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Matrices which describe the surface downward protons created by the primary protons. First row: the normalized Martian atmospheric matrices of primary protons generating surface downward directed protons from physics lists A, B, C and D (Table 1). Second row: Normalized statistical uncertainty of the matrices. Third row: Image Differencing Matrices (IDM) of model A and B (1st column), B and C (2nd column), C and D (3rd column) which is also visualized with a 2D Gaussian filter applied (4th column). Fourth row: the normalized IDM. represents the average value in each matrix (while bins with zero statistics have been excluded) and σ is the standard deviation. All matrices are shown in the energy range from 1 MeV to 100 GeV (in logarithmic scale) for both input bins and output bins.
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