@inbook{21056,
  abstract     = {In this work, we introduce and study what we believe is an intriguing, and, to the best of our knowledge, previously unknown connection between two fundamental areas in computational topology, namely topological data analysis (TDA) and knot theory. Given a function from a topological space to ℝ, TDA provides tools to simplify and study the importance of topological features: in particular, the 𝑙^𝑡⁢ℎ-dimensional persistence diagram encodes the topological changes (or 𝑙-homology) in the sublevel set as the function value increases into a set of points in the plane. Given a continuous one parameter family of such functions, we can combine the persistence diagrams into an object known as a vineyard, which tracks the evolution of points in the persistence diagram as the function changes. If we further restrict that family of functions to be periodic, we identify the two ends of the vineyard, yielding a closed vineyard. This allows the study of monodromy, which in this context means that following the family of functions for a period permutes the set of points in a non-trivial way. Recent work has studied monodromy in the directional persistent homology transform, demonstrating some interesting connections between an input shape and monodromy in the persistent homology transform for 0-dimensional homology embedded in ℝ^2.
In this work, given a link and a value 𝑙, we construct a topological space (based on the given link) and periodic family of functions on this space (based on the Euclidean distance function), such that the closed 𝑙-vineyard contains this link. This shows that vineyards are topologically as rich as one could possibly hope, suggesting many future directions of work. Importantly, it has at least two immediate consequences we explicitly point out:
1.	Monodromy of any periodicity can occur in a 𝑙-vineyard for any 𝑙. This answers a variant of a question by Arya and collaborators. To exhibit this as a consequence of our first main result we also reformulate monodromy in a more geometric way, which may be of interest in itself.
2.	Topologically distinguishing closed vineyards is likely to be difficult (from a complexity theory as well as from a practical perspective) because of the difficulty of knot and link recognition, which have strong connections to many NP-hard problems.},
  author       = {Chambers, Erin W. and Fillmore, Christopher D and Stephenson, Elizabeth R and Wintraecken, Mathijs},
  booktitle    = {Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms},
  editor       = {Green Larsen, Kasper and Saha, Barna},
  pages        = {6240--6263},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Braiding Vineyards}},
  doi          = {10.1137/1.9781611978971.225},
  year         = {2026},
}

@article{21115,
  abstract     = {Quantifying cell morphology is central to understanding cellular regulation, fate, and heterogeneity, yet conventional image-based analyses often struggle with diverse or irregular shapes. We present a computational framework that uses topological data analysis to characterise and compare single-cell morphologies from fluorescence microscopy. Each cell is represented by its contour together with the position of its nucleus, from which we construct a filtration based on a radial distance function and derive a persistence diagram encoding the shape’s topological evolution. The similarity between two cells is quantified using the 2-Wasserstein distance between their diagrams, yielding a shape distance we call the PH distance. We apply this method to two representative experimental systems—primary human mesenchymal stem cells (hMSCs) and HeLa cells—and show that PH distances enable the detection of outliers in those systems, the identification of sub-populations, and the quantification of shape heterogeneity. We benchmark PH against three established contour-based distances (aspect ratio, Fourier descriptors, and elastic shape analysis) and show that PH offers better separation between cell types and greater robustness when clustering heterogeneous populations. Together, these results demonstrate that persistent-homology-based signatures provide a principled and sensitive approach for analysing cell morphology in settings where traditional geometric or image-based descriptors are insufficient.},
  author       = {Bleile, Yossi and Yadav, Pooja and Koehl, Patrice and Rehfeldt, Florian},
  issn         = {1553-7358},
  journal      = {PLoS Computational Biology},
  publisher    = {Public Library of Science},
  title        = {{Persistence diagrams as morphological signatures of cells: A method to measure and compare cells within a population}},
  doi          = {10.1371/journal.pcbi.1013890},
  volume       = {22},
  year         = {2026},
}

@article{21232,
  abstract     = {<jats:title>Abstract</jats:title>
                  <jats:p>In this paper, we consider a simple class of stratified spaces – 2-complexes. We present an algorithm that learns the abstract structure of an embedded 2-complex from a point cloud sampled from it. We use tools and inspiration from computational geometry, algebraic topology, and topological data analysis and prove the correctness of the identified abstract structure under assumptions on the embedding.</jats:p>},
  author       = {Bleile, Yossi},
  issn         = {2730-9657},
  journal      = {La Matematica},
  publisher    = {Springer Nature},
  title        = {{Towards stratified space learning: 2-complexes}},
  doi          = {10.1007/s44007-025-00183-9},
  volume       = {5},
  year         = {2026},
}

