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Publications (2 of 2) Show all publications
Groh, A., Kohr, H. & Louis, A. K. (2016). Numerical rate function determination in partial differential equations modeling cell population dynamics. Journal of Mathematical Biology, 1-33
Open this publication in new window or tab >>Numerical rate function determination in partial differential equations modeling cell population dynamics
2016 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, p. 1-33Article in journal (Refereed) Published
Abstract [en]

This paper introduces a method to solve the inverse problem of determining an unknown rate function in a partial differential equation (PDE) based on discrete measurements of the modeled quantity. The focus is put on a size-structured population balance equation (PBE) predicting the evolution of the number distribution of a single cell population as a function of the size variable. Since the inverse problem at hand is ill-posed, an adequate regularization scheme is required to avoid amplification of measurement errors in the solution method. The technique developed in this work to determine a rate function in a PBE is based on the approximate inverse method, a pointwise regularization scheme, which employs two key ideas. Firstly, the mollification in the directions of time and size variables are separated. Secondly, instable numerical data derivatives are circumvented by shifting the differentiation to an analytically given function. To examine the performance of the introduced scheme, adapted test scenarios have been designed with different levels of data disturbance simulating the model and measurement errors in practice. The success of the method is substantiated by visualizing the results of these numerical experiments.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Cell population dynamics, Inverse problem, Parameter estimation, Partial differential equation, Population balance equation
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-197230 (URN)10.1007/s00285-016-1032-2 (DOI)2-s2.0-84974777794 (Scopus ID)
Note

QC 20161205

Available from: 2016-12-05 Created: 2016-11-30 Last updated: 2017-11-29Bibliographically approved
Dahmen, T., Kohr, H., de Jonge, N. & Slusallek, P. (2015). Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series. Microscopy and Microanalysis, 21(3), 725-738
Open this publication in new window or tab >>Matched Backprojection Operator for Combined Scanning Transmission Electron Microscopy Tilt- and Focal Series
2015 (English)In: Microscopy and Microanalysis, ISSN 1431-9276, E-ISSN 1435-8115, Vol. 21, no 3, p. 725-738Article in journal (Refereed) Published
Abstract [en]

Combined tilt- and focal series scanning transmission electron microscopy is a recently developed method to obtain nanoscale three-dimensional (3D) information of thin specimens. In this study, we formulate the forward projection in this acquisition scheme as a linear operator and prove that it is a generalization of the Ray transform for parallel illumination. We analytically derive the corresponding backprojection operator as the adjoint of the forward projection. We further demonstrate that the matched backprojection operator drastically improves the convergence rate of iterative 3D reconstruction compared to the case where a backprojection based on heuristic weighting is used. In addition, we show that the 3D reconstruction is of better quality.

Place, publisher, year, edition, pages
Cambridge University Press, 2015
Keywords
STEM, tomography, 3D, focal series, iterative reconstruction, backprojection, depth of field
National Category
Computational Mathematics Other Physics Topics
Research subject
Materials Science and Engineering; Mathematics
Identifiers
urn:nbn:se:kth:diva-167055 (URN)10.1017/S1431927615000525 (DOI)000358836400020 ()2-s2.0-84936891955 (Scopus ID)
Note

QC 20150615

Available from: 2015-05-21 Created: 2015-05-21 Last updated: 2017-12-04Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-0727-9561

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