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Staged Self-Assembly and Polyomino Context-Free GrammarsPowerPoint Presentation

Staged Self-Assembly and Polyomino Context-Free Grammars

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Morphogenesis

Mixing

Staged self-assembly

Input

n

Θ(n) system size

Θ(log(n)) system size

Input

Finding small systems is (NP-)hard.

Study a simplified model.

One dimension

Ο(1)

? ? ?

? ? ?

Ο(#glues2)

Ω(n1/2/log(n)), Ο(n2/3)

Staged System

Grammar

E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, 2011.

? ? ? ?

Polyomino Grammar

Two dimensions

Ο(log(n))

w/scaling

Macrotile

…

…

Ω(n/log3n)

Grammar

Staged System

A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, 2013.

Values are distinct

Values are contiguous

[1..3] +4

Shifting

[4..6] +4

Shifting

[2..5] +3

Staged System

Grammars are small,

staged systems are always smaller

Ο(log(n))

Ο(1)

Ω(n1/2/log(n)), Ο(n2/3)

Ω(n/log3n)

w/scaling

Thank you

Committee:

Collaborators:

Lenore Cowen

Sarah Eisenstat

Erik Demaine

MashhoodIshaque

Ben Hescott

Matthew Patitz

Diane Souvaine

Robert Schweller

Hyunmin Yi

Damien Woods

NSF grants 0941538 and 0830734

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