Search results for "Approximation error"
showing 10 items of 62 documents
Near-infrared diffuse reflectance spectroscopy and neural networks for measuring nutritional parameters in chocolate samples.
2007
Abstract A rapid and non-destructive method has been developed for the characterization of chocolate samples based on diffuse reflectance near-infrared Fourier transform spectroscopy (DRIFTS) and artificial neural networks (ANNs). This methodology provides a potentially useful alternative to time-consuming chemical methods of analysis. To assess its utility, 36 chocolate samples purchased from the Spanish market were analyzed for the determination of the main nutritional parameters like carbohydrates, fat, proteins, energetic value and cocoa content. Direct triplicate measurements of each sample were carried out by DRIFTS. Cluster hierarchical analysis was used for selecting calibration and…
Artificial neural network for quantitative determination of total protein in yogurt by infrared spectrometry
2009
Abstract A method has been introduced for quantitative determination of protein content in yogurt samples based on the characteristic absorbance of protein in 1800–1500 cm− 1 spectral region by mid-FTIR spectroscopy and chemometrics. Successive Projection Algorithm (SPA) wavelength selection procedure, coupled with feed forward Back-Propagation Artificial Neural Network (BP-ANN) model was the benefited chemometric technique. Relative Error of Prediction (REP) in BP-ANN and SPA-BP-ANN methods for training set was 7.25 and 3.70 respectively. Considering the complexity of the sample, the ANN model was found to be reliable, while the proposed method is rapid and simple, without any sample prepa…
Prediction of peak shape as a function of retention in reversed-phase liquid chromatography
2004
Optimisation of the resolution of multicomponent samples in HPLC is usually carried out by changing the elution conditions and considering the variation in retention of the analytes, to which a standard peak shape is assigned. However, the change in peak shape with the composition of the mobile phase can ruin the optimisation process, yielding unexpected overlaps in the experimental chromatograms for the predicted optimum, especially for complex mixtures. The possibility of modelling peak shape, in addition to peak position, is therefore attractive. A simple modified-Gaussian model with a parabolic variance, which is a function of conventional experimental parameters: retention time (tR), p…
Upper Bound for the Approximation Error for the Kirchhoff-Love Arch Problem
2013
In this paper, a guaranteed and computable upper bound of approximation errors for the Kirchhoff-Love arch problem is derived. In general, it belongs to the class of functional a posteriori error estimates. The derivation method uses purely functional arguments and, therefore, the estimates are valid for any conforming approximation within the energy space. The computational implementation of the upper bound is discussed and demonstrated by a numerical example.
Automatic left ventricle volume calculation with explainability through a deep learning weak-supervision methodology
2021
[EN] Background and objective: Magnetic resonance imaging is the most reliable imaging technique to assess the heart. More specifically there is great importance in the analysis of the left ventricle, as the main pathologies directly affect this region. In order to characterize the left ventricle, it is necessary to extract its volume. In this work we present a neural network architecture that is capable of directly estimating the left ventricle volume in short axis cine Magnetic Resonance Imaging in the end-diastolic frame and provide a segmentation of the region which is the basis of the volume calculation, thus offering explain-ability to the estimated value. Methods: The network was des…
The Use of Easily Computed Checks as a Trigger for Error Elimination
1970
Several checks have been inserted in the three main programs in order to learn about their correlation to the average relative error.
Sequential Learning with LS-SVM for Large-Scale Data Sets
2006
We present a subspace-based variant of LS-SVMs (i.e. regularization networks) that sequentially processes the data and is hence especially suited for online learning tasks. The algorithm works by selecting from the data set a small subset of basis functions that is subsequently used to approximate the full kernel on arbitrary points. This subset is identified online from the data stream. We improve upon existing approaches (esp. the kernel recursive least squares algorithm) by proposing a new, supervised criterion for the selection of the relevant basis functions that takes into account the approximation error incurred from approximating the kernel as well as the reduction of the cost in th…
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
2013
We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed
Extremal problems of approximation theory in fuzzy context
1999
Abstract The problem of approximation of a fuzzy subset of a normed space is considered. We study the error of approximation, which in this case is characterized by an L -fuzzy number. In order to do this we define the supremum of an L -fuzzy set of real numbers as well as the supremum and the infimum of a crisp set of L -fuzzy numbers. The introduced concepts allow us to investigate the best approximation and the optimal linear approximation. In particular, we consider approximation of a fuzzy subset in the space L p m of differentiable functions in the L q -metric. We prove the fuzzy counterparts of duality theorems, which in crisp case allows effectively to solve extremal problems of the…
Evaluation of the LSA-SAF gross primary production product derived from SEVIRI/MSG data (MGPP)
2020
The objective of this study is to describe a completely new 10-day gross primary production (GPP) product (MGPP LSA-411) based on data from the geostationary SEVIRI/MSG satellite within the LSA SAF (Land Surface Analysis SAF) as part of the SAF (Satellite Application Facility) network of EUMETSAT. The methodology relies on the Monteith approach. It considers that GPP is proportional to the absorbed photosynthetically active radiation APAR and the proportionality factor is known as the light use efficiency ε. A parameterization of this factor is proposed as the product of a εmax, corresponding to the canopy functioning under optimal conditions, and a coefficient quantifying the reduction of …