@phdthesis{18301,
  abstract     = {Physics simulation in computer graphics can bring triangle meshes into topologically invalid states. The method in this thesis contributed to Heiss-Synak* and Kalinov* et al. [2024] who devised a non-manifold hybrid surface tracker—a surface tracker that repairs explicit non-manifold triangle meshes with the help of the implicit domain. Specifically, this thesis provides an algorithm for filling the holes that are left after removing problematic parts of the mesh.},
  author       = {Etemadihaghighi, Arian},
  issn         = {2791-4585},
  keywords     = {surface tracking, non-manifold, hole-filling, topology change, multi-material, solid-modeling},
  pages        = {39},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Filling the holes of non-manifold self-intersecting meshes for implicit topology changes in surface tracking}},
  doi          = {10.15479/at:ista:18301},
  year         = {2024},
}

@phdthesis{7460,
  abstract     = {Many methods for the reconstruction of shapes from sets of points produce ordered simplicial complexes, which are collections of vertices, edges, triangles, and their higher-dimensional analogues, called simplices, in which every simplex gets assigned a real value measuring its size. This thesis studies ordered simplicial complexes, with a focus on their topology, which reflects the connectedness of the represented shapes and the presence of holes. We are interested both in understanding better the structure of these complexes, as well as in developing algorithms for applications.

For the Delaunay triangulation, the most popular measure for a simplex is the radius of the smallest empty circumsphere. Based on it, we revisit Alpha and Wrap complexes and experimentally determine their probabilistic properties for random data. Also, we prove the existence of tri-partitions, propose algorithms to open and close holes, and extend the concepts from Euclidean to Bregman geometries.},
  author       = {Ölsböck, Katharina},
  issn         = {2663-337X},
  keywords     = {shape reconstruction, hole manipulation, ordered complexes, Alpha complex, Wrap complex, computational topology, Bregman geometry},
  pages        = {155},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{The hole system of triangulated shapes}},
  doi          = {10.15479/AT:ISTA:7460},
  year         = {2020},
}

@article{11579,
  abstract     = {CR7 is the brightest z = 6.6 Ly α emitter (LAE) known to date, and spectroscopic follow-up by Sobral et al. suggests that CR7 might host Population (Pop) III stars. We examine this interpretation using cosmological hydrodynamical simulations. Several simulated galaxies show the same ‘Pop III wave’ pattern observed in CR7. However, to reproduce the extreme CR7 Ly α/He II1640 line luminosities (⁠Lα/HeII⁠) a top-heavy initial mass function and a massive ( ≳ 107 M⊙) Pop III burst with age ≲ 2 Myr are required. Assuming that the observed properties of Ly α and He II emission are typical for Pop III, we predict that in the COSMOS/UDS/SA22 fields, 14 out of the 30 LAEs at z = 6.6 with Lα > 1043.3 erg s−1 should also host Pop III stars producing an observable LHeII≳1042.7ergs−1⁠. As an alternate explanation, we explore the possibility that CR7 is instead powered by accretion on to a direct collapse black hole. Our model predicts Lα, LHeII⁠, and X-ray luminosities that are in agreement with the observations. In any case, the observed properties of CR7 indicate that this galaxy is most likely powered by sources formed from pristine gas. We propose that further X-ray observations can distinguish between the two above scenarios.},
  author       = {Pallottini, A. and Ferrara, A. and Pacucci, F. and Gallerani, S. and Salvadori, S. and Schneider, R. and Schaerer, D. and Sobral, D. and Matthee, Jorryt J},
  issn         = {1365-2966},
  journal      = {Monthly Notices of the Royal Astronomical Society},
  keywords     = {Space and Planetary Science, Astronomy and Astrophysics, black hole physics, stars: Population III, galaxies: high-redshift},
  number       = {3},
  pages        = {2465--2470},
  publisher    = {Oxford University Press},
  title        = {{The brightest Lyα emitter: Pop III or black hole?}},
  doi          = {10.1093/mnras/stv1795},
  volume       = {453},
  year         = {2015},
}