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Assigned and unassigned distance geometry: applications to biological molecules and nanostructures

Abstract

Considering geometry based on the concept of distance, the results found by Menger and Blumenthal originated a body of knowledge called distance geometry. This survey covers some recent developments for assigned and unassigned distance geometry and focuses on two main applications: determination of three-dimensional conformations of biological molecules and nanostructures.

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Acknowledgments

Support for work at Michigan State University by the MSU foundation is gratefully acknowledged. Collaborations with Pavol Juhas, Luke Granlund, Saurabh Gujarathi, Chris Farrow and Connor Glosser are much appreciated. PMD, CL and AM would like to thank Leo Liberti for interesting and motivating discussions. AM was supported by a grant of University of Rennes 1 for the development of international collaborations. PMD and CL were financially supported by the Brazilian research agencies FAPESP and CNPq. Work in the Billinge group was supported by the US National Science foundation DMREF program through grant: DMR-1534910.

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Correspondence to Douglas S. Gonçalves.

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Billinge, S.J.L., Duxbury, P.M., Gonçalves, D.S. et al. Assigned and unassigned distance geometry: applications to biological molecules and nanostructures. 4OR-Q J Oper Res 14, 337–376 (2016). https://doi.org/10.1007/s10288-016-0314-2

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  • DOI: https://doi.org/10.1007/s10288-016-0314-2

Keywords

  • Distance geometry
  • Graph rigidity
  • Molecular conformations
  • Nanostructures
  • Discretization orders

Mathematics Subject Classification

  • 51Kxx
  • 82D80
  • 92E10