Constant scale factor, on-line CORDIC algorithm in the circular coordinate system

Real time digital signal processing requires the development of high performance arithmetic algorithms suitable for VLSI design. In this paper, a new online, circular coordinate system CORDIC algorithm is described, which has a constant scale factor. This algorithm was developed using a new Angular Representation (AR) model A radix 2 version of the CORDIC algorithm is presented, along with an architecture suitable for VLSI implementation.

The Synergistic Organization of Muscle Recruitment Constrains Visuomotor Adaptation

Reaching to visual targets engages the nervous system in a series of transformations between sensory information and motor commands. That which remains to be determined is the extent to which the processes that mediate sensorimotor adaptation to novel environments engage neural circuits that represent the required movement in joint-based or muscle-based coordinate systems. We sought to establish the contribution of these alternative representations to the process of visuomotor adaptation. To do so we applied a visuomotor rotation during a center-out isometric torque production task that involved flexion/extension and supination/pronation at the elbow-joint complex. In separate sessions, distinct half-quadrant rotations (i.e., 45°) were applied such that adaptation could be achieved either by only rescaling the individual joint torques (i.e., the visual target and torque target remained in the same quadrant) or by additionally requiring torque reversal at a contributing joint (i.e., the visual target and torque target were in different quadrants). Analysis of the time course of directional errors revealed that the degree of adaptation was lower (by ~20%) when reversals in the direction of joint torques were required. It has been established previously that in this task space, a transition between supination and pronation requires the engagement of a different set of muscle synergists, whereas in a transition between flexion and extension no such change is required. The additional observation that the initial level of adaptation was lower and the subsequent aftereffects were smaller, for trials that involved a pronation–supination transition than for those that involved a flexion–extension transition, supports the conclusion that the process of adaptation engaged, at least in part, neural circuits that represent the required motor output in a muscle-based coordinate system.

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.

A virtual inspection framework for precision manufacturing of aerofoil components

The finite element method plays an extremely important role in forging process design as it provides a valid means to quantify forging errors and thereby govern die shape modification to improve the dimensional accuracy of the component. However, this dependency on process simulation could raise significant problems and present a major drawback if the finite element simulation results were inaccurate. This paper presents a novel approach to assess the dimensional accuracy and shape quality of aeroengine blades formed from finite element hot-forging simulation. The proposed virtual inspection system uses conventional algorithms adopted by modern coordinate measurement processes as well as the latest free-form surface evaluation techniques to provide a robust framework for virtual forging error assessment. Established techniques for the physical registration of real components have been adapted to localise virtual models in relation to a nominal Design Coordinate System. Blades are then automatically analysed using a series of intelligent routines to generate measurement data and compute dimensional errors. The results of a comparison study indicate that the virtual inspection results and actual coordinate measurement data are highly comparable, validating the approach as an effective and accurate means to quantify forging error in a virtual environment. Consequently, this provides adequate justification for the implementation of the virtual inspection system in the virtual process design, modelling and validation of forged aeroengine blades in industry.