--- _id: '833' abstract: - lang: eng text: We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our implementation handles terabyte scale images on commodity hardware. Due to lock-free parallelism, it scales well with the number of processor cores. Additionally, we put the concept of the Euler characteristic curve in the wider context of computational topology. In particular, we explain the connection with persistence diagrams. alternative_title: - LNCS article_processing_charge: No author: - first_name: Teresa full_name: Heiss, Teresa id: 4879BB4E-F248-11E8-B48F-1D18A9856A87 last_name: Heiss orcid: 0000-0002-1780-2689 - first_name: Hubert full_name: Wagner, Hubert id: 379CA8B8-F248-11E8-B48F-1D18A9856A87 last_name: Wagner citation: ama: 'Heiss T, Wagner H. Streaming algorithm for Euler characteristic curves of multidimensional images. In: Felsberg M, Heyden A, Krüger N, eds. Vol 10424. Springer; 2017:397-409. doi:10.1007/978-3-319-64689-3_32' apa: 'Heiss, T., & Wagner, H. (2017). Streaming algorithm for Euler characteristic curves of multidimensional images. In M. Felsberg, A. Heyden, & N. Krüger (Eds.) (Vol. 10424, pp. 397–409). Presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden: Springer. https://doi.org/10.1007/978-3-319-64689-3_32' chicago: Heiss, Teresa, and Hubert Wagner. “Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images.” edited by Michael Felsberg, Anders Heyden, and Norbert Krüger, 10424:397–409. Springer, 2017. https://doi.org/10.1007/978-3-319-64689-3_32. ieee: 'T. Heiss and H. Wagner, “Streaming algorithm for Euler characteristic curves of multidimensional images,” presented at the CAIP: Computer Analysis of Images and Patterns, Ystad, Sweden, 2017, vol. 10424, pp. 397–409.' ista: 'Heiss T, Wagner H. 2017. Streaming algorithm for Euler characteristic curves of multidimensional images. CAIP: Computer Analysis of Images and Patterns, LNCS, vol. 10424, 397–409.' mla: Heiss, Teresa, and Hubert Wagner. Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images. Edited by Michael Felsberg et al., vol. 10424, Springer, 2017, pp. 397–409, doi:10.1007/978-3-319-64689-3_32. short: T. Heiss, H. Wagner, in:, M. Felsberg, A. Heyden, N. Krüger (Eds.), Springer, 2017, pp. 397–409. conference: end_date: 2017-08-24 location: Ystad, Sweden name: 'CAIP: Computer Analysis of Images and Patterns' start_date: 2017-08-22 date_created: 2018-12-11T11:48:45Z date_published: 2017-07-28T00:00:00Z date_updated: 2023-09-26T16:10:03Z day: '28' department: - _id: HeEd doi: 10.1007/978-3-319-64689-3_32 editor: - first_name: Michael full_name: Felsberg, Michael last_name: Felsberg - first_name: Anders full_name: Heyden, Anders last_name: Heyden - first_name: Norbert full_name: Krüger, Norbert last_name: Krüger external_id: isi: - '000432085900032' intvolume: ' 10424' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1705.02045 month: '07' oa: 1 oa_version: Submitted Version page: 397 - 409 publication_identifier: issn: - '03029743' publication_status: published publisher: Springer publist_id: '6815' quality_controlled: '1' scopus_import: '1' status: public title: Streaming algorithm for Euler characteristic curves of multidimensional images type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 10424 year: '2017' ... --- _id: '84' abstract: - lang: eng text: The advent of high-throughput technologies and the concurrent advances in information sciences have led to a data revolution in biology. This revolution is most significant in molecular biology, with an increase in the number and scale of the “omics” projects over the last decade. Genomics projects, for example, have produced impressive advances in our knowledge of the information concealed into genomes, from the many genes that encode for the proteins that are responsible for most if not all cellular functions, to the noncoding regions that are now known to provide regulatory functions. Proteomics initiatives help to decipher the role of post-translation modifications on the protein structures and provide maps of protein-protein interactions, while functional genomics is the field that attempts to make use of the data produced by