Characterization of researchers in condensed matter physics using simple quantity based on h -index. M. A. Pustovoit

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1 Caracterization of researcers in condensed matter pysics using simple quantity based on -index M. A. Pustovoit Petersburg Nuclear Pysics Institute, Gatcina Leningrad district Russia Analysis of citation records of 52 active and productive condensed matter pysicists sows tat te ratio of -index to te mean age of most igly cited publications is a reliable quantity tat allows meaningful comparison of scientists of different age. Introduction Te need in quantitative estimation of individual researcer s scientific level as greatly increased in last years. Tis led to numerous attempts to obtain simple and informative indices of scientist s output based on citations of is or er publications. Probably te most interesting and promising example is te recently proposed Hirsc index ( -index) [1]. It can be obtained simply by sorting te publications of a researcer (or any relevant group of researcers) in descending order by te number of citations Nc and finding te maximum index in te list for wic N c. Popular databases like Tomson ISI or Scopus sow -index in teir citation analysis. Besides of its simplicity, -index is informative being considered togeter wit total number of citations and wit scientific age 1. Using a fairly large sample of prominent pysicists, Hirsc made interesting observations (e.g., mean -index about 40 for Nobel prize winners compared wit 45 as a lower tresold for membersip in US National Academy of Sciences) and provocative suggestions (e.g., taking a pysicist as outstanding wen e/se as -index 40 after 20 years of career). It was pointed out later tat -index as imperfections and limitations [2-5]. It is not surprising for a single-number measure, so it would be useful to find oter simple quantities tat can be combined wit -index to obtain a more satisfactory picture of individual scientific activity. In our study we analyze te large sample of researcers in a rater narrow field (52 condensed matter pysicists) in order to obtain a fair statistics for several important quantities. We found tat te ratio of -index to te mean age of publications tat contribute to -index (tat is, most igly cited publications) is a good quantity for comparison of scientists of different age. We also consider te problem of self-citations and sow tat te level of selfcitations in our sample is low. Details of te sample Selection of condensed matter pysicists was made by te following criteria: i) te unique name tat gives a single result in ISI autor searc; ii) te considerable productivity, i.e., ten or larger publications in Pysical Review B, Pysical Review Letters or arxiv.org/cond-mat as a result of autor searc at te website; iii) te ongoing scientific activity, tat is, at least one publication in te current year (2006) in te sources mentioned above. In addition, care was taken to keep te balance between experimentalists and teorists and between ages. Te special attention was given to exclude coautorsip between selected scientists. Te final sample included 52 researcers. Te following quantities were measured for every of tem using Tomson ISI Web of Knowledge: 1) total number N of publications autored (ISI does not account for preprints, conference tesis and book capters);

2 2) Total number C of publications tat cite te person s publications. Tis number is definitely le ss tan te total number of citations Nc. However, te former can be obtained muc easier tan te latter; 3) Te Hirsc index ; 4) Te mean age T of most cited papers. Te age of a particular publication is te difference between 2006 and te year of tis publication. 5) Te number N s of self-citing papers. Tis quantity is easily obtained by sorting te list of citing papers by autor in descending order. 6) Te scientific age T of a person defined as te difference between 2006 and te year of te first publication in te database. Since ISI contains records from year 1955, we assume tat tis quantity does not differ from te true scientific age. Index p and its properties We construct a new index as a ratio of te Hirsc index and te mean age of papers tat contribute to it: p = (1) T In order to examine its properties, let us consider te linear citation model used by Hirsc [1]. In tat model te scientist writes n papers every year, and eac paper receives c citations every year beginning wit te year next to its publication. Notating as y te year of publication of most recent papers tose contribute to te -index, we get after T years: ny =, ( ) T - y c=. (2) One can easily derive from ere bot and y. Since T y» T -, (3) 2 we obtain: 2nc p =. 2n+ c (4) Te extreme cases are: p 2 n, c n, p c, c n. (5) In words, te index p for low citation rate is limited by tis quantity, and for ig one by productivity. Tis means tat its value is unlikely to be very ig, and one can expect tat for particular field of science te distribution of tis index is rater narrow. Te index p migt resemble te supplemental index m proposed by Hirsc [1], m= T. Indeed, for te linear citation model we ave: 2

