@article{18087,
  abstract     = {We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements.},
  author       = {Maslov, Mikhail and Koutentakis, Georgios and Hrast, Mateja and Heckl, Oliver H. and Lemeshko, Mikhail},
  issn         = {2643-1564},
  journal      = {Physical Review Research},
  number       = {3},
  publisher    = {American Physical Society},
  title        = {{Theory of angular momentum transfer from light to molecules}},
  doi          = {10.1103/physrevresearch.6.033277},
  volume       = {6},
  year         = {2024},
}

@phdthesis{15020,
  abstract     = {This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty.
Chapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance?
Chapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance.
Chapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2.
Chapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal.},
  author       = {Hledik, Michal},
  issn         = {2663-337X},
  keywords     = {Theoretical biology, Optimality, Evolution, Information},
  pages        = {158},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Genetic information and biological optimization}},
  doi          = {10.15479/at:ista:15020},
  year         = {2024},
}

@phdthesis{17225,
  abstract     = {This thesis describes the development of an atom interferometer designed to exploit the
advantages of utilizing quantum entanglement for enhanced precision measurements beyond
the standard quantum limit. While the project remains ongoing, significant progress has been
made.
A key contribution of this work is the development of Quantrol, an experimental control
system leveraging the ARTIQ framework. This software enables precise timing and control
without requiring prior knowledge of ARTIQ’s implementation details or coding experience.
The interface offers user friendly visual comprehension of the experimental sequence and
extended capabilities, allowing researchers to scan variables with a simple click of a mouse.
The main proposed project is to implement atom interferometric sequence with squeezed input
states inside of a dipole trap generated by a high finesse cavity. The presence of the dipole
trap allows one dimensional atomic cloud split while maintaining relatively strong confinement
in other directions.
We are currently able to trap and cool 87Rb atoms to few micro kelvin temperatures, load
them into the dipole trap and state prepare them to be used for squeezing and interferometric
sequence.},
  author       = {Li, Vyacheslav},
  issn         = {2663-337X},
  pages        = {79},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Towards a quantum entanglement enhanced atom interferomter}},
  doi          = {10.15479/at:ista:17225},
  year         = {2024},
}

@article{14542,
  abstract     = {It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ
 and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit.},
  author       = {Henheik, Sven Joscha and Lauritsen, Asbjørn Bækgaard and Roos, Barbara},
  issn         = {1793-6659},
  journal      = {Reviews in Mathematical Physics},
  number       = {9},
  publisher    = {World Scientific Publishing},
  title        = {{Universality in low-dimensional BCS theory}},
  doi          = {10.1142/s0129055x2360005x},
  volume       = {36},
  year         = {2024},
}

@article{18107,
  abstract     = {We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions  d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order  adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and  ρ  is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).},
  author       = {Lauritsen, Asbjørn Bækgaard and Seiringer, Robert},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Pressure of a dilute spin-polarized Fermi gas: Lower bound}},
  doi          = {10.1017/fms.2024.56},
  volume       = {12},
  year         = {2024},
}

@phdthesis{18443,
  abstract     = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between
the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they
conjecture an equivalence between categories of BBB and BAA-branes. At the classical
level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on
algebraic integrable systems.
In this thesis, we investigate the T-duality relation between hyperkähler structures and the
corresponding branes on affine torus bundles. We use the techniques of generalized geometry
to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.
We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform
we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed
with U(1)-bundles and connections. This T-duality in the appropriate context specializes to
T-duality between BBB and BAA-branes.
},
  author       = {Sisak, Maria A},
  issn         = {2663-337X},
  keywords     = {hyperkaehler geometry, branes, mirror symmetry, T-duality},
  pages        = {178},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{T-dual branes on hyperkähler manifolds}},
  doi          = {10.15479/at:ista:18443},
  year         = {2024},
}

@inproceedings{17634,
  abstract     = {System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems.},
  author       = {Chalupa, Marek and Henzinger, Thomas A and Mazzocchi, Nicolas Adrien and Sarac, Naci E},
  booktitle    = {12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation},
  isbn         = {9783031753862},
  issn         = {1611-3349},
  location     = {Crete, Greece},
  pages        = {3--20},
  publisher    = {Springer Nature},
  title        = {{QuAK: Quantitative Automata Kit}},
  doi          = {10.1007/978-3-031-75387-9_1},
  volume       = {15222},
  year         = {2024},
}

