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Intensity and background data for each element were calculated using Imagene 5.5 (BioDiscovery Inc., Australia).

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The p value for each element was calculated using the Cox proportional hazard univariable regression model with overall survival as the endpoint.

Finally, the PR for each discretized element was calculated using (7): (7) ν = − 0.5 ln ⁡ (A / A ο ) ln ⁡ (1 + ε A ).

The sequence coverage of each position in the element was calculated using mpileup command in SAMtools v0.1.1938 (mpileup -d 8000).

The sequence coverage of each position in the element was calculated using mpileup command in SAMtools (mpileup -d 100000).

For selected uncorrelated atomic configurations, dipole matrix elements were calculated using the prescription described in ref. 36.

These matrix elements were calculated using the pure electronic wave functions obtained by the energy level calculations for 4f and 5d configurations.

Assessment values for lowest-level elements are calculated using a series algorithm that relates composite scores uniquely to the scoring scale.

The correlation coefficient and element-to-element ratios were calculated using Microsoft Excel 2003.

Genome coverage and copy number estimations for each element were calculated by alignment of each repeat to the assembled genomes using RepeatMasker.

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