The 2015 CAP Congress, Edmonton
Which subfield of Physics is More Influential?
Jinshan Wu
School of Systems Science, Beijing Normal University
19/6/2015
J. Wu (BNU) More Influential Fields CAP2015 1 / 23
Outline
A table of contents
1 Two questions
2 Basic ideas
3 Definitions and some Math
4 Results
5 Acknowledgement
J. Wu (BNU) More Influential Fields CAP2015 2 / 23
Two Questions
What are we interested in?
Question 1: How one field is related to others? Given a field, whatare fields that it supports/is supported the most
Question 2: Which are the most influential fields and measure of theirrelative importance to the whole discipline (or even the whole science)
J. Wu (BNU) More Influential Fields CAP2015 3 / 23
Basic Ideas
Very simple ideas
Both direct and indirect input-output relations among the fieldsshould be considered
Similar ideas have been proposed and developed in Leontief’sInput-Output Analysis (LIOA) in Economics and in Google’sPageRank Algorithm
Not all citations are equal, links from the more important/influentialwebsites are weighted moreEigenvectors (PageRank) or inverse (LIOA) of matrices take bothdirect and indirect relation into consideration
J. Wu (BNU) More Influential Fields CAP2015 4 / 23
Basic Ideas
Why considers only subfields of Physics
In principle, we need the BIG input-output system about academia:Records of scientific publication, patents, funds, or even the economyand research grants
However, we have only records of publications in APS journals fromAPS
In any studies, we have to truncate the targeted system from thewhole system
The ideas and the mathematics defined in the following should bemore generally applicable
J. Wu (BNU) More Influential Fields CAP2015 5 / 23
Definition and Some Math
Key ideas in the Input-Output Analysis
Economists ask: Among industrial sectors, which one is moreimportant to the economy, which one is closely related to a givensectorOpen system approach:
Definition, x ij means the amount of input from the sector i to thesector jDefinition, total output from the sector i
X i =N−1∑j=1
x ij + y i =N−1∑j=1
bijXj + y i ,∀i 6= N. (1)
bij = x ij /Xj . (2)
where X = (X 1,X 2, . . . ,XN−1)T ,Y = (y1, y2, . . . , yN−1)T .Thus that in order to supply enough Y , X has to be
B(N−1)X + Y = X ⇐⇒ X =(
1− B(N−1))−1
Y (3)
LB ,(
1− B(N−1))−1
(4)J. Wu (BNU) More Influential Fields CAP2015 6 / 23
Definition and Some Math
HEM: what if one sector is removed
Removing sector i from the whole matrix B(N−1) while keeping Y asthe same except the demand on sector i itself:
X̂−i = LB(N−1−i)Y−i =(
1− B(N−1−i))−1
Y−i (5)
Difference between X and X̂−i tells the importance of sector i
The components which change the most correspond to the closelyrelated sectors
J. Wu (BNU) More Influential Fields CAP2015 7 / 23
Definition and Some Math
Why not simply X i?
Yes, one can do that however, without indirect influence of sector i
Google’s PageRank takes indirect influence into considerations too
J. Wu (BNU) More Influential Fields CAP2015 8 / 23
Definition and Some Math
Applicable to subfields in physics?
No. In the case of subfields in Physics, there is no such a well-definedexogenous sector, so a closed system modification is required
Turn to eigenvectors of the closed system, i.e. matrix B(N) (simply Bin the future) instead of B(N−1)
We still have
X i =N∑j=1
x ij =N∑j=1
bijXj ,∀i . (6)
BX = X . (7)
B is a non-negative (element) matrix with maximum eigenvalue 1,corresponds to a unique maximum eigenvector (for simplicity) X
However, Eq. (7) and X are trivial. Not much information can beextracted from them
J. Wu (BNU) More Influential Fields CAP2015 9 / 23
Definition and Some Math
Close-system Input-Output Analysis
Since X is the maximum eigenvector of B, what are the intuitivemeaning of the maximum eigenvector of B−i?
Let us denote them as λ−imax and∣∣λ−imax
⟩, in a sense
∣∣λ−imax
⟩corresponds to the max output of the system B−i
From this intuition, we define
S jIO = 1− λ(−j), (8)
∆jk =〈k |X 〉 − λ(−j)
(∑l 6=j X
l) ⟨
k |λ(−j)⟩〈k |X 〉
. (9)
J. Wu (BNU) More Influential Fields CAP2015 10 / 23
Results
Construction of the Input-Output matrix
PACS code as subfields, not exact, but works
Citations from papers turned into input-output relations among fields
b Paper A (DOI:PhysRevLett.101.170504)
Reference (total 21)
PACS: 03.67.Lx;42.50.-p
1.Paper B (DOI:PhysRevLett.85.2208) PACS: 03.67.Lx;32.80.Pj;32.80.Rm2. ......
