# Read Before You Cite!

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4 272 M. V. Simkin and V. P. Roychowdhury The evolution of the misprint distribution (here K denotes the number of misprints that propagated K times, and is the total number of citations) is described by the following rate equations: d 1 d M (1 R) (1 M) 1, d K d (1 R) (1 M) (K 1) K 1 K K (K > 1). (2) These equations can be easily solved using methods developed in [4] to get: K 1 K Γ Γ 1 1 (1 R) (1 M). (3) As the exponent of the number frequency distribution Γ is related to the exponent of the rank frequency distribution Α by a relation Γ 1 (1/Α), equation (3) implies that: Α (1 R) (1 M). (4) The rate equation for the total number of misprints is: dt d M (1 R) (1 M) T. (5) The stationary solution of equation (5) is: T M R M MR. (6) The expectation value for the number of distinct misprints is obviously D M. (7) From equations (6) and (7) we obtain: R D T T D. (8) Substituting D 45, T 96, and 4300 in equation (8), we obtain R 0.22, which is very close to the initial estimate obtained using equation (1). This low value of R is consistent with the Principle of Least Effort [11]. One can ask: Why did we not choose to extract R using equations (3) or (4)? This is because Α and Γ are not very sensitive to R when it is small. In contrast, T scales as 1/R. We can slightly modify our model and assume that original misprints are only introduced when the reference is derived from the original paper, while those who copy references do not introduce new misprints (e.g., they cut-and-paste). In this case one can show that T M

5 Read Before You Cite! 273 and D M R. As a consequence, equation (1) becomes exact (in terms of expectation values, of course). The preceding analysis assumes that the stationary state had been reached. Is this reasonable? Equation (5) can be rewritten as: d T M T d ln. (9) (R M M R) As long as M is small it is natural to assume that the first citation was correct. Then the initial condition is 1; T 0. Equation (9) can be solved to get: M T R M M R 1 1. (10) R M M R This should be solved numerically for R. For our guinea pig, equation (10) gives R Just as a cautionary note, equation (10) can be rewritten as: T D 1 x 1 1 x R M M R. (11) X The definition of the natural logarithm is: a x 1 ln a lim. x 0 x Comparing this with equation (11) we see that when R is small (M is obviously always small): T ln. D (12) This means that a naïve analysis using equations (1) or (8) can lead to an erroneous belief that more cited papers are less read. One can augment our results with a closer scrutiny of the data. In order to make sure that misprints have not been introduced by the ISI as it sometimes happens [13], we explicitly verified a dozen misprinted citations in the original articles. All of them were exactly as in the ISI database. There are also occasional repeat identical misprints in papers, which share individuals in their author lists. Such events constitute a minority of repeat misprints. It is not obvious what to do with such cases when the author lists are not identical: Should the set of citations be counted as a single occurrence (under the premise that the common co-author is the only source of the misprint); or as multiple repetitions? However, even if we count all such repetitions as only a single misprint occurrence, then the number of citation-copiers (i.e., T D) shall drop from 151 to 112, bringing the upper bound for R (equation (1)) from 23% up to 29%. However a more detailed analysis via our model

6 274 M. V. Simkin and V. P. Roychowdhury [14] will bring down the estimate closer to 20%, keeping the original conclusions unaltered. We conclude that misprints in scientific citations should not be discarded as a mere happenstance, but, similar to Freudian slips, analyzed. Acknowledgments We are grateful to J. M. Kosterlitz, A. V. Melechko,. Sarshar, H. Muir, and many others for correspondence. References [1] Z. K. Silagadze, Citations and the Zipf Mandelbrot Law, Complex Systems, 11 (1997) ; [2] S. Redner, European Physics Journal B, 4 (1998) ; [3] C. Tsallis, and M. P. de Albuquerque, European Physics Journal B, 13 (2000) ; [4] P. L. Krapivsky and S. Redner, Physical Review E, 63 (2001) Art. o ; [5] H. Jeong, Z. eda, and A.-L. Barabasi, [6] A. Vazquez, [7] H. M. Gupta, J. R. Campanha, and B. A. Ferrari, [8] S. Lehmann, B. Lautrup, and A. D. Jackson, [9] S. Freud, Zur Psychopathologie des Alltagslebens (Internationaler psychoanalytischer Verlag, Leipzig, 1920). [10] Our guinea pig is the Kosterlitz Thouless paper (J. M. Kosterlitz and D. J. Thouless, Journal of Physics C, 6 (1973) ). The misprint distribution for a dozen other studied papers look very similar. [11] G. K. Zipf, Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology, (Addison-Wesley, Cambridge, MA, 1949). [12] H. A. Simon, Models of Man (Wiley, ew York, 1957). [13] A. Smith, ew Library World, 84 (1983) 198. [14] M. V. Simkin and V. P. Roychowdhury, to be published.

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