\section*{Discussion}
The discussed measures --- {\it tori} and {\it riq} --- eliminate the most important systematic factors
affecting the use of citations to measure the performance of
individuals: the number of authors of each paper, the number of
references in each paper, and the age of the individual.  In addition,
they remove the self citation bias.  The shot noise problem is not
directly addressed, however it is essentially eliminated by the number
of authors correction \cite{Spruit}.  The problem of curation was
addressed in this study by careful selection of non-ambiguous names; it is
being addressed more generally by initiatives such as
ORCID \cite{orcid}.

Both {\it tori} and {\it riq} are designed to measure individuals; aggregations
of individuals such as countries, universities, and departments, can be
characterized by simple summary statistics, such as the number of
scientists and their mean {\it riq}. An extension of {\it tori} to measure
journals would be straight forward: it would consist of the simple
removal of the normalization by the number of authors.  The result would
be similar to SNIP \cite{moed}; we suggest that SNIP and Eigenfactor \cite{west} continue to be used
for the purpose of measuring journals.

While {\it tori} and {\it riq} remove the largest systematic problems with
citation counts, they are citation-derived measures and, as such, 
they necessarily suffer from two systematic problems of citation
counts which
do not lend themselves to programmatic solutions. First, it is not in
general possible to tell the differing contributions of various
co-authors to a paper ({\it tori} assumes all authors contribute equally ---
a technique obviously more correct in the aggregate than for any individual paper).
Modifications, such as giving extra weight to the first (or last) author are necessarily ad hoc and discipline-dependent stratagems. The second fundamental problem with the use of citations for the evaluation of
individuals is that citations chiefly measure usefulness
While usefulness can be correlated with importance, these are clearly
different concepts; oftentimes, importance is what is actually desired.

Measuring the research performance of scholars
is a delicate and controversial procedure. That a scientists's career output
cannot be condensed in a bare number is beyond discussion. 
Yet, providing an accurate and concise quantitative
indication of a scholar's individual research output is important, and  
oftentimes necessary. For a faculty member at the early stages of her
career, for example, a quantitative indication of her scientific
productivity can be the factor determining whether she will be
promoted to tenure or whether she will be awarded a research grant. In
some other contexts, it may be crucial for funding bodies to know the aggregated research
output of individuals working in academic institutions and scientific
organizations as this can affect the course of science policy
decisions. 

But, most importantly, measuring research output with
accuracy is important chiefly because \textit{scholars themselves are
interested in knowing their own research performance and impact}.
The measures discussed here --- {\it tori} and {\it riq} --- while not easily computed by an individual, are
easily derived from information already available in virtually all bibliographic
repositories, such as Web of
Science (\url{http://wokinfo.com/}),
Scopus (\url{http://www.scopus.com}), SciFinder (\url{http://www.cas.org/products/scifindr/}),
and ACM-DL (\url{http://dl.acm.org/}).
The Astrophysics Data System (ADS) (\url{http://adsabs.org/}) has already implemented them and
they are currently available to the entire
community of astronomers and astrophysicists. We suggest that these
measures become part other academic databases as well, to allow a
fair measurement of researchers' output across time and disciplines. 


