---
_id: '14226'
abstract:
- lang: eng
text: "We introduce the notion of a Faustian interchange in a 1-parameter family
of smooth\r\nfunctions to generalize the medial axis to critical points of index
larger than 0.\r\nWe construct and implement a general purpose algorithm for approximating
such\r\ngeneralized medial axes."
alternative_title:
- ISTA Master's Thesis
article_processing_charge: No
author:
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
citation:
ama: Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:10.15479/at:ista:14226
apa: Stephenson, E. R. (2023). Generalizing medial axes with homology switches.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14226
chicago: Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14226.
ieee: E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute
of Science and Technology Austria, 2023.
ista: Stephenson ER. 2023. Generalizing medial axes with homology switches. Institute
of Science and Technology Austria.
mla: Stephenson, Elizabeth R. Generalizing Medial Axes with Homology Switches.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14226.
short: E.R. Stephenson, Generalizing Medial Axes with Homology Switches, Institute
of Science and Technology Austria, 2023.
date_created: 2023-08-24T13:01:18Z
date_published: 2023-08-24T00:00:00Z
date_updated: 2024-02-26T23:30:04Z
day: '24'
ddc:
- '500'
degree_awarded: MS
department:
- _id: GradSch
- _id: HeEd
doi: 10.15479/at:ista:14226
file:
- access_level: closed
checksum: 453caf851d75c3478c10ed09bd242a91
content_type: application/x-zip-compressed
creator: cchlebak
date_created: 2023-08-24T13:02:49Z
date_updated: 2024-02-26T23:30:03Z
embargo_to: open_access
file_id: '14227'
file_name: documents-export-2023-08-24.zip
file_size: 15501411
relation: source_file
- access_level: open_access
checksum: 7349d29963d6695e555e171748648d9a
content_type: application/pdf
creator: cchlebak
date_created: 2023-08-24T13:03:42Z
date_updated: 2024-02-26T23:30:03Z
embargo: 2024-02-25
file_id: '14228'
file_name: thesis_pdf_a.pdf
file_size: 6854783
relation: main_file
file_date_updated: 2024-02-26T23:30:03Z
has_accepted_license: '1'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: '43'
publication_identifier:
issn:
- 2791-4585
publication_status: published
publisher: Institute of Science and Technology Austria
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: Generalizing medial axes with homology switches
type: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2023'
...
---
_id: '10754'
abstract:
- lang: eng
text: Targeting dysregulated Ca2+ signaling in cancer cells is an emerging chemotherapy
approach. We previously reported that store-operated Ca2+ entry (SOCE) blockers,
such as RP4010, are promising antitumor drugs for esophageal cancer. As a tyrosine
kinase inhibitor (TKI), afatinib received FDA approval to be used in targeted
therapy for patients with EGFR mutation-positive cancers. While preclinical studies
and clinical trials have shown that afatinib has benefits for esophageal cancer
patients, it is not known whether a combination of afatinib and RP4010 could achieve
better anticancer effects. Since TKI can alter intracellular Ca2+ dynamics through
EGFR/phospholipase C-γ pathway, in this study, we evaluated the inhibitory effect
of afatinib and RP4010 on intracellular Ca2+ oscillations in KYSE-150, a human
esophageal squamous cell carcinoma cell line, using both experimental and mathematical
simulations. Our mathematical simulation of Ca2+ oscillations could fit well with
experimental data responding to afatinib or RP4010, both separately or in combination.
Guided by simulation, we were able to identify a proper ratio of afatinib and
RP4010 for combined treatment, and such a combination presented synergistic anticancer-effect
evidence by experimental measurement of intracellular Ca2+ and cell proliferation.
