Difference between revisions of "Two-Handed Assembly Model (2HAM)"

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The 2-Handed Assembly Model (2HAM) is a variant of the [[Tile Assembly Model]] in which an assembly does not need to begin from a specified [[seed]] and grow only one [[tile]] at a time, but instead allows for assemblies to form from the combination of any 2 existing assemblies which can attach to each other with sufficient strength and without overlapping.
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==Informal model description==
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The 2HAM <ref name="AGKS05g"><bibtex> description/definition goes here.
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@article{AGKS05g,
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  author = "Qi Cheng and Gagan Aggarwal and Michael H. Goldwasser and Ming-Yang Kao and Robert T. Schweller and Pablo Moisset de Espan&eacute;s",
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  title = "Complexities for Generalized Models of Self-Assembly",
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  journal = "SIAM Journal on Computing",
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  volume = "34",
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  pages = "1493--1515",
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  year = "2005",
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}
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</bibtex></ref>
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<ref name="DDFIRSS07">
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<bibtex>
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@article{DDFIRSS07,
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  author    = {Erik D. Demaine and
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              Martin L. Demaine and
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              S&aacute;ndor P. Fekete and
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              Mashhood Ishaque and
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              Eynat Rafalin and
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              Robert T. Schweller and
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              Diane L. Souvaine},
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  title    = {Staged self-assembly: nanomanufacture of arbitrary shapes
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              with O(1) glues},
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  journal  = {Natural Computing},
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  volume    = {7},
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  number    = {3},
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  year      = {2008},
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  pages    = {347-370},
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  ee        = {http://dx.doi.org/10.1007/s11047-008-9073-0},
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  bibsource = {DBLP, http://dblp.uni-trier.de}
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}
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</bibtex>
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</ref>
  
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Winfree’s original model, the seeded [[aTAM]], stipulates that assembly begins from a specially-designated “[[seed]]” tile type, and all binding events consist of the attachment of a single tile to the growing assembly that contains the seed. The seed thus serves as a nucleation point from which all further growth occurs. In reality, such single-point nucleation is difficult to enforce as tiles with matching glues may attach to each other in solution, even if neither of them is connected to the seed tile. The two-handed assembly model models this sort of growth by dispensing with the idea of a seed, and simply defining an assembly to be producible if 1) it consists of a single tile (base case), or 2) it results from the stable aggregation of two producible assemblies (recursive case). Not only is the 2HAM a more realistic model, it allows us to use the geometry of partially-formed assemblies, rather than relying solely on (error-prone) glue specificity, to enforce binding rules between subassemblies.
 
  
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==Characteristics==
 
  
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A [[supertile]] (e.g., assembly) is a positioning of tiles on the integer lattice $\mathbb{Z}^2$. Two adjacent tiles in a supertile interact if the glues on their abutting sides are equal. Each supertile induces a binding graph, a grid graph whose vertices are tiles, with an edge between two tiles if they interact. The supertile is $\tau$ -stable if every cut of its binding graph has strength at least $\tau$ , where the weight of an edge is the strength of the glue it represents. That is, the supertile is stable if at least energy 2 is required to separate the supertile into two parts. A tile assembly system (TAS) is a pair $T = (T, \tau )$, where $T$ is a finite tile set and $\tau$ is the temperature, usually 1 or 2. Given a TAS $T = (T, \tau )$, a supertile is producible if either it is a single tile from $T$, or it is the $\tau$ -stable result of translating two producible assemblies. An supertile $\alpha$ is terminal if for every producible supertile $\beta$, $\alpha$ and $\beta$ cannot be $\tau$ -stably attached. A TAS is directed (e.g., deterministic, confluent) if it has only one terminal, producible supertile. Given a connected shape $X \subseteq \mathbb{Z}^2$, a TAS $T$ produces $X$ uniquely if every producible, terminal supertile places tiles only on positions in $X$ (appropriately translated if necessary).
 
  
 
==References==
 
==References==
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<references />
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<references />
 
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Sarah Cannon, Erik Demaine, Martin Demaine, Sarah Eisenstat, Matthew Patitz, Robert Schweller, Scott Summers, and Andrew Winslow, Two Hands are Better Than One (up to constant factors).
 
  
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David Doty, Matthew J. Patitz, Dustin Reishus, Robert T. Schweller, and Scott M. Summers, [[Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature]], Proceedings of the 16th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010). Las Vegas, Nevada, Oct. 2010
 
  
 
[[category:Tile Assembly Models]]
 
[[category:Tile Assembly Models]]

Revision as of 11:19, 21 May 2013

Informal model description

The 2HAM [1] [2]



References

  1. ↑ Qi Cheng, Gagan Aggarwal, Michael H. Goldwasser, Ming-Yang Kao, Robert T. Schweller, Pablo Moisset de Espanés - Complexities for Generalized Models of Self-Assembly
    ,2005
    Bibtex
    Author : Qi Cheng, Gagan Aggarwal, Michael H. Goldwasser, Ming-Yang Kao, Robert T. Schweller, Pablo Moisset de Espanés
    Title : Complexities for Generalized Models of Self-Assembly
    In : -
    Address :
    Date : 2005
  2. ↑ Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Mashhood Ishaque, Eynat Rafalin, Robert T. Schweller, Diane L. Souvaine - Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
    Natural Computing 7(3):347-370,2008
    Bibtex
    Author : Erik D. Demaine, Martin L. Demaine, Sándor P. Fekete, Mashhood Ishaque, Eynat Rafalin, Robert T. Schweller, Diane L. Souvaine
    Title : Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
    In : Natural Computing -
    Address :
    Date : 2008
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