Cahit Arf: Exploring His Scientific Influence Using

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Cahit Arf: Exploring His Scientific Influence Using Social Network Analysis, Author Co-citation

Maps and Single Publication h Index

Yaşar Tonta

tonta@hacettepe.edu.tr

yunus.hacettepe.edu.tr/~tonta/tonta.html Department of Information Management,

Faculty of Letters, Hacettepe University, 06800 Beytepe, Ankara, TR

A. Esra Özkan Çelik

esra@hacettepe.edu.tr

Registrar's Office, Hacettepe University, 06800 Beytepe, Ankara, TR

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Ord. Prof. Dr. Cahit Arf (1910-1997)

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Outline

• Biographical sketch of Cahit Arf

• Literature Review

• Research Questions

• Data Sources

• Method

• Findings

• Conclusions

• Recommendations

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• 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)

Cahit Arf

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Arf’s portrait graces the 10 Turkish Lira

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• 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

Cahit Arf’s scientific legacy

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• 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

Literature review

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• 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?

Research questions

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• 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

Data Sources

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• 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(tf

_i,j

)) log(N/df

_i

)

– 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)

Method

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Findings

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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)

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Author Co-citation Network of Arf

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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

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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.

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Pennant diagram: Section A

• RIEHM CR. (1965). “Integral representations of 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”

• TROJAN A.(1966). “Integral extension of

isometries of quadratic forms over local fields”

• RIEHM C. (1964). “On integral representations of quadratic forms over local fields”

• SPRINGER TA. (1955). “Quadratic forms over fields with a discrete valuation”

• SAH C. (1972). “Symmetric bilinear forms and quadratic forms”

Sector %

REFERENCE tf df N (tf/df)*100 tf*idf log(1+tf) log(5mil/df)

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

KLINGENBERG W,1954 5 7 5E+06 29.023 9.946 1.699 5.854

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

TROJAN A,1966 4 16 5E+06 29.156 8.803 1.602 5.495

RIEHM C,1964 5 33 5E+06 32.796 8.801 1.699 5.180

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

CAPPELL SE,1974 4 40 5E+06 31.432 8.166 1.602 5.097 Freq

Juniors of Arf

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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”)

• 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.)

Peers of Arf

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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)

– And a highly cited (449 times)

article by Kervaire MA (and Milnor J): “Groups of Homotopy Spheres: I”.

Seniors of Arf

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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

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Single publication h index of Arf (1941)

http://labs.dbs.uni-leipzig.de/gsh

Single pub h index: 24

• h

²

upper: 67%

(high impact citing pubs)

• h

²

center: 16%

(h index area)

• h

²

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)

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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

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• 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

Conclusions

Collnet 2011, September 20-23, Istanbul, Turkey

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• Further study needed to incorporate implicit citations to the calculation of the performance measures to have a fuller understanding of

the scientific impact of authors

• Calculation of the indirect influence of papers needs to be refined by assigning weights to

indirect citations (as suggested by Rousseau in 1987 long before h index came into being)

Recommendations

Collnet 2011, September 20-23, Istanbul, Turkey

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