3 nc m =, (6) n+ c wic is very similar to Eq.(4). However, i) p can be obtained from real database records muc easier tan m, and ii) it favors ig citation rate: p c 2, c n, = 1+ m 2n+ c 1, c n. (7) Results and discussion Te quantities of special attention in tis paper are te Hirsc index and te mean age of publications tat form it. Te distributions of and T are sown in Figure 1. Figure 1. Distribution of our sample of condensed matter scientists: (a) by teir Hirsc index,, and (b) by te mean age of most cited publications, T. Te median values are 24 for and 14 years for T. We see tat te distribution of as a single sarp peak near = 25 followed by a rater long tail. Probably tis value can be considered as typical for condensed matter pysics, and te tail is formed, in particular, by suc persons as J.G.Bednorz ( = 40) and J.D.Jorgensen ( = 63 ). Te distribution of publication age T is single-peaked around 15 years; suc beavior probably is a result of our selection procedure. Figure 2. Scatter plot of versus T. Line is a one-parameter fit of te data. Te correlation coefficient is r =

4 Figure 2 demonstrates significant linear correlation between and (correlation coefficient is r = 0.46 ), and te usage of te new index p as teir ratio is well justified ere. T Figure 3. Probability density of te index p. Te median value is p =1.78. Inset: cumulative distribution function of p ; only 10% of individuals ave p > 3. Figure 3 sows te distribution of p. It is again single-peaked around p = 2. Hence one can see tat a successful condensed matter pysicist wit = 20 wrote is/er igly cited papers ten years ago on average. Te inset of Figure 3 sows te cumulative distribution function (te probability tat a scientist s p is less tan a certain value). We see tat about 90% of considered persons ave p < 3. Hence we can suggest tat an individual wit tis index iger tan 3 is eiter a respected scientist wit large formed by is/er famous papers written some time ago, or a young active one wose Hirsc index is due to considerable amount of igly cited recent papers. Te examination of our sample supports tis suggestion, and te numbers of young and well-known scientists appear to be equal. We stress ere tat young sould be understood ere as scientifically young, wit most of igly cited papers written recently. Suc property is one of te main advantages of te index p. Figure 4. a) Probability density of te index m ; b) te same for te ratio pm. For comparison, te distribution of te index m is sown in Figure 4a. It as two peaks, for unclear reasons. It is just interesting to note tat most of scientists in our sample ave m less tan 2, te value suggested by Hirsc [1] for outstanding pysicist. 4

5 Te correlation coefficient between p and m in our sample as a ig value Tus we can safely use te ratio p m as a reliable index. Its distribution is sown in Figure 4b. Te most notable result is te eavy tail wit pm> 2 (te maximum value in Eq.(7)), wic clearly demonstrates not only te fail of linear citation model but te superiority of p over m in distinguising scientifically young individuals. Figure 5. Distributions of fractions of self-citing papers (inset). Ns C (main grap) and Ns N Finally, we estimate te role of self-citations in our sample. Figure 5 displays te distribution of fractions of self-citing papers Ns C and Ns N. We see tat te first one is low (on average, only 8% of citing papers), and te second one is ig (wic is natural for a scientist involved in a particular problem for some time). Summary and conclusions We obtain citation data for a representative sample of 52 scientists working in te rater narrow field, te pysics of condensed matter. We calculate te mean age T of igly cited papers tat contribute to individual s Hirsc index. Tis quantity can be fairly easy obtained from database searc results. Its rater strong correlation wit -index allows to construct te new index p = T. In our sample tis index as a distribution wit a single peak around p = 2, tat is, an average successful condensed matter pysicist wit Hirsc index wrote is/er igly cited papers 2 years ago on average. Te small fraction (about 10%) of te individuals wo ave p > 3 includes respected as well as promising scientists. Te index p is correlated to te quantity m, te rate of increase of -index, but is more easily obtainable and favors scientists wo wrote teir igly cited papers recently. Acknowledgements Te autor is grateful for support and ospitality to Laboratory of Pysical and Structural Biology, National Institute of Cild Healt and Human Development (USA), were most of te data as been collected. Te work was also partially supported by RFBR grant and Russian State programs Macropysics and Strongly correlated electrons in semiconductors, metals, superconductors and magnetic materials. 5

6 References 1. J. E. HIRSCH, An index to quantify an individual s scientific output, Proceedings of te National Academy of Sciences of te United States of America, 102 (2005) [ttp://arxiv.org/abs/pysics/ ]. 2. C.D. KELLY, M.D. JENNIONS, Te -index and career assessment by numbers, Trends in Ecology and Evolution, 21 (2006) M. SCHREIBER, Self-citation corrections for te Hirsc index, Europysics Letters, 78 (2007) [ttp://arxiv.org/abs/pysics/ ]. 4. B. JIN, L. LIANG, R. ROUSSEAU, L. EGGHE, Te R- and AR-indices: Complementing te -index, Cinese Science Bulletin, 52 (6) (2007) J. E. HIRSCH, Does te -index ave predictive power?, ttp://arxiv.org/abs/