1546. - The relativity of the indexes (II)

Let's explain the mini post of the one of the dawn, at this hour it was not to write much more. Let's define the necessary minimal thing so that the formula is understood.

An investigator published different (je) papers that we can call a1, a2..., an.

Each of them is quoted by himself, his friends, and other investigators, with which we count the number of appointments and see that
there are c1 works that they quote a1, c2 that they quote to a2..., cn
they quote an.

That defines an index of very rapid impact to us to evaluate the quality of the investigator:

c = c1 + c2 +... + cn
(many appointments not always guarantee that he is a good investigator, but very few guarantee to us that it is not very good).

* * *
In 2005, Jorge Hirsch (an Argentine physicist who spent to better life in '70 (*)), introduced the h-index: let's suppose that we arrange the works as the number of appointments, of bigger than minor, and we place below the succession of natural numbers of minor to major:
c1>...> cn
1
Now, we have c1> major or equal to 1, and it will be last j such that cj is major or equal to j (since there are two lists of points, the decreasing one and another flood).

That one is h, the h-index, that it is understood easier saying that there is j papers, each one with j or more appointments.

* * *
Hirsch had already said that h it was climbing like the root of the entire appointments. Now, Redner demonstrates (**) the formula of the previous post:

c = 4h2
Redner analyzes the cases where the quotient √c/2h moves away much of 1, and finds common characteristics in every class of scientists. Very pretty.

* * *
The formula walks well with me (the quotient is 0.98) and with Caffarelli (1.02), so we can make sure that it covers both ends of the quality bogey.

* * *

(*) It Emigrated, it is in California.

(**) It Demonstrates to the physical thing: plotea semilog 255 information. I believe that with the mathscinet thousands might be obtained. Equal, I have fondness to R, believe that it was referee of a paper that we start with Matías in this blog.