Cahit Arf: Exploring His Scientific Influence Using Social Network Analysis, Author Co-citation Maps and Single Publication h Index Yaşar Tonta [email protected] yunus.hacettepe.edu.tr/~tonta/tonta.html Department of Information Management, Faculty of Letters, Hacettepe University, 06800 Beytepe, Ankara, TR A. Esra Özkan Çelik [email protected] Registrar's Office, Hacettepe University, 06800 Beytepe, Ankara, TR Ord. Prof. Dr. Cahit Arf (1910-1997) Collnet 2011, September 20-23, Istanbul, Turkey Outline • Biographical sketch of Cahit Arf • Literature Review • Research Questions • Data Sources • Method • Findings • Conclusions • Recommendations Collnet 2011, September 20-23, Istanbul, Turkey Cahit Arf • Born in Selanik (Thessaloniki) (Feb. 18, 1910) • Graduate of École Normale Supérieure in Paris • Worked at Galatasaray High School and then joined the Math Dept of Istanbul University in 1933 • Went to Göttingen for his PhD degree (1937) – The Hasse-Arf Theorem • Published the Arf invariant of quadratic forms over a field of characteristic two (1941) and Arf rings (1948), among others • Worked at Robert College, METU, TUBITAK, Princeton, Berkeley • Received the Inonu Award, TUBITAK Science Award, Commandeur des Palmes Académiques, among others • Member of several academies • Died in Istanbul (Dec. 26, 1997) Collnet 2011, September 20-23, Istanbul, Turkey Arf’s portrait graces the 10 Turkish Lira Collnet 2011, September 20-23, Istanbul, Turkey Cahit Arf’s scientific legacy • Published 23 papers between 1939 and 1966 – 12 in French, 6 in German, 4 in English and 1 in Italian • Only two of his English papers were listed in Thomson Reuters’ citation indexes • Arf’s h index score is 1! • Arf invariant Arf(X), Arf(M), Arf(K) and Arf(q), Arf rings, Arf closure, the Hasse-Arf theorem, among others, are all well known and used in papers’ titles and keywords • Several books with “Arf” in their titles, e.g., Stable homotopy around the Arf-Kervaire invariant, by Snaith (2009) • Yet Arf has not been cited very heavily Collnet 2011, September 20-23, Istanbul, Turkey Literature review • Social network analysis (SNA) • Author co-citation analysis (ACA) • ACA + Information Retrieval (IR) + Relevance Theory (RT) (White, 2007) • Pennant diagrams • Single publication h index (Shubert, 2009) • Works on Cahit Arf Collnet 2011, September 20-23, Istanbul, Turkey Research questions • Who were the authors being co-cited most often with Arf? • How high were their h index scores? • Can we trace the scientific influence of Arf through paper titles and topics that contain the terms “Arf invariant”, “Arf rings” and so on? • Which paper of Arf received the highest number of citations? • Will the pennant diagram of Arf’s most frequently cited paper provide further insight into his influence in mathematics as well as in other disciplines? • What is the single publication h index of his most significant work? Collnet 2011, September 20-23, Istanbul, Turkey Data Sources • Thomson Reuters Web of Science (WoS) – Records of Cahit Arf (“Arf C*”) – Cited references of Arf – Records having “Arf*” in their titles and/or topics – Records of authors co-cited with Arf – h index scores of authors co-cited with Arf – Records of top 50 most cited math papers of all times • Google Scholar (GS) – Records of Cahit Arf – Records of authors citing Arf’s works – Single publication h index scores of top 50 most cited math papers of all times Collnet 2011, September 20-23, Istanbul, Turkey Method • Citation analysis – Author search – Cited reference search – Title and topic search – h index • Author co-citation analysis (ACA) – White (2007) combined ACA + IR and RT – Term frequency (tf): cognitive effects of works – Inverse document frequency (idf): ease of processing – weight (i,j) = (1 + log(tfi,j)) log(N/dfi) – Pennant diagrams plot tf values on the x axis and idf values on the y axis • Social network analysis – CiteSpace • Single publication h index – “the set of papers citing the work in question” (Schubert, 2009, p. 559) Collnet 2011, September 20-23, Istanbul, Turkey Findings Collnet 2011, September 20-23, Istanbul, Turkey Arf’s papers in Thomson Reuters WoS 1. Arf, C., Imre, K. & Ozizmir, E. (1965). On algebraic structure of cluster expansion in statistical mechanics. Journal of Mathematical Physics, 6(8): 1179-&. (Times cited: 3) 2. Arf, C. (1952). On methods of Rayleigh-Ritz-Weinstein. Proceedings of the American Mathematical Society, 3(2): 223- 232. (Times cited: 1) 3. Arf, C. (1951). On Rayleigh-Ritz-Weinstein method. Bulletin of the American Mathematical Society, 57(4): 269-270. (Times cited: 0) 4. Arf, C. (1951). On a free boundary problem in elasticity. Bulletin of the American Mathematical Society, 57(2): 136-136. (Times cited: 0) Collnet 2011, September 