[{"citation":{"apa":"Maslov, M., Koutentakis, G., Hrast, M., Heckl, O. H., &#38; Lemeshko, M. (2024). Theory of angular momentum transfer from light to molecules. <i>Physical Review Research</i>. American Physical Society. <a href=\"https://doi.org/10.1103/physrevresearch.6.033277\">https://doi.org/10.1103/physrevresearch.6.033277</a>","ama":"Maslov M, Koutentakis G, Hrast M, Heckl OH, Lemeshko M. Theory of angular momentum transfer from light to molecules. <i>Physical Review Research</i>. 2024;6(3). doi:<a href=\"https://doi.org/10.1103/physrevresearch.6.033277\">10.1103/physrevresearch.6.033277</a>","short":"M. Maslov, G. Koutentakis, M. Hrast, O.H. Heckl, M. Lemeshko, Physical Review Research 6 (2024).","ieee":"M. Maslov, G. Koutentakis, M. Hrast, O. H. Heckl, and M. Lemeshko, “Theory of angular momentum transfer from light to molecules,” <i>Physical Review Research</i>, vol. 6, no. 3. American Physical Society, 2024.","mla":"Maslov, Mikhail, et al. “Theory of Angular Momentum Transfer from Light to Molecules.” <i>Physical Review Research</i>, vol. 6, no. 3, 033277, American Physical Society, 2024, doi:<a href=\"https://doi.org/10.1103/physrevresearch.6.033277\">10.1103/physrevresearch.6.033277</a>.","chicago":"Maslov, Mikhail, Georgios Koutentakis, Mateja Hrast, Oliver H. Heckl, and Mikhail Lemeshko. “Theory of Angular Momentum Transfer from Light to Molecules.” <i>Physical Review Research</i>. American Physical Society, 2024. <a href=\"https://doi.org/10.1103/physrevresearch.6.033277\">https://doi.org/10.1103/physrevresearch.6.033277</a>.","ista":"Maslov M, Koutentakis G, Hrast M, Heckl OH, Lemeshko M. 2024. Theory of angular momentum transfer from light to molecules. Physical Review Research. 6(3), 033277."},"publication_status":"published","publication_identifier":{"eissn":["2643-1564"]},"external_id":{"arxiv":["2310.00095"]},"title":"Theory of angular momentum transfer from light to molecules","article_number":"033277","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","has_accepted_license":"1","project":[{"grant_number":"F100403","name":"Coherent Optical Metrology Beyond Electric-Dipole-Allowed Transitions","_id":"7c040762-9f16-11ee-852c-dd79eeee4ab3"},{"call_identifier":"H2020","_id":"fc2ed2f7-9c52-11eb-aca3-c01059dda49c","name":"IST-BRIDGE: International postdoctoral program","grant_number":"101034413"},{"_id":"2688CF98-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Angulon: physics and applications of a new quasiparticle","grant_number":"801770"},{"call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund"}],"type":"journal_article","issue":"3","related_material":{"record":[{"id":"19048","relation":"dissertation_contains","status":"public"}]},"arxiv":1,"article_type":"original","doi":"10.1103/physrevresearch.6.033277","oa_version":"Published Version","fulldoi":"https://doi.org/10.1103/physrevresearch.6.033277","language":[{"iso":"eng"}],"_id":"18087","day":"10","article_processing_charge":"Yes","date_created":"2024-09-18T11:43:16Z","acknowledgement":"We are grateful to Emilio Pisanty and Philipp Lunt for valuable discussions. This research was funded wholly or in part by the Austrian Science Fund (FWF) [10.55776/F1004]. G.M.K. gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413. M.L. acknowledges support by the European Research Council (ERC) Starting Grant No. 801770 (ANGULON). O.H.H. acknowledges support by the Austrian Science Fund (FWF) [10.55776/P36040]. Furthermore, the financial support by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development, and the Christian Doppler Research Association is gratefully acknowledged.","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"MiLe"}],"date_updated":"2026-10-02T11:36:24Z","das_tickbox":"0","file":[{"file_id":"18125","file_size":1563824,"content_type":"application/pdf","relation":"main_file","file_name":"2024_PhysicalReviewResearch_Maslov.pdf","date_created":"2024-09-23T09:46:20Z","success":1,"checksum":"8f744d94956a1683b473b1cf9b411a37","creator":"dernst","date_updated":"2024-09-23T09:46:20Z","access_level":"open_access"}],"supplementarymaterial":"yes","OA_place":"publisher","month":"09","date_published":"2024-09-10T00:00:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We present a theory describing the interaction of structured light, such as light carrying orbital angular momentum, with molecules. The light-matter interaction Hamiltonian we derive is expressed through couplings between spherical gradients of the electric field and the (transition) electric multipole moments of a particle of any nontrivial rotation point group. Our model can therefore accommodate an arbitrary complexity of the molecular and electric field structure, and it can be straightforwardly extended to atoms or nanostructures. Applying this framework to rovibrational spectroscopy of molecules, we uncover the general mechanism of angular momentum exchange between the spin and orbital angular momenta of light, molecular rotation, and its center-of-mass motion. We show that the nonzero vorticity of Laguerre-Gaussian beams can strongly enhance certain rovibrational transitions that are considered forbidden in the case of nonhelical light. We discuss the experimental requirements for the observation of these forbidden transitions in state-of-the-art spatially resolved spectroscopy measurements."}],"corr_author":"1","author":[{"last_name":"Maslov","first_name":"Mikhail","id":"2E65BB0E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-4074-2570","full_name":"Maslov, Mikhail"},{"id":"d7b23d3a-9e21-11ec-b482-f76739596b95","first_name":"Georgios","full_name":"Koutentakis, Georgios","last_name":"Koutentakis"},{"last_name":"Hrast","first_name":"Mateja","id":"48dbb294-2a9c-11ef-905d-f56be71f0e5d","full_name":"Hrast, Mateja"},{"first_name":"Oliver H.","full_name":"Heckl, Oliver H.","last_name":"Heckl"},{"full_name":"Lemeshko, Mikhail","id":"37CB05FA-F248-11E8-B48F-1D18A9856A87","first_name":"Mikhail","orcid":"0000-0002-6990-7802","last_name":"Lemeshko"}],"file_date_updated":"2024-09-23T09:46:20Z","oa":1,"publisher":"American Physical Society","researchdata_availability":"no","APC_amount":"3028,31 EUR","publication":"Physical Review Research","year":"2024","volume":6,"intvolume":"         6","status":"public","ddc":["530"],"OA_type":"gold","quality_controlled":"1","scopus_import":"1","DOAJ_listed":"1"},{"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Genetic information and biological optimization","supervisor":[{"last_name":"Barton","full_name":"Barton, Nicholas H","orcid":"0000-0002-8548-5240","first_name":"Nicholas H","id":"4880FE40-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Tkačik","full_name":"Tkačik, Gašper","orcid":"0000-0002-6699-1455","id":"3D494DCA-F248-11E8-B48F-1D18A9856A87","first_name":"Gašper"}],"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","citation":{"chicago":"Hledik, Michal. “Genetic Information and Biological Optimization.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:15020\">https://doi.org/10.15479/at:ista:15020</a>.","ista":"Hledik M. 2024. Genetic information and biological optimization. Institute of Science and Technology Austria.","short":"M. Hledik, Genetic Information and Biological Optimization, Institute of Science and Technology Austria, 2024.","ama":"Hledik M. Genetic information and biological optimization. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:15020\">10.15479/at:ista:15020</a>","ieee":"M. Hledik, “Genetic information and biological optimization,” Institute of Science and Technology Austria, 2024.","mla":"Hledik, Michal. <i>Genetic Information and Biological Optimization</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:15020\">10.15479/at:ista:15020</a>.","apa":"Hledik, M. (2024). <i>Genetic information and biological optimization</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:15020\">https://doi.org/10.15479/at:ista:15020</a>"},"acknowledged_ssus":[{"_id":"ScienComp"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.15479/at:ista:15020","oa_version":"Published Version","_id":"15020","keyword":["Theoretical biology","Optimality","Evolution","Information"],"day":"23","doi":"10.15479/at:ista:15020","page":"158","related_material":{"record":[{"id":"7606","status":"public","relation":"part_of_dissertation"},{"id":"12081","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","id":"7553","status":"public"}]},"project":[{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"},{"name":"Can evolution minimize spurious signaling crosstalk to reach optimal performance?","grant_number":"RGP0034/2018","_id":"2665AAFE-B435-11E9-9278-68D0E5697425"},{"_id":"bd6958e0-d553-11ed-ba76-86eba6a76c00","name":"Understanding the evolution of continuous genomes","grant_number":"101055327"}],"has_accepted_license":"1","type":"dissertation","doi_confirm":"1","date_published":"2024-02-23T00:00:00Z","month":"02","OA_place":"publisher","supplementarymaterial":"no","file":[{"date_created":"2024-02-23T13:50:53Z","success":1,"file_name":"hledik thesis pdfa 2b.pdf","checksum":"b2d3da47c98d481577a4baf68944fe41","date_updated":"2024-02-23T13:50:53Z","access_level":"open_access","creator":"mhledik","file_id":"15021","file_size":7102089,"relation":"main_file","content_type":"application/pdf"},{"relation":"source_file","content_type":"application/zip","file_size":14014790,"file_id":"15022","access_level":"closed","date_updated":"2024-02-23T14:20:16Z","creator":"mhledik","checksum":"eda9b9430da2610fee7ce1c1419a479a","date_created":"2024-02-23T13:50:54Z","file_name":"hledik thesis source.zip"}],"date_updated":"2026-10-02T11:40:30Z","das_tickbox":"0","department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"GaTk"}],"degree_awarded":"PhD","date_created":"2024-02-23T14:02:04Z","ec_funded":1,"ddc":["576","519"],"status":"public","year":"2024","researchdata_availability":"no","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","author":[{"last_name":"Hledik","first_name":"Michal","id":"4171253A-F248-11E8-B48F-1D18A9856A87","full_name":"Hledik, Michal"}],"file_date_updated":"2024-02-23T14:20:16Z","oa":1,"corr_author":"1","abstract":[{"lang":"eng","text":"This thesis consists of four distinct pieces of work within theoretical biology, with two themes in common: the concept of optimization in biological systems, and the use of information-theoretic tools to quantify biological stochasticity and statistical uncertainty.\r\nChapter 2 develops a statistical framework for studying biological systems which we believe to be optimized for a particular utility function, such as retinal neurons conveying information about visual stimuli. We formalize such beliefs as maximum-entropy Bayesian priors, constrained by the expected utility. We explore how such priors aid inference of system parameters with limited data and enable optimality hypothesis testing: is the utility higher than by chance?