Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Regional differences in HIV prevalence among drug users in China: potential for future spread of HIV?

Kretzschmar M, Zhang W, Mikolajczyk RT, et al. Regional differences in HIV prevalence among drug users in China: potential for future spread of HIV? BMC Infectious Diseases. 2008;8(1):108.Background: Drug use and in particular injecting drug use has been at the forefront of the explosive spread of HIV in general populations in many countries in Asia. There is concern that also in China increased HIV incidence in drug users might spark off a generalized epidemic in the wider population. Close monitoring of HIV incidence and risk factors in drug users is therefore important to be able to target interventions effectively. Second generation surveillance was launched to assess HIV prevalence and risk behaviours jointly with the purpose of describing trends and predicting future developments. To assess whether these goals were fulfilled among drug users in China we provide an analysis of risk factors for HIV infection and of regional differences in HIV prevalence. Methods: We analysed data collected in 2005 in 21 drug user second generation surveillance sentinel sites from 14 provinces in China. We used random effects logistic regression to test for risk factors for HIV infection and regional differences. Results: The overall HIV-1 antibody prevalence was 5.4% (279/5128); 4.9% among injecting drug users (IDU) not sharing needles and 3.7% among non-injecting drug users. We found substantial heterogeneity among the surveillance sites with prevalence rates ranging between 0% and 54%. HIV status was strongly affected by the regional prevalence of HIV. Risk behaviours were highly prevalent in regions where HIV prevalence is still low. The distribution of duration of drug use in different sites indicated different stages of the drug use epidemics. Conclusion: ]Regional differences in HIV prevalence in China reflect different stages of the drug use and HIV epidemics rather than differences in risk behaviours. Therefore, outbreaks of HIV among drug users in regions where prevalence is still low can be expected in the future. However, methodological limitations of surveillance embedded into routine systems limit the usability of existing data. More standardized approaches to data collection in secondary generation HIV surveillance are necessary to better understand regional differences in risk behaviour and prevalence and to design targeted intervention for those regions at risk of experiencing outbreaks

A new measurement of antineutrino oscillation with the full detector configuration at Daya Bay

We report a new measurement of electron antineutrino disappearance using the fully-constructed Daya Bay Reactor Neutrino Experiment. The final two of eight antineutrino detectors were installed in the summer of 2012. Including the 404 days of data collected from October 2012 to November 2013 resulted in a total exposure of 6.9$\times$10$^5$ GW$_{\rm th}$-ton-days, a 3.6 times increase over our previous results. Improvements in energy calibration limited variations between detectors to 0.2%. Removal of six $^{241}$Am-$^{13}$C radioactive calibration sources reduced the background by a factor of two for the detectors in the experimental hall furthest from the reactors. Direct prediction of the antineutrino signal in the far detectors based on the measurements in the near detectors explicitly minimized the dependence of the measurement on models of reactor antineutrino emission. The uncertainties in our estimates of $\sin^{2}2\theta_{13}$ and $|\Delta m^2_{ee}|$ were halved as a result of these improvements. Analysis of the relative antineutrino rates and energy spectra between detectors gave $\sin^{2}2\theta_{13} = 0.084\pm0.005$ and $|\Delta m^{2}_{ee}|= (2.42\pm0.11) \times 10^{-3}$ eV$^2$ in the three-neutrino framework.Comment: Updated to match final published versio

New measurement of θ13\theta_{13} via neutron capture on hydrogen at Daya Bay

This article reports an improved independent measurement of neutrino mixing angle $\theta_{13}$ at the Daya Bay Reactor Neutrino Experiment. Electron antineutrinos were identified by inverse $\beta$-decays with the emitted neutron captured by hydrogen, yielding a data-set with principally distinct uncertainties from that with neutrons captured by gadolinium. With the final two of eight antineutrino detectors installed, this study used 621 days of data including the previously reported 217-day data set with six detectors. The dominant statistical uncertainty was reduced by 49%. Intensive studies of the cosmogenic muon-induced $^9$Li and fast neutron backgrounds and the neutron-capture energy selection efficiency, resulted in a reduction of the systematic uncertainty by 26%. The deficit in the detected number of antineutrinos at the far detectors relative to the expected number based on the near detectors yielded $\sin^22\theta_{13} = 0.071 \pm 0.011$ in the three-neutrino-oscillation framework. The combination of this result with the gadolinium-capture result is also reported.Comment: 26 pages, 23 figure

Implementation of Fourier transform infrared spectroscopy for the rapid typing of uropathogenic Escherichia coli.

In this paper, we demonstrate that Fourier transform infrared (FT-IR) spectroscopy is able to discriminate rapidly between uropathogenic Escherichia coli (UPEC) of key lineages with only relatively simple sample preparation. A total of 95 bacteria from six different epidemiologically important multilocus sequence types (ST10, ST69, ST95, ST73, ST127 and ST131) were used in this project and principal component-discriminant function analysis (PC-DFA) of these samples produced clear separate clustering of isolates, based on the ST. Analysis of data using partial least squares-discriminant analysis (PLS-DA), incorporating cross-validation, indicated a high prediction accuracy of 91.19% for ST131. These results suggest that FT-IR spectroscopy could be a useful method for the rapid identification of members of important UPEC STs

Improved Measurement of the Reactor Antineutrino Flux and Spectrum at Daya Bay

A new measurement of the reactor antineutrino flux and energy spectrum by the Daya Bay reactor neutrino experiment is reported. The antineutrinos were generated by six 2.9~GW$_{\mathrm{th}}$ nuclear reactors and detected by eight antineutrino detectors deployed in two near (560~m and 600~m flux-weighted baselines) and one far (1640~m flux-weighted baseline) underground experimental halls. With 621 days of data, more than 1.2 million inverse beta decay (IBD) candidates were detected. The IBD yield in the eight detectors was measured, and the ratio of measured to predicted flux was found to be $0.946\pm0.020$ ($0.992\pm0.021$) for the Huber+Mueller (ILL+Vogel) model. A 2.9~$\sigma$ deviation was found in the measured IBD positron energy spectrum compared to the predictions. In particular, an excess of events in the region of 4-6~MeV was found in the measured spectrum, with a local significance of 4.4~$\sigma$. A reactor antineutrino spectrum weighted by the IBD cross section is extracted for model-independent predictions.Comment: version published in Chinese Physics