This paper presents a new representation for root images based on Reeb graphs. The representation proposed captures lengths and distances in root structures as well as locations of branches, numbers of lateral roots and the locations of the root tips. An analysis of root images using Reeb graphs is presented and results are compared to ground truth measurements. This paper shows, that the Reeb ...

Numerical methods for solving the heat equation via potential theory have been hampered by the high cost of evaluating heat potentials. When M points are used in the discretization of the boundary and N time steps are computed, an amount of work of the order O(N M) has traditionally been required. In this paper, we present an algorithm which requires an amount of work of the order O(NM), and we...

Adjoint Algorithmic Differentiation is an efficient way to obtain price derivatives with respect to the data inputs. We describe how the process efficiency can be further improved when a model calibration is performed. Using the implicit function theorem, differentiating the numerical process used in calibration is not required. The resulting implementation is more efficient than automatic diff...