--- _id: '7803' abstract: - lang: eng text: "We settle the complexity of the (Δ+1)-coloring and (Δ+1)-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This matches the complexity of the recent breakthrough randomized constant-round (Δ+1)-list coloring algorithm due to Chang et al. (PODC'19), and significantly improves upon the state-of-the-art O(logΔ)-round deterministic (Δ+1)-coloring bound of Parter (ICALP'18).\r\nA remarkable property of our algorithm is its simplicity. Whereas the state-of-the-art randomized algorithms for this problem are based on the quite involved local coloring algorithm of Chang et al. (STOC'18), our algorithm can be described in just a few lines. At a high level, it applies a careful derandomization of a recursive procedure which partitions the nodes and their respective palettes into separate bins. We show that after O(1) recursion steps, the remaining uncolored subgraph within each bin has linear size, and thus can be solved locally by collecting it to a single node. This algorithm can also be implemented in the Massively Parallel Computation (MPC) model provided that each machine has linear (in n, the number of nodes in the input graph) space.\r\nWe also show an extension of our algorithm to the MPC regime in which machines have sublinear space: we present the first deterministic (Δ+1)-list coloring algorithm designed for sublinear-space MPC, which runs in O(logΔ+loglogn) rounds." article_processing_charge: No author: - first_name: Artur full_name: Czumaj, Artur last_name: Czumaj orcid: 0000-0002-5646-9524 - first_name: Peter full_name: Davies, Peter id: 11396234-BB50-11E9-B24C-90FCE5697425 last_name: Davies orcid: 0000-0002-5646-9524 - first_name: Merav full_name: Parter, Merav last_name: Parter citation: ama: 'Czumaj A, Davies P, Parter M. Simple, deterministic, constant-round coloring in the congested clique. In: Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing. Association for Computing Machinery; 2020:309-318. doi:10.1145/3382734.3405751' apa: 'Czumaj, A., Davies, P., & Parter, M. (2020). Simple, deterministic, constant-round coloring in the congested clique. In Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing (pp. 309–318). Salerno, Italy: Association for Computing Machinery. https://doi.org/10.1145/3382734.3405751' chicago: Czumaj, Artur, Peter Davies, and Merav Parter. “Simple, Deterministic, Constant-Round Coloring in the Congested Clique.” In Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing, 309–18. Association for Computing Machinery, 2020. https://doi.org/10.1145/3382734.3405751. ieee: A. Czumaj, P. Davies, and M. Parter, “Simple, deterministic, constant-round coloring in the congested clique,” in Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing, Salerno, Italy, 2020, pp. 309–318. ista: 'Czumaj A, Davies P, Parter M. 2020. Simple, deterministic, constant-round coloring in the congested clique. Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing. PODC: Symposium on Principles of Distributed Computing, 309–318.' mla: Czumaj, Artur, et al. “Simple, Deterministic, Constant-Round Coloring in the Congested Clique.” Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2020, pp. 309–18, doi:10.1145/3382734.3405751. short: A. Czumaj, P. Davies, M. Parter, in:, Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing, Association for Computing Machinery, 2020, pp. 309–318. conference: end_date: 2020-08-07 location: Salerno, Italy name: 'PODC: Symposium on Principles of Distributed Computing' start_date: 2020-08-03 date_created: 2020-05-06T09:02:14Z date_published: 2020-07-01T00:00:00Z date_updated: 2021-01-12T08:15:37Z day: '01' ddc: - '000' department: - _id: DaAl doi: 10.1145/3382734.3405751 ec_funded: 1 external_id: arxiv: - '2009.06043' file: - access_level: open_access checksum: 46fe4fc58a64eb04068115573f631d4c content_type: application/pdf creator: pdavies date_created: 2020-10-08T08:17:36Z date_updated: 2020-10-08T08:17:36Z file_id: '8624' file_name: ColoringArxiv.pdf file_size: 520051 relation: main_file success: 1 file_date_updated: 2020-10-08T08:17:36Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Submitted Version page: 309-318 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Proceedings of the 2020 ACM Symposium on Principles of Distributed Computing publication_status: published publisher: Association for Computing Machinery quality_controlled: '1' status: public title: Simple, deterministic, constant-round coloring in the congested clique type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2020' ... --- _id: '7806' abstract: - lang: eng text: "We consider the following decision problem EMBEDk→d in computational topology (where k ≤ d are fixed positive integers): Given a finite simplicial complex K of dimension k, does there exist a (piecewise-linear) embedding of K into ℝd?