Gauss Sums and Quantum Mechanics

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved. The toroidal nature of the classical phase space leads to discrete position and momentum, and hence discrete time. The corresponding `path integrals' are finite sums whose normalisations are derived and which are shown to intertwine cyclicity and discreteness to give a finite version of Kelvin's method of images.Comment: 14 pages, LaTe

Demographic, social cognitive and social ecological predictors of intention and participation in screening for colorectal cancer

Extent: 10p.Background: Previous research points to differences between predictors of intention to screen for colorectal cancer (CRC) and screening behavior, and suggests social ecological factors may influence screening behavior. The aim of this study was to compare the social cognitive and social ecological predictors of intention to screen with predictors of participation. Methods: People aged 50 to 74 years recruited from the electoral roll completed a baseline survey (n = 376) and were subsequently invited to complete an immunochemical faecal occult blood test (iFOBT). Results: Multivariate analyses revealed five predictors of intention to screen and two predictors of participation. Perceived barriers to CRC screening and perceived benefits of CRC screening were the only predictor of both outcomes. There was little support for social ecological factors, but measurement problems may have impacted this finding. Conclusions: This study has confirmed that the predictors of intention to screen for CRC and screening behaviour, although overlapping, are not the same. Research should focus predominantly on those factors shown to predict participation. Perceptions about the barriers to screening and benefits of screening are key predictors of participation, and provide a focus for intervention programs.Tess A Gregory, Carlene Wilson, Amy Duncan, Deborah Turnbull, Stephen R Cole and Graeme Youn

Engaging diverse underserved communities to bridge the mammography divide

<p>Abstract</p> <p>Background</p> <p>Breast cancer screening continues to be underutilized by the population in general, but is particularly underutilized by traditionally underserved minority populations. Two of the most at risk female minority groups are American Indians/Alaska Natives (AI/AN) and Latinas. American Indian women have the poorest recorded 5-year cancer survival rates of any ethnic group while breast cancer is the number one cause of cancer mortality among Latina women. Breast cancer screening rates for both minority groups are near or at the lowest among all racial/ethnic groups. As with other health screening behaviors, women may intend to get a mammogram but their intentions may not result in initiation or follow through of the examination process. An accumulating body of research, however, demonstrates the efficacy of developing 'implementation intentions' that define when, where, and how a specific behavior will be performed. The formulation of intended steps in addition to addressing potential barriers to test completion can increase a person's self-efficacy, operationalize and strengthen their intention to act, and close gaps between behavioral intention and completion. To date, an evaluation of the formulation of implementation intentions for breast cancer screening has not been conducted with minority populations.</p> <p>Methods/Design</p> <p>In the proposed program, community health workers will meet with rural-dwelling Latina and American Indian women one-on-one to educate them about breast cancer and screening and guide them through a computerized and culturally tailored "implementation intentions" program, called <it>Healthy Living Kansas - Breast Health</it>, to promote breast cancer screening utilization. We will target Latina and AI/AN women from two distinct rural Kansas communities. Women attending community events will be invited by CHWs to participate and be randomized to either a mammography "implementation intentions" (<b>MI</b>^<b>2</b>) intervention or a comparison general breast cancer prevention informational intervention (<b>C</b>). CHWs will be armed with notebook computers loaded with our Healthy Living Kansas - Breast Health program and guide their peers through the program. Women in the <b>MI</b>^{<b>2 </b>}condition will receive assistance with operationalizing their screening intentions and identifying and addressing their stated screening barriers with the goal of guiding them toward accessing screening services near their community. Outcomes will be evaluated at 120-days post randomization via self-report and will include mammography utilization status, barriers, and movement along a behavioral stages of readiness to screen model.</p> <p>Discussion</p> <p>This highly innovative project will be guided and initiated by AI/AN and Latina community members and will test the practical application of emerging behavioral theory among minority persons living in rural communities.</p> <p>Trial Registration</p> <p>ClinicalTrials (NCT): <a href="http://www.clinicaltrials.gov/ct2/show/NCT01267110">NCT01267110</a></p

Tocilizumab in patients admitted to hospital with COVID-19 (RECOVERY): a randomised, controlled, open-label, platform trial

