Optimal fits of diffusion constants from single-time data points of Brownian trajectories

Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe interactions between a particle and its environment but the price to be paid is the absence of ensemble averaging and a consequent lack of statistics. Here we address the benchmark question of how to accurately extract the diffusion constant of one single Brownian trajectory. We analyze a class of estimators based on weighted functionals of the square displacement. For a certain choice of the weight function these functionals provide the true ensemble averaged diffusion coefficient, with a precision that increases with the trajectory resolution.

On ergodic least-squares estimators of the generalized diffusion coefficient for fractional Brownian motion

We analyse a class of estimators of the generalized diffusion coefficient for fractional Brownian motion Bt of known Hurst index H, based on weighted functionals of the single time square displacement. We show that for a certain choice of the weight function these functionals possess an ergodic property and thus provide the true, ensemble-averaged, generalized diffusion coefficient to any necessary precision from a single trajectory data, but at expense of a progressively higher experimental resolution. Convergence is fastest around H ? 0.30, a value in the subdiffusive regime.

Quantitative assessment based on kinematic measures of functional impairments during upper extremity movements: a review

Quantitative measures of human movement quality are important for discriminating healthy and pathological conditions and for expressing the outcomes and clinically important changes in subjects' functional state. However the most frequently used instruments for the upper extremity functional assessment are clinical scales, that previously have been standardized and validated, but have a high subjective component depending on the observer who scores the test. But they are not enough to assess motor strategies used during movements, and their use in combination with other more objective measures is necessary. The objective of the present review is to provide an overview on objective metrics found in literature with the aim of quantifying the upper extremity performance during functional tasks, regardless of the equipment or system used for registering kinematic data.

Effects of different swimming race constraints on turning movements

The aim of this study was to investigate the effects of different swimming race constraints on the evolution of turn parameters. One hundred and fifty-eight national and regional level 200-m (meters) male swimming performances were video-analyzed using the individualized-distance model in the Open Comunidad de Madrid tournament. Turn (p < .001, ES = 0.36) and underwater distances (p < .001, ES = 0.38) as well as turn velocity (p < .001, ES = 0.69) significantly dropped throughout the race, although stroke velocity and underwater velocity were maintained in the last lap of the race (p > .05). Higher expertise swimmers obtained faster average velocities and longer distances in all the turn phases (p < .001, ES = 0.59), except the approach distance. In addition, national level swimmers showed the ability to maintain most of the turn parameters throughout the race, which assisted them in improving average velocity at the end of races. Therefore, the variations in the turning movements of a swimming race were expertise-related and focused on optimizing average velocity. Turning skills should be included in the swimming race action plan.