these projects to understand protein functions. The biggest challenge today is to assimilate the wealth of information provided by these initiatives into a conceptual framework that will help us decipher life. For example, the current views of the relationship between protein structure and function remain fragmented. We know of their sequences, more and more about their structures, we have information on their biological activities, but we have difficulties connecting this dotted line into an informed whole. We lack the experimental and computational tools for directly studying protein structure, function, and dynamics at the molecular and supra-molecular levels. In this chapter, we review some of the current developments in building the computational tools that are needed, focusing on the role that geometry and topology play in these efforts. One of our goals is to raise the general awareness about the importance of geometric methods in elucidating the mysterious foundations of our very existence. Another goal is the broadening of what we consider a geometric algorithm. There is plenty of valuable no-man’s-land between combinatorial and numerical algorithms, and it seems opportune to explore this land with a computational-geometric frame of mind. article_processing_charge: No author: - first_name: Herbert full_name: Edelsbrunner, Herbert id: 3FB178DA-F248-11E8-B48F-1D18A9856A87 last_name: Edelsbrunner orcid: 0000-0002-9823-6833 - first_name: Patrice full_name: Koehl, Patrice last_name: Koehl citation: ama: 'Edelsbrunner H, Koehl P. Computational topology for structural molecular biology. In: Toth C, O’Rourke J, Goodman J, eds. Handbook of Discrete and Computational Geometry, Third Edition. Handbook of Discrete and Computational Geometry. Taylor & Francis; 2017:1709-1735. doi:10.1201/9781315119601' apa: Edelsbrunner, H., & Koehl, P. (2017). Computational topology for structural molecular biology. In C. Toth, J. O’Rourke, & J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition (pp. 1709–1735). Taylor & Francis. https://doi.org/10.1201/9781315119601 chicago: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” In Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth, Joseph O’Rourke, and Jacob Goodman, 1709–35. Handbook of Discrete and Computational Geometry. Taylor & Francis, 2017. https://doi.org/10.1201/9781315119601. ieee: H. Edelsbrunner and P. Koehl, “Computational topology for structural molecular biology,” in Handbook of Discrete and Computational Geometry, Third Edition, C. Toth, J. O’Rourke, and J. Goodman, Eds. Taylor & Francis, 2017, pp. 1709–1735. ista: 'Edelsbrunner H, Koehl P. 2017.Computational topology for structural molecular biology. In: Handbook of Discrete and Computational Geometry, Third Edition. , 1709–1735.' mla: Edelsbrunner, Herbert, and Patrice Koehl. “Computational Topology for Structural Molecular Biology.” Handbook of Discrete and Computational Geometry, Third Edition, edited by Csaba Toth et al., Taylor & Francis, 2017, pp. 1709–35, doi:10.1201/9781315119601. short: H. Edelsbrunner, P. Koehl, in:, C. Toth, J. O’Rourke, J. Goodman (Eds.), Handbook of Discrete and Computational Geometry, Third Edition, Taylor & Francis, 2017, pp. 1709–1735. date_created: 2018-12-11T11:44:32Z date_published: 2017-11-09T00:00:00Z date_updated: 2023-10-16T11:15:22Z day: '09' department: - _id: HeEd doi: 10.1201/9781315119601 editor: - first_name: Csaba full_name: Toth, Csaba last_name: Toth - first_name: Joseph full_name: O'Rourke, Joseph last_name: O'Rourke - first_name: Jacob full_name: Goodman, Jacob last_name: Goodman language: - iso: eng month: '11' oa_version: None page: 1709 - 1735 publication: Handbook of Discrete and Computational Geometry, Third Edition publication_identifier: eisbn: - '9781498711425' publication_status: published publisher: Taylor & Francis publist_id: '7970' quality_controlled: '1' scopus_import: '1' series_title: Handbook of Discrete and Computational Geometry status: public title: Computational topology for structural molecular biology type: book_chapter user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2017' ... --- _id: '909' abstract: - lang: eng text: We study the lengths of curves passing through a fixed number of points on the boundary of a convex shape in the plane. We show that, for any convex shape K, there exist four points on the boundary of K such that the length of any curve passing through these points is at least half of the perimeter of K. It is also shown that the same statement does not remain valid with the additional constraint that the points are extreme points of K. Moreover, the factor ½ cannot be achieved with any fixed number of extreme points. We conclude the paper with a few other inequalities related to the perimeter of a convex shape. 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: Vladislav full_name: Vysotsky, Vladislav last_name: Vysotsky citation: ama: Akopyan A, Vysotsky V. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 2017;124(7):588-596. doi:10.4169/amer.math.monthly.124.7.588 apa: Akopyan, A., & Vysotsky, V. (2017). On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. Mathematical Association of America. https://doi.org/10.4169/amer.math.monthly.124.7.588 chicago: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly. Mathematical Association of America, 2017. https://doi.org/10.4169/amer.math.monthly.124.7.588. ieee: A. Akopyan and V. Vysotsky, “On the lengths of curves passing through boundary points of a planar convex shape,” The American Mathematical Monthly, vol. 124, no. 7. Mathematical Association of America, pp. 588–596, 2017. ista: Akopyan A, Vysotsky V. 2017. On the lengths of curves passing through boundary points of a planar convex shape. The American Mathematical Monthly. 124(7), 588–596. mla: Akopyan, Arseniy, and Vladislav Vysotsky. “On the Lengths of Curves Passing through Boundary Points of a Planar Convex Shape.” The American Mathematical Monthly, vol. 124, no. 7, Mathematical Association of America, 2017, pp. 588–96, doi:10.4169/amer.math.monthly.124.7.588. short: A. Akopyan, V. Vysotsky, The American Mathematical Monthly 124 (2017) 588–596. date_created: 2018-12-11T11:49:09Z date_published: 2017-01-01T00:00:00Z date_updated: 2023-10-17T11:24:57Z day: '01' department: - _id: HeEd doi: 10.4169/amer.math.monthly.124.7.588 ec_funded: 1 external_id: arxiv: - '1605.07997' isi: - '000413947300002' intvolume: ' 124' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1605.07997 month: '01' oa: 1 oa_version: Submitted Version page: 588 - 596 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: The American Mathematical Monthly publication_identifier: issn: - '00029890' publication_status: published publisher: Mathematical Association of America publist_id: '6534' quality_controlled: '1' scopus_import: '1' status: public title: On the lengths of curves passing through boundary points of a planar convex shape type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 124 year: '2017' ... --- _id: '1149' abstract: - lang: eng text: 'We study the usefulness of two most prominent publicly available rigorous ODE integrators: one provided by the CAPD group (capd.ii.uj.edu.pl), the other based on the COSY Infinity project (cosyinfinity.org). Both integrators are capable of handling entire sets of initial conditions and provide tight rigorous outer enclosures of the images under a time-T map. We conduct extensive benchmark computations using the well-known Lorenz system, and compare the computation time against the final accuracy achieved. We also discuss the effect of a few technical parameters, such as the order of the numerical integration method, the value of T, and the phase space resolution. We conclude that COSY may provide more precise results due to its ability of avoiding the variable dependency problem. However, the overall cost of computations conducted using CAPD is typically lower, especially when intervals of parameters are involved. Moreover, access to COSY is limited (registration required) and the rigorous ODE integrators are not publicly available, while CAPD is an open source free software project. Therefore, we recommend the latter integrator for this kind of computations. Nevertheless, proper choice of the various integration parameters turns out to