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We introduce a new method to evaluate algebraic integrals over the simplex numerically.
1902
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A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four particle phase space integrals in massless QCD , Nucl. Phys. B 682
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T. Hahn, CUBA: A library for multidimensional numerical integration , Comput. Phys. Commun. 168
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2005
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S. Bloch, H. Esnault and D. Kreimer, On motives associated to graph polynomials , Comm. Math. Phys. 267
2006
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D. Kreimer and K. Yeats, An etude in non-linear Dyson-Schwinger equations , Nucl. Phys. B Proc. Suppl. 160
2006
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M. Berghoff and D. Kreimer, Graph complexes and Feynman rules , 2008.09540
2008
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2008
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D.E. Knuth, The Art of Computer Programming, Volume 2: Seminumerical Algorithms , Addison-Wesley (2014)
2014
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D.A. Spielman and S.-H. Teng, Nearly linear time algorithms for preconditioning and solving symmetric, diagonally dominant linear systems , SIAM J. Matrix Anal. Appl. 35
2014
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2015
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F. Brown and O. Schnetz, Single-valued multiple polylogarithms and a proof of the zig-zag conjecture , J. Number Theor. 148
2015
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J.M. Henn, Lectures on differential equations for Feynman integrals , J. Phys. A 48
2015
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D. Maclagan and B. Sturmfels, Introduction to tropical geometry , AMS (2015)
2015
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2015
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2015
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N. Arkani-Hamed, Y. Bai and T. Lam, Positive Geometries and Canonical Forms , JHEP 11
2017
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M. Borinsky, Renormalized asymptotic enumeration of Feynman diagrams , Annals Phys. 385
2017
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2017
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2017
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E. Panzer and O. Schnetz, The Galois coaction on ϕ 4 \phi^{4} periods , Commun. Num. Theor. Phys. 11
2017
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2018
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2018
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2018
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2018
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2018
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M. Henk, J. Richter-Gebert and G.M. Ziegler, Basic properties of convex polytopes , Handbook of discrete and computational geometry (2018) 383
2018
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F. Herzog, Geometric IR subtraction for final state real radiation , JHEP 08
2018
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O. Schnetz, Numbers and functions in quantum field theory , Phys. Rev. D 97
2018
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2019
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2019
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2019
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M. Berghoff, Feynman amplitudes on moduli spaces of graphs , Annales de l’I.H.P. D 7
2020
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E. Panzer. personal communication, 2020-09-15
2020
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