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Self-correcting Self-assembly: Growth Models and the Hammersley Process

  • Yuliy Baryshnikov
  • Ed Coffman
  • Nadrian Seeman
  • Teddy Yimwadsana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3892)

Abstract

This paper extends the stochastic analysis of self assembly in DNA-based computation. The new analysis models an error-correcting technique called pulsing which is analogous to checkpointing in computer operation. The model is couched in terms of the well-known tiling models of DNA-based computation and focuses on the calculation of computation times, in particular the times to self assemble rectangular structures. Explicit asymptotic results are found for small error rates q, and exploit the connection between these times and the classical Hammersley process. Specifically, it is found that the expected number of pulsing stages needed to complete the self assembly of an N ×N square lattice is asymptotically \(2N\sqrt{q}\) as N →∞ within a suitable scaling. Simulation studies are presented which yield performance under more general assumptions.

Keywords

Completion Time Totally Asymmetric Simple Exclusion Process Asymmetric Simple Exclusion Process Input Label Layer Tile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yuliy Baryshnikov
    • 1
  • Ed Coffman
    • 2
  • Nadrian Seeman
    • 3
  • Teddy Yimwadsana
    • 2
  1. 1.Bell LabsLucent TechnologiesMurray HillUSA
  2. 2.Department of Electrical EngineeringColumbia UniversityUSA
  3. 3.Chemistry Dept.New York UniversityNew York

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