The Berry-Keating Hamiltonian and the Local Riemann Hypothesis

The local Riemann hypothesis states that the zeros of the Mellin transform of a harmonic-oscillator eigenfunction (on a real or p-adic configuration space) have real part 1/2. For the real case, we show that the imaginary parts of these zeros are the eigenvalues of the Berry-Keating hamiltonian H=(xp+px)/2 projected onto the subspace of oscillator eigenfunctions of lower level. This gives a spectral proof of the local Riemann hypothesis for the reals, in the spirit of the Hilbert-Polya conjecture. The p-adic case is also discussed.Comment: 9 pages, no figures; v2 included more mathematical background, v3 has minor edits for clarit

Effectiveness of non-pharmaceutical interventions in nine fields of activity to decrease SARS-CoV-2 transmission (Spain, September 2020–May 2021)

Background: We estimated the association between the level of restriction in nine different fields of activity and SARS-CoV-2 transmissibility in Spain, from 15 September 2020 to 9 May 2021. Methods: A stringency index (0–1) was created for each Spanish province (n = 50) daily. A hierarchical multiplicative model was fitted. The median of coefficients across provinces (95% bootstrap confidence intervals) quantified the effect of increasing one standard deviation in the stringency index over the logarithmic return of the weekly percentage variation of the 7-days SARS-CoV-2 cumulative incidence, lagged 12 days. Results: Overall, increasing restrictions reduced SARS-CoV-2 transmission by 22% (RR = 0.78; one-sided 95%CI: 0, 0.82) in 1 week, with highest effects for culture and leisure 14% (0.86; 0, 0.98), social distancing 13% (0.87; 0, 0.95), indoor restaurants 10% (0.90; 0, 0.95) and indoor sports 6% (0.94; 0, 0.98). In a reduced model with seven fields, culture and leisure no longer had a significant effect while ceremonies decreased transmission by 5% (0.95; 0, 0.96). Models R2 was around 70%. Conclusion: Increased restrictions decreased COVID-19 transmission. Limitations include remaining collinearity between fields, and somewhat artificial quantification of qualitative restrictions, so the exact attribution of the effect to specific areas must be done with caution.This work has been partially supported by GAIN (Galician Innovation Agency) and the Regional Ministry of Economy, Employment and Industry, Xunta de Galicia IN845D 2020/26 (Grant COV20/00604) through the ERDF (2014-2020). The research of DGU has been financed in part by the Spanish Agencia Estatal de Investigación under grants PID2021-122154NB-I00 and TED2021-129455B-I00, and by a 2021 BBVA Foundation project for research in Mathematics. He also acknowledges support from the EU under the 2014-2020 ERDF Operational Programme and the Department of Economy, Knowledge, Business and University of the Regional Government of Andalusia (FEDER-UCA18-108393).S

Effectiveness of mRNA COVID-19 vaccines in preventing SARS-CoV-2 infections and COVID-19 hospitalisations and deaths in elderly long-term care facility residents, Spain, weeks 53 2020 to 13 2021

Residents in long-term care facilities (LTCF) experienced a large morbidity and mortality during the COVID-19 pandemic in Spain and were prioritised for early COVID-19 vaccination. We used the screening method and population-based data sources to obtain estimates of mRNA COVID-19 vaccine effectiveness for elderly LTCF residents. The estimates were 71% (95% CI: 56-82%), 88% (95% CI: 75-95%), and 97% (95% CI: 92-99%), against SARS-CoV-2 infections (symptomatic and asymptomatic), and COVID-19 hospitalisations and deaths, respectively.S

The Role of Women in Economic Transformation: Market Women in Sierra Leone.

yesVarious research has concluded that economic life did not die out during the conflict in Sierra Leone, but took on different forms. Different stakeholders at all levels were engaged in economic activities during the war. The specific roles of women in the shadow economy are under-researched with the result that most analysis and policy-options are inadequate. While some of Sierra Leone¿s Market Women strategically participated in war economies to `do well out of war¿, most did so out of the need to survive. With the end of the war, market women have been able to make a successful transformation to peace economies through micro-credit assistance

Comparative severity of COVID-19 cases caused by Alpha, Delta or Omicron SARS-CoV-2 variants and its association with vaccination

[EN] Background: This study compares the severity of SARS-CoV-2 infections caused by Alpha, Delta or Omicron variants in periods of co-circulation in Spain, and estimates the variant-specific association of vaccination with severe disease. Methods: SARS-CoV-2 infections notified to the national epidemiological surveillance network with information on genetic variant and vaccination status were considered cases if they required hospitalisation or controls otherwise. Alpha and Delta were compared during June-July 2021; and Delta and Omicron during December 2021-January 2022. Adjusted odds ratios (aOR) were estimated using logistic regression, comparing variant and vaccination status between cases and controls. Results: We included 5,345 Alpha and 11,974 Delta infections in June-July and 5,272 Delta and 10,578 Omicron in December-January. Unvaccinated cases of Alpha (aOR: 0.57; 95% CI: 0.46-0.69) or Omicron (0.28; 0.21-0.36) had lower probability of hospitalisation vs. Delta. Complete vaccination reduced hospitalisation, similarly for Alpha (0.16; 0.13-0.21) and Delta (June-July: 0.16; 0.14-0.19; December-January: 0.36; 0.30-0.44) but lower from Omicron (0.63; 0.53-0.75) and individuals aged 65+ years. Conclusion: Results indicate higher intrinsic severity of the Delta variant, compared with Alpha or Omicron, with smaller differences among vaccinated individuals. Nevertheless, vaccination was associated to reduced hospitalisation in all groups. [ES]Introducción: El objetivo es comprar la gravedad de las infecciones por las variantes Alfa, Delta y Ómicron del SARS-CoV-2 en periodos de co-circulación en España, y estimar la asociación entre vacunación y gravedad en cada variante. Métodos: Las infecciones por SARS-CoV-2 notificadas a la red nacional de vigilancia epidemiológica con información sobre la variante viral y el estado de vacunación se clasificaron como casos si habían requerido hospitalización, o como controles en caso contrario. Alfa y Delta se compararon durante junio-julio de 2021, y Delta y Ómicron durante diciembre de 2021-enero de 2022. Se estimaron odds ratios ajustadas (ORa) mediante regresión logística, comparando la variante y el estado de vacunación entre casos y controles. Resultados: Se incluyeron 5.345 infecciones por variante Alfa y 11.974 por Delta en junio-julio y 5.272 infecciones por Delta y 10.578 por Ómicron en diciembre-enero. Los casos no vacunados por Alfa (aOR: 0,57; IC 95%: 0,46-0,69) u Ómicron (0,28; IC 95%: 0,21-0,36) tuvieron menor probabilidad de hospitalización comparados con Delta. La vacunación completa se asoció a menor hospitalización de forma similar para Alfa (0,16; IC 95%: 0,13-0,21) y Delta (junio-julio: 0,16; IC 95%: 0,14-0,19; diciembre-enero: 0,36; IC 95%: 0,30-0,44) pero menor para Ómicron (0,63; IC 95%: 0,53-0,75) y para individuos con 65+ años. Conclusión: Los resultados indican una mayor gravedad intrínseca de la variante Delta comparada con Alfa u Ómicron, con menor diferencia entre personas vacunadas. La vacunación se asoció a menor hospitalización en todos los grupos.In this study the identification of variants by genomic sequencing has been partially supported by HERA-Incubator ECDC/GRANT/2021/024-Enhancing Whole Genome Sequencing (WGS) and/or Reverse Transcription Polymerase Chain Reaction (RT-PCR) national infrastructures and capacities to respond to the Covid-19 pandemic in Spain.S

Measurements of long-range near-side angular correlations in sNN=5\sqrt{s_{\text{NN}}}=5TeV proton-lead collisions in the forward region

Two-particle angular correlations are studied in proton-lead collisions at a nucleon-nucleon centre-of-mass energy of $\sqrt{s_{\text{NN}}}=5$TeV, collected with the LHCb detector at the LHC. The analysis is based on data recorded in two beam configurations, in which either the direction of the proton or that of the lead ion is analysed. The correlations are measured in the laboratory system as a function of relative pseudorapidity, $\Delta\eta$, and relative azimuthal angle, $\Delta\phi$, for events in different classes of event activity and for different bins of particle transverse momentum. In high-activity events a long-range correlation on the near side, $\Delta\phi \approx 0$, is observed in the pseudorapidity range $2.0<\eta<4.9$. This measurement of long-range correlations on the near side in proton-lead collisions extends previous observations into the forward region up to $\eta=4.9$. The correlation increases with growing event activity and is found to be more pronounced in the direction of the lead beam. However, the correlation in the direction of the lead and proton beams are found to be compatible when comparing events with similar absolute activity in the direction analysed.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-040.htm

