Research papers that studied the Triple Helix in relation to international co-authorship considered international collaboration as the fourth element of the system. This paper suggests considering three levels of study to assess the effect of international collaboration on an innovation system: the domestic one, the foreign one and the global one. The mutual information and the transmission power are used as indicators. Bibliographic data of South Korea and the West African region for a 10-year period (2001–2010) were downloaded and imported to a bibliographic software application. Searches are run to determine the Triple Helix actors and their bi- or trilateral collaboration contributions per considered area, year and level. Then, the mutual information and the transmission power were computed. Results show that at the domestic level, the South Korean innovation system is more integrated, whereas the West African one is less integrated than that of their partners. Results also show that international collaboration has strengthened knowledge sharing at the domestic level for both South Korea and West Africa, but to a different extent; in other words, the two areas have benefited from international collaboration in terms of knowledge flow.
The online version of this article (doi:10.1186/s40604-015-0027-0) contains supplementary material, which is available to authorized users.
Multilingual abstract
Please see Additional file 1 for translation of the abstract into Arabic.
Introduction
Two types of models of innovation were proposed up to now to explain the functioning of an economy: the linear and the nonlinear models. Each explains how growth is generated. The linear model postulated that ‘innovation starts with basic research, is followed by applied research and development, and ends with production and diffusion’ (Godin 2005; Godin 2006; Godin 2014). The nonlinear model introduced with the national innovation system concept ‘suggests that the research system’s ultimate goal is innovation and that the system is a part of a larger system composed of sectors like government, university and industry and their environment. The system also emphasized the relations between the components or sectors as the “cause” explaining the performance of innovation systems’ (Godin 2007). Both models have been criticised (Godin 2005; Godin 2006; Godin 2007) and variants of them were proposed. In the national innovation system model, analysis focuses on the flows of knowledge between actors (OECD 1997).
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The Triple Helix laid down by Etzkowitz and Leydesdorff (1995) and Etzkowitz and Leydesdorff (2000) is one of the variants of the nonlinear model of innovation (cf. Etzkowitz and Leydesdorff 2000; Leydesdorff 2012; Meyer et al. 2014). The model postulates that the interactions between university, industry and government maintain a knowledge infrastructure that generates knowledge of which circulation among innovation actors drives economic growth and social welfare (Leydesdorff and Etzkowitz 2001). The mutual information (Leydesdorff 2003) was elaborated as an indicator of the Triple Helix relationships between university, industry and government. It has been used widely to assess countries or region profiles (e.g. Leydesdorff and Sun 2009; Khan and Park 2011; Shin et al. 2012; Leydesdorff et al. 2013a; Mêgnigbêto 2013a; Mêgnigbêto 2015a; Mêgnigbêto 2015b) or assess the knowledge base of economies (e.g. Park et al. 2005; Park et al. 2005; Leydesdorff and Zhou 2013; Leydesdorff et al. 2015). The transmission power was proposed by Mêgnigbêto (2014a) as the normalisation of the mutual information. It was used to assess the knowledge flow within the West African innovation systems, both at national and regional levels (Mêgnigbêto 2014b; Mêgnigbêto 2014c); it was also used to compare the knowledge production profiles of six OECD countries (Mêgnigbêto 2015a; Mêgnigbêto 2015b). Jointly with other indicators, it helped in studying the Norwegian innovation system both at national and county levels, based on data including the number of establishments in geographical, organisational and technological dimensions over a 13-year period (Ivanova et al. 2014).
