Phase separation mechanisms can produce a variety of complicated and intricate
microstructures, which often can be difficult to characterize in a quantitative way. In recent …

In this paper we present a new algorithm for computing the homology of regular CW-
complexes. This algorithm is based on the coreduction algorithm due to Mrozek and Batko …

A cohomology ring algorithm in a dimension-independent framework of combinatorial
cubical complexes is developed with the aim of applying it to the topological analysis of high …

We demonstrate how topological methods can be used to study pattern formation and
pattern evolution in phase-field models of materials science. In the context of the diblock …

In this work we develop a method for computing mathematically rigorous enclosures of some
one dimensional manifolds of heteroclinic orbits for nonlinear maps. Our method exploits a …

Discrete gradient vector fields are combinatorial structures that can be used for accelerating
the homology computation of CW complexes, such as simplicial or cubical complexes, by …

Understanding and predicting critical transitions in spatially explicit ecological systems is
particularly challenging due to their complex spatial and temporal dynamics and high …

Isolated invariant sets and their associated Conley indices are valuable tools for studying
dynamical systems and their global invariant structures. Through their design, they aim to …

While one-dimensional persistent homology can be an effective way to discriminate data, it
has limitations. Multidimensional persistent homology is a technique amenable to data …

The interaction between discrete and continuous mathematics lies at the heart of many
fundamental problems in applied mathematics and computational sciences. In this paper we …