Graph theory is now becoming a standard tool in system‐level neuroscience. However,
endowing observed brain anatomy and dynamics with a complex network representation …

Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

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 …

Combining concepts from topology and algorithms, this book delivers what its title promises:
an introduction to the field of computational topology. Starting with motivating problems in …

Our intention, at the beginning, was to write a short paper resolving some technical issues in
the theory of topological persistence. Specifically, we wished to present a clean easy-to-use …

We present DisPerSE, a novel approach to the coherent multiscale identification of all types
of astrophysical structures, in particular the filaments, in the large-scale distribution of the …

Persistent homology is an algebraic tool for measuring topological features of shapes and
functions. It casts the multi-scale organization we frequently observe in nature into a …

Morse Theory for Filtrations and Efficient Computation of Persistent Homology |
SpringerLink Skip to main content Advertisement SpringerLink Log in Menu Find a journal …