Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe th...

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Autores principales:	Kathrin Hellmuth, Christian Klingenberg, Qin Li, Min Tang
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	inverse problems Bayesian approach kinetic chemotaxis equation Keller–Segel model multiscale modeling asymptotic analysis Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/24418025d2d4405ea1cb9357a8feca2d
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id	oai:doaj.org-article:24418025d2d4405ea1cb9357a8feca2d
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spelling	oai:doaj.org-article:24418025d2d4405ea1cb9357a8feca2d2021-11-25T17:17:16ZMultiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting10.3390/computation91101192079-3197https://doaj.org/article/24418025d2d4405ea1cb9357a8feca2d2021-11-01T00:00:00Zhttps://www.mdpi.com/2079-3197/9/11/119https://doaj.org/toc/2079-3197Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism’s movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms’ population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.Kathrin HellmuthChristian KlingenbergQin LiMin TangMDPI AGarticleinverse problemsBayesian approachkinetic chemotaxis equationKeller–Segel modelmultiscale modelingasymptotic analysisElectronic computers. Computer scienceQA75.5-76.95ENComputation, Vol 9, Iss 119, p 119 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	inverse problems Bayesian approach kinetic chemotaxis equation Keller–Segel model multiscale modeling asymptotic analysis Electronic computers. Computer science QA75.5-76.95
spellingShingle	inverse problems Bayesian approach kinetic chemotaxis equation Keller–Segel model multiscale modeling asymptotic analysis Electronic computers. Computer science QA75.5-76.95 Kathrin Hellmuth Christian Klingenberg Qin Li Min Tang Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
description	Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller–Segel equation and a chemotaxis kinetic equation. These two equations describe the organism’s movement at the macro- and mesoscopic level, respectively, and are asymptotically equivalent in the parabolic regime. The way in which the organism responds to a chemical stimulus is embedded in the diffusion/advection coefficients of the Keller–Segel equation or the turning kernel of the chemotaxis kinetic equation. Experiments are conducted to measure the time dynamics of the organisms’ population level movement when reacting to certain stimulation. From this, one infers the chemotaxis response, which constitutes an inverse problem. In this paper, we discuss the relation between both the macro- and mesoscopic inverse problems, each of which is associated with two different forward models. The discussion is presented in the Bayesian framework, where the posterior distribution of the turning kernel of the organism population is sought. We prove the asymptotic equivalence of the two posterior distributions.
format	article
author	Kathrin Hellmuth Christian Klingenberg Qin Li Min Tang
author_facet	Kathrin Hellmuth Christian Klingenberg Qin Li Min Tang
author_sort	Kathrin Hellmuth
title	Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
title_short	Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
title_full	Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
title_fullStr	Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
title_full_unstemmed	Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting
title_sort	multiscale convergence of the inverse problem for chemotaxis in the bayesian setting
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/24418025d2d4405ea1cb9357a8feca2d
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Multiscale Convergence of the Inverse Problem for Chemotaxis in the Bayesian Setting

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