fab 2 mas 960 special topics: how to make something that makes (almost) anything...
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FAB2
MAS 960 Special Topics:How To Make Something That Makes (almost) Anything
1.Air inlets 2.Crushers 3.Ganglion 4.Multiple Visual sensors 5.Muscles 6.Pincers 7.Sensory receptors 8.Stridulatory pegs 9.Wings
Avogadro Scale Engineering~Achieving the Limits of Fabricational Complexity~
Simple molecules<1nm
IBM PowerPC 750TM Microprocessor
7.56mm×8.799mm6.35×106 transistors
Semiconductor Nanocrystal~1 nm
10-10 10-510-9 10-7 10-610-8 10-4 10-3 10-2
m
Circuit designCopper wiringwidth 0.1m
red blood cell~5 m (SEM)DNA
proteins nm
bacteria1 m
Nanotube Transistor(Dekker)
Complexity vs. Size
SOI transistorwidth 0.12m
diatom30 m
• Error Correcting Fabrication • Fault Tolerant Hardware Architectures • Fault Tolerant Software or Codes • Quantum Phase Space
Resources which increase the complexity of a system exponentially with a linear addition of
resources
Resources for Exponential Scaling
n MAJ
p
p
p
MAJMAJ
p
p
p
MAJ
p
p
p
k
Threshold Theorem - Winograd and Cowan 1963
A circuit containing N error-free gates can be simulated with probability of failure ε using O(N poly(log(⋅ N/ε))) error-prone gates which fail with probability p, provided p < pth, where pth is a constant threshold independent of N.
Number of gates consumed: k3
Find k such that NpPkk
k /3 212
2ln
ln3ln)/ln(2ln
ln
~
pN
k
)/ln(~3 NPolyk Number of Gates ConsumedPer Perfect Gate is
Caruthers Synthesis
DNA Synthesis
http://www.med.upenn.edu/naf/services/catalog99.pdf
Error Rate:1: 102
300 SecondsPer step
http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html
1. Beese et al. (1993), Science, 260, 352-355.
Replicate Linearly with Proofreading and Error Correction
Fold to 3D Functionality
template dependant 5'-3' primer extension
5'-3' error-correcting exonuclease
3'-5' proofreading exonuclease
Error Rate:1: 106
100 Steps per second
Fabricational Complexity
Ffab = ln (W) / [ a3 fab Efab ]
Ffab = ln (M)-1 / [ a3 fab Efab ]
•Total Complexity•Complexity Per Unit Volume•Complexity Per Unit Time*Energy•Complexity Per unit Cost
…Can we use this map as a guide towards future
directions in fabrication?
Genome (Natural)
Gene Chip (Chemical Parallel Synthesis)
Semi-conductor Chip
High Speed Offset Web TFT DVD-6
Liquid Embossing
Design Rule Smallest Dimension (microns) 0.0003 0.0003 0.1 10 2 0.25 0.2Number of Types of Elements 4 4 8 6 8 2 4Area of SOA Artifact (Sq. Microns) NA 7.E+08 7.E+10 2.E+12 1.E+12 1.E+10 8.E+09Volume of SOA Artifact (Cubic Microns) 6.E+01 5.E+06 7.E+09 2.E+12 1.E+11 7.E+12 8.E+08Number of Elements in SOA Artifact 3.E+09 7.E+04 7.E+12 2.E+10 3.E+11 2.E+11 2.E+11Volume Per Element(Cubic Microns) 2.E-08 8.E+01 1.E-03 1.E+02 4.E-01 4.E+01 4.E-03Fabrication Time(seconds) 4.E+03 2.E+04 9.E+04 1.E-01 7.E+02 3 6.E+01Time Per Element (Seconds) 1.E-06 3.E+02 1.E-08 7.E-12 2.E-09 2.E-11 3.E-10Fabrication Cost for SOA Artifact($) 1.E-07 1.E+02 1.E+02 1.E-01 2.E+03 3.E-02 2.E-01Cost Per Element 3.E-17 2.E-03 2.E-11 6.E-12 6.E-09 2.E-13 1.E-12Complexity 4.E+09 9.E+04 2.E+13 4.E+10 6.E+11 1.E+11 3.E+11Complexity Per Unit Volume of SOA(um 3̂) 7.E+07 2.E-02 2.E+03 2.E-02 5.E+00 2.E-02 3.E+02Complexity Per Unit Time 1.E+06 6.E+00 2.E+08 3.E+11 9.E+08 4.E+10 5.E+09Complexity Per Unit Cost 4.E+16 9.E+02 1.E+11 3.E+11 3.E+08 4.E+12 1.E+12Cost Per Area NA 2.E-07 2.E-09 6.E-14 2.E-09 3.E-12 3.E-11
Fabricational Complexity
Fabricational Complexity
n
n
nFAB mpF ln
1
200 400 600 800 1000
10
20
30
40
50
60
70
A
A G
G T C
A T A C G T …
A G T A G C …
p2p3p
Total Complexity:
Complexity Per Unit Cost:For given complexity n*:
Cmpf nFAB /ln
*
Where C is cost per step
Cmpf nFAB /ln
*
Fabricational Complexity
Non Error Correcting:
Triply Error Correcting:
Cmpppfn
FAB 3/ln)1(3*332
3
A G T C
A G T C
A G T C
A G T C
50 100 150 200 250 300
20
40
60
80
100
120
140
P = 0.9
n
FAB
FAB
f
f 3
p
0.86 0.88 0.92 0.94 0.96 0.98
500
1000
1500
2000
2500
3000
n = 300
50 100 150 200
0.05
0.1
0.15
0.2
0.25
0.3
FAB
FAB
f
f 3
n
P = 0.85
http://www.ornl.gov/hgmis/publicat/microbial/image3.html
[Nature Biotechnology 18, 85-90 (January 2000)]
Uniformed Services University of the Health
Deinococcus radiodurans (3.2 Mb, 4-10 Copies of Genome )
D. radiodurans: 1.7 Million Rads (17kGy) – 200 DS breaksE. coli: 25 Thousand Rads – 2 or 3 DS breaks
D. radiodurans 1.75 million rads, 24 h
D. radiodurans 1.75 million rads, 0 h
photos provided by David Schwartz (University of Wisconsin, Madison)]
Caruthers Synthesis
DNA Synthesis
http://www.med.upenn.edu/naf/services/catalog99.pdf
Error Rate:1: 102
300 SecondsPer step
http://www.biochem.ucl.ac.uk/bsm/xtal/teach/repl/klenow.html
1. Beese et al. (1993), Science, 260, 352-355.
Replicate Linearly with Proofreading and Error Correction
Fold to 3D Functionality
template dependant 5'-3' primer extension
5'-3' error-correcting exonuclease
3'-5' proofreading exonuclease
Error Rate:1: 106
100 Steps per second