This intracellular Ca2+ dynamic-based mathematical simulation approach could be
useful for a rapid and cost-effective evaluation of combined targeting therapy
drugs.
acknowledgement: "This work was partially supported by grants from National Institutes
of Health (NIH) (R01 CA185055, S10OD0252300) and The University of Texas System
STARs Award (to Z.P.),\r\nThe University of Texas at Arlington Interdisciplinary
Research Program (to B.C., H.V.K. and Z.P.). "
article_number: '1763'
article_processing_charge: Yes
article_type: original
author:
- first_name: Yan
full_name: Chang, Yan
last_name: Chang
- first_name: Marah
full_name: Funk, Marah
last_name: Funk
- first_name: Souvik
full_name: Roy, Souvik
last_name: Roy
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Sangyong
full_name: Choi, Sangyong
last_name: Choi
- first_name: Hristo V.
full_name: Kojouharov, Hristo V.
last_name: Kojouharov
- first_name: Benito
full_name: Chen, Benito
last_name: Chen
- first_name: Zui
full_name: Pan, Zui
last_name: Pan
citation:
ama: Chang Y, Funk M, Roy S, et al. Developing a mathematical model of intracellular
Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010
in esophageal cancer. International Journal of Molecular Sciences. 2022;23(3).
doi:10.3390/ijms23031763
apa: Chang, Y., Funk, M., Roy, S., Stephenson, E. R., Choi, S., Kojouharov, H. V.,
… Pan, Z. (2022). Developing a mathematical model of intracellular Calcium dynamics
for evaluating combined anticancer effects of afatinib and RP4010 in esophageal
cancer. International Journal of Molecular Sciences. MDPI. https://doi.org/10.3390/ijms23031763
chicago: Chang, Yan, Marah Funk, Souvik Roy, Elizabeth R Stephenson, Sangyong Choi,
Hristo V. Kojouharov, Benito Chen, and Zui Pan. “Developing a Mathematical Model
of Intracellular Calcium Dynamics for Evaluating Combined Anticancer Effects of
Afatinib and RP4010 in Esophageal Cancer.” International Journal of Molecular
Sciences. MDPI, 2022. https://doi.org/10.3390/ijms23031763.
ieee: Y. Chang et al., “Developing a mathematical model of intracellular
Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010
in esophageal cancer,” International Journal of Molecular Sciences, vol.
23, no. 3. MDPI, 2022.
ista: Chang Y, Funk M, Roy S, Stephenson ER, Choi S, Kojouharov HV, Chen B, Pan
Z. 2022. Developing a mathematical model of intracellular Calcium dynamics for
evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer.
International Journal of Molecular Sciences. 23(3), 1763.
mla: Chang, Yan, et al. “Developing a Mathematical Model of Intracellular Calcium
Dynamics for Evaluating Combined Anticancer Effects of Afatinib and RP4010 in
Esophageal Cancer.” International Journal of Molecular Sciences, vol. 23,
no. 3, 1763, MDPI, 2022, doi:10.3390/ijms23031763.
short: Y. Chang, M. Funk, S. Roy, E.R. Stephenson, S. Choi, H.V. Kojouharov, B.
Chen, Z. Pan, International Journal of Molecular Sciences 23 (2022).
date_created: 2022-02-13T23:01:35Z
date_published: 2022-02-01T00:00:00Z
date_updated: 2023-08-09T10:17:07Z
day: '01'
ddc:
- '510'
- '576'
department:
- _id: HeEd
doi: 10.3390/ijms23031763
external_id:
isi:
- '000754773500001'
file:
- access_level: open_access
checksum: 8890ad20c54e90dc58ad5ea97c902998
content_type: application/pdf
creator: dernst
date_created: 2022-02-14T07:46:30Z
date_updated: 2022-02-14T07:46:30Z
file_id: '10756'
file_name: 2022_IJMS_Chang.pdf
file_size: 24416183
relation: main_file
success: 1
file_date_updated: 2022-02-14T07:46:30Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
publication: International Journal of Molecular Sciences
publication_identifier:
eissn:
- '14220067'
issn:
- '16616596'
publication_status: published
publisher: MDPI
quality_controlled: '1'
scopus_import: '1'
status: public
title: Developing a mathematical model of intracellular Calcium dynamics for evaluating
combined anticancer effects of afatinib and RP4010 in esophageal cancer
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2022'
...
---
_id: '11428'
abstract:
- lang: eng
text: The medial axis of a set consists of the points in the ambient space without
a unique closest point on the original set. Since its introduction, the medial
axis has been used extensively in many applications as a method of computing a
topologically equivalent skeleton. Unfortunately, one limiting factor in the use
of the medial axis of a smooth manifold is that it is not necessarily topologically
stable under small perturbations of the manifold. To counter these instabilities
various prunings of the medial axis have been proposed. Here, we examine one type
of pruning, called burning. Because of the good experimental results, it was hoped
that the burning method of simplifying the medial axis would be stable. In this
work we show a simple example that dashes such hopes based on Bing’s house with
two rooms, demonstrating an isotopy of a shape where the medial axis goes from
collapsible to non-collapsible.
acknowledgement: 'Partially supported by the DFG Collaborative Research Center TRR
109, “Discretization in Geometry and Dynamics” and the European Research Council
(ERC), grant no. 788183, “Alpha Shape Theory Extended”. Erin Chambers: Supported
in part by the National Science Foundation through grants DBI-1759807, CCF-1907612,
and CCF-2106672. Mathijs Wintraecken: Supported by the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement
No. 754411. The Austrian science fund (FWF) M-3073 Acknowledgements We thank André
Lieutier, David Letscher, Ellen Gasparovic, Kathryn Leonard, and Tao Ju for early
discussions on this work. We also thank Lu Liu, Yajie Yan and Tao Ju for sharing
code to generate the examples.'
article_processing_charge: No
author:
- first_name: Erin
full_name: Chambers, Erin
last_name: Chambers
- first_name: Christopher D
full_name: Fillmore, Christopher D
id: 35638A5C-AAC7-11E9-B0BF-5503E6697425
last_name: Fillmore
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
- first_name: Mathijs
full_name: Wintraecken, Mathijs
id: 307CFBC8-F248-11E8-B48F-1D18A9856A87
last_name: Wintraecken
orcid: 0000-0002-7472-2220
citation:
ama: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale:
Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. 38th International
Symposium on Computational Geometry. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik; 2022:66:1-66:9. doi:10.4230/LIPIcs.SoCG.2022.66'
apa: 'Chambers, E., Fillmore, C. D., Stephenson, E. R., & Wintraecken, M. (2022).
A cautionary tale: Burning the medial axis is unstable. In X. Goaoc & M. Kerber
(Eds.), 38th International Symposium on Computational Geometry (Vol. 224,
p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.SoCG.2022.66'
chicago: 'Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs
Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In 38th
International Symposium on Computational Geometry, edited by Xavier Goaoc
and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum
für Informatik, 2022. https://doi.org/10.4230/LIPIcs.SoCG.2022.66.'
ieee: 'E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary
tale: Burning the medial axis is unstable,” in 38th International Symposium
on Computational Geometry, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.'
ista: 'Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. 2022. A cautionary
tale: Burning the medial axis is unstable. 38th International Symposium on Computational
Geometry. SoCG: Symposium on Computational GeometryLIPIcs vol. 224, 66:1-66:9.'
mla: 'Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.”
38th International Symposium on Computational Geometry, edited by Xavier
Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik,
2022, p. 66:1-66:9, doi:10.4230/LIPIcs.SoCG.2022.66.'
short: E. Chambers, C.D. Fillmore, E.R. Stephenson, M. Wintraecken, in:, X. Goaoc,
M. Kerber (Eds.), 38th International Symposium on Computational Geometry, Schloss
Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9.
