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Papers by Reidar Arneberg
Physica Scripta, 1983
Radiative electron rearrangement (RER) and hole-mixing effects in molecular ultra-soft X-ray spec... more Radiative electron rearrangement (RER) and hole-mixing effects in molecular ultra-soft X-ray spectra (USX) are theoretically analyzed at several levels of approximation and compared with X-ray photoelectron (XPS) transitions which result in the same residual ionic states. Numerical applications are carried out for the CO molecule with configuration interaction wavefunctions built on orbitals separately optimized for initial and final states. The USX spectra are more complex than the XPS spectrum in the energy ranges corresponding to RER and break-down of the MO-model due to interference from excited components of the initial state wavefunctions and due to non-orthogonality. This breaks the branching ratio rule that predicts equal satellite to parent ionic intensities for the XPS and the different core-sited USX spectra and does accordingly also limit the applicability of local selection rules for the hole-mixing in the USX spectrum.
Journal of Chemometrics, 2009
ABSTRACT Target projection (TP) also called target rotation (TR) was introduced to facilitate int... more ABSTRACT Target projection (TP) also called target rotation (TR) was introduced to facilitate interpretation of latent-variable regression models. Orthogonal partial least squares (OPLS) regression and PLS post-processing by similarity transform (PLS + ST) represent two alternative algorithms for the same purpose. In addition, OPLS and PLS + ST provide components to explain systematic variation in X orthogonal to the response. We show, that for the same number of components, OPLS and PLS + ST provide score and loading vectors for the predictive latent variable that are the same as for TP except for a scaling factor. Furthermore, we show how the TP approach can be extended to become a hybrid of latent-variable (LV) regression and exploratory LV analysis and thus embrace systematic variation in X unrelated to the response. Principal component analysis (PCA) of the residual variation after removal of the target component is here used to extract the orthogonal components, but X-tended TP (XTP) permits other criteria for decomposition of the residual variation. If PCA is used for decomposing the orthogonal variation in XTP, the variance of the major orthogonal components obtained for OPLS and XTP is observed to be almost the same, showing the close relationship between the methods. The XTP approach is tested and compared with OPLS for a three-component mixture analyzed by infrared spectroscopy and a multicomponent mixture measured by near infrared spectroscopy in a reactor. Copyright © 2008 John Wiley & Sons, Ltd.
Journal of Chemometrics, 2014
ABSTRACT The quality and practical usefulness of a regression model are a function of both interp... more ABSTRACT The quality and practical usefulness of a regression model are a function of both interpretability and prediction performance. This work presents some new graphical tools for improved interpretation of latent variable regression models that can also assist in improved algorithms for variable selection. Thus, these graphs provide visualization of the explanatory variables' content of response related as well as systematic orthogonal variation at a quantitative level. Furthermore, these graphs are able to reveal and partition the explanatory variables into those that are crucial for both interpretation and predictive performance of the model, and those that are crucial for prediction performance but confounded by large contributions of orthogonal variation. Tools for assessment of explanatory variables may not only aid interpretation and understanding of the model but also be crucial for performing variable selection with the purpose of obtaining parsimonious models with high explanatory information content as well as predictive performance. We show by example that by just using prediction performance as criterion for variable selection, it is possible to end up with a reduced model where the most selective variables are lost in the selection process. Copyright © 2014 John Wiley & Sons, Ltd.
The Journal of Chemical Physics, 1982
A high resolution ESCA spectrum of C2H2 was recorded using monochromatized AlKα excitation and wa... more A high resolution ESCA spectrum of C2H2 was recorded using monochromatized AlKα excitation and was analyzed by means of configuration interaction and multiple configuration SCF wave functions. The role of different schemes for electron-configurational selection in the initial and final states on transition moments and energies was investigated. The spectrum shows a prominent satellite structure in the inner valence region,
European Journal of Pharmaceutical Sciences, 2008
Environmental Health Perspectives, 2002
The present paper describes a strategy for toxicological evaluation of complex mixtures based on ... more The present paper describes a strategy for toxicological evaluation of complex mixtures based on chemical "fingerprinting" followed by pattern recognition (multivariate data analysis). The purpose is to correlate chemical fingerprints to measured toxicological endpoints, identify all major contributors to toxicity, and predict toxicity of additional mixtures. The strategy is illustrated with organic extracts of exhaust particles which are characterized by full scan gas chromatography-mass spectrometry (GC-MS). The complex GC-MS data are resolved into peaks and spectra for individual compounds using an automated curve resolution procedure. Projections to latent structures (PLS) is used for the regression modeling to correlate the GC-MS data to the measured responses; mutagenicity in the Ames Salmonella assay. The regression model identifies those peaks that co-vary with the observed mutagenicity. These peaks may be identified chemically from their spectra. Furthermore, the regression model can be used to predict mutagenicity from GC-MS chromatograms of additional samples.