@article{14345,
  abstract     = {For a locally finite set in R2, the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)).},
  author       = {Edelsbrunner, Herbert and Garber, Alexey and Ghafari, Mohadese and Heiss, Teresa and Saghafian, Morteza},
  issn         = {1432-0444},
  journal      = {Discrete and Computational Geometry},
  pages        = {29--48},
  publisher    = {Springer Nature},
  title        = {{On angles in higher order Brillouin tessellations and related tilings in the plane}},
  doi          = {10.1007/s00454-023-00566-1},
  volume       = {72},
  year         = {2024},
}

@inproceedings{17144,
  abstract     = {We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms.},
  author       = {Kourimska, Hana and Lieutier, André and Wintraecken, Mathijs},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms}},
  doi          = {10.4230/LIPIcs.SoCG.2024.69},
  volume       = {293},
  year         = {2024},
}

@inproceedings{17146,
  abstract     = {The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry.},
  author       = {Edelsbrunner, Herbert and Pach, János},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Maximum Betti numbers of Čech complexes}},
  doi          = {10.4230/LIPIcs.SoCG.2024.53},
  volume       = {293},
  year         = {2024},
}

@inproceedings{17145,
  abstract     = {Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.},
  author       = {Rote, Günter and Rüber, Moritz and Saghafian, Morteza},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Grid peeling of parabolas}},
  doi          = {10.4230/LIPIcs.SoCG.2024.76},
  volume       = {293},
  year         = {2024},
}

@article{17891,
  abstract     = {Abstract
Methods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics.},
  author       = {Edelsbrunner, Herbert and Ölsböck, Katharina and Wagner, Hubert},
  issn         = {1099-4300},
  journal      = {Entropy},
  number       = {8},
  publisher    = {MDPI},
  title        = {{Understanding higher-order interactions in information space}},
  doi          = {10.3390/e26080637},
  volume       = {26},
  year         = {2024},
}

@inproceedings{15012,
  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},
  booktitle    = {31st International Symposium on Graph Drawing and Network Visualization},
  isbn         = {9783031492716},
  issn         = {1611-3349},
  location     = {Isola delle Femmine, Palermo, Italy},
  pages        = {339--346},
  publisher    = {Springer Nature},
  title        = {{Decomposition of geometric graphs into star-forests}},
  doi          = {10.1007/978-3-031-49272-3_23},
  volume       = {14465},
  year         = {2024},
}

@article{17190,
  abstract     = {For a locally finite set, 𝐴⊆ℝ𝑑
, the 𝑘
th Brillouin zone of 𝑎∈𝐴
 is the region of points 𝑥∈ℝ𝑑
 for which ‖𝑥−𝑎‖
 is the 𝑘
th smallest among the Euclidean distances between 𝑥
 and the points in 𝐴
. If 𝐴
 is a lattice, the 𝑘
th Brillouin zones of the points in 𝐴
 are translates of each other, and together they tile space. Depending on the value of 𝑘
, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2
, and the convergence of the maximum volume of a chamber to zero for the integer lattice.},
  author       = {Edelsbrunner, Herbert and Garber, Alexey and Ghafaris, Mohadese and Heiss, Teresa and Saghafiant, Morteza and Wintraecken, Mathijs},
  issn         = {0895-4801},
  journal      = {SIAM Journal on Discrete Mathematics},
  number       = {2},
  pages        = {1784--1807},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Brillouin zones of integer lattices and their perturbations}},
  doi          = {10.1137/22M1489071},
  volume       = {38},
  year         = {2024},
}

@inproceedings{18556,
  abstract     = {Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25.},
  author       = {Cultrera di Montesano, Sebastiano and Draganov, Ondrej and Edelsbrunner, Herbert and Saghafian, Morteza},
  booktitle    = {32nd International Symposium on Graph Drawing and Network Visualization},
  isbn         = {9783959773430},
  issn         = {1868-8969},
  location     = {Vienna, Austria},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The Euclidean MST-ratio for bi-colored lattices}},
  doi          = {10.4230/LIPIcs.GD.2024.3},
  volume       = {320},
  year         = {2024},
}

@inproceedings{18097,
  abstract     = {In our companion paper "Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape 𝒮 (either manifold or general set with positive reach) such that one can infer the homotopy of 𝒮 from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting.},
  author       = {Attali, Dominique and Kourimska, Hana and Fillmore, Christopher D and Ghosh, Ishika and Lieutier, Andre and Stephenson, Elizabeth R and Wintraecken, Mathijs},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The ultimate frontier: An optimality construction for homotopy inference (media exposition)}},
  doi          = {10.4230/LIPIcs.SoCG.2024.87},
  volume       = {293},
  year         = {2024},
}

