Gilbert, N. (1997) 'A Simulation
of the Structure of Academic Science'
Sociological Research
Online, vol. 2, no. 2,
<http://www.socresonline.org.uk/2/2/3.html>
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Received: 11/2/97 Accepted: 19/5/97 Published: 30/6/97
This paper reports on a simulation designed to see whether it is possible to reproduce the form of these observed relationships using a small number of simple assumptions. The simulation succeeds in generating a specialty structure with 'areas' of science displaying growth and decline. It also reproduces Lotka's Law concerning the distribution of citations among authors.
The simulation suggests that it is possible to generate many of the quantitative features of the present structure of science and that one way of looking at scientific activity is as a system in which scientific papers generate further papers, with authors (scientists) playing a necessary but incidental role. The theoretical implications of these suggestions are briefly explored.
Chemical Abstracts | Econometrica | |||||
Number of contributions | Actual | Simon's estimate | Simulation | Actual | Simon's estimate | Simulation |
1 | 3991 | 4050 | 4066 | 436 | 453 | 458 |
2 | 1059 | 1160 | 1175 | 107 | 119 | 120 |
3 | 493 | 522 | 526 | 61 | 51 | |
4 | 287 | 288 | 302 | 40 | 27 | |
5 | 184 | 179 | 176 | 14 | 16 | |
6 | 131 | 120 | 122 | 23 | 11 | |
7 | 113 | 86 | 93 | 6 | 7 | 7 |
8 | 85 | 64 | 63 | 11 | 5 | 6 |
9 | 64 | 49 | 50 | 1 | 4 | 4< /td> |
10 | 65 | 38 | 45 | 0 | 3 | 2 |
11 or more | 419 | 335 | 273 | 22 | 25 | 18< /td> |
0.30 | 0.41 |
where m is a value between zero and one which increases randomly but monotonically for each successive citation. A similar equation determines the new y coordinate.
Parameter | Value |
0.41 | |
400 | |
7000 | |
480 | |
0.0025 |
Number of Papers | Simulation | Zipf Distribution |
1 | 667 | 717 |
2 | 218 | 193 |
3 | 93 | 82 |
4 | 56 | 43 |
5 | 29 | 26 |
6 | 20 | 17 |
7 | 11 | 12 |
8 | 9 | 9 |
9 | 12 | 7 |
10 | 3 | 5 |
11 or more | 15 | 24 |
(n, the number of authors, is 1,539; p, the number of papers, is 3,703; and is 0.41)
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;;;; Simulation of Lotka's Law ;;; ;;; Based on the exposition by H.A. Simon, On a class of skew distribution functions, ;;; in Models of Man (Wiley, 1957), Chapter 9, pp. 145-164 ;;; (originally Biometrika, vol. 42, December 1955) ;;; ;;; Constants n and alpha are set to reproduce estimates for contributions to ;;; Econometrica in Table 3, column 9 of Simon (1957) ;;; ;;; Written in Common Lisp ;;; ;;; Nigel Gilbert January 14, 1996 (defparameter author-total 721) ;total number of authors (defparameter alpha 41) ;percentage probability that a paper will ; be published by a new author (defun lotka (bins) "Function to simulate the distribution of authors of scientific papers who publish different numbers of papers in a journal over some period of time. Args: BINS is a vector to hold the number of authors publishing 0 ... 11 or more papers" (let ((published (make-array n :initial-element 0)) ; element i of the array holds the ; number of papers published by ; author i (papers '()) ;list of published papers (actually consists of a list of the ; index numbers of the authors who wrote each paper) (npapers 0) ;number of papers published so far (nauthors 0) ;number of authors who have published at least one paper so far new ;index number of author of the next paper to be published bin) ;index of the vector collecting the publication distribution (do () ((= author-total nauthors)) ;go round the loop until we have ; created total-authors ;; decide who will be the author of the next new paper (cond ;; it's a new author with probability alpha ;; or it is always a new author if this is the first ever paper ((or (< (random 100) alpha) (= npapers 0)) ;; create new author (setq new nauthors) (incf nauthors)) (t ;; old author ;; select a paper at random from those already published and set the author ;; to the author of that paper (setq new (nth (random npapers) papers)))) ;; 'publish' this new paper (add it to the list of published papers) (setq papers (cons new papers)) ;; and increment the number of published papers (incf npapers) ;; note that this author has published another paper. This is the end of the loop (incf (aref published new))) ;; obtain the distribution of the numbers of authors who have published x papers ;; any who have published 11 or more are put into the top bin (dotimes (a author-total) ;for each author... (setq bin (aref published a)) ;get the number of papers this author ; has published (when (> bin 11) (setq bin 11)) ;if more than 11, set to 11 ;finally, increment the count of the ; number of authors who have published (incf (aref bins bin))))) ; this many papers (defun run (&optional (trials 10)) "run the simulated distribution TRIALS times and print out the average over the trials" (let ((bins (make-array 12 :initial-element 0))) (dotimes (i trials) ;;execute the Lotka function trials (lotka bins)) ;; times, accumulating the results ;; print out the results, after dividing each by the number of trials to get the mean (format t "Averages of ~D trials: " trials) (dotimes (b 12) (format t "~D " (round (/ (aref bins b) trials))))))
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