157 citations · 252 across the 26 of their papers we have counts for
27 papers
Topological Learning for Motion Data via Mixed Coordinates
Hengrui Luo, Jisu Kim, Alice Patania +1
Topology can extract the structural information in a dataset efficiently. In this paper, we attempt to incorporate topological information into a multiple output Gaussian process m…
An improved algorithm for Generalized Čech complex construction
Jie Chu, Mikael Vejdemo-Johansson, Ping Ji
In this paper, we present an algorithm that computes the generalized Čech complex for a finite set of disks where each may have a different radius in 2D space. An extension of this…
Generalized Penalty for Circular Coordinate Representation
Hengrui Luo, Alice Patania, Jisu Kim +1
Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA…
Algorithms in -algebras
Mikael Vejdemo-Johansson
Building on Kadeishvili's original theorem inducing -algebra structures on the homology of dg-algebras, several directions of algorithmic research in -algebras…
3d-printing Identification Spaces of the Square
Mikael Vejdemo-Johansson
We describe three identification spaces of the square, interesting choices of immersion into , and a process to construct 3d-printable models of their parametrization…
Multiple testing with persistent homology
Mikael Vejdemo-Johansson, Sayan Mukherjee
In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our procedure is based on the ob…
Certified Mapper: Repeated testing for acyclicity and obstructions to the nerve lemma
Mikael Vejdemo-Johansson, Alisa Leshchenko
The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma…
Fibres of Failure: Classifying errors in predictive processes
Leo Carlsson, Gunnar Carlsson, Mikael Vejdemo-Johansson
We describe Fibres of Failure (FiFa), a method to classify failure modes of predictive processes using the Mapper algorithm from Topological Data Analysis. Our method uses Mapper t…
Weighted growth functions of automatic groups
Mikael Vejdemo-Johansson
The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for auto…
Computing minimum area homologies
Erin Wolf Chambers, Mikael Vejdemo-Johansson
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algo…
Aspects of an internal logic for persistence
João Pita Costa, Primož Škraba, Mikael Vejdemo-Johansson
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respecti…
Variable sets over an algebra of lifetimes: a contribution of lattice theory to the study of computational topology
João Pita Costa, Mikael Vejdemo Johansson, Primož Škraba
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is…
More ties than we thought
Dan Hirsch, Ingemar Markström, Meredith L Patterson +2
We extend the existing enumeration of neck tie-knots to include tie-knots with a textured front, tied with the narrow end of a tie. These tie-knots have gained popularity in recent…
Automatic recognition and tagging of topologically different regimes in dynamical systems
Jesse Berwald, Marian Gidea, Mikael Vejdemo-Johansson
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through…
Persistence modules: Algebra and algorithms
Primoz Skraba, Mikael Vejdemo-Johansson
Persistent homology was shown by Carlsson and Zomorodian to be homology of graded chain complexes with coefficients in the graded ring $\kk[t]$. As such, the behavior of persistenc…
Sketches of a platypus: persistent homology and its algebraic foundations
Mikael Vejdemo-Johansson
The subject of persistent homology has vitalized applications of algebraic topology to point cloud data and to application fields far outside the realm of pure mathematics. The are…
Interleaved equivalence of categories of persistence modules
Mikael Vejdemo-Johansson
We demonstrate that an equivalence of categories using -interleavings as a fundamental component exists between the model of persistence modules as graded modules over…
A spectral sequence for parallelized persistence
David Lipsky, Primoz Skraba, Mikael Vejdemo-Johansson
We approach the problem of the computation of persistent homology for large datasets by a divide-and-conquer strategy. Dividing the total space into separate but overlapping compon…
Dualities in persistent (co)homology
Vin de Silva, Dmitriy Morozov, Mikael Vejdemo-Johansson
We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their p…
Interleaved computation for persistent homology
Mikael Vejdemo-Johansson
We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to…
A parallel Buchberger algorithm for multigraded ideals
Mikael Vejdemo-Johansson, Emil Sköldberg, Jason Dusek
We demonstrate a method to parallelize the computation of a Gröbner basis for a homogenous ideal in a multigraded polynomial ring. Our method uses anti-chains in the lattice $\math…
Implementing Gröbner bases for operads
Vladimir Dotsenko, Mikael Vejdemo-Johansson
We present an implementation of the algorithm for computing Groebner bases for operads due to the first author and A. Khoroshkin. We discuss the actual algorithms, the choices made…
Persistent Cohomology and Circular Coordinates
Vin de Silva, Mikael Vejdemo-Johansson
Nonlinear dimensionality reduction (NLDR) algorithms such as Isomap, LLE and Laplacian Eigenmaps address the problem of representing high-dimensional nonlinear data in terms of low…
Blackbox computation of -algebras
Mikael Vejdemo-Johansson
Kadeishvili's proof of the minimality theorem induces an algorithm for the inductive computation of an -algebra structure on the homology of a dg-algebra. In this paper,…