---
_id: '1617'
abstract:
- lang: eng
  text: 'We study the discrepancy of jittered sampling sets: such a set P⊂ [0,1]d
    is generated for fixed m∈ℕ by partitioning [0,1]d into md axis aligned cubes of
    equal measure and placing a random point inside each of the N=md cubes. We prove
    that, for N sufficiently large, 1/10 d/N1/2+1/2d ≤EDN∗(P)≤ √d(log N) 1/2/N1/2+1/2d,
    where the upper bound with an unspecified constant Cd was proven earlier by Beck.
    Our proof makes crucial use of the sharp Dvoretzky-Kiefer-Wolfowitz inequality
    and a suitably taylored Bernstein inequality; we have reasons to believe that
    the upper bound has the sharp scaling in N. Additional heuristics suggest that
    jittered sampling should be able to improve known bounds on the inverse of the
    star-discrepancy in the regime N≳dd. We also prove a partition principle showing
    that every partition of [0,1]d combined with a jittered sampling construction
    gives rise to a set whose expected squared L2-discrepancy is smaller than that
    of purely random points.'
acknowledgement: We are grateful to the referee whose suggestions greatly improved
  the quality and clarity of the exposition.
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
- first_name: Stefan
  full_name: Steinerberger, Stefan
  last_name: Steinerberger
citation:
  ama: Pausinger F, Steinerberger S. On the discrepancy of jittered sampling. <i>Journal
    of Complexity</i>. 2016;33:199-216. doi:<a href="https://doi.org/10.1016/j.jco.2015.11.003">10.1016/j.jco.2015.11.003</a>
  apa: Pausinger, F., &#38; Steinerberger, S. (2016). On the discrepancy of jittered
    sampling. <i>Journal of Complexity</i>. Academic Press. <a href="https://doi.org/10.1016/j.jco.2015.11.003">https://doi.org/10.1016/j.jco.2015.11.003</a>
  chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
    Sampling.” <i>Journal of Complexity</i>. Academic Press, 2016. <a href="https://doi.org/10.1016/j.jco.2015.11.003">https://doi.org/10.1016/j.jco.2015.11.003</a>.
  ieee: F. Pausinger and S. Steinerberger, “On the discrepancy of jittered sampling,”
    <i>Journal of Complexity</i>, vol. 33. Academic Press, pp. 199–216, 2016.
  ista: Pausinger F, Steinerberger S. 2016. On the discrepancy of jittered sampling.
    Journal of Complexity. 33, 199–216.
  mla: Pausinger, Florian, and Stefan Steinerberger. “On the Discrepancy of Jittered
    Sampling.” <i>Journal of Complexity</i>, vol. 33, Academic Press, 2016, pp. 199–216,
    doi:<a href="https://doi.org/10.1016/j.jco.2015.11.003">10.1016/j.jco.2015.11.003</a>.
  short: F. Pausinger, S. Steinerberger, Journal of Complexity 33 (2016) 199–216.
date_created: 2018-12-11T11:53:03Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2021-01-12T06:52:02Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.11.003
intvolume: '        33'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1510.00251
month: '04'
oa: 1
oa_version: Submitted Version
page: 199 - 216
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5549'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the discrepancy of jittered sampling
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2016'
...
---
_id: '1662'
abstract:
- lang: eng
  text: We introduce a modification of the classic notion of intrinsic volume using
    persistence moments of height functions. Evaluating the modified first intrinsic
    volume on digital approximations of a compact body with smoothly embedded boundary
    in Rn, we prove convergence to the first intrinsic volume of the body as the resolution
    of the approximation improves. We have weaker results for the other modified intrinsic
    volumes, proving they converge to the corresponding intrinsic volumes of the n-dimensional
    unit ball.
acknowledgement: "This research is partially supported by the Toposys project FP7-ICT-318493-STREP,
  and by ESF under the ACAT Research Network Programme.\r\nBoth authors thank Anne
  Marie Svane for her comments on an early version of this paper. The second author
  wishes to thank Eva B. Vedel Jensen and Markus Kiderlen from Aarhus University for
  enlightening discussions and their kind hospitality during a visit of their department
  in 2014."
