deletions | additions       diff --git a/tori and riq.tex b/tori and riq.tex  index 2adda33..bbefbd0 100644  --- a/tori and riq.tex  +++ b/tori and riq.tex 
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the proposed measure employs two more bits of bibliographic information,  readily available by modern scholarly databases: the  number of authors and the number of references in a paper.  Both these measures have been used before, separately. Adjusting  citation counts for the number of authors seems obvious  system since 1996 \cite{kurtz05b}. Adjusting for the number of  references has become a standard technique in evaluating journals,  with Web of Science using Eigenfactor \cite{west} and SCOPUS using SNIP  indices have been proposed in the literature, as discussed above. For example, dividing  the \textit{h}-index by the number of authors in a paper  discipline \cite{radicchi} both yield promising results for  cross-disciplinary impact comparison.  Thus, we normalize every external (non-self) citation received by a scholar  in two ways: by the number of authors in the cited paper and by the  number of references in the citing article. We speculate that {\it a  simple double normalization, by number of authors and by number of  references in the citing article, has the effect of grounding  productivity index in the authorship and citation practices of a given  field at a given time.}  We define the Total Research Impact, {\it tori}, of a scholar as:  \begin{equation}  tori = \displaystyle\sum_{n} \frac{1}{a \cdot r}  \end{equation}  where $n$ is the collection of external (non-self) citations accrued  by the researcher, $a$ is the number of authors of the cited paper,  and $r$ is the number of bibliographic references of the citing  paper. One calculates the overall, cumulative output of a scholar by  summing the impact of every external citation accrued in his/her  career. As such, the total research impact of a scholar ({\it tori}) is  simply defined as \textit{the amount of work that others have devoted  to his/her research, measured in research papers}.  The definition of {\it tori} influences the self-citation correction. The  standard self-citation correction \cite{Wuchty} removes a citation  if any of the authors of the citing paper are the same as the authors  of the cited paper. With the computation of {\it tori}, we only remove a citation {\it if the  author being measured is an author of the citing paper.} \cite{glanzel}  We can also compute the research impact averaged over a scholar's  career, equivalent to the \textit{m}-quotient. For a scholar with a  career span of $y$ years, the Research Impact Quotient, \textit{riq},  is defined as:  \label{formula:ror2}  \begin{equation}  riq = \frac{\sqrt{tori}}{{y}}  \end{equation}  We test the performance of this measure on the same corpus discussed  above, finding that the research output quotient performs very well  both over time and across sub-disciplines of astronomy, as shown in  Figures 3 and 4.  Temporal debasement effects are greatly attenuated when computing the  perform, on average, similar to astronomers who started publishing 50  years later (global mean is $x = 0.098$). An exponential best-fit  regression line (shown as solid line, with a $0.95$ confidence band)  still shows a positive gradient ($b = 0.00659$), but considerably  smaller than that of {\it m}. (A similar analysis on a cohort of 544  astronomy Ph.D. confirmed this result, finding an exponential  regression line with slope $b = 0.00417$). The large attenuation of  temporal effects obtained with the computation of {\it riq} is not  predominately due to either of the two normalizations: they both  contribute roughly equally. The temporal slope after removing the  effects of multiple co-authors is $b = 0.015$ and the slope after the  normalization by number of references only is $b = 0.020$.  The disciplinary bias observed for the \textit{m}-quotient, previously  discussed and depicted in Figure 1, are greatly  improved when the \textit{riq} is computed, as shown in Figure  do perform below (i.e., ``gravitational waves'' and ``cosmic rays'')  or above average (i.e., ``stars parameters'', ``galaxies clusters'', and  ``particles''), the lower and upper {\it riq} quartile band  measured for the majority of  fields analyzed (18 out of 23) tends to fall within the global mean