The Triple Helix model lays on collaboration. When publications serve as unit of analysis, co-authorship is taken as a measurement of collaboration (Katz and Martin 1997; Bordons and Gomez 2000; Olmeda-Gómez et al. 2008; Abbassi et al. 2012); indeed, it entails the tacit transfer of information and knowledge (Olmeda-Gómez et al. 2008) and ensures diffusion of ideas and knowledge circulation (Guns and Rousseau 2014). The importance of co-authorship in knowledge creation and sharing may be measured by the international co-authorship trend. Indeed, publications on co-authorship worldwide all reported an increasing trend in the number of authors who contributed to an article (e.g. Bordons and Gomez 2000; Tijssen 2007; Leydesdorff and Wagner 2008; Boshoff 2009; Adams et al. 2010a; Onyancha and Maluleka 2011; Toivanen and Ponomariov 2011; Adams 2012; Leydesdorff et al. 2013b; Mêgnigbêto 2013b; Adams et al. 2014; Ossenblok et al. 2014). Some of them underlined the concentration of the growth in the group of papers with five or more authors, lending strong importance to collaboration. As an illustration, research collaboration networks have been evolving and countries that were at the periphery are becoming a member of the core; besides, the global international collaboration network had become denser (Leydesdorff and Wagner 2008). Globally, co-authorship has exploded recently (Adams 2012) and internationalisation of collaboration characterises science today (Adams 2013) due mainly to globalisation. Therefore, by means of collaboration, innovation actors contributed to synergy and knowledge creation at both national and international levels. Leydesdorff and Zawdie (2010) affirmed that ‘knowledge-based economy develops as a dynamic system at the global level, thus transcending national or geographical boundaries’.
At our knowledge, few papers studied international co-authorship in relation to the Triple Helix. Firstly, Leydesdorff and Sun (2009), Kwon (2011) and Kwon et al. (2012) included the internationally co-authored papers as the fourth element of the model; this method requires a huge amount of data processing and cleaning of the institutional address information (Leydesdorff and Sun 2009). Secondly, Choi et al. (2015) studied the intra-sector co-authorship at the international level. And thirdly, Shin et al. (2012) combined domestic and international collaboration by university, industry and government and their bi- or trilateral output. The abovementioned studies computed neither the synergy or knowledge the national innovation actors contributed abroad nor its effect on the synergy or knowledge creation and sharing at national level; therefore, they could not measure the real amount of knowledge that circulates among an areas’ innovation actors (Mêgnigbêto 2015a; Mêgnigbêto 2015b). Indeed, globalisation has given opportunities to researchers to collaborate worldwide regardless the distance. Besides, it has eroded some countries’ mutual information (Leydesdorff and Sun 2009; Kwon et al. 2012; Leydesdorff and Park 2014), and should have affected how knowledge is shared at the country level.
Because the mutual information at a country’s level could have been eroded by international co-authorship, it is not sufficient alone to indicate how knowledge-based an economy is (Mêgnigbêto 2015a; Mêgnigbêto 2015b). So, while comparing countries on the basis of the mutual information or derived indicators, the effect of international collaboration remains unilluminated. Thus, the comparison may be biassed. As an example, the Japanese research performance is driven by domestic activity (Adams et al. 2010b); this country’s mutual information was always higher compared with that of other countries (Leydesdorff 2003; Park et al. 2005; Ye et al. 2013; Mêgnigbêto 2014a; Mêgnigbêto 2015a; Mêgnigbêto 2015b). The conclusion that the synergy at the Japanese national level is higher than elsewhere is true, but deriving that the Japanese economy is more knowledge-based than that of another country may not be.
Anzeige
In this paper, we hypothesise that the synergy or knowledge contributed at the international level by a country’s domestic innovation actors may have affected the synergy or knowledge they created at the national level. In other words, foreign innovation actors can influence the synergy and knowledge creation and sharing at a country’s level. Our research question is twofold. (1) How is the synergy or knowledge contributed abroad by an area’s innovation actors due to their relations with their foreign partners measured? (2) What is the effect of international collaboration on knowledge flow within an innovation system?
Methods
The mutual information is borrowed from Shannon’s (1948) information theory. Central to this theory is the notion of entropy defined as the average quantity of information contained in a variable. The transmission power is derived from the mutual information. Appendix 1 gives the mathematical relations between entropy, mutual information and transmission power.
