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

R. E. Steen to Mrs. McKellar, 24 March 1941

Professional correspondenc

Critical roles of endogenous glucocorticoids for disease tolerance in malaria

During malaria, the hypothalamic-pituitary-adrenal (HPA) axis is activated and glucocorticoid (GC) levels are increased, but their essential roles have been largely overlooked. GCs are decisive for systemic regulation of vital processes such as immune responses, vascular function, and metabolism, which are crucial in malaria. Here, we introduce GCs in general, followed by their versatile roles for disease tolerance in malaria. A complementary comparison is provided with their role in sepsis. Finally, potential translational implications are considered. The failed clinical trials of dexamethasone against cerebral malaria in the past have diminished the interest in GCs in malaria. However, the issue of relative corticosteroid insufficiency has barely been explored in malaria patients, but may hold promise for a better understanding and treatment of specific malaria complications

First measurement of cluster temperature using the thermal Sunyaev-Zeldovich effect

We discuss a new method of finding the cluster temperatures which is independent of distance and therefore very useful for distant clusters. The hot gas of electrons in clusters of galaxies scatters and distorts the cosmic microwave background radiation in a well determined way. This Sunyaev-Zel'dovich (SZ) effect is a useful tool for extracting information about clusters such as their peculiar radial velocity and optical depth. Here we show how the temperature of the cluster can be inferred from the SZ effect, in principle without use of X-ray data. We use recent millimetre observation of Abell 2163 to determine for the first time a cluster temperature using SZ observations only. The result T_e = 26^+34_-19 keV at 68% confidence level (at 95% c.l. we find T>1.5 keV) is in reasonable agreement with the X-ray results, T_e =12.4^+2.8_-1.9 keV.Comment: 7 pages, 2 figure

Taming the neutrophil : Balance between anti‐parasite defence and pathogenesis

Non peer reviewedPublisher PD