[{"abstract":[{"lang":"eng","text":"A central problem of algebraic topology is to understand the homotopy groups  𝜋𝑑(𝑋)  of a topological space X. For the computational version of the problem, it is well known that there is no algorithm to decide whether the fundamental group  𝜋1(𝑋)  of a given finite simplicial complex X is trivial. On the other hand, there are several algorithms that, given a finite simplicial complex X that is simply connected (i.e., with   𝜋1(𝑋)  trivial), compute the higher homotopy group   𝜋𝑑(𝑋)  for any given   𝑑≥2 . However, these algorithms come with a caveat: They compute the isomorphism type of   𝜋𝑑(𝑋) ,   𝑑≥2  as an abstract finitely generated abelian group given by generators and relations, but they work with very implicit representations of the elements of   𝜋𝑑(𝑋) . Converting elements of this abstract group into explicit geometric maps from the d-dimensional sphere   𝑆𝑑  to X has been one of the main unsolved problems in the emerging field of computational homotopy theory. Here we present an algorithm that, given a simply connected space X, computes   𝜋𝑑(𝑋)  and represents its elements as simplicial maps from a suitable triangulation of the d-sphere   𝑆𝑑  to X. For fixed d, the algorithm runs in time exponential in   size(𝑋) , the number of simplices of X. Moreover, we prove that this is optimal: For every fixed   𝑑≥2 , we construct a family of simply connected spaces X such that for any simplicial map representing a generator of   𝜋𝑑(𝑋) , the size of the triangulation of   𝑆𝑑  on which the map is defined, is exponential in size(𝑋) ."}],"_id":"6774","date_published":"2018-12-01T00:00:00Z","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"6775","date_created":"2019-08-08T06:55:21Z","file_name":"2018_JourAppliedComputTopology_Filakovsky.pdf","file_size":1056278,"creator":"dernst","checksum":"cf9e7fcd2a113dd4828774fc75cdb7e8","date_updated":"2020-07-14T12:47:40Z","access_level":"open_access"}],"issue":"3-4","volume":2,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"file_date_updated":"2020-07-14T12:47:40Z","oa":1,"publication_status":"published","year":"2018","has_accepted_license":"1","oa_version":"Published Version","article_type":"original","publication_identifier":{"eissn":["2367-1734"],"issn":["2367-1726"]},"date_updated":"2023-09-07T13:10:36Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-08-08T06:47:40Z","month":"12","page":"177-231","status":"public","intvolume":"         2","quality_controlled":"1","department":[{"_id":"UlWa"}],"publication":"Journal of Applied and Computational Topology","publisher":"Springer","type":"journal_article","author":[{"id":"3E8AF77E-F248-11E8-B48F-1D18A9856A87","last_name":"Filakovský","first_name":"Marek","full_name":"Filakovský, Marek"},{"first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8878-8397"},{"full_name":"Wagner, Uli","first_name":"Uli","last_name":"Wagner","orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Zhechev","first_name":"Stephan Y","full_name":"Zhechev, Stephan Y","id":"3AA52972-F248-11E8-B48F-1D18A9856A87"}],"day":"01","title":"Computing simplicial representatives of homotopy group elements","citation":{"ama":"Filakovský M, Franek P, Wagner U, Zhechev SY. Computing simplicial representatives of homotopy group elements. <i>Journal of Applied and Computational Topology</i>. 2018;2(3-4):177-231. doi:<a href=\"https://doi.org/10.1007/s41468-018-0021-5\">10.1007/s41468-018-0021-5</a>","apa":"Filakovský, M., Franek, P., Wagner, U., &#38; Zhechev, S. Y. (2018). Computing simplicial representatives of homotopy group elements. <i>Journal of Applied and Computational Topology</i>. Springer. <a href=\"https://doi.org/10.1007/s41468-018-0021-5\">https://doi.org/10.1007/s41468-018-0021-5</a>","short":"M. Filakovský, P. Franek, U. Wagner, S.Y. Zhechev, Journal of Applied and Computational Topology 2 (2018) 177–231.","mla":"Filakovský, Marek, et al. “Computing Simplicial Representatives of Homotopy Group Elements.” <i>Journal of Applied and Computational Topology</i>, vol. 2, no. 3–4, Springer, 2018, pp. 177–231, doi:<a href=\"https://doi.org/10.1007/s41468-018-0021-5\">10.1007/s41468-018-0021-5</a>.","chicago":"Filakovský, Marek, Peter Franek, Uli Wagner, and Stephan Y Zhechev. “Computing Simplicial Representatives of Homotopy Group Elements.” <i>Journal of Applied and Computational Topology</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s41468-018-0021-5\">https://doi.org/10.1007/s41468-018-0021-5</a>.","ista":"Filakovský M, Franek P, Wagner U, Zhechev SY. 2018. Computing simplicial representatives of homotopy group elements. Journal of Applied and Computational Topology. 