\r\nChapter 3 examines the ultimate biological optimization process: evolution by natural selection. As some individuals survive and reproduce more successfully than others, populations evolve towards fitter genotypes and phenotypes. We formalize this as accumulation of genetic information, and use population genetics theory to study how much such information can be accumulated per generation and maintained in the face of random mutation and genetic drift. We identify the population size and fitness variance as the key quantities that control information accumulation and maintenance.\r\nChapter 4 reuses the concept of genetic information from Chapter 3, but from a different perspective: we ask how much genetic information organisms actually need, in particular in the context of gene regulation. For example, how much information is needed to bind transcription factors at correct locations within the genome? Population genetics provides us with a refined answer: with an increasing population size, populations achieve higher fitness by maintaining more genetic information. Moreover, regulatory parameters experience selection pressure to optimize the fitness-information trade-off, i.e. minimize the information needed for a given fitness. This provides an evolutionary derivation of the optimization priors introduced in Chapter 2.\r\nChapter 5 proves an upper bound on mutual information between a signal and a communication channel output (such as neural activity). Mutual information is an important utility measure for biological systems, but its practical use can be difficult due to the large dimensionality of many biological channels. Sometimes, a lower bound on mutual information is computed by replacing the high-dimensional channel outputs with decodes (signal estimates). Our result provides a corresponding upper bound, provided that the decodes are the maximum posterior estimates of the signal."}]},{"title":"Towards a quantum entanglement enhanced atom interferomter","publication_status":"published","supervisor":[{"full_name":"Hosten, Onur","orcid":"0000-0002-2031-204X","id":"4C02D85E-F248-11E8-B48F-1D18A9856A87","first_name":"Onur","last_name":"Hosten"}],"publication_identifier":{"issn":["2663-337X"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"chicago":"Li, Vyacheslav. “Towards a Quantum Entanglement Enhanced Atom Interferomter.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17225\">https://doi.org/10.15479/at:ista:17225</a>.","ista":"Li V. 2024. Towards a quantum entanglement enhanced atom interferomter. Institute of Science and Technology Austria.","short":"V. Li, Towards a Quantum Entanglement Enhanced Atom Interferomter, Institute of Science and Technology Austria, 2024.","ama":"Li V. Towards a quantum entanglement enhanced atom interferomter. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17225\">10.15479/at:ista:17225</a>","ieee":"V. Li, “Towards a quantum entanglement enhanced atom interferomter,” Institute of Science and Technology Austria, 2024.","mla":"Li, Vyacheslav. <i>Towards a Quantum Entanglement Enhanced Atom Interferomter</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17225\">10.15479/at:ista:17225</a>.","apa":"Li, V. (2024). <i>Towards a quantum entanglement enhanced atom interferomter</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17225\">https://doi.org/10.15479/at:ista:17225</a>"},"fulldoi":"https://doi.org/10.15479/at:ista:17225","language":[{"iso":"eng"}],"oa_version":"Published Version","_id":"17225","day":"11","doi":"10.15479/at:ista:17225","article_processing_charge":"No","project":[{"_id":"bdb2a702-d553-11ed-ba76-f12e3e5a3bc6","grant_number":"101087907","name":"A quantum hybrid of atoms and milligram-scale pendulums: towards gravitational quantum mechanics"}],"has_accepted_license":"1","type":"dissertation","page":"79","related_material":{"record":[{"relation":"part_of_dissertation","id":"11438","status":"public"}]},"month":"07","supplementarymaterial":"no","OA_place":"publisher","doi_confirm":"1","date_published":"2024-07-11T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"OnHo"}],"degree_awarded":"PhD","date_created":"2024-07-11T09:46:48Z","file":[{"file_name":"PhD_Thesis_Vyacheslav_Li_no_signatures_PDFA.pdf","date_created":"2024-07-11T10:26:22Z","success":1,"checksum":"15b2dbe8d2c9ed7ca5dd413827928077","date_updated":"2024-07-11T10:26:22Z","access_level":"open_access","creator":"vli","file_id":"17228","file_size":6729761,"relation":"main_file","content_type":"application/pdf"},{"relation":"source_file","content_type":"application/x-zip-compressed","file_id":"17229","file_size":9542859,"date_updated":"2024-07-11T10:26:22Z","access_level":"closed","creator":"vli","file_name":"PhD Thesis Vyacheslav Li.zip","date_created":"2024-07-11T10:26:22Z","checksum":"16e904a11d8d0ebb167cb654ddfc7fe5"}],"date_updated":"2026-10-02T11:41:41Z","das_tickbox":"0","year":"2024","researchdata_availability":"no","ddc":["530"],"status":"public","author":[{"last_name":"Li","first_name":"Vyacheslav","id":"3A4FAA92-F248-11E8-B48F-1D18A9856A87","full_name":"Li, Vyacheslav"}],"file_date_updated":"2024-07-11T10:26:22Z","oa":1,"corr_author":"1","tmp":{"image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"abstract":[{"lang":"eng","text":"This thesis describes the development of an atom interferometer designed to exploit the\r\nadvantages of utilizing quantum entanglement for enhanced precision measurements beyond\r\nthe standard quantum limit. While the project remains ongoing, significant progress has been\r\nmade.\r\nA key contribution of this work is the development of Quantrol, an experimental control\r\nsystem leveraging the ARTIQ framework. This software enables precise timing and control\r\nwithout requiring prior knowledge of ARTIQ’s implementation details or coding experience.\r\nThe interface offers user friendly visual comprehension of the experimental sequence and\r\nextended capabilities, allowing researchers to scan variables with a simple click of a mouse.\r\nThe main proposed project is to implement atom interferometric sequence with squeezed input\r\nstates inside of a dipole trap generated by a high finesse cavity. The presence of the dipole\r\ntrap allows one dimensional atomic cloud split while maintaining relatively strong confinement\r\nin other directions.\r\nWe are currently able to trap and cool 87Rb atoms to few micro kelvin temperatures, load\r\nthem into the dipole trap and state prepare them to be used for squeezing and interferometric\r\nsequence."}],"alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria"},{"intvolume":"        36","status":"public","quality_controlled":"1","ddc":["510"],"OA_type":"hybrid","scopus_import":"1","researchdata_availability":"no","publication":"Reviews in Mathematical Physics","year":"2024","volume":36,"publisher":"World Scientific Publishing","abstract":[{"lang":"eng","text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"corr_author":"1","author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen"},{"last_name":"Roos","orcid":"0000-0002-9071-5880","first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara"}],"file_date_updated":"2025-01-09T07:56:28Z","oa":1,"date_published":"2024-10-01T00:00:00Z","OA_place":"publisher","supplementarymaterial":"no","month":"10","date_updated":"2026-10-02T11:43:00Z","das_tickbox":"0","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"18786","file_size":503910,"creator":"dernst","date_updated":"2025-01-09T07:56:28Z","access_level":"open_access","success":1,"file_name":"2024_ReviewsmathPhysics_Henheik.pdf","date_created":"2025-01-09T07:56:28Z","checksum":"2b053a4223b4db14b90520999ec56054"}],"date_created":"2023-11-15T23:48:14Z","acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"article_processing_charge":"Yes (in subscription journal)","doi":"10.1142/s0129055x2360005x","fulldoi":"https://doi.org/10.1142/s0129055x2360005x","oa_version":"Published Version","language":[{"iso":"eng"}],"_id":"14542","day":"01","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"},{"relation":"dissertation_contains","id":"18135","status":"public"}]},"issue":"9","isi":1,"arxiv":1,"article_type":"original","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"has_accepted_license":"1","type":"journal_article","article_number":"2360005 ","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"title":"Universality in low-dimensional BCS theory","citation":{"ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9. World Scientific Publishing, 2024.","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2024;36(9). doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2024). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>"}},{"date_created":"2024-09-20T12:25:25Z","acknowledgement":"Financial support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as part of the SFB/TRR 352) is gratefully acknowledged.","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"date_updated":"2026-10-02T11:43:00Z","das_tickbox":"0","file":[{"checksum":"330b881240013213a8e08538fec13d29","file_name":"2024_ForumMath_Lauritsen.pdf","date_created":"2024-09-23T09:56:17Z","success":1,"creator":"dernst","access_level":"open_access","date_updated":"2024-09-23T09:56:17Z","file_size":599886,"file_id":"18126","content_type":"application/pdf","relation":"main_file"}],"supplementarymaterial":"no","month":"09","date_published":"2024-09-09T00:00:00Z","corr_author":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions  d∈{1,2,3} . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order  adρ2+2/d, where a is the p-wave scattering length of the repulsive interaction and  ρ  is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260)."}],"author":[{"full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"file_date_updated":"2024-09-23T09:56:17Z","oa":1,"publisher":"Cambridge University Press","researchdata_availability":"no","publication":"Forum of Mathematics, Sigma","year":"2024","volume":12,"intvolume":"        12","ddc":["510"],"status":"public","quality_controlled":"1","scopus_import":"1","citation":{"ama":"Lauritsen AB, Seiringer R. Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. 2024;12. doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>","short":"A.B. Lauritsen, R. Seiringer, Forum of Mathematics, Sigma 12 (2024).","ieee":"A. B. Lauritsen and R. Seiringer, “Pressure of a dilute spin-polarized Fermi gas: Lower bound,” <i>Forum of Mathematics, Sigma</i>, vol. 12. Cambridge University Press, 2024.","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>, vol. 12, e78, Cambridge University Press, 2024, doi:<a href=\"https://doi.org/10.1017/fms.2024.56\">10.1017/fms.2024.56</a>.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Pressure of a dilute spin-polarized Fermi gas: Lower bound. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>","chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Pressure of a Dilute Spin-Polarized Fermi Gas: Lower Bound.