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Physarum polycephalum
1cm
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Physarum polycephalum
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Solving maze
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Discrete Form
2N
jN
iN
1N
ijM
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Discrete Form
1ijM
iN jN
2ijM
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Discrete Form
2N
jN
iN
1N
ijM
Start point
Goal
1N
2N
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
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Modeling of the flux of the sol
)( jiij
ijij pp
L
DQ
iN )(tip Pressure
ijM ijL
)(tijD
)(tijQ Flux
Length
Conductivity
)(tip Electric Pressure
)( tij
ij
D
LElectric Resistance
)(tijQ Electric Current
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Kirchhoff law
jN
2,1j0 iij Q
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1N
0I
FS2N
0IFS
Electric sources
0
0
0 2
0 1
I Q
I Q
ii
ii
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Modeling of the tube growth
ijij rDijQD
dt
d || r :degenerate rate
(constant)
time
rijQ ||
ijD )(tijD
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Model equations
Flux of sol Tube growth
ijij rDijQD
dt
d ||
2,1j
0
0
0 2
0 1
I Q
I Q
ii
ii
0 iij Q)( ji
ij
ijij pp
L
DQ
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T shape vessel
The tube at dead end disappears
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Ring shape vessel
Only shortest tube remains
)( 212
112 LL
Stable equilibrium pointUnstable equilibrium point
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Ring shape vessel
Both tubes remain
)( 212
112 LL
Stable equilibrium pointUnstable equilibrium point
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Solving Maze
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Solving Maze
スタート
ゴール
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Solving Maze
スタート
ゴール
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Apply for road navigation system
START
GOAL
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1. We can reproduce the adaptive network of the true slime mold.
2. “Physarum Solver” can find the shortest path.
Summary
1. Simulation with many food sources
Current Work
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That’s all. Thank you very much!!
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Apply for road navigation system
START
GOAL
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Ex 2. Shortest path on Weighted graph
food
food
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Ex 2. Shortest path on Weighted graph
nyflexibilit
region
::
nyflexibilit
region
::
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Ex 2. Shortest path on Weighted graph
ijij DrijQD
dt
d)(|| x
1
3)(xr
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Solving Maze
START
GOAL
Does physarum have enough intelligence to solve the maze?
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Shortest Path From Seattle to Houston
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Ex. 3 Path choice
food
vessel
Physarum
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Model Equation
ijijij rDQDdt
d
Model of Tube Growth
One(Short)
Both
180180
1
1
10
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)1(
Both tubes remain
Stable equilibrium pointUnstable equilibrium point
Simulation Result
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)1(
Almost all tube remain
数値シミュレーション
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)1( Simulation Result
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One tube remains (chose by initial condition )
Simulation Result )1(
Stable equilibrium pointUnstable equilibrium point
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One tube remains (chose by initial condition )
数値シミュレーション )1(
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Simulation Result
One(initial condition)
One(Short)
Both
Both
180180
1
1
10
ijijij rDQDdt
d
Model of Tube Growth
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Model Equation
Q
jiD
1
1
ijij rDQ
QD
dt
d
1||
||
01||
||
ijrDQ
Q
)3(
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Simulation Result with each 0I
Flux
Number of the tube
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Both tubes remain
)0.3(1||
||0
IrDQ
QD
dt
dij
ij
ijij
Simulation Result
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Application
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Application
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Thank you for your attention!!
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a2 Q
Modeling of the flux of the sol
FluxPoiseuille Flow
ij
jiijij L
ppaQ
)(
8
4
8
4ij
ij
aD )( ji
ij
ijij pp
L
DQ
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Ex 2. Shortest path on Weighted graph
ijjiij
ij LrppL
D)(x
partlower
partupperr
3/11
3/23)(x
ijji
ij
ij LppL
Dr ˆˆ)(
x
ijijij DrQDdt
d)(x
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)0.2(1||
||0
IrDQ
QD
dt
dij
ij
ijij
One tube remains
Simulation Result