26 research outputs found
Numerical evaluation of two-loop integrals with pySecDec
We describe the program pySecDec, which factorises endpoint singularities
from multi-dimensional parameter integrals and can serve to calculate integrals
occurring in higher order perturbative calculations numerically. We focus on
the new features and on frequently asked questions about the usage of the
program.Comment: 11 pages, to appear in the proceedings of the HiggsTools Final
Meeting, IPPP, University of Durham, UK, September 201
Computations of volumes in five candidates elections
We describe several analytical results obtained in five candidates social
choice elections under the assumption of the Impartial Anonymous Culture. These
include the Condorcet and Borda paradoxes, as well as the Condorcet efficiency
of plurality, negative plurality and Borda voting, including their runoff
versions. The computations are done by Normaliz. It finds precise probabilities
as volumes of polytopes in dimension 119, using its recent implementation of
the Lawrence algorithm
Graver bases of shifted numerical semigroups with 3 generators
A numerical semigroup is a subset of the non-negative integers that is
closed under addition. A factorization of is an expression of as
a sum of generators of , and the Graver basis of is a collection
of trades between the generators of that allows for efficient
movement between factorizations. Given positive integers ,
consider the family of
"shifted" numerical semigroups whose generators are obtained by translating
by an integer parameter . In this paper, we characterize
the Graver basis of for sufficiently large in the case , in the form of a recursive construction of from that of smaller
values of . As a consequence of our result, the number of trades in
, when viewed as a function of , is eventually quasilinear. We also
obtain a sharp lower bound on the start of quasilinear behavior