Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Clinical evaluation of a novel test strip technology for blood glucose monitoring:accuracy at hypoglycaemic glucose levels

Aim: To evaluate OneTouch® Verio™ test strip performance at hypoglycaemic blood glucose (BG) levels (<3.9mmol/L [<70mg/dL]) at seven clinical studies. Methods: Trained clinical staff performed duplicate capillary BG monitoring system tests on 700 individuals with type 1 and type 2 diabetes using blood from a single fingerstick lancing. BG reference values were obtained using a YSI 2300 STAT™ Glucose Analyzer. The number and percentage of BG values within ±0.83. mmol/L (±15. mg/dL) and ±0.56. mmol/L (±10. mg/dL) were calculated at BG concentrations of <3.9. mmol/L (<70. mg/dL), <3.3. mmol/L (<60. mg/dL), and <2.8. mmol/L (<50. mg/dL). Results: At BG concentrations <3.9. mmol/L (<70. mg/dL), 674/674 (100%) of meter results were within ±0.83. mmol/L (±15. mg/dL) and 666/674 (98.8%) were within ±0.56. mmol/L (±10. mg/dL) of reference values. At BG concentrations <3.3. mmol/L (<60. mg/dL), and <2.8. mmol/L (<50. mg/dL), 358/358 (100%) and 270/270 (100%) were within ±0.56. mmol/L (±10. mg/dL) of reference values, respectively. Conclusion: In this analysis of data from seven independent studies, OneTouch Verio test strips provide highly accurate results at hypoglycaemic BG levels. © 2012 Elsevier Ireland Ltd.

High accuracy discrimination of Parkinson's disease participants from healthy controls using smartphones

The aim of this study is to accurately distinguish Parkinson's disease (PD) participants from healthy controls using self-administered tests of gait and postural sway. Using consumer-grade smartphones with in-built accelerometers, we objectively measure and quantify key movement severity symptoms of Parkinson's disease. Specifically, we record tri-axial accelerations, and extract a range of different features based on the time and frequency-domain properties of the acceleration time series. The features quantify key characteristics of the acceleration time series, and enhance the underlying differences in the gait and postural sway accelerations between PD participants and controls. Using a random forest classifier, we demonstrate an average sensitivity of 98.5% and average specificity of 97.5% in discriminating PD participants from controls. © 2014 IEEE.

Intelligence Algorithms for Increasing Navigation Systems Accuracy

Application of neural network algorithm for increasing the accuracy of navigation systems are showing. Various navigation systems, where a couple of sensors are used in the same device in different positions and the disturbances act equally on both sensors, the trained neural network can be advantageous for increasing the accuracy of system. The neural algorithm had used for determination the interconnection between the sensors errors in two channels to avoid the unobservation of navigation system. Representation of thermal error of two- component navigation sensors by time model, which coefficients depend only on parameters of the device, its orientations relative to disturbance vector allows to predict thermal errors change, measuring the current temperature and having identified preliminary parameters of the model for the set position. These properties of thermal model are used for training the neural network and compensation the errors of navigation system in non- stationary thermal fields.

Spline interpolation to evaluate foveation parameters in congenital nystagmus recordings

Infantile Nystagmus Syndrome, or Congenital Nystagmus, is an ocular-motor disorder characterized by involuntary, conjugated and bilateral to and fro ocular oscillations. Good visual acuity in congenital nystagmus can be achieved during the foveation periods in which eye velocity slows down while the target image crosses the fovea. Visual acuity was found to be mainly dependent on the duration of the foveation periods. In this work a new approach is proposed for estimation of foveation parameters: a cubic spline interpolation of the nystagmus recording before localizing the start point of foveation window and to estimate its duration. The performances of the proposed algorithm were assessed in comparison with a previously developed algorithm, used here as gold standard. The obtained results suggest that the spline interpolation could be a useful tool to filter the eye movement recordings before applying an algorithm to estimate the foveation window parameters. © 2013 IEEE.

Extension of the C-XSC Library with Scalar Products with Selectable Accuracy

The C++ class library C-XSC for scientific computing has been extended with the possibility to compute scalar products with selectable accuracy in version 2.3.0. In previous versions, scalar products have always been computed exactly with the help of the so-called long accumulator. Additionally, optimized floating point computation of matrix and vector operations using BLAS-routines are added in C-XSC version 2.4.0. In this article the algorithms used and their implementations, as well as some potential pitfalls in the compilation, are described in more detail. Additionally, the theoretical background of the employed DotK algorithm and the necessary modifications of the concrete implementation in C-XSC are briefly explained. Run-time tests and numerical examples are presented as well.

