Natural Intrinsic Geometrical Symmetries

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.Comment: Theorem 20 is corrected and References [13, 14] are adde

On the extrinsic principal directions and curvatures of Lagrangian submanifolds

From the basic geometry of submanifolds will be recalled what are the extrinsic principal tangential directions, (first studied by Camille Jordan in the $18$seventies), and what are the principal first normal directions, (first studied by Kostadin Trencevski in the $19$nineties), and what are their corresponding Casorati curvatures. For reasons of simplicity of exposition only, hereafter this will merely be done explicitly in the case of arbitrary submanifolds in Euclidean spaces. Then, for the special case of Lagrangian submanifolds in complex Euclidean spaces, the natural relationships between these distinguished tangential and normal directions and their corresponding curvatures will be established

Ideally embedded space-times

Due to the growing interest in embeddings of space-time in higher-dimensional spaces we consider a specific type of embedding. After proving an inequality between intrinsically defined curvature invariants and the squared mean curvature, we extend the notion of ideal embeddings from Riemannian geometry to the indefinite case. Ideal embeddings are such that the embedded manifold receives the least amount of tension from the surrounding space. Then it is shown that the de Sitter spaces, a Robertson-Walker space-time and some anisotropic perfect fluid metrics can be ideally embedded in a five-dimensional pseudo-Euclidean space.Comment: layout changed and typos corrected; uses revtex

A Computational Model of Visual Anisotropy

Visual anisotropy has been demonstrated in multiple tasks where performance differs between vertical, horizontal, and oblique orientations of the stimuli. We explain some principles of visual anisotropy by anisotropic smoothing, which is based on a variation on Koenderink's approach in [1]. We tested the theory by presenting Gaussian elongated luminance profiles and measuring the perceived orientations by means of an adjustment task. Our framework is based on the smoothing of the image with elliptical Gaussian kernels and it correctly predicted an illusory orientation bias towards the vertical axis. We discuss the scope of the theory in the context of other anisotropies in perception

The epidemiology of bacterial vaginosis in relation to sexual behaviour

<p>Abstract</p> <p>Background</p> <p>Bacterial vaginosis (BV) has been most consistently linked to sexual behaviour, and the epidemiological profile of BV mirrors that of established sexually transmitted infections (STIs). It remains a matter of debate however whether BV pathogenesis does actually involve sexual transmission of pathogenic micro-organisms from men to women. We therefore made a critical appraisal of the literature on BV in relation to sexual behaviour.</p> <p>Discussion</p> <p><it>G. vaginalis </it>carriage and BV occurs rarely with children, but has been observed among adolescent, even sexually non-experienced girls, contradicting that sexual transmission is a necessary prerequisite to disease acquisition. <it>G. vaginalis </it>carriage is enhanced by penetrative sexual contact but also by non-penetrative digito-genital contact and oral sex, again indicating that sex <it>per se</it>, but not necessarily coital transmission is involved. Several observations also point at female-to-male rather than at male-to-female transmission of <it>G. vaginalis</it>, presumably explaining the high concordance rates of <it>G. vaginalis </it>carriage among couples. Male antibiotic treatment has not been found to protect against BV, condom use is slightly protective, whereas male circumcision might protect against BV. BV is also common among women-who-have-sex-with-women and this relates at least in part to non-coital sexual behaviours. Though male-to-female transmission cannot be ruled out, overall there is little evidence that BV acts as an STD. Rather, we suggest BV may be considered a sexually enhanced disease (SED), with frequency of intercourse being a critical factor. This may relate to two distinct pathogenetic mechanisms: (1) in case of unprotected intercourse alkalinisation of the vaginal niche enhances a shift from lactobacilli-dominated microflora to a BV-like type of microflora and (2) in case of unprotected and protected intercourse mechanical transfer of perineal enteric bacteria is enhanced by coitus. A similar mechanism of mechanical transfer may explain the consistent link between non-coital sexual acts and BV. Similar observations supporting the SED pathogenetic model have been made for vaginal candidiasis and for urinary tract infection.</p> <p>Summary</p> <p>Though male-to-female transmission cannot be ruled out, overall there is incomplete evidence that BV acts as an STI. We believe however that BV may be considered a <it>sexually enhanced disease</it>, with frequency of intercourse being a critical factor.</p

On Angles and Pseudo-Angles in Minkowskian Planes

The main purpose of the present paper is to well define Minkowskian angles and pseudo-angles between the two null directions and between a null direction and any non-null direction, respectively. Moreover, in a kind of way that will be tried to be made clear at the end of the paper, these new sorts of angles and pseudo-angles can similarly to the previously known angles be seen as (combinations of) Minkowskian lengths of arcs on a Minkowskian unit circle together with Minkowskian pseudo-lengths of parts of the straight null lines

Topics in modern differential geometry

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain