[{"type":"dissertation","day":"24","supervisor":[{"first_name":"Herbert","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"status":"public","file_date_updated":"2024-02-26T23:30:03Z","page":"43","date_published":"2023-08-24T00:00:00Z","month":"08","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"degree_awarded":"MS","has_accepted_license":"1","file":[{"date_updated":"2024-02-26T23:30:03Z","access_level":"closed","embargo_to":"open_access","date_created":"2023-08-24T13:02:49Z","checksum":"453caf851d75c3478c10ed09bd242a91","file_name":"documents-export-2023-08-24.zip","file_size":15501411,"creator":"cchlebak","file_id":"14227","content_type":"application/x-zip-compressed","relation":"source_file"},{"date_updated":"2024-02-26T23:30:03Z","access_level":"open_access","date_created":"2023-08-24T13:03:42Z","checksum":"7349d29963d6695e555e171748648d9a","file_name":"thesis_pdf_a.pdf","file_size":6854783,"embargo":"2024-02-25","creator":"cchlebak","file_id":"14228","content_type":"application/pdf","relation":"main_file"}],"date_created":"2023-08-24T13:01:18Z","publication_status":"published","citation":{"mla":"Stephenson, Elizabeth R. <i>Generalizing Medial Axes with Homology Switches</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:14226\">10.15479/at:ista:14226</a>.","ama":"Stephenson ER. Generalizing medial axes with homology switches. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:14226\">10.15479/at:ista:14226</a>","short":"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.","ieee":"E. R. Stephenson, “Generalizing medial axes with homology switches,” Institute of Science and Technology Austria, 2023.","apa":"Stephenson, E. R. (2023). <i>Generalizing medial axes with homology switches</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14226\">https://doi.org/10.15479/at:ista:14226</a>","chicago":"Stephenson, Elizabeth R. “Generalizing Medial Axes with Homology Switches.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:14226\">https://doi.org/10.15479/at:ista:14226</a>."},"author":[{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","first_name":"Elizabeth R"}],"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."}],"date_updated":"2024-02-26T23:30:04Z","oa":1,"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa_version":"Published Version","_id":"14226","publication_identifier":{"issn":["2791-4585"]},"year":"2023","doi":"10.15479/at:ista:14226","title":"Generalizing medial axes with homology switches","alternative_title":["ISTA Master's Thesis"],"ddc":["500"]},{"file_date_updated":"2022-02-14T07:46:30Z","publication":"International Journal of Molecular Sciences","issue":"3","type":"journal_article","day":"01","status":"public","intvolume":"        23","department":[{"_id":"HeEd"}],"has_accepted_license":"1","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"10756","creator":"dernst","success":1,"date_updated":"2022-02-14T07:46:30Z","access_level":"open_access","file_name":"2022_IJMS_Chang.pdf","file_size":24416183,"date_created":"2022-02-14T07:46:30Z","checksum":"8890ad20c54e90dc58ad5ea97c902998"}],"date_created":"2022-02-13T23:01:35Z","date_published":"2022-02-01T00:00:00Z","article_type":"original","month":"02","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"MDPI","article_processing_charge":"Yes","oa":1,"volume":23,"date_updated":"2023-08-09T10:17:07Z","quality_controlled":"1","oa_version":"Published Version","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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.). ","publication_identifier":{"issn":["16616596"],"eissn":["14220067"]},"_id":"10754","citation":{"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.","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).","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.” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3, 1763, MDPI, 2022, doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>.","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. <i>International Journal of Molecular Sciences</i>. 2022;23(3). doi:<a href=\"https://doi.org/10.3390/ijms23031763\">10.3390/ijms23031763</a>","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.” <i>International Journal of Molecular Sciences</i>. MDPI, 2022. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>.","ieee":"Y. Chang <i>et al.</i>, “Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer,” <i>International Journal of Molecular Sciences</i>, vol. 23, no. 3. MDPI, 2022.","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. <i>International Journal of Molecular Sciences</i>. MDPI. <a href=\"https://doi.org/10.3390/ijms23031763\">https://doi.org/10.3390/ijms23031763</a>"},"publication_status":"published","author":[{"last_name":"Chang","full_name":"Chang, Yan","first_name":"Yan"},{"first_name":"Marah","full_name":"Funk, Marah","last_name":"Funk"},{"full_name":"Roy, Souvik","last_name":"Roy","first_name":"Souvik"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X"},{"last_name":"Choi","full_name":"Choi, Sangyong","first_name":"Sangyong"},{"first_name":"Hristo V.","full_name":"Kojouharov, Hristo V.","last_name":"Kojouharov"},{"last_name":"Chen","full_name":"Chen, Benito","first_name":"Benito"},{"first_name":"Zui","last_name":"Pan","full_name":"Pan, Zui"}],"abstract":[{"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.","lang":"eng"}],"isi":1,"article_number":"1763","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)"},"ddc":["510","576"],"year":"2022","doi":"10.3390/ijms23031763","external_id":{"isi":["000754773500001"]},"title":"Developing a mathematical model of intracellular Calcium dynamics for evaluating combined anticancer effects of afatinib and RP4010 in esophageal cancer"},{"ec_funded":1,"year":"2022","doi":"10.4230/LIPIcs.SoCG.2022.66","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)"},"ddc":["510"],"citation":{"chicago":"Chambers, Erin, Christopher D Fillmore, Elizabeth R Stephenson, and Mathijs Wintraecken. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” In <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, 224:66:1-66:9. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>.","ieee":"E. Chambers, C. D. Fillmore, E. R. Stephenson, and M. Wintraecken, “A cautionary tale: Burning the medial axis is unstable,” in <i>38th International Symposium on Computational Geometry</i>, Berlin, Germany, 2022, vol. 224, p. 66:1-66:9.","apa":"Chambers, E., Fillmore, C. D., Stephenson, E. R., &#38; Wintraecken, M. (2022). A cautionary tale: Burning the medial axis is unstable. In X. Goaoc &#38; M. Kerber (Eds.), <i>38th International Symposium on Computational Geometry</i> (Vol. 224, p. 66:1-66:9). Berlin, Germany: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">https://doi.org/10.4230/LIPIcs.SoCG.2022.66</a>","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.","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.","mla":"Chambers, Erin, et al. “A Cautionary Tale: Burning the Medial Axis Is Unstable.” <i>38th International Symposium on Computational Geometry</i>, edited by Xavier Goaoc and Michael Kerber, vol. 224, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022, p. 66:1-66:9, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>.","ama":"Chambers E, Fillmore CD, Stephenson ER, Wintraecken M. A cautionary tale: Burning the medial axis is unstable. In: Goaoc X, Kerber M, eds. <i>38th International Symposium on Computational Geometry</i>. Vol 224. LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2022:66:1-66:9. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2022.66\">10.4230/LIPIcs.SoCG.2022.66</a>"},"publication_status":"published","author":[{"first_name":"Erin","full_name":"Chambers, Erin","last_name":"Chambers"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","full_name":"Fillmore, Christopher D","last_name":"Fillmore","first_name":"Christopher D"},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","last_name":"Stephenson","full_name":"Stephenson, Elizabeth R","orcid":"0000-0002-6862-208X","first_name":"Elizabeth R"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","first_name":"Mathijs"}],"abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","volume":224,"date_updated":"2023-02-21T09:50:52Z","oa":1,"editor":[{"full_name":"Goaoc, Xavier","last_name":"Goaoc","first_name":"Xavier"},{"first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"oa_version":"Published Version","quality_controlled":"1","project":[{"name":"Learning and triangulating manifolds via collapses","_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073"},{"call_identifier":"H2020","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183"},{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"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.","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["1868-8969"],"isbn":["978-3-95977-227-3"]},"_id":"11428","date_published":"2022-06-01T00:00:00Z","month":"06","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","department":[{"_id":"HeEd"}],"has_accepted_license":"1","date_created":"2022-06-01T14:18:04Z","file":[{"success":1,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"11437","file_size":17580705,"file_name":"2022_LIPICs_Chambers.pdf","checksum":"b25ce40fade4ebc0bcaae176db4f5f1f","date_created":"2022-06-07T07:58:30Z","access_level":"open_access","date_updated":"2022-06-07T07:58:30Z"}],"conference":{"start_date":"2022-06-07","end_date":"2022-06-10","location":"Berlin, Germany","name":"SoCG: Symposium on Computational Geometry"},"series_title":"LIPIcs","type":"conference","day":"01","status":"public","intvolume":"       224","page":"66:1-66:9","file_date_updated":"2022-06-07T07:58:30Z","publication":"38th International Symposium on Computational Geometry"},{"volume":32,"date_updated":"2023-01-30T13:02:30Z","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"None","quality_controlled":"1","_id":"12307","publication_identifier":{"eissn":["1935-4053"],"issn":["1051-1970"]},"publication_status":"published","citation":{"short":"B.A. Shipman, E.R. Stephenson, PRIMUS 32 (2022) 593–609.","ista":"Shipman BA, Stephenson ER. 2022. Tangible topology through the lens of limits. PRIMUS. 32(5), 593–609.","ama":"Shipman BA, Stephenson ER. Tangible topology through the lens of limits. <i>PRIMUS</i>. 2022;32(5):593-609. doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>","mla":"Shipman, Barbara A., and Elizabeth R. Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>, vol. 32, no. 5, Taylor &#38; Francis, 2022, pp. 593–609, doi:<a href=\"https://doi.org/10.1080/10511970.2021.1872750\">10.1080/10511970.2021.1872750</a>.","chicago":"Shipman, Barbara A., and Elizabeth R Stephenson. “Tangible Topology through the Lens of Limits.” <i>PRIMUS</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>.","ieee":"B. A. Shipman and E. R. Stephenson, “Tangible topology through the lens of limits,” <i>PRIMUS</i>, vol. 32, no. 5. Taylor &#38; Francis, pp. 593–609, 2022.","apa":"Shipman, B. A., &#38; Stephenson, E. R. (2022). Tangible topology through the lens of limits. <i>PRIMUS</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/10511970.2021.1872750\">https://doi.org/10.1080/10511970.2021.1872750</a>"},"keyword":["Education","General Mathematics"],"author":[{"first_name":"Barbara A.","last_name":"Shipman","full_name":"Shipman, Barbara A."},{"id":"2D04F932-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6862-208X","full_name":"Stephenson, Elizabeth R","last_name":"Stephenson","first_name":"Elizabeth R"}],"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."}],"doi":"10.1080/10511970.2021.1872750","year":"2022","title":"Tangible topology through the lens of limits","page":"593-609","issue":"5","publication":"PRIMUS","type":"journal_article","day":"28","status":"public","intvolume":"        32","department":[{"_id":"HeEd"},{"_id":"GradSch"}],"date_created":"2023-01-16T10:07:21Z","article_type":"original","date_published":"2022-05-28T00:00:00Z","month":"05","language":[{"iso":"eng"}],"publisher":"Taylor & Francis","scopus_import":"1"}]