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

Adult cancer risk in women who were breastfed as infants: large UK prospective study.

There are known short-term benefits in breastfed infants versus bottle-fed infants in terms of lower risks of infection and obesity in infancy and childhood, but the long-term effect on the risk of adult cancers is unclear. In a cohort of 1 in 4 UK women born in 1935-1950 we report the incidence of adult cancers in relation to having been breastfed in infancy. In median year 2001 (interquartile range 2000-2003) 548,741 women without prior cancer reported whether they had been breastfed. There was 81% agreement between women's report of having been breastfed and information on breastfeeding recorded when they were 2 years old. Participants were followed by record-linkage to national cancer registration, hospital admission and death databases. Cox regression yielded adjusted relative risks (RRs) and 95% confidence intervals (CI) by having been breastfed or not for eight cancer sites with > 2000 incident cases and for related conditions, where appropriate. Of the eight cancers examined here one association was highly statistically significant: an increase in colorectal cancer incidence among women who had been breastfed versus not (RR 1.18, 95% CI 1.12-1.24, n = 8651). To investigate further the findings for colorectal cancer, we studied eight other gastro-intestinal conditions, and found increased risks in women who had been breastfed versus not for benign colorectal polyps (RR 1.09, 95% CI 1.05-1.13, n = 17,677) and for appendicitis (RR 1.19, 95% CI 1.07-1.31, n = 2108). The greater risks of adult colorectal cancer, colorectal polyps and appendicitis associated with having been breastfed in infancy suggest possible long-term effects of infant feeding practices on the gastrointestinal tract. Further studies are required to clarify this novel association

Breast Cancer Risk in Relation to the Interval Between Menopause and Starting Hormone Therapy

Background: Although breast cancer risk is greater in users of estrogen-progestin than estrogen-only formulations of menopausal hormonal therapy, reports on their effects have been somewhat inconsistent. We investigated whether the timing of these therapies affected breast cancer incidence. Methods: A total of 1 129 025 postmenopausal UK women provided prospective information on hormonal therapy use and other factors relevant for breast cancer risk. We used Cox regression to estimate adjusted relative risks (RRs) of breast cancer in hormonal therapy users vs never users and calculated standardized incidence rates. All statistical tests were two-sided. Results: During 4.05 million woman-years of follow-up, 15 759 incident breast cancers occurred, with 7107 in current users of hormonal therapy. Breast cancer incidence was increased in current users of hormonal therapy, returning to that of never users a few years after use had ceased. The relative risks for breast cancer in current users were greater if hormonal therapy was begun before or soon after menopause than after a longer gap (Pheterogeneity <. 001, for both estrogen-only and estrogen-progestin formulations). Among current users of estrogen-only formulations, there was little or no increase in risk if use began 5 years or more after menopause (RR = 1.05, 95% confidence interval [CI] = 0.89 to 1.24), but risk was statistically significantly increased if use began before or less than 5 years after menopause (RR = 1.43, 95% CI = 1.35 to 1.51). A similar pattern was observed among current users of estrogen-progestin formulations (RR = 1.53, 95% CI = 1.38 to 1.70, and RR = 2.04, 95% CI = 1.95 to 2.14, respectively). At 50-59 years of age, annual standardized incidence rates for breast cancer were 0.30% (95% CI = 0.29% to 0.31%) among never users of hormone therapy and 0.43% (95% CI = 0.42% to 0.45%) and 0.61% (95% CI = 0.59% to 0.64%), respectively, among current users of estrogen-only and estrogen-progestin formulations who began use less than 5 years after menopause. Conclusions: There was substantial heterogeneity in breast cancer risk among current users of hormonal therapy. Risks were greater among users of estrogen-progestin than estrogen-only formulations and if hormonal therapy started at around the time of menopause than later

Adiposity and ischemic and hemorrhagic stroke: Prospective study in women and meta-analysis.

OBJECTIVE: To compare associations of body mass index (BMI) with ischemic stroke and hemorrhagic stroke risk, and to review the worldwide evidence. METHODS: We recruited 1.3 million previously stroke-free UK women between 1996 and 2001 (mean age 57 years [SD 5]) and followed them by record linkage for hospital admissions and deaths. We used Cox regression to estimate adjusted relative risks for ischemic and hemorrhagic (intracerebral or subarachnoid hemorrhage) stroke in relation to BMI. We conducted a meta-analysis of published findings from prospective studies on these associations. RESULTS: During an average follow-up of 11.7 years, there were 20,549 first strokes, of which 9,993 were specified as ischemic and 5,852 as hemorrhagic. Increased BMI was associated with an increased risk of ischemic stroke (relative risk 1.21 per 5 kg/m2 BMI, 95% confidence interval 1.18-1.23, p < 0.0001) but a decreased risk of hemorrhagic stroke (relative risk 0.89 per 5 kg/m2 BMI, 0.86-0.92, p < 0.0001). The BMI-associated trends for ischemic and hemorrhagic stroke were significantly different (heterogeneity: p < 0.0001) but were not significantly different for intracerebral hemorrhage (n = 2,790) and subarachnoid hemorrhage (n = 3,062) (heterogeneity: p = 0.5). Published data from prospective studies showed consistently greater BMI-associated relative risks for ischemic than hemorrhagic stroke with most evidence (prior to this study) coming from Asian populations. CONCLUSIONS: In UK women, higher BMI is associated with increased risk of ischemic stroke but decreased risk of hemorrhagic stroke. The totality of the available published evidence suggests that BMI-associated risks are greater for ischemic than for hemorrhagic stroke

