名古屋大集中講義 iwatawiki lec01 s


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2016/11/29 13:00-14:30

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h.p://www.new-fukushima.jp/archives/4992.html




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“On Growth and Form” D’Arcy Thompson



– 
– 
– 

8


t

y

• 





=




N

9

#
2nπt
2nπt &
y(t) = ∑% c n cos
+ dn sin
(
$
T
T '
i=0

f ( x) =

a0 ∞
+ ∑ (an cos nx + bn sin nx )
2 n =1
an =
bn =

10

11

1

π∫



0

1

π∫



0

f ( x) cos nxdx
f ( x) sin nxdx

12

4

f(x)

0.0
-1.0

6

8

10

f1(x)+f2(x)

2

8

10

0

6

8

1.0
-1.0 0.0

4

6

8

10

2

4

6

8

10

N = 20

N = 40

N = 80

x

2

4

6

8

10

6

8

10

f1(x)+f2(x)+f3(x)+f4(x)

f3(x)

2

10

-1.0 0.0

1.0

x

f4(x)

N = 10

-1.0 0.0 1.0

4

f1(x)+f2(x)+f3(x)

2

0

0

4
sin 7 x


N=5

x

x

4
sin 5 x


N=1

-1.0 0.0 1.0

f2(x)

-1.0 0.0 1.0

4
sin 3x


0

f 4 ( x) =

6
x

x

f 3 ( x) =

4

-1.0 0.0 1.0

0

f 2 ( x) =

2



sin x
f1(x)

4

π


0

-1.0 0.0 1.0

f1 ( x) =

1.0

⎧ 1 (0 ≤ x < π )
f ( x) = ⎨
⎩− 1 (π ≤ x < 2π )
f ( x + 2π ) = f ( x)

0

2

4

6

8

10

x

0

2

4
x



4
4
4
4
4
f (x) = sin x +
sin 3x +
sin5x +
sin 7x + ... = ∑
sin(2k −1)π
π



k =1 (2k −1)π




(

2

(
2

2
8

15





y(t) = c1 cos

2πt
2πt
+ d1 sin
T
T

2πt
2πt
+ d1 sin
T
T
10πt
10πt
+....+ c 5 cos
+ d5 sin
T
T
y(t) = c1 cos

2πt
2πt
+ d1 sin
T
T
20πt
20πt
+....+ c10 cos
+ d10 sin
T
T
y(t) = c1 cos

2πt
2πt
+ c1 sin
T
T
80πt
80πt
+....+ c 40 cos
+ d40 sin
T
T
y(t) = c1 cos



2

=7

2

3

a1=1, b1=0, c116
=0

PC2

cn

PC1

an

PC1=1.2

( 

bn

PC2=0.8

17

19


PC2

cn

an

PC1

bn
Pictured by Dr. Satoshi Niikura
77

PC1=1.2 PC2=0.8
18

20


p

t p = ∑ Δt i
i =1

T = tK
2ntπ
2ntπ ⎞

x(t ) = ∑ ⎜ an cos
+ bn sin

T
T ⎠
i =0 ⎝
N

2ntπ
2ntπ ⎞

y (t ) = ∑ ⎜ cn cos
+ d n sin

T
T ⎠
i =0 ⎝
N


2nπ t
2nπ t ⎞

y (t ) = ∑ ⎜ cn cos
+ d n sin

T
T ⎠
n =1 ⎝

cn =

dn =

SHAPE
h.p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/

6×6

T
2n 2π 2

T
2n 2π 2

21

K

Δy p

∑ Δt
p =1

K

2nπ t p
T

p

Δy p

∑ Δt
p =1

(cos

(sin

2nπ t p

p

T

− cos

− sin

2nπ t p −1
T

)

⎡ 2(a b + c d ) ⎤

θ1 = arctan⎢ 2 1 21 21 1 2 ⎥
2
⎣ a1 + c1 − b1 − d1 ⎦

1

⎡a1*
⎢ *
⎣b1

1

2

)


1

256

T

Kuhl and Giardina (1982)23

...

1

RGB

2nπ t p −1

E*

c1* ⎤ ⎡ cosθ1 sin θ1 ⎤ ⎡a1 c1 ⎤
⎥=⎢
⎥⎢

d1* ⎦ ⎣− sin θ1 cosθ1 ⎦ ⎣b1 d1 ⎦

ψ 1 = arctan

c1*
a1*

E* = a1*2 + c1*2
⎡an** cn** ⎤ 1 ⎡ cosψ 1 sinψ 1 ⎤ ⎡an
=
⎢ **

⎥⎢
** ⎥
⎣bn d n ⎦ E * ⎣− sinψ 1 cosψ 1 ⎦ ⎣bn
22

...

cn ⎤ ⎡ cos nθ1 sin nθ1 ⎤
d n ⎥⎦ ⎢⎣− sin nθ1 cos nθ1 ⎥⎦
24

h.p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/

25

27

26

28



73.9%

78.9%

14.2%

10.3%

3.9%

5.6%

1.9%

3.8%
h.p://lbm.ab.a.u-tokyo.ac.jp/~iwata/shape/

… T ... C ......... T ... A ...... G ... C ..... T ...
… A ... G ......... C ... A ...... G ... T ..... T ...
… T ... C ......... C ... A ...... A ... C ..... G ...
… A ... C ......... C ... A ...... G ... C ..... G ...

… T ... C ......... T ... C ...... A ... C ..... G ...





DNA



… T ... C ......... T ... C ...... A ... T ..... T ...

… A ... C ......... C ... C ...... G ... C ..... T ...
… A ... G ......... T ... C ...... A ... C ..... T ...

2

29


31



0.01

0.02



0.00

)

PC2

0

8
• 

−0.01

2

2
2

−0.02

2

DNA

• 

0

−0.20

−0.15

−0.10

−0.05

0.00

0.05

0.10

0.15

PC1

2
=7
30

(

2

2

32




1

y1

x1
DNA

36,901

x2

t1

y2

s1


77

x3

t2

y3

s2

x4

y4
PLS

DNA
DNA
33

GS

PLS


input space)

y = f (x)
223 273 173 142
373 234 138 304




423 203 133
x


feature space)

y



y1

φ1 x
x
T
yi = x i w + ei

φ2 x

t1

s1

y2

φ3 x

t2

s2

y3

x

φ x

yi = φ (x i )T w + ei

77

y4

φ4 x

y = \\\f (x)




x


PLS


(Goto et al. 2005)




39



• 

• 

8.3 m
tower

HP

(Goto
(Yoshioka

2004)

2005)
38

40






Table 4. Estimation of parameters in regresssion models.


Variables

Estimate

SE

P (Prob>|t|)

t

AP3

-21.214

5.549

-3.820

0.0003

AP5

-41.990

14.138

-2.970

0.0040

BP3

-38.009

18.649

-2.040

0.0452

Area

0.013

0.002

5.250

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