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B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications. ispartof: PLOS ONE vol:12 issue:3 ispartof: location:United States status: published

This paper examines the application of a bootstrap test error estimation of radial basis functions, specifically thin-plate spline fitting, in surface smoothing. The presence of noisy data is a common issue of the point set model that is generated from 3D scanning devices, and hence, point set denoising is one of the main concerns in point set modelling. Bootstrap test error estimation, which is applied when searching for the smoothing parameters of radial basis functions, is revisited. The main contribution of this paper is a smoothing algorithm that relies on a bootstrap-based radial basis function. The proposed method incorporates a k-nearest neighbour search and then projects the point set to the approximated thin-plate spline surface. Therefore, the denoising process is achieved, and the features are well preserved. A comparison of the proposed method with other smoothing methods is also carried out in this study.

International audience; Eye tracking systems have recently experienced a diversity of novel calibration procedures, including smooth pursuit and vestibulo-ocular reflex based calibrations. These approaches allowed collecting more data compared to the standard 9-point calibration. However, the computation of the mapping function which provides planar gaze positions from pupil features given as input is mostly based on polynomial regressions, and little work has investigated alternative approaches. This paper fills this gap by providing a new calibration computation method based on symbolic regression. Instead of making prior assumptions on the polynomial transfer function between input and output records, symbolic regression seeks an optimal model among different types of functions and their combinations. This approach offers an interesting perspective in terms of flexibility and accuracy. Therefore, we designed two experiments in which we collected ground truth data to compare vestibulo-ocular and smooth pursuit calibrations based on symbolic regression, both using a marker or a finger as a target, resulting in four different calibrations. As a result, we improved calibration accuracy by more than 30%, with reasonable extra computation time.

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation. peerReviewed

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Delay represents a significant phenomenon in the dynamics of many human-related systems - including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin delay values in multiple-delay linear systems. The characteristic quasi-polynomial - the roots of which decide about stability - is subjected to iterative discretization by means of pre-warped bilinear transformation. Then, a linear and a quadratic interpolation are applied to obtain the associated characteristic polynomial with integer powers. The roots of the associated characteristic polynomial are closely related to the estimation of roots of the original characteristic quasi-polynomial which agrees with the system's eigenvalues. Since the stability border is crossed by the leading one, the switching root locus is enhanced using the Regula Falsi interpolation method. Our methodology is implemented on - and verified by - a numerical bio-cybernetic example of the stabilization of a human-being's movement on a controlled swaying bow. The advantage of the proposed novel algorithm lies in the possibility of the rapid computation of polynomial zeros by means of standard programs for technical computing; in the low level of mathematical knowledge required; and, in the sufficiently high precision of the roots loci estimation. The relationship to the direct search QuasiPolynomial (mapping) Rootfinder algorithm and computational complexity are discussed as well. This algorithm is also applicable for systems with non-commensurate delays. © 2017 Pekař et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited., CZ.1.05/2.1.00/19.0376, ERDF, European Regional Development Fund, Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]

A large-scale multiple surveillance system for infectious disease outbreaks has been in operation in England and Wales since the early 1990s. Changes to the statistical algorithm at the heart of the system were proposed and the purpose of this paper is to compare two new algorithms with the original algorithm. Test data to evaluate performance are created from weekly counts of the number of cases of each of more than 2000 diseases over a twenty-year period. The time series of each disease is separated into one series giving the baseline (background) disease incidence and a second series giving disease outbreaks. One series is shifted forward by twelve months and the two are then recombined, giving a realistic series in which it is known where outbreaks have been added. The metrics used to evaluate performance include a scoring rule that appropriately balances sensitivity against specificity and is sensitive to variation in probabilities near 1. In the context of disease surveillance, a scoring rule can be adapted to reflect the size of outbreaks and this was done. Results indicate that the two new algorithms are comparable to each other and better than the algorithm they were designed to replace.

In the current paper the decoding algorithms for motor-related BCI systems for continuous upper limb trajectory prediction are considered. Two methods for the smooth prediction, namely Sobolev and Polynomial Penalized Multi-Way Partial Least Squares (PLS) regressions, are proposed. The methods are compared to the Multi-Way Partial Least Squares and Kalman Filter approaches. The comparison demonstrated that the proposed methods combined the prediction accuracy of the algorithms of the PLS family and trajectory smoothness of the Kalman Filter. In addition, the prediction delay is significantly lower for the proposed algorithms than for the Kalman Filter approach. The proposed methods could be applied in a wide range of applications beyond neuroscience.