\r\nThe special case EMBED1→2 is graph planarity, which is decidable in linear time, as shown by Hopcroft and Tarjan. In higher dimensions, EMBED2→3 and EMBED3→3 are known to be decidable (as well as NP-hard), and recent results of Čadek et al. in computational homotopy theory, in combination with the classical Haefliger–Weber theorem in geometric topology, imply that EMBEDk→d can be solved in polynomial time for any fixed pair (k, d) of dimensions in the so-called metastable range .\r\nHere, by contrast, we prove that EMBEDk→d is algorithmically undecidable for almost all pairs of dimensions outside the metastable range, namely for . This almost completely resolves the decidability vs. undecidability of EMBEDk→d in higher dimensions and establishes a sharp dichotomy between polynomial-time solvability and undecidability.\r\nOur result complements (and in a wide range of dimensions strengthens) earlier results of Matoušek, Tancer, and the second author, who showed that EMBEDk→d is undecidable for 4 ≤ k ϵ {d – 1, d}, and NP-hard for all remaining pairs (k, d) outside the metastable range and satisfying d ≥ 4." article_processing_charge: No author: - first_name: Marek full_name: Filakovský, Marek id: 3E8AF77E-F248-11E8-B48F-1D18A9856A87 last_name: Filakovský - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 - first_name: Stephan Y full_name: Zhechev, Stephan Y id: 3AA52972-F248-11E8-B48F-1D18A9856A87 last_name: Zhechev citation: ama: 'Filakovský M, Wagner U, Zhechev SY. Embeddability of simplicial complexes is undecidable. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. Vol 2020-January. SIAM; 2020:767-785. doi:10.1137/1.9781611975994.47' apa: 'Filakovský, M., Wagner, U., & Zhechev, S. Y. (2020). Embeddability of simplicial complexes is undecidable. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2020–January, pp. 767–785). Salt Lake City, UT, United States: SIAM. https://doi.org/10.1137/1.9781611975994.47' chicago: Filakovský, Marek, Uli Wagner, and Stephan Y Zhechev. “Embeddability of Simplicial Complexes Is Undecidable.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2020–January:767–85. SIAM, 2020. https://doi.org/10.1137/1.9781611975994.47. ieee: M. Filakovský, U. Wagner, and S. Y. Zhechev, “Embeddability of simplicial complexes is undecidable,” in Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, Salt Lake City, UT, United States, 2020, vol. 2020–January, pp. 767–785. ista: 'Filakovský M, Wagner U, Zhechev SY. 2020. Embeddability of simplicial complexes is undecidable. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. SODA: Symposium on Discrete Algorithms vol. 2020–January, 767–785.' mla: Filakovský, Marek, et al. “Embeddability of Simplicial Complexes Is Undecidable.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2020–January, SIAM, 2020, pp. 767–85, doi:10.1137/1.9781611975994.47. short: M. Filakovský, U. Wagner, S.Y. Zhechev, in:, Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 2020, pp. 767–785. conference: end_date: 2020-01-08 location: Salt Lake City, UT, United States name: 'SODA: Symposium on Discrete Algorithms' start_date: 2020-01-05 date_created: 2020-05-10T22:00:48Z date_published: 2020-01-01T00:00:00Z date_updated: 2021-01-12T08:15:38Z day: '01' department: - _id: UlWa doi: 10.1137/1.9781611975994.47 language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1137/1.9781611975994.47 month: '01' oa: 1 oa_version: Published Version page: 767-785 project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms publication_identifier: isbn: - '9781611975994' publication_status: published publisher: SIAM quality_controlled: '1' scopus_import: 1 status: public title: Embeddability of simplicial complexes is undecidable type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2020-January year: '2020' ... --- _id: '7814' abstract: - lang: eng text: 'Scientific research is to date largely restricted to wealthy laboratories in developed nations due to the necessity of complex and expensive equipment. This inequality limits the capacity of science to be used as a diplomatic channel. Maker movements use open-source technologies including additive