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Edelsbrunner H, Pausinger F. Approximation and convergence of the intrinsic
    volume. <i>Advances in Mathematics</i>. 2016;287:674-703. doi:<a href="https://doi.org/10.1016/j.aim.2015.10.004">10.1016/j.aim.2015.10.004</a>
  apa: Edelsbrunner, H., &#38; Pausinger, F. (2016). Approximation and convergence
    of the intrinsic volume. <i>Advances in Mathematics</i>. Academic Press. <a href="https://doi.org/10.1016/j.aim.2015.10.004">https://doi.org/10.1016/j.aim.2015.10.004</a>
  chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
    of the Intrinsic Volume.” <i>Advances in Mathematics</i>. Academic Press, 2016.
    <a href="https://doi.org/10.1016/j.aim.2015.10.004">https://doi.org/10.1016/j.aim.2015.10.004</a>.
  ieee: H. Edelsbrunner and F. Pausinger, “Approximation and convergence of the intrinsic
    volume,” <i>Advances in Mathematics</i>, vol. 287. Academic Press, pp. 674–703,
    2016.
  ista: Edelsbrunner H, Pausinger F. 2016. Approximation and convergence of the intrinsic
    volume. Advances in Mathematics. 287, 674–703.
  mla: Edelsbrunner, Herbert, and Florian Pausinger. “Approximation and Convergence
    of the Intrinsic Volume.” <i>Advances in Mathematics</i>, vol. 287, Academic Press,
    2016, pp. 674–703, doi:<a href="https://doi.org/10.1016/j.aim.2015.10.004">10.1016/j.aim.2015.10.004</a>.
  short: H. Edelsbrunner, F. Pausinger, Advances in Mathematics 287 (2016) 674–703.
date_created: 2018-12-11T11:53:20Z
date_published: 2016-01-10T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '10'
ddc:
- '004'
department:
- _id: HeEd
doi: 10.1016/j.aim.2015.10.004
ec_funded: 1
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file_date_updated: 2020-07-14T12:45:10Z
has_accepted_license: '1'
intvolume: '       287'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 674 - 703
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: Advances in Mathematics
publication_status: published
publisher: Academic Press
publist_id: '5488'
pubrep_id: '774'
quality_controlled: '1'
related_material:
  record:
  - id: '1399'
    relation: dissertation_contains
    status: public
scopus_import: 1
status: public
title: Approximation and convergence of the intrinsic volume
tmp:
  image: /images/cc_by_nc_nd.png
  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 287
year: '2016'
...
---
_id: '1792'
abstract:
- lang: eng
  text: Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop
    a new concept of variation of multivariate functions on a compact Hausdorff space
    with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka
    theorem that holds for this notion of variation and discrepancy with respect to
    D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions,
    such as extreme or isotropic discrepancy. For extreme discrepancy, our result
    coincides with the usual Koksma-Hlawka theorem. We show that the space of functions
    of bounded D-variation contains important discontinuous functions and is closed
    under natural algebraic operations. Finally, we illustrate the results on concrete
    integration problems from integral geometry and stereology.
acknowledgement: F.P. is supported by the Graduate School of IST Austria, A.M.S is
  supported by the Centre for Stochastic Geometry and Advanced Bioimaging funded by
  a grant from the Villum Foundation.
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
- first_name: Anne
  full_name: Svane, Anne
  last_name: Svane
citation:
  ama: Pausinger F, Svane A. A Koksma-Hlawka inequality for general discrepancy systems.
    <i>Journal of Complexity</i>. 2015;31(6):773-797. doi:<a href="https://doi.org/10.1016/j.jco.2015.06.002">10.1016/j.jco.2015.06.002</a>
  apa: Pausinger, F., &#38; Svane, A. (2015). A Koksma-Hlawka inequality for general
    discrepancy systems. <i>Journal of Complexity</i>. Academic Press. <a href="https://doi.org/10.1016/j.jco.2015.06.002">https://doi.org/10.1016/j.jco.2015.06.002</a>
  chicago: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
    Discrepancy Systems.” <i>Journal of Complexity</i>. Academic Press, 2015. <a href="https://doi.org/10.1016/j.jco.2015.06.002">https://doi.org/10.1016/j.jco.2015.06.002</a>.
  ieee: F. Pausinger and A. Svane, “A Koksma-Hlawka inequality for general discrepancy
    systems,” <i>Journal of Complexity</i>, vol. 31, no. 6. Academic Press, pp. 773–797,
    2015.
  ista: Pausinger F, Svane A. 2015. A Koksma-Hlawka inequality for general discrepancy
    systems. Journal of Complexity. 31(6), 773–797.
