Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

A rapid method for assessing the RNA-binding potential of a protein

In recent years, evidence has emerged for the existence of many diverse types of RNA, which play roles in a wide range of biological processes in all kingdoms of life. These molecules generally do not, however, act in isolation, and identifying which proteins partner with RNA is a major challenge. Many methods, in vivo and in vitro, have been used to address this question, including combinatorial or high-throughput approaches, such as systematic evolution of ligands, cross-linking and immunoprecipitation and RNA immunoprecipitation combined with deep sequencing. However, most of these methods are not trivial to pursue and often require substantial optimization before results can be achieved. Here, we demonstrate a simple technique that allows one to screen proteins for RNA-binding properties in a gel-shift experiment and can be easily implemented in any laboratory. This assay should be a useful first-pass tool for assessing whether a protein has RNA- or DNA-binding properties, prior to committing resources to more complex procedure

Association between active commuting and incident cardiovascular disease, cancer, and mortality: prospective cohort study

Objective: To investigate the association between active commuting and incident cardiovascular disease (CVD), cancer, and all cause mortality. Design: Prospective population based study. Setting: UK Biobank. Participants: 263 450 participants (106 674 (52%) women; mean age 52.6), recruited from 22 sites across the UK. The exposure variable was the mode of transport used (walking, cycling, mixed mode v non-active (car or public transport)) to commute to and from work on a typical day. Main outcome measures: Incident (fatal and non-fatal) CVD and cancer, and deaths from CVD, cancer, or any causes. Results: 2430 participants died (496 were related to CVD and 1126 to cancer) over a median of 5.0 years (interquartile range 4.3-5.5) follow-up. There were 3748 cancer and 1110 CVD events. In maximally adjusted models, commuting by cycle and by mixed mode including cycling were associated with lower risk of all cause mortality (cycling hazard ratio 0.59, 95% confidence interval 0.42 to 0.83, P=0.002; mixed mode cycling 0.76, 0.58 to 1.00, P&lt;0.05), cancer incidence (cycling 0.55, 0.44 to 0.69, P&lt;0.001; mixed mode cycling 0.64, 0.45 to 0.91, P=0.01), and cancer mortality (cycling 0.60, 0.40 to 0.90, P=0.01; mixed mode cycling 0.68, 0.57 to 0.81, P&lt;0.001). Commuting by cycling and walking were associated with a lower risk of CVD incidence (cycling 0.54, 0.33 to 0.88, P=0.01; walking 0.73, 0.54 to 0.99, P=0.04) and CVD mortality (cycling 0.48, 0.25 to 0.92, P=0.03; walking 0.64, 0.45 to 0.91, P=0.01). No statistically significant associations were observed for walking commuting and all cause mortality or cancer outcomes. Mixed mode commuting including walking was not noticeably associated with any of the measured outcomes. Conclusions: Cycle commuting was associated with a lower risk of CVD, cancer, and all cause mortality. Walking commuting was associated with a lower risk of CVD independent of major measured confounding factors. Initiatives to encourage and support active commuting could reduce risk of death and the burden of important chronic conditions

The impact of confounding on the associations of different adiposity measures with the incidence of cardiovascular disease: a cohort study of 296 535 adults of white European descent

Aims: The data regarding the associations of body mass index (BMI) with cardiovascular (CVD) risk, especially for those at the low categories of BMI, are conflicting. The aim of our study was to examine the associations of body composition (assessed by five different measures) with incident CVD outcomes in healthy individuals. Methods and results: A total of 296 535 participants (57.8% women) of white European descent without CVD at baseline from the UK biobank were included. Exposures were five different measures of adiposity. Fatal and non-fatal CVD events were the primary outcome. Low BMI (≤18.5 kg m−2) was associated with higher incidence of CVD and the lowest CVD risk was exhibited at BMI of 22–23 kg m−2 beyond, which the risk of CVD increased. This J-shaped association attenuated substantially in subgroup analyses, when we excluded participants with comorbidities. In contrast, the associations for the remaining adiposity measures were more linear; 1 SD increase in waist circumference was associated with a hazard ratio of 1.16 [95% confidence interval (CI) 1.13–1.19] for women and 1.10 (95% CI 1.08–1.13) for men with similar magnitude of associations for 1 SD increase in waist-to-hip ratio, waist-to-height ratio, and percentage body fat mass. Conclusion: Increasing adiposity has a detrimental association with CVD health in middle-aged men and women. The association of BMI with CVD appears more susceptible to confounding due to pre-existing comorbidities when compared with other adiposity measures. Any public misconception of a potential ‘protective’ effect of fat on CVD risk should be challenged

Sleep characteristics modify the association between genetic predisposition to obesity and anthropometric measurements in 119,679 UK Biobank participants

