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.
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 • 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.
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.
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
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
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
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