Network-based modeling of complex systems and data using the language of graphs has
become an essential topic across a range of different disciplines. Arguably, this graph-based …

Modeling of heterogeneous materials and media is a problem of fundamental importance to
a wide class of phenomena and systems, ranging from condensed matter physics, soft …

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 …

An elementary question in porous media research is in regard to the relationship between
structure and function. In most fields, the porosity and permeability of porous media are …

This paper introduces persistent homology, which is a powerful tool to characterize the
shape of data using the mathematical concept of topology. We explain the fundamental idea …

Accelerated materials development with machine learning (ML) assisted screening and high
throughput experimentation for new photovoltaic materials holds the key to addressing our …

Persistent homology (PH) provides topological descriptors for geometric data, such as
weighted graphs, which are interpretable, stable to perturbations, and invariant under, eg …

Abstract Characterization of the morphology, identification of patterns and quantification of
order encountered in colloidal assemblies is essential for several reasons. First of all, it is …

It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate
dramatically different properties in a protein folding process. Even with the enormous …

The persistent homology of a stationary point process on RN is studied in this paper. As a
generalization of continuum percolation theory, we study higher dimensional topological …