Presentation is loading. Please wait.

Presentation is loading. Please wait.

Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition.

Similar presentations


Presentation on theme: "Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition."— Presentation transcript:

1 Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition

2 Simple particles coalescing into complex superstructures. Self-Assembly

3 Simple particles coalescing into complex superstructures.

4 Self-Assembly Simple particles coalescing into complex superstructures.

5 Self-Assembly Simple particles coalescing into complex superstructures.

6 Crystallization

7 Morphogenesis

8 Natural Self-Assembly

9 Synthetic Self-Assembly with DNA

10

11 Tile

12 Glues

13

14

15 Our work: Study an abstract self-assembly model based on DNA tile systems.

16 Tile

17 Glues

18 Assembly

19 Mixing

20 Bin

21 Reagents

22 Products

23

24 Size

25

26 Staged self-assembly

27 InputOutput (polyomino) (small staged assembly system)

28 n Input

29

30

31

32 Θ( n) system size

33

34 Θ (log(n)) system size

35 n Θ (n) Θ (log(n))

36 Input

37 Study a simplified model. Finding small systems is (NP-)hard.

38

39 Rule

40 Grammar

41 Ο (#glues 2 ) Ω (n 1/2 /log(n)), Ο (n 2/3 ) Staged System ? ? ? One dimension Ο (1) E. D. Demaine, S. Eisenstat, M. Ishaque, A. Winslow, One-dimensional staged self-assembly, DNA 17, Grammar ? ? ?

42 ? ?

43 Polyomino Grammar

44 w/scaling Two dimensions GrammarStaged System … … A. Winslow, Staged Self-Assembly and Polyomino Context-Free Grammars, DNA 19, Ω (n/log 3 n) Ο (log(n)) Macrotile

45 ? ? ? ? ? ?

46 Values

47 Values are distinct Values are contiguous

48 Activation

49

50

51

52 ? ? ?

53

54

55 Shifting [1..3] +4

56 Shifting [4..6] +4

57 Activation Shifting [1..3] +4

58 ? ? ?

59 [2..5] +3

60 ? ? ?

61 [1..4] +2

62 ? ? ?

63 [1..4] +4

64 Reagent 1 Reagent 2 Product Activated reagent 1 Shifted reagent 2 Activated & shifted reagent 2

65 ? ? ? ? ? ?

66 A R1 S R2 A & S R2 A R1 S R2 A & S R2 A R1 S R2 A & S R2

67 A R1 S R2 A & S R2 A R1 S R2 A & S R2 A R1 S R2 A & S R2 w/scaling Ο (log(n))

68 … … Ω (n/log 3 n)

69 Ο (loglog(n)) … Ω (n/loglog(n)) …

70 … … Ο (log(n)) Ω (n/log 2 n)

71 Ο (log(n)) … Ω (n/log 2 n) …

72 GrammarStaged System Ο (1) Ω (n 1/2 /log(n)), Ο (n 2/3 ) w/scaling Ο (log(n)) Ω (n/log 3 n) Grammars are small, staged systems are always smaller

73 Thank you Committee: Diane Souvaine Erik Demaine Ben Hescott Lenore Cowen Hyunmin Yi Collaborators: Matthew Patitz Sarah Eisenstat Robert Schweller Mashhood Ishaque Damien Woods NSF grants and


Download ppt "Staged Self-Assembly and Polyomino Context-Free Grammars Andrew Winslow Defense Edition."

Similar presentations


Ads by Google