@inproceedings{21374,
  abstract     = {Let . S be a set of distinct points in general position in the
Euclidean plane. A plane Hamiltonian path on . S is a crossing-free geometric path such that every point of .S is a vertex of the path. It is
known that, if. S is sufficiently large, there exist three edge-disjoint plane
Hamiltonian paths on . S. In this paper we study an edge-constrained
version of the problem of finding Hamiltonian paths on a point set. We
first consider the problem of finding a single plane Hamiltonian path . π
with endpoints .s, t ∈ S and constraints given by a segment . ab, where
.a, b ∈ S. We consider the following scenarios: (i) .ab ∈ π; (ii) .ab π. We
characterize those quintuples . S, a, b, s, t for which . π exists. Secondly,
we consider the problem of finding two plane Hamiltonian paths . π1, π2
on a set . S with constraints given by a segment . ab, where .a, b ∈ S. We
consider the following scenarios: (i) .π1 and .π2 share no edges and .ab is
an edge of . π1; (ii) .π1 and .π2 share no edges and none of them includes
.ab as an edge; (iii) both .π1 and .π2 include .ab as an edge and share no
other edges. In all cases, we characterize those triples . S, a, b for which
.π1 and .π2 exist.},
  author       = {Antić, Todor and Džuklevski, Aleksa and Fiala, Jiří and Kratochvíl, Jan and Liotta, Giuseppe and Saghafian, Morteza and Saumell, Maria and Zink, Johannes},
  booktitle    = {51st International Conference on Current Trends in Theory and Practice of Computer Science},
  isbn         = {9783032178008},
  issn         = {1611-3349},
  location     = {Krakow, Poland},
  pages        = {532--546},
  publisher    = {Springer Nature},
  title        = {{Edge-constrained Hamiltonian paths on a point set}},
  doi          = {10.1007/978-3-032-17801-5_39},
  volume       = {16448},
  year         = {2026},
}

@article{21407,
  abstract     = {This note proves that only a linear number of holes in a Cech complex of n points in R^d
can persist over an interval of constant length. Specifically, for any fixed dimension p <
d and fixed ε > 0, the number of p-dimensional holes in the ˇ Cech complex at radius 1
that persist to radius 1+ε is bounded above by a constant times n,where n is the number
of points. The proof uses a packing argument supported by relating theCˇ ech complexes
with corresponding snap complexes over the cells in a partition of space. The argument
is self-contained and elementary, relying on geometric and combinatorial constructions
rather than on the existing theory of sparse approximations or interleavings. The bound
also applies to Alpha complexes and Vietoris–Rips complexes. While our result can be
inferred from prior work on sparse filtrations, to our knowledge, no explicit statement
or direct proof of this bound appears in the literature.},
  author       = {Edelsbrunner, Herbert and Kahle, Matthew and Kanazawa, Shu},
  issn         = {2367-1734},
  journal      = {Journal of Applied and Computational Topology},
  publisher    = {Springer Nature},
  title        = {{Maximum persistent Betti numbers of Čech complexes}},
  doi          = {10.1007/s41468-026-00233-3},
  volume       = {10},
  year         = {2026},
}

@inproceedings{21410,
  abstract     = {Given a finite set of red and blue points in R^d, the MST-ratio is defined as the total length of the Euclidean minimum spanning trees of the red points and the blue points, divided by the length of the Euclidean minimum spanning tree of their union. The MST-ratio has recently gained attention due to its direct interpretation in topological models for studying point sets with applications in spatial biology. The maximum MST-ratio of a point set is the maximum MST-ratio over all proper colorings of its points by red and blue. We prove that finding the maximum MST-ratio of a given point set is NP-hard when the dimension is part of the input. Moreover, we present a quadratic-time 3-approximation algorithm for this problem. As part of the proof, we show that in any metric space, the maximum MST-ratio is smaller than 3. Furthermore, we study the average MST-ratio over all colorings of a set of n points. We show that this average is always at least n-2/n-1, and for n random points uniformly distributed in a d-dimensional unit cube, the average tends to (math formular) in expectation as n approaches infinity.},
  author       = {Jabal Ameli, Afrouz and Motiei, Faezeh and Saghafian, Morteza},
  booktitle    = {20th International Conference and Workshops on Algorithms and Computation},
  isbn         = {9789819571260},
  issn         = {1611-3349},
  location     = {Perugia, Italy},
  pages        = {386--401},
  publisher    = {Springer Nature},
  title        = {{On the MST-ratio: Theoretical bounds and complexity of finding the maximum}},
  doi          = {10.1007/978-981-95-7127-7_26},
  volume       = {16444},
  year         = {2026},
}

