Linear law for the logarithms of the Riemann periods at simple critical zeta zeros

Each simple zero 1/2 + iγn of the Riemann zeta function on the critical line with γn > 0 is a center for the flow s˙ = ξ(s) of the Riemann xi function with an associated period Tn. It is shown that, as γn →∞, log Tn ≥ π/4 γn + O(log γn). Numerical evaluation leads to the conjecture that this inequality can be replaced by an equality. Assuming the Riemann Hypothesis and a zeta zero separation conjecture γn+1 − γn≥ γn-θ for some exponent θ > 0, we obtain the upper bound log Tn ≤ γn2 + θ Assuming a weakened form of a conjecture of Gonek, giving a bound for the reciprocal of the derivative of zeta at each zero, we obtain the expected upper bound for the periods so, conditionally, log Tn = π/ 4 γn +O(log γn). Indeed, this linear relationship is equivalent to the given weakened conjecture, which implies the zero separation conjecture, provided the exponent is sufficiently large. The frequencies corresponding to the periods relate to natural eigenvalues for the Hilbert–Polya conjecture. They may provide a goal for those seeking a self-adjoint operator related to the Riemann hypothesis

The Lotic Intersite Nitrogen Experiments: an example of successful ecological research collaboration

Collaboration is an essential skill for modern ecologists because it brings together diverse expertise, viewpoints, and study systems. The Lotic Intersite Nitrogen eXperiments (LINX I and II), a 17-y research endeavor involving scores of early- to late-career stream ecologists, is an example of the benefits, challenges, and approaches of successful collaborative research in ecology. The scientific success of LINX reflected tangible attributes including clear scientific goals (hypothesis-driven research), coordinated research methods, a team of cooperative scientists, excellent leadership, extensive communication, and a philosophy of respect for input from all collaborators. Intangible aspects of the collaboration included camaraderie and strong team chemistry. LINX further benefited from being part of a discipline in which collaboration is a tradition, clear data-sharing and authorship guidelines, an approach that melded field experiments and modeling, and a shared collaborative goal in the form of a universal commitment to see the project and resulting data products through to completion

Improved dietary guidelines for vitamin D: application of individual participant data (IPD)-level meta-regression analyses

Dietary Reference Values (DRVs) for vitamin D have a key role in the prevention of vitamin D deficiency. However, despite adopting similar risk assessment protocols, estimates from authoritative agencies over the last 6 years have been diverse. This may have arisen from diverse approaches to data analysis. Modelling strategies for pooling of individual subject data from cognate vitamin D randomized controlled trials (RCTs) are likely to provide the most appropriate DRV estimates. Thus, the objective of the present work was to undertake the first-ever individual participant data (IPD)-level meta-regression, which is increasingly recognized as best practice, from seven winter-based RCTs (with 882 participants ranging in age from 4 to 90 years) of the vitamin D intake–serum 25-hydroxyvitamin D (25(OH)D) dose-response. Our IPD-derived estimates of vitamin D intakes required to maintain 97.5% of 25(OH)D concentrations >25, 30, and 50 nmol/L across the population are 10, 13, and 26 µg/day, respectively. In contrast, standard meta-regression analyses with aggregate data (as used by several agencies in recent years) from the same RCTs estimated that a vitamin D intake requirement of 14 µg/day would maintain 97.5% of 25(OH)D >50 nmol/L. These first IPD-derived estimates offer improved dietary recommendations for vitamin D because the underpinning modeling captures the between-person variability in response of serum 25(OH)D to vitamin D intake

Population-level risks of alcohol consumption by amount, geography, age, sex, and year: a systematic analysis for the Global Burden of Disease Study 2020

Background: The health risks associated with moderate alcohol consumption continue to be debated. Small amounts of alcohol might lower the risk of some health outcomes but increase the risk of others, suggesting that the overall risk depends, in part, on background disease rates, which vary by region, age, sex, and year. Methods: For this analysis, we constructed burden-weighted dose–response relative risk curves across 22 health outcomes to estimate the theoretical minimum risk exposure level (TMREL) and non-drinker equivalence (NDE), the consumption level at which the health risk is equivalent to that of a non-drinker, using disease rates from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2020 for 21 regions, including 204 countries and territories, by 5-year age group, sex, and year for individuals aged 15–95 years and older from 1990 to 2020. Based on the NDE, we quantified the population consuming harmful amounts of alcohol. Findings: The burden-weighted relative risk curves for alcohol use varied by region and age. Among individuals aged 15–39 years in 2020, the TMREL varied between 0 (95% uncertainty interval 0–0) and 0·603 (0·400–1·00) standard drinks per day, and the NDE varied between 0·002 (0–0) and 1·75 (0·698–4·30) standard drinks per day. Among individuals aged 40 years and older, the burden-weighted relative risk curve was J-shaped for all regions, with a 2020 TMREL that ranged from 0·114 (0–0·403) to 1·87 (0·500–3·30) standard drinks per day and an NDE that ranged between 0·193 (0–0·900) and 6·94 (3·40–8·30) standard drinks per day. Among individuals consuming harmful amounts of alcohol in 2020, 59·1% (54·3–65·4) were aged 15–39 years and 76·9% (73·0–81·3) were male. Interpretation: There is strong evidence to support recommendations on alcohol consumption varying by age and location. Stronger interventions, particularly those tailored towards younger individuals, are needed to reduce the substantial global health loss attributable to alcohol

