Exhaustive enumeration of functions up to complexity k across operator bases shows the integrability fraction declines with k but rises sharply with logarithms, and the method discovers three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima, and Giac.
author Olivetti de Franca , F
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Exhaustive symbolic regression identifies low-complexity functional forms for luminosity and mass functions that outperform Schechter and Press-Schechter parametrizations while satisfying physical extrapolation and integration constraints.
Exhaustive symbolic regression on mock weak lensing excess surface density data recovers NFW profiles at 5% fractional errors with as few as 20 clusters but favors simpler functions at higher uncertainties because errors are smallest in the outskirts.
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Exhaustive Symbolic Integration: Integration by Differentiation and the Landscape of Symbolic Integrability
Exhaustive enumeration of functions up to complexity k across operator bases shows the integrability fraction declines with k but rises sharply with logarithms, and the method discovers three integrals that resist SymPy, Mathematica, RUBI, FriCAS, Maxima, and Giac.
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The functional form of galaxy and halo luminosity and mass functions
Exhaustive symbolic regression identifies low-complexity functional forms for luminosity and mass functions that outperform Schechter and Press-Schechter parametrizations while satisfying physical extrapolation and integration constraints.
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Constraining dark matter halo profiles with symbolic regression
Exhaustive symbolic regression on mock weak lensing excess surface density data recovers NFW profiles at 5% fractional errors with as few as 20 clusters but favors simpler functions at higher uncertainties because errors are smallest in the outskirts.