Motion capture allows accurate recording of human motion, with applications in many fields, including entertainment, medicine, sports science and human computer interaction. A common difficulty with this technology is the occurrence of missing data, due to occlusions, or recording conditions. Various models have been proposed to estimate missing data. Some are based on interpolation, low-rank properties or inter-correlations. Others involve dataset matching or skeleton constraints. While the latter have the advantage of promoting a realistic motion estimation, they require prior knowledge of skeleton constraints, or the availability of a prerecorded dataset. In this article, we propose a probabilistic averaging method of several recovery models (referred to as Probabilistic Model Averaging (PMA) in this paper), based on the likelihoods of the distances between body points. This method has the advantage of being automatic, while allowing an efficient gap data recovery. To support and validate the proposed method, we use a set of four individual recovery models, based on linear/nonlinear regression in local coordinate systems. Finally, we propose two heuristic algorithms to enforce skeleton constraints in the reconstructed motion, which can be used on any individual recovery model. For validation purposes, random gaps were introduced into motion-capture sequences, and the effects of factors such as the number of simultaneous gaps, gap length and sequence duration were analyzed. Results show that the proposed probabilistic averaging method yields better recovery than (i) each of the four individual models and (ii) two recent state-of-the-art models, regardless of gap length, sequence duration and number of simultaneous gaps. Moreover, both of our heuristic skeleton-constraint algorithms significantly improve the recovery for 7 out of 8 tested motion-capture sequences (p < 0.05), for 10 simultaneous gaps of 5 seconds. The code is available for free download at: https://github.com/numediart/MocapRecovery.

In this paper, we consider the Markov-Chain Monte Carlo (MCMC) approach for random sampling of combinatorial objects. The running time of such an algorithm depends on the total mixing time of the underlying Markov chain and is unknown in general. For some Markov chains, upper bounds on this total mixing time exist but are too large to be applicable in practice. We try to answer the question, whether the total mixing time is close to its upper bounds, or if there is a significant gap between them. In doing so, we present the software library marathon which is designed to support the analysis of MCMC based sampling algorithms. The main application of this library is to compute properties of so-called state graphs which represent the structure of Markov chains. We use marathon to investigate the quality of several bounding methods on four well-known Markov chains for sampling perfect matchings and bipartite graph realizations. In a set of experiments, we compute the total mixing time and several of its bounds for a large number of input instances. We find that the upper bound gained by the famous canonical path method is several magnitudes larger than the total mixing time and deteriorates with growing input size. In contrast, the spectral bound is found to be a precise approximation of the total mixing time.

A fast and robust interpolation filter based on finite difference TPS has been proposed in this paper. The proposed method employs discrete cosine transform to efficiently solve the linear system of TPS equations in case of gridded data, and by a pre-defined weight function with respect to simulation residuals to reduce the effect of outliers and misclassified non-ground points on the accuracy of reference ground surface construction. Fifteen groups of benchmark datasets, provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) commission, were employed to compare the performance of the proposed method with that of the multi-resolution hierarchical classification method (MHC). Results indicate that with respect to kappa coefficient and total error, the proposed method is averagely more accurate than MHC. Specifically, the proposed method is 1.03 and 1.32 times as accurate as MHC in terms of kappa coefficient and total errors. More importantly, the proposed method is averagely more than 8 times faster than MHC. In comparison with some recently developed methods, the proposed algorithm also achieves a good performance.

This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC).

In a queueing system with the dropping function the arriving customer can be denied service (dropped) with the probability that is a function of the queue length at the time of arrival of this customer. The potential applicability of such mechanism is very wide due to the fact that by choosing the shape of this function one can easily manipulate several performance characteristics of the queueing system. In this paper we carry out analysis of the queueing system with the dropping function and a very general model of arrival process--the model which includes batch arrivals and the interarrival time autocorrelation, and allows for fitting the actual shape of the interarrival time distribution and its moments. For such a system we obtain formulas for the distribution of the queue length and the overall customer loss ratio. The analytical results are accompanied with numerical examples computed for several dropping functions.

We describe in this paper the experimental procedure, the data treatment and the quantification of the black body correction: an experimental approach to compensate for scattering and systematic biases in quantitative neutron imaging based on experimental data. The correction algorithm is based on two steps; estimation of the scattering component and correction using an enhanced normalization formula. The method incorporates correction terms into the image normalization procedure, which usually only includes open beam and dark current images (open beam correction). Our aim is to show its efficiency and reproducibility: we detail the data treatment procedures and quantitatively investigate the effect of the correction. Its implementation is included within the open source CT reconstruction software MuhRec. The performance of the proposed algorithm is demonstrated using simulated and experimental CT datasets acquired at the ICON and NEUTRA beamlines at the Paul Scherrer Institut.