Evidence for the strangeness-changing weak decay Ξb−→Λb0π−\Xi_b^-\to\Lambda_b^0\pi^-

Using a $pp$ collision data sample corresponding to an integrated luminosity of 3.0~fb$^{-1}$, collected by the LHCb detector, we present the first search for the strangeness-changing weak decay $\Xi_b^-\to\Lambda_b^0\pi^-$. No $b$ hadron decay of this type has been seen before. A signal for this decay, corresponding to a significance of 3.2 standard deviations, is reported. The relative rate is measured to be ${{f_{\Xi_b^-}}\over{f_{\Lambda_b^0}}}{\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-) = (5.7\pm1.8^{+0.8}_{-0.9})\times10^{-4}$, where $f_{\Xi_b^-}$ and $f_{\Lambda_b^0}$ are the $b\to\Xi_b^-$ and $b\to\Lambda_b^0$ fragmentation fractions, and ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ is the branching fraction. Assuming $f_{\Xi_b^-}/f_{\Lambda_b^0}$ is bounded between 0.1 and 0.3, the branching fraction ${\cal{B}}(\Xi_b^-\to\Lambda_b^0\pi^-)$ would lie in the range from $(0.57\pm0.21)\%$ to $(0.19\pm0.07)\%$.Comment: 7 pages, 2 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-047.htm

Study of the production of Λb0\Lambda_b^0 and B‾0\overline{B}^0 hadrons in pppp collisions and first measurement of the Λb0→J/ψpK−\Lambda_b^0\rightarrow J/\psi pK^- branching fraction

The product of the $\Lambda_b^0$ ($\overline{B}^0$) differential production cross-section and the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ ($\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$) is measured as a function of the beauty hadron transverse momentum, $p_{\rm T}$, and rapidity, $y$. The kinematic region of the measurements is $p_{\rm T}<20~{\rm GeV}/c$ and $2.0<y<4.5$. The measurements use a data sample corresponding to an integrated luminosity of $3~{\rm fb}^{-1}$ collected by the LHCb detector in $pp$ collisions at centre-of-mass energies $\sqrt{s}=7~{\rm TeV}$ in 2011 and $\sqrt{s}=8~{\rm TeV}$ in 2012. Based on previous LHCb results of the fragmentation fraction ratio, $f_{\Lambda_B^0}/f_d$, the branching fraction of the decay $\Lambda_b^0\rightarrow J/\psi pK^-$ is measured to be \begin{equation*} \mathcal{B}(\Lambda_b^0\rightarrow J/\psi pK^-)= (3.17\pm0.04\pm0.07\pm0.34^{+0.45}_{-0.28})\times10^{-4}, \end{equation*} where the first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the branching fraction of the decay $\overline{B}^0\rightarrow J/\psi\overline{K}^*(892)^0$, and the fourth is due to the knowledge of $f_{\Lambda_b^0}/f_d$. The sum of the asymmetries in the production and decay between $\Lambda_b^0$ and $\overline{\Lambda}_b^0$ is also measured as a function of $p_{\rm T}$ and $y$. The previously published branching fraction of $\Lambda_b^0\rightarrow J/\psi p\pi^-$, relative to that of $\Lambda_b^0\rightarrow J/\psi pK^-$, is updated. The branching fractions of $\Lambda_b^0\rightarrow P_c^+(\rightarrow J/\psi p)K^-$ are determined.Comment: 29 pages, 19figures. All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-032.htm

Search for the rare decays B0→J/ψγB^{0}\to J/\psi \gamma and Bs0→J/ψγB^{0}_{s} \to J/\psi \gamma

A search for the rare decay of a $B^{0}$ or $B^{0}_{s}$ meson into the final state $J/\psi\gamma$ is performed, using data collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}=7$ and $8$ TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$. The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than $1.7\times 10^{-6}$ for the $B^{0}\to J/\psi\gamma$ decay mode are excluded at 90% confidence level. For the $B^{0}_{s}\to J/\psi\gamma$ decay mode, branching fraction values larger than $7.4\times 10^{-6}$ are excluded at 90% confidence level, this is the first branching fraction limit for this decay.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-044.htm

Compressed representation of a partially defined integer function over multiple arguments

In OLAP (OnLine Analitical Processing) data are analysed in an n-dimensional cube. The cube may be represented as a partially defined function over n arguments. Considering that often the function is not defined everywhere, we ask: is there a known way of representing the function or the points in which it is defined, in a more compact manner than the trivial one