be of even greater importance than the choice of the integrator itself. © 2016 IMACS. Published by Elsevier B.V. All rights reserved.' acknowledgement: "MG was partially supported by FAPESP grants 2013/07460-7 and 2010/00875-9, and by CNPq grants 305860/2013-5 and 306453/2009-6, Brazil. The work of HK was partially supported by Grant-in-Aid for Scientific Research (Nos.24654022, 25287029), Ministry of Education, Science, Technology, Culture and Sports, Japan. KM was supported by NSF grants NSF-DMS-0835621, 0915019, 1125174, 1248071, and contracts from AFOSR and DARPA. TM was supported by Grant-in-Aid for JSPS Fellows No. 245312. A part of the research of TM and HK was also supported by JST, CREST.\r\n\r\nResearch conducted by PP has received funding from Fundo Europeu de Desenvolvimento Regional (FEDER) through COMPETE – Programa Operacional Factores de Competitividade (POFC) and from the Portuguese national funds through Fundação para a Ciência e a Tecnologia (FCT) in the framework of the research project FCOMP-01-0124-FEDER-010645 (Ref. FCT PTDC/MAT/098871/2008); from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement No. 622033; and from the same sources as HK.\r\n\r\nThe authors express their gratitude to the Department of Mathematics of Kyoto University for making their server available for conducting the computations described in the paper, and to the reviewers for helpful comments that contributed towards increasing the quality of the paper." author: - first_name: Tomoyuki full_name: Miyaji, Tomoyuki last_name: Miyaji - first_name: Pawel full_name: Pilarczyk, Pawel id: 3768D56A-F248-11E8-B48F-1D18A9856A87 last_name: Pilarczyk - first_name: Marcio full_name: Gameiro, Marcio last_name: Gameiro - first_name: Hiroshi full_name: Kokubu, Hiroshi last_name: Kokubu - first_name: Konstantin full_name: Mischaikow, Konstantin last_name: Mischaikow citation: ama: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 2016;107:34-47. doi:10.1016/j.apnum.2016.04.005 apa: Miyaji, T., Pilarczyk, P., Gameiro, M., Kokubu, H., & Mischaikow, K. (2016). A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. Elsevier. https://doi.org/10.1016/j.apnum.2016.04.005 chicago: Miyaji, Tomoyuki, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics. Elsevier, 2016. https://doi.org/10.1016/j.apnum.2016.04.005. ieee: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, and K. Mischaikow, “A study of rigorous ODE integrators for multi scale set oriented computations,” Applied Numerical Mathematics, vol. 107. Elsevier, pp. 34–47, 2016. ista: Miyaji T, Pilarczyk P, Gameiro M, Kokubu H, Mischaikow K. 2016. A study of rigorous ODE integrators for multi scale set oriented computations. Applied Numerical Mathematics. 107, 34–47. mla: Miyaji, Tomoyuki, et al. “A Study of Rigorous ODE Integrators for Multi Scale Set Oriented Computations.” Applied Numerical Mathematics, vol. 107, Elsevier, 2016, pp. 34–47, doi:10.1016/j.apnum.2016.04.005. short: T. Miyaji, P. Pilarczyk, M. Gameiro, H. Kokubu, K. Mischaikow, Applied Numerical Mathematics 107 (2016) 34–47. date_created: 2018-12-11T11:50:25Z date_published: 2016-09-01T00:00:00Z date_updated: 2021-01-12T06:48:38Z day: '01' department: - _id: HeEd doi: 10.1016/j.apnum.2016.04.005 ec_funded: 1 intvolume: ' 107' language: - iso: eng month: '09' oa_version: None page: 34 - 47 project: - _id: 255F06BE-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '622033' name: Persistent Homology - Images, Data and Maps publication: Applied Numerical Mathematics publication_status: published publisher: Elsevier publist_id: '6209' quality_controlled: '1' scopus_import: 1 status: public title: A study of rigorous ODE integrators for multi scale set oriented computations type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 107 year: '2016' ... --- _id: '1216' abstract: - lang: eng text: 'A framework fo r extracting features in 2D transient flows, based on the acceleration field to ensure Galilean invariance is proposed in this paper. The minima of the acceleration magnitude (a superset of acceleration zeros) are extracted and discriminated into vortices and saddle points, based on