Cahit Arf's Scientific Influence Through Social Network Analysis

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

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


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)

Arf’s portrait graces the 10 Turkish Lira


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

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


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?


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

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)


Findings


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)


Author Co-citation Network of Arf


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


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.


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
SPRINGER TA,1955
5 33 5E+06
4 37 5E+06
32.796
31.225
8.801
8.220
1.699
1.602
5.180
5.131
• SAH C. (1972). “Symmetric bilinear forms and
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


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.)


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”.


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

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


Arf (1941) in perspective
• 5,653 math papers under WoS categories of
“Mathematics” and “Mathematics Applied”
• Only 18 papers 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


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


Recommendations
• 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)


Cahit Arf's Scientific Influence Through Social Network Analysis

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