Hermite and Gegenbauer polynomials in superspace using Clifford analysis

The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.Comment: 18 pages, accepted for publication in J. Phys.

A tool for subjective and interactive visual data exploration

We present SIDE, a tool for Subjective and Interactive Visual Data Exploration, which lets users explore high dimensional data via subjectively informative 2D data visualizations. Many existing visual analytics tools are either restricted to specific problems and domains or they aim to find visualizations that align with user’s belief about the data. In contrast, our generic tool computes data visualizations that are surprising given a user’s current understanding of the data. The user’s belief state is represented as a set of projection tiles. Hence, this user-awareness offers users an efficient way to interactively explore yet-unknown features of complex high dimensional datasets

Spherical harmonics and integration in superspace

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of this operator, a new type of integration over the supersphere is introduced by exploiting the formal equivalence with an old result of Pizzetti. This integral is then used to prove orthogonality of spherical harmonics of different degree, Green-like theorems and also an extension of the important Funk-Hecke theorem to superspace. Finally, this integration over the supersphere is used to define an integral over the whole superspace and it is proven that this is equivalent with the Berezin integral, thus providing a more sound definition of the Berezin integral.Comment: 22 pages, accepted for publication in J. Phys.

Spherical harmonics and integration in superspace II

The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic pieces, which also determines the irreducible pieces under the action of SO(m) x Sp(2n). In the second part of the paper, this decomposition is used to describe all possible integrations over the supersphere. It is then shown that only one possibility yields the orthogonality of spherical harmonics of different degree. This is the so-called Pizzetti-integral of which it was shown in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212] that it leads to the Berezin integral.Comment: 18 pages, accepted for publication in J. Phys.

Operator identities in q-deformed Clifford analysis

In this paper, we define a q-deformation of the Dirac operator as a generalization of the one dimensional q-derivative. This is done in the abstract setting of radial algebra. This leads to a q-Dirac operator in Clifford analysis. The q-integration on R(m), for which the q-Dirac operator satisfies Stokes' formula, is defined. The orthogonal q-Clifford-Hermite polynomials for this integration are briefly studied

The effect of non-Newtonian behavior on contact formation in an external gear pump

In an extrusion process, an external gear pump can be used to control the flow rate of the system. When extruding polymers, the viscosity is quite high, resulting in negligible inertia and thus laminar flow. The external gear pump contains two gears, one driven by a motor and one driven by means of contact with the other gear. In our previous work, the flow of a viscous fluid through an external gear pump was studied using the finite element method. Local mesh refinement was applied based on the respective distance between boundaries. Furthermore, the rotation of both gears was imposed. In this work, the rotation of one gear is imposed, whereas the other gear is freely rotating. However, the minimum distance between the gears is limited to a minimum value. When this value is reached, contact is assumed and also the rotation of second gear is imposed. A reversion of the torque on this gear results in a release of contact. In this manner, a quasi driver/driven situation is created in the numerical simulations. It is observed that contact is released periodically, and thus cannot be assumed present continuously, as is often prescribed. Non-Newtonian material properties, such as shear thinning and the pressure dependence of the density or the viscosity, alter how long contact is released during a tooth rotation

ISAR image matching and three-dimensional scattering imaging based on extracted dominant scatterers

This paper studies inverse synthetic aperture radar (ISAR) image matching and three-dimensional (3D) scattering imaging based on extracted dominant scatterers. In the condition of a long baseline between two radars, it is easy for obvious rotation, scale, distortion, and shift to occur between two-dimensional (2D) radar images. These problems lead to the difficulty of radar-image matching, which cannot be resolved by motion compensation and cross-correlation. What is more, due to the anisotropy, existing image-matching algorithms, such as scale invariant feature transform (SIFT), do not adapt to ISAR images very well. In addition, the angle between the target rotation axis and the radar line of sight (LOS) cannot be neglected. If so, the calibration result will be smaller than the real projection size. Furthermore, this angle cannot be estimated by monostatic radar. Therefore, instead of matching image by image, this paper proposes a novel ISAR imaging matching and 3D imaging based on extracted scatterers to deal with these issues. First, taking advantage of ISAR image sparsity, radar images are converted into scattering point sets. Then, a coarse scatterer matching based on the random sampling consistency algorithm (RANSAC) is performed. The scatterer height and accurate affine transformation parameters are estimated iteratively. Based on matched scatterers, information such as the angle and 3D image can be obtained. Finally, experiments based on the electromagnetic simulation software CADFEKO have been conducted to demonstrate the effectiveness of the proposed algorithm

Preliminary inconclusive results of a randomised double blinded cross-over pilot trial in long-term-care dwelling elderly assessing the feasibility of stochastic resonance whole-body vibration

Background This randomised double-blinded controlled cross-over pilot study examined feasibility and preliminary effects of stochastic resonance whole-body vibration training applied in long term care elderly. Findings Nine long term care elderly were recruited and randomized to group A (6 Hz, Noise 4 SR-WBV/ Sham) or B (Sham / 1 Hz, Noise 1 SR-WBV). Feasibility outcomes included recruitment rate, attrition, adherence and safety. Physical performance outcomes focused on the Expanded Timed Get Up-and-Go (ETGUG) test, the Short Physical Performance Battery (SPPB), and lower extremity muscle strength. Of 24 subjects initially approached 9 started and 5 completed the study resulting in 37.5 recruitment, 44.4 attrition and 81.7 % adherence rates. No adverse events were reported. There is more evidence of improved performance levels in the SR-WBV treatment group with significant differences in average change for isometric rate of force development (p = 0.016 left leg; p = 0.028 right leg). No statistical significance was reached for other parameters. Conclusions The findings of this study indicate that the used training protocol for long term care elderly is feasible, however, requires more closely monitoring of participants; e.g. needs protocol modifications that target improved compliance with the intervention in this setting. SR-WBV shows beneficial effects on physical performance for those adhering to the intervention. Trial registration U.S. National Institutes of Health NCT01543243 Physical activity (PA) for elderly is one of the major elements for general health prevention [1] and inactive or sedentary elderly should increase their PA [2]. Despite the known benefits of PA, residents living in long-term care (LTC) are relatively sedentary [3, 4]. Low baseline fitness and mobility levels in (pre-)frail elderly should be considered when starting exercise and this exercise should be adapted to the physical capabilities of these individuals [5]. Whole body vibration (WBV) seems a safe and beneficial type of balance exercise [6, 7]. Pilot studies showed that stochastic resonance WBV (SR-WBV) in (untrained) elderly is both safe and feasible [8, 9]. SR-WBV might also be valuable for (pre-)frail elderly in LTC where the neuromuscular systems of the trainees might not be able withstanding higher loading and long training sessions [8]. However, confirmatory results of such positive effects of WBV in LTC settings is not available and no evidence concerning the feasibility of SR-WBV in LTC dwelling elderly exists. This study tested the feasibility and effects of SR-WBV training in LTC elderly with the aim to (I) evaluate the intervention process and the ability to recruit and retain LTC elderly for such an intervention, and (II) assess the impact of 4-week SR-WBV on physical performance. Finding