  mla: Pausinger, Florian, and Anne Svane. “A Koksma-Hlawka Inequality for General
    Discrepancy Systems.” <i>Journal of Complexity</i>, vol. 31, no. 6, Academic Press,
    2015, pp. 773–97, doi:<a href="https://doi.org/10.1016/j.jco.2015.06.002">10.1016/j.jco.2015.06.002</a>.
  short: F. Pausinger, A. Svane, Journal of Complexity 31 (2015) 773–797.
date_created: 2018-12-11T11:54:02Z
date_published: 2015-12-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
department:
- _id: HeEd
doi: 10.1016/j.jco.2015.06.002
intvolume: '        31'
issue: '6'
language:
- iso: eng
month: '12'
oa_version: None
page: 773 - 797
publication: Journal of Complexity
publication_status: published
publisher: Academic Press
publist_id: '5320'
quality_controlled: '1'
related_material:
  record:
  - id: '1399'
    relation: dissertation_contains
    status: public
scopus_import: 1
status: public
title: A Koksma-Hlawka inequality for general discrepancy systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2015'
...
---
_id: '1938'
abstract:
- lang: eng
  text: 'We numerically investigate the distribution of extrema of ''chaotic'' Laplacian
    eigenfunctions on two-dimensional manifolds. Our contribution is two-fold: (a)
    we count extrema on grid graphs with a small number of randomly added edges and
    show the behavior to coincide with the 1957 prediction of Longuet-Higgins for
    the continuous case and (b) we compute the regularity of their spatial distribution
    using discrepancy, which is a classical measure from the theory of Monte Carlo
    integration. The first part suggests that grid graphs with randomly added edges
    should behave like two-dimensional surfaces with ergodic geodesic flow; in the
    second part we show that the extrema are more regularly distributed in space than
    the grid Z2.'
acknowledgement: "F.P. was supported by the Graduate School of IST Austria. S.S. was
  partially supported by CRC1060 of the DFG\r\nThe authors thank Olga Symonova and
  Michael Kerber for sharing their implementation of the persistence algorithm. "
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
- first_name: Stefan
  full_name: Steinerberger, Stefan
  last_name: Steinerberger
citation:
  ama: Pausinger F, Steinerberger S. On the distribution of local extrema in quantum
    chaos. <i>Physics Letters, Section A</i>. 2015;379(6):535-541. doi:<a href="https://doi.org/10.1016/j.physleta.2014.12.010">10.1016/j.physleta.2014.12.010</a>
  apa: Pausinger, F., &#38; Steinerberger, S. (2015). On the distribution of local
    extrema in quantum chaos. <i>Physics Letters, Section A</i>. Elsevier. <a href="https://doi.org/10.1016/j.physleta.2014.12.010">https://doi.org/10.1016/j.physleta.2014.12.010</a>
  chicago: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
    Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>. Elsevier, 2015.
    <a href="https://doi.org/10.1016/j.physleta.2014.12.010">https://doi.org/10.1016/j.physleta.2014.12.010</a>.
  ieee: F. Pausinger and S. Steinerberger, “On the distribution of local extrema in
    quantum chaos,” <i>Physics Letters, Section A</i>, vol. 379, no. 6. Elsevier,
    pp. 535–541, 2015.
  ista: Pausinger F, Steinerberger S. 2015. On the distribution of local extrema in
    quantum chaos. Physics Letters, Section A. 379(6), 535–541.
  mla: Pausinger, Florian, and Stefan Steinerberger. “On the Distribution of Local
    Extrema in Quantum Chaos.” <i>Physics Letters, Section A</i>, vol. 379, no. 6,
    Elsevier, 2015, pp. 535–41, doi:<a href="https://doi.org/10.1016/j.physleta.2014.12.010">10.1016/j.physleta.2014.12.010</a>.
  short: F. Pausinger, S. Steinerberger, Physics Letters, Section A 379 (2015) 535–541.
date_created: 2018-12-11T11:54:49Z
date_published: 2015-03-06T00:00:00Z
date_updated: 2021-01-12T06:54:12Z
day: '06'
department:
- _id: HeEd
doi: 10.1016/j.physleta.2014.12.010
intvolume: '       379'
issue: '6'
language:
- iso: eng
month: '03'
oa_version: None
page: 535 - 541
publication: Physics Letters, Section A
publication_status: published
publisher: Elsevier
publist_id: '5152'
quality_controlled: '1'
scopus_import: 1
status: public
title: On the distribution of local extrema in quantum chaos
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 379
year: '2015'
...