manufacturing (3D printing) and laser cutting, together with low-cost computers for developing novel products. This movement is setting the groundwork for a revolution, allowing scientific equipment to be sourced at a fraction of the cost and has the potential to increase the availability of equipment for scientists around the world. Science education is increasingly recognized as another channel for science diplomacy. In this perspective, we introduce the idea that the Maker movement and open-source technologies have the potential to revolutionize science, technology, engineering and mathematics (STEM) education worldwide. We present an open-source STEM didactic tool called SCOPES (Sparking Curiosity through Open-source Platforms in Education and Science). SCOPES is self-contained, independent of local resources, and cost-effective. SCOPES can be adapted to communicate complex subjects from genetics to neurobiology, perform real-world biological experiments and explore digitized scientific samples. We envision such platforms will enhance science diplomacy by providing a means for scientists to share their findings with classrooms and for educators to incorporate didactic concepts into STEM lessons. By providing students the opportunity to design, perform, and share scientific experiments, students also experience firsthand the benefits of a multinational scientific community. We provide instructions on how to build and use SCOPES on our webpage: http://scopeseducation.org.' acknowledged_ssus: - _id: Bio - _id: LifeSc - _id: PreCl - _id: EM-Fac article_number: '48' article_processing_charge: No article_type: original author: - first_name: Robert J full_name: Beattie, Robert J id: 2E26DF60-F248-11E8-B48F-1D18A9856A87 last_name: Beattie orcid: 0000-0002-8483-8753 - first_name: Simon full_name: Hippenmeyer, Simon id: 37B36620-F248-11E8-B48F-1D18A9856A87 last_name: Hippenmeyer orcid: 0000-0003-2279-1061 - first_name: Florian full_name: Pauler, Florian id: 48EA0138-F248-11E8-B48F-1D18A9856A87 last_name: Pauler citation: ama: 'Beattie RJ, Hippenmeyer S, Pauler F. SCOPES: Sparking curiosity through Open-Source platforms in education and science. Frontiers in Education. 2020;5. doi:10.3389/feduc.2020.00048' apa: 'Beattie, R. J., Hippenmeyer, S., & Pauler, F. (2020). SCOPES: Sparking curiosity through Open-Source platforms in education and science. Frontiers in Education. Frontiers Media. https://doi.org/10.3389/feduc.2020.00048' chicago: 'Beattie, Robert J, Simon Hippenmeyer, and Florian Pauler. “SCOPES: Sparking Curiosity through Open-Source Platforms in Education and Science.” Frontiers in Education. Frontiers Media, 2020. https://doi.org/10.3389/feduc.2020.00048.' ieee: 'R. J. Beattie, S. Hippenmeyer, and F. Pauler, “SCOPES: Sparking curiosity through Open-Source platforms in education and science,” Frontiers in Education, vol. 5. Frontiers Media, 2020.' ista: 'Beattie RJ, Hippenmeyer S, Pauler F. 2020. SCOPES: Sparking curiosity through Open-Source platforms in education and science. Frontiers in Education. 5, 48.' mla: 'Beattie, Robert J., et al. “SCOPES: Sparking Curiosity through Open-Source Platforms in Education and Science.” Frontiers in Education, vol. 5, 48, Frontiers Media, 2020, doi:10.3389/feduc.2020.00048.' short: R.J. Beattie, S. Hippenmeyer, F. Pauler, Frontiers in Education 5 (2020). date_created: 2020-05-11T08:18:48Z date_published: 2020-05-08T00:00:00Z date_updated: 2021-01-12T08:15:42Z day: '08' ddc: - '570' department: - _id: SiHi doi: 10.3389/feduc.2020.00048 ec_funded: 1 file: - access_level: open_access checksum: a24ec24e38d843341ae620ec76c53688 content_type: application/pdf creator: dernst date_created: 2020-05-11T11:34:08Z date_updated: 2020-07-14T12:48:03Z file_id: '7818' file_name: 2020_FrontiersEduc_Beattie.pdf file_size: 1402146 relation: main_file file_date_updated: 2020-07-14T12:48:03Z has_accepted_license: '1' intvolume: ' 5' language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 264E56E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02416 name: Molecular Mechanisms Regulating Gliogenesis in the Cerebral Cortex - _id: 260018B0-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '725780' name: Principles of Neural Stem Cell Lineage Progression in Cerebral Cortex Development publication: Frontiers in Education publication_identifier: issn: - 2504-284X publication_status: published publisher: Frontiers Media quality_controlled: '1' status: public title: 'SCOPES: Sparking curiosity through