Carlo . Master’s thesis, Stockholm University (2015). [34] Geant4 collaboration. Reference Physics Lists (2013). URL http://geant4.cern.ch/support/proc_mod_catalog/ physics_lists/referencePL.shtml . Retrieved Aug 18, 2016. [35] Geant4 collaboration. Geant4 10.1 Release Notes (2014). URL http://geant4.cern.ch/support/ReleaseNotes4.10.1. html . Retrieved Aug 18, 2016. [36] Grevillot, L. et al. Optimization of GEANT4 settings for Proton Pencil Beam Scanning simulations using GATE. Nuclear Instruments and Methods in Physics Research Section B 268 , 3295–3305 (2010). [37] GATE collaboration. Documentation and Recommendations for Users (2017). URL http://www.opengatecollaboration. org/UsersGuide . Retrieved Aug 18, 2016. [38] Jarlskog, C. Z. & Paganetti, H. Physics settings for using the Geant4 toolkit in proton therapy. IEEE Transactions on Nuclear Science 55 , 1018–1025 (2008). [39] ICRU. Stopping of ions heavier than Helium. ICRU Report 73 (2009). [40] James, F. A review of pseudorandom number generators. Comput. Phys. Commun. 60 , 329–344 (1990). [41] Schellhammer, S. M., Matthes, A., Pipek, J. & Apostolakis, J. Problem 1879 - Segfault at magnetic field edges (2017). URL https://bugzilla-geant4.kek.jp/show_bug.cgi?id=1879 . Retrieved Nov 15, 2016. [42] Kurosu, K., Takashina, M., Koizumi, M., Das, I. J. & Moskvin, V. Optimization of GATE and PHITS Monte Carlo code parameters for uniform scanning proton beam based on simulation with FLUKA general-purpose code. Nuclear Instruments and Methods in Physics Research Section B 336 , 45–54 (2014). References [26] to [42] are referred to in the Supplementary Information section only. 11