--- _id: '9156' abstract: - lang: eng text: The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy. acknowledgement: "The authors of this paper thank Roland Roth for suggesting the analysis of theweighted\r\ncurvature derivatives for the purpose of improving molecular dynamics simulations. They also thank Patrice Koehl for the implementation of the formulas and for his encouragement and advise along the road. Finally, they thank two anonymous reviewers for their constructive criticism.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 78818 Alpha). It is also partially supported by the DFG Collaborative Research Center TRR 109, ‘Discretization in Geometry and Dynamics’, through grant no. I02979-N35 of the Austrian Science Fund (FWF)." article_processing_charge: No article_type: original author: - first_name: Arseniy full_name: Akopyan, Arseniy id: 430D2C90-F248-11E8-B48F-1D18A9856A87 last_name: Akopyan orcid: 0000-0002-2548-617X - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 citation: ama: Akopyan A, Edelsbrunner H. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 2020;8(1):74-88. doi:10.1515/cmb-2020-0101 apa: Akopyan, A., & Edelsbrunner, H. (2020). The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. De Gruyter. https://doi.org/10.1515/cmb-2020-0101 chicago: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics. De Gruyter, 2020. https://doi.org/10.1515/cmb-2020-0101. ieee: A. Akopyan and H. Edelsbrunner, “The weighted Gaussian curvature derivative of a space-filling diagram,” Computational and Mathematical Biophysics, vol. 8, no. 1. De Gruyter, pp. 74–88, 2020. ista: Akopyan A, Edelsbrunner H. 2020. The weighted Gaussian curvature derivative of a space-filling diagram. Computational and Mathematical Biophysics. 8(1), 74–88. mla: Akopyan, Arseniy, and Herbert Edelsbrunner. “The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram.” Computational and Mathematical Biophysics, vol. 8, no. 1, De Gruyter, 2020, pp. 74–88, doi:10.1515/cmb-2020-0101. short: A. Akopyan, H. Edelsbrunner, Computational and Mathematical Biophysics 8 (2020) 74–88. date_created: 2021-02-17T15:12:44Z date_published: 2020-07-21T00:00:00Z date_updated: 2023-10-17T12:35:10Z day: '21' ddc: - '510' department: - _id: HeEd doi: 10.1515/cmb-2020-0101 ec_funded: 1 external_id: arxiv: - '1908.06777' file: - access_level: open_access checksum: ca43a7440834eab6bbea29c59b56ef3a content_type: application/pdf creator: dernst date_created: 2021-02-19T13:33:19Z date_updated: 2021-02-19T13:33:19Z file_id: '9170' file_name: 2020_CompMathBiophysics_Akopyan.pdf file_size: 707452 relation: main_file success: 1 file_date_updated: 2021-02-19T13:33:19Z has_accepted_license: '1' intvolume: ' 8' issue: '1' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '07' oa: 1 oa_version: Published Version page: 74-88 project: - _id: 266A2E9E-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '788183' name: Alpha Shape Theory Extended - _id: 2561EBF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: I02979-N35 name: Persistence and stability of geometric complexes publication: Computational and Mathematical Biophysics publication_identifier: issn: - 2544-7297 publication_status: published publisher: De Gruyter quality_controlled: '1' status: public title: The weighted Gaussian curvature derivative of a space-filling diagram 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: 8 year: '2020' ...