Harmonic analysis of fractal measures induced by representations of a certain C∗^*-algebra

We describe a class of measurable subsets $\Omega$ in \br^d such that $L^2(\Omega)$ has an orthogonal basis of frequencies $e_\lambda(x)=e^{i2\pi\lambda\cdot x}(x\in\Omega)$ indexed by \lambda\in\Lambda\subset\br^d. We show that such spectral pairs $(\Omega ,\Lambda)$ have a self-similarity which may be used to generate associated fractal measures $\mu$ with Cantor set support. The Hilbert space $L^2(\mu)$ does not have a total set of orthogonal frequencies, but a harmonic analysis of $\mu$ may be built instead from a natural representation of the Cuntz C$^*$- algebra which is constructed from a pair of lattices supporting the given spectral pair $(\Omega ,\Lambda)$. We show conversely that such a pair may be reconstructed from a certain Cuntz-representation given to act on $L^2(\mu)$.Comment: 7 page

What research we no longer need in neurodegenerative disease at the end of life : The case of research in dementia

A complete silence. That was what we got back from the European experts who had been energetically discussing research priorities in palliative care in neurodegenerative disease (ND) until a short while ago.1 The chair, an entertaining professor with good manners, must have felt the unease and quickly refocused the group to their task. But, wasn’t this the best question of all day? What research we no longer need? As scientists able to consider different perspectives, shouldn’t we have some idea of what research is, by contrast, no longer necessary? Palliative care research and research with people who have ND and are at the end of their life is, by definition, difficult. Making choices is a sensitive issue, but funds are limited. Therefore, we take a counterpoint to the research agenda recently reported by European Union (EU) Joint Programme – Neurodegenerative Disease Research (JPND),1 and consider whether there are studies we no longer need or are low priority, taking the example of dementiaPeer reviewedFinal Accepted Versio

Vaginal yeasts in the era of "over the counter" antifungals

OBJECTIVE: To establish whether there has been any rise in the prevalence of non-albicans Candida species isolated from vaginal swabs since the introduction of “over the counter” antifungal treatments. METHOD: A retrospective review looking at all positive vaginal yeast isolates collected from women attending one genitourinary medicine clinic during the 6 year period from 1993 to 1998 inclusive. All positive vaginal yeast isolates were included, regardless of whether or not the patients were symptomatic. Isolates from HIV positive women were excluded from the analysis. RESULT: No increase in non-albicans vaginal yeast isolates was shown during the period studied. The proportion of non-albicans yeasts remained constant at approximately 5% of the total yeasts isolated. The most common non-albicans yeast isolated was C glabrata. CONCLUSION: There is no evidence from this study to suggest that the increasing use of “over the counter” antifungal treatment has selected for atypical, possibly inherently azole resistant, strains of vaginal yeasts in HIV seronegative women