@article{21781,
  abstract     = {Given a set A of n points (vertices) in general position in the plane, the complete geometric graph 
Kn[A] consists of all (n2) segments (edges) between the elements of A. It is known that the edge set of every complete geometric graph on n vertices can be partitioned into O(n3∕2) crossing-free paths (or matchings). We strengthen this result under various additional assumptions on the point set. In particular, we prove that for a set A of n randomly selected points, uniformly distributed in [0,1]2, with probability tending to 1 as n→∞, the edge set of Kn[A] can be covered by O(nlogn) crossing-free paths and by O(n√logn) crossing-free matchings. On the other hand, we construct n-element point sets such that covering the edge set of Kn[A] requires a quadratic number of monotone paths.},
  author       = {Dumitrescu, Adrian and Pach, János and Saghafian, Morteza and Scott, Alex},
  issn         = {2996-220X},
  journal      = {Combinatorics and Number Theory},
  number       = {1},
  pages        = {73--82},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Covering complete geometric graphs by monotone paths}},
  doi          = {10.2140/cnt.2026.15.73},
  volume       = {15},
  year         = {2026},
}

@article{21931,
  abstract     = {In 1873, James C. Maxwell conjectured that the electric field generated by n point charges in generic position has at most (n-1)^2 isolated zeroes. The first (nonoptimal) upper bound was only obtained in 2007 by Gabrielov, Novikov, and Shapiro, who also posed two additional interesting conjectures. In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to Conjecture 1.8 by Gabrielov, Novikov, and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find lower bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day.},
  author       = {Edelsbrunner, Herbert and Fillmore, Christopher D and Oliveira, Goncalo},
  issn         = {1460-244X},
  journal      = {Proceedings of the London Mathematical Society},
  number       = {5},
  publisher    = {Wiley},
  title        = {{Counting equilibria of the electrostatic potential}},
  doi          = {10.1112/plms.70163},
  volume       = {132},
  year         = {2026},
}

@misc{21971,
  abstract     = {A Rust library for analyzing dendritic structures using quadric matrices. This project provides efficient tools for representing dendritic trees, computing quadric error metrics, and visualizing eigenvalue distributions on hexagonal plots.

This library implements quadric-based geometric analysis of dendritic structures, commonly found in neuroscience applications. Key features include:

Tree data structures: Hierarchical vertex and edge representations for dendritic trees
Quadric matrices: Computation of quadric error metrics for edges and vertices
Visualisation: Hexagonal plot generation using NormPolar transformations
Interactive tools: Desktop application with plotting capabilities},
  author       = {Bleile, Yossi and Cortinovis, Emanuele},
  keywords     = {quadratics, mathematics, dendrites, geometry, topology},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Quadrix}},
  doi          = {10.15479/AT-ISTA-21971},
  year         = {2026},
}

@article{20456,
  abstract     = {Given a locally finite set A⊆Rd and a coloring χ:A→{0,1,…,s}, we introduce the chromatic Delaunay mosaic of χ, which is a Delaunay mosaic in Rs+d that represents how points of different colors mingle. Our main results are bounds on the size of the chromatic Delaunay mosaic, in which we assume that d and s are constants. For example, if A is finite with n=#A, and the coloring is random, then the chromatic Delaunay mosaic has O(n⌈d/2⌉) cells in expectation. In contrast, for Delone sets and Poisson point processes in Rd, the expected number of cells within a closed ball is only a constant times the number of points in this ball. Furthermore, in R2 all colorings of a dense set of n points have chromatic Delaunay mosaics of size O(n). This encourages the use of chromatic Delaunay mosaics in applications.},
  author       = {Biswas, Ranita and Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza},
  issn         = {1432-0444},
  journal      = {Discrete and Computational Geometry},
  pages        = {24--47},
  publisher    = {Springer Nature},
  title        = {{On the size of chromatic Delaunay mosaics}},
  doi          = {10.1007/s00454-025-00778-7},
  volume       = {75},
  year         = {2026},
}

