Teresa Heiss

Flips in two-dimensional hypertriangulations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

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Merge Trees of Periodic Filtrations

Herbert Edelsbrunner, Teresa Heiss

Motivated by applications to crystalline materials, we generalize the merge tree and the related barcode of a filtered complex to the periodic setting in Euclidean space. They are invariant under isometries, changing bases, and indeed changing lattices. In addition, we prove stability …

Brillouin Zones of Integer Lattices and Their Perturbations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

Abstract. For a locally finite set, [Formula: see text], the [Formula: see text] th Brillouin zone of [Formula: see text] is the region of points [Formula: see text] for which [Formula: see text] is the [Formula: see text]th smallest among the Euclidean …

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On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

Abstract For a locally finite set in $${{{\mathbb {R}}}}^2$$ R 2 , 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 …

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Flips in Two-dimensional Hypertriangulations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

We study flips in hypertriangulations of planar points sets. Here a level-$k$ hypertriangulation of $n$ points in the planes is a subdivision induced by the projection of a $k$-hypersimplex, which is the convex hull of the barycenters of the $(k-1)$-dimensional faces of …

On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

For a locally finite set in $\mathbb{R}^2$, 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 …

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Brillouin Zones of Integer Lattices and Their Perturbations

Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss et autres

For a locally finite set, $A \subseteq \mathbb{R}^d$, the $k$-th Brillouin zone of $a \in A$ is the region of points $x \in \mathbb{R}^d$ for which $\|x-a\|$ is the $k$-th smallest among the Euclidean distances between $x$ and the points in $A$. …

The Persistent Homology of Dual Digital Image Constructions

Beatrice Bleile, Adélie Garin, Teresa Heiss, Kelly Maggs et autres

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The Impact of Changes in Resolution on the Persistent Homology of Images

Teresa Heiss, Sarah Tymochko, Brittany Story, Adélie Garin et autres

Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if …

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1. How to Tutorial-a-thon by Henry Adams, Hana Dal Poz Kouřimská, Teresa Heiss, Sarah Percival, and Lori Ziegelmeier

Henry Hugh Adams, Hana Dal Poz Kouřimská, Teresa Heiss, Sarah Percival et autres

The Persistent Homology of Dual Digital Image Constructions

Beatrice Bleile, Adélie Garin, Teresa Heiss, Kelly Maggs et autres

To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the …

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The Density Fingerprint of a Periodic Point Set

Herbert Edelsbrunner, Teresa Heiss, Vitaliy Kurlin, Philip Smith et autres

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. We prove invariance under isometries, continuity, and completeness in the generic case, which are necessary …

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