Train bearing is one of the key parts of a train wheel, and its fault diagnosis is crucial for train
safety. This paper proposes an Improved Linear Discriminant Analysis (ILDA) algorithm to …

A common first step in the terrain processing pipeline of large Triangulated Irregular
Networks (TINs) is simplifying the TIN to make it manageable for further processing. The …

In this paper, we define the homological Morse numbers of a filtered cell complex in terms of
relative homology of nested filtration pieces, and derive inequalities relating these numbers …

The main objective of this paper is to extend Morse–Forman theory to vector-valued
functions. This is mostly motivated by the need to develop new tools and methods to …

We address the problem of performing a topology-aware simplification algorithm on a
compact and distributed data structure for triangle meshes, the Terrain trees. Topology …

A multiparameter filtration, or a multifiltration, may in many cases be seen as the collection of
sublevel sets of a vector function, which we call a multifiltering function. The main objective …

One common function class in machine learning is the class of ReLU neural networks. ReLU
neural networks induce a piecewise linear decomposition of their input space called the …

Locating neck-like features, or locally narrow parts, of a surface is crucial in various
applications such as segmentation, shape analysis, path planning, and robotics. Topological …

Advances in high-performance computing require new ways to represent large-scale
scientific data to support data storage, data transfers, and data analysis within scientific …

In the context of CAD CAM CAE (Computer-Aided Design, Manufacturing and Engineering)
and Additive Manufacturing, the computation of level sets of closed 2-manifold triangular …