36 citations · 177 across the 35 of their papers we have counts for
15 papers · 1 filter
Polynomial-time algorithms for continuous metrics on atomic clouds of unordered points
Vitaliy Kurlin
The most fundamental model of a molecule is a cloud of unordered atoms, even without chemical bonds that can depend on thresholds for distances and angles. The strongest equivalenc…
Exactly computable and continuous metrics on isometry classes of finite and 1-periodic sequences
Vitaliy Kurlin
The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ord…
Generic families of finite metric spaces with identical or trivial 1-dimensional persistence
Philip Smith, Vitaliy Kurlin
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into m…
Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence
Yury Elkin, Vitaliy Kurlin
Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point cl…
A complete and continuous map of the Lattice Isometry Space for all 3-dimensional lattices
Matthew Bright, Andrew I Cooper, Vitaliy Kurlin
This paper extends the recently obtained complete and continuous map of the Lattice Isometry Space (LISP) to the practical case of dimension 3. A periodic 3-dimensional lattice is…
The Density Fingerprint of a Periodic Point Set
Herbert Edelsbrunner, Teresa Heiss, Vitaliy Kurlin +2
Modeling a crystal as a periodic point set, we present a fingerprint consisting of density functions that facilitates the efficient search for new materials and material properties…
Introduction to Periodic Geometry and Topology
Olga Anosova, Vitaliy Kurlin
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystall…
The mergegram of a dendrogram and its stability
Yury Elkin, Vitaliy Kurlin
This paper extends the key concept of persistence within Topological Data Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in unorganized data such as cl…
A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space
Yury Elkin, Di Liu, Vitaliy Kurlin
The tree reconstruction problem is to find an embedded straight-line tree that approximates a given cloud of unorganized points in up to a certain error. A practical…
Voronoi-based similarity distances between arbitrary crystal lattices
Marco Michele Mosca, Vitaliy Kurlin
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substant…
Skeletonisation Algorithms with Theoretical Guarantees for Unorganised Point Clouds with High Levels of Noise
Vitaliy Kurlin, Philip Smith
Data Science aims to extract meaningful knowledge from unorganised data. Real datasets usually come in the form of a cloud of points with only pairwise distances. Numerous applicat…
Relaxed Disk Packing
Herbert Edelsbrunner, Mabel Iglesias-Ham, Vitaliy Kurlin
Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a…
Book embeddings of Reeb graphs
Vitaliy Kurlin
Let be a simplicial complex with a piecewise linear function . The Reeb graph is the quotient of , where we collapse each connected component o…
Approximating persistent homology for a cloud of points in a subquadratic time
Vitaliy Kurlin
The Vietoris-Rips filtration for an -point metric space is a sequence of large simplicial complexes adding a topological structure to the otherwise disconnected space. The persi…
A fast and robust algorithm to count topologically persistent holes in noisy clouds
Vitaliy Kurlin
Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in unorganized clouds in the plane. The holes in a given cloud are…