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2024. <a href=\"https://doi.org/10.1017/fms.2024.56\">https://doi.org/10.1017/fms.2024.56</a>.","ista":"Lauritsen AB, Seiringer R. 2024. Pressure of a dilute spin-polarized Fermi gas: Lower bound. Forum of Mathematics, Sigma. 12, e78."},"publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"external_id":{"isi":["001307817400001"],"arxiv":["2407.05990"]},"title":"Pressure of a dilute spin-polarized Fermi gas: Lower bound","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"e78","project":[{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"has_accepted_license":"1","type":"journal_article","related_material":{"record":[{"relation":"dissertation_contains","id":"18135","status":"public"}]},"arxiv":1,"isi":1,"article_type":"original","doi":"10.1017/fms.2024.56","fulldoi":"https://doi.org/10.1017/fms.2024.56","oa_version":"Published Version","language":[{"iso":"eng"}],"_id":"18107","day":"09","article_processing_charge":"Yes"},{"date_published":"2024-10-24T00:00:00Z","doi_confirm":"1","supplementarymaterial":"no","OA_place":"publisher","month":"10","date_updated":"2026-10-02T11:43:57Z","das_tickbox":"0","file":[{"success":1,"file_name":"MASisak_dissertation.pdf","date_created":"2024-10-23T14:42:45Z","checksum":"8c4893e726aaa4b3efb82758da9b6851","date_updated":"2024-10-23T14:42:45Z","access_level":"open_access","creator":"msisak","file_id":"18467","file_size":1672547,"content_type":"application/pdf","relation":"main_file"},{"checksum":"1831b072e861a1e5481024ca9d02b036","file_name":"MASisak_source.zip","date_created":"2024-10-23T14:43:56Z","access_level":"closed","date_updated":"2024-10-24T08:09:13Z","creator":"msisak","file_size":617913,"file_id":"18468","content_type":"application/x-zip-compressed","relation":"source_file"}],"degree_awarded":"PhD","date_created":"2024-10-19T12:00:37Z","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"OA_type":"free access","status":"public","ddc":["516"],"researchdata_availability":"no","year":"2024","publisher":"Institute of Science and Technology Austria","alternative_title":["ISTA Thesis"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"text":"In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n","lang":"eng"}],"corr_author":"1","author":[{"last_name":"Sisak","first_name":"Maria A","id":"44A03D04-AEA4-11E9-B225-EA2DE6697425","full_name":"Sisak, Maria A"}],"oa":1,"file_date_updated":"2024-10-24T08:09:13Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"supervisor":[{"orcid":"0000-0002-9582-2634","first_name":"Tamás","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","full_name":"Hausel, Tamás","last_name":"Hausel"}],"title":"T-dual branes on hyperkähler manifolds","citation":{"chicago":"Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>.","ista":"Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria.","apa":"Sisak, M. A. (2024). <i>T-dual branes on hyperkähler manifolds</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>","short":"M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024.","ama":"Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>","ieee":"M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024.","mla":"Sisak, Maria A. <i>T-Dual Branes on Hyperkähler Manifolds</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>."},"article_processing_charge":"No","doi":"10.15479/at:ista:18443","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.15479/at:ista:18443","oa_version":"Published Version","_id":"18443","keyword":["hyperkaehler geometry","branes","mirror symmetry","T-duality"],"day":"24","page":"178","has_accepted_license":"1","project":[{"name":"Branes on hyperkähler manifolds","grant_number":"26069","_id":"6286e8c4-2b32-11ec-9570-f5297902f67f"}],"type":"dissertation"},{"supplementarymaterial":"no","OA_place":"publisher","month":"10","date_published":"2024-10-26T00:00:00Z","date_created":"2024-09-05T14:27:08Z","acknowledgement":"This work was supported in part by the ERC-2020-AdG 101020093. N. Mazzocchi was affiliated with ISTA when his collaboration started.","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"ToHe"}],"date_updated":"2026-10-02T11:44:52Z","das_tickbox":"0","file":[{"file_size":847422,"file_id":"17635","content_type":"application/pdf","relation":"main_file","checksum":"43e432f82be376434b358f3dd7a94b71","date_created":"2024-09-05T14:26:02Z","file_name":"isola24.pdf","success":1,"creator":"esarac","access_level":"open_access","date_updated":"2024-09-05T14:26:02Z"},{"checksum":"6bc04f07bb5612c0e7ea00ac121a69b6","date_created":"2025-01-21T14:39:49Z","success":1,"file_name":"2024_LNCS_Chalupa.pdf","access_level":"open_access","date_updated":"2025-01-21T14:39:49Z","creator":"dernst","file_size":1358706,"file_id":"18865","content_type":"application/pdf","relation":"main_file"}],"researchdata_availability":"no","APC_amount":"2748 EUR","publication":"12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation","volume":15222,"year":"2024","intvolume":"     15222","OA_type":"hybrid","ddc":["000"],"quality_controlled":"1","status":"public","scopus_import":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"corr_author":"1","abstract":[{"lang":"eng","text":"System behaviors are traditionally evaluated through binary classifications of correctness, which do not suffice for properties involving quantitative aspects of systems and executions. Quantitative automata offer a more nuanced approach, mapping each execution to a real number by incorporating weighted transitions and value functions generalizing acceptance conditions. In this paper, we introduce QuAK, the first tool designed to automate the analysis of quantitative automata. QuAK currently supports a variety of quantitative automaton types, including Inf, Sup, LimInf, LimSup, LimInfAvg, and LimSupAvg automata, and implements decision procedures for problems such as emptiness, universality, inclusion, equivalence, as well as for checking whether an automaton is safe, live, or constant. Additionally, QuAK is able to compute extremal values when possible, construct safety-liveness decompositions, and monitor system behaviors. We demonstrate the effectiveness of QuAK through experiments focusing on the inclusion, constant-function check, and monitoring problems."}],"author":[{"last_name":"Chalupa","first_name":"Marek","id":"87e34708-d6c6-11ec-9f5b-9391e7be2463","full_name":"Chalupa, Marek"},{"full_name":"Henzinger, Thomas A","id":"40876CD8-F248-11E8-B48F-1D18A9856A87","first_name":"Thomas A","orcid":"0000-0002-2985-7724","last_name":"Henzinger"},{"last_name":"Mazzocchi","full_name":"Mazzocchi, Nicolas Adrien","first_name":"Nicolas Adrien","id":"b26baa86-3308-11ec-87b0-8990f34baa85"},{"full_name":"Sarac, Naci E","id":"8C6B42F8-C8E6-11E9-A03A-F2DCE5697425","first_name":"Naci E","last_name":"Sarac"}],"file_date_updated":"2025-01-21T14:39:49Z","oa":1,"publisher":"Springer Nature","alternative_title":["LNCS"],"publication_status":"published","publication_identifier":{"eissn":["1611-3349"],"isbn":["9783031753862"],"issn":["0302-9743"]},"external_id":{"arxiv":["2409.03569"],"isi":["001419008700001"]},"title":"QuAK: Quantitative Automata Kit","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"apa":"Chalupa, M., Henzinger, T. A., Mazzocchi, N. A., &#38; Sarac, N. E. (2024). QuAK: Quantitative Automata Kit. In <i>12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation</i> (Vol. 15222, pp. 3–20). Crete, Greece: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-75387-9_1\">https://doi.org/10.1007/978-3-031-75387-9_1</a>","short":"M. Chalupa, T.A. Henzinger, N.A. Mazzocchi, N.E. Sarac, in:, 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Springer Nature, 2024, pp. 3–20.","ama":"Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. QuAK: Quantitative Automata Kit. In: <i>12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation</i>. Vol 15222. Springer Nature; 2024:3-20. doi:<a href=\"https://doi.org/10.1007/978-3-031-75387-9_1\">10.1007/978-3-031-75387-9_1</a>","mla":"Chalupa, Marek, et al. “QuAK: Quantitative Automata Kit.” <i>12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation</i>, vol. 15222, Springer Nature, 2024, pp. 3–20, doi:<a href=\"https://doi.org/10.1007/978-3-031-75387-9_1\">10.1007/978-3-031-75387-9_1</a>.","ieee":"M. Chalupa, T. A. Henzinger, N. A. Mazzocchi, and N. E. Sarac, “QuAK: Quantitative Automata Kit,” in <i>12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation</i>, Crete, Greece, 2024, vol. 15222, pp. 3–20.","chicago":"Chalupa, Marek, Thomas A Henzinger, Nicolas Adrien Mazzocchi, and Naci E Sarac. “QuAK: Quantitative Automata Kit.” In <i>12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation</i>, 15222:3–20. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-75387-9_1\">https://doi.org/10.1007/978-3-031-75387-9_1</a>.","ista":"Chalupa M, Henzinger TA, Mazzocchi NA, Sarac NE. 2024. QuAK: Quantitative Automata Kit. 12th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation. ISoLA: International Symposium on Leveraging Applications, LNCS, vol. 15222, 3–20."},"conference":{"end_date":"2024-10-31","name":"ISoLA: International Symposium on Leveraging Applications","location":"Crete, Greece","start_date":"2024-10-27"},"doi":"10.1007/978-3-031-75387-9_1","fulldoi":"https://doi.org/10.1007/978-3-031-75387-9_1","oa_version":"Published Version","language":[{"iso":"eng"}],"day":"26","_id":"17634","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","project":[{"name":"Vigilant Algorithmic Monitoring of Software","grant_number":"101020093","call_identifier":"H2020","_id":"62781420-2b32-11ec-9570-8d9b63373d4d"}],"type":"conference","related_material":{"record":[{"relation":"dissertation_contains","id":"20147","status":"public"}]},"isi":1,"arxiv":1,"page":"3-20"},{"citation":{"ieee":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, and M. Saghafian, “On angles in higher order Brillouin tessellations and related tilings in the plane,” <i>Discrete and Computational Geometry</i>, vol. 72. Springer Nature, pp. 29–48, 2024.","mla":"Edelsbrunner, Herbert, et al. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>, vol. 72, Springer Nature, 2024, pp. 29–48, doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>.","ama":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. 2024;72:29-48. doi:<a href=\"https://doi.org/10.1007/s00454-023-00566-1\">10.1007/s00454-023-00566-1</a>","short":"H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.","apa":"Edelsbrunner, H., Garber, A., Ghafari, M., Heiss, T., &#38; Saghafian, M. (2024). On angles in higher order Brillouin tessellations and related tilings in the plane. <i>Discrete and Computational Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>","ista":"Edelsbrunner H, Garber A, Ghafari M, Heiss T, Saghafian M. 2024. On angles in higher order Brillouin tessellations and related tilings in the plane. Discrete and Computational Geometry. 