I returned to the Allometric Expression.
y=B*x^(A)
このグラフは、Aの値で、以下の４つのエリアに分かれる。
This graph divides into the following 4 areas by the value of A.
~~~
Area:AP1 (1 < A < +∞)
*)A=1:??? ：境界問題をどうするか？, How is the boundary problem done? TODO)
Area:AP0 (0 < A < 1)
*)A=0:??? ：How is the boundary problem done? TODO)
Area:AM0 (-1 < A < 0)
*)A=-1:??? ：How is the boundary problem done? TODO)
Area:AM1 (-∞ < A < -1)
~~~
今までは、'A<0' で、意図的に、A>0の世界は避けていた。
しかし、'A>0' の世界(正確には、0<A<1)も以下のように式の変形で、
'A<0' にできるので、こちらで、A,B値を割り出す。
The current is done by 'A<0'. Intentionally, The world of 'A>0' was avoided.
However, the world of 'A>0' (0< A<1 accurately) is made 'A<0' in the
transformation of the expression as follows, too. A and B value are
calculated by this expression.
y = B*x^(A)
->
y/x = B'*x^(A - 1)
~~~
ゾウの時間 ネズミの時間―サイズの生物学 (中公新書) 本川 達雄 (新書 - 1992/8)
例として、この本のグラフを処理してみる。
The graph of this book is processed as an example.
~~~
[1]p.27, Fig.3-1:代謝量と体重の関係(哺乳類), Relation between amount of metabolizing and weight(mammal)
y = (4.1)*x^(0.751)
log
(x, y)=(1e-2, 0.129),(1e4, 4137.94)
：変換する, It converts it.
(x, y/x)=(1e-2, 0.129/1e-2),(1e4, 4137.94/1e4)
=(1e-2, 0.129e2),(1e4, 0.4138)
：相対値とする, It is assumed a relative value.
(x, y/x)=(1, 0.129e2/0.4138),(1e4/1e-2, 1)
=(1, 31.174),(1e6, 1)
A=-0.249
B=31.174
~~~
[2]p.36, Fig.3-2:代謝量と体重の関係(恒温動物,変温動物,単細胞生物), Relation between amount of metabolizing and weight(homeothermal animal,
poikilothermal animal, and monad)
[2-1]p.37, Table.3-2:標準代謝量, Amount of standard metabolizing
恒温動物(homeothermal animal) :y = (4.1)*x^(0.751)
変温動物(poikilothermal animal) :y = (0.14)*x^(0.751)
単細胞生物(monad) :y = (0.018)*x^(0.751)
~~~
[2-2]変温動物(poikilothermal animal)
y = (0.14)*x^(0.751)
log
(x, y)=(141.25e-9, 1.004e-6),(316.23, 10.559)
：converts it.
(x, y/x)=(141.25e-9, 1.004e-6/141.25e-9),(316.23, 10.559/316.23)
=(141.25e-9, 7.108),(316.23, 3.339e-2)
：for relative value.
(x, y/x)=(1, 7.108/3.339e-2),(316.23/141.25e-9, 1)
=(1, 212.878),(2.239e9, 1)
A=-0.249
B=212.878
~~~
[2-3]単細胞生物(monad)
y = (0.018)*x^(0.751)
log
(x, y)=(562.3e-18, 6.346e-14),(398.11e-9, 2.811e-7)
：converts it.
(x, y/x)=(562.3e-18, 6.346e-14/562.3e-18),(398.11e-9, 2.811e-7/398.11e-9)
=(562.3e-18, 1.129e2),(398.11e-9, 0.706)
：for relative value.
(x, y/x)=(1, 1.129e2/0.706),(398.11e-9/562.3e-18, 1)
=(1, 159.9),(0.708e9, 1)
A=-0.249
B=159.9
~~~
[3]グラフ, Graph
今回得た３点をグラフに追加する。
3 points obtained this time are added to the graph.
1)恒温動物(homeothermal animal) :y = (4.1)*x^(0.751)
A=-0.249
B=31.174
2)変温動物(poikilothermal animal) :y = (0.14)*x^(0.751)
A=-0.249
B=212.878
3)単細胞生物(monad) :y = (0.018)*x^(0.751)
A=-0.249
B=159.9
~~~
データをcsvにする。今後の追加分を同形式で処理する。
Data is made csv. The addition in the future is processed by this form.
F1=0.4
F2=18
LN(B_mod)=LN(exp(F1*F2)/B^J1)=LN(exp(7.2)/B^0.4)
~~~
"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
~~~
F1=0.4
F2=18
LN(B_mod)=LN(exp(F1*F2)/B^J1)=LN(exp(7.2)/B^0.4)
x=LN(ABS(A))
y=LN(B_mod) (when ABS(A) > 1)
y=LN(B) (when ABS(A) <= 1)
：今回の追加分は、赤丸で囲った。
:It enclosed it with the red circle this addition.
べき分布が、工業とバイオで両端に分かれているようにも見える。
中心部分は、共鳴するのか？分野が混在している？
The distribution of Power Law seems to have divided into both ends
by industry and bio.
Does a center part resonate? Does the field exist together?
~~~
home）「七瀬ふたたび」のエスパーになりたいといったら、
メタパー、メタボ○○？、、、とかいわれてしまった(メタボをかけた何かしらの造語？)。
：録画しても、上書きされて見れません。お金も時間もないですが。
~~~
end
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