---
_id: '1399'
abstract:
- lang: eng
  text: This thesis is concerned with the computation and approximation of intrinsic
    volumes. Given a smooth body M and a certain digital approximation of it, we develop
    algorithms to approximate various intrinsic volumes of M using only measurements
    taken from its digital approximations. The crucial idea behind our novel algorithms
    is to link the recent theory of persistent homology to the theory of intrinsic
    volumes via the Crofton formula from integral geometry and, in particular, via
    Euler characteristic computations. Our main contributions are a multigrid convergent
    digital algorithm to compute the first intrinsic volume of a solid body in R^n
    as well as an appropriate integration pipeline to approximate integral-geometric
    integrals defined over the Grassmannian manifold.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Pausinger F. On the approximation of intrinsic volumes. 2015.
  apa: Pausinger, F. (2015). <i>On the approximation of intrinsic volumes</i>. Institute
    of Science and Technology Austria.
  chicago: Pausinger, Florian. “On the Approximation of Intrinsic Volumes.” Institute
    of Science and Technology Austria, 2015.
  ieee: F. Pausinger, “On the approximation of intrinsic volumes,” Institute of Science
    and Technology Austria, 2015.
  ista: Pausinger F. 2015. On the approximation of intrinsic volumes. Institute of
    Science and Technology Austria.
  mla: Pausinger, Florian. <i>On the Approximation of Intrinsic Volumes</i>. Institute
    of Science and Technology Austria, 2015.
  short: F. Pausinger, On the Approximation of Intrinsic Volumes, Institute of Science
    and Technology Austria, 2015.
date_created: 2018-12-11T11:51:48Z
date_published: 2015-06-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
degree_awarded: PhD
department:
- _id: HeEd
language:
- iso: eng
month: '06'
oa_version: None
page: '144'
publication_identifier:
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '5808'
related_material:
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  - id: '1662'
    relation: part_of_dissertation
    status: public
  - id: '1792'
    relation: part_of_dissertation
    status: public
  - id: '2255'
    relation: part_of_dissertation
    status: public
status: public
supervisor:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
title: On the approximation of intrinsic volumes
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2015'
...
---
_id: '2255'
abstract:
- lang: eng
  text: Motivated by applications in biology, we present an algorithm for estimating
    the length of tube-like shapes in 3-dimensional Euclidean space. In a first step,
    we combine the tube formula of Weyl with integral geometric methods to obtain
    an integral representation of the length, which we approximate using a variant
    of the Koksma-Hlawka Theorem. In a second step, we use tools from computational
    topology to decrease the dependence on small perturbations of the shape. We present
    computational experiments that shed light on the stability and the convergence
    rate of our algorithm.
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes. <i>Journal
    of Mathematical Imaging and Vision</i>. 2014;50(1):164-177. doi:<a href="https://doi.org/10.1007/s10851-013-0468-x">10.1007/s10851-013-0468-x</a>
  apa: Edelsbrunner, H., &#38; Pausinger, F. (2014). Stable length estimates of tube-like
    shapes. <i>Journal of Mathematical Imaging and Vision</i>. Springer. <a href="https://doi.org/10.1007/s10851-013-0468-x">https://doi.org/10.1007/s10851-013-0468-x</a>
  chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
    of Tube-like Shapes.” <i>Journal of Mathematical Imaging and Vision</i>. Springer,
    2014. <a href="https://doi.org/10.1007/s10851-013-0468-x">https://doi.org/10.1007/s10851-013-0468-x</a>.
  ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
    <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1. Springer, pp.
    164–177, 2014.
  ista: Edelsbrunner H, Pausinger F. 2014. Stable length estimates of tube-like shapes.
