to describe physics on the manifold of orbits defined by the timelike curves, but one must then develop a parametric theory to handle the time dependent objects defined on the manifold of orbits. I will present two equivalent descriptions of parametric manifolds. The first is based on a generalized Gauss-Codazzi formalism which involves projection to a lower-dimensional "surface". The second is an intrinsic description which involves redefining the action of vector fields on functions. In either description one is lead to generalized notions of connections, Lie bracket, and exterior differentiation. Unique to a parametric theory of geometry is the deficiency. Although independent of the torsion, the deficiency behaves like torsion in the parametric direction. We will show how the deficiency emerges as a result of the above generalizations. The 3+1 formalism arises naturally in considering initial-value formulations both for fields on a fixed background spacetime and for the spacetime itself. The applicability of parametric manifolds to such problems will be discussed

Parametric manifolds. II. Intrinsic approach

A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one‐form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action of vector fields on functions. There is a new geometric object, called the deficiency, which behaves much like torsion, and which measures whether a parametric manifold can be viewed as a one‐parameter family of orthogonal hypersurfaces.Keywords: MATHEMATICAL MANIFOLDS, SPACE−TIME, RIEMANN SPACE, TORSION, TENSOR FIELDS, DIFFERENTIAL GEOMETRY, GENERAL RELATIVITY THEORY, SURFACES, VECTOR FIELDS, GRAVITATIONAL FIELD

Attitude toward contraception and abortion among Curaçao women. Ineffective contraception due to limited sexual education?

Background In Curaçao is a high incidence of unintended pregnancies and induced abortions. Most of the induced abortions in Curaçao are on request of the woman and performed by general practitioners. In Curaçao, induced abortion is strictly prohibited, but since 1999 there has been a policy of connivance. We present data on the relevance of economic and socio-cultural factors for the high abortion-rates and the ineffective use of contraception. Methods Structured interviews to investigate knowledge and attitudes toward sexuality, contraception and abortion and reasons for ineffective use of contraceptives among women, visiting general practitioners. Results Of 158 women, 146 (92%) participated and 82% reported that their education on sexuality and about contraception was of good quality. However 'knowledge of reliable contraceptive methods' appeared to be - in almost 50% of the cases - false information, misjudgements or erroneous views on the chance of getting pregnant using coitus interruptus and about the reliability and health effects of oral contraceptive pills. Almost half of the interviewed women had incorrect or no knowledge about reliability of condom use and IUD. 42% of the respondents risked by their behavior an unplanned pregnancy. Most respondents considered abortion as an emergency procedure, not as contraception. Almost two third experienced emotional, physical or social problems after the abortion. Conclusions Respondents had a negative attitude toward reliable contraceptives due to socio-cultural determined ideas about health consequences and limited sexual education. Main economic factors were costs of contraceptive methods, because most health insurances in Curaçao do not cover contraceptives. To improve the effective use of reliable contraceptives, more adequate information should be given, targeting the wrong beliefs and false information. The government should encourage health insurance companies to reimburse contraceptives. Furthermore, improvement of counseling during the abortion procedure is important

The effect of age on outcomes of coronary artery bypass surgery compared with balloon angioplasty or bare-metal stent implantation among patients with multivessel coronary disease. A collaborative analysis of individual patient data from 10 randomized trials.

OBJECTIVES: This study sought to assess whether patient age modifies the comparative effectiveness of coronary artery bypass graft (CABG) surgery and percutaneous coronary intervention (PCI). BACKGROUND: Increasingly, CABG and PCI are performed in older patients to treat multivessel disease, but their comparative effectiveness is uncertain. METHODS: Individual data from 7,812 patients randomized in 1 of 10 clinical trials of CABG or PCI were pooled. Age was analyzed as a continuous variable in the primary analysis and was divided into tertiles for descriptive purposes (≤56.2 years, 56.3 to 65.1 years, ≥65.2 years). The outcomes assessed were death, myocardial infarction and repeat revascularization over complete follow-up, and angina at 1 year. RESULTS: Older patients were more likely to have hypertension, diabetes, and 3-vessel disease compared with younger patients (p < 0.001 for trend). Over a median follow-up of 5.9 years, the effect of CABG versus PCI on mortality varied according to age (interaction p < 0.01), with adjusted CABG-to-PCI hazard ratios and 95% confidence intervals (CI) of 1.23 (95% CI: 0.95 to 1.59) in the youngest tertile; 0.89 (95% CI: 0.73 to 1.10) in the middle tertile; and 0.79 (95% CI: 0.67 to 0.94) in the oldest tertile. The CABG-to-PCI hazard ratio of less than 1 for patients 59 years of age and older. A similar interaction of age with treatment was present for the composite outcome of death or myocardial infarction. In contrast, patient age did not alter the comparative effectiveness of CABG and PCI on the outcomes of repeat revascularization or angina. CONCLUSIONS: Patient age modifies the comparative effectiveness of CABG and PCI on hard cardiac events, with CABG favored at older ages and PCI favored at younger ages