Domestic, foreign and global systems
Leydesdorff and Sun (2009), Kwon (2011) and Kwon et al. (2012) named ‘foreign’ institutions from partner countries and considered it as the fourth element of the innovation system composed of the three national actors that are university (u), industry (i) and government (g), leading to the computation of the mutual information (Tuigf) of the Quadruple Helix. The type of the institutions involved is not taken into account (Fig. 1a). Our method suggests considering three levels of analysis: (1) the domestic one grouping the country- or area-based innovation actors as done in the literature hitherto, (2) the foreign one grouping the innovation actors from the partner countries, and (3) the global one grouping the two previously defined systems. Hence, the global system may be considered as composed of the ‘domestic’ and foreign sub-systems, each with three innovation actors leading to six actors at the global level (Fig. 1b). The two sub-systems interact and exert on each other a mutual influence that may act on the synergy within each other by the mutual relationships they entertain. The relationships existing between the actors on Fig. 1a (as represented by arrows) also exist within the domestic sub-system on the one hand and the foreign one on the other hand (Fig. 1b). Abstraction is done of these relationships on Fig. 1b, however. Studying such a Sextuple Helix (Leydesdorff 2012) requires the computation of 26 = 64 sectors data.1 A simpler way to proceed consists in considering the global system as if actors were from the same geographical area and studying separately the three domestic, foreign and global Triple Helix systems. Thus, one can compute the mutual information and transmission power of the domestic, foreign and the global systems using the formulas given above. We suggest using the normalised difference between the global and domestic transmission power as the effect of international collaboration on knowledge flow within an innovation system.
Fig. 1
Illustration of the method used by Leydesdorff and Sun (2009), Kwon (2011) and Kwon et al. (2012) (a) and the one proposed by this study (b) for integrating the international co-authorship in the Triple Helix relations. Sectors are represented by small circles meaning the intra-sectorial relations (loops)
×
International collaboration and transmission power
Because a record could have both foreign and domestic co-authors, the method of entropy decomposition suggested by Theil (1972) is not applicable; indeed, the number of records from ‘domestic’ and that from foreign do not sum up to the number of records at the global level. We suggest computing the mutual information and transmission power of the domestic, foreign and the global systems using the formulas given above. Hence, the method (Shin et al. 2012) used computed the domestic and global mutual informations for Saudi Arabia. If we denote τd the domestic transmission power, τf the foreign one and τg the global one, the effect of the international collaboration on an area may be measured with the scalar \( \frac{\tau_{\mathrm{g}}-{\tau}_{\mathrm{d}}}{\tau_{\mathrm{g}}} \) expressed as percentage. We argue that the total synergy within such a system is measured by τg. Therefore, one can compute the total transmission power for such a country and compare countries on this basis. In this section, we do not consider the synergy created at the foreign level solely, because it does not add any value to our interpretation; furthermore, its effects combined with that of the domestic synergy are already included into the global values.
Data collection
The data source is the Web of Science. Our research question requires the distinction between the papers originated from a geographic area’s university, industry and government relationships and those resulting from the collaboration with at least one university, industry or government abroad. If we could search for the first category with the Web of Science’s search function, we could not for the second category. Therefore, we opted for data downloading for further relevant treatment. The primary area for the application is the West African region2; however, Korea, a country which some decades ago has the same economic and social conditions as the West African countries, has been steadily studied with regard to Triple Helix dynamics (e.g. Park et al. 2005; Park and Leydesdorff 2010; Khan and Park 2011; Kwon et al. 2012; Mêgnigbêto 2015a; Mêgnigbêto 2015b); therefore, it is chosen for comparison purpose. So, this article treats the scientific data of the West African region and South Korea. West African3 and South Korean4 publication data from Web of Science5 over a 10-year period (2001–2010) were downloaded. The records resulting from these two searches were imported into two different bibliographic databases6 managed with CDS/ISIS7 thanks to a programme coded into CDS/ISIS Pascal8.
Data treatment
Based on the method of Leydesdorff (2003) and Park et al. (2005) for address assignment, a list of words or abbreviations was established to attribute each record address a label: UNIV for university, INDU for industry or GOV for government. A second CDS/ISIS Pascal programme was coded for this task. A record may contain many addresses; therefore, one record may have two or more different labels. The CDS/ISIS Pascal programmes were also instructed to read the countries’ name from the addresses and automatically add the associated area name: West Africa for the West African database and Korea for the South Korean database. Addresses that do not relate to any West African country or South Korea are labelled ‘FOREIGN’. So, in the inverted file of the databases, a university in West Africa appears under the label UNIV-WEST-AFRICA, an enterprise in South Korea appears under the label INDU-SOUTH KOREA and a foreign university (from the West Africa or South Korean point of view) under UNIV-FOREIGN, etc. As a result, the inverted file contains only the following keywords, in alphabetical order:9 GOV-FOREIGN, GOV-SOUTH KOREA, INDU-FOREIGN, INDU-SOUTH KOREA, UNIV-FOREIGN and UNIV-SOUTH KOREA for the South Korean data and GOV-FOREIGN, GOV-WEST-AFRICA, INDU-FOREIGN, INDU-WEST-AFRICA, UNIV-FOREIGN and UNIV-WEST-AFRICA for the West African data.