Open-Source platforms in education and science' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 5 year: '2020' ... --- _id: '7866' abstract: - lang: eng text: In this paper, we establish convergence to equilibrium for a drift–diffusion–recombination system modelling the charge transport within certain semiconductor devices. More precisely, we consider a two-level system for electrons and holes which is augmented by an intermediate energy level for electrons in so-called trapped states. The recombination dynamics use the mass action principle by taking into account this additional trap level. The main part of the paper is concerned with the derivation of an entropy–entropy production inequality, which entails exponential convergence to the equilibrium via the so-called entropy method. The novelty of our approach lies in the fact that the entropy method is applied uniformly in a fast-reaction parameter which governs the lifetime of electrons on the trap level. Thus, the resulting decay estimate for the densities of electrons and holes extends to the corresponding quasi-steady-state approximation. acknowledgement: Open access funding provided by Austrian Science Fund (FWF). The second author has been supported by the International Research Training Group IGDK 1754 “Optimization and Numerical Analysis for Partial Differential Equations with Nonsmooth Structures”, funded by the German Research Council (DFG) and the Austrian Science Fund (FWF) under grant number [W 1244-N18]. article_processing_charge: No article_type: original author: - first_name: Klemens full_name: Fellner, Klemens last_name: Fellner - first_name: Michael full_name: Kniely, Michael id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87 last_name: Kniely orcid: 0000-0001-5645-4333 citation: ama: Fellner K, Kniely M. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 2020;6:529-598. doi:10.1007/s41808-020-00068-8 apa: Fellner, K., & Kniely, M. (2020). Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. Springer Nature. https://doi.org/10.1007/s41808-020-00068-8 chicago: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations. Springer Nature, 2020. https://doi.org/10.1007/s41808-020-00068-8. ieee: K. Fellner and M. Kniely, “Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model,” Journal of Elliptic and Parabolic Equations, vol. 6. Springer Nature, pp. 529–598, 2020. ista: Fellner K, Kniely M. 2020. Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model. Journal of Elliptic and Parabolic Equations. 6, 529–598. mla: Fellner, Klemens, and Michael Kniely. “Uniform Convergence to Equilibrium for a Family of Drift–Diffusion Models with Trap-Assisted Recombination and the Limiting Shockley–Read–Hall Model.” Journal of Elliptic and Parabolic Equations, vol. 6, Springer Nature, 2020, pp. 529–98, doi:10.1007/s41808-020-00068-8. short: K. Fellner, M. Kniely, Journal of Elliptic and Parabolic Equations 6 (2020) 529–598. date_created: 2020-05-17T22:00:45Z date_published: 2020-12-01T00:00:00Z date_updated: 2021-01-12T08:15:47Z day: '01' ddc: - '510' department: - _id: JuFi doi: 10.1007/s41808-020-00068-8 file: - access_level: open_access checksum: 6bc6832caacddceee1471291e93dcf1d content_type: application/pdf creator: dernst date_created: 2020-11-25T08:59:59Z date_updated: 2020-11-25T08:59:59Z file_id: '8802' file_name: 2020_JourEllipticParabEquat_Fellner.pdf file_size: 8408694 relation: main_file success: 1 file_date_updated: 2020-11-25T08:59:59Z has_accepted_license: '1' intvolume: ' 6' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 529-598 project: - _id: 3AC91DDA-15DF-11EA-824D-93A3E7B544D1 call_identifier: FWF name: FWF Open Access Fund publication: Journal of Elliptic and Parabolic Equations publication_identifier: eissn: - '22969039' issn: - '22969020' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Uniform convergence to equilibrium for a family of drift–diffusion models with trap-assisted recombination and the limiting Shockley–Read–Hall model tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 6 year: '2020' ... --- _id: '7919' abstract: - lang: eng text: We explore the time evolution of two impurities in a trapped one-dimensional Bose gas that follows a change of the boson-impurity interaction. We study the induced impurity-impurity interactions and their effect on the quench dynamics. In particular, we report on the size of the impurity cloud, the impurity-impurity entanglement, and the impurity-impurity correlation function. The