72, 29–48.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. “On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane.” <i>Discrete and Computational Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00454-023-00566-1\">https://doi.org/10.1007/s00454-023-00566-1</a>."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_identifier":{"issn":["0179-5376"],"eissn":["1432-0444"]},"publication_status":"published","external_id":{"arxiv":["2204.01076"],"isi":["001060727600004"],"pmid":["39610762"]},"title":"On angles in higher order Brillouin tessellations and related tilings in the plane","isi":1,"arxiv":1,"page":"29-48","article_type":"original","has_accepted_license":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00454-023-00566-1","oa_version":"Published Version","fulldoi":"https://doi.org/10.1007/s00454-023-00566-1","language":[{"iso":"eng"}],"day":"01","_id":"14345","date_updated":"2026-10-02T11:45:50Z","das_tickbox":"0","file":[{"date_created":"2024-07-22T09:43:19Z","success":1,"file_name":"2024_DiscreteComputGeom_Edelsbrunner.pdf","checksum":"b207b4e00f904e8ea8a30e24f0251f79","date_updated":"2024-07-22T09:43:19Z","access_level":"open_access","creator":"dernst","file_id":"17301","file_size":892019,"relation":"main_file","content_type":"application/pdf"}],"date_created":"2023-09-17T22:01:10Z","acknowledgement":"Work by all authors but A. Garber is supported by the European Research Council (ERC), Grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), Grant No. I 02979-N35. Work by A. Garber is partially supported by the Alexander von Humboldt Foundation.","ec_funded":1,"department":[{"_id":"HeEd"}],"date_published":"2024-07-01T00:00:00Z","supplementarymaterial":"yes","month":"07","publisher":"Springer Nature","abstract":[{"lang":"eng","text":"For a locally finite set in R2, 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 monotonic in k. As an example, a stationary Poisson point process in R2  is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970))."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"corr_author":"1","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Garber","first_name":"Alexey","full_name":"Garber, Alexey"},{"last_name":"Ghafari","first_name":"Mohadese","full_name":"Ghafari, Mohadese"},{"last_name":"Heiss","orcid":"0000-0002-1780-2689","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","full_name":"Heiss, Teresa"},{"full_name":"Saghafian, Morteza","first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","last_name":"Saghafian"}],"oa":1,"file_date_updated":"2024-07-22T09:43:19Z","intvolume":"        72","ddc":["510"],"quality_controlled":"1","status":"public","pmid":1,"scopus_import":"1","researchdata_availability":"no","publication":"Discrete and Computational Geometry","year":"2024","volume":72},{"citation":{"ista":"Kourimska H, Lieutier A, Wintraecken M. 2024. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 69.","chicago":"Kourimska, Hana, André Lieutier, and Mathijs Wintraecken. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>.","mla":"Kourimska, Hana, et al. “The Medial Axis of Any Closed Bounded Set Is Lipschitz Stable with Respect to the Hausdorff Distance Under Ambient Diffeomorphisms.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 69, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>.","ieee":"H. Kourimska, A. Lieutier, and M. Wintraecken, “The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","short":"H. Kourimska, A. Lieutier, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ama":"Kourimska H, Lieutier A, Wintraecken M. The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">10.4230/LIPIcs.SoCG.2024.69</a>","apa":"Kourimska, H., Lieutier, A., &#38; Wintraecken, M. (2024). The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.69\">https://doi.org/10.4230/LIPIcs.SoCG.2024.69</a>"},"conference":{"location":"Athens, Greece","name":"SoCG: Symposium on Computational Geometry","end_date":"2024-06-14"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"69","publication_status":"published","publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"external_id":{"arxiv":["2212.01118"]},"title":"The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms","arxiv":1,"project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","name":"Learning and triangulating manifolds via collapses","grant_number":"M03073"}],"has_accepted_license":"1","type":"conference","article_processing_charge":"No","doi":"10.4230/LIPIcs.SoCG.2024.69","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.69","oa_version":"Published Version","language":[{"iso":"eng"}],"day":"01","_id":"17144","date_updated":"2026-10-02T11:46:39Z","das_tickbox":"0","file":[{"access_level":"open_access","date_updated":"2024-06-17T08:33:40Z","creator":"dernst","checksum":"b40ff456c19294adb5d9613fcfd751c6","success":1,"file_name":"2024_LIPICS_Kourimska.pdf","date_created":"2024-06-17T08:33:40Z","relation":"main_file","content_type":"application/pdf","file_size":1612558,"file_id":"17150"}],"acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I 02979-N35.\r\nSupported 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) grant No. M-3073, and the welcome package from IDEX of the Université Cô d'Azur.\r\nWe are greatly indebted to Fred Chazal for sharing his insights. We further thank Erin Chambers, Christopher Fillmore, and Elizabeth Stephenson for early discussions and all members of the Edelsbrunner group (Institute of Science and Technology Austria) and the Datashape team (Inria) for the atmosphere in which this research was conducted.","date_created":"2024-06-16T22:01:06Z","ec_funded":1,"department":[{"_id":"HeEd"}],"date_published":"2024-06-01T00:00:00Z","supplementarymaterial":"no","month":"06","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"abstract":[{"text":"We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"author":[{"last_name":"Kourimska","full_name":"Kourimska, Hana","orcid":"0000-0001-7841-0091","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","first_name":"Hana"},{"full_name":"Lieutier, André","first_name":"André","last_name":"Lieutier"},{"last_name":"Wintraecken","full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs"}],"file_date_updated":"2024-06-17T08:33:40Z","oa":1,"intvolume":"       293","quality_controlled":"1","status":"public","ddc":["510"],"scopus_import":"1","researchdata_availability":"no","publication":"40th International Symposium on Computational Geometry","volume":293,"year":"2024"},{"file":[{"date_updated":"2024-06-17T08:46:33Z","access_level":"open_access","creator":"dernst","date_created":"2024-06-17T08:46:33Z","success":1,"file_name":"2024_LIPICS_Edelsbrunner.pdf","checksum":"5442d44fb89d77477a87668d6e61aac9","relation":"main_file","content_type":"application/pdf","file_id":"17152","file_size":766562}],"das_tickbox":"0","date_updated":"2026-10-02T11:48:01Z","department":[{"_id":"HeEd"}],"ec_funded":1,"date_created":"2024-06-16T22:01:06Z","acknowledgement":"The first author is supported by the European Research Council (ERC), grant no. 788183, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant no. {I 02979-N35.} The second author is supported by the European Research Council (ERC), grant \"GeoScape\" and by the Hungarian Science Foundation (NKFIH), grant K-131529. Both authors are supported by the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31.\r\nThe authors thank Matt Kahle for communicating the question about extremal Čech complexes, Ben Schweinhart for early discussions on the linked circles construction in three dimensions, and Gábor Tardos for helpful remarks and suggestions.","date_published":"2024-06-01T00:00:00Z","month":"06","supplementarymaterial":"no","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","oa":1,"file_date_updated":"2024-06-17T08:46:33Z","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert"},{"full_name":"Pach, János","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","last_name":"Pach"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"The Upper Bound Theorem for convex polytopes implies that the p-th Betti number of the Čech complex of any set of N points in ℝ^d and any radius satisfies β_p = O(N^m), with m = min{p+1, ⌈d/2⌉}. We construct sets in even and odd dimensions, which prove that this upper bound is asymptotically tight. For example, we describe a set of N = 2(n+1) points in ℝ³ and two radii such that the first Betti number of the Čech complex at one radius is (n+1)² - 1, and the second Betti number of the Čech complex at the other radius is n². In particular, there is an arrangement of n contruent balls in ℝ³ that enclose a quadratic number of voids, which answers a long-standing open question in computational geometry."}],"scopus_import":"1","status":"public","ddc":["510"],"quality_controlled":"1","intvolume":"       293","volume":293,"year":"2024","publication":"40th International Symposium on Computational Geometry","researchdata_availability":"no","conference":{"location":"Athens, Greece","name":"SoCG: Symposium on Computational Geometry","end_date":"2024-06-14","start_date":"2024-06-11"},"citation":{"ista":"Edelsbrunner H, Pach J. 2024. Maximum Betti numbers of Čech complexes. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 53.","chicago":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">https://doi.org/10.4230/LIPIcs.SoCG.2024.53</a>.","apa":"Edelsbrunner, H., &#38; Pach, J. (2024). Maximum Betti numbers of Čech complexes. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">https://doi.org/10.4230/LIPIcs.SoCG.2024.53</a>","mla":"Edelsbrunner, Herbert, and János Pach. “Maximum Betti Numbers of Čech Complexes.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 53, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">10.4230/LIPIcs.SoCG.2024.53</a>.","ieee":"H. Edelsbrunner and J. Pach, “Maximum Betti numbers of Čech complexes,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","short":"H. Edelsbrunner, J. Pach, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ama":"Edelsbrunner H, Pach J. Maximum Betti numbers of Čech complexes. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.53\">10.4230/LIPIcs.SoCG.2024.53</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"53","title":"Maximum Betti numbers of Čech complexes","external_id":{"arxiv":["2310.14801"]},"publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773164"]},"publication_status":"published","arxiv":1,"related_material":{"record":[{"id":"20657","relation":"later_version","status":"public"}]},"type":"conference","has_accepted_license":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"article_processing_charge":"No","day":"01","_id":"17146","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.53","language":[{"iso":"eng"}],"oa_version":"Published Version","doi":"10.4230/LIPIcs.SoCG.2024.53"},{"acknowledgement":"Part of this work was done while G.R. enjoyed the hospitality of the Institute of Science and Technology Austria (ISTA) as a visiting professor during his sabbatical in the winter semester 2022/23.","date_created":"2024-06-16T22:01:06Z","department":[{"_id":"HeEd"}],"date_updated":"2026-10-02T11:47:18Z","das_tickbox":"0","file":[{"date_updated":"2024-06-17T08:40:04Z","access_level":"open_access","creator":"dernst","success":1,"date_created":"2024-06-17T08:40:04Z","file_name":"2024_LIPICS_Rote.pdf","checksum":"fbad1de06383a6b7e8a1cb3e8c7205ce","relation":"main_file","content_type":"application/pdf","file_id":"17151","file_size":1430896}],"supplementarymaterial":"no","month":"06","date_published":"2024-06-01T00:00:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"text":"Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.","lang":"eng"}],"author":[{"full_name":"Rote, Günter","first_name":"Günter","last_name":"Rote"},{"last_name":"Rüber","full_name":"Rüber, Moritz","first_name":"Moritz"},{"id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"oa":1,"file_date_updated":"2024-06-17T08:40:04Z","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"researchdata_availability":"no","publication":"40th International Symposium on Computational Geometry","volume":293,"year":"2024","intvolume":"       293","status":"public","quality_controlled":"1","ddc":["510"],"scopus_import":"1","citation":{"mla":"Rote, Günter, et al. “Grid Peeling of Parabolas.” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 76, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>.","ieee":"G. Rote, M. Rüber, and M. Saghafian, “Grid peeling of parabolas,” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","short":"G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ama":"Rote G, Rüber M, Saghafian M. Grid peeling of parabolas. In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">10.4230/LIPIcs.SoCG.2024.76</a>","apa":"Rote, G., Rüber, M., &#38; Saghafian, M. (2024). Grid peeling of parabolas. In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>","ista":"Rote G, Rüber M, Saghafian M. 2024. Grid peeling of parabolas. 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 76.","chicago":"Rote, Günter, Moritz Rüber, and Morteza Saghafian. “Grid Peeling of Parabolas.” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.76\">https://doi.org/10.4230/LIPIcs.SoCG.2024.76</a>."},"conference":{"end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry","location":"Athens, Greece","start_date":"2024-06-11"},"publication_identifier":{"isbn":["9783959773164"],"issn":["1868-8969"]},"publication_status":"published","external_id":{"arxiv":["2402.15787"]},"title":"Grid peeling of parabolas","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"76","has_accepted_license":"1","type":"conference","arxiv":1,"doi":"10.4230/LIPIcs.SoCG.2024.76","oa_version":"Published Version","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.76","language":[{"iso":"eng"}],"day":"01","_id":"17145","article_processing_charge":"No"},{"publication":"Entropy","year":"2024","volume":26,"researchdata_availability":"yes","status":"public","ddc":["510"],"quality_controlled":"1","pmid":1,"scopus_import":"1","intvolume":"        26","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"full_name":"Ölsböck, Katharina","orcid":"0000-0002-4672-8297","id":"4D4AA390-F248-11E8-B48F-1D18A9856A87","first_name":"Katharina","last_name":"Ölsböck"},{"first_name":"Hubert","id":"379CA8B8-F248-11E8-B48F-1D18A9856A87","orcid":"0009-0009-9111-8429","full_name":"Wagner, Hubert","last_name":"Wagner"}],"oa":1,"file_date_updated":"2024-09-09T09:01:12Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"Abstract\r\nMethods used in topological data analysis naturally capture higher-order interactions in point cloud data embedded in a metric space. This methodology was recently extended to data living in an information space, by which we mean a space measured with an information theoretical distance. One such setting is a finite collection of discrete probability distributions embedded in the probability simplex measured with the relative entropy (Kullback–Leibler divergence). More generally, one can work with a Bregman divergence parameterized by a different notion of entropy. While theoretical algorithms exist for this setup, there is a paucity of implementations for exploring and comparing geometric-topological properties of various information spaces. The interest of this work is therefore twofold. First, we propose the first robust algorithms and software for geometric and topological data analysis in information space. Perhaps surprisingly, despite working with Bregman divergences, our design reuses robust libraries for the Euclidean case. Second, using the new software, we take the first steps towards understanding the geometric-topological structure of these spaces. In particular, we compare them with the more familiar spaces equipped with the Euclidean and Fisher metrics."}],"publisher":"MDPI","month":"08","supplementarymaterial":"yes","dataavailabilitystatement":"The software and data used for this study is available at: https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/ (accessed on 19 July 2024).","date_published":"2024-08-01T00:00:00Z","department":[{"_id":"HeEd"}],"acknowledgement":"We thank Anton Nikitenko for first observing that the Wrap complex can be characterized as stated in Claim (ii) of the Wrap Complex Lemma, and Ondrej Draganov for correcting a critical mistake in one of our formulas in Section 2.","date_created":"2024-09-08T22:01:11Z","file":[{"checksum":"624a9e2c5b49d6c38b88b0f675467ba3","date_created":"2024-09-09T09:01:12Z","success":1,"file_name":"2024_Entropy_Edelsbrunner.pdf","access_level":"open_access","date_updated":"2024-09-09T09:01:12Z","creator":"dernst","file_size":8025139,"file_id":"17948","relation":"main_file","content_type":"application/pdf"}],"date_updated":"2026-10-02T11:50:23Z","das_tickbox":"1","fulldoi":"https://doi.org/10.3390/e26080637","oa_version":"Published Version","language":[{"iso":"eng"}],"day":"01","_id":"17891","doi":"10.3390/e26080637","article_processing_charge":"Yes","has_accepted_license":"1","type":"journal_article","article_type":"original","issue":"8","related_material":{"link":[{"relation":"software","url":"https://git.ista.ac.at/katharina.oelsboeck/wrap_2_3-public/"}]},"isi":1,"title":"Understanding higher-order interactions in information space","publication_status":"published","publication_identifier":{"eissn":["1099-4300"]},"external_id":{"pmid":["39202107"],"isi":["001305543500001"]},"article_number":"637","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"short":"H. Edelsbrunner, K. Ölsböck, H. Wagner, Entropy 26 (2024).","ama":"Edelsbrunner H, Ölsböck K, Wagner H. Understanding higher-order interactions in information space. <i>Entropy</i>. 2024;26(8). doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>","mla":"Edelsbrunner, Herbert, et al. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>, vol. 26, no. 8, 637, MDPI, 2024, doi:<a href=\"https://doi.org/10.3390/e26080637\">10.3390/e26080637</a>.","ieee":"H. Edelsbrunner, K. Ölsböck, and H. Wagner, “Understanding higher-order interactions in information space,” <i>Entropy</i>, vol. 26, no. 8. MDPI, 2024.","apa":"Edelsbrunner, H., Ölsböck, K., &#38; Wagner, H. (2024). Understanding higher-order interactions in information space. <i>Entropy</i>. MDPI. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>","chicago":"Edelsbrunner, Herbert, Katharina Ölsböck, and Hubert Wagner. “Understanding Higher-Order Interactions in Information Space.” <i>Entropy</i>. MDPI, 2024. <a href=\"https://doi.org/10.3390/e26080637\">https://doi.org/10.3390/e26080637</a>.","ista":"Edelsbrunner H, Ölsböck K, Wagner H. 2024. Understanding higher-order interactions in information space. Entropy. 26(8), 637."}},{"publication":"31st International Symposium on Graph Drawing and Network Visualization","volume":14465,"year":"2024","researchdata_availability":"no","quality_controlled":"1","status":"public","scopus_import":"1","intvolume":"     14465","author":[{"last_name":"Pach","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","first_name":"János","full_name":"Pach, János"},{"full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza","last_name":"Saghafian"},{"last_name":"Schnider","full_name":"Schnider, Patrick","first_name":"Patrick"}],"oa":1,"abstract":[{"text":"We solve a problem of Dujmović and Wood (2007) by showing that a complete convex geometric graph on n vertices cannot be decomposed into fewer than n-1 star-forests, each consisting of noncrossing edges. This bound is clearly tight. We also discuss similar questions for abstract graphs.","lang":"eng"}],"alternative_title":["LNCS"],"publisher":"Springer Nature","month":"01","supplementarymaterial":"no","date_published":"2024-01-01T00:00:00Z","department":[{"_id":"HeEd"}],"acknowledgement":"János Pach’s Research partially supported by European Research Council (ERC), grant “GeoScape” No. 882971 and by the Hungarian Science Foundation (NKFIH), grant K-131529. Work by Morteza Saghafian is partially supported by the European Research Council (ERC), grant No. 788183, and by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31.","date_created":"2024-02-18T23:01:03Z","ec_funded":1,"date_updated":"2026-10-02T11:50:59Z","das_tickbox":"0","oa_version":"Preprint","fulldoi":"https://doi.org/10.1007/978-3-031-49272-3_23","language":[{"iso":"eng"}],"day":"01","_id":"15012","doi":"10.1007/978-3-031-49272-3_23","article_processing_charge":"No","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"type":"conference","page":"339-346","related_material":{"record":[{"id":"21253","status":"public","relation":"later_version"}]},"isi":1,"arxiv":1,"title":"Decomposition of geometric graphs into star-forests","publication_identifier":{"eissn":["1611-3349"],"issn":["0302-9743"],"isbn":["9783031492716"],"eisbn":["9783031492723"]},"publication_status":"published","external_id":{"arxiv":["2306.13201"],"isi":["001207939600023"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","conference":{"start_date":"2023-09-20","end_date":"2023-09-22","location":"Isola delle Femmine, Palermo, Italy","name":"GD: Graph Drawing and Network Visualization"},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.13201","open_access":"1"}],"citation":{"chicago":"Pach, János, Morteza Saghafian, and Patrick Schnider. “Decomposition of Geometric Graphs into Star-Forests.” In <i>31st International Symposium on Graph Drawing and Network Visualization</i>, 14465:339–46. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>.","ista":"Pach J, Saghafian M, Schnider P. 2024. Decomposition of geometric graphs into star-forests. 