conference:
end_date: 2022-06-10
location: Berlin, Germany
name: 'SoCG: Symposium on Computational Geometry'
start_date: 2022-06-07
date_created: 2022-06-01T14:18:04Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2023-02-21T09:50:52Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.4230/LIPIcs.SoCG.2022.66
ec_funded: 1
editor:
- first_name: Xavier
full_name: Goaoc, Xavier
last_name: Goaoc
- first_name: Michael
full_name: Kerber, Michael
last_name: Kerber
file:
- access_level: open_access
checksum: b25ce40fade4ebc0bcaae176db4f5f1f
content_type: application/pdf
creator: dernst
date_created: 2022-06-07T07:58:30Z
date_updated: 2022-06-07T07:58:30Z
file_id: '11437'
file_name: 2022_LIPICs_Chambers.pdf
file_size: 17580705
relation: main_file
success: 1
file_date_updated: 2022-06-07T07:58:30Z
has_accepted_license: '1'
intvolume: ' 224'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 66:1-66:9
project:
- _id: fc390959-9c52-11eb-aca3-afa58bd282b2
grant_number: M03073
name: Learning and triangulating manifolds via collapses
- _id: 266A2E9E-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '788183'
name: Alpha Shape Theory Extended
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 38th International Symposium on Computational Geometry
publication_identifier:
isbn:
- 978-3-95977-227-3
issn:
- 1868-8969
publication_status: published
publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
quality_controlled: '1'
scopus_import: '1'
series_title: LIPIcs
status: public
title: 'A cautionary tale: Burning the medial axis is unstable'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: conference
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 224
year: '2022'
...
---
_id: '12307'
abstract:
- lang: eng
text: Point-set topology is among the most abstract branches of mathematics in that
it lacks tangible notions of distance, length, magnitude, order, and size. There
is no shape, no geometry, no algebra, and no direction. Everything we are used
to visualizing is gone. In the teaching and learning of mathematics, this can
present a conundrum. Yet, this very property makes point set topology perfect
for teaching and learning abstract mathematical concepts. It clears our minds
of preconceived intuitions and expectations and forces us to think in new and
creative ways. In this paper, we present guided investigations into topology through
questions and thinking strategies that open up fascinating problems. They are
intended for faculty who already teach or are thinking about teaching a class
in topology or abstract mathematical reasoning for undergraduates. They can be
used to build simple to challenging projects in topology, proofs, honors programs,
and research experiences.
article_processing_charge: No
article_type: original
author:
- first_name: Barbara A.
full_name: Shipman, Barbara A.
last_name: Shipman
- first_name: Elizabeth R
full_name: Stephenson, Elizabeth R
id: 2D04F932-F248-11E8-B48F-1D18A9856A87
last_name: Stephenson
orcid: 0000-0002-6862-208X
citation:
ama: Shipman BA, Stephenson ER. Tangible topology through the lens of limits. PRIMUS.
2022;32(5):593-609. doi:10.1080/10511970.2021.1872750
apa: Shipman, B. A., & Stephenson, E. R. (2022). Tangible topology through the
lens of limits. PRIMUS. Taylor & Francis. https://doi.org/10.1080/10511970.2021.1872750
chicago: Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through
the Lens of Limits.” PRIMUS. Taylor & Francis, 2022. https://doi.org/10.1080/10511970.2021.1872750.
ieee: B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of
limits,” PRIMUS, vol. 32, no. 5. Taylor & Francis, pp. 593–609, 2022.
ista: Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits.
PRIMUS. 32(5), 593–609.
mla: Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through
the Lens of Limits.” PRIMUS, vol. 32, no. 5, Taylor & Francis, 2022,
pp. 593–609, doi:10.1080/10511970.2021.1872750.
short: B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.
date_created: 2023-01-16T10:07:21Z
date_published: 2022-05-28T00:00:00Z
date_updated: 2023-01-30T13:02:30Z
day: '28'
department:
- _id: HeEd
- _id: GradSch
doi: 10.1080/10511970.2021.1872750
intvolume: ' 32'
issue: '5'
keyword:
- Education
- General Mathematics
language:
- iso: eng
month: '05'
oa_version: None
page: 593-609
publication: PRIMUS
publication_identifier:
eissn:
- 1935-4053
issn:
- 1051-1970
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Tangible topology through the lens of limits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2022'
...