The CDS/ISIS search functions were used to compute the university, industry and government output and their bi or trilateral collaboration data at the three levels (Cf. Appendix 2). The print service of CDS/ISIS was used to output the publication year of the search results into text files for statistical analyses with the R software (R Development Core Team 2014); then, the repartition of records per year of publication was obtained. We coded a PHP programme that computes the sectorial entropies, the bilateral entropies and mutual informations, and the trilateral entropies and mutual information and the transmission powers according to the formulas given above. All the levels of analysis (domestic, foreign and global) were taken into account.
Result
Output and international collaboration
Table 1 provides basic data on the two areas’ scientific publishing over the considered periods of time: output, number of co-authors, average number of co-authors per paper, number and percentage of papers resulting from international collaboration. Over the decade, South Korea outputs a total of 368,729 papers and West Africa 30,717 papers; this leads to an annual average of 38,873 publications for South Korea and 3072 publications for West Africa. One South Korean publication out of five has at least one foreign co-author and about one half of West African publications has at least one foreign co-author. For both areas, the number of papers with at least one foreign address is increasing in absolute value; however, the trend seems to decrease very slowly in percentage. The number of co-authors per paper rose progressively from 2.39 in 2001 to 3.02 in 2010 in the case of West Africa and from 2.09 in 2001 to 2.65 in 2010 in the case of South Korea (Table 2).
Table 1
Total annual output and international collaboration data in the scientific publishing in South Korea (2001–2010)
Indicator
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total
Annual output
20,512
22,369
25,559
30,283
34,661
38,817
45,740
47,854
50,677
52,257
368,729
(Co-) authors
42,958
51,462
59,090
69,485
83,158
92,318
107,731
113,332
129,140
138,592
887,266
Authors per paper
2.09
2.30
2.31
2.29
2.40
2.38
2.36
2.37
2.55
2.65
2.41
International coll.
3918
4705
5933
6334
7271
8005
8857
9685
11,142
12,243
78,093
International coll. (%)
19.10
21.03
23.21
20.92
20.98
20.62
19.36
20.24
21.15
23.43
20.98
Table 2
Total annual output and international collaboration data in the scientific publishing in West Africa (2001–2010)
Indicator
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Total
Annual output
1646
1796
1945
2097
2779
2835
3642
4198
4735
5044
30,717
(Co-)authors
3932
4372
4998
5588
7233
7927
9916
11,745
13,080
15,215
84,006
Authors per paper
2.39
2.43
2.57
2.66
2.60
2.80
2.72
2.80
2.76
3.02
2.74
International coll.
863
927
1045
1123
1421
1464
1655
1849
2108
2386
14,814
International coll. (%)
50.79
51.61
53.73
53.55
51.13
51.64
45.44
44.04
44.52
47.30
48.23
Triple Helix sectorial outputs
The university (U), industry (I) and government (G) and their bi or trilateral collaboration (UI, UG, IG and UIG) outputs with regard to the level of production (e.g. domestic (d), foreign (f) and global (g)) are presented in Tables 3 and 4 for South Korea and Table 5 for West Africa. These tables illustrate the problematic of the study: for example, the line labelled 2001 in Table 5 indicates that for the West African region, U produces 829 publications at the domestic level, 376 publications at the foreign level and 816 publications at the global one. A closer analysis reveals that 829 − 816 = 13 publications attributed to U at the domestic level no longer belong to this sector at the global level. In fact, they were co-authored with other innovation actors (I or G) from foreign; so, they accounted for the collaboration of U (UI, UG or UIG) at the global level. For both areas, whatever the sectorial output is, the domestic value is higher than the global one for the Triple Helix actors but lower for their bi- or trilateral combinations.
