7 citations · 18 across the 6 of their papers we have counts for
8 papers
Many toric ideals generated by quadratic binomials possess no quadratic Gröbner bases
Takayuki Hibi, Kenta Nishiyama, Hidefumi Ohsugi +1
Let be a finite connected simple graph and the toric ideal of the edge ring of . In the present paper, we study finite graphs with the property that $I_{G…
Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups
Takayuki Hibi, Kenta Nishiyama, Nobuki Takayama
This is the third revision. We study bases of Pfaffian systems for -hypergeometric system. Gröbner deformations give bases. These bases also give those for twisted cohomology gr…
The Holonomic Rank of the Fisher-Bingham System of Differential Equations
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
The Fisher-Bingham system is a system of linear partial differential equations satisfied by the Fisher-Bingham integral for the -dimensional sphere . The system is given in…
Holonomic Gradient Descent for the Fisher-Bingham Distribution on the -dimensional Sphere
Tamio Koyama, Hiromasa Nakayama, Kenta Nishiyama +1
We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a -di…
Incomplete Hypergeometric Systems Associated to 1-Simplex (n-1)-Simplex
Kenta Nishiyama
The A-hypergeometric system was introduced by Gel'fand, Kapranov and Zelevinsky in the 1980's. Among several classes of A-hypergeometric functions, those for 1-simplex (n-…
Holonomic Gradient Descent and its Application to Fisher-Bingham Integral
Tomonari Sei, Nobuki Takayama, Akimichi Takemura +4
We give a new algorithm to find local maximum and minimum of a holonomic function and apply it for the Fisher-Bingham integral on the sphere , which is used in the directional…