31st International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LNCS, vol. 14465, 339–346.","ama":"Pach J, Saghafian M, Schnider P. Decomposition of geometric graphs into star-forests. In: <i>31st International Symposium on Graph Drawing and Network Visualization</i>. Vol 14465. Springer Nature; 2024:339-346. doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>","short":"J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.","mla":"Pach, János, et al. “Decomposition of Geometric Graphs into Star-Forests.” <i>31st International Symposium on Graph Drawing and Network Visualization</i>, vol. 14465, Springer Nature, 2024, pp. 339–46, doi:<a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">10.1007/978-3-031-49272-3_23</a>.","ieee":"J. Pach, M. Saghafian, and P. Schnider, “Decomposition of geometric graphs into star-forests,” in <i>31st International Symposium on Graph Drawing and Network Visualization</i>, Isola delle Femmine, Palermo, Italy, 2024, vol. 14465, pp. 339–346.","apa":"Pach, J., Saghafian, M., &#38; Schnider, P. (2024). Decomposition of geometric graphs into star-forests. In <i>31st International Symposium on Graph Drawing and Network Visualization</i> (Vol. 14465, pp. 339–346). Isola delle Femmine, Palermo, Italy: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-49272-3_23\">https://doi.org/10.1007/978-3-031-49272-3_23</a>"}},{"page":"1784-1807","article_type":"original","issue":"2","isi":1,"arxiv":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","grant_number":"788183","name":"Alpha Shape Theory Extended"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"},{"grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","name":"Mathematics, Computer Science","grant_number":"Z00342"}],"type":"journal_article","article_processing_charge":"No","fulldoi":"https://doi.org/10.1137/22M1489071","language":[{"iso":"eng"}],"oa_version":"Preprint","_id":"17190","day":"07","doi":"10.1137/22M1489071","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2204.01077"}],"citation":{"ista":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. 2024. Brillouin zones of integer lattices and their perturbations. SIAM Journal on Discrete Mathematics. 38(2), 1784–1807.","chicago":"Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafaris, Teresa Heiss, Morteza Saghafiant, and Mathijs Wintraecken. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics, 2024. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>.","mla":"Edelsbrunner, Herbert, et al. “Brillouin Zones of Integer Lattices and Their Perturbations.” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2, Society for Industrial and Applied Mathematics, 2024, pp. 1784–807, doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>.","ieee":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, and M. Wintraecken, “Brillouin zones of integer lattices and their perturbations,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 38, no. 2. Society for Industrial and Applied Mathematics, pp. 1784–1807, 2024.","ama":"Edelsbrunner H, Garber A, Ghafaris M, Heiss T, Saghafiant M, Wintraecken M. Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. 2024;38(2):1784-1807. doi:<a href=\"https://doi.org/10.1137/22M1489071\">10.1137/22M1489071</a>","short":"H. Edelsbrunner, A. Garber, M. Ghafaris, T. Heiss, M. Saghafiant, M. Wintraecken, SIAM Journal on Discrete Mathematics 38 (2024) 1784–1807.","apa":"Edelsbrunner, H., Garber, A., Ghafaris, M., Heiss, T., Saghafiant, M., &#38; Wintraecken, M. (2024). Brillouin zones of integer lattices and their perturbations. <i>SIAM Journal on Discrete Mathematics</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/22M1489071\">https://doi.org/10.1137/22M1489071</a>"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Brillouin zones of integer lattices and their perturbations","publication_identifier":{"issn":["0895-4801"]},"publication_status":"published","external_id":{"isi":["001292728600001"],"arxiv":["2204.01077"]},"publisher":"Society for Industrial and Applied Mathematics","author":[{"last_name":"Edelsbrunner","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Garber, Alexey","first_name":"Alexey","last_name":"Garber"},{"full_name":"Ghafaris, Mohadese","first_name":"Mohadese","last_name":"Ghafaris"},{"last_name":"Heiss","full_name":"Heiss, Teresa","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689"},{"last_name":"Saghafiant","first_name":"Morteza","full_name":"Saghafiant, Morteza"},{"id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","orcid":"0000-0002-7472-2220","full_name":"Wintraecken, Mathijs","last_name":"Wintraecken"}],"oa":1,"abstract":[{"lang":"eng","text":"For a locally finite set, 𝐴⊆ℝ𝑑\r\n, the 𝑘\r\nth Brillouin zone of 𝑎∈𝐴\r\n is the region of points 𝑥∈ℝ𝑑\r\n for which ‖𝑥−𝑎‖\r\n is the 𝑘\r\nth smallest among the Euclidean distances between 𝑥\r\n and the points in 𝐴\r\n. If 𝐴\r\n is a lattice, the 𝑘\r\nth Brillouin zones of the points in 𝐴\r\n are translates of each other, and together they tile space. Depending on the value of 𝑘\r\n, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2\r\n, and the convergence of the maximum volume of a chamber to zero for the integer lattice."}],"corr_author":"1","status":"public","quality_controlled":"1","scopus_import":"1","intvolume":"        38","publication":"SIAM Journal on Discrete Mathematics","year":"2024","volume":38,"researchdata_availability":"no","date_updated":"2026-10-02T11:49:10Z","das_tickbox":"0","department":[{"_id":"HeEd"}],"date_created":"2024-06-30T22:01:05Z","acknowledgement":"The second author is partially supported by the Alexander von Humboldt Foundation. The sixth author is supported by the European Union's Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement 754411, and by Austrian Science Fund(FWF) grant M-3073. All other authors are supported by European Research Council (ERC) grant 788183, by the Wittgenstein Prize, by Austrian Science Fund (FWF) grant Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF) grant I 02979-N35.","ec_funded":1,"date_published":"2024-06-07T00:00:00Z","month":"06","supplementarymaterial":"no"},{"intvolume":"       320","ddc":["510"],"quality_controlled":"1","OA_type":"gold","status":"public","scopus_import":"1","researchdata_availability":"no","publication":"32nd International Symposium on Graph Drawing and Network Visualization","year":"2024","volume":320,"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","alternative_title":["LIPIcs"],"abstract":[{"text":"Given a finite set, A ⊆ ℝ², and a subset, B ⊆ A, the MST-ratio is the combined length of the minimum spanning trees of B and A⧵B divided by the length of the minimum spanning tree of A. The question of the supremum, over all sets A, of the maximum, over all subsets B, is related to the Steiner ratio, and we prove this sup-max is between 2.154 and 2.427. Restricting ourselves to 2-dimensional lattices, we prove that the sup-max is 2, while the inf-max is 1.25. By some margin the most difficult of these results is the upper bound for the inf-max, which we prove by showing that the hexagonal lattice cannot have MST-ratio larger than 1.25.","lang":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"corr_author":"1","author":[{"orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","full_name":"Cultrera di Montesano, Sebastiano","last_name":"Cultrera di Montesano"},{"last_name":"Draganov","full_name":"Draganov, Ondrej","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","first_name":"Ondrej","orcid":"0000-0003-0464-3823"},{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"file_date_updated":"2024-11-18T07:49:25Z","oa":1,"date_published":"2024-10-28T00:00:00Z","supplementarymaterial":"no","OA_place":"publisher","month":"10","date_updated":"2026-10-02T11:52:23Z","das_tickbox":"0","file":[{"file_size":908541,"file_id":"18560","content_type":"application/pdf","relation":"main_file","checksum":"5f9b35e115c3d375e99be78da9054cb4","date_created":"2024-11-18T07:49:25Z","file_name":"2024_LIPIcs_CultreradiMontesano.pdf","success":1,"creator":"dernst","access_level":"open_access","date_updated":"2024-11-18T07:49:25Z"}],"date_created":"2024-11-17T23:01:47Z","acknowledgement":"This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, \"Discretization in Geometry and Dynamics\", Austrian Science Fund (FWF), grant no. I 02979-N35.","ec_funded":1,"department":[{"_id":"HeEd"}],"article_processing_charge":"Yes","doi":"10.4230/LIPIcs.GD.2024.3","fulldoi":"https://doi.org/10.4230/LIPIcs.GD.2024.3","oa_version":"Published Version","language":[{"iso":"eng"}],"day":"28","_id":"18556","arxiv":1,"isi":1,"has_accepted_license":"1","project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"name":"Mathematics, Computer Science","grant_number":"Z00342","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"},{"call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"}],"type":"conference","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"3","publication_status":"published","publication_identifier":{"issn":["1868-8969"],"isbn":["9783959773430"]},"external_id":{"isi":["001540278400001"],"arxiv":["2403.10204"]},"title":"The Euclidean MST-ratio for bi-colored lattices","citation":{"apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (2024). The Euclidean MST-ratio for bi-colored lattices. In <i>32nd International Symposium on Graph Drawing and Network Visualization</i> (Vol. 320). Vienna, Austria: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. The Euclidean MST-ratio for bi-colored lattices. In: <i>32nd International Symposium on Graph Drawing and Network Visualization</i>. Vol 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>","short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “The Euclidean MST-ratio for bi-colored lattices,” in <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vienna, Austria, 2024, vol. 320.","mla":"Cultrera di Montesano, Sebastiano, et al. “The Euclidean MST-Ratio for Bi-Colored Lattices.” <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, vol. 320, 3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">10.4230/LIPIcs.GD.2024.3</a>.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “The Euclidean MST-Ratio for Bi-Colored Lattices.” In <i>32nd International Symposium on Graph Drawing and Network Visualization</i>, Vol. 320. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.GD.2024.3\">https://doi.org/10.4230/LIPIcs.GD.2024.3</a>.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. 2024. The Euclidean MST-ratio for bi-colored lattices. 32nd International Symposium on Graph Drawing and Network Visualization. GD: Graph Drawing and Network Visualization, LIPIcs, vol. 320, 3."