2(3–4), 177–231.","ieee":"M. Filakovský, P. Franek, U. Wagner, and S. Y. Zhechev, “Computing simplicial representatives of homotopy group elements,” <i>Journal of Applied and Computational Topology</i>, vol. 2, no. 3–4. Springer, pp. 177–231, 2018."},"ddc":["514"],"doi":"10.1007/s41468-018-0021-5","language":[{"iso":"eng"}],"project":[{"call_identifier":"FWF","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","name":"Robust invariants of Nonlinear Systems","grant_number":"M01980"},{"call_identifier":"FWF","_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund"}],"related_material":{"record":[{"status":"public","id":"6681","relation":"dissertation_contains"}]}},{"publication":"The International Journal of Robotics Research","department":[{"_id":"UlWa"}],"quality_controlled":"1","status":"public","intvolume":"        37","publisher":"SAGE Publications","isi":1,"month":"10","date_created":"2019-02-13T09:36:20Z","page":"1500-1516","language":[{"iso":"eng"}],"doi":"10.1177/0278364918808367","day":"24","type":"journal_article","author":[{"last_name":"Rohou","full_name":"Rohou, Simon","first_name":"Simon"},{"last_name":"Franek","full_name":"Franek, Peter","first_name":"Peter","orcid":"0000-0001-8878-8397","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Clément","full_name":"Aubry, Clément","last_name":"Aubry"},{"full_name":"Jaulin, Luc","first_name":"Luc","last_name":"Jaulin"}],"citation":{"ieee":"S. Rohou, P. Franek, C. Aubry, and L. Jaulin, “Proving the existence of loops in robot trajectories,” <i>The International Journal of Robotics Research</i>, vol. 37, no. 12. SAGE Publications, pp. 1500–1516, 2018.","ista":"Rohou S, Franek P, Aubry C, Jaulin L. 2018. Proving the existence of loops in robot trajectories. The International Journal of Robotics Research. 37(12), 1500–1516.","chicago":"Rohou, Simon, Peter Franek, Clément Aubry, and Luc Jaulin. “Proving the Existence of Loops in Robot Trajectories.” <i>The International Journal of Robotics Research</i>. SAGE Publications, 2018. <a href=\"https://doi.org/10.1177/0278364918808367\">https://doi.org/10.1177/0278364918808367</a>.","mla":"Rohou, Simon, et al. “Proving the Existence of Loops in Robot Trajectories.” <i>The International Journal of Robotics Research</i>, vol. 37, no. 12, SAGE Publications, 2018, pp. 1500–16, doi:<a href=\"https://doi.org/10.1177/0278364918808367\">10.1177/0278364918808367</a>.","short":"S. Rohou, P. Franek, C. Aubry, L. Jaulin, The International Journal of Robotics Research 37 (2018) 1500–1516.","apa":"Rohou, S., Franek, P., Aubry, C., &#38; Jaulin, L. (2018). Proving the existence of loops in robot trajectories. <i>The International Journal of Robotics Research</i>. SAGE Publications. <a href=\"https://doi.org/10.1177/0278364918808367\">https://doi.org/10.1177/0278364918808367</a>","ama":"Rohou S, Franek P, Aubry C, Jaulin L. Proving the existence of loops in robot trajectories. <i>The International Journal of Robotics Research</i>. 2018;37(12):1500-1516. doi:<a href=\"https://doi.org/10.1177/0278364918808367\">10.1177/0278364918808367</a>"},"title":"Proving the existence of loops in robot trajectories","volume":37,"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.01341"}],"oa":1,"_id":"5960","date_published":"2018-10-24T00:00:00Z","abstract":[{"lang":"eng","text":"In this paper we present a reliable method to verify the existence of loops along the uncertain trajectory of a robot, based on proprioceptive measurements only, within a bounded-error context. The loop closure detection is one of the key points in simultaneous localization and mapping (SLAM) methods, especially in homogeneous environments with difficult