Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm a computational biologist trying to interpret this equation correctly.

$$CI(x)= 1- \frac{2}{(N(N-1))} \sum_i^N\sum_j^N [ S(x_i,x_j) / \sqrt{S(x_i,x_i)S(x_j,x_j)}\ ] $$

i=1 ; j=i+1

I'm confused about the part before the summation

This is how I under stand this:

This is a nested summation, so if N=3 then you sum the partitions like[(1+2)+(1+3)]+[(2+3)]

Then do you multiply by $ 1- \frac{2}{(N(N-1))}$ ? or are you multiplying the sum of i (and j?) for each summation cycle, such as multiplying for 1 and 2 instead of multiplying 1+2?

Thanks a lot, it's been a while since I worked with stuff like this. This is a conservation index metric for multiple sequence alignments using a BLOSUM62 substitution matrix (The S(x,x) part).

share|improve this question
First, calculate the double sum. Then you multiply by $2/(N(N-1))$, which is a fixed number, since $N$ is fixed. Finally subtract all that from $1$. –  angryavian Feb 27 '14 at 4:07
THANK YOU SO MUCH! I feel so dumb now. –  QVINTVS FABIVS MAXIMVS Feb 27 '14 at 4:11

1 Answer 1

up vote 1 down vote accepted

Just focus first on the summation; it write $$\sum _{i=1}^N \sum _{j=i+1}^N \frac{S(x(i),x(j))}{\sqrt{S(x(i),x(i)) S(x(j),x(j))}}$$ For clarity, I shall expand this sum for $N=4$ in order you see how the terms appear $$\frac{S(x(1),x(2))}{\sqrt{S(x(1),x(1)) S(x(2),x(2))}}+\frac{S(x(1),x(3))}{\sqrt{S(x(1),x(1)) S(x(3),x(3))}}+\frac{S(x(2),x(3))}{\sqrt{S(x(2),x(2)) S(x(3),x(3))}}+\frac{S(x(1),x(4))}{\sqrt{S(x(1),x(1)) S(x(4),x(4))}}+\frac{S(x(2),x(4))}{\sqrt{S(x(2),x(2)) S(x(4),x(4))}}+\frac{S(x(3),x(4))}{\sqrt{S(x(3),x(3)) S(x(4),x(4))}}$$ Once this summation is done, just multiply the sum by $ \frac{2}{(N(N-1))}$ and substract the result from $1$.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.