Background - Obesity is a multifactorial condition influenced by genetics, lifestyle and environment. Objective - To investigate whether the association between a validated genetic profile risk score for obesity (GPRS-obesity) with body mass index (BMI) and waist circumference (WC) was modified by sleep characteristics. Design - This study included cross-sectional data from 119,859 white European adults, aged 37-73 years, participating on the UK Biobank. Interactions between GPRS-obesity, and sleep characteristics (sleep duration, chronotype, day napping, and shift work) in their effects on BMI and WC were investigated. Results - The GPRS-obesity was associated with BMI (β:0.57 kg.m-2 per standard deviation (SD) increase in GPRS, [95%CI:0.55, 0.60]; P=6.3x10-207) and WC (β:1.21 cm, [1.15, 1.28]; P=4.2x10-289). There were significant interactions between GPRS-obesity and a variety of sleep characteristics in their relationship with BMI (P-interaction &lt;0.05). In participants who slept &lt;7 hrs or &gt;9 hrs daily, the effect of GPRS-obesity on BMI was stronger (β:0.60 [0.54, 0.65] and 0.73 [0.49, 0.97] kg.m-2 per SD increase in GPRS, respectively) than in normal length sleepers (7-9 hours; β:0.52 [0.49, 0.55] kg.m-2 per SD). A similar pattern was observed for shiftworkers (β:0.68 [0.59, 0.77] versus 0.54 [0.51, 0.58] kg.m-2 for non-shiftworkers) and for night-shiftworkers (β:0.69 [0.56, 0.82] versus 0.55 [0.51, 0.58] kg.m-2 for non-night- shiftworkers), for those taking naps during the day (β:0.65 [0.52, 0.78] versus 0.51 [0.48, 0.55] kg.m-2 for those who never/rarely had naps) and for those with a self-reported evening chronotype (β:0.72 [0.61, 0.82] versus β:0.52 [0.47, 0.57] kg.m-2 for morning chronotype). Similar findings were obtained using WC as the outcome. Conclusions – This study shows that the association between genetic risk for obesity and phenotypic adiposity measures is exacerbated by adverse sleeping characteristics

Dietary fat and total energy intake modifies the association of genetic profile risk score on obesity: evidence from 48 170 UK Biobank participants

Background: Obesity is a multifactorial condition influenced by both genetics and lifestyle. The aim of this study was to investigate whether the association between a validated genetic profile risk score for obesity (GPRS-obesity) and body mass index (BMI) or waist circumference (WC) was modified by macronutrient intake in a large general population study. Methods: This study included cross-sectional data from 48 170 white European adults, aged 37–73 years, participating on the UK Biobank. Interactions between GPRS-obesity, and macronutrient intake (including total energy, protein, fat, carbohydrate and dietary fibre intake) and its effects on BMI and WC were investigated. Results: The 93-SNPs genetic profile risk score was associated with a higher BMI (β:0.57 kg.m−2 per standard deviation (s.d.) increase in GPRS, [95%CI:0.53–0.60]; P=1.9 × 10−183) independent of major confounding factors. There was a significant interaction between GPRS and total fat intake (P[interaction]=0.007). Among high fat intake individuals, BMI was higher by 0.60 [0.52, 0.67] kg.m−2 per s.d. increase in GPRS-obesity; the change in BMI with GPRS was lower among low fat intake individuals (β:0.50 [0.44, 0.57] kg.m-2). Significant interactions with similar patterns were observed for saturated fat intake (High β:0.66 [0.59, 0.73] versus Low β:0.49 [0.42, 0.55] kg.m-2, P-interaction=2 × 10-4), and total energy intake (High β:0.58 [0.51, 0.64] versus Low β:0.49 [0.42, 0.56] kg.m−2, P-interaction=0.019), but not for protein intake, carbohydrate intake and fiber intake (P-interaction &gt;0.05). The findings were broadly similar using WC as the outcome. Conclusions: These data suggest that the benefits of reducing the intake of fats and total energy intake, may be more important in individuals with high genetic risk for obesity

Associations between diabetes and both cardiovascular disease and all-cause mortality are modified by grip strength: evidence from UK Biobank, a prospective population-based cohort study

OBJECTIVE Grip strength and diabetes are predictors of mortality and cardiovascular disease (CVD), but whether these risk factors interact to predispose to adverse health outcomes is unknown. This study determined the interactions between diabetes and grip strength and their association with health outcomes. RESEARCH DESIGN AND METHODS We undertook a prospective, general population cohort study by using UK Biobank. Cox proportional hazards models were used to explore the associations between both grip strength and diabetes and the outcomes of all-cause mortality and CVD incidence/mortality as well as to test for interactions between diabetes and grip strength. RESULTS 347,130 UK Biobank participants with full data available (mean age 55.9 years, BMI 27.2 kg/m2, 54.2% women) were included in the analysis, of which 13,373 (4.0%) had diabetes. Over a median follow-up of 4.9 years (range 3.3–7.8 years), 6,209 died (594 as a result of CVD), and 4,301 developed CVD. Participants with diabetes were at higher risk of all-cause and CVD mortality and CVD incidence. Significant interactions (P &lt; 0.05) existed whereby the risk of CVD mortality was higher in participants with diabetes with low (hazard ratio [HR] 4.05 [95% CI 2.72, 5.80]) versus high (HR 1.46 [0.87, 2.46]) grip strength. Similar results were observed for all-cause mortality and CVD incidence. CONCLUSIONS Risk of adverse health outcomes among people with diabetes is lower in those with high grip strength. Low grip strength may be useful to identify a higher-risk subgroup of patients with diabetes. Intervention studies are required to determine whether resistance exercise can reduce risk

