An index measuring the mathematical content of an interdisciplinary area is described and calculated for the MATH/CHEM/COMP conference. Some further areas of application of this index in mathematical chemistry are indicated

Marija Došlić

Nađa Došlić

Tomislav Došlić

English

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On Appel Index of MATH/CHEM/COMP ConferenceMarija Do{li},a Na|a Do{li},b and Tomislav Do{li}c,*aJaneza Polde 1, 10000 Zagreb, CroatiabRu|er Bo{kovi} Institute, Bijeni~ka c. 54, 10000 Zagreb, CroatiacFaculty of Agriculture, Sveto{imunska c. 25, 10000 Zagreb, CroatiaRECEIVED JULY 20, 2001; REVISED OCTOBER 30, 2002; ACCEPTED DECEMBER 2, 2002An index measuring the mathematical content of an interdisciplinary area is described and cal-culated for the MATH/CHEM/COMP conference. Some further areas of application of this in-dex in mathematical chemistry are indicated.Key wordsAppel index* Author to whom correspondence should be addressed. (E-mail: doslic@math.hr)INTRODUCTIONIt is of utmost importance for any conference in an inter-disciplinary or multidisciplinary area to maintain a properbalance of contributions from its constituent basic disci-plines. Unfortunately, it is not always easy to determinesuch quantities; detailed knowledge of the area is a neces-sary prerequisite. For the members of the scientific com-mittee of the conference such a knowledge may be safelyassumed, but for a mortal considering to attend the confer-ence this is not always the case. We present here a simplemethod, proposed by Appel in Ref. 1 (no, not that Appel ofthe Four Color fame), that enables one to easily determinethe mathematical content of a given conference, or moregenerally, of a given interdisciplinary area. The method re-quires no specialist knowledge; all that is required are oldconference proceedings, elementary reading and countingabilities and a software capable of plotting simple graphs.As a case study, we apply this method to the proceedingsfrom the last eleven MATH/CHEM/COMP conferencesand analyze its degree of mathematicity. Finally, we indi-cate some further possibilities of application of this methodin mathematical chemistry.THEORETICAL FOUNDATIONSThe method of determining the mathematical content ofa given area rests on the following key observation, ma-de by Appel:1When writing a joint paper, mathematicians ordertheir names alphabetically, while other scientists use dif-ferent criteria to order their names, but only rarely thealphabetical one.For example, the chief of the lab goes first, or last;or the host goes first or last; or the one with money goesfirst, or last; or the one that did most of the work goesfirst, or last; or the most senior author goes first, or last.The reader can, probably, continue the list by someequally imaginative examples from his own experience.There may be an objection that this is not always thecase, but for the sake of the story, we will stick to this ob-servation, and take it as an axiom. Assuming it as an ax-iom, we will make no attempts to explain the key obser-vation. One possible explanation, offered by Shalosh B.Ekhad,2 and not necessarily supported by all authors ofthe present article, is that mathematicians are inherentlynicer and less competitive, while other scientists have apecking order.CROATICA CHEMICA ACTACCACAA 76 (2) 125¿127 (2003)ISSN-0011-1643CCA-2862Feature ArticleOf course, it is possible that the names of authorsappear in alphabetic order even on a paper jointly writ-ten by non-mathematicians. The probability of such anevent is 1/k! for a paper with k authors.Suppose, now, that in a particular community of au-thors fraction p are non-mathematicians and 1–p are ma-thematicians. Then the probability that a given k-authorpaper is signed in alphabetic order is (1–p) + p/k!.The second term describes the probability that thenames of k non-mathematicians on a joint paper appearin alphabetic order.If there are nk k-author papers, k  2, the probabilityof having exactly ak alphabetic k-author papers for all k 2 is given byL p ppkppknaa n akkkk k k( )! !  	 		