Impaired frequency selectivity and sensitivity to temporal fine structure, but not envelope cues, in children with mild-to-moderate sensorineural hearing loss.

Psychophysical thresholds were measured for 8-16 year-old children with mild-to-moderate sensorineural hearing loss (MMHL; N = 46) on a battery of auditory processing tasks that included measures designed to be dependent upon frequency selectivity and sensitivity to temporal fine structure (TFS) or envelope cues. Children with MMHL who wore hearing aids were tested in both unaided and aided conditions, and all were compared to a group of normally hearing (NH) age-matched controls. Children with MMHL performed more poorly than NH controls on tasks considered to be dependent upon frequency selectivity, sensitivity to TFS, and speech discrimination (/bɑ/-/dɑ/), but not on tasks measuring sensitivity to envelope cues. Auditory processing deficits remained regardless of age, were observed in both unaided and aided conditions, and could not be attributed to differences in nonverbal IQ or attention between groups. However, better auditory processing in children with MMHL was predicted by better audiometric thresholds and, for aided tasks only, higher levels of maternal education. These results suggest that, as for adults with MMHL, children with MMHL may show deficits in frequency selectivity and sensitivity to TFS, but sensitivity to the envelope may remain intact.Economic and Social Research Council First Grants Award (RES-061-25- 0440) and Medical Research Council Senior Fellowship in Hearing Research (MR/S002464/1) awarded to L.F.H

Bronchiectasis in Europe:data on disease characteristics from the European Bronchiectasis registry (EMBARC)

Background: Bronchiectasis is a heterogeneous, neglected disease with few multicentre studies exploring the causes, severity, microbiology, and treatment of the disease across Europe. This aim of this study was to describe the clinical characteristics of bronchiectasis and compare between different European countries.Methods: EMBARC is an international clinical research network for bronchiectasis. We report on a multicentre, prospective, observational, non-interventional, cohort study (the EMBARC registry) conducted across 27 European countries and Israel. Comprehensive clinical data were collected from adult patients (aged ≥18 years) at baseline and annual follow-up visits using electronic case report form. Data from individual countries were grouped into four regions (the UK, northern and western Europe, southern Europe, and central and eastern Europe according to modified EU EuroVoc classification). Follow-up data were used to explore differences in exacerbation frequency between regions using a negative binomial regression model.Findings: Between Jan 12, 2015, and April 12, 2022, 16 963 individuals were enrolled. Median age was 67 years (IQR 57-74), 10 335 (60·9%) participants were female and 6628 (39·1%) were male. The most common cause of bronchiectasis in all 16 963 participants was post-infective disease in 3600 (21·2%); 6466 individuals (38·1%) were classified as idiopathic. Individuals with bronchiectasis experienced a median of two exacerbations (IQR 1-4) per year and 4483 (26·4%) patients had a hospitalisation for exacerbation in the previous year. When examining the percentage of all isolated bacteria, marked differences in microbiology were seen between countries, with a higher frequency of Pseudomonas aeruginosa and lower Haemophilus influenzae frequency in southern Europe, compared with higher H influenzae in the UK and northern and western Europe. Compared with other regions, patients in central and eastern Europe had more severe bronchiectasis measured by the Bronchiectasis Severity Index (51·3% vs 35·1% in the overall cohort) and more exacerbations leading to hospitalisations (57·9% vs 26·4% in the overall cohort). Overall, patients in central and eastern Europe had an increased frequency of exacerbations (adjusted rate ratio [RR] 1·12, 95% CI 1·01-1·25) and a higher frequency of exacerbations leading to hospitalisations (adjusted RR 1·71, 1·44-2·02) compared with patients in other regions. Treatment of bronchiectasis was highly heterogeneous between regions.Interpretation: Bronchiectasis shows important geographical variation in causes, microbiology, severity, and outcomes across Europe.</p