We consider the genus-one curves which arise in cuts of sunrise and elliptic double-box Feynman integrals. compute compare invariants these a number ways, including parametrization, lightcone Baikov (in full loop-by-loop variants). find that same geometry for arises all cases, lends support to idea there exists an invariant notion geometry, independent on way it is computed. further indicate ho...

We propose a new class of Foundation-Penalty (FP) cuts for GUB-constrained (and ordinary) mixed-integer programs, which are easy to generate by exploiting standard penalty calculations that are routinely employed in branch-and-bound contexts. The FP cuts are derived with reference to a selected integer variable or GUB set, and a foundation function that is typically a reduced cost function corr...

This paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts for the VRPTW. In particular, any reachability cut dominates one or more k-path cuts. The paper presents sepa...