presented numerical simulations are based upon the variational multilayer multiconfiguration time-dependent Hartree method for bosons. To analyze and quantify induced impurity-impurity correlations, we employ an effective two-body Hamiltonian with a contact interaction. We show that the effective model consistent with the mean-field attraction of two heavy impurities explains qualitatively our results for weak interactions. Our findings suggest that the quench dynamics in cold-atom systems can be a tool for studying impurity-impurity correlations. article_number: '023154 ' article_processing_charge: No article_type: original author: - first_name: S. I. full_name: Mistakidis, S. I. last_name: Mistakidis - first_name: Artem full_name: Volosniev, Artem id: 37D278BC-F248-11E8-B48F-1D18A9856A87 last_name: Volosniev orcid: 0000-0003-0393-5525 - first_name: P. full_name: Schmelcher, P. last_name: Schmelcher citation: ama: Mistakidis SI, Volosniev A, Schmelcher P. Induced correlations between impurities in a one-dimensional quenched Bose gas. Physical Review Research. 2020;2. doi:10.1103/physrevresearch.2.023154 apa: Mistakidis, S. I., Volosniev, A., & Schmelcher, P. (2020). Induced correlations between impurities in a one-dimensional quenched Bose gas. Physical Review Research. American Physical Society. https://doi.org/10.1103/physrevresearch.2.023154 chicago: Mistakidis, S. I., Artem Volosniev, and P. Schmelcher. “Induced Correlations between Impurities in a One-Dimensional Quenched Bose Gas.” Physical Review Research. American Physical Society, 2020. https://doi.org/10.1103/physrevresearch.2.023154. ieee: S. I. Mistakidis, A. Volosniev, and P. Schmelcher, “Induced correlations between impurities in a one-dimensional quenched Bose gas,” Physical Review Research, vol. 2. American Physical Society, 2020. ista: Mistakidis SI, Volosniev A, Schmelcher P. 2020. Induced correlations between impurities in a one-dimensional quenched Bose gas. Physical Review Research. 2, 023154. mla: Mistakidis, S. I., et al. “Induced Correlations between Impurities in a One-Dimensional Quenched Bose Gas.” Physical Review Research, vol. 2, 023154, American Physical Society, 2020, doi:10.1103/physrevresearch.2.023154. short: S.I. Mistakidis, A. Volosniev, P. Schmelcher, Physical Review Research 2 (2020). date_created: 2020-06-03T11:30:10Z date_published: 2020-05-11T00:00:00Z date_updated: 2023-02-23T13:20:16Z day: '11' ddc: - '530' department: - _id: MiLe doi: 10.1103/physrevresearch.2.023154 ec_funded: 1 file: - access_level: open_access checksum: e1c362fe094d6b246b3cd4a49722e78b content_type: application/pdf creator: dernst date_created: 2020-06-04T13:51:59Z date_updated: 2020-07-14T12:48:05Z file_id: '7926' file_name: 2020_PhysRevResearch_Mistakidis.pdf file_size: 1741098 relation: main_file file_date_updated: 2020-07-14T12:48:05Z has_accepted_license: '1' intvolume: ' 2' language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Physical Review Research publication_identifier: issn: - 2643-1564 publication_status: published publisher: American Physical Society quality_controlled: '1' status: public title: Induced correlations between impurities in a one-dimensional quenched Bose gas tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2020' ... --- _id: '7991' abstract: - lang: eng text: 'We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.' alternative_title: - LIPIcs article_number: 12:1 - 12:15 article_processing_charge: No author: - first_name: Sergey full_name: Avvakumov, Sergey id: 3827DAC8-F248-11E8-B48F-1D18A9856A87 last_name: Avvakumov - first_name: Gabriel full_name: Nivasch, Gabriel last_name: Nivasch citation: ama: 'Avvakumov S, Nivasch G. Homotopic curve shortening and the affine curve-shortening flow. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.12' apa: 'Avvakumov, S., & Nivasch, G. (2020). Homotopic curve shortening and the affine curve-shortening flow. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.12' chicago: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.12. ieee: S. Avvakumov and G. Nivasch, “Homotopic curve shortening and the affine curve-shortening flow,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Avvakumov S, Nivasch G. 2020. Homotopic curve shortening and the affine curve-shortening flow. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 12:1-12:15.' mla: Avvakumov, Sergey, and Gabriel Nivasch. “Homotopic Curve Shortening and the Affine Curve-Shortening Flow.” 36th International Symposium on Computational Geometry, vol. 164, 12:1-12:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.12. short: S. Avvakumov, G. Nivasch, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:19Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.12 external_id: arxiv: - '1909.00263' file: - access_level: open_access checksum: 6872df6549142f709fb6354a1b2f2c06 content_type: application/pdf creator: dernst date_created: 2020-06-23T11:13:49Z date_updated: 2020-07-14T12:48:06Z file_id: '8007' file_name: 2020_LIPIcsSoCG_Avvakumov.pdf file_size: 575896 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng license: https://creativecommons.org/licenses/by/3.0/ month: '06' oa: 1 oa_version: Published Version project: - _id: 26611F5C-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P31312 name: Algorithms for Embeddings and Homotopy Theory publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Homotopic curve shortening and the affine curve-shortening flow tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/3.0/legalcode name: Creative Commons Attribution 3.0 Unported (CC BY 3.0) short: CC BY (3.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7989' abstract: - lang: eng text: 'We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.' alternative_title: - LIPIcs article_number: 61:1-61:13 article_processing_charge: No author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 citation: ama: 'Patakova Z. Bounding radon number via Betti numbers. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.61' apa: 'Patakova, Z. (2020). Bounding radon number via Betti numbers. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.61' chicago: Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.61. ieee: Z. Patakova, “Bounding radon number via Betti numbers,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Patakova Z. 2020. Bounding radon number via Betti numbers. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 61:1-61:13.' mla: Patakova, Zuzana. “Bounding Radon Number via Betti Numbers.” 36th International Symposium on Computational Geometry, vol. 164, 61:1-61:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.61. short: Z. Patakova, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:18Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:22Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.61 external_id: arxiv: - '1908.01677' file: - access_level: open_access checksum: d0996ca5f6eb32ce955ce782b4f2afbe content_type: application/pdf creator: dernst date_created: 2020-06-23T06:56:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8005' file_name: 2020_LIPIcsSoCG_Patakova_61.pdf file_size: 645421 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Bounding radon number via Betti numbers tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7992' abstract: - lang: eng text: 'Let K be a convex body in ℝⁿ (i.e., a compact convex set with nonempty interior). Given a point p in the interior of K, a hyperplane h passing through p is called barycentric if p is the barycenter of K ∩ h. In 1961, Grünbaum raised the question whether, for every K, there exists an interior point p through which there are at least n+1 distinct barycentric hyperplanes. Two years later, this was seemingly resolved affirmatively by showing that this is the case if p=p₀ is the point of maximal depth in K. However, while working on a related question, we noticed that one of the auxiliary claims in the proof is incorrect. Here, we provide a counterexample; this re-opens Grünbaum’s question. It follows from known results that for n ≥ 2, there are always at least three distinct barycentric cuts through the point p₀ ∈ K of maximal depth. Using tools related to Morse theory we are able to improve this bound: four distinct barycentric cuts through p₀ are guaranteed if n ≥ 3.' alternative_title: - LIPIcs article_number: 62:1 - 62:16 article_processing_charge: No author: - first_name: Zuzana full_name: Patakova, Zuzana id: 48B57058-F248-11E8-B48F-1D18A9856A87 last_name: Patakova orcid: 0000-0002-3975-1683 - first_name: Martin full_name: Tancer, Martin id: 38AC689C-F248-11E8-B48F-1D18A9856A87 last_name: Tancer orcid: 0000-0002-1191-6714 - first_name: Uli full_name: Wagner, Uli id: 36690CA2-F248-11E8-B48F-1D18A9856A87 last_name: Wagner orcid: 0000-0002-1494-0568 citation: ama: 'Patakova Z, Tancer M, Wagner U. Barycentric cuts through a convex body. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.62' apa: 'Patakova, Z., Tancer, M., & Wagner, U. (2020). Barycentric cuts through a convex body. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.62' chicago: Patakova, Zuzana, Martin Tancer, and Uli Wagner. “Barycentric Cuts through a Convex Body.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.62. ieee: Z. Patakova, M. Tancer, and U. Wagner, “Barycentric cuts through a convex body,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Patakova Z, Tancer M, Wagner U. 2020. Barycentric cuts through a convex body. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 62:1-62:16.' mla: Patakova, Zuzana, et al. “Barycentric Cuts through a Convex Body.” 36th International Symposium on Computational Geometry, vol. 164, 62:1-62:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.62. short: Z. Patakova, M. Tancer, U. Wagner, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:20Z date_published: 2020-06-01T00:00:00Z date_updated: 2021-01-12T08:16:23Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.62 external_id: arxiv: - '2003.13536' file: - access_level: open_access checksum: ce1c9194139a664fb59d1efdfc88eaae content_type: application/pdf creator: dernst date_created: 2020-06-23T06:45:52Z date_updated: 2020-07-14T12:48:06Z file_id: '8004' file_name: 2020_LIPIcsSoCG_Patakova.pdf file_size: 750318 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: 1 status: public title: Barycentric cuts through a convex body tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '7994' abstract: - lang: eng text: In the recent study of crossing numbers, drawings of graphs that can be extended to an arrangement of pseudolines (pseudolinear drawings) have played an important role as they are a natural combinatorial extension of rectilinear (or straight-line) drawings. A characterization of the pseudolinear drawings of K_n was found recently. We extend this characterization to all graphs, by describing the set of minimal forbidden subdrawings for pseudolinear drawings. Our characterization also leads to a polynomial-time algorithm to recognize pseudolinear drawings and construct the pseudolines when it is possible. alternative_title: - LIPIcs article_number: 9:1 - 9:14 article_processing_charge: No author: - first_name: Alan M full_name: Arroyo Guevara, Alan M id: 3207FDC6-F248-11E8-B48F-1D18A9856A87 last_name: Arroyo Guevara orcid: 0000-0003-2401-8670 - first_name: Julien full_name: Bensmail, Julien last_name: Bensmail - first_name: R. full_name: Bruce Richter, R. last_name: Bruce Richter citation: ama: 'Arroyo Guevara AM, Bensmail J, Bruce Richter R. Extending drawings of graphs to arrangements of pseudolines. In: 36th International Symposium on Computational Geometry. Vol 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2020. doi:10.4230/LIPIcs.SoCG.2020.9' apa: 'Arroyo Guevara, A. M., Bensmail, J., & Bruce Richter, R. (2020). Extending drawings of graphs to arrangements of pseudolines. In 36th International Symposium on Computational Geometry (Vol. 164). Zürich, Switzerland: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.4230/LIPIcs.SoCG.2020.9' chicago: Arroyo Guevara, Alan M, Julien Bensmail, and R. Bruce Richter. “Extending Drawings of Graphs to Arrangements of Pseudolines.” In 36th International Symposium on Computational Geometry, Vol. 164. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. https://doi.org/10.4230/LIPIcs.SoCG.2020.9. ieee: A. M. Arroyo Guevara, J. Bensmail, and R. Bruce Richter, “Extending drawings of graphs to arrangements of pseudolines,” in 36th International Symposium on Computational Geometry, Zürich, Switzerland, 2020, vol. 164. ista: 'Arroyo Guevara AM, Bensmail J, Bruce Richter R. 2020. Extending drawings of graphs to arrangements of pseudolines. 36th International Symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 164, 9:1-9:14.' mla: Arroyo Guevara, Alan M., et al. “Extending Drawings of Graphs to Arrangements of Pseudolines.” 