The limits of normal approximation for adult height

Adult height inspired the first biometrical and quantitative genetic studies and is a test-case trait for understanding heritability. The studies of height led to formulation of the classical polygenic model, that has a profound influence on the way we view and analyse complex traits. An essential part of the classical model is an assumption of additivity of effects and normality of the distribution of the residuals. However, it may be expected that the normal approximation will become insufficient in bigger studies. Here, we demonstrate that when the height of hundreds of thousands of individuals is analysed, the model complexity needs to be increased to include non-additive interactions between sex, environment and genes. Alternatively, the use of log-normal approximation allowed us to still use the additive effects model. These findings are important for future genetic and methodologic studies that make use of adult height as an exemplar trait

Study of the process e+e-\to \mu+\mu- in the energy region \sqrt{s}=980, 1040 -- 1380 MeV

The cross section of the process e+e-\to\mu+\mu- was measured in the SND experiment at the VEPP-2M e+e- collider in the energy region \sqrt{s}=980, 1040 -- 1380 MeV. The event numbers of the process e+e-\to\mu+\mu- were normalized to the integrated luminosity measured using e+e-\to e+e- and e+e-\to\gamma\gamma processes. The ratio of the measured cross section to the theoretically predicted value is 1.006\pm 0.007 \pm 0.016 and 1.005 \pm 0.007 \pm 0.018 in the first and second case respectively. Using results of the measurements, the electromagnetic running coupling constant \alpha in the energy region \sqrt{s}=1040 -- 1380 MeV was obtained = 134.1\pm 0.5 \pm 1.2 and this is in agreement with theoretical expectation.Comment: 29 pages, 23 figure

Review of experimental results from SND detector

The review of experimental results obtained with SND detector at VEPP-2M $e^+e^-$ collider in the energy region $\sqrt[]{s}=0.36$ -- 1.38 GeV is given. The presented results include the following items: studies of the light vector mesons radiative decays, OZI-rule and G-parity suppressed $\phi$-meson rare decays, $\phi$-meson parameters measurements, studies of $e^+e^-\to\pi^+\pi^-\pi^0$ process dynamics, $\eta$ and $K_S$ mesons rare decays, $\eta$ and $\phi$ mesons conversion decays, and study of the $e^+e^-$ annihilation into hadrons.Comment: 12 pages and 6 figures. Talk given at the IX International Conference on Hadron Spectroskopy, Protvino, Russia, August 25 - September 1, 200