HRT: a reappraisal of the risks and benefits

The document attached has been archived with permission from the editor of the Medical Journal of Australia. An external link to the publisher’s copy is included.In 2002, when results of the Women's Health Initiative (WHI) randomised controlled trial of hormone replacement therapy (HRT) showed an increased occurrence of breast cancer and thromboembolism, up to two-thirds of women taking HRT stopped the therapy, often without medical consultation. Recent analyses of the WHI data and other randomised controlled trials suggest that, although there are potential side effects and risks involved in taking HRT, these may be reduced by: using lower HRT doses; minimising or eliminating systemic progestogens; using non-oral routes in some women; and initiating HRT in symptomatic women near menopause. When HRT is initiated near menopause for symptom control, there may be additional benefits (reduced fracture and cardiovascular risk) that outweigh the risks (which are not significantly raised in women under age 60 years). Older women with continuing symptoms should not be denied HRT if their therapy and risks are assessed on an individual basis and each patient is aware of the risks.Alastair H MacLenna

Market outlook for satellite-based RE index insurance in agribusiness

In the current report a market outlook for satellite-based RE index insurance is elaborated on. Special thanks for the contributions of Andries Rosema of EARS Earth Environment Monitoring BV and Erik Klaassens of ECORYS Nederland BV. Also the views of experts who were consulted are acknowledged (see for the list of experts Appendix I)

Reproductive factors and specific histological types of breast cancer: prospective study and meta-analysis

Little is known about how reproductive factors affect the risk of breast cancers of different histology. In an analysis of prospective data on 1.2 million middle-aged UK women, we used proportional hazards models to estimate the relative risks of six histological types in relation to menarche, childbearing and menopause. During 8.7 million person-years of follow-up, 17 923 ductal, 3332 lobular, 1062 tubular, 944 mixed ductal lobular, 330 mucinous and 117 medullary cancers were diagnosed. The effect of both age at menarche and age at first birth was greatest for lobular tumours; relative risks per 5-year increase in age at menarche for ductal, lobular, and tubular cancers were 0.93 (0.87–0.99), 0.65 (0.56–0.76), and 0.75 (0.57–0.98), respectively (P-value for heterogeneity=0.0001); and the relative risks per 5-year increase in age at first birth were 1.10 (1.07–1.12), 1.23 (1.17–1.29), and 1.13 (1.03–1.23), respectively (P-value for heterogeneity=0.0006). Increasing parity reduced the risk of each tumour type, except medullary cancers, but the reduction in risk was greater for mucinous cancers than for any other subtype considered (P<0.05 for comparison with each other subtype in turn). The effect of menopause did not vary significantly by tumour histology. Meta-analysis of published results on the effects of age at menarche and age at first birth on ductal and lobular cancers were in keeping with our findings

Informing women about hormone replacement therapy: the consensus conference statement

Background: The risks/benefits balance of hormone replacement therapy is controversial. Information can influence consumers' knowledge and behavior; research findings about hormone replacement therapy are uncertain and the messages provided by the media are of poor quality and incomplete, preventing a fully informed decision making process. We therefore felt that an explicit, rigorous and structured assessment of the information needs on this issue was urgent and we opted for the organisation of a national consensus conference (CC) to assess the current status of the quality of information on hormone replacement therapy (HRT) and re-visit recent research findings on its risks/ benefits. Methods: We chose a structured approach based on the traditional CC method combined with a structured preparatory work supervised by an organising committee (OC) and a scientific board (SB). The OC and SB chose the members of the CC's jury and appointed three multidisciplinary working groups (MWG) which were asked to review clinical issues and different aspects of the quality of information. Before the CC, the three MWGs carried out: A literature review on the risk/benefit profile of HRT and two surveys on the quality of information on lay press and booklets targeted to women. A population survey on women's knowledge, attitude and practice was also carried out. The jury received the documents in advance, listened the presentations during the two-day meeting of the CCs, met immediately after in a closed-door meeting and prepared the final document. Participants were researchers, clinicians, journalists as well as consumers' representatives. Results: Key messages in the CC's deliberation were: a) women need to be fully informed about the transient nature of menopausal symptoms, about HRT risks and benefits and about the availability of non-pharmacological interventions; b) HRT is not recommended to prevent menopausal symptoms; c) the term "HRT" is misleading and "post menopausal hormone therapy" should be the preferred definition. Conclusion: This CC led to the identification of specific information drawbacks. Women are exposed to messages that are often partial, non evidence-based nor transparently developed. The structured and participative methodology of this CC allowed a multidisciplinary perspective and a substantial lay people input

Recent declines in breast cancer incidence: mounting evidence that reduced use of menopausal hormones is largely responsible

Substantial reductions in breast cancer incidence in women 50 years old or older have been observed recently in many developed countries, and falling use of menopausal hormone therapy (HT) remains the most plausible explanation. In keeping with recent observations from the Women's Health Initiative, a report from the California Teachers Study cohort in this issue of Breast Cancer Research adds to this growing evidence. The investigators found a 26% reduction in invasive breast cancer in the cohort from 2000-2002 to 2003-2005, which accompanied an estimated 64% drop in HT use between 2000-2001 and 2005-2006. By collating individual data on the use of HT and breast cancer incidence, they also demonstrated that the decline in incidence was concentrated in women who had ceased HT use. The decline reflected a decrease predominantly in oestrogen receptor-positive tumours in the context of stable screening patterns over the study period. Millions of women continue to use HT, and these findings support carefully targeted short duration use as an important ongoing strategy to minimise breast cancer risk