53 citations · 123 across the 30 of their papers we have counts for
32 papers
Restrictions of Pfaffian Systems for Feynman Integrals
Vsevolod Chestnov, Saiei J. Matsubara-Heo, Henrik J. Munch +1
This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering ampl…
Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
Vsevolod Chestnov, Federico Gasparotto, Manoj K. Mandal +4
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose…
Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
Nobuki Takayama, Takaharu Yaguchi, Yi Zhang
Definite integrals with parameters of holonomic functions satisfy holonomic systems of linear partial differential equations. When we restrict parameters to a one dimensional curve…
Algorithm for direct sampling from conditional distributions of toric models
Shuhei Mano, Nobuki Takayama
We show that contiguity relations of hypergeometric functions of several variables give a direct sampling algorithm from the conditional distribution of toric models in statistics.…
Fast evaluation of some p-adic transcendental functions
Xavier Caruso, Marc Mezzarobba, Nobuki Takayama +1
We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our…
An algorithm of computing cohomology intersection number of hypergeometric integrals
Saiei-Jaeyeong Matsubara-Heo, Nobuki Takayama
We show that the cohomology intersection number of a twisted Gauss-Manin connection with regularization condition is a rational function. As an application, we obtain a new quadrat…