------------
a
c
1
2 3
4
d32.80.Pj
32.80.Rm
03.67.Lx
42.50.-p
fromto
0
0
0
0
0
0
0
0
0
1/126
0
32.80.Rm
32.80.Rm
32.80.Pj
32.80.Pj
03.67.Lx
03.67.Lx
42.50.-p
42.50.-p
1/126
1/1261/126
1/1261/126
Figure : PA (PB) is the numberof PACS codes of paper A (B),CA the number of references of A
x ij (A→ B) =1
PAPBCA. (10)
J. Wu (BNU) More Influential Fields CAP2015 11 / 23
Results
Results on IOF, S jIO
Fields are ranked according to their IOF and simply number of papersand citations
Figure : Please focus on 05(StatPhys), 02(MathPhys), 04(Relativity) and98(Stellar)
J. Wu (BNU) More Influential Fields CAP2015 12 / 23
Results
Results on IOF, S jIO
J. Wu (BNU) More Influential Fields CAP2015 13 / 23
Results
Results on IOF, S jIO
J. Wu (BNU) More Influential Fields CAP2015 14 / 23
Results
Results on IOF, S jIO
Fields are ranked according to their IOF and simply number of papersand citations
Figure : Please focus on 05(StatPhys), 02(MathPhys), 04(Relativity) and98(Stellar)
J. Wu (BNU) More Influential Fields CAP2015 15 / 23
Results
Results on IOF, S jIO , continued
Animated version of the above figure
Figure : Time evolution
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Results
Results on interrelations, ∆jk
Among all level-1 subfields
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
J. Wu (BNU) More Influential Fields CAP2015 17 / 23
Results
Results on interrelations,continued
Among all level-2 subfields
01
01
02
02
03
03
04
04
05
05
06
06
07
07
11
11
12
12
13
13
14
14
21
21
23
23
24
24
25
25
26
26
27
27
28
28
29
29
31
31
32
32
33
33
34
34
36
36
37
37
39
39
41
41
42
42
43
43
44
44
45
45
46
46
47
47
51
51
52
52
61
61
62
62
63
63
64
64
65
65
66
66
67
67
68
68
71
71
72
72
73
73
74
74
75
75
76
76
77
77
78
78
79
79
81
81
82
82
83
83
84
84
85
85
87
87
89
89
91
91
92
92
93
93
94
94
95
95
96
96
97
97
98
98
99
99
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
J. Wu (BNU) More Influential Fields CAP2015 18 / 23
Results
Results on interrelations,continued
Given a field, say for example 98(Stellar systems) and 03(QuantumMechanics), what are other fields that closely related to it
100101
Citation ranking
100
101
IOI ra
nki
ng
95
04
97
9611
1412
2613
25
a 98
100101
Citation ranking
100
101
39
89
37
3242
6734
3305
84
b 03
Figure : For 03, firstly, the plot is further away from the diagonal line andsecondly, 37(atomic control) and 39(instruments, later merged to 37) havecloser relationship that what would have been seen simply from countingcitations.
J. Wu (BNU) More Influential Fields CAP2015 19 / 23
Results
An overview
Divide the whole level-3 fields into 4 group according to their IOFevery year (25% for each group)
1991 2001 201100 General10 Physics of Elementry Particles and Fields20 Nuclear Physics30 Atomic and Molecular Physics40 Electromagnetism, Optics,Classical Mechanics50 Physics of Gases, Plasmas, and Eletric Discharges60 Condensed Matter: Structural, Mechanical, and Thermal Properties70 Condensed Matter: Electronic Structure, Electrical, Magnetic, and Optical Properties80 Interdisciplinary Physics andRelated Areas of Science & Technology90 Geophysics, Astronomy , Astrophysics
Figure : You May take a look at General Physics (00)and interdisciplinary(80) in the top 25%
J. Wu (BNU) More Influential Fields CAP2015 20 / 23
Results
Results:shift of subfields’ ranks
Top 20 Level-2 subfields every year
1 05 05 032 71 71 053 61 61 424 73 03 715 78 73 736 68 42 757 74 75 788 64 78 619 75 68 6810 42 64 7411 72 74 7212 03 72 6413 82 11 1114 32 02 4715 79 82 8716 63 32 0217 02 12 1218 31 81 8119 34 47 8220 11 87 67
1991 2001 2011
J. Wu (BNU) More Influential Fields CAP2015 21 / 23
Conclusions
Conclusions and discussion
A new approach to describe influences of elements in a system withinput-output relation
Both direct and indirect effects are considered
Some fields stand out (deviate from the diagonal line), and moreimportantly, meaningfully
Method is more generally applicable
Applications to other more detailed and more specific fields for studiesof policy makers should be done (by others using the proposedanalysis)
J. Wu (BNU) More Influential Fields CAP2015 22 / 23
Acknowledgement
Acknowledgement and time for questions
Team member: Zhesi Shen, Menghui Li,Jianzhang Bao, Tian Wei,Jiansuo Pei, Liying Yang, Chensheng Wu, Zengru Di, RonaldRousseau
Thank to APS for providing the APS publication data, NSFC
Thank organizers of CAP 2015 for this invitation
J. Wu (BNU) More Influential Fields CAP2015 23 / 23