Determination of the number of factors and the experimental error in a data matrix

Malinowski, Edmund R.

doi:10.1021/ac50012a027

Cited by 499 publications

(274 citation statements)

References 16 publications

(15 reference statements)

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“…Spectra from clean spores [intracellular Mn(II)] and the birnessite product known to be present (12,13) were included in the principal component analysis sample set to mathematically decouple likely component correlations between Mn(III) and the end-member products or reactants. This analysis showed that there were three significant components present in the system, as determined by use of the indicator function (23,28,29), and definitively shows that -XANES has detected a third species of Mn in the oxidation samples.…”

Section: Resultsmentioning

confidence: 85%

Evidence for the presence of Mn(III) intermediates in the bacterial oxidation of Mn(II)

Webb

Dick

Bargar

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

291

199

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Bacterial oxidation of Mn(II) to Mn(IV) is believed to drive the oxidative segment of the global biogeochemical Mn cycle and regulates the concentration of dissolved Mn(II) in the oceanic water column, where it is a critical nutrient for planktonic primary productivity. Mn(II) oxidizing activity is expressed by numerous phylogenetically diverse bacteria and fungi, suggesting that it plays a fundamental and ubiquitous role in the environment. This important redox system is believed to be driven by an enzyme or enzyme complex involving a multicopper oxidase, although the biochemical mechanism has never been conclusively demonstrated. Here, we show that Mn(II) oxidation by spores of the marine Bacillus sp. strain SG-1 is a result of two sequential one-step electron transfer processes, both requiring the putative multicopper oxidase, MnxG, in which Mn(III) is a transient intermediate. A kinetic model of the oxidation pathway is presented, which shows that the Mn(II) to Mn(III) step is the rate-limiting step. Thus, oxidation of Mn(II) appears to involve a unique multicopper oxidase system capable of the overall two-electron oxidation of its substrate. This enzyme system may serve as a source for environmental Mn(III), a strong oxidant and competitor for siderophorebound Fe(III) in nutrient-limited environments. That metabolically dormant spores catalyze an important biogeochemical process intimately linked to the C, N, Fe, and S cycles requires us to rethink the role of spores in the environment.kinetics ͉ multicopper oxidase ͉ spores ͉ x-ray absorption near-edge spectroscopy

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Section: Resultsmentioning

confidence: 85%

Evidence for the presence of Mn(III) intermediates in the bacterial oxidation of Mn(II)

Webb

Dick

Bargar

et al. 2005

Proc. Natl. Acad. Sci. U.S.A.

291

199

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“…Several methods for estimating the number of pure components exist, [39][40][41]. However, all of them assume NM.…”

Section: ) Calculate Function F(a)mentioning

confidence: 99%

Extraction of multiple pure component 1H and 13C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

Kopriva

Jerić

Smrečki

2009

Analytica Chimica Acta

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Sparse Component Analysis (SCA) is demonstrated for blind extraction of three pure component spectra from only two measured mixed spectra in 13 C and 1 H nuclear magnetic resonance (NMR) spectroscopy. This appears to be the first time to report such results and that is the first novelty of the paper. Presented concept is general and directly applicable to experimental scenarios that possibly would require use of more than two mixtures. However, it is important to emphasize that number of required mixtures is always less than number of components present in these mixtures. The second novelty is formulation of blind NMR spectra decomposition exploiting sparseness of the pure components in the wavelet basis defined by either Morlet or Mexican hat wavelet. This enabled accurate estimation of the concentration matrix and number of pure components by means of data clustering algorithm and pure components § Patent pending under the number PCT/HR2008/000037. 2 spectra by means of linear programming with constraints from both 1 H and 13 C NMR experimental data.The third novelty is capability of proposed method to estimate number of pure components in demanding underdetermined blind source separation (uBSS) scenario. This is in contrast to majority of the BSS algorithms that assume this information to be known in advance. Presented results are important for the NMR spectroscopy-associated data analysis in pharmaceutical industry, medicine diagnostics and natural products research.

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“…eigenvalues of the covariance or correlation matrix. Methods in this group are GAP [32], [33], RAE (ratio of adjacent eigenvalues) [34], SORTE (second order statistic of the eigenvalues) [33], [32], RAESORTE [34], and EIF (empirical indicator function) [35], [36]. Former methods estimate mode-n rank from the unfolded tensor ( ) n X by searching for dominant eigenvalues of the Gramm matrix ( ) ( ) T n n X X according to some criterion, e.g.…”

Section: Dimensions Of the Core Tensormentioning

confidence: 99%

Noninvasive diagnosis of melanoma with tensor decomposition-based feature extraction from clinical color image

Jukić

Kopriva

Cichocki

2013

Biomedical Signal Processing and Control

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Determination of the number of factors and the experimental error in a data matrix

Cited by 499 publications

References 16 publications

Evidence for the presence of Mn(III) intermediates in the bacterial oxidation of Mn(II)

Evidence for the presence of Mn(III) intermediates in the bacterial oxidation of Mn(II)

Extraction of multiple pure component 1H and 13C NMR spectra from two mixtures: Novel solution obtained by sparse component analysis-based blind decomposition

Noninvasive diagnosis of melanoma with tensor decomposition-based feature extraction from clinical color image

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