We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byMariam Lucy
Modified over 2 years ago
The Power of Seeds in Tile Self-Assembly Andrew Winslow Department of Computer Science, Tufts University
Abstract Tile Assembly Model (aTAM)
P. W. K. Rothemund, N. Papadakis, E. Winfree, Algorithmic self- assembly of DNA Sierpinski triangles. PLoS Biology (12), 2004. Tile Assembly
A Seedless World?
Two-Handed Assembly Model (2HAM)
How powerful is 2HAM relative to aTAM? Are there techniques that require a seed? No.
Every aTAM system can be simulated with a 2HAM system.
Simulation captures dynamics
Simulation captures production
Starting the Seed Mortar
Single-Bond Brick & Mortar
Double-Bond Brick &Mortar
That simulation is mostly correct…
Interacting Seed Assemblies
Inward and Outward Glues Invariant: every exposed glue on an assembly containing a seed is outward.
Inward and Outward Glues
Minimal Glue Sets
Preventing Seed Assembly Interaction Idea #1: maintain that all exposed glues on any seed assembly are outward glues. Idea #2: ensure every attaching brick uses all inward glues to attach, leaving only outward glues exposed.
Simulating 2HAM dynamics with aTAM? ? Can’t simulate dynamics
A Troublesome Shape
A Troublesome Shape
2HAM Binary Counter Counter Tiles
2HAM Staircase Assembly Counter Tiles
aTAM needs ≈2 b tiles 2HAM needs ≈b tiles b 2 b pillars Can’t simulate production
aTAM ≤ 2HAM always Conclusions 2HAM ≤ aTAM at times
Acknowledgements Joint work with: Sarah Cannon, Erik and Martin Demaine, Sarah Eisenstat, Matthew Patitz, Robert Schweller, and Scott Summers. Research funded in part by NSF grant CBET-0941538
An Introduction to Algorithmic Tile Self-Assembly.
Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition.
Self-Assembly with Geometric Tiles ICALP 2012 Bin FuUniversity of Texas – Pan American Matt PatitzUniversity of Arkansas Robert Schweller (Speaker)University.
1 SODA January 23, 2011 Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D Matthew CookUniversity of Zurich and.
Strict Self-Assembly of Discrete Sierpinski Triangles James I. Lathrop, Jack H. Lutz, and Scott M. Summers Iowa State University © James I. Lathrop, Jack.
1 Proceedings of the 24 th Annual ACM-SIAM Symposium on Discrete Algorithms January, 2013 Fuel Efficient Computation in Passive Self-Assembly Robert SchwellerUniversity.
4/4/20131 EECS 395/495 Algorithmic DNA Self-Assembly General Introduction Thursday, 4/4/2013 Ming-Yang Kao General Introduction.
Flipping Tiles: Concentration Independent Coin Flips in Tile Self- Assembly Cameron T. Chalk, Bin Fu, Alejandro Huerta, Mario A. Maldonado, Eric Martinez,
Self-Assembly Ho-Lin Chen Nov Self-Assembly is the process by which simple objects autonomously assemble into complexes. Geometry, dynamics,
Reducing Tile Complexity for Self-Assembly Through Temperature Programming Symposium on Discrete Algorithms SODA 2006 January 23, 2006 Robert Schweller.
Intrinsic Universality in Tile Self-Assembly Requires Cooperation Pierre-Etienne Meunier Matthew J. Patitz Scott M. Summers Guillaume Theyssier Damien.
Reducing Tile Complexity for Self-Assembly Through Temperature Programming Midwest Theory Day, December 10, 2006 Based on paper to appear in SODA 2006.
One-Dimensional Staged Self-Assembly Erik Demaine, Sarah Eisenstat, Mashhood Ishaque, Andrew Winslow Funding in part by NSF grant CBET
1 David DotyCalifornia Institute of Technology Matthew J. PatitzUniversity of Texas Pan-American Dustin ReishusUniversity of Southern California Robert.
One-dimensional Staged Self-Assembly Andrew Winslow Ph.D. Qualifications Research Talk Department of Computer Science, Tufts University.
Design of a Minimal System for Self-replication of Rectangular Patterns of DNA Tiles Vinay K Gautam 1, Eugen Czeizler 2, Pauline C Haddow 1 and Martin.
Matthew J. Patitz Explorations of Theory and Programming in Self-Assembly Matthew J. Patitz Department of Computer Science University of Texas-Pan American.
Ashish Goel Stanford University Joint work with Len Adleman, Holin Chen, Qi Cheng, Ming-Deh Huang, Pablo Moisset, Paul.
1 35 th International Colloquium on Automata, Languages and Programming July 8, 2008 Randomized Self-Assembly for Approximate Shapes Robert Schweller University.
Complexities for Generalized Models of Self-Assembly Gagan Aggarwal Stanford University Michael H. Goldwasser St. Louis University Ming-Yang Kao Northwestern.
© 2017 SlidePlayer.com Inc. All rights reserved.