This article surveys recent work of Carlsson and collaborators on applications of
computational algebraic topology to problems of feature detection and shape recognition in …

Recently, machine learning (ML) has established itself in various worldwide benchmarking
competitions in computational biology, including Critical Assessment of Structure Prediction …

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 …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

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 …

The ability to predict protein–protein interactions is crucial to our understanding of a wide
range of biological activities and functions in the human body, and for guiding drug …

Proteins are the most important biomolecules for living organisms. The understanding of
protein structure, function, dynamics, and transport is one of the most challenging tasks in …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

This thesis develops the theory of sheaves and cosheaves with an eye towards applications
in science and engineering. To provide a theory that is computable, we focus on a …

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