36th International Symposium on Computational Geometry, vol. 164, 9:1-9:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020, doi:10.4230/LIPIcs.SoCG.2020.9. short: A.M. Arroyo Guevara, J. Bensmail, R. Bruce Richter, in:, 36th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. conference: end_date: 2020-06-26 location: Zürich, Switzerland name: 'SoCG: Symposium on Computational Geometry' start_date: 2020-06-22 date_created: 2020-06-22T09:14:21Z date_published: 2020-06-01T00:00:00Z date_updated: 2023-02-23T13:22:12Z day: '01' ddc: - '510' department: - _id: UlWa doi: 10.4230/LIPIcs.SoCG.2020.9 ec_funded: 1 external_id: arxiv: - '1804.09317' file: - access_level: open_access checksum: 93571b76cf97d5b7c8aabaeaa694dd7e content_type: application/pdf creator: dernst date_created: 2020-06-23T11:06:23Z date_updated: 2020-07-14T12:48:06Z file_id: '8006' file_name: 2020_LIPIcsSoCG_Arroyo.pdf file_size: 592661 relation: main_file file_date_updated: 2020-07-14T12:48:06Z has_accepted_license: '1' intvolume: ' 164' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: 36th International Symposium on Computational Geometry publication_identifier: isbn: - '9783959771436' issn: - '18688969' publication_status: published publisher: Schloss Dagstuhl - Leibniz-Zentrum für Informatik quality_controlled: '1' scopus_import: '1' status: public title: Extending drawings of graphs to arrangements of pseudolines tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 164 year: '2020' ... --- _id: '8011' abstract: - lang: eng text: 'Relaxation to a thermal state is the inevitable fate of nonequilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional arrays of Rydberg atoms via the mechanism of quantum scars, i.e., initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow us to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with nonconstant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars.' article_number: '022065' article_processing_charge: No article_type: original author: - first_name: Alexios full_name: Michailidis, Alexios id: 36EBAD38-F248-11E8-B48F-1D18A9856A87 last_name: Michailidis - first_name: C. J. full_name: Turner, C. J. last_name: Turner - first_name: Z. full_name: Papić, Z. last_name: Papić - first_name: D. A. full_name: Abanin, D. A. last_name: Abanin - first_name: Maksym full_name: Serbyn, Maksym id: 47809E7E-F248-11E8-B48F-1D18A9856A87 last_name: Serbyn orcid: 0000-0002-2399-5827 citation: ama: Michailidis A, Turner CJ, Papić Z, Abanin DA, Serbyn M. Stabilizing two-dimensional quantum scars by deformation and synchronization. Physical Review Research. 2020;2(2). doi:10.1103/physrevresearch.2.022065 apa: Michailidis, A., Turner, C. J., Papić, Z., Abanin, D. A., & Serbyn, M. (2020). Stabilizing two-dimensional quantum scars by deformation and synchronization. Physical Review Research. American Physical Society. https://doi.org/10.1103/physrevresearch.2.022065 chicago: Michailidis, Alexios, C. J. Turner, Z. Papić, D. A. Abanin, and Maksym Serbyn. “Stabilizing Two-Dimensional Quantum Scars by Deformation and Synchronization.” Physical Review Research. American Physical Society, 2020. https://doi.org/10.1103/physrevresearch.2.022065. ieee: A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, and M. Serbyn, “Stabilizing two-dimensional quantum scars by deformation and synchronization,” Physical Review Research, vol. 2, no. 2. American Physical Society, 2020. ista: Michailidis A, Turner CJ, Papić Z, Abanin DA, Serbyn M. 2020. Stabilizing two-dimensional quantum scars by deformation and synchronization. Physical Review Research. 2(2), 022065. mla: Michailidis, Alexios, et al. “Stabilizing Two-Dimensional Quantum Scars by Deformation and Synchronization.” Physical Review Research, vol. 2, no. 2, 022065, American Physical Society, 2020, doi:10.1103/physrevresearch.2.022065. short: A. Michailidis, C.J. Turner, Z. Papić, D.A. Abanin, M. Serbyn, Physical Review Research 2 (2020). date_created: 2020-06-23T12:00:19Z date_published: 2020-06-22T00:00:00Z date_updated: 2021-01-12T08:16:30Z day: '22' ddc: - '530' department: - _id: MaSe doi: 10.1103/physrevresearch.2.022065 ec_funded: 1 file: - access_level: open_access checksum: e6959dc8220f14a008d1933858795e6d content_type: application/pdf creator: dernst date_created: 2020-06-29T14:41:27Z date_updated: 2020-07-14T12:48:08Z file_id: '8050' file_name: 2020_PhysicalReviewResearch_Michailidis.pdf file_size: 2066011 relation: main_file file_date_updated: 2020-07-14T12:48:08Z has_accepted_license: '1' intvolume: ' 2' issue: '2' language: - iso: eng month: '06' oa: 1 oa_version: Published Version project: - _id: 23841C26-32DE-11EA-91FC-C7463DDC885E call_identifier: H2020 grant_number: '850899' name: 'Non-Ergodic Quantum Matter: Universality, Dynamics and Control' publication: Physical Review Research publication_identifier: issn: - 2643-1564 publication_status: published publisher: American Physical Society quality_controlled: '1' status: public title: Stabilizing two-dimensional quantum scars by deformation and synchronization tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2 year: '2020' ...