12 .Now, take a pile of conference proceedings, and de-termine nk and ak for all k  2. (Unfortunately, single-au-thor papers carry no information, at least no informationrelevant for our purpose.) The problem is now to deter-mine the most likely value of p to produce these proce-edings. In other words, we want to maximize the func-tion L(p). The easiest way to do this (and still goodenough for our goal) is to plot the function L(p) for val-ues of p between 0 and 1 and to read off the approximateposition of the maximum. The resulting value pmax wesubtract from 1 (remember, we want to determine thefraction of mathematicians) and call this quantity theAppel index of the considered conference. (The name ofAppel factor was proposed in reference,2 but we preferthe term index. The reason is that there are many otherindices in mathematical chemistry. On the other hand,the term factor appears also in context of sun-protectinglotions, and the first association of many Croatian read-ers may be very far from the field of mathematicalchemistry, or even science at all.) The Appel index of agiven conference C we denote by  (C).THE MATH/CHEM/COMP CONFERENCE:A CASE STUDYAs a case study of the applicability of the Appel index tomathematical chemistry, we consider the MATH/CHEM/COMP conference. The conference seems almost ideallysuitable for this purpose, due to its interdisciplinarycharacter, long tradition and excellent record in the formof books of abstracts. The Appel index was calculatedfor the years 1991–2001. The results are summarized inTable I and graphically presented in Figure 1.From the data in Table I we can compute the aver-age of Appel index of the conference over the last elevenyears. This quantity is equal to 0.166. It means that theconference is only 16.6 % mathematical. Is it enough forthe conference that proudly puts mathematics on the firstplace in its name, we leave to the reader to decide. Cer-tain comfort can be found in the fact that overall trendseems to be improving, as indicated by the positivity ofthe leading coefficient in the line of the best fit. The best126 M. DO[LI] et al.Croat. Chem. Acta 76 (2) 125¿127 (2003)Table I. The Appel index for the MATH/CHEM/COMP conference by yearsY 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 (Y) 0.000 0.110 0.240 0.145 0.220 0.000 0.140 0.230 0.430 0.220 0.095YearTheAppelindex()Figure 1. The Appel index for the MATH/ CHEM/COMP conference by years and the line of thebest fit.linear fit is given by y = 0.0143 (x – 1990) + 0.08. Thus,the mathematical content of the conference is growing atthe rate of about 1.4 percent by year. We hope that thisanalysis will help the reader to determine in whichyear(s) the conference will be (or had been) just to histaste.As a kind of a control experiment, we have alsocomputed the Appel index for the DU'2000 NMR con-ference, and found it to be zero, in full accordance withour expectations.FURTHER RESEARCHAs it was noted by author of reference,2 the Appel indexcan be calculated not only for conferences, but also forthe bibliography of any interdisciplinary book. It wouldbe very interesting to determine the Appel index for thechemical graph theory, as given in the bibliography ofRef. 3. Also, extending the Ekhad’s line of thought, itwould be interesting to analyze trends of Appel index ofsome interdisciplinary journals, such as Match, the Jour-nal of Mathematical Chemistry and the Journal of Che-mical Information and Computer Sciences.Acknowledgment. – The authors are deeply grateful to Dr.Ante Graovac for making available to them copies of all sur-viving books of abstracts of the MATH/CHEM/COMP confer-ence.REFERENCES1. A. W. Appel, ACM SIGPLAN Notices 27 (1992) 87–89.2. S. B. Ekhad, The Theory of Self-Avoiding Walks is Only%66.81 Mathematical (According to the Appel Test), http://www.math.temple.edu/ekhad3. N. Trinajsti}, Chemical Graph Theory, CRC Press, BocaRaton, 1991.SA@ETAKO Appelovome indeksu znanstvenih skupova MATH/CHEM/COMPMarija Do{li}, Na|a Do{li} i Tomislav Do{li}Opisan je indeks koji mjeri matemati~ki sadr`aj danoga interdisciplinarnoga podru~ja. Izra~unane su vrije-dnost toga indeksa me|unarodnih znanstvenih skupova MATH/CHEM/COMP i navedena neka podru~ja mo-gu}e primjene toga indeksa u matemati~koj kemiji.ON APPEL INDEX 127Croat. Chem. Acta 76 (2) 125¿127 (2003)

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