Associations of grip strength with cardiovascular, respiratory, and cancer outcomes and all cause mortality: prospective cohort study of half a million UK Biobank participants

Objective: To investigate the association of grip strength with disease specific incidence and mortality and whether grip strength enhances the prediction ability of an established office based risk score. Design: Prospective population based study. Setting: UK Biobank. Participants: 502 293 participants (54% women) aged 40-69 years. Main outcome measures: All cause mortality as well as incidence of and mortality from cardiovascular disease, respiratory disease, chronic obstructive pulmonary disease, and cancer (all cancer, colorectal, lung, breast, and prostate). Results: Of the participants included in analyses, 13 322 (2.7%) died over a mean of 7.1 (range 5.3-9.9) years’ follow-up. In women and men, respectively, hazard ratios per 5 kg lower grip strength were higher (all at P&lt;0.05) for all cause mortality (1.20, 95% confidence interval 1.17 to 1.23, and 1.16, 1.15 to 1.17) and cause specific mortality from cardiovascular disease (1.19, 1.13 to 1.25, and 1.22, 1.18 to 1.26), all respiratory disease (1.31, 1.22 to 1.40, and 1.24, 1.20 to 1.28), chronic obstructive pulmonary disease (1.24, 1.05 to 1.47, and 1.19, 1.09 to 1.30), all cancer (1.17, 1.13 to 1.21, 1.10, 1.07 to 1.13), colorectal cancer (1.17, 1.04 to 1.32, and 1.18, 1.09 to 1.27), lung cancer (1.17, 1.07 to 1.27, and 1.08, 1.03 to 1.13), and breast cancer (1.24, 1.10 to 1.39) but not prostate cancer (1.05, 0.96 to 1.15). Several of these relations had higher hazard ratios in the younger age group. Muscle weakness (defined as grip strength &lt;26 kg for men and &lt;16 kg for women) was associated with a higher hazard for all health outcomes, except colon cancer in women and prostate cancer and lung cancer in both men and women. The addition of handgrip strength improved the prediction ability, based on C index change, of an office based risk score (age, sex, diabetes diagnosed, body mass index, systolic blood pressure, and smoking) for all cause (0.013) and cardiovascular mortality (0.012) and incidence of cardiovascular disease (0.009). Conclusion: Higher grip strength was associated with a range of health outcomes and improved prediction of an office based risk score. Further work on the use of grip strength in risk scores or risk screening is needed to establish its potential clinical utility

Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page

Red and processed meat consumption and breast cancer: UK Biobank cohort study and meta-analysis

Aim: Red and processed meat may be risk factors for breast cancer due to their iron content, administration of oestrogens to cattle or mutagens created during cooking. We studied the associations in UK Biobank and then included the results in a meta-analysis of published cohort studies. Methods: UK Biobank, a general population cohort study, recruited participants aged 40–69 years. Incident breast cancer was ascertained via linkage to routine hospital admission, cancer registry and death certificate data. Univariate and multivariable Cox proportional hazard models were used to explore the associations between red and processed meat consumption and breast cancer. Previously published cohort studies were identified from a systematic review using PubMed and Ovid and a meta-analysis conducted using a random effects model. Results: Over a median of 7 years follow-up, 4819 of the 262,195 women developed breast cancer. The risk was increased in the highest tertile (&gt;9 g/day) of processed meat consumption (adjusted hazard ratio [HR] 1.21, 95% confidence interval [CI] 1.08–1.35, p = 0.001). Collation with 10 previous cohort studies provided data on 40,257 incident breast cancers in 1.65 million women. On meta-analysis, processed meat consumption was associated with overall (relative risk [RR] 1.06, 95% CI 1.01–1.11) and post-menopausal (RR 1.09, 95% CI 1.03–1.15), but not pre-menopausal (RR 0.99, 95% CI 0.88–1.10), breast cancer. In UK Biobank and the meta-analysis, red meat consumption was not associated with breast cancer (adjusted HR 0.99 95% CI 0.88–1.12 and RR 1.03, 95% CI 0.99–1.08, respectively). Conclusions: Consumption of processed meat, but not red meat, may increase the risk of breast cancer