Higher topological Hochschild homology of periodic complex K-theory

We describe the topological Hochschild homology of the periodic complex $K$-theory spectrum, $THH(KU)$, as a commutative $KU$-algebra: it is equivalent to $KU[K(\mathbb{Z},3)]$ and to $F(\Sigma KU_{\mathbb{Q}})$, where $F$ is the free commutative $KU$-algebra functor on a $KU$-module. Moreover, $F(\Sigma KU_{\mathbb{Q}})\simeq KU \vee \Sigma KU_{\mathbb{Q}}$, a square-zero extension. In order to prove these results, we first establish that topological Hochschild homology commutes, as an algebra, with localization at an element. Then, we prove that $THH^n(KU)$, the $n$-fold iteration of $THH(KU)$, i.e. $T^n\otimes KU$, is equivalent to $KU[G]$ where $G$ is a certain product of integral Eilenberg-Mac Lane spaces, and to a free commutative $KU$-algebra on a rational $KU$-module. We prove that $S^n \otimes KU$ is equivalent to $KU[K(\mathbb{Z},n+2)]$ and to $F(\Sigma^n KU_{\mathbb{Q}})$. We describe the topological Andr\'e-Quillen homology of $KU$.Comment: 40 pages. Final versio

The OGLE View of Microlensing towards the Magellanic Clouds. III. Ruling out sub-solar MACHOs with the OGLE-III LMC data

In the third part of the series presenting the Optical Gravitational Lensing Experiment (OGLE) microlensing studies of the dark matter halo compact objects (MACHOs) we describe results of the OGLE-III monitoring of the Large Magellanic Cloud (LMC). This unprecedented data set contains almost continuous photometric coverage over 8 years of about 35 million objects spread over 40 square degrees. We report a detection of two candidate microlensing events found with the automated pipeline and an additional two, less probable, candidate events found manually. The optical depth derived for the two main candidates was calculated following a detailed blending examination and detection efficiency determination and was found to be tau=(0.16+-0.12)10^-7. If the microlensing signal we observe originates from MACHOs it means their masses are around 0.2 M_Sun and they compose only f=3+-2 per cent of the mass of the Galactic Halo. However, the more likely explanation of our detections does not involve dark matter compact objects at all and rely on natural effect of self-lensing of LMC stars by LMC lenses. In such a scenario we can almost completely rule out MACHOs in the sub-solar mass range with an upper limit at f<7 per cent reaching its minimum of f<4 per cent at M=0.1 M_Sun. For masses around M=10 M_Sun the constraints on the MACHOs are more lenient with f ~ 20 per cent. Owing to limitations of the survey there is no reasonable limit found for heavier masses, leaving only a tiny window of mass spectrum still available for dark matter compact objects.Comment: Accepted for publication in MNRAS. On-line data available on OGLE website: http://ogle.astrouw.edu.p

Optimizing the colour and fabric of targets for the control of the tsetse fly Glossina fuscipes fuscipes

Background: Most cases of human African trypanosomiasis (HAT) start with a bite from one of the subspecies of Glossina fuscipes. Tsetse use a range of olfactory and visual stimuli to locate their hosts and this response can be exploited to lure tsetse to insecticide-treated targets thereby reducing transmission. To provide a rational basis for cost-effective designs of target, we undertook studies to identify the optimal target colour. Methodology/Principal Findings: On the Chamaunga islands of Lake Victoria , Kenya, studies were made of the numbers of G. fuscipes fuscipes attracted to targets consisting of a panel (25 cm square) of various coloured fabrics flanked by a panel (also 25 cm square) of fine black netting. Both panels were covered with an electrocuting grid to catch tsetse as they contacted the target. The reflectances of the 37 different-coloured cloth panels utilised in the study were measured spectrophotometrically. Catch was positively correlated with percentage reflectance at the blue (460 nm) wavelength and negatively correlated with reflectance at UV (360 nm) and green (520 nm) wavelengths. The best target was subjectively blue, with percentage reflectances of 3%, 29%, and 20% at 360 nm, 460 nm and 520 nm respectively. The worst target was also, subjectively, blue, but with high reflectances at UV (35% reflectance at 360 nm) wavelengths as well as blue (36% reflectance at 460 nm); the best low UV-reflecting blue caught 3× more tsetse than the high UV-reflecting blue. Conclusions/Significance: Insecticide-treated targets to control G. f. fuscipes should be blue with low reflectance in both the UV and green bands of the spectrum. Targets that are subjectively blue will perform poorly if they also reflect UV strongly. The selection of fabrics for targets should be guided by spectral analysis of the cloth across both the spectrum visible to humans and the UV region

Residual spectrum of GL2n\mathrm{GL}_{2n} distinguished by GLn×GLn\mathrm{GL}_n \times \mathrm{GL}_n

Following the regularization method presented by Zydor, we study in this paper the regularized linear periods of square-integrable automormphic forms on $\mathrm{GL}_{2n}(\mathbb{A}_F)$, where $F$ is a number field and $\mathbb{A}_F$ its ring of adeles. We obtain a formula that expresses the regularized period of a noncuspidal, square-integrable automorphic form in terms of degenerate Whittaker functions in an inductive manner. As a consequence we characterize irreducible automorphic representations in the discrete spectrum of $\mathrm{GL}_{2n}(\mathbb{A})$ that are distinguished by $\mathrm{GL}_n(\mathbb{A}) \times \mathrm{GL}_n(\mathbb{A})$. We also show the vanishing of the regularized periods of square-integrable automorphic forms on $\mathrm{GL}_n(\mathbb{A})$ over $\mathrm{GL}_p(\mathbb{A}) \times \mathrm{GL}_q(\mathbb{A})$ when $p$ is not equal to $q$.Comment: Comments are welcome