45 citations · 163 across the 16 of their papers we have counts for
16 papers
Continuity of Magnitude at Finite Subsets of
Sara Kališnik, Davorin Lešnik
Magnitude is an isometric invariant of metric spaces introduced by Leinster in 2011. It is nowhere continuous on the Gromov--Hausdorff space of finite metric spaces, however, posit…
Topology of a Smile: Persistent Homology in Dental Imaging
Leon Dahlmeier, Sara Kališnik, Albert Mehl +1
CBCT (Cone Beam Computed Tomography) scans provide detailed three-dimensional images, widely used in dentistry for diagnostic and treatment planning tasks. While invaluable, analyz…
Continuity of Magnitude at Skew Finite Subsets of
Sara Kalisnik, Davorin Lesnik
Magnitude is an isometric invariant of metric spaces introduced by Leinster. Although magnitude is nowhere continuous on the Gromov-Hausdorff space of finite metric spaces, continu…
Tractable Metric Spaces and Magnitude Continuity
Sara Kališnik, Davorin Lešnik
Magnitude is an isometric invariant of metric spaces introduced by Leinster. Since its inception, it has inspired active research into its connections with integral geometry, geome…
Alpha magnitude
Miguel O'Malley, Sara Kalisnik, Nina Otter
Magnitude is an isometric invariant for metric spaces that was introduced by Leinster around 2010, and is currently the object of intense research, since it has been shown to encod…
Finding the Homology of Manifolds using Ellipsoids
Sara Kalisnik, Davorin Lesnik
A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn…
Geometric and Probabilistic Limit Theorems in Topological Data Analysis
Sara Kalisnik, Christian Lehn, Vlada Limic
We develop a general framework for the probabilistic analysis of random finite point clouds in the context of topological data analysis. We extend the notion of a barcode of a fini…
Learning Algebraic Varieties from Samples
Paul Breiding, Sara Kalisnik Verovsek, Bernd Sturmfels +1
We seek to determine a real algebraic variety from a fixed finite subset of points. Existing methods are studied and new methods are developed. Our focus lies on aspects of topolog…
Symmetric Polynomials in Upper-bound Semirings
Sara Kališnik, Davorin Lešnik
The fundamental theorem of symmetric polynomials over rings is a classical result which states that every unital commutative ring is fully elementary, i.e. we can express symmetric…
Tropical Sufficient Statistics for Persistent Homology
Anthea Monod, Sara Kališnik, Juan Ángel Patiño-Galindo +1
We show that an embedding in Euclidean space based on tropical geometry generates stable sufficient statistics for barcodes. In topological data analysis, barcodes are multiscale s…
The Higher-Dimensional Skeletonization Problem
Sara Kalisnik Verovsek, Vitaliy Kurlin, Davorin Lesnik
Real data is often given as a point cloud, i.e. a finite set of points with pairwise distances between them. An important problem is to detect the topological shape of data --- for…
Symmetric Polynomials in Tropical Algebra Semirings
Sara Kalisnik Verovsek, Davorin Lesnik
The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide…
Parametrized Homology via Zigzag Persistence
Gunnar Carlsson, Vin de Silva, Sara Kalisnik +1
This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding…
Tropical Coordinates on the Space of Persistence Barcodes
Sara Kalisnik Verovsek
The aim of applied topology is to use and develop topological methods for applied mathematics, science and engineering. One of the main tools is persistent homology, an adaptation…
Symmetric and r-Symmetric Tropical Polynomials and Rational Functions
Sara Kalisnik Verovsek, Gunnar Carlsson
A tropical polynomial in nr variables divided into blocks of r variables each, is r-symmetric, if it is invariant under the action of Sn that permutes the blocks. For r=1 we call t…
Alexander Duality for Parametrized Homology
Sara Kalisnik Verovsek
This paper extends Alexander duality to the setting of parametrized homology. Let X with be a compact subset of R^n x R (n \geq 2) satisfying certain conditions, let Y be its compl…