    Journal of Mathematical Imaging and Vision. 50(1), 164–177.
  mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
    Shapes.” <i>Journal of Mathematical Imaging and Vision</i>, vol. 50, no. 1, Springer,
    2014, pp. 164–77, doi:<a href="https://doi.org/10.1007/s10851-013-0468-x">10.1007/s10851-013-0468-x</a>.
  short: H. Edelsbrunner, F. Pausinger, Journal of Mathematical Imaging and Vision
    50 (2014) 164–177.
date_created: 2018-12-11T11:56:36Z
date_published: 2014-09-01T00:00:00Z
date_updated: 2023-09-07T11:41:25Z
day: '01'
ddc:
- '000'
department:
- _id: HeEd
doi: 10.1007/s10851-013-0468-x
ec_funded: 1
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  date_created: 2018-12-12T10:16:18Z
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  file_id: '5204'
  file_name: IST-2016-549-v1+1_2014-J-06-LengthEstimate.pdf
  file_size: 3941391
  relation: main_file
file_date_updated: 2020-07-14T12:45:35Z
has_accepted_license: '1'
intvolume: '        50'
issue: '1'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Submitted Version
page: 164 - 177
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
  issn:
  - '09249907'
publication_status: published
publisher: Springer
publist_id: '4691'
pubrep_id: '549'
quality_controlled: '1'
related_material:
  record:
  - id: '2843'
    relation: earlier_version
    status: public
  - id: '1399'
    relation: dissertation_contains
    status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 50
year: '2014'
...
---
_id: '2843'
abstract:
- lang: eng
  text: 'Mathematical objects can be measured unambiguously, but not so objects from
    our physical world. Even the total length of tubelike shapes has its difficulties.
    We introduce a combination of geometric, probabilistic, and topological methods
    to design a stable length estimate for tube-like shapes; that is: one that is
    insensitive to small shape changes.'
alternative_title:
- LNCS
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: 'Edelsbrunner H, Pausinger F. Stable length estimates of tube-like shapes.
    In: <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>.
    Vol 7749. Springer; 2013:XV-XIX. doi:<a href="https://doi.org/10.1007/978-3-642-37067-0">10.1007/978-3-642-37067-0</a>'
  apa: 'Edelsbrunner, H., &#38; Pausinger, F. (2013). Stable length estimates of tube-like
    shapes. In <i>17th IAPR International Conference on Discrete Geometry for Computer
    Imagery</i> (Vol. 7749, pp. XV–XIX). Seville, Spain: Springer. <a href="https://doi.org/10.1007/978-3-642-37067-0">https://doi.org/10.1007/978-3-642-37067-0</a>'
  chicago: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates
    of Tube-like Shapes.” In <i>17th IAPR International Conference on Discrete Geometry
    for Computer Imagery</i>, 7749:XV–XIX. Springer, 2013. <a href="https://doi.org/10.1007/978-3-642-37067-0">https://doi.org/10.1007/978-3-642-37067-0</a>.
  ieee: H. Edelsbrunner and F. Pausinger, “Stable length estimates of tube-like shapes,”
    in <i>17th IAPR International Conference on Discrete Geometry for Computer Imagery</i>,
    Seville, Spain, 2013, vol. 7749, pp. XV–XIX.
  ista: 'Edelsbrunner H, Pausinger F. 2013. Stable length estimates of tube-like shapes.
    17th IAPR International Conference on Discrete Geometry for Computer Imagery.
    DGCI: Discrete Geometry for Computer Imagery, LNCS, vol. 7749, XV–XIX.'
  mla: Edelsbrunner, Herbert, and Florian Pausinger. “Stable Length Estimates of Tube-like
    Shapes.” <i>17th IAPR International Conference on Discrete Geometry for Computer
    Imagery</i>, vol. 7749, Springer, 2013, pp. XV–XIX, doi:<a href="https://doi.org/10.1007/978-3-642-37067-0">10.1007/978-3-642-37067-0</a>.
  short: H. Edelsbrunner, F. Pausinger, in:, 17th IAPR International Conference on
    Discrete Geometry for Computer Imagery, Springer, 2013, pp. XV–XIX.
conference:
  end_date: 2013-03-22
  location: Seville, Spain
  name: 'DGCI: Discrete Geometry for Computer Imagery'
  start_date: 2013-03-20
date_created: 2018-12-11T11:59:53Z
date_published: 2013-02-21T00:00:00Z
date_updated: 2023-02-23T10:35:00Z
day: '21'
department:
- _id: HeEd
doi: 10.1007/978-3-642-37067-0
intvolume: '      7749'
language:
- iso: eng
month: '02'
oa_version: None
page: XV - XIX
publication: 17th IAPR International Conference on Discrete Geometry for Computer
  Imagery
publication_status: published
publisher: Springer
publist_id: '3952'
quality_controlled: '1'
related_material:
  record:
  - id: '2255'
    relation: later_version
    status: public
scopus_import: 1
status: public
title: Stable length estimates of tube-like shapes
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7749
year: '2013'
...
