The geometry of modified Riemannian extensions

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extension is Einstein. We exhibit Riemannian extension Osserman manifolds of signature (3,3) whose Jacobi operators have non-trivial Jordan normal form and which are not nilpotent. We present new four dimensional results in Osserman geometry

Stanilov-Tsankov-Videv Theory

We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

I know your face but can’t remember your name:Age-related differences in the FNAME-12NL

OBJECTIVE: The Face-Name Associative Memory test (FNAME) has recently received attention as a test for early diagnosis of Alzheimer’s disease. So far, however, there has been no systematic investigation of the effects of aging. Here, we aimed to assess the extent to which the FNAME performance is modulated by normal ageing. METHOD: In a first step, we adapted the FNAME material to the Dutch population. In a second step, younger (n = 29) and older adults (n = 29) were compared on recall and recognition performance. RESULTS: Significant age effects on name recall were observed after the first exposure of new face-name pairs: younger adults remembered eight, whereas older adults remembered a mean of four out of twelve names. Although both age groups increased the number of recalled names with repeated face-name exposure, older adults did not catch up with the performance of the younger adults, and the age-effects remained stable. Despite of that, both age groups maintained their performance after a 30-min delay. Considering recognition, no age differences were demonstrated, and both age groups succeeded in the recognition of previously shown faces and names when presented along with distractors. CONCLUSIONS: This study presents for the first time the results of different age groups regarding cross-modal associative memory performance on the FNAME. The recall age effects support the hypothesis of age-related differences in associative memory. To use the FNAME as an early cognitive biomarker, further subscales are suggested to increase sensitivity and specificity in the clinical context

The Probability Distribution Function of Column Density in Molecular Clouds

(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation length'' can be defined as the distance over which the density auto-correlation function has decayed to, for example, 10% of its zero-lag value, so that the density ``events'' along a line of sight can be assumed to be independent over distances larger than this, and the Central Limit Theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high- density tail. Thus, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio $\eta$ of the column length to the decorrelation length increases. Simultaneously, the PDF's variance decreases. For intermediate values of $\eta$, the column density PDF assumes a nearly exponential decay. We then discuss the density power spectrum and the expected value of $\eta$ in actual molecular clouds. Observationally, our results suggest that $\eta$ may be inferred from the shape and width of the column density PDF in optically-thin-line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, non-isothermal neutral medium (temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for $\eta \gtrsim 100$, the dynamic range in column density is small ($\lesssim$ a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.Comment: 13 pages, 7 figures (10 postscript files). Accepted in ApJ. Eliminated implication that ratio of column length to correlation length necessarily increases with resolution, and thus that 3D simulations are unresolved. Added discussion of dependence of autocorrelation function with parameters of the turbulenc