Proof of the Hyperplane Zeros Conjecture of Lagarias and Wang

We prove that a real analytic subset of a torus group that is contained in its image under an expanding endomorphism is a finite union of translates of closed subgroups. This confirms the hyperplane zeros conjecture of Lagarias and Wang for real analytic varieties. Our proof uses real analytic geometry, topological dynamics and Fourier analysis.Comment: 25 page

Regional health expenditure and health outcomes after out-of-hospital cardiac arrest in Japan: an observational study

Objectives: Japan is considering policies to set the target health expenditure level for each region, a policy approach that has been considered in many other countries. The objective of this study was to examine the relationship between regional health expenditure and health outcomes after out-of-hospital cardiac arrest (OHCA), which incorporates the qualities of prehospital, in-hospital and posthospital care systems. Design: We examined the association between prefecture-level per capita health expenditure and patients’ health outcomes after OHCA. Setting: We used a nationwide, population-based registry system of OHCAs that captured all cases with OHCA resuscitated by emergency responders in Japan from 2005 to 2011. Participants: All patients with OHCA aged 1–100 years were analysed. Outcome measures The patients’ 1-month survival rate, and favourable neurological outcome (defined as cerebral performance category 1–2) at 1-month. Results: Among 618 154 cases with OHCA, the risk-adjusted 1-month survival rate varied from 3.3% (95% CI 2.9% to 3.7%) to 8.4% (95% CI 7.7% to 9.1%) across prefectures. The risk-adjusted probabilities of favourable neurological outcome ranged from 1.6% (95% CI 1.4% to 1.9%) to 3.7% (95% CI 3.4% to 3.9%). Compared with prefectures with lowest tertile health expenditure, 1-month survival rate was significantly higher in medium-spending (adjusted OR 1.31, 95% CI 1.03 to 1.66, p=0.03) and high-spending prefectures (adjusted OR 1.30, 95% CI 1.03 to 1.64, p=0.02), after adjusting for patient characteristics. There was no difference in the survival between medium-spending and high-spending regions. We observed similar patterns for favourable neurological outcome. Additional adjustment for regional per capita income did not affect our overall findings. Conclusions: We observed a wide variation in the health outcomes after OHCA across regions. Low-spending regions had significantly worse health outcomes compared with medium-spending or high-spending regions, but no difference was observed between medium-spending and high-spending regions. Our findings suggest that focusing on the median spending may be the optimum that allows for saving money without compromising patient outcomes

Search for two-neutrino double electron capture on 124^{124}Xe with the XMASS-I detector

Double electron capture is a rare nuclear decay process in which two orbital electrons are captured simultaneously in the same nucleus. Measurement of its two-neutrino mode would provide a new reference for the calculation of nuclear matrix elements whereas observation of its neutrinoless mode would demonstrate lepton number violation. A search for two-neutrino double electron capture on $^{124}$Xe is performed using 165.9 days of data collected with the XMASS-I liquid xenon detector. No significant excess above background was observed and we set a lower limit on the half-life as $4.7 \times 10^{21}$ years at 90% confidence level. The obtained limit has ruled out parts of some theoretical expectations. We obtain a lower limit on the $^{126}$Xe two-neutrino double electron capture half-life of $4.3 \times 10^{21}$ years at 90% confidence level as well.Comment: 6 pages, 3 figures, accepted for publication in Physics Letters

Direct dark matter search by annual modulation in XMASS-I

A search for dark matter was conducted by looking for an annual modulation signal due to the Earth's rotation around the Sun using XMASS, a single phase liquid xenon detector. The data used for this analysis was 359.2 live days times 832 kg of exposure accumulated between November 2013 and March 2015. When we assume Weakly Interacting Massive Particle (WIMP) dark matter elastically scattering on the target nuclei, the exclusion upper limit of the WIMP-nucleon cross section 4.3$\times$10$^{-41}$cm$^2$ at 8 GeV/c$^2$ was obtained and we exclude almost all the DAMA/LIBRA allowed region in the 6 to 16 GeV/c$^2$ range at $\sim$10$^{-40}$cm$^2$. The result of a simple modulation analysis, without assuming any specific dark matter model but including electron/$\gamma$ events, showed a slight negative amplitude. The $p$-values obtained with two independent analyses are 0.014 and 0.068 for null hypothesis, respectively. we obtained 90\% C.L. upper bounds that can be used to test various models. This is the first extensive annual modulation search probing this region with an exposure comparable to DAMA/LIBRA.Comment: 5 pages, 4 figure

Search for solar axions in XMASS, a large liquid-xenon detector

XMASS, a low-background, large liquid-xenon detector, was used to search for solar axions that would be produced by bremsstrahlung and Compton effects in the Sun. With an exposure of 5.6ton days of liquid xenon, the model-independent limit on the coupling for mass $\ll$ 1keV is $|g_{aee}|< 5.4\times 10^{-11}$ (90% C.L.), which is a factor of two stronger than the existing experimental limit. The bounds on the axion masses for the DFSZ and KSVZ axion models are 1.9 and 250eV, respectively. In the mass range of 10-40keV, this study produced the most stringent limit, which is better than that previously derived from astrophysical arguments regarding the Sun to date