---
_id: '2304'
abstract:
- lang: eng
  text: This extended abstract is concerned with the irregularities of distribution
    of one-dimensional permuted van der Corput sequences that are generated from linear
    permutations. We show how to obtain upper bounds for the discrepancy and diaphony
    of these sequences, by relating them to Kronecker sequences and applying earlier
    results of Faure and Niederreiter.
acknowledgement: This research is supported by the Graduate school of IST Austria
  (Institute of Science and Technology Austria).
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Pausinger F. Van der Corput sequences and linear permutations. <i>Electronic
    Notes in Discrete Mathematics</i>. 2013;43:43-50. doi:<a href="https://doi.org/10.1016/j.endm.2013.07.008">10.1016/j.endm.2013.07.008</a>
  apa: Pausinger, F. (2013). Van der Corput sequences and linear permutations. <i>Electronic
    Notes in Discrete Mathematics</i>. Elsevier. <a href="https://doi.org/10.1016/j.endm.2013.07.008">https://doi.org/10.1016/j.endm.2013.07.008</a>
  chicago: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.”
    <i>Electronic Notes in Discrete Mathematics</i>. Elsevier, 2013. <a href="https://doi.org/10.1016/j.endm.2013.07.008">https://doi.org/10.1016/j.endm.2013.07.008</a>.
  ieee: F. Pausinger, “Van der Corput sequences and linear permutations,” <i>Electronic
    Notes in Discrete Mathematics</i>, vol. 43. Elsevier, pp. 43–50, 2013.
  ista: Pausinger F. 2013. Van der Corput sequences and linear permutations. Electronic
    Notes in Discrete Mathematics. 43, 43–50.
  mla: Pausinger, Florian. “Van Der Corput Sequences and Linear Permutations.” <i>Electronic
    Notes in Discrete Mathematics</i>, vol. 43, Elsevier, 2013, pp. 43–50, doi:<a
    href="https://doi.org/10.1016/j.endm.2013.07.008">10.1016/j.endm.2013.07.008</a>.
  short: F. Pausinger, Electronic Notes in Discrete Mathematics 43 (2013) 43–50.
date_created: 2018-12-11T11:56:53Z
date_published: 2013-09-05T00:00:00Z
date_updated: 2021-01-12T06:56:39Z
day: '05'
department:
- _id: HeEd
doi: 10.1016/j.endm.2013.07.008
intvolume: '        43'
language:
- iso: eng
month: '09'
oa_version: None
page: 43 - 50
publication: Electronic Notes in Discrete Mathematics
publication_status: published
publisher: Elsevier
publist_id: '4623'
quality_controlled: '1'
scopus_import: 1
status: public
title: Van der Corput sequences and linear permutations
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 43
year: '2013'
...
---
_id: '2904'
abstract:
- lang: eng
  text: Generalized van der Corput sequences are onedimensional, infinite sequences
    in the unit interval. They are generated from permutations in integer base b and
    are the building blocks of the multi-dimensional Halton sequences. Motivated by
    recent progress of Atanassov on the uniform distribution behavior of Halton sequences,
    we study, among others, permutations of the form P(i) = ai (mod b) for coprime
    integers a and b. We show that multipliers a that either divide b - 1 or b + 1
    generate van der Corput sequences with weak distribution properties. We give explicit
    lower bounds for the asymptotic distribution behavior of these sequences and relate
    them to sequences generated from the identity permutation in smaller bases, which
    are, due to Faure, the weakest distributed generalized van der Corput sequences.
- lang: fre
  text: Les suites de Van der Corput généralisées sont dessuites unidimensionnelles
    et infinies dans l’intervalle de l’unité.Elles sont générées par permutations
    des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles
    deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de
    distribution uniforme des suites de Halton nous nousintéressons aux permutations
    de la formuleP(i)  =ai(modb)pour les entiers premiers entre euxaetb. Dans cet
    article nousidentifions des multiplicateursagénérant des suites de Van derCorput
    ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites
    pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières
    aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins
    bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée.
article_processing_charge: No
article_type: original
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Pausinger F. Weak multipliers for generalized van der Corput sequences. <i>Journal
    de Theorie des Nombres des Bordeaux</i>. 2012;24(3):729-749. doi:<a href="https://doi.org/10.5802/jtnb.819">10.5802/jtnb.819</a>
  apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences.