Chemometrics and Intelligent Laboratory Systems, 2009
... The limit between spectral regions with marker candidates and less interesting regions is cho... more ... The limit between spectral regions with marker candidates and less interesting regions is chosen by the user. In this work, we use a limit of three, corresponding to 75% explained variance in a spectral variable to be selected as a marker candidate. ...
Analytical Chemistry, 2007
Physica Scripta, 1984
Energies and intensities of transitions in the discrete and near continuum parts of the K-shell E... more Energies and intensities of transitions in the discrete and near continuum parts of the K-shell EELS spectra are evaluated by means of ab initio methods. The fine structure superponing the carbon continuum spectrum is interpreted as due to an analogous shake effect associated with the strong 2sigma-2pi* discrete resonance.
Chemical Physics Letters, 1982
Chemical Physics, 1984
ABSTRACT Soft X-ray emission from gas-phase N2 molecules is calculated as dipole transitions in n... more ABSTRACT Soft X-ray emission from gas-phase N2 molecules is calculated as dipole transitions in neutral, singly and doubly ionized molecules. The role of electron correlation for the initial-state creation and for the de-excitation with X-ray emission is investigated, i.e. for processes of resonance core-electron excitation in the neutral molecule, for shake-up and shake-off processes leading to singly and doubly ionized states, respectively, as well as for radiative electron rearrangement (RER) in the emission. A total theoretical X-ray emission spectrum of the N2 molecule is constructed from ab initio configuration-interaction wavefunctions and is compared with the available experimental spectrum. Transition moments are evaluated in the dipole-length form between non-orthogonal sets of molecular orbitals. The multiply bonded character of N2 and its low-lying 1πg orbital give rise to strong resonance transitions, strong transitions from multiply excited initial shake-up states and lead to a break-down of the MO picture in a large interval of the spectrum from doubly excited states. Significant RER transitions are predicted and compared with corresponding structures in the photoelectron spectrum.
Chemical Physics Letters, 1982
Environmental toxicology and pharmacology, 2004
The present paper describes a strategy for toxicological evaluation of complex mixtures based on ... more The present paper describes a strategy for toxicological evaluation of complex mixtures based on chemical "fingerprinting" followed by pattern recognition (multivariate data analysis). The purpose is to correlate chemical fingerprints to measured toxicological endpoints, identify all major contributors to toxicity, and predict toxicity of additional mixtures. The strategy is illustrated with organic extracts of exhaust particles which are characterized by full scan gas chromatography-mass spectrometry (GC-MS). The complex GC-MS data are resolved into peaks and spectra for individual compounds using an automated curve resolution procedure. Projections to latent structures (PLS) is used for the regression modeling to correlate the GC-MS data to the measured responses; mutagenicity in the Ames Salmonella assay. The regression model identifies those peaks that co-vary with the observed mutagenicity. These peaks may be identified chemically from their spectra. Furthermore, the regression model can be used to predict mutagenicity from GC-MS chromatograms of additional samples.