Background: In this study, we aimed to evaluate the effects of tocilizumab in adult patients admitted to hospital with COVID-19 with both hypoxia and systemic inflammation. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]), is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. Those trial participants with hypoxia (oxygen saturation &lt;92% on air or requiring oxygen therapy) and evidence of systemic inflammation (C-reactive protein ≥75 mg/L) were eligible for random assignment in a 1:1 ratio to usual standard of care alone versus usual standard of care plus tocilizumab at a dose of 400 mg–800 mg (depending on weight) given intravenously. A second dose could be given 12–24 h later if the patient's condition had not improved. The primary outcome was 28-day mortality, assessed in the intention-to-treat population. The trial is registered with ISRCTN (50189673) and ClinicalTrials.gov (NCT04381936). Findings: Between April 23, 2020, and Jan 24, 2021, 4116 adults of 21 550 patients enrolled into the RECOVERY trial were included in the assessment of tocilizumab, including 3385 (82%) patients receiving systemic corticosteroids. Overall, 621 (31%) of the 2022 patients allocated tocilizumab and 729 (35%) of the 2094 patients allocated to usual care died within 28 days (rate ratio 0·85; 95% CI 0·76–0·94; p=0·0028). Consistent results were seen in all prespecified subgroups of patients, including those receiving systemic corticosteroids. Patients allocated to tocilizumab were more likely to be discharged from hospital within 28 days (57% vs 50%; rate ratio 1·22; 1·12–1·33; p&lt;0·0001). Among those not receiving invasive mechanical ventilation at baseline, patients allocated tocilizumab were less likely to reach the composite endpoint of invasive mechanical ventilation or death (35% vs 42%; risk ratio 0·84; 95% CI 0·77–0·92; p&lt;0·0001). Interpretation: In hospitalised COVID-19 patients with hypoxia and systemic inflammation, tocilizumab improved survival and other clinical outcomes. These benefits were seen regardless of the amount of respiratory support and were additional to the benefits of systemic corticosteroids. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research

Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial

Background: Many patients with COVID-19 have been treated with plasma containing anti-SARS-CoV-2 antibodies. We aimed to evaluate the safety and efficacy of convalescent plasma therapy in patients admitted to hospital with COVID-19. Methods: This randomised, controlled, open-label, platform trial (Randomised Evaluation of COVID-19 Therapy [RECOVERY]) is assessing several possible treatments in patients hospitalised with COVID-19 in the UK. The trial is underway at 177 NHS hospitals from across the UK. Eligible and consenting patients were randomly assigned (1:1) to receive either usual care alone (usual care group) or usual care plus high-titre convalescent plasma (convalescent plasma group). The primary outcome was 28-day mortality, analysed on an intention-to-treat basis. The trial is registered with ISRCTN, 50189673, and ClinicalTrials.gov, NCT04381936. Findings: Between May 28, 2020, and Jan 15, 2021, 11558 (71%) of 16287 patients enrolled in RECOVERY were eligible to receive convalescent plasma and were assigned to either the convalescent plasma group or the usual care group. There was no significant difference in 28-day mortality between the two groups: 1399 (24%) of 5795 patients in the convalescent plasma group and 1408 (24%) of 5763 patients in the usual care group died within 28 days (rate ratio 1·00, 95% CI 0·93–1·07; p=0·95). The 28-day mortality rate ratio was similar in all prespecified subgroups of patients, including in those patients without detectable SARS-CoV-2 antibodies at randomisation. Allocation to convalescent plasma had no significant effect on the proportion of patients discharged from hospital within 28 days (3832 [66%] patients in the convalescent plasma group vs 3822 [66%] patients in the usual care group; rate ratio 0·99, 95% CI 0·94–1·03; p=0·57). Among those not on invasive mechanical ventilation at randomisation, there was no significant difference in the proportion of patients meeting the composite endpoint of progression to invasive mechanical ventilation or death (1568 [29%] of 5493 patients in the convalescent plasma group vs 1568 [29%] of 5448 patients in the usual care group; rate ratio 0·99, 95% CI 0·93–1·05; p=0·79). Interpretation: In patients hospitalised with COVID-19, high-titre convalescent plasma did not improve survival or other prespecified clinical outcomes. Funding: UK Research and Innovation (Medical Research Council) and National Institute of Health Research

Jørgensen’s

inequality for non-Archimedean metric space