Binomial-coefficient multiples of irrationals

Denote by $x$ a random infinite path in the graph of Pascal's triangle (left and right turns are selected independently with fixed probabilities) and by $d_n(x)$ the binomial coefficient at the $n$'th level along the path $x$. Then for a dense $G_{\delta}$ set of $\theta$ in the unit interval, $\{d_n(x)\theta \}$ is almost surely dense but not uniformly distributed modulo 1.Comment: 10 pages, to appear in Monatshefte f. Mat

Persistent Pesticides in Human Breast Milk and Cryptorchidism

INTRODUCTION: Prenatal exposure to some pesticides can adversely affect male reproductive health in animals. We investigated a possible human association between maternal exposure to 27 organochlorine compounds used as pesticides and cryptorchidism among male children. DESIGN: Within a prospective birth cohort, we performed a case–control study; 62 milk samples from mothers of cryptorchid boys and 68 from mothers of healthy boys were selected. Milk was collected as individual pools between 1 and 3 months postpartum and analyzed for 27 organochlorine pesticides. RESULTS: Eight organochlorine pesticides were measurable in all samples (medians; nanograms per gram lipid) for cases/controls: 1,1-dichloro-2,2-bis(4-chlorophenyl)ethylene (p,p′-DDE): 97.3/83.8; β-hexachlorocyclohexane (β-HCH): 13.6/12.3; hexachlorobenzene (HCB): 10.6/8.8; α -endosulfan: 7.0/6.7; oxychlordane: 4.5/4.1; 1,1,1-trichloro-2,2-bis(4-chlorophenyl)ethane (p,p′-DDT): 4.6/4.0; dieldrin: 4.1/3.1; cis-heptachloroepoxide (cis-HE): 2.5/2.2. Five compounds [octachlorostyrene (OCS); pentachlorobenzene, 1,1-dichloro-2,2-bis(4-chlorophenyl)ethane (p,p′-DDD); o,p′-DDT; mirex] were measurable in most samples (detection rates 90.8–99.2%) but in lower concentrations. For methoxychlor, cis-chlordane, pentachloroanisole (PCA), γ -HCH, 1,1-dichloro-2-(2-chlorophenyl)-2,2(4-chlorophenyl)ethane, trans-chlordane, α -HCH, and o,p′-DDE, both concentrations and detection rates were low (26.5–71.5%). Heptachlor, HCH (δ, ɛ ), aldrin, β-endosulfan and trans-heptachloroepoxide were detected at negligible concentrations and low detection rates and were not analyzed further. Seventeen of 21 organochlorine pesticides [p,p′-DDT, p,p′-DDE, p,p′-DDD, o,p′-DDT, HCH (α , β, γ ), HCB, PCA, α -endosulfan, cis-HE, chlordane (cis-, trans-) oxychlordane, methoxychlor, OCS, and dieldrin] were measured in higher median concentrations in case milk than in control milk. Apart from trans-chlordane (p = 0.012), there were no significant differences between cryptorchid and healthy boys for individual chemicals. However, combined statistical analysis of the eight most abundant persistent pesticides showed that pesticide levels in breast milk were significantly higher in boys with cryptorchidism (p = 0.032). CONCLUSION: The association between congenital cryptorchidism and some persistent pesticides in breast milk as a proxy for maternal exposure suggests that testicular descent in the fetus may be adversely affected

Persistent and changing job strain and risk of coronary heart disease. A population-based cohort study of 1.6 million employees in Denmark

Objectives This study aimed to examine the association between job strain and incident coronary heart disease (CHD) in Denmark, while accounting for changes of job strain. Methods We included all employees residing in Denmark in 2000, aged 30-59 years with no prevalent CHD (N=1660 150). We determined exposure to job strain from 1996-2009 using a job exposure matrix (JEM) with annual updates. Follow-up for incident CHD was from 2001-2010 via linkage to health records. We used Cox regression to calculate hazard ratios (HR) and 95% confidence intervals (CI) for the association between job strain and incident CHD. Results During 16.1 million person-years, we identified 24 159 incident CHD cases (15.0 per 10 000 person-years). After adjustment for covariates, job strain in 2000 predicted onset of CHD during a mean follow-up of 9.71 years (HR 1.10, 95% CI 1.07-1.13). When analyzing changes in job strain from one year to the next and CHD in the subsequent year, persistent job strain (HR 1.07, 95% CI 1.03-1.10), onset of job strain (HR 1.20, 95% CI 1.12-1.29) and removal of strain (HR 1.20, 95% CI 1.12-1.28) were associated with higher CHD incidence compared to persistent no job strain. Associations were similar among men and women. Conclusions Job strain is associated with a higher risk of incident CHD in Denmark. As we used a JEM, we can rule out reporting bias. However, under- or overestimation of associations is possible due to non-differential misclassification of job strain and residual confounding by socioeconomic position.Peer reviewe