20-23, Istanbul, Turkey Author Co-citation Network of Arf Collnet 2011, September 20-23, Istanbul, Turkey Co-cited author distributions Co-cited Authors Frequencies h Index Scores ARF C 146 1 SERRE JP 30 23 WITT E 23 (No ISI records under his name) BOURBAKI N 21 (No ISI records under his name) MILNOR J 20 29 DIEUDONNE J 20 11 SAH CH 20 14 KERVAIRE MA 18 9 (with respect to 10 papers) OMEARA OT 18 11 WALL CTC 18 25 KNESER M 14 8 Collnet 2011, September 20-23, Istanbul, Turkey Pennant diagram of items co-cited with Arf (1941) Seed work: Arf, C. (1941). Untersuchungen über quadratische Formen in Körpern der Charakteristik 2. (Teil I.) Journal für die Reine und Angewandte Mathematik, 183, 148-167. Collnet 2011, September 20-23, Istanbul, Turkey Pennant diagram: Section A • RIEHM CR. (1965). “Integral representations of Juniors of Arf quadratic forms in characteristic 2” • KLINGENBERG W. (1954). “Über die Arfsche Invariante quadratischer Formen mod 2” • WITT E. (1954). “Über eine Invariante quadratischer Formen mod 2” • SAH CH. (1960). “Quadratic forms over fields of characteristic-2” Freq Sector % • TROJAN A.(1966). “Integral extension of REFERENCE tf df N (tf/df)*100 tf*idf log(1+tf) log(5mil/df) isometries of quadratic forms over local fields” ARF C,1943 5 5 5E+06 28.316 10.194 1.699 6.000 RIEHM CR,1965 5 6 5E+06 28.694 10.059 1.699 5.921 • RIEHM C. (1964). “On integral representations KLINGENBERG W,1954 5 7 5E+06 29.023 9.946 1.699 5.854 of quadratic forms over local fields” WITT E,1954 5 7 5E+06 29.023 9.946 1.699 5.854 • SAH CH,1960 9 13 5E+06 34.991 10.914 1.954 5.585 SPRINGER TA. (1955). “Quadratic forms over TROJAN A,1966 4 16 5E+06 29.156 8.803 1.602 5.495 fields with a discrete valuation” RIEHM C,1964 5 33 5E+06 32.796 8.801 1.699 5.180 • SAH C. (1972). “Symmetric bilinear forms and SPRINGER TA,1955 4 37 5E+06 31.225 8.220 1.602 5.131 SAH C,1972 7 40 5E+06 36.200 9.404 1.845 5.097 quadratic forms” CAPPELL SE,1974 4 40 5E+06 31.432 8.166 1.602 5.097 Collnet 2011, September 20-23, Istanbul, Turkey Pennant diagram: Section B • Papers in section B are no longer on “quadratic forms” (e.g., CAPPELL SE. (1974). “Unitary Nilpotent Groups and Hermitian K-Theory. 1”) Peers of Arf • Authors in section B are top mathematicians with high h index scores – Atiyah MF 34 – Milnor J 29 – Wall CTC 25 – Cappell SE 17 – Frohlich A 16… • Some (just like Arf himself) not properly represented in indexes (e.g. Kervaire M 9) , or not represented at all (e.g., Witt E.) Collnet 2011, September 20-23, Istanbul, Turkey Pennant diagram: Section C • Papers in section C are generic titles, world classics, and cited references as classic mathematics texts and classic articles, – Corps Locaux by Serre JP (1962) – Algebre by Bourbaki N (1959) – Linear Groups with an Exposition of the Galois Field Theory by Dickson LE (1958) – Introduction to Quadratic Forms over Fields by Lam TY (1973) – Introduction to Quadratic Forms by O’Meara (1963) – La Géométrie Des Groupes Classiques by Dieudonne (1955) – Algebraic Theory SPI by Chevalley C (1954) Seniors of Arf – And a highly cited (449 times) article by Kervaire MA (and Milnor J): “Groups of Homotopy Spheres: I”. Collnet 2011, September 20-23, Istanbul, Turkey Partial list of papers citing Arf (1941) • Based on Google Scholar data • Citing papers themselves were cited between 0 (one third have yet to be cited) and 827 times http://labs.dbs.uni-leipzig.de/gsh Collnet 2011, September 20-23, Istanbul, Turkey Single publication h index of Arf (1941) Single pub h index: 24 • h2 upper: 67% (high impact citing pubs) • h2 center: 16% (h index area) • h2 lower: 17% (low impact citing pubs) • m: median # of citations received by citing pubs in the Hirsch core (Bornmann, Mutz & Daniel, 2008) Solution of Arf-Kervaire invariant will further increase Arf’s (1941) single pub h index (Önder, 2011) http://labs.dbs.uni-leipzig.de/gsh Collnet 2011, September 20-23, Istanbul, Turkey Arf (1941) in perspective • 5,653 math papers under WoS categories of “Mathematics” and “Mathematics Applied” • Only 18 were cited more than 100 times • Checked the first 50 papers with the highest # of citations (max. 1,027 - min. 56) • Only 15 papers had single publication h index score higher than 24 Collnet 2011, September 20-23, Istanbul, Turkey Conclusions • Cahit Arf’s works are still influential today and being cited frequently, despite the fact that his last contribution was in 1960s • His paper on Arf invariant has been among the top 15 or 20 most influential math papers ever published • White’s (2007) approach and pennant diagrams, along with Schubert’s (2009) single publication h index, can be used to study the scientific influence of authors retrospectively and indirectly Collnet 2011, September 20-23, Istanbul, Turkey