1 code implementation • 23 Dec 2013 • Justin Curry, Robert Ghrist, Vidit Nanda
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology.
Algebraic Topology 55-04
no code implementations • 7 Jan 2016 • Chad Giusti, Robert Ghrist, Danielle S. Bassett
Specifically, we explore the use of \emph{simplicial complexes}, a theoretical notion developed in the field of mathematics known as algebraic topology, which is now becoming applicable to real data due to a rapidly growing computational toolset.
Neurons and Cognition Algebraic Topology Quantitative Methods 92-02, 92B20, 57Q05
3 code implementations • 1 Jun 2016 • Gregory Henselman, Robert Ghrist
This technical report introduces a novel approach to efficient computation in homological algebra over fields, with particular emphasis on computing the persistent homology of a filtered topological cell complex.
Algebraic Topology Combinatorics
1 code implementation • 4 Aug 2018 • Jakob Hansen, Robert Ghrist
This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves.
Algebraic Topology Combinatorics 55N30, 05C50
1 code implementation • 2 Jul 2020 • Darrick Lee, Robert Ghrist
We lift the theory of path signatures to the setting of Lie group valued time series, adapting these tools for time series with underlying geometric constraints.
no code implementations • 1 Sep 2020 • Hans Riess, Yiannis Kantaros, George Pappas, Robert Ghrist
We show that these constraints along with the requirement of propagating information in the network can be captured by a Linear Temporal Logic (LTL) framework.
no code implementations • 22 Oct 2020 • Alejandro Parada-Mayorga, Hans Riess, Alejandro Ribeiro, Robert Ghrist
In this paper we state the basics for a signal processing framework on quiver representations.
no code implementations • NeurIPS Workshop TDA_and_Beyond 2020 • Hans Riess, Jakob Hansen, Robert Ghrist
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms.