68 citations · 98 across the 11 of their papers we have counts for
16 papers
Computing complete hyperbolic structures on cusped 3-manifolds
Clément Maria, Owen Rouillé
A fundamental way to study 3-manifolds is through the geometric lens, one of the most prominent geometries being the hyperbolic one. We focus on the computation of a complete hyper…
Hard Diagrams of the Unknot
Benjamin A. Burton, Hsien-Chih Chang, Maarten Löffler +5
We present three "hard" diagrams of the unknot. They require (at least) three extra crossings before they can be simplified to the trivial unknot diagram via Reidemeister moves in…
Computation of Large Asymptotics of 3-Manifold Quantum Invariants
Clément Maria, Owen Rouillé
Quantum topological invariants have played an important role in computational topology, and they are at the heart of major modern mathematical conjectures. In this article, we stud…
Computing Persistent Homology with Various Coefficient Fields in a Single Pass
Jean-Daniel Boissonnat, Clément Maria
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-…
The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes
Jean-Daniel Boissonnat, Clément Maria
This paper introduces a data structure, called simplex tree, to represent abstract simplicial complexes of any dimension. All faces of the simplicial complex are explicitly stored…
Intrinsic Topological Transforms via the Distance Kernel Embedding
Clément Maria, Steve Oudot, Elchanan Solomon
Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measure…
Parameterized complexity of quantum invariants
Clément Maria
We give a general fixed parameter tractable algorithm to compute quantum invariants of links presented by diagrams, whose complexity is singly exponential in the carving-width (or…
Discrete Morse Theory for Computing Zigzag Persistence
Clément Maria, Hannah Schreiber
We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology. From a zigzag filt…
Treewidth, crushing, and hyperbolic volume
Clément Maria, Jessica S. Purcell
We prove that there exists a universal constant such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most times its volume. The converse is not…
Computing Zigzag Persistent Cohomology
Clément Maria, Steve Oudot
Zigzag persistent homology is a powerful generalisation of persistent homology that allows one not only to compute persistence diagrams with less noise and using less memory, but a…
A polynomial time algorithm to compute quantum invariants of 3-manifolds with bounded first Betti number
Clément Maria, Jonathan Spreer
In this article, we introduce a fixed parameter tractable algorithm for computing the Turaev-Viro invariants TV(4,q), using the dimension of the first homology group of the manifol…
Admissible colourings of 3-manifold triangulations for Turaev-Viro type invariants
Clément Maria, Jonathan Spreer
Turaev Viro invariants are amongst the most powerful tools to distinguish 3-manifolds: They are implemented in mathematical software, and allow practical computations. The invarian…
Algorithms and complexity for Turaev-Viro invariants
Benjamin A. Burton, Clément Maria, Jonathan Spreer
The Turaev-Viro invariants are a powerful family of topological invariants for distinguishing between different 3-manifolds. They are invaluable for mathematical software, but curr…
Introduction to the R package TDA
Brittany Terese Fasy, Jisu Kim, Fabrizio Lecci +1
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of func…
The Compressed Annotation Matrix: an Efficient Data Structure for Computing Persistent Cohomology
Jean-Daniel Boissonnat, Tamal K. Dey, Clément Maria
The persistent homology with coefficients in a field F coincides with the same for cohomology because of duality. We propose an implementation of a recently introduced algorithm fo…
An Exponential Lower Bound on the Complexity of Regularization Paths
Bernd Gärtner, Martin Jaggi, Clément Maria
For a variety of regularized optimization problems in machine learning, algorithms computing the entire solution path have been developed recently. Most of these methods are quadra…