Reconstruction of density functions by sk-splines

Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an analytic extension into an appropriate tube and "bell-shaped" with rapidly decaying tails. Unfortunately, the domain of such functions is not compact which creates various technical difficulties. We solve interpolation problem on an infinite rectangular grid for a wide range of kernel functions and calculate explicitly their Fourier transform to obtain representations for the respective density functions

Stable multispeed lattice Boltzmann methods

We demonstrate how to produce a stable multispeed lattice Boltzmann method (LBM) for a wide range of velocity sets, many of which were previously thought to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method operates stably for almost zero viscosity, has second-order accuracy, suppresses typical spurious oscillation (only a modest Gibbs effect is present) and introduces no artificial viscosity. There is almost no computational cost for this innovation. DISCLAIMER: Additional tests and wide discussion of this preprint show that the claimed property of coupled steps: no artificial dissipation and the second-order accuracy of the method are valid only on sufficiently fine grids. For coarse grids the higher-order terms destroy coupling of steps and additional dissipation appears. The equations are true.Comment: Disclaimer about the area of applicability is added to abstrac

Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length -- the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.Comment: 10 pages, 3 figures, In Proc. A4A5, Chester UK, Jul. 18-22 200

Development of a mechatronic sorting system for removing contaminants from wool

Automated visual inspection (AVI) systems have been extended to many fields, such as agriculture and the food, plastic and textile industries. Generally, most visual systems only inspect product defects, and then analyze and grade them due to the lack of any sorting function. This main reason rests with the difficulty of using the image data in real time. However, it is increasingly important to either sort good products from bad or grade products into separate groups usingAVI systems. This article describes the development of a mechatronic sorting system and its integration with a vision system for automatically removing contaminants from wool in real time. The integration is implemented by a personal computer, which continuously processes live images under the Windows 2000 operating system. The developed real-time sorting approach is also applicable to many other AVI systems

Extending the range of error estimates for radial approximation in Euclidean space and on spheres

We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds for scattered data interpolation by radial basis functions. Math. Comp., 68(225):201--216, 1999.] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of R^d and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.Comment: 12 page

A System in the Wild: Deploying a Two Player Arm Rehabilitation System for Children With Cerebral Palsy in a School Environment

This paper outlines a system for arm rehabilitation for children with upper-limb hemiplegia resulting from cerebral palsy. Our research team designed a two-player, interactive (competitive or collaborative) computer play therapy system that provided powered assistance to children while they played specially designed games that promoted arm exercises. We designed the system for a school environment. To assess the feasibility of deploying the system in a school environment, the research team enlisted the help of teachers and staff in nine schools. Once the system was set up, it was used to deliver therapy without supervision from the research team. Ultimately, the system was found to be suitable for use in schools. However, the overriding need for schools to focus on academic activities meant that children could not use the system enough to achieve the amount of use desired for therapeutic benefit. In this paper, we identify the key challenges encountered during this study. For example, there was a marked reluctance to report system issues (which could have been fixed) that prevented children from using the system. We also discuss future implications of deploying similar studies with this type of system

A Hand-Held Device Presenting Haptic Directional Cues for the Visually Impaired

Haptic information is essential in everyday activities, especially for visually impaired people in terms of real-world navigation. Since human haptic sensory processing is nonlinear, asymmetric vibrations have been widely studied to create a pulling sensation for the delivery of directional haptic cues. However, the design of an input control signal that generates asymmetric vibrations has not yet been parameterised. In particular, it is unclear how to quantify the asymmetry of the output vibrations to create a better pulling sensation. To better understand the design of an input control signal that generates haptic directional cues, we evaluated the effect of the pulling sensations corresponding to the three adjustable parameters (i.e., delay time, ramp-down step length, and cut-off voltage) in a commonly applied step-ramp input signal. The results of a displacement measurement and a psychophysical experiment demonstrate that when the quantified asymmetry ratio is in a range of 0.3430–0.3508 with an optimised cut-off voltage for our hand-held device, the haptic directional cues are better perceived by participants. Additionally, the results also showed a superior performance in haptic delivery by shear forces than normal forces