scenes recognitions. The proposed approach is generic and could be coupled with conventional SLAM algorithms to reliably reduce their computing burden, thus improving the localization and mapping processes in the most challenging environments such as unexplored underwater extents. To prove that a robot performed a loop whatever the uncertainties in its evolution, we employ the notion of topological degree that originates in the field of differential topology. We show that a verification tool based on the topological degree is an optimal method for proving robot loops. This is demonstrated both on datasets from real missions involving autonomous underwater vehicles and by a mathematical discussion."}],"arxiv":1,"article_processing_charge":"No","issue":"12","external_id":{"arxiv":["1712.01341"],"isi":["000456881100004"]},"scopus_import":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_updated":"2023-09-19T10:41:59Z","publication_identifier":{"eissn":["1741-3176"],"issn":["0278-3649"]},"year":"2018","oa_version":"Preprint"},{"publication_identifier":{"issn":["15320073"]},"scopus_import":1,"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:03:12Z","year":"2017","oa_version":"Submitted Version","publist_id":"7246","volume":19,"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1507.04310"}],"publication_status":"published","_id":"568","date_published":"2017-01-01T00:00:00Z","abstract":[{"text":"We study robust properties of zero sets of continuous maps f: X → ℝn. Formally, we analyze the family Z&lt; r(f) := (g-1(0): ||g - f|| &lt; r) of all zero sets of all continuous maps g closer to f than r in the max-norm. All of these sets are outside A := (x: |f(x)| ≥ r) and we claim that Z&lt; r(f) is fully determined by A and an element of a certain cohomotopy group which (by a recent result) is computable whenever the dimension of X is at most 2n - 3. By considering all r &gt; 0 simultaneously, the pointed cohomotopy groups form a persistence module-a structure leading to persistence diagrams as in the case of persistent homology or well groups. Eventually, we get a descriptor of persistent robust properties of zero sets that has better descriptive power (Theorem A) and better computability status (Theorem B) than the established well diagrams. Moreover, if we endow every point of each zero set with gradients of the perturbation, the robust description of the zero sets by elements of cohomotopy groups is in some sense the best possible (Theorem C).","lang":"eng"}],"issue":"2","doi":"10.4310/HHA.2017.v19.n2.a16","language":[{"iso":"eng"}],"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"},{"grant_number":"701309","name":"Atomic-Resolution Structures of Mitochondrial Respiratory Chain Supercomplexes (H2020)","call_identifier":"H2020","_id":"2590DB08-B435-11E9-9278-68D0E5697425"}],"author":[{"first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krcál, Marek","first_name":"Marek","last_name":"Krcál","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","day":"01","title":"Persistence of zero sets","citation":{"short":"P. Franek, M. Krcál, Homology, Homotopy and Applications 19 (2017) 313–342.","ama":"Franek P, Krcál M. Persistence of zero sets. <i>Homology, Homotopy and Applications</i>. 2017;19(2):313-342. doi:<a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">10.4310/HHA.2017.v19.n2.a16</a>","apa":"Franek, P., &#38; Krcál, M. (2017). Persistence of zero sets. <i>Homology, Homotopy and Applications</i>. International Press. <a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">https://doi.org/10.4310/HHA.2017.v19.n2.a16</a>","chicago":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” <i>Homology, Homotopy and Applications</i>. International Press, 2017. <a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">https://doi.org/10.4310/HHA.2017.v19.n2.a16</a>.","ista":"Franek P, Krcál M. 2017. Persistence of zero sets. Homology, Homotopy and Applications. 19(2), 313–342.","ieee":"P. Franek and M. Krcál, “Persistence of zero sets,” <i>Homology, Homotopy and Applications</i>, vol. 19, no. 2. International Press, pp. 313–342, 2017.","mla":"Franek, Peter, and Marek Krcál. “Persistence of Zero Sets.” <i>Homology, Homotopy and Applications</i>, vol. 19, no. 2, International Press, 2017, pp. 313–42, doi:<a href=\"https://doi.org/10.4310/HHA.2017.v19.n2.a16\">10.4310/HHA.2017.v19.n2.a16</a>."