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, Volume 14, Issue 4, pp 337–376 | Cite as

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

  • Simon J. L. Billinge
  • Phillip M. Duxbury
  • Douglas S. Gonçalves
  • Carlile Lavor
  • Antonio Mucherino
Invited Survey

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.

Keywords

Distance geometry Graph rigidity Molecular conformations Nanostructures Discretization orders 

Mathematics Subject Classification

51Kxx 82D80 92E10 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Simon J. L. Billinge
    • 1
    • 2
  • Phillip M. Duxbury
    • 3
  • Douglas S. Gonçalves
    • 4
  • Carlile Lavor
    • 5
  • Antonio Mucherino
    • 6
  1. 1.Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA
  2. 2.X-ray Scattering GroupBrookhaven National LaboratoryUptonUSA
  3. 3.Department of Physics and AstronomyMichigan State UniversityEast LansingUSA
  4. 4.Centro de Ciências Físicas e MatemáticasUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  5. 5.Department of Applied Mathematics (IMECC-UNICAMP)University of CampinasCampinasBrazil
  6. 6.Institut de Recherche en Informatique et Systèmes AléatoiresUniversité de Rennes 1RennesFrance

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