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Basics of Multivariate Analysis in Neuroimaging Data
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    Non-linearities in x-ray free electron laser data can stem from non-uniform sample spectra, not just detector saturation. A new multivariate regression method using photon energy corrects this, improving data normalization for challenging experiments.

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    Area of Science:

    • X-ray science
    • Materials science
    • Spectroscopy

    Background:

    • Accurate data analysis from stochastic X-ray Free Electron Laser (XFEL) sources requires normalizing scattered intensity by incident flux.
    • Non-linearities in this normalization are often incorrectly attributed solely to detector saturation.
    • Non-uniform sample spectra within the monochromator bandwidth can also introduce significant non-linearities.

    Purpose of the Study:

    • To identify and address the underrecognized source of non-linearities in XFEL data normalization.
    • To develop a robust method for modeling and correcting non-linearities caused by spectral variations.
    • To enable the re-analysis of previously challenging XFEL datasets.

    Main Methods:

    • Utilized multivariate regression analysis to model the observed non-linearities.
    • Employed shot-by-shot X-ray photon energy as a key independent variable in the regression model.
    • Implemented event building techniques for efficient data processing and analysis.

    Main Results:

    • Demonstrated that non-uniform sample spectra within the monochromator bandwidth are a significant cause of non-linearities.
    • Successfully modeled and quantified the non-linear effects using the proposed multivariate regression approach.
    • Validated the effectiveness of the method in correcting normalization errors.

    Conclusions:

    • The developed method effectively corrects non-linearities in XFEL data arising from spectral variations.
    • This approach enhances the accuracy of data normalization, crucial for reliable scientific interpretation.
    • Facilitates the re-evaluation of past XFEL data, potentially unlocking new insights.