Results 1 - 10 of 482

Randomized self-assembly for exact shapes

by David Doty , 2009
"... Abstract — Working in Winfree’s abstract tile assembly model, we show that a constant-size tile assembly system can be programmed through relative tile concentrations to build an n × n square with high probability, for any sufficiently large n. This answers an open question of Kao and Schweller (Ran ..."
Abstract - Cited by 33 (10 self) - Add to MetaCart
(Randomized Self-Assembly for Approximate Shapes, ICALP 2008), who showed how to build an approximately n × n square using tile concentration programming, and asked whether the approximation could be made exact with high probability. 1.

Randomized Self-Assembly for Approximate Shapes

by Ming-yang Kao, Robert Schweller - In ICALP (1 , 2008
"... Abstract. In this paper we design tile self-assembly systems which assemble arbitrarily close approximations to target squares with arbitrarily high probability. This is in contrast to previous work which has only considered deterministic assemblies of a single shape. Our technique takes advantage o ..."
Abstract - Cited by 26 (2 self) - Add to MetaCart
of the ability to assign tile concentrations to each tile type of a self-assembly system. Such an assignment yields a probability distribution over the set of possible assembled shapes. We show that by considering the assembly of close approximations to target shapes with high probability, as opposed to exact

Size-Separable Tile Self-Assembly: A Tight Bound for Temperature-1 Mismatch-Free Systems

by Andrew Winslow
"... We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical problem of filtering completed assemblies from a ..."
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We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical problem of filtering completed assemblies from

One dimensional boundaries for DNA tile self-assembly

by Rebecca Schulman, Shaun Lee, Nick Papadakis, Erik Winfree - In DNA Based Computers 9, volume 2943 of LNCS , 2004
"... Abstract. In this paper we report the design and synthesis of DNA molecules (referred to as DNA tiles) with specific binding interactions that guide self-assembly to make one-dimensional assemblies shaped as lines, V’s and X’s. These DNA tile assemblies have been visualized by atomic force microscop ..."
Abstract - Cited by 9 (1 self) - Add to MetaCart
microscopy. The highly-variable distribution of shapes – e.g., the length of the arms of X-shaped assemblies – gives us insight into how the assembly process is occurring. Using stochastic models that simulate addition and dissociation of each type of DNA tile, as well as simplified models that more cleanly

Asynchronous Signal Passing for Tile Self-Assembly: Fuel Efficient Computation and Efficient Assembly of Shapes

by Robert Sheline, Scott M. Summers, Xingsi Zhong
"... Abstract. In this paper we study the power of a model of tile self-assembly in which individual tiles of the system have the ability to turn on or off glue types based on the bonding of other glues on the given tile. This work is motivated by the desire for a system that can effect recursive self as ..."
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recursive assembly process. We then present a system of signal passing tiles that simulate an arbitrary Turing machine which is fuel efficient in that only a constant number of tiles are used up per computation step. To the best of our knowledge, this is the first tile self-assembly model that is able

Tile Self-Assembly Simulations Senior Honors Thesis

by Sarah Cannon , 2012
"... Tile self-assembly models describe both mathematically and computationally the ways in which small square tiles can attach to each other to form larger assemblies. Two such models are the abstract tile assembly model, in which all tiles attach to one main assembly containing a seed tile, and the two ..."
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into the relative fundamental computational power of both models. This work has direct applications in DNA computing, where biologists are using these models to self-assemble pieces of DNA (represented abstractly by tiles) into structures at the nanoscale level.

Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature

by David Doty, Matthew J. Patitz, Dustin Reishus, Robert T. Schweller, Scott M. Summers
"... We consider the problem of fault-tolerance in nanoscale algorithmic self-assembly. We employ a variant of Winfree’s abstract Tile Assembly Model (aTAM), the two-handed aTAM, in which square “tiles ” – a model of molecules constructed from DNA for the purpose of engineering selfassembled nanostructu ..."
Abstract - Cited by 16 (11 self) - Add to MetaCart
is stable at temperature 2. We study a common self-assembly benchmark problem, that of assembling an n × n square using O(log n) unique tile types, under the two-handed model of self-assembly. Our main result achieves a much stronger notion of fault-tolerance than those achieved previously. Arbitrary

Parallelism and Time in Hierarchical Self-Assembly

by Ho-lin Chen, David Doty , 2012
"... We study the role that parallelism plays in time complexity of variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the “hierarchical ” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the ..."
Abstract - Cited by 17 (6 self) - Add to MetaCart
in the “seeded” aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang (Running Time and Program Size for Self-Assembled Squares, STOC 2001) showed how to assemble an n×n square in O(n) time in log n the seeded aTAM using O ( ) unique tile types, where log log n both

Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D

by Matthew Cook, Yunhui Fu, Robert Schweller , 2011
"... We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no temperature 1 assembly system has been shown to build a shape with ..."
Abstract - Cited by 24 (5 self) - Add to MetaCart
We investigate the power of the Wang tile self-assembly model at temperature 1, a threshold value that permits attachment between any two tiles that share even a single bond. When restricted to deterministic assembly in the plane, no temperature 1 assembly system has been shown to build a shape

Toward Reliable Algorithmic Self-Assembly of DNA Tiles: A Fixed-Width Cellular Automaton Pattern NANO LETTERS

by Kenichi Fujibayashi, Rizal Hariadi, Sung Ha Park, Erik Winfree, Satoshi Murata , 2007
"... Bottom-up fabrication of nanoscale structures relies on chemical processes to direct self-assembly. The complexity, precision, and yield achievable by a one-pot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for inv ..."
Abstract - Cited by 35 (2 self) - Add to MetaCart
for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a one-pot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed
Results 1 - 10 of 482