@article{20867,
  abstract     = {We discuss the embeddability of subspaces of the Gromov–Hausdorff space, which consists of isometry classes of compact metric spaces endowed with the Gromov–Hausdorff distance, into Hilbert spaces. These embeddings are particularly valuable for applications to topological data analysis. We prove that its subspace consisting of metric spaces with at most n points has asymptotic dimension n(n−1)∕2. Thus, there exists a coarse embedding of that space into a Hilbert space. On the contrary, if the number of points is not bounded, then the subspace cannot be coarsely embedded into any uniformly convex Banach space and so, in particular, into any Hilbert space. Furthermore, we prove that, even if we restrict to finite metric spaces whose diameter is bounded by some constant, the subspace still cannot be bi-Lipschitz embedded into any finite-dimensional Hilbert space. We obtain both nonembeddability results by finding obstructions to coarse and bi-Lipschitz embeddings in families of isometry classes of finite subsets of the real line endowed with the Euclidean–Hausdorff distance.},
  author       = {Zava, Nicolò},
  issn         = {1472-2739},
  journal      = {Algebraic & Geometric Topology},
  number       = {8},
  pages        = {5153--5174},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Coarse and bi-Lipschitz embeddability of subspaces of the Gromov–Hausdorff space into Hilbert spaces}},
  doi          = {10.2140/agt.2025.25.5153},
  volume       = {25},
  year         = {2025},
}

@unpublished{21016,
  abstract     = {Motivated by applications in chemistry, we give a homlogical definition of tunnels, or more generally cobordisms, connecting disjoint parts of a cell complex. For a filtered complex, this defines a persistence module. We give a method for identifying birth and death times using kernel persistence and a matrix reduction algorithm for pairing birth and death times.},
  author       = {Bleile, Yossi and Fajstrup, Lisbeth and Heiss, Teresa and Svane, Anne Marie and Sørensen, Søren Strandskov},
  booktitle    = {arXiv},
  title        = {{Identifying cobordisms using kernel persistence}},
  doi          = {10.48550/arXiv.2505.17858},
  year         = {2025},
}

@unpublished{21050,
  abstract     = {In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and Shapiro, who also posed two additional interesting conjectures.
 In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to a conjecture of Gabrielov, Novikov and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges.
 Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find smaller bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day.},
  author       = {Edelsbrunner, Herbert and Fillmore, Christopher D and Olivera, Gonçalo},
  booktitle    = {arXiv},
  title        = {{Counting equilibria of the electrostatic potential}},
  doi          = {10.48550/ARXIV.2501.05315},
  year         = {2025},
}

@article{21253,
  abstract     = {We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n - 1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.},
  author       = {Pach, János and Saghafian, Morteza and Schnider, Patrick},
  issn         = {0925-7721},
  journal      = {Computational Geometry},
  publisher    = {Elsevier},
  title        = {{Decomposition of geometric graphs into star-forests}},
  doi          = {10.1016/j.comgeo.2025.102186},
  volume       = {129},
  year         = {2025},
}

@article{17149,
  abstract     = {The approximation of a circle with the edges of a fine square grid distorts the perimeter by a factor about 4/Pi. We prove that this factor is the same on average (in the ergodic sense) for approximations of any rectifiable curve by the edges of any non-exotic Delaunay mosaic (known as Voronoi path), and extend the results to all dimensions, generalizing Voronoi paths to Voronoi scapes.},
  author       = {Edelsbrunner, Herbert and Nikitenko, Anton},
  issn         = {1432-0444},
  journal      = {Discrete & Computational Geometry},
  pages        = {490--499},
  publisher    = {Springer Nature},
  title        = {{Average and expected distortion of Voronoi paths and scapes}},
  doi          = {10.1007/s00454-024-00660-y},
  volume       = {73},
  year         = {2025},
}

@article{18626,
  abstract     = {The local angle property of the (order-1) Delaunay triangulations of a generic set in R2
 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. We also use our method of establishing (2) to give a new short proof of the angle vector optimality for the (order-1) Delaunay triangulation. For order-1, both properties have been instrumental in numerous applications of Delaunay triangulations, and we expect that their generalization will make order-2 Delaunay triangulations more attractive to applications as well.},
  author       = {Edelsbrunner, Herbert and Garber, Alexey and Saghafian, Morteza},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  publisher    = {Elsevier},
  title        = {{Order-2 Delaunay triangulations optimize angles}},
  doi          = {10.1016/j.aim.2024.110055},
  volume       = {461},
  year         = {2025},
}

@phdthesis{18979,
  abstract     = {Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.