the spectral properties of the velocity Jacobian. The extraction of topological features is performed with purely combinatorial algorithms from discrete computational topology. The feature points are prioritized with persistence, as a physically meaningful importance measure. These feature points are tracked in time with a robust algorithm for tracking features. Thus, a space-time hierarchy of the minima is built and vortex merging events are detected. We apply the acceleration feature extraction strategy to three two-dimensional shear flows: (1) an incompressible periodic cylinder wake, (2) an incompressible planar mixing layer and (3) a weakly compressible planar jet. The vortex-like acceleration feature points are shown to be well aligned with acceleration zeros, maxima of the vorticity magnitude, minima of the pressure field and minima of λ2.' acknowledgement: "The authors acknowledge funding of the German Re-\r\nsearch Foundation \ (DFG) via the Collaborative Re-\r\nsearch Center (SFB 557) \\Control of \ Complex Turbu-\r\nlent Shear Flows\" and the Emmy Noether Program.\r\nFurther \ funding was provided by the Zuse Institute\r\nBerlin (ZIB), the DFG-CNRS \ research group \\Noise\r\nGeneration in Turbulent Flows\" (2003{2010), the Chaire\r\nd'Excellence 'Closed-loop control of turbulent shear ows\r\nusing reduced-order models' (TUCOROM) of the French\r\nAgence Nationale de la Recherche (ANR), and the Eu-\r\nropean Social \ Fund (ESF App. No. 100098251). We\r\nthank the Ambrosys Ltd. Society \ for Complex Sys-\r\ntems Management and the Bernd R. Noack Cybernet-\r\nics \ Foundation for additional support. A part of this\r\nwork was performed using HPC resources from GENCI-[CCRT/CINES/IDRIS] supported by the Grant 2011-\r\n[x2011020912" author: - first_name: Jens full_name: Kasten, Jens last_name: Kasten - first_name: Jan full_name: Reininghaus, Jan id: 4505473A-F248-11E8-B48F-1D18A9856A87 last_name: Reininghaus - first_name: Ingrid full_name: Hotz, Ingrid last_name: Hotz - first_name: Hans full_name: Hege, Hans last_name: Hege - first_name: Bernd full_name: Noack, Bernd last_name: Noack - first_name: Guillaume full_name: Daviller, Guillaume last_name: Daviller - first_name: Marek full_name: Morzyński, Marek last_name: Morzyński citation: ama: Kasten J, Reininghaus J, Hotz I, et al. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 2016;68(1):55-80. apa: Kasten, J., Reininghaus, J., Hotz, I., Hege, H., Noack, B., Daviller, G., & Morzyński, M. (2016). Acceleration feature points of unsteady shear flows. Archives of Mechanics. Polish Academy of Sciences Publishing House. chicago: Kasten, Jens, Jan Reininghaus, Ingrid Hotz, Hans Hege, Bernd Noack, Guillaume Daviller, and Marek Morzyński. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics. Polish Academy of Sciences Publishing House, 2016. ieee: J. Kasten et al., “Acceleration feature points of unsteady shear flows,” Archives of Mechanics, vol. 68, no. 1. Polish Academy of Sciences Publishing House, pp. 55–80, 2016. ista: Kasten J, Reininghaus J, Hotz I, Hege H, Noack B, Daviller G, Morzyński M. 2016. Acceleration feature points of unsteady shear flows. Archives of Mechanics. 68(1), 55–80. mla: Kasten, Jens, et al. “Acceleration Feature Points of Unsteady Shear Flows.” Archives of Mechanics, vol. 68, no. 1, Polish Academy of Sciences Publishing House, 2016, pp. 55–80. short: J. Kasten, J. Reininghaus, I. Hotz, H. Hege, B. Noack, G. Daviller, M. Morzyński, Archives of Mechanics 68 (2016) 55–80. date_created: 2018-12-11T11:50:46Z date_published: 2016-01-01T00:00:00Z date_updated: 2021-01-12T06:49:09Z day: '01' department: - _id: HeEd intvolume: ' 68' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: http://am.ippt.pan.pl/am/article/viewFile/v68p55/pdf month: '01' oa: 1 oa_version: Published Version page: 55 - 80 publication: Archives of Mechanics publication_status: published publisher: Polish Academy of Sciences Publishing House publist_id: '6118' quality_controlled: '1' scopus_import: 1 status: public title: Acceleration feature points of unsteady shear flows type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 68 year: '2016' ...