Table 3
Triple Helix sectorial outputs for South Korea (2001–2010)
U
I
G
D
f
G
D
F
g
D
f
g
2001
12,836
2416
12,221
271
32
246
3107
513
2740
2002
14,400
2946
13,628
311
41
260
3238
606
2810
2003
17,685
3703
16,732
334
65
298
3899
804
3322
2004
19,595
3909
18,543
391
68
342
4108
787
3502
2005
22,412
4534
21,207
440
55
380
4853
901
4126
2006
25,114
5055
23,845
478
67
398
5390
996
4621
2007
30,263
5557
28,884
561
68
488
6591
1049
5682
2008
30,939
6195
29,349
526
46
422
6023
1152
5067
2009
33,626
6964
31,863
399
86
381
6186
1207
5105
2010
34,325
7823
32,371
381
67
289
6478
1305
5240
Total
241,195
49,102
228,643
4092
595
3504
49,873
9320
42,215
Table 4
Triple Helix sectorial outputs for South Korea (2001–2010)
UI
UG
IG
UIG
d
F
g
D
F
G
D
f
g
d
f
g
2001
276
32
334
2160
497
3246
72
11
85
57
17
102
2002
343
45
432
2551
599
3853
71
13
89
87
16
136
2003
463
44
547
3339
711
4978
78
24
103
106
21
180
2004
476
55
597
3728
842
5502
100
15
115
129
26
199
2005
541
53
654
4258
1065
6369
127
19
141
119
30
197
2006
615
79
772
4752
1084
6931
150
16
167
157
35
245
2007
742
70
888
5282
1300
7804
113
14
134
192
45
290
2008
850
70
998
6084
1479
8852
128
23
145
190
51
313
2009
962
89
1144
6989
1716
10,062
136
32
157
255
64
392
2010
994
86
1156
7658
1969
11,106
141
33
157
255
75
409
Total
6262
623
7522
46,801
11,262
68,703
1116
200
1293
1547
380
2463
Table 5
Triple Helix sectorial outputs for the West African region (2001–2010)
U
I
G
UI
UG
IG
UIG
d
F
g
D
f
g
D
F
g
D
F
G
D
f
g
d
f
g
d
f
g
2001
829
376
819
4
1
4
471
161
321
1
1
2
112
146
387
1
0
2
0
4
4
2002
940
395
896
7
5
6
474
189
307
0
3
3
134
185
458
1
0
2
0
2
6
2003
1002
471
971
10
6
6
509
180
310
3
2
8
162
212
526
1
2
4
0
6
10
2004
1149
525
1112
4
4
2
491
184
297
2
2
9
163
237
562
0
2
2
0
2
3
2005
1525
653
1450
6
6
4
673
294
421
3
2
8
272
272
774
1
1
3
0
2
5
2006
1594
700
1547
6
2
4
667
235
393
6
3
11
253
324
763
0
6
4
2
5
11
2007
2198
805
2058
9
6
9
750
285
439
8
3
12
351
350
964
1
6
6
0
6
12
2008
2632
928
2497
11
5
7
783
272
437
13
8
25
426
407
1094
5
3
6
3
14
22
2009
3055
1056
2887
10
6
7
788
308
434
12
8
22
468
492
1234
2
0
2
1
4
11
2010
3053
1160
2825
12
10
5
999
377
563
13
5
23
546
587
1457
2
3
3
2
13
28
Total
17,977
7069
17,062
79
51
54
6605
2485
3922
61
37
123
2887
3212
8219
14
23
34
8
58
112
Mutual information and transmission power time series
The mutual information and the transmission power are presented in Table 6 for West Africa and Table 7 for South Korea. They are related to the domestic, foreign and global levels. The mutual information values reveal that there is synergy within the considered innovation systems over the period of study at all levels. For the two areas under consideration, the curves of the three levels do not show the same relative positions over the period. In the case of South Korea, the domestic mutual information has the highest (absolute) value and decreased, except in 2009 where it took the median position. The global mutual information is lower (in absolute value) than the domestic one over the period; the foreign mutual information has either the top position or the median one (Fig. 2). In the case of West Africa, however, the relative positions of the curves are no longer identic (Fig. 3). Indeed, the foreign mutual information has the highest (absolute) value except in 2001 and 2006 where it has the lowest. The domestic mutual information has the highest absolute value in 2001 and 2006 and keeps the median position over the rest of the period. The global mutual information gets the lowest absolute value over the period except 2001 and 2006.