@article{13182,
  abstract     = {We characterize critical points of 1-dimensional maps paired in persistent homology
geometrically and this way get elementary proofs of theorems about the symmetry
of persistence diagrams and the variation of such maps. In particular, we identify
branching points and endpoints of networks as the sole source of asymmetry and
relate the cycle basis in persistent homology with a version of the stable marriage
problem. Our analysis provides the foundations of fast algorithms for maintaining a
collection of sorted lists together with its persistence diagram.},
  author       = {Biswas, Ranita and Cultrera Di Montesano, Sebastiano and Edelsbrunner, Herbert and Saghafian, Morteza},
  issn         = {2367-1734},
  journal      = {Journal of Applied and Computational Topology},
  pages        = {1101--1119},
  publisher    = {Springer Nature},
  title        = {{Geometric characterization of the persistence of 1D maps}},
  doi          = {10.1007/s41468-023-00126-9},
  volume       = {8},
  year         = {2024},
}

@article{15380,
  abstract     = {The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements.},
  author       = {Biswas, Ranita and Cultrera Di Montesano, Sebastiano and Edelsbrunner, Herbert and Saghafian, Morteza},
  issn         = {2367-1734},
  journal      = {Journal of Applied and Computational Topology},
  pages        = {557--578},
  publisher    = {Springer Nature},
  title        = {{Depth in arrangements: Dehn–Sommerville–Euler relations with applications}},
  doi          = {10.1007/s41468-024-00173-w},
  volume       = {8},
  year         = {2024},
}

@article{15247,
  abstract     = {Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples.},
  author       = {Frankl, Peter and Pach, János and Pálvölgyi, Dömötör},
  issn         = {1096-0899},
  journal      = {Journal of Combinatorial Theory, Series A},
  number       = {8},
  publisher    = {Elsevier},
  title        = {{Odd-sunflowers}},
  doi          = {10.1016/j.jcta.2024.105889},
  volume       = {206},
  year         = {2024},
}

@phdthesis{18667,
  abstract     = {Many chemical and physical properties of materials are determined by the material’s shape,
for example the size of its pores and the width of its tunnels. This makes materials science
a prime application area for geometrical and topological methods. Nevertheless many
methods in topological data analysis have not been satisfyingly extended to the needs of
materials science. This thesis provides new methods and new mathematical theorems
targeted at those specific needs by answering four different research questions. While the
motivation for each of the research questions arises from materials science, the methods
are versatile and can be applied in different areas as well. 

The first research question is concerned with image data, for example a three-dimensional
computed tomography (CT) scan of a material, like sand or stone. There are two commonly
used topologies for digital images and depending on the application either of them might be
required. However, software for computing the topological data analysis method persistence
homology, usually supports only one of the two topologies. We answer the question how to
compute persistent homology of an image with respect to one of the two topologies using
software that is intended for the other topology. 

The second research question is concerned with image data as well, and asks how much
of the topological information of an image is lost when the resolution is coarsened. As
computer tomography scanners are more expensive the higher the resolution, it is an
important question in materials science to know which resolution is enough to get satisfying
persistent homology. We give theoretical bounds on the information loss based on different
geometrical properties of the object to be scanned. In addition, we conduct experiments on
sand and stone CT image data. 

The third research question is motivated by comparing crystalline materials efficiently. As
the atoms within a crystal repeat periodically, crystalline materials are either modeled by
unmanageable infinite periodic point sets, or by one of their fundamental domains, which is
unstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with
appropriate properties such that comparing the crystals can be eased by comparing the
fingerprints instead. We define the density fingerprint and prove the necessary properties. 

The fourth research question is motivated by studying the hole-structure or connectedness,
i.e. persistent homology or merge trees, of crystalline materials. A common way to deal
with periodicity is to take a fundamental domain and identify opposite boundaries to form a
torus. However, computing persistent homology or merge trees on that torus loses some
of the information materials scientists are interested in and is additionally not stable under
certain noise. We therefore decorate the merge tree stemming from the torus with additional
information describing the density and growth rate of the periodic copies of a component
within a growing spherical window. We prove all desired properties, like stability and efficient
computability.},
  author       = {Heiss, Teresa},
  isbn         = {978-3-99078-052-7},
  issn         = {2663-337X},
  keywords     = {persistent homology, topological data analysis, periodic, crystalline materials, images, fingerprint},
  pages        = {111},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{New methods for applying topological data analysis to materials science}},
  doi          = {10.15479/at:ista:18667},
  year         = {2024},
}