The first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.

The aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.

We describe a construction of a chromatic alpha complex, which enables  efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.

The second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.

In the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot.},
  author       = {Draganov, Ondrej},
  issn         = {2663-337X},
  keywords     = {topological data analysis, chromatic point set, alpha complex, persistent homology, six pack, sheaf, microlocal discrete Morse, injective resolution, collapse, knot, discrete Morse theory},
  pages        = {140},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Structures and computations in topological data analysis}},
  doi          = {10.15479/at:ista:18979},
  year         = {2025},
}

@article{19937,
  abstract     = {Simplets are elementary units within simplicial complexes and are fundamental for analyzing the structure of simplicial complexes. Previous efforts have mainly focused on accurately counting or approximating the number of simplets rather than studying their frequencies. However, analyzing simplet frequencies is more practical for large-scale simplicial complexes. This paper introduces the Simplet Frequency Distribution (SFD) vector, which enables the analysis of simplet frequencies in simplicial complexes. Additionally, we provide a bound on the sample complexity required to approximate the SFD vector using any uniform sampling-based algorithm accurately. We extend the definition of simplet frequency distribution to encompass simplices, allowing for the analysis of simplet frequencies within simplices of simplicial complexes. This paper introduces the Simplet Degree Vector (SDV) and the Simplet Degree Centrality (SDC), facilitating this analysis for each simplex. Furthermore, we present a bound on the sample complexity required for accurately approximating the SDV and SDC for a set of simplices using any uniform sampling-based algorithm. We also introduce algorithms for approximating SFD, geometric SFD, SDV, and SDC. We also validate the theoretical bounds with experiments on random simplicial complexes and demonstrate the practical application through a case study.},
  author       = {Mahini, Mohammad and Beigy, Hamid and Qadami, Salman and Saghafian, Morteza},
  issn         = {0020-0255},
  journal      = {Information Sciences},
  number       = {11},
  publisher    = {Elsevier},
  title        = {{Simplet-based signatures and approximation in simplicial complexes: Frequency, degree, and centrality}},
  doi          = {10.1016/j.ins.2025.122425},
  volume       = {719},
  year         = {2025},
}

@inproceedings{20005,
  abstract     = {We generalize a classical result by Boris Delaunay that introduced Delaunay triangulations. In particular, we prove that for a locally finite and coarsely dense generic point set A in ℝ^d, every generic point of ℝ^d belongs to exactly binom(d+k,d) simplices whose vertices belong to A and whose circumspheres enclose exactly k points of A. We extend this result to the cases in which the points are weighted, and when A contains only finitely many points in ℝ^d or in 𝕊^d. Furthermore, we use the result to give a new geometric proof for the fact that volumes of hypersimplices are Eulerian numbers.},
  author       = {Edelsbrunner, Herbert and Garber, Alexey and Saghafian, Morteza},
  booktitle    = {41st International Symposium on Computational Geometry},
  isbn         = {9783959773706},
  issn         = {1868-8969},
  location     = {Kanazawa, Japan},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{On spheres with k points inside}},
  doi          = {10.4230/LIPIcs.SoCG.2025.43},
  volume       = {332},
  year         = {2025},
}

@inproceedings{20006,
  abstract     = {In numerous fields, dynamic time series data require continuous updates, necessitating efficient data processing techniques for accurate analysis. This paper examines the banana tree data structure, specifically designed to efficiently maintain the multi-scale topological descriptor commonly known as persistent homology for dynamically changing time series data. We implement this data structure and conduct an experimental study to assess its properties and runtime for update operations. Our findings indicate that banana trees are highly effective with unbiased random data, outperforming state-of-the-art static algorithms in these scenarios. Additionally, our results show that real-world time series share structural properties with unbiased random walks, suggesting potential practical utility for our implementation.},
  author       = {Ost, Lara and Cultrera di Montesano, Sebastiano and Edelsbrunner, Herbert},
  booktitle    = {41st International Symposium on Computational Geometry},
  isbn         = {9783959773706},
  issn         = {1868-8969},
  location     = {Kanazawa, Japan},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Banana trees for the persistence in time series experimentally}},
  doi          = {10.4230/LIPIcs.SoCG.2025.71},
  volume       = {332},
  year         = {2025},
}