GymCam

Worn sensors are popular for automatically tracking exercises. However, a wearable is usually attached to one part of the body, tracks only that location, and thus is inadequate for capturing a wide range of exercises, especially when other limbs are involved. Cameras, on the other hand, can fully track a user's body, but suffer from noise and occlusion. We present GymCam, a camera-based system for automatically detecting, recognizing and tracking multiple people and exercises simultaneously in unconstrained environments without any user intervention. We collected data in a varsity gym, correctly segmenting exercises from other activities with an accuracy of 84.6%, recognizing the type of exercise at 93.6% accuracy, and counting the number of repetitions to within ± 1.7 on average. GymCam advances the field of real-time exercise tracking by filling some crucial gaps, such as tracking whole body motion, handling occlusion, and enabling single-point sensing for a multitude of users.</jats:p

Solving the chemical master equation using sliding windows

<p>Abstract</p> <p>Background</p> <p>The chemical master equation (CME) is a system of ordinary differential equations that describes the evolution of a network of chemical reactions as a stochastic process. Its solution yields the probability density vector of the system at each point in time. Solving the CME numerically is in many cases computationally expensive or even infeasible as the number of reachable states can be very large or infinite. We introduce the sliding window method, which computes an approximate solution of the CME by performing a sequence of local analysis steps. In each step, only a manageable subset of states is considered, representing a "window" into the state space. In subsequent steps, the window follows the direction in which the probability mass moves, until the time period of interest has elapsed. We construct the window based on a deterministic approximation of the future behavior of the system by estimating upper and lower bounds on the populations of the chemical species.</p> <p>Results</p> <p>In order to show the effectiveness of our approach, we apply it to several examples previously described in the literature. The experimental results show that the proposed method speeds up the analysis considerably, compared to a global analysis, while still providing high accuracy.</p> <p>Conclusions</p> <p>The sliding window method is a novel approach to address the performance problems of numerical algorithms for the solution of the chemical master equation. The method efficiently approximates the probability distributions at the time points of interest for a variety of chemically reacting systems, including systems for which no upper bound on the population sizes of the chemical species is known a priori.</p