Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016....
Transcript of Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016....
![Page 1: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/1.jpg)
Algorithms in Nature
Slime mold network design
![Page 2: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/2.jpg)
Physarum polycephalum
1cm
![Page 3: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/3.jpg)
Physarum polycephalum
![Page 4: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/4.jpg)
Discrete Form
2N
jN
iN
1N
ijM
Start point
Goal 1N2N
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
![Page 5: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/5.jpg)
Modeling of the flux
)( jiij
ijij pp
LD
Q −=
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
)(tip Electric Pressure
)( tij
ij
DL
Electric Resistance
)(tijQ Electric Current
![Page 6: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/6.jpg)
Modeling of the tube growth
ijij rDijQDdtd
−= || r :degenerate rate
(constant)
time
rijQ ||
ijD)(tijD
![Page 7: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/7.jpg)
T shape vessel
The tube at dead end disappears
![Page 8: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/8.jpg)
Ring shape vessel
Only shortest tube remains
)( 212
112 LL ≠
Stable equilibrium point Unstable equilibrium point
![Page 9: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/9.jpg)
Ring shape vessel
Both tubes remain
)( 212
112 LL =
Stable equilibrium point Unstable equilibrium point
![Page 10: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/10.jpg)
Solving Maze
![Page 11: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/11.jpg)
Apply for road navigation system
START
GOAL
![Page 12: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/12.jpg)
Using constraints for limiting search space
food
food
![Page 13: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/13.jpg)
Ex 2. Shortest path on Weighted graph
ijij DrijQDdtd
)(|| x−=
=13
)(xr
![Page 14: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/14.jpg)
Slime Mold: Rules for Biologically Inspired
Adaptive Network Design
Tero et al. Science 2010
![Page 15: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/15.jpg)
![Page 16: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/16.jpg)
Network design
• At each iteration select two random points • One acts as a food source, the other as the sink • Compute flux between them based on all other points / tubes in the graph
![Page 17: Slime mold network design - Carnegie Mellon School of Computer …02317/slides/lec_13.pdf · 2016. 2. 24. · Slime Mold: Rules for Biologically Inspired Adaptive Network Design .](https://reader036.fdocuments.in/reader036/viewer/2022071412/61098253ea07500cf367c9b4/html5/thumbnails/17.jpg)
1. We can reproduce the adaptive network of the true slime mold.
2. “Physarum Solver” can find the shortest path.
Summary
1. What about multiple food sources?