},"ec_funded":1,"status":"public","intvolume":"        19","publication":"Homology, Homotopy and Applications","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","publisher":"International Press","date_created":"2018-12-11T11:47:14Z","month":"01","page":"313 - 342"},{"day":"01","author":[{"id":"473294AE-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek"},{"last_name":"Krcál","full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"type":"journal_article","citation":{"short":"P. Franek, M. Krcál, Discrete &#38; Computational Geometry 56 (2016) 126–164.","apa":"Franek, P., &#38; Krcál, M. (2016). On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. Springer. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>","ama":"Franek P, Krcál M. On computability and triviality of well groups. <i>Discrete &#38; Computational Geometry</i>. 2016;56(1):126-164. doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1. Springer, pp. 126–164, 2016.","ista":"Franek P, Krcál M. 2016. On computability and triviality of well groups. Discrete &#38; Computational Geometry. 56(1), 126–164.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>. Springer, 2016. <a href=\"https://doi.org/10.1007/s00454-016-9794-2\">https://doi.org/10.1007/s00454-016-9794-2</a>.","mla":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups.” <i>Discrete &#38; Computational Geometry</i>, vol. 56, no. 1, Springer, 2016, pp. 126–64, doi:<a href=\"https://doi.org/10.1007/s00454-016-9794-2\">10.1007/s00454-016-9794-2</a>."},"ec_funded":1,"title":"On computability and triviality of well groups","language":[{"iso":"eng"}],"ddc":["510"],"doi":"10.1007/s00454-016-9794-2","project":[{"call_identifier":"FWF","_id":"25F8B9BC-B435-11E9-9278-68D0E5697425","grant_number":"M01980","name":"Robust invariants of Nonlinear Systems"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"related_material":{"record":[{"status":"public","id":"1510","relation":"earlier_version"}]},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","month":"07","date_created":"2018-12-11T11:51:51Z","page":"126 - 164","publication":"Discrete & Computational Geometry","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","status":"public","intvolume":"        56","publisher":"Springer","publist_id":"5799","oa_version":"Published Version","has_accepted_license":"1","year":"2016","scopus_import":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-02-23T10:02:11Z","file":[{"date_created":"2018-12-12T10:10:55Z","content_type":"application/pdf","relation":"main_file","file_id":"4846","checksum":"e0da023abf6b72abd8c6a8c76740d53c","date_updated":"2020-07-14T12:44:53Z","access_level":"open_access","file_name":"IST-2016-614-v1+1_s00454-016-9794-2.pdf","creator":"system","file_size":905303}],"_id":"1408","date_published":"2016-07-01T00:00:00Z","abstract":[{"text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map (Formula presented.) on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within (Formula presented.) distance r from f for a given (Formula presented.). The main drawback of the approach is that the computability of well groups was shown only when (Formula presented.) or (Formula presented.). Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of (Formula presented.) by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and (Formula presented.), our approximation of the (Formula presented.)th well group is exact. For the second part, we find examples of maps (Formula presented.) with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","issue":"1","file_date_updated":"2020-07-14T12:44:53Z","pubrep_id":"614","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":56,"publication_status":"published","oa":1},{"title":"On computability and triviality of well groups","conference":{"location":"Eindhoven, Netherlands","name":"SoCG: Symposium on Computational Geometry","start_date":"2015-06-22","end_date":"2015-06-25"},"citation":{"short":"P. Franek, M. Krcál, in:, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–856.","apa":"Franek, P., &#38; Krcál, M. (2015). On computability and triviality of well groups (Vol. 34, pp. 842–856). Presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>","ama":"Franek P, Krcál M. On computability and triviality of well groups. In: Vol 34. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2015:842-856. doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>","ieee":"P. Franek and M. Krcál, “On computability and triviality of well groups,” presented at the SoCG: Symposium on Computational Geometry, Eindhoven, Netherlands, 2015, vol. 34, pp. 842–856.","ista":"Franek P, Krcál M. 2015. On computability and triviality of well groups. SoCG: Symposium on Computational Geometry, LIPIcs, vol. 34, 842–856.","chicago":"Franek, Peter, and Marek Krcál. “On Computability and Triviality of Well Groups,” 34:842–56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. <a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">https://doi.org/10.4230/LIPIcs.SOCG.2015.842</a>.","mla":"Franek, Peter, and Marek Krcál. <i>On Computability and Triviality of Well Groups</i>. Vol. 34, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015, pp. 842–56, doi:<a href=\"https://doi.org/10.4230/LIPIcs.SOCG.2015.842\">10.4230/LIPIcs.SOCG.2015.842</a>."},"ec_funded":1,"author":[{"first_name":"Peter","full_name":"Franek, Peter","last_name":"Franek","id":"473294AE-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krcál","full_name":"Krcál, Marek","first_name":"Marek","id":"33E21118-F248-11E8-B48F-1D18A9856A87"}],"type":"conference","alternative_title":["LIPIcs"],"day":"11","project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"1408"}]},"ddc":["510"],"doi":"10.4230/LIPIcs.SOCG.2015.842","language":[{"iso":"eng"}],"page":"842 - 856","date_created":"2018-12-11T11:52:26Z","month":"06","publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","intvolume":"        34","status":"public","department":[{"_id":"UlWa"},{"_id":"HeEd"}],"quality_controlled":"1","has_accepted_license":"1","year":"2015","oa_version":"Published Version","publist_id":"5667","scopus_import":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-02-21T17:02:57Z","_id":"1510","date_published":"2015-06-11T00:00:00Z","abstract":[{"lang":"eng","text":"The concept of well group in a special but important case captures homological properties of the zero set of a continuous map f from K to R^n on a compact space K that are invariant with respect to perturbations of f. The perturbations are arbitrary continuous maps within L_infty distance r from f for a given r &gt; 0. The main drawback of the approach is that the computability of well groups was shown only when dim K = n or n = 1. Our contribution to the theory of well groups is twofold: on the one hand we improve on the computability issue, but on the other hand we present a range of examples where the well groups are incomplete invariants, that is, fail to capture certain important robust properties of the zero set. For the first part, we identify a computable subgroup of the well group that is obtained by cap product with the pullback of the orientation of R^n by f. In other words, well groups can be algorithmically approximated from below. When f is smooth and dim K &lt; 2n-2, our approximation of the (dim K-n)th well group is exact. For the second part, we find examples of maps f, f' from K to R^n with all well groups isomorphic but whose perturbations have different zero sets. We discuss on a possible replacement of the well groups of vector valued maps by an invariant of a better descriptive power and computability status. "}],"file":[{"access_level":"open_access","date_updated":"2020-07-14T12:44:59Z","checksum":"49eb5021caafaabe5356c65b9c5f8c9c","file_size":623563,"creator":"system","file_name":"IST-2016-503-v1+1_32.pdf","date_created":"2018-12-12T10:13:19Z","relation":"main_file","file_id":"5001","content_type":"application/pdf"}],"oa":1,"publication_status":"published","pubrep_id":"503","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"volume":34,"file_date_updated":"2020-07-14T12:44:59Z"}]