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 Aug31 comment Expected distance traversed between 2 vertices on probabilistic graph why "-1" to the question? Oct5 comment Building a graph from pairwise distances Cris, I'm sorry, but I don't understand your point. Since I wrote that $d$ is a metric in mathematical sense, it will always be finite. In other words, I can always construct a graph by combining all vertices. Hence, the problem has always a solution. Oct5 comment Building a graph from pairwise distances Actually I just want to know if this is a known problem or if there is a field of study for this kind of problem. What would be the complexity of your algorithm? I think it is $O(n^2)$ Oct5 comment I need to compute one integral in terms of another integral. could you give me a clue on how you got this result? You have a +1 from me. Oct5 comment I need to compute one integral in terms of another integral. I can do so, but why do you need all this? It's just computation of an integral, nothing more than that. The problem is well defined. There are LOTS of answered posts in this forum just like this one. Oct5 comment I need to compute one integral in terms of another integral. ok, ok, ok....... Sep16 comment is a direct sum of Hilbert spaces a Hilbert space.? But Wikipédia presents a condition that is not present on proofwiki: the sum of all norms for each function on the direct sum must converge. Sep16 comment Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? Very good coment! However I would like to know why it is not an inner product, since it is linear in the first argument, positive definite, and symmetric. Sep14 comment Set of Bounded linear Operators on $l_2$ is dense on the set of bounded operators on $l_2$? This is not the core of the question. Anyways, a nonlinear operator is an operator which does not have the superposition property. Aug23 comment A quasimetric for a space formed by nouns very good answer! actually you are representing "popularity" of the noun as a function that takes an article and returns some quantity related to the number of appearances of the noun in the article. About your pseudometric $d(x, y)$: if $x$ and $y$ are close related, then $d(x,y)$ is very close to $0$, which is really what I need. About the "pseudo": I can always construct the set $A$ such that, for all $x \in S$ there will exist an article $a \in A$ with $R(a) \cap S = \{x\}$. Therefore, under this restriction, $d(x,y)$ is a metric, which solves my problem. Aug21 comment A quasimetric for a space formed by nouns Actually I don't want to measure similarity between strings. I want to measure similarity between string meanings. $A$ represents the set of all journal articles. Aug21 comment A quasimetric for a space formed by nouns I have changed the problem definition to account for these doubts. Thank you for your answer.