## Validation of Homology ComputationsHomology is an important computable tool for
quantifying complex structures. In many applications these structures
arise as nodal domains of real-valued functions and are therefore
amenable only to a numerical study, based on suitable discretizations.
Such an approach immediately raises the question of how accurate the
resulting homology computations are. In the papers cited below, we present a
probabilistic approach to quantifying the validity of homology
computations for nodal domains of random Fourier series in one and two
space dimensions, which furnishes explicit probabilistic a-priori
bounds for the suitability of certain discretization sizes. In
addition, we introduce a numerical method for verifying the homology
computation using interval arithmetic. |

Probabilistic and numerical validation of homology computations for nodal domains, S. Day, W.D. Kalies, K. Mischaikow, T. Wanner,

Probabilistic validation of homology computations for nodal domains, K. Mischaikow, T. Wanner,

Verified homology computations for nodal domains, S. Day, W.D. Kalies, T. Wanner,

Topology-guided sampling of nonhomogeneous random processes, K. Mischaikow, T. Wanner,