Motion Analysis of the 2009 Men’s 100 m World Record

The fabulous 100 m world record of Jamaica’s Usain Bolt (9.58 s on Aug. 16th, 2009, in Berlin) has intrigued not only sports fans. It can also be fruitfully used in physics teaching as a real life event, although there are some caveats. After downloading public-domain, high-resolution renditions of the record race for a motion analysis, we first used video-cutting software to clock individual frames when the winning athlete passed the ten 10 visible on-track markers. A polynomial fit of these data was possible with r2 = 0.9998, however, it failed to produce physically plausible velocities and accelerations. Data published by the IAAF, when evaluated in the same way, did not produce these artifacts, and showed the record-breaking dash to be composed of a 3-second phase with decreasing acceleration, followed by a high-speed phase peaking at 44,2 km/h near 7,5 s. A slight deceleration at the very end can be used as an estimate for still further improvements of the 100 m world record, as had been down before.1 The relevance of the results w.r. to biokinematics as well as training methods are discussed. 1H.K. Eriksen et al., Am. J. Phys 77, 324 (2009

Motion Analysis of the 2009 Men’s 100 m World Record

The fabulous 100 m world record of Jamaica’s Usain Bolt (9.58 s on Aug. 16th, 2009, in Berlin) has intrigued not only sports fans. It can also be fruitfully used in physics teaching as a real life event, although there are some caveats. After downloading public-domain, high-resolution renditions of the record race for a motion analysis, we first used video-cutting software to clock individual frames when the winning athlete passed the ten 10 visible on-track markers. A polynomial fit of these data was possible with r2 = 0.9998, however, it failed to produce physically plausible velocities and accelerations. Data published by the IAAF, when evaluated in the same way, did not produce these artifacts, and showed the record-breaking dash to be composed of a 3-second phase with decreasing acceleration, followed by a high-speed phase peaking at 44,2 km/h near 7,5 s. A slight deceleration at the very end can be used as an estimate for still further improvements of the 100 m world record, as had been down before.1 The relevance of the results w.r. to biokinematics as well as training methods are discussed. 1H.K. Eriksen et al., Am. J. Phys 77, 324 (2009

Functional limit theorems for random regular graphs

Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We consider limit theorems for various combinatorial and analytical properties of this graph (or the matrix) as n grows to infinity, either when d is kept fixed or grows slowly with n. In a suitable weak convergence framework, we prove that the (finite but growing in length) sequences of the number of short cycles and of cyclically non-backtracking walks converge to distributional limits. We estimate the total variation distance from the limit using Stein's method. As an application of these results we derive limits of linear functionals of the eigenvalues of the adjacency matrix. A key step in this latter derivation is an extension of the Kahn-Szemer\'edi argument for estimating the second largest eigenvalue for all values of d and n.Comment: Added Remark 27. 39 pages. To appear in Probability Theory and Related Field

Antichains on Three Levels

An antichain A is flat if there exists an integer k * 0 such that every set in A has cardinality either k or k + 1. The size of A is jAj and the volume of A is P A2A jAj. The flat antichain theorem states that for any antichain A on [n] = f1; 2; : : : ; ng there exists a flat antichain on [n] with the same size and volum

Identifying anatomical shape difference by regularized discriminative direction

Identifying the shape difference between two groups of anatomical objects is important for medical image analysis and computer-aided diagnosis. A method called ldquodiscriminative directionrdquo in the literature has been proposed to solve this problem. In that method, the shape difference between groups is identified by deforming a shape along the discriminative direction. This paper conducts a thorough study about inferring this discriminative direction in an efficient and accurate way. First, finding the discriminative direction is reformulated as a preimage problem in kernel-based learning. This provides a complementary but conceptually simpler solution than the previous method. More importantly, we find that a shape deforming along the original discriminative direction cannot faithfully maintain its anatomical correctness. This unnecessarily introduces spurious shape differences and leads to inaccurate analysis. To overcome this problem, this paper further proposes a regularized discriminative direction by requiring a shape to conform to its underlying distribution when it deforms. Two different approaches are developed to impose the regularization, one from the perspective of probability distributions and the other from a geometric point of view, and their relationship is discussed. After verifying their superior performance through controlled experiments, we apply the proposed methods to detecting and localizing the hippocampal shape difference between sexes. We get results consistent with other independent research, providing a more compact representation of the shape difference compared with the established discriminative direction method

Aspects moléculaires et spécificités fines des auto-anticorps antiphospholipides (contribution à la compréhension de leur origine et de leur pathogénicité)

STRASBOURG-Sc. et Techniques (674822102) / SudocSudocFranceF