caa a22 4500 606166149 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10440-014-9950-8 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9950-8 Optimal Geometric Control Applied to the Protein Misfolding Cyclic Amplification Process [Elektronische Daten] [Monique Chyba, Jean-Michel Coron, Pierre Gabriel, Alain Jacquemard, Geoff Patterson, Gautier Picot, Peipei Shang] Protein Misfolding Cyclic Amplification is a procedure used to accelerate the prion-replication process involved during the incubation period of transmissible spongiform encephalopathies. This technique could be used to design an efficient diagnosis test detecting the abnormally-shaped protein responsible of the decease before the affected person is at an advanced stage of the illness. In this paper, we investigate the open problem to determine what is the optimal strategy to produce maximum replication in a fixed time. Primarily, we expand on prior attempt to answer this question in general, and provide results under some specific assumptions. Springer Science+Business Media Dordrecht, 2014 Transmissible spongiform encephalopathies nationallicence Nucleated polymerization nationallicence Optimal control nationallicence Singular extremals nationallicence Chyba Monique Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut Coron Jean-Michel Laboratoire Jacques-Louis Lions, UMR 7598, Université Pierre et Marie Curie-Paris 6, 75005, Paris, France aut Gabriel Pierre Laboratoire de Mathématiques de Versailles, CNRS UMR 8100, Université de Versailles Saint-Quentin, 45 Avenue des Etats-Unis, 78035, Versailles, France aut Jacquemard Alain Institut de Mathématiques de Bourgogne, UMR 5584, Université de Bourgogne, 9 avenue Alain Savary, 21078, Dijon, France aut Patterson Geoff Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut Picot Gautier Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut Shang Peipei Department of Mathematics, Tongji University, 200092, Shanghai, China aut Acta Applicandae Mathematicae Springer Netherlands 135/1(2015-02-01), 145-173 0167-8019 135:1<145 2015 135 10440 https://doi.org/10.1007/s10440-014-9950-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9950-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chyba Monique Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut NATIONALLICENCE 700 1- Coron Jean-Michel Laboratoire Jacques-Louis Lions, UMR 7598, Université Pierre et Marie Curie-Paris 6, 75005, Paris, France aut NATIONALLICENCE 700 1- Gabriel Pierre Laboratoire de Mathématiques de Versailles, CNRS UMR 8100, Université de Versailles Saint-Quentin, 45 Avenue des Etats-Unis, 78035, Versailles, France aut NATIONALLICENCE 700 1- Jacquemard Alain Institut de Mathématiques de Bourgogne, UMR 5584, Université de Bourgogne, 9 avenue Alain Savary, 21078, Dijon, France aut NATIONALLICENCE 700 1- Patterson Geoff Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut NATIONALLICENCE 700 1- Picot Gautier Mathematics Department, University of Hawai‘i, 96822, Honolulu, HI, USA aut NATIONALLICENCE 700 1- Shang Peipei Department of Mathematics, Tongji University, 200092, Shanghai, China aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 135/1(2015-02-01), 145-173 0167-8019 135:1<145 2015 135 10440