Identification of Boundary Conditions Using Natural Frequencies

The present investigation concerns a disc of varying thickness of whose flexural stiffness $D$ varies with the radius $r$ according to the law $D=D_0 r^m$, where $D_0$ and $m$ are constants. The problem of finding boundary conditions for fastening this disc, which are inaccessible to direct observation, from the natural frequencies of its axisymmetric flexural oscillations is considered. The problem in question belongs to the class of inverse problems and is a completely natural problem of identification of boundary conditions. The search for the unknown conditions for fastening the disc is equivalent to finding the span of the vectors of unknown conditions coefficients. It is shown that this inverse problem is well posed. Two theorems on the uniqueness and a theorem on stability of the solution of this problem are proved, and a method for establishing the unknown conditions for fastening the disc to the walls is indicated. An approximate formula for determining the unknown conditions is obtained using first three natural frequencies. The method of approximate calculation of unknown boundary conditions is explained with the help of three examples of different cases for the fastening the disc (rigid clamping, free support, elastic fixing). Keywords: Boundary conditions, a disc of varying thickness,inverse problem, Plucker condition.Comment: 19 page

Whole genome sequencing of elite athletes

Whole genome sequencing (WGS) has great potential to explore all possible DNA variants associated with physical performance, psychological traits and health conditions of athletes. Here we present, for the first time, annotation of genomic variants of elite athletes, based on the WGS of 20 Tatar male wrestlers. The maximum number of high-quality variants per sample was over 3.8 M for single nucleotide polymorphisms (SNPs) and about 0.64 M for indels. The maximum number of nonsense mutations was 148 single nucleotide variants (SNVs) per individual. Athletes' genomes on average contained 18.9 nonsense SNPs in a homozygous state per sample, while non-Athletes' exomes (Tatar controls, n = 19) contained 18 nonsense SNPs. Finally, we applied genomic data for the association analysis and used reaction time (RT) as an example. Out of 1884 known genome-wide significant SNPs related to RT, we identified four SNPs (KIF27 rs10125715, APC rs518013, TMEM229A rs7783359, LRRN3 rs80054135) associated with RT in wrestlers. The cumulative number of favourable alleles (KIF27 A, APC A, TMEM229A T, LRRN3 T) was significantly correlated with RT both in wrestlers (P = 0.0003) and an independent cohort (n = 43) of physically active subjects (P = 0.029). Furthermore, we found that the frequencies of the APC A (53.3 vs 44.0%, P = 0.033) and LRRN3 T (7.5 vs 2.8%, P = 0.009) alleles were significantly higher in elite athletes (n = 107) involved in sports with RT as an essential component of performance (combat sports, table tennis and volleyball) compared to less successful (n = 176) athletes. The LRRN3 T allele was also over-represented in elite athletes (7.5%) in comparison with 189 controls (2.9%, P = 0.009). In conclusion, we present the first WGS study of athletes showing that WGS can be applied in sport and exercise science

The formation of human populations in South and Central Asia

By sequencing 523 ancient humans, we show that the primary source of ancestry in modern South Asians is a prehistoric genetic gradient between people related to early hunter-gatherers of Iran and Southeast Asia. After the Indus Valley Civilization’s decline, its people mixed with individuals in the southeast to form one of the two main ancestral populations of South Asia, whose direct descendants live in southern India. Simultaneously, they mixed with descendants of Steppe pastoralists who, starting around 4000 years ago, spread via Central Asia to form the other main ancestral population. The Steppe ancestry in South Asia has the same profile as that in Bronze Age Eastern Europe, tracking a movement of people that affected both regions and that likely spread the distinctive features shared between Indo-Iranian and Balto-Slavic languages