Table 6
Mutual information (Tuig, in millibits) and transmission power (τ) for West Africa (2001–2010) at domestic, foreign and global levels
Domestic, foreign and global mutual informations of South Korea (2001–2010)
Fig. 3
Domestic, foreign and global mutual informations of West Africa (2001–2010)
×
×
In summary, globally, the foreign mutual information is higher (in absolute value) than the domestic one in the case of West Africa, but the South Korean innovation system exhibits an opposite pattern. In other words, the synergy operates more at the foreign level than at the domestic one in the case of West Africa but the reverse is recorded in the case of South Korea. These results suggest that the South Korean domestic system is more integrated than the foreign one and that the West African system is less integrated than the foreign one.
At a country level, innovation actors are submitted to the same rules and policies; they have the same domestic socioeconomic backgrounds and research agendas. On the other side, the foreign actors come from different countries; they are submitted to different policies and research agendas; therefore, the cohesion in their actions could not have the same strength as in the case of national actors. West African institutional partners even coming from different horizons seem more organised than the West Africa-based innovation actors.
The global transmission power is highest in the case of South Korea. The foreign transmission power’s relative position has changed over the period: it was the lowest over the period, except in 2004 and 2009, where it was median; it has interchanged its position with the domestic transmission power (Fig. 4). The same global trend was registered in the case of West Africa: the global transmission power is higher than the domestic one but the foreign one changed positions over the period (Fig. 5). The mutual information measures the quantity of information common to the random variables in the system (Shannon 1948). It then measures the quantity of information or knowledge shared within the innovation actors. The transmission power is ‘the strength of the information flow within the system or between its actors.’ (Mêgnigbêto 2014a). Therefore, the knowledge sharing is more efficient in the global system than the domestic one, for both South Korea and West Africa. The global system ensures a better knowledge circulation among innovation actors.
Fig. 4
Domestic, foreign and global transmission power for South Korea (2001–2010)
Fig. 5
Domestic, foreign and global transmission power for West Africa (2001–2010)
×
×
Effect of international collaboration
The effect of the international collaboration on the knowledge flow is computed in the last columns of Table 6 and Table 7 and displayed in Fig. 6. If South Korea has gained a little with regard to its domestic transmission power (7–24 %, with an average of 12 % over the 10-year period), the involvement in international collaboration has even doubled the West African knowledge circulation capacity. The region has gained from 5.33 to 100 % of its knowledge-sharing capacity with an average of 54.04 % over the 10-year period.
Fig. 6
Effect of international collaboration on transmission power in South Korea and West Africa (2001–2010)
×
Discussion
West Africa and South Korea display opposite patterns with regard to the relative positions of the foreign and domestic mutual information curves. Indeed, whereas the domestic mutual information is higher in absolute value than the foreign one in the case of South Korea, the reverse is recorded for West Africa. According to Leydesdorff (2003) and Leydesdorff (2008), when the mutual information is negative, it indicates the level of synergy within a system, the extent to which a system is self-organised. This result leads to the conclusion that the West African innovation system is less organised than the set of its institutional partners considered as coming from the same country, and conversely that the South Korean innovation system is more integrated by itself. In fact, South Korea has strengthened its national innovation system after years of benefiting from international collaboration (Mêgnigbêto 2015a; Mêgnigbêto 2015b) following changes in its policies over decades (Kwon et al. 2012). The stead investment in research and development may have strengthened the collaboration between innovation actors at the country level and explains the performance of South Korea (Mêgnigbêto 2015a; Mêgnigbêto 2015b). It illustrates the efforts done by South Korea to catch-up with leading economies (OECD 2009).