European Journal of Pharmaceutical Sciences, 2008
Analytical Chemistry, 2009
The discriminating variable (DIVA) test and the selectivity ratio (SR) plot are developed as quan... more The discriminating variable (DIVA) test and the selectivity ratio (SR) plot are developed as quantitative tools for revealing the variables in spectral or chromatographic profiles discriminating best between two groups of samples. The SR plot is visually similar to a spectrum or a chromatogram, but with the most intense regions corresponding to the most discriminating variables. Thus, the variables with highest SR represent the variables most important for interpretation of differences between groups. Regions with variables that are positively or negatively correlated to each other are displayed as corresponding negative and positive regions in the SR plot. The nonparametric DIVA test is designed for connecting SR to discriminatory ability of a variable quantified as probability for correct classification. A mean probability for a certain SR range is calculated as the mean correct classification rate (MCCR) for all variables in the same SR interval. The MCCR is thus similar to a mean sensitivity in each SR interval. In addition to the ranking of all variables according to their discriminatory ability provided by the SR plot, the DIVA test connects a probability measure to each SR interval. Thus, the DIVA test makes it possible to objectively define thresholds corresponding to mean probability levels in the SR plot and provides a quantitative means to select discriminating variables. In order to validate the approach, samples of untreated cerebrospinal fluid (CSF) and samples spiked with a multicomponent peptide standard were analyzed by matrix-assisted laser desorption ionization (MALDI) mass spectrometry. The differences in the multivariate spectral profiles of the two groups were revealed using partial least-squares discriminant analysis (PLS-DA) followed by target projection (TP). The most discriminating mass-to-charge (m/z) regions were revealed by calculating the ratio of explained to unexplained variance for each m/z number on the target-projected component and displaying this measure in SR plots with quantitative boundaries determined from the DIVA test. The results are compared to some established methods for variable selection.
PROTEOMICS – Clinical Applications, 2007
Journal of Proteome Research, 2010
Mass spectral profiles from cerebrospinal fluid (CSF) are used as input to a novel multivariate a... more Mass spectral profiles from cerebrospinal fluid (CSF) are used as input to a novel multivariate approach to select features responsible for the separation of patients with multiple sclerosis (MS) from control groups. Our targeted statistical approach makes it possible to systematically remove features in the spectral fingerprints masking the components expressing the disease pattern. The low molecular weight CSF proteome from 54 patients with MS and a range of other neurological diseases (OND), as well as neurological healthy controls (NHC), is analyzed in replicates using mass spectral profiling. Statistically validated partial least-squares discriminant analysis (PLS-DA) models are created as a first step to separate the groups. Using the group membership as a target, the most discriminatory projection in the multivariate space spanned by the spectral profiles is revealed. From the resulting target-projected component, the spectral regions most significantly contributing to group separation are identified using the nonparametric discriminating variable (DIVA) test together with the so-called selectivity ratio (SR) plot. Our approach is general and can be applied for other diseases and instrumental techniques as well.
Physica Scripta, 1983
Radiative electron rearrangement (RER) and hole-mixing effects in molecular ultra-soft X-ray spec... more Radiative electron rearrangement (RER) and hole-mixing effects in molecular ultra-soft X-ray spectra (USX) are theoretically analyzed at several levels of approximation and compared with X-ray photoelectron (XPS) transitions which result in the same residual ionic states. Numerical applications are carried out for the CO molecule with configuration interaction wavefunctions built on orbitals separately optimized for initial and final states. The USX spectra are more complex than the XPS spectrum in the energy ranges corresponding to RER and break-down of the MO-model due to interference from excited components of the initial state wavefunctions and due to non-orthogonality. This breaks the branching ratio rule that predicts equal satellite to parent ionic intensities for the XPS and the different core-sited USX spectra and does accordingly also limit the applicability of local selection rules for the hole-mixing in the USX spectrum.
Journal of Chemometrics, 2009
ABSTRACT Target projection (TP) also called target rotation (TR) was introduced to facilitate int... more ABSTRACT Target projection (TP) also called target rotation (TR) was introduced to facilitate interpretation of latent-variable regression models. Orthogonal partial least squares (OPLS) regression and PLS post-processing by similarity transform (PLS + ST) represent two alternative algorithms for the same purpose. In addition, OPLS and PLS + ST provide components to explain systematic variation in X orthogonal to the response. We show, that for the same number of components, OPLS and PLS + ST provide score and loading vectors for the predictive latent variable that are the same as for TP except for a scaling factor. Furthermore, we show how the TP approach can be extended to become a hybrid of latent-variable (LV) regression and exploratory LV analysis and thus embrace systematic variation in X unrelated to the response. Principal component analysis (PCA) of the residual variation after removal of the target component is here used to extract the orthogonal components, but X-tended TP (XTP) permits other criteria for decomposition of the residual variation. If PCA is used for decomposing the orthogonal variation in XTP, the variance of the major orthogonal components obtained for OPLS and XTP is observed to be almost the same, showing the close relationship between the methods. The XTP approach is tested and compared with OPLS for a three-component mixture analyzed by infrared spectroscopy and a multicomponent mixture measured by near infrared spectroscopy in a reactor. Copyright © 2008 John Wiley & Sons, Ltd.