An evaluation of the effect of an angiotensin-converting enzyme inhibitor on the growth rate of small abdominal aortic aneurysms: a randomized placebo-controlled trial (AARDVARK)

Aims: The AARDVARK (Aortic Aneurysmal Regression of Dilation: Value of ACE-Inhibition on RisK) trial investigated whether ACE-inhibition reduces small abdominal aortic aneurysms (AAA) growth rate, independent of blood pressure (BP) lowering. Methods and results: A three-arm, multi-centre, single-blind, and randomized controlled trial (ISRCTN51383267) was conducted in 14 hospitals in England. Subjects aged ≥55 years with AAA diameter 3.0–5.4 cm were randomized 1:1:1 to receive perindopril arginine 10 mg, or amlodipine 5 mg, or placebo and followed 3–6 monthly over 2 years. The primary outcome was aneurysm growth rate (based on external antero-posterior ultrasound measurements in the longitudinal plane), determined by multi-level modelling to provide maximum likelihood estimates. Two hundred and twenty-four subjects were randomized (2011–2013) to placebo (n = 79), perindopril (n = 73), or amlodipine (n = 72). Mean (SD) changes in mid-trial systolic BP (12 months) were 0.5 (14.3) mmHg, P = 0.78 compared with baseline, −9.5 (13.1) mmHg (P < 0.001), and −6.7 (12.0) mmHg (P < 0.001), respectively. No significant differences in the modelled annual growth rates were apparent [1.68 mm (SE 0.2), 1.77 mm (0.2), and 1.81 mm (0.2), respectively]. The estimated difference in annual growth between the perindopril and placebo groups was 0.08 mm (CI −0.50, 0.65). Similar numbers of AAAs in each group reached 5.5 cm diameter and/or underwent elective surgery: 11 receiving placebo, 10 perindopril, and 11 amlodipine. Conclusion: Small AAA growth rates were lower than anticipated, but there was no significant impact of perindopril compared with placebo or placebo and amlodipine, combined despite more effective BP lowering

Short-term outcome of treatment limitation discussions for newborn infants, a multicentre prospective observational cohort study

Objective To determine the short-term outcomes of babies for whom clinicians or parents discussed the limitation of life-sustaining treatment (LST). Design Prospective multicentre observational study. Setting Two level 3, six level 2 and one level 1 neonatal units in the North-East London Neonatal Network. Participants A total of 87 babies including 68 for whom limiting LST was discussed with parents and 19 babies died without discussion of limiting LST in the labour ward or neonatal unit. Outcome measures Final decision reached after discussions about limiting LST and neonatal unit outcomes (death or survived to discharge) for babies. Results Withdrawing LST, withholding LST and do not resuscitate (DNR) order was discussed with 48, 16 and 4 parents, respectively. In 49/68 (72%) cases decisions occurred in level 3 and 19 cases in level 2 units. Following the initial discussions, 34/68 parents made the decision to continue LST. In 33/68 cases, a second opinion was obtained. The parents of 14/48 and 2/16 babies did not agree to withdraw and withhold LST, respectively. Forty-seven out of 87 babies (54%) died following limitation of LST, 28/87 (32%) died receiving full intensive care support, 5/87 (6%) survived following a decision to limit LST and 7/87 (8%) babies survived following decision to continue LST. Conclusions A significant proportion of parents chose to continue treatment following discussions regarding limiting LST for their babies, and a proportion of these babies survived to neonatal unit discharge. The long-term outcomes of babies who survive following limiting LST discussion need to be investigated

Endovascular Abdominal Aortic Aneurysm Repair With Ovation Alto Stent Graft: Protocol for the ALTAIR (ALTo endogrAft Italian Registry) Study

