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Highly Cited

2017

Highly Cited

2017

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize… Expand

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Highly Cited

2015

Highly Cited

2015

We address the fundamental problem of goal-directed path planning in an uncertain environment represented as a probability (of… Expand

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Highly Cited

2014

Highly Cited

2014

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are… Expand

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Highly Cited

2014

Highly Cited

2014

The computation of persistent homology has proven a fundamental component of the nascent field of topological data analysis and… Expand

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Highly Cited

2013

Highly Cited

2013

We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its… Expand

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Highly Cited

2011

Highly Cited

2011

It is known that the brain network has small-world and scale-free topology, but the network structures drastically change… Expand

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Highly Cited

2011

Highly Cited

2011

The persistence diagram of a filtered simplicial complex is usually computed by reducing the boundary matrix of the complex. We… Expand

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Highly Cited

2009

Highly Cited

2009

We study the problem of computing zigzag persistence of a sequence of homology groups and study a particular sequence derived… Expand

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Highly Cited

2005

Highly Cited

2005

Abstract
We show that the persistent homology of a filtered d-dimensional
simplicial complex is simply the standard homology of a… Expand

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Highly Cited

2004

Highly Cited

2004

We study the homology of a filtered d-dimensional simplicial complex K as a single algebraic entity and establish a… Expand

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