A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

Compression aims to reduce the size of an input, while maintaining its relevant properties.
For multi-parameter persistent homology, compression is a necessary step in any …

Boissonnat and Pritam introduced an algorithm to reduce a filtration of flag (or clique)
complexes, which can in particular speed up the computation of its persistent homology …

The application of solid mechanics theory for material behavior faces the discrete nature of
modern or biological material. Despite the developed methods of homogenization, there are …

Persistence modules are representations of products of totally ordered sets in the category
of vector spaces. They appear naturally in the representation theory of algebras, but in …

The expanding presence in space will place an increased dependency on networked
communications-a scalable communications infrastructure; that is, the Solar System Internet …

Persistent homology is a leading tool in topological data analysis (TDA). Many problems in
TDA can be solved via homological--and indeed, linear--algebra. However, matrices in this …

Solving polynomial systems of equations of both many degrees and variables is not a simple
computation. A method of solving these systems is to transform them into a Gröbner basis …

Refactoring tools, whether fully automated or semi-automated, are essential components of
the software development life cycle. As software libraries and frameworks evolve over time …

The Standard Competition Ranking (SCR) is a commonly adopted ranking strategy and has
been used in a wide range of applications, such as statistics, text mining, image processing …