    <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux. <a
    href="https://doi.org/10.5802/jtnb.819">https://doi.org/10.5802/jtnb.819</a>
  chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
    <i>Journal de Theorie Des Nombres Des Bordeaux</i>. Université de Bordeaux, 2012.
    <a href="https://doi.org/10.5802/jtnb.819">https://doi.org/10.5802/jtnb.819</a>.
  ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,”
    <i>Journal de Theorie des Nombres des Bordeaux</i>, vol. 24, no. 3. Université
    de Bordeaux, pp. 729–749, 2012.
  ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences.
    Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.
  mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
    <i>Journal de Theorie Des Nombres Des Bordeaux</i>, vol. 24, no. 3, Université
    de Bordeaux, 2012, pp. 729–49, doi:<a href="https://doi.org/10.5802/jtnb.819">10.5802/jtnb.819</a>.
  short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.
date_created: 2018-12-11T12:00:15Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2023-10-18T07:53:47Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.5802/jtnb.819
file:
- access_level: open_access
  checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67
  content_type: application/pdf
  creator: dernst
  date_created: 2020-05-11T12:40:39Z
  date_updated: 2020-07-14T12:45:52Z
  file_id: '7819'
  file_name: JTNB_2012__24_3_729_0.pdf
  file_size: 819275
  relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
intvolume: '        24'
issue: '3'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 729 - 749
publication: Journal de Theorie des Nombres des Bordeaux
publication_identifier:
  eissn:
  - 2118-8572
  issn:
  - 1246-7405
publication_status: published
publisher: Université de Bordeaux
publist_id: '3843'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak multipliers for generalized van der Corput sequences
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2012'
...
---
_id: '6588'
abstract:
- lang: eng
  text: First we note that the best polynomial approximation to vertical bar x vertical
    bar on the set, which consists of an interval on the positive half-axis and a
    point on the negative half-axis, can be given by means of the classical Chebyshev
    polynomials. Then we explore the cases when a solution of the related problem
    on two intervals can be given in elementary functions.
acknowledgement: "This work is supported by the Austrian Science Fund (FWF), Project
  P22025-N18.\r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Florian
  full_name: Pausinger, Florian
  id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
  last_name: Pausinger
  orcid: 0000-0002-8379-3768
citation:
  ama: Pausinger F. Elementary solutions of the Bernstein problem on two intervals.
    <i>Journal of Mathematical Physics, Analysis, Geometry</i>. 2012;8(1):63-78.
  apa: Pausinger, F. (2012). Elementary solutions of the Bernstein problem on two
    intervals. <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin
    Institute for Low Temperature Physics and Engineering.
  chicago: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two
    Intervals.” <i>Journal of Mathematical Physics, Analysis, Geometry</i>. B. Verkin
    Institute for Low Temperature Physics and Engineering, 2012.
  ieee: F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals,”
    <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1. B.
    Verkin Institute for Low Temperature Physics and Engineering, pp. 63–78, 2012.
  ista: Pausinger F. 2012. Elementary solutions of the Bernstein problem on two intervals.
    Journal of Mathematical Physics, Analysis, Geometry. 8(1), 63–78.
  mla: Pausinger, Florian. “Elementary Solutions of the Bernstein Problem on Two Intervals.”
    <i>Journal of Mathematical Physics, Analysis, Geometry</i>, vol. 8, no. 1, B.
    Verkin Institute for Low Temperature Physics and Engineering, 2012, pp. 63–78.
  short: F. Pausinger, Journal of Mathematical Physics, Analysis, Geometry 8 (2012)
    63–78.
date_created: 2019-06-27T08:16:56Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2023-10-16T09:41:31Z
day: '01'
department:
- _id: HeEd
external_id:
  isi:
  - '000301173600004'
intvolume: '         8'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://mi.mathnet.ru/eng/jmag525
month: '01'
oa: 1
oa_version: Published Version
page: 63-78
publication: Journal of Mathematical Physics, Analysis, Geometry
publication_identifier:
  issn:
  - 1812-9471
publication_status: published
publisher: B. Verkin Institute for Low Temperature Physics and Engineering
quality_controlled: '1'
scopus_import: '1'
status: public
title: Elementary solutions of the Bernstein problem on two intervals
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2012'
...