Exponential Curve

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Leticia Andrade - One of the best experts on this subject based on the ideXlab platform.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

Soren Balling Engelsen - One of the best experts on this subject based on the ideXlab platform.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

  • comparative chemometric analysis of transverse low field 1h nmr relaxation data
    Advances in Magnetic Resonance in Food Science, 1999
    Co-Authors: Iben Ellegaard Bechmann, Henrik Toft Pedersen, Lars Norgaard, Soren Balling Engelsen
    Abstract:

    1 Abstract Transverse relaxation data from low-field (23.2 MHz) 1H NMR was investigated by different data analytical approaches. The quantitative information in the relaxation data of 200 intact salmon samples with respect to overall water and fat content was evaluated by four different data analytical methods: (a) bi-Exponential Curve fitting followed by linear regression, (b) forward selection of variables followed by multiple linear regression (FS-MLR), (c) partial least squares regression (PLS) and (d) non-negative alternating least squares regression (NN-ALSR). The investigation demonstrates that the quantitative prediction performance is significantly enhanced (reduction of the prediction error from 14% to 34%) by the use of multivariate chemometric procedures such as PLS. While PLS is an extraordinarily robust and efficient algorithm its strictly orthogonal latent variables suffer from a difficult qualitative interpretation. NN-ALSR and FS-MLR which exhibit a quantitative performance comparable to PLS do not suffer from this problem, but are more unstable and ineffective data analytical techniques.

Elisabeth Micklander - One of the best experts on this subject based on the ideXlab platform.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

Imad A. Farhat - One of the best experts on this subject based on the ideXlab platform.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

  • doubleslicing a non iterative single profile multi Exponential Curve resolution procedure application to time domain nmr transverse relaxation data
    Journal of Magnetic Resonance, 2007
    Co-Authors: Leticia Andrade, Elisabeth Micklander, Imad A. Farhat, Soren Balling Engelsen
    Abstract:

    Abstract A new non-iterative Curve resolution technique for resolving single decay profiles is proposed. The new technique, called DoubleSlicing , is based on the Decra (Direct Exponential Curve Resolution Algorithm) principle. While the original Decra was designed to resolve several decay Curves simultaneously and thus fitting common pure Exponentials, DoubleSlicing can resolve single decay profiles by a simple double data transformation followed by an analytical and unique three-way decomposition. The new approach is successfully demonstrated on experimental NMR CPMG relaxation data, measured on combinations of unmixed paramagnetic CuSO 4 solutions. Decay signals of the water component were acquired following an innovative experimental design that ensured no interaction between the components present in each sample under observation. DoubleSlicing proved to be accurate in estimating relaxation times differing in one order of magnitude (range: 19.6–159.4 ms). Its performance was comparable to discrete Exponential fitting with the advantage of being much faster – in terms of computation time, DoubleSlicing outperformed Exponential fitting by a factor of four.

Syyen Kuo - One of the best experts on this subject based on the ideXlab platform.

  • analysis of incorporating logistic testing effort function into software reliability modeling
    IEEE Transactions on Reliability, 2002
    Co-Authors: Chinyu Huang, Syyen Kuo
    Abstract:

    This paper investigates a SRGM (software reliability growth model) based on the NHPP (nonhomogeneous Poisson process) which incorporates a logistic testing-effort function. SRGM proposed in the literature consider the amount of testing-effort spent on software testing which can be depicted as an Exponential Curve, a Rayleigh Curve, or a Weibull Curve. However, it might not be appropriate to represent the consumption Curve for testing-effort by one of those Curves in some software development environments. Therefore, this paper shows that a logistic testing-effort function can be expressed as a software-development/test-effort Curve and that it gives a good predictive capability based on real failure-data. Parameters are estimated, and experiments performed on actual test/debug data sets. Results from applications to a real data set are analyzed and compared with other existing models to show that the proposed model predicts better. In addition, an optimal software release policy for this model, based on cost-reliability criteria, is proposed.

  • analysis of a software reliability growth model with logistic testing effort function
    International Symposium on Software Reliability Engineering, 1997
    Co-Authors: Chinyu Huang, Syyen Kuo, Ingyi Chen
    Abstract:

    We investigate a software reliability growth model (SRGM) based on the Non Homogeneous Poisson Process (NHPP) which incorporates a logistic testing effort function. Software reliability growth models proposed in the literature incorporate the amount of testing effort spent on software testing which can be described by an Exponential Curve, a Rayleigh Curve, or a Weibull Curve. However it may not be reasonable to represent the consumption Curve for testing effort only by an Exponential, a Rayleigh or a Weibull Curve in various software development environments. Therefore, we show that a logistic testing effort function can be expressed as a software development/test effort Curve and give a reasonable predictive capability for the real failure data. Parameters are estimated and experiments on three actual test/debug data sets are illustrated. The results show that the software reliability growth model with logistic testing effort function can estimate the number of initial faults better than the model with Weibull type consumption Curve. In addition, the optimal release policy of this model based on cost reliability criterion is discussed.