The geography of collaborative knowledge production: entropy techniques and results for the European Union



Example (for three countries)

Co-occurrences in the Science Citation Index:

FRANCE - FRA

FRANCE - UK:

FRANCE - GER

NCE: 250   UK - FR

ANCE: 120 GERMANY - FRANCE:

140

90

750

80 UK - U

:       800 GERMANY - UK:

MANY: 160 UK - GE

RMANY: 110 GERMANY - GERMANY:

Collaboration matrix:18

FRANCE

FRANCE           250

UK                  100

GERMANY        150

SUM               500

Frequency matrix:

FRANCE

FRANCE             q11 = 0.10

UK                    q12 = 0.04

GERMANY          q13 = 0.06

(q1. = 0.20)

Tij-values:

FRANCE

FRANCE       T11= ln(0.10/0.04)= 0.92

UK        GERMANY   SUM

100            150            500

800            100            1000

100            750            1000

1000           1000          2500

UK        GERMANY

q21 = 0.04        q31 = 0.06        (q.1 = 0.20)

q22 = 0.32        q32 = 0.04        (q.2 = 0.40)

q23 = 0.04        q33 = 0.30        (q.3 = 0.40)

(q2. = 0.40)        (q3. = 0.40)        (q.. = 1.00)

UK             GERMANY

T21= ln(0.04/0.08)= -0.69 T31= ln(0.06/0.08)=

-0.29

UK

T12= ln(0.04/0.08)= -0.69

T22= ln(0.32/0.16)= 0.69 T32= ln(0.04/0.16)=

-1.39

GERMANY

T13= ln(0.06/0.08)= -0.29

T23= ln(0.04/0.16)= -1.39 T33= ln(0.30/0.16)=

0.63

Integration indicators :

T = (0.10 ∙ 0.92) + (0.04 ∙ -0.69) + (0.06 ∙ -0.29) + (0.04 ∙ -0.69) + (0.32 ∙ 0.69) + (0.04 ∙ -1.39) + (0.06 ∙
-0.29) + (0.04 ∙ -1.39) + (0.30 ∙ 0.63) = 0.30

Ti=j = (1/0.72) ∙ ((0.10 ∙ 0.92) + (0.32 ∙ 0.69) + (0.30 ∙0. 63)) = 0.70

Ti j= (1/0.28) ∙ ((0.04 ∙ -0.69) + (0.06 ∙ -0.29) + (0.04 ∙ -0.69) + (0.04 ∙ -1.39) + (0.06 ∙ -0.29) + (0.04 ∙ -
1.39)) = -0.72

T1 = (1/0.2) ∙ ((0.10 ∙ 0.92) + (0.04 ∙ -0.69) + (0.06 ∙ -0.29)) = 0.23

T2 = (1/0.4) ∙ ((0.04 ∙ -0.69) + (0.32 ∙ 0.69) + (0.04 ∙ -1.39)) = 0.35

T3 = (1/0.4) ∙ ((0.06 ∙ -0.29) + (0.04 ∙ -1.39) + (0.30 ∙ 0.63)) = 0.29

Table 1. Example of application of integration indicators

18 An address that is listed before or after another address is treated in the same way. The share of
collaborations between two different countries is therefore computed as half the mean to obtain qij=qji.

19



More intriguing information

1. The ultimate determinants of central bank independence
2. Income Taxation when Markets are Incomplete
3. Consumption Behaviour in Zambia: The Link to Poverty Alleviation?
4. A production model and maintenance planning model for the process industry
5. The name is absent
6. The name is absent
7. The name is absent
8. The name is absent
9. On the Integration of Digital Technologies into Mathematics Classrooms
10. The name is absent