},"conference":{"start_date":"2024-09-18","location":"Vienna, Austria","name":"GD: Graph Drawing and Network Visualization","end_date":"2024-09-20"}},{"date_published":"2024-06-06T00:00:00Z","month":"06","supplementarymaterial":"yes","file":[{"checksum":"9355c2e60b8ec285e1b22719c5b73f1a","date_created":"2024-09-19T10:30:37Z","success":1,"file_name":"2024_LIPICs_Attali.pdf","creator":"dernst","access_level":"open_access","date_updated":"2024-09-19T10:30:37Z","file_size":3507177,"file_id":"18098","relation":"main_file","content_type":"application/pdf"}],"date_updated":"2026-10-02T11:51:50Z","das_tickbox":"0","department":[{"_id":"HeEd"}],"date_created":"2024-09-19T10:29:48Z","acknowledgement":"This research has been supported by the European Research Council (ERC), grant No. 788183, by the Wittgenstein Prize, Austrian Science Fund (FWF), grant No. Z 342-N31, and by the DFG Collaborative Research Center TRR 109, Austrian Science Fund (FWF), grant No. I02979-N35. 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) grant No. M-3073, and the welcome package from IDEX of the Université Côte d’Azur.\r\nWe thank Jean-Daniel Boissonnat, Herbert Edelsbrunner, and Mariette Yvinec for discussion.","ec_funded":1,"quality_controlled":"1","status":"public","ddc":["000"],"intvolume":"       293","publication":"40th International Symposium on Computational Geometry","year":"2024","volume":293,"researchdata_availability":"no","alternative_title":["LIPIcs"],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"full_name":"Kourimska, Hana","first_name":"Hana","id":"D9B8E14C-3C26-11EA-98F5-1F833DDC885E","orcid":"0000-0001-7841-0091","last_name":"Kourimska"},{"id":"35638A5C-AAC7-11E9-B0BF-5503E6697425","first_name":"Christopher D","full_name":"Fillmore, Christopher D","last_name":"Fillmore"},{"first_name":"Ishika","id":"ee449b28-344d-11ef-a6d5-9ca430e9e9ff","full_name":"Ghosh, Ishika","last_name":"Ghosh"},{"first_name":"Andre","full_name":"Lieutier, Andre","last_name":"Lieutier"},{"orcid":"0000-0002-6862-208X","id":"2D04F932-F248-11E8-B48F-1D18A9856A87","first_name":"Elizabeth R","full_name":"Stephenson, Elizabeth R","last_name":"Stephenson"},{"full_name":"Wintraecken, Mathijs","orcid":"0000-0002-7472-2220","id":"307CFBC8-F248-11E8-B48F-1D18A9856A87","first_name":"Mathijs","last_name":"Wintraecken"}],"file_date_updated":"2024-09-19T10:30:37Z","oa":1,"corr_author":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"In our companion paper \"Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of Euclidean spaces and of Riemannian manifolds\" we gave optimal bounds (in terms of the two one-sided Hausdorff distances) on a sample P of an input shape 𝒮 (either manifold or general set with positive reach) such that one can infer the homotopy of 𝒮 from the union of balls with some radius centred at P, both in Euclidean space and in a Riemannian manifold of bounded curvature. The construction showing the optimality of the bounds is not straightforward. The purpose of this video is to visualize and thus elucidate said construction in the Euclidean setting."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"87","title":"The ultimate frontier: An optimality construction for homotopy inference (media exposition)","publication_status":"published","publication_identifier":{"isbn":["9783959773164"]},"conference":{"end_date":"2024-06-14","name":"SoCG: Symposium on Computational Geometry","location":"Athens, Greece","start_date":"2024-06-11"},"citation":{"apa":"Attali, D., Kourimska, H., Fillmore, C. D., Ghosh, I., Lieutier, A., Stephenson, E. R., &#38; Wintraecken, M. (2024). The ultimate frontier: An optimality construction for homotopy inference (media exposition). In <i>40th International Symposium on Computational Geometry</i> (Vol. 293). Athens, Greece: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>","mla":"Attali, Dominique, et al. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” <i>40th International Symposium on Computational Geometry</i>, vol. 293, 87, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>.","ieee":"D. Attali <i>et al.</i>, “The ultimate frontier: An optimality construction for homotopy inference (media exposition),” in <i>40th International Symposium on Computational Geometry</i>, Athens, Greece, 2024, vol. 293.","short":"D. Attali, H. Kourimska, C.D. Fillmore, I. Ghosh, A. Lieutier, E.R. Stephenson, M. Wintraecken, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.","ama":"Attali D, Kourimska H, Fillmore CD, et al. The ultimate frontier: An optimality construction for homotopy inference (media exposition). In: <i>40th International Symposium on Computational Geometry</i>. Vol 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2024. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">10.4230/LIPIcs.SoCG.2024.87</a>","ista":"Attali D, Kourimska H, Fillmore CD, Ghosh I, Lieutier A, Stephenson ER, Wintraecken M. 2024. The ultimate frontier: An optimality construction for homotopy inference (media exposition). 40th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 293, 87.","chicago":"Attali, Dominique, Hana Kourimska, Christopher D Fillmore, Ishika Ghosh, Andre Lieutier, Elizabeth R Stephenson, and Mathijs Wintraecken. “The Ultimate Frontier: An Optimality Construction for Homotopy Inference (Media Exposition).” In <i>40th International Symposium on Computational Geometry</i>, Vol. 293. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024. <a href=\"https://doi.org/10.4230/LIPIcs.SoCG.2024.87\">https://doi.org/10.4230/LIPIcs.SoCG.2024.87</a>."},"article_processing_charge":"Yes","fulldoi":"https://doi.org/10.4230/LIPIcs.SoCG.2024.87","language":[{"iso":"eng"}],"oa_version":"Published Version","day":"06","_id":"18097","doi":"10.4230/LIPIcs.SoCG.2024.87","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"call_identifier":"FWF","_id":"268116B8-B435-11E9-9278-68D0E5697425","grant_number":"Z00342","name":"Mathematics, Computer Science"},{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc390959-9c52-11eb-aca3-afa58bd282b2","grant_number":"M03073","name":"Learning and triangulating manifolds via collapses"}],"has_accepted_license":"1","type":"conference"},{"ddc":["000"],"quality_controlled":"1","OA_type":"hybrid","status":"public","scopus_import":"1","pmid":1,"intvolume":"         8","publication":"Journal of Applied and Computational Topology","volume":8,"year":"2024","researchdata_availability":"no","publisher":"Springer Nature","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","first_name":"Ranita","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas"},{"full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera Di Montesano"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"},{"first_name":"Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","full_name":"Saghafian, Morteza","last_name":"Saghafian"}],"file_date_updated":"2025-01-09T07:39:41Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"We characterize critical points of 1-dimensional maps paired in persistent homology\r\ngeometrically and this way get elementary proofs of theorems about the symmetry\r\nof persistence diagrams and the variation of such maps. In particular, we identify\r\nbranching points and endpoints of networks as the sole source of asymmetry and\r\nrelate the cycle basis in persistent homology with a version of the stable marriage\r\nproblem. Our analysis provides the foundations of fast algorithms for maintaining a\r\ncollection of sorted lists together with its persistence diagram."}],"corr_author":"1","date_published":"2024-10-01T00:00:00Z","month":"10","supplementarymaterial":"no","OA_place":"publisher","file":[{"creator":"dernst","date_updated":"2025-01-09T07:39:41Z","access_level":"open_access","file_name":"2024_JourApplCompTopo_Biswas.pdf","success":1,"date_created":"2025-01-09T07:39:41Z","checksum":"d493df5088c222b88d9ca46b623ad0ee","relation":"main_file","content_type":"application/pdf","file_id":"18783","file_size":476896}],"date_updated":"2026-10-02T11:52:56Z","das_tickbox":"0","department":[{"_id":"HeEd"}],"date_created":"2023-07-02T22:00:44Z","acknowledgement":"Open access funding provided by Austrian Science Fund (FWF). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant no. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35. The authors of this paper thank anonymous reviewers for their constructive criticism and Monika Henzinger for detailed comments on an earlier version of this paper.","ec_funded":1,"article_processing_charge":"Yes (via OA deal)","fulldoi":"https://doi.org/10.1007/s41468-023-00126-9","language":[{"iso":"eng"}],"oa_version":"Published Version","_id":"13182","day":"01","doi":"10.1007/s41468-023-00126-9","page":"1101-1119","article_type":"original","related_material":{"record":[{"id":"11660","relation":"earlier_version","status":"public"},{"id":"15094","status":"public","relation":"dissertation_contains"}]},"project":[{"call_identifier":"H2020","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","name":"Alpha Shape Theory Extended","grant_number":"788183"},{"grant_number":"I4887","name":"Persistent Homology, Algorithms and Stochastic Geometry","_id":"0aa4bc98-070f-11eb-9043-e6fff9c6a316"},{"grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"has_accepted_license":"1","type":"journal_article","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"Geometric characterization of the persistence of 1D maps","publication_status":"published","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"external_id":{"pmid":["39678706"]},"citation":{"mla":"Biswas, Ranita, et al. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 1101–19, doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Geometric characterization of the persistence of 1D maps,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 1101–1119, 2024.","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. 2024;8:1101-1119. doi:<a href=\"https://doi.org/10.1007/s41468-023-00126-9\">10.1007/s41468-023-00126-9</a>","apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Geometric characterization of the persistence of 1D maps. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Geometric characterization of the persistence of 1D maps. Journal of Applied and Computational Topology. 8, 1101–1119.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Geometric Characterization of the Persistence of 1D Maps.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-023-00126-9\">https://doi.org/10.1007/s41468-023-00126-9</a>."}},{"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s41468-024-00173-w","_id":"15380","day":"01","fulldoi":"https://doi.org/10.1007/s41468-024-00173-w","oa_version":"Published Version","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"earlier_version","status":"public","id":"11658"}]},"article_type":"original","page":"557-578","type":"journal_article","has_accepted_license":"1","project":[{"name":"Alpha Shape Theory Extended","grant_number":"788183","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"268116B8-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Mathematics, Computer Science","grant_number":"Z00342"},{"name":"Persistence and stability of geometric complexes","grant_number":"I02979-N35","call_identifier":"FWF","_id":"2561EBF4-B435-11E9-9278-68D0E5697425"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","external_id":{"pmid":["39308789"]},"publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"publication_status":"published","title":"Depth in arrangements: Dehn–Sommerville–Euler relations with applications","citation":{"apa":"Biswas, R., Cultrera di Montesano, S., Edelsbrunner, H., &#38; Saghafian, M. (2024). Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>","mla":"Biswas, Ranita, et al. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>, vol. 8, Springer Nature, 2024, pp. 557–78, doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>.","ieee":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, and M. Saghafian, “Depth in arrangements: Dehn–Sommerville–Euler relations with applications,” <i>Journal of Applied and Computational Topology</i>, vol. 8. Springer Nature, pp. 557–578, 2024.","ama":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. <i>Journal of Applied and Computational Topology</i>. 2024;8:557-578. doi:<a href=\"https://doi.org/10.1007/s41468-024-00173-w\">10.1007/s41468-024-00173-w</a>","short":"R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.","ista":"Biswas R, Cultrera di Montesano S, Edelsbrunner H, Saghafian M. 2024. Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Journal of Applied and Computational Topology. 8, 557–578.","chicago":"Biswas, Ranita, Sebastiano Cultrera di Montesano, Herbert Edelsbrunner, and Morteza Saghafian. “Depth in Arrangements: Dehn–Sommerville–Euler Relations with Applications.” <i>Journal of Applied and Computational Topology</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s41468-024-00173-w\">https://doi.org/10.1007/s41468-024-00173-w</a>."},"intvolume":"         8","pmid":1,"scopus_import":"1","quality_controlled":"1","status":"public","OA_type":"hybrid","ddc":["510"],"researchdata_availability":"no","year":"2024","volume":8,"publication":"Journal of Applied and Computational Topology","publisher":"Springer Nature","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"lang":"eng","text":"The depth of a cell in an arrangement of n (non-vertical) great-spheres in Sd is the number of great-spheres that pass above the cell. We prove Euler-type relations, which imply extensions of the classic Dehn–Sommerville relations for convex polytopes to sublevel sets of the depth function, and we use the relations to extend the expressions for the number of faces of neighborly polytopes to the number of cells of levels in neighborly arrangements."}],"corr_author":"1","file_date_updated":"2025-04-23T08:01:36Z","oa":1,"author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","first_name":"Ranita","last_name":"Biswas"},{"last_name":"Cultrera Di Montesano","full_name":"Cultrera Di Montesano, Sebastiano","orcid":"0000-0001-6249-0832","first_name":"Sebastiano","id":"34D2A09C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Edelsbrunner","orcid":"0000-0002-9823-6833","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"},{"last_name":"Saghafian","full_name":"Saghafian, Morteza","id":"f86f7148-b140-11ec-9577-95435b8df824","first_name":"Morteza"}],"date_published":"2024-09-01T00:00:00Z","supplementarymaterial":"no","OA_place":"publisher","month":"09","das_tickbox":"0","date_updated":"2026-10-02T11:55:12Z","file":[{"checksum":"0ee15c1493a6413cf356ab2f32c81a9e","file_name":"2024_JourApplCompTopo_BiswasRa.pdf","date_created":"2025-04-23T08:01:36Z","success":1,"creator":"dernst","access_level":"open_access","date_updated":"2025-04-23T08:01:36Z","file_size":522831,"file_id":"19612","relation":"main_file","content_type":"application/pdf"}],"ec_funded":1,"date_created":"2024-05-12T22:01:03Z","acknowledgement":"The authors thank Uli Wagner and Emo Welzl for comments on an earlier version of this paper, and for pointing out related work in the prior literature.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, Grant No. 788183, from the Wittgenstein Prize, Austrian Science Fund (FWF), Grant No. Z 342-N31, and from the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF), Grant No. I 02979-N35.","department":[{"_id":"HeEd"}]},{"oa_version":"Published Version","fulldoi":"https://doi.org/10.1016/j.jcta.2024.105889","language":[{"iso":"eng"}],"_id":"15247","day":"01","doi":"10.1016/j.jcta.2024.105889","article_processing_charge":"No","has_accepted_license":"1","type":"journal_article","article_type":"original","issue":"8","arxiv":1,"isi":1,"title":"Odd-sunflowers","publication_status":"published","publication_identifier":{"issn":["0097-3165"],"eissn":["1096-0899"]},"external_id":{"arxiv":["2310.16701"],"isi":["001217739200001"]},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_number":"105889","citation":{"chicago":"Frankl, Peter, János Pach, and Dömötör Pálvölgyi. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>.","ista":"Frankl P, Pach J, Pálvölgyi D. 2024. Odd-sunflowers. Journal of Combinatorial Theory, Series A. 206(8), 105889.","short":"P. Frankl, J. Pach, D. Pálvölgyi, Journal of Combinatorial Theory, Series A 206 (2024).","ama":"Frankl P, Pach J, Pálvölgyi D. Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. 2024;206(8). doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>","ieee":"P. Frankl, J. Pach, and D. Pálvölgyi, “Odd-sunflowers,” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8. Elsevier, 2024.","mla":"Frankl, Peter, et al. “Odd-Sunflowers.” <i>Journal of Combinatorial Theory, Series A</i>, vol. 206, no. 8, 105889, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">10.1016/j.jcta.2024.105889</a>.","apa":"Frankl, P., Pach, J., &#38; Pálvölgyi, D. (2024). Odd-sunflowers. <i>Journal of Combinatorial Theory, Series A</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcta.2024.105889\">https://doi.org/10.1016/j.jcta.2024.105889</a>"},"publication":"Journal of Combinatorial Theory, Series A","volume":206,"year":"2024","researchdata_availability":"not applicable","ddc":["510"],"quality_controlled":"1","status":"public","OA_type":"hybrid","scopus_import":"1","intvolume":"       206","author":[{"last_name":"Frankl","first_name":"Peter","full_name":"Frankl, Peter"},{"last_name":"Pach","first_name":"János","id":"E62E3130-B088-11EA-B919-BF823C25FEA4","full_name":"Pach, János"},{"last_name":"Pálvölgyi","full_name":"Pálvölgyi, Dömötör","first_name":"Dömötör"}],"file_date_updated":"2025-01-09T08:37:20Z","oa":1,"abstract":[{"lang":"eng","text":"Extending the notion of sunflowers, we call a family of at least two sets an odd-sunflower if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erdős–Szemerédi conjecture, recently proved by Naslund and Sawin, that there is a constant <2 such that every family of subsets of an n-element set that contains no odd-sunflower consists of at most n sets. We construct such families of size at least 1.5021n. We also characterize minimal odd-sunflowers of triples."}],"tmp":{"name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)","short":"CC BY-NC (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","image":"/images/cc_by_nc.png"},"corr_author":"1","publisher":"Elsevier","month":"08","supplementarymaterial":"yes","OA_place":"publisher","dataavailabilitystatement":"No data was used for the research described in the article.","date_published":"2024-08-01T00:00:00Z","department":[{"_id":"HeEd"}],"date_created":"2024-03-31T22:01:11Z","acknowledgement":"We are grateful to Balázs Keszegh, and to the members of the Miklós Schweitzer Competition committee of 2022 for valuable discussions, and Shira Zerbib for pointing out several important mathematical typos.","file":[{"creator":"dernst","date_updated":"2025-01-09T08:37:20Z","access_level":"open_access","success":1,"date_created":"2025-01-09T08:37:20Z","file_name":"2024_JourCombiTheoryA_Frankl.pdf","checksum":"ffc29d65e712849f0d31009271e06a63","content_type":"application/pdf","relation":"main_file","file_id":"18791","file_size":366029}],"date_updated":"2026-10-02T11:54:47Z","das_tickbox":"1"},{"citation":{"apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024.","ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>.","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>.","ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","title":"New methods for applying topological data analysis to materials science","supervisor":[{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner"}],"publication_identifier":{"isbn":["978-3-99078-052-7"],"issn":["2663-337X"]},"publication_status":"published","page":"111","related_material":{"record":[{"id":"10828","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"11440","status":"public"},{"id":"9345","relation":"part_of_dissertation","status":"public"},{"id":"18673","relation":"part_of_dissertation","status":"public"}]},"has_accepted_license":"1","project":[{"grant_number":"788183","name":"Alpha Shape Theory Extended","_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"type":"dissertation","article_processing_charge":"No","fulldoi":"https://doi.org/10.15479/at:ista:18667","language":[{"iso":"eng"}],"oa_version":"Published Version","keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"_id":"18667","day":"17","doi":"10.15479/at:ista:18667","file":[{"creator":"theiss","date_updated":"2024-12-19T10:24:46Z","access_level":"open_access","file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","date_created":"2024-12-19T10:24:46Z","success":1,"checksum":"247bb057aed2fba1cd4711917aaa2d77","content_type":"application/pdf","relation":"main_file","file_id":"18686","file_size":7752253},{"content_type":"application/zip","relation":"source_file","file_id":"18687","file_size":17197731,"date_updated":"2024-12-19T10:24:50Z","access_level":"closed","creator":"theiss","file_name":"PhD_Thesis.zip","date_created":"2024-12-19T10:24:50Z","checksum":"9648b45c07a008ee11a07f99856a139d"}],"date_updated":"2026-10-02T11:55:42Z","das_tickbox":"0","department":[{"_id":"GradSch"},{"_id":"HeEd"}],"acknowledgement":"I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020.","date_created":"2024-12-17T16:17:55Z","degree_awarded":"PhD","ec_funded":1,"doi_confirm":"1","date_published":"2024-12-17T00:00:00Z","month":"12","supplementarymaterial":"no","OA_place":"publisher","alternative_title":["ISTA Thesis"],"publisher":"Institute of Science and Technology Austria","author":[{"last_name":"Heiss","first_name":"Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-1780-2689","full_name":"Heiss, Teresa"}],"file_date_updated":"2024-12-19T10:24:50Z","oa":1,"corr_author":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"abstract":[{"text":"Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability.","lang":"eng"}],"status":"public","ddc":["514","516","004"],"year":"2024","researchdata_availability":"no"}]