Background: Since 2010, the Ovation Abdominal Stent Graft System has offered an innovative sealing option for abdominal aortic aneurysm (AAA) by including a sealing ring filled with polymer 13 mm from the renal arteries. In August 2020, the redesigned Ovation Alto, with a sealing ring 6 mm closer to the top of the fabric, received CE Mark approval. Objective: This registry study aims to evaluate intraoperative, perioperative, and postoperative results in patients treated by the Alto stent graft (Endologix Inc.) for elective AAA repair in a multicentric consecutive experience. Methods: All consecutive eligible patients submitted to endovascular aneurysm repair (EVAR) by Alto Endovascular AAA implantation will be included in this analysis. Patients will be submitted to EVAR procedures based on their own preferences, anatomical features, and operators experience. An estimated number of 300 patients submitted to EVAR with Alto stent graft should be enrolled. It is estimated that the inclusion period will be 24 months. The follow-up period is set to be 5 years. Full data sets and cross-sectional images of contrast-enhanced computed tomography scan performed before EVAR, at the first postoperative month, at 24 or 36 months, and at 5-year follow-up interval will be reported in the central database for a centralized core laboratory review of morphological changes. The primary endpoint of the study is to evaluate the technical and clinical success of EVAR with the Alto stent graft in short- (90-day), mid- (1-year), and long-term (5-year) follow-up periods. The following secondary endpoints will be also addressed: operative time; intraoperative radiation exposure; contrast medium usage; AAA sac shrinkage at 12-month and 5-year follow-up; any potential role of patients' baseline characteristics, valuated on preoperative computed tomography angiographic study, and of device configuration (number of component) in the primary endpoint. Results: The study is currently in the recruitment phase and the final patient is expected to be treated by the end of 2023 and then followed up for 5 years. A total of 300 patients will be recruited. Analyses will focus on primary and secondary endpoints. Updated results will be shared at 1- and 3-5-year follow-ups. Conclusions: The results from this registry study could validate the safety and effectiveness of the new design of the Ovation Alto Stent Graft. The technical modifications to the endograft could allow for accommodation of a more comprehensive range of anatomies on-label

Effects of alteplase for acute stroke on the distribution of functional outcomes: a pooled analysis of 9 trials

Background—Thrombolytic therapy with intravenous alteplase within 4.5 hours of ischemic stroke onset increases the overall likelihood of an excellent outcome (no, or nondisabling, symptoms). Any improvement in functional outcome distribution has value, and herein we provide an assessment of the effect of alteplase on the distribution of the functional level by treatment delay, age, and stroke severity. Methods—Prespecified pooled analysis of 6756 patients from 9 randomized trials comparing alteplase versus placebo/open control. Ordinal logistic regression models assessed treatment differences after adjustment for treatment delay, age, stroke severity, and relevant interaction term(s). Results—Treatment with alteplase was beneficial for a delay in treatment extending to 4.5 hours after stroke onset, with a greater benefit with earlier treatment. Neither age nor stroke severity significantly influenced the slope of the relationship between benefit and time to treatment initiation. For the observed case mix of patients treated within 4.5 hours of stroke onset (mean 3 hours and 20 minutes), the net absolute benefit from alteplase (ie, the difference between those who would do better if given alteplase and those who would do worse) was 55 patients per 1000 treated (95% confidence interval, 13–91; P=0.004). Conclusions—Treatment with intravenous alteplase initiated within 4.5 hours of stroke onset increases the chance of achieving an improved level of function for all patients across the age spectrum, including the over 80s and across all severities of stroke studied (top versus bottom fifth means: 22 versus 4); the earlier that treatment is initiated, the greater the benefit

The impact of the UK COVID-19 pandemic on patient-reported health outcomes after stroke: a retrospective sequential comparison

BACKGROUND AND PURPOSE: The COVID-19 pandemic and related social isolation measures are likely to have adverse consequences on community healthcare provision and outcome after acute illnesses treated in hospital, including stroke. We aimed to evaluate the impact of the COVID-19 pandemic on patient-reported health outcomes after hospital admission for acute stroke. METHODS: This retrospective study included adults with acute stroke admitted to the University College Hospital NHS Foundation Trust Hyperacute Stroke Unit. We included two separate cohorts of consecutively enrolled patients from the same geographical population at two time points: 16th March-16th May 2018 (pre-COVID-19 pandemic); and 16th March-16th May 2020 (during the COVID-19 pandemic). Patients in both cohorts completed the validated Patient Reported Outcomes Measurement Information System-29 (PROMIS-29 version 2.0) at 30 days after stroke. RESULTS: We included 205 patients who were alive at 30 days (106 admitted before and 99 admitted during the COVID-19 pandemic), of whom 201/205 (98%) provided patient-reported health outcomes. After adjustment for confounding factors, admission with acute stroke during the COVID-19 pandemic was independently associated with increased anxiety (β = 28.0, p < 0.001), fatigue (β = 9.3, p < 0.001), depression (β = 4.5, p = 0.002), sleep disturbance (β = 2.3, p = 0.018), pain interference (β = 10.8, p < 0.001); and reduced physical function (β = 5.2, p < 0.001) and participation in social roles and activities (β = 6.9, p < 0.001). CONCLUSION: Compared with the pre-pandemic cohort, patients admitted with acute stroke during the first wave of the COVID-19 pandemic reported poorer health outcomes at 30 day follow-up in all domains. Stroke service planning for any future pandemic should include measures to mitigate this major adverse impact on patient health