Journal of Chemometrics, 2014
ABSTRACT The quality and practical usefulness of a regression model are a function of both interp... more ABSTRACT The quality and practical usefulness of a regression model are a function of both interpretability and prediction performance. This work presents some new graphical tools for improved interpretation of latent variable regression models that can also assist in improved algorithms for variable selection. Thus, these graphs provide visualization of the explanatory variables' content of response related as well as systematic orthogonal variation at a quantitative level. Furthermore, these graphs are able to reveal and partition the explanatory variables into those that are crucial for both interpretation and predictive performance of the model, and those that are crucial for prediction performance but confounded by large contributions of orthogonal variation. Tools for assessment of explanatory variables may not only aid interpretation and understanding of the model but also be crucial for performing variable selection with the purpose of obtaining parsimonious models with high explanatory information content as well as predictive performance. We show by example that by just using prediction performance as criterion for variable selection, it is possible to end up with a reduced model where the most selective variables are lost in the selection process. Copyright © 2014 John Wiley & Sons, Ltd.
The Journal of Chemical Physics, 1982
A high resolution ESCA spectrum of C2H2 was recorded using monochromatized AlKα excitation and wa... more A high resolution ESCA spectrum of C2H2 was recorded using monochromatized AlKα excitation and was analyzed by means of configuration interaction and multiple configuration SCF wave functions. The role of different schemes for electron-configurational selection in the initial and final states on transition moments and energies was investigated. The spectrum shows a prominent satellite structure in the inner valence region,
European Journal of Pharmaceutical Sciences, 2008
Environmental Health Perspectives, 2002
The present paper describes a strategy for toxicological evaluation of complex mixtures based on ... more The present paper describes a strategy for toxicological evaluation of complex mixtures based on chemical "fingerprinting" followed by pattern recognition (multivariate data analysis). The purpose is to correlate chemical fingerprints to measured toxicological endpoints, identify all major contributors to toxicity, and predict toxicity of additional mixtures. The strategy is illustrated with organic extracts of exhaust particles which are characterized by full scan gas chromatography-mass spectrometry (GC-MS). The complex GC-MS data are resolved into peaks and spectra for individual compounds using an automated curve resolution procedure. Projections to latent structures (PLS) is used for the regression modeling to correlate the GC-MS data to the measured responses; mutagenicity in the Ames Salmonella assay. The regression model identifies those peaks that co-vary with the observed mutagenicity. These peaks may be identified chemically from their spectra. Furthermore, the regression model can be used to predict mutagenicity from GC-MS chromatograms of additional samples.
Chemometrics and Intelligent Laboratory Systems, 2009
... The limit between spectral regions with marker candidates and less interesting regions is cho... more ... The limit between spectral regions with marker candidates and less interesting regions is chosen by the user. In this work, we use a limit of three, corresponding to 75% explained variance in a spectral variable to be selected as a marker candidate. ...
Analytical Chemistry, 2007
Physica Scripta, 1984
Energies and intensities of transitions in the discrete and near continuum parts of the K-shell E... more Energies and intensities of transitions in the discrete and near continuum parts of the K-shell EELS spectra are evaluated by means of ab initio methods. The fine structure superponing the carbon continuum spectrum is interpreted as due to an analogous shake effect associated with the strong 2sigma-2pi* discrete resonance.
Chemical Physics Letters, 1982
Chemical Physics, 1984
ABSTRACT Soft X-ray emission from gas-phase N2 molecules is calculated as dipole transitions in n... more ABSTRACT Soft X-ray emission from gas-phase N2 molecules is calculated as dipole transitions in neutral, singly and doubly ionized molecules. The role of electron correlation for the initial-state creation and for the de-excitation with X-ray emission is investigated, i.e. for processes of resonance core-electron excitation in the neutral molecule, for shake-up and shake-off processes leading to singly and doubly ionized states, respectively, as well as for radiative electron rearrangement (RER) in the emission. A total theoretical X-ray emission spectrum of the N2 molecule is constructed from ab initio configuration-interaction wavefunctions and is compared with the available experimental spectrum. Transition moments are evaluated in the dipole-length form between non-orthogonal sets of molecular orbitals. The multiply bonded character of N2 and its low-lying 1πg orbital give rise to strong resonance transitions, strong transitions from multiply excited initial shake-up states and lead to a break-down of the MO picture in a large interval of the spectrum from doubly excited states. Significant RER transitions are predicted and compared with corresponding structures in the photoelectron spectrum.
