yeast PIN nD

controllability for yPIN with Dang's data



```{r eigen-spectrum}
e=eig$values;
summary(e)
digits = c(1:30)
zeros = digits
debug = 0
for ( i in 1:length(digits ) ) {
 tmp = sort(table(round(e, roundings[i])), decreasing = T)
 if (debug > 0) { print(tmp[1:3]) }
 zeros[i] = tmp[1]
}
cbind( digits , zeros)
```

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-59.919  -1.696   0.000   0.000   1.384  97.758 
      digits zeros
 [1,]      1   228
 [2,]      2   158
 [3,]      3   140
 [4,]      4   136
 [5,]      5   135
 [6,]      6   135
 [7,]      7   135
 [8,]      8   135
 [9,]      9   135
[10,]     10   135
[11,]     11   135
[12,]     12   135
[13,]     13   135
[14,]     14   135
[15,]     15   112
[16,]     16    45
[17,]     17     9
[18,]     18     3
[19,]     19     2
[20,]     20     1
[21,]     21     1
[22,]     22     1
[23,]     23     1
[24,]     24     1
[25,]     25     1
[26,]     26     1
[27,]     27     1
[28,]     28     1
[29,]     29     1
[30,]     30     1

Conclusion: frequency of zero eigen values stabilize between 5 and 14 at 135.