The effect of signal acquisition and processing choices on ApEn values: Towards a “gold standard” for distinguishing effort levels from isometric force records

Approximate Entropy (ApEn) is frequently used to identify changes in the complexity of isometric force records with ageing and disease. Different signal acquisition and processing parameters have been used, making comparison or confirmation of results difficult. This study determined the effect of sampling and parameter choices by examining changes in ApEn values across a range of submaximal isometric contractions of the First Dorsal Interosseus. Reducing the sample rate by decimation changed both the value and pattern of ApEn values dramatically. The pattern of ApEn values across the range of effort levels was not sensitive to the filter cut-off frequency, or the criterion used to extract the section of data for analysis. The complexity increased with increasing effort levels using a fixed ‘r’ value (which accounts for measurement noise) but decreased with increasing effort level when ‘r’ was set to 0.1 of the standard deviation of force. It is recommended isometric force records are sampled at frequencies >200 Hz, template length (‘m’) is set to 2, and 'r' set to measurement system noise or 0.1 SD depending on physiological process to be distinguished. It is demonstrated that changes in ApEn across effort levels are related to changes in force gradation strategy

Singularity results for functional equations driven by linear fractional transformations

We consider functional equations driven by linear fractional transformations, which are special cases of de Rham's functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.Comment: 14 pages, Title changed, to appear in Journal of Theoretical Probabilit

Design of Optimum Ducts Using an Efficient 3-D Viscous Computational Flow Analysis

Design of fluid dynamically efficient ducts is addressed through the combination of an optimization analysis with a three-dimensional viscous fluid dynamic analysis code. For efficiency, a parabolic fluid dynamic analysis was used. Since each function evaluation in an optimization analysis is a full three-dimensional viscous flow analysis requiring 200,000 grid points, it is important to use both an efficient fluid dynamic analysis and an efficient optimization technique. Three optimization techniques are evaluated on a series of test functions. The Quasi-Newton (BFGS, eta = .9) technique was selected as the preferred technique. A series of basic duct design problems are performed. On a two-parameter optimization problem, the BFGS technique is demonstrated to require half as many function evaluations as a steepest descent technique

A lattice model of hydrophobic interactions

Hydrogen bonding is modeled in terms of virtual exchange of protons between water molecules. A simple lattice model is analyzed, using ideas and techniques from the theory of correlated electrons in metals. Reasonable parameters reproduce observed magnitudes and temperature dependence of the hydrophobic interaction between substitutional impurities and water within this lattice.Comment: 7 pages, 3 figures. To appear in Europhysics Letter