Chemical Physics Letters, 1982
Environmental toxicology and pharmacology, 2004
The present paper describes a strategy for toxicological evaluation of complex mixtures based on ... more The present paper describes a strategy for toxicological evaluation of complex mixtures based on chemical "fingerprinting" followed by pattern recognition (multivariate data analysis). The purpose is to correlate chemical fingerprints to measured toxicological endpoints, identify all major contributors to toxicity, and predict toxicity of additional mixtures. The strategy is illustrated with organic extracts of exhaust particles which are characterized by full scan gas chromatography-mass spectrometry (GC-MS). The complex GC-MS data are resolved into peaks and spectra for individual compounds using an automated curve resolution procedure. Projections to latent structures (PLS) is used for the regression modeling to correlate the GC-MS data to the measured responses; mutagenicity in the Ames Salmonella assay. The regression model identifies those peaks that co-vary with the observed mutagenicity. These peaks may be identified chemically from their spectra. Furthermore, the regression model can be used to predict mutagenicity from GC-MS chromatograms of additional samples.
European Journal of Pharmaceutical Sciences, 2008
Analytical Chemistry, 2009
The discriminating variable (DIVA) test and the selectivity ratio (SR) plot are developed as quan... more The discriminating variable (DIVA) test and the selectivity ratio (SR) plot are developed as quantitative tools for revealing the variables in spectral or chromatographic profiles discriminating best between two groups of samples. The SR plot is visually similar to a spectrum or a chromatogram, but with the most intense regions corresponding to the most discriminating variables. Thus, the variables with highest SR represent the variables most important for interpretation of differences between groups. Regions with variables that are positively or negatively correlated to each other are displayed as corresponding negative and positive regions in the SR plot. The nonparametric DIVA test is designed for connecting SR to discriminatory ability of a variable quantified as probability for correct classification. A mean probability for a certain SR range is calculated as the mean correct classification rate (MCCR) for all variables in the same SR interval. The MCCR is thus similar to a mean sensitivity in each SR interval. In addition to the ranking of all variables according to their discriminatory ability provided by the SR plot, the DIVA test connects a probability measure to each SR interval. Thus, the DIVA test makes it possible to objectively define thresholds corresponding to mean probability levels in the SR plot and provides a quantitative means to select discriminating variables. In order to validate the approach, samples of untreated cerebrospinal fluid (CSF) and samples spiked with a multicomponent peptide standard were analyzed by matrix-assisted laser desorption ionization (MALDI) mass spectrometry. The differences in the multivariate spectral profiles of the two groups were revealed using partial least-squares discriminant analysis (PLS-DA) followed by target projection (TP). The most discriminating mass-to-charge (m/z) regions were revealed by calculating the ratio of explained to unexplained variance for each m/z number on the target-projected component and displaying this measure in SR plots with quantitative boundaries determined from the DIVA test. The results are compared to some established methods for variable selection.
PROTEOMICS – Clinical Applications, 2007
Journal of Proteome Research, 2010
Mass spectral profiles from cerebrospinal fluid (CSF) are used as input to a novel multivariate a... more Mass spectral profiles from cerebrospinal fluid (CSF) are used as input to a novel multivariate approach to select features responsible for the separation of patients with multiple sclerosis (MS) from control groups. Our targeted statistical approach makes it possible to systematically remove features in the spectral fingerprints masking the components expressing the disease pattern. The low molecular weight CSF proteome from 54 patients with MS and a range of other neurological diseases (OND), as well as neurological healthy controls (NHC), is analyzed in replicates using mass spectral profiling. Statistically validated partial least-squares discriminant analysis (PLS-DA) models are created as a first step to separate the groups. Using the group membership as a target, the most discriminatory projection in the multivariate space spanned by the spectral profiles is revealed. From the resulting target-projected component, the spectral regions most significantly contributing to group separation are identified using the nonparametric discriminating variable (DIVA) test together with the so-called selectivity ratio (SR) plot. Our approach is general and can be applied for other diseases and instrumental techniques as well.