West Africa is a ‘region’ composed of 15 countries. It is also an economic integration area with supranational institutions that have the role to conceive and apply policies at regional level. Even though the ECOWAS has formulated sectorial policies (e.g. agriculture and industry), it is recently, in 2012, that the Economic Community of West African States Policy on Science and Technology (ECOPOST) was adopted. Actually, it is hard to know the actions executed and the progress achieved toward a regional innovation system. Furthermore, not all ECOWAS member states have a science and technology policy (Oti-Boateng 2010).10 Globally, the West African national innovation system is hindered by many factors among which are the following: (1) the instability of the institutional framework, (2) the inadequate coordination within the system, (3) the lack of coordination between research programmes and research activities, (4) the lack of optimal use of human resources and loss of motivation of researchers, (5) the lack of human and financial resources and equipment, (6) the weaknesses in the institutional framework, (7) the lack or weaknesses in the actors network, (8) the weak improvement of research status and (9) the insufficiencies or inadequacies of funding and equipment (cf. (African Union et al. 2011; Mêgnigbêto 2013c). Consequently, research in this part of the word is driven by foreign actors and not by national or regional agendas. Even the intraregional collaboration is driven by international organisations or institutions with national representations in countries of West Africa (Mêgnigbêto 2013c). That explains the high rate of international collaboration in the West African science (about 50 % against 21 % for South Korea); that also explains why the West African domestic mutual information is weaker (in absolute value) than the foreign one.
In our opinion, the relative positions of the South Korean mutual information at the foreign and domestic levels seem to be the normal one. Indeed, a national system should be more integrated than a set of institutions from different horizons (named here foreign) because the components of the former are ruled by the same policies and have the same research agendas. This normal situation was also registered by (Shin et al. 2012) for Saudi Arabia.
West Africa does not appear like a single unit of analysis; indeed, member countries do not exhibit the same pattern. Some are more integrated and others less than their partners. In other words, some countries are affected positively by international collaboration (e.g. Burkina Faso, Ghana and Nigeria) and others negatively (e.g. The Gambia, Cape Verde, Cote d’Ivoire). However, the size of the sample we considered may have affected the West African results at both regional and national levels. Therefore, the resulting analysis could not be confident. The large variability of the effect of international collaboration on knowledge sharing in West Africa (cf. Fig. 6) is an illustration.
The main result of this research is that the international collaboration the two areas under study are involved in affected the synergy at their domestic level and also how knowledge is created and flows between innovation actors. In the case of South Korea, international collaboration makes that the country gained about 20 % of its domestic strength of information flow. In case of the West Africa, the effect goes up to 100 %. The relative positions of the mutual informations and the transmission powers in the two areas indicate that the West African innovation system is less integrated than the set of its international partners.
Conclusion
The objective of this paper was to measure the effect of international collaboration on the mutual information and how knowledge flows among innovations actors. We formulated two research questions. (1) How is the synergy or knowledge contributed to abroad by an area’s innovation actors due to their relations with their foreign partners measured? (2) What is the effect of international collaboration on knowledge flow within an innovation system? To answer these questions, we distinguished three levels of analysis: the domestic one grouping innovation actors based in the country under study, the foreign level grouping institutional partners and the global one merging the innovations actors from both domestic and foreign levels. We computed the mutual information and the transmission power for South Korea and West Africa for the three levels, and then, we could derive the effect of international collaboration. We found that the foreign mutual information is globally higher (in absolute value) than the domestic one in the case of West Africa, and lower in the case of South Korea meaning that the South Korean innovation system is integrated by itself, whereas the West African is less integrated than its foreign system. We also found that in the two areas, the global transmission power is higher than the domestic one meaning that international collaboration has strengthened knowledge sharing at the domestic level; in other words, the two areas have benefited from international collaboration in terms of knowledge flow.
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where log2 is the logarithm to the base 2; the entropy may, however, be computed to other bases, e.g. 3, 4, …, 10). More generally, if X = (x1, x2, …, xn) is a random variable and its components occur with the probabilities p1, p2, …, pn, respectively, then the entropy generated by X is (Shannon 1948; Shannon and Weaver 1949)
For two random variables X and Y, if HX is the entropy of X and HY that of Y, the joint entropy HXY of the system of the two variables is equal to the entropy HX plus HY minus the entropy of the overlay of X and Y. The latter is called ‘rate of transmission’ (Shannon 1948) or mutual information (Yeung 2001; Leydesdorff 2003; Cover and Thomas 2006; Mori 2006; Leydesdorff 