Measurement of intervertebral cervical motion by means of dynamic X-ray image processing and data interpolation

Accurate measurement of intervertebral kinematics of the cervical spine can support the diagnosis of widespread diseases related to neck pain, such as chronic whiplash dysfunction, arthritis, and segmental degeneration. The natural inaccessibility of the spine, its complex anatomy, and the small range of motion only permit concise measurement in vivo. Low dose X-ray fluoroscopy allows time-continuous screening of cervical spine during patient's spontaneous motion. To obtain accurate motion measurements, each vertebra was tracked by means of image processing along a sequence of radiographic images. To obtain a time-continuous representation of motion and to reduce noise in the experimental data, smoothing spline interpolation was used. Estimation of intervertebral motion for cervical segments was obtained by processing patient's fluoroscopic sequence; intervertebral angle and displacement and the instantaneous centre of rotation were computed. The RMS value of fitting errors resulted in about 0.2 degree for rotation and 0.2 mm for displacements. © 2013 Paolo Bifulco et al.

PSD modifications of FHRV due to interpolation and CTG storage rate

Cardiotocographic data provide physicians information about foetal development and permit to assess conditions such as foetal distress. An incorrect evaluation of the foetal status can be of course very dangerous. To improve interpretation of cardiotocographic recordings, great interest has been dedicated to foetal heart rate variability spectral analysis. It is worth reminding, however, that foetal heart rate is intrinsically an uneven series, so in order to produce an evenly sampled series a zero-order, linear or cubic spline interpolation can be employed. This is not suitable for frequency analyses because interpolation introduces alterations in the foetal heart rate power spectrum. In particular, interpolation process can produce alterations of the power spectral density that, for example, affects the estimation of the sympatho-vagal balance (computed as low-frequency/high-frequency ratio), which represents an important clinical parameter. In order to estimate the frequency spectrum alterations of the foetal heart rate variability signal due to interpolation and cardiotocographic storage rates, in this work, we simulated uneven foetal heart rate series with set characteristics, their evenly spaced versions (with different orders of interpolation and storage rates) and computed the sympatho-vagal balance values by power spectral density. For power spectral density estimation, we chose the Lomb method, as suggested by other authors to study the uneven heart rate series in adults. Summarising, the obtained results show that the evaluation of SVB values on the evenly spaced FHR series provides its overestimation due to the interpolation process and to the storage rate. However, cubic spline interpolation produces more robust and accurate results. © 2010 Elsevier Ltd. All rights reserved.

Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015

On the Convergence of (0,1,2) Interpolation

2000 Mathematics Subject Classification: 41A05.

Loss of Accuracy in Numerical Computations

Михаил М. Константинов, Петко Х. Петков - Разгледани са възможните катастрофални ефекти от неправилното използване на крайна машинна аритметика с плаваща точка. За съжаление, тази тема не винаги се разбира достатъчно добре от студентите по приложна и изчислителна математика, като положението в инженерните и икономическите специалности в никакъв случай не е по-добро. За преодоляване на този образователен пропуск тук сме разгледали главните виновници за загубата на точност при числените компютърни пресмятания. Надяваме се, че представените резултати ще помогнат на студентите и лекторите за по-добро разбиране и съответно за избягване на основните фактори, които могат да разрушат точността при компютърните числени пресмятания. Последното не е маловажно – числените катастрофи понякога стават истински, с големи щети и човешки жертви.

High accuracy mobile robot positioning using external large volume metrology instruments

A method of accurately controlling the position of a mobile robot using an external large volume metrology (LVM) instrument is presented in this article. By utilising an LVM instrument such as a laser tracker or indoor GPS (iGPS) in mobile robot navigation, many of the most difficult problems in mobile robot navigation can be simplified or avoided. Using the real-time position information from the laser tracker, a very simple navigation algorithm, and a low cost robot, 5mm repeatability was achieved over a volume of 30m radius. A surface digitisation scan of a wind turbine blade section was also demonstrated, illustrating possible applications of the method for manufacturing processes. Further, iGPS guidance of a small KUKA omni-directional robot has been demonstrated, and a full scale prototype system is being developed in cooperation with KUKA Robotics, UK. © 2011 Taylor & Francis.

Metrology enhanced tooling for aerospace (META):strategies for improved accuracy of jig built structures

The accuracy of many aerospace structures is limited by the accuracy of assembly tooling which is in turn limited by the accuracy of the measurements used to set the tooling. Further loss of accuracy results from different rates of thermal expansion for the components and tooling. This paper describes improved tooling designs and setting processes which have the potential to significantly improve the accuracy of aerospace structures. The most advanced solution described is environmentally isolated interferometer networks embedded within tooling combined with active compensation of component pick-ups. This would eliminate environmental effects on measurements while also allowing compensation for thermal expansion. A more immediately realizable solution is the adjustment of component pick-ups using micrometer jacking screws allowing multilateration to be employed during the final stages of the setting process to generate the required offsets. Copyright © 2011 SAE International.

Polyharmonic Hardy Spaces on the Klein-Dirac Quadric with Application to Polyharmonic Interpolation and Cubature Formulas

2010 Mathematics Subject Classification: Primary 65D30, 32A35, Secondary 41A55.