{"quality_controlled":"1","scopus_import":1,"title":"Scale-invariant systems realize nonlinear differential operators","oa_version":"Preprint","publist_id":"5950","language":[{"iso":"eng"}],"file":[{"file_id":"5203","creator":"system","date_updated":"2020-07-14T12:44:43Z","date_created":"2018-12-12T10:16:17Z","checksum":"7219432b43defc62a0d45f48d4ce6a19","access_level":"local","relation":"main_file","file_name":"IST-2017-810-v1+1_root.pdf","file_size":539166,"content_type":"application/pdf"}],"pubrep_id":"810","day":"28","year":"2016","publisher":"IEEE","ec_funded":1,"date_published":"2016-07-28T00:00:00Z","_id":"1320","conference":{"start_date":"2016-07-06","end_date":"2016-07-08","location":"Boston, MA, USA","name":"ACC: American Control Conference"},"doi":"10.1109/ACC.2016.7526722","author":[{"last_name":"Lang","id":"29E0800A-F248-11E8-B48F-1D18A9856A87","full_name":"Lang, Moritz","first_name":"Moritz"},{"last_name":"Sontag","first_name":"Eduardo","full_name":"Sontag, Eduardo"}],"article_number":"7526722","abstract":[{"text":"In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u → pu, p &gt; 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input.","lang":"eng"}],"publication_status":"published","has_accepted_license":"1","type":"conference","date_updated":"2021-01-12T06:49:51Z","volume":"2016-July","status":"public","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"file_date_updated":"2020-07-14T12:44:43Z","ddc":["003","621"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° [291734]. Work supported in part by grants AFOSR FA9550-14-1-0060 and NIH 1R01GM100473.","department":[{"_id":"CaGu"},{"_id":"GaTk"}],"month":"07","date_created":"2018-12-11T11:51:21Z","citation":{"short":"M. Lang, E. Sontag, in:, IEEE, 2016.","ama":"Lang M, Sontag E. Scale-invariant systems realize nonlinear differential operators. In: Vol 2016-July. IEEE; 2016. doi:<a href=\"https://doi.org/10.1109/ACC.2016.7526722\">10.1109/ACC.2016.7526722</a>","mla":"Lang, Moritz, and Eduardo Sontag. <i>Scale-Invariant Systems Realize Nonlinear Differential Operators</i>. Vol. 2016–July, 7526722, IEEE, 2016, doi:<a href=\"https://doi.org/10.1109/ACC.2016.7526722\">10.1109/ACC.2016.7526722</a>.","ieee":"M. Lang and E. Sontag, “Scale-invariant systems realize nonlinear differential operators,” presented at the ACC: American Control Conference, Boston, MA, USA, 2016, vol. 2016–July.","ista":"Lang M, Sontag E. 2016. Scale-invariant systems realize nonlinear differential operators. ACC: American Control Conference vol. 2016–July, 7526722.","chicago":"Lang, Moritz, and Eduardo Sontag. “Scale-Invariant Systems Realize Nonlinear Differential Operators,” Vol. 2016–July. IEEE, 2016. <a href=\"https://doi.org/10.1109/ACC.2016.7526722\">https://doi.org/10.1109/ACC.2016.7526722</a>.","apa":"Lang, M., &#38; Sontag, E. (2016). Scale-invariant systems realize nonlinear differential operators (Vol. 2016–July). Presented at the ACC: American Control Conference, Boston, MA, USA: IEEE. <a href=\"https://doi.org/10.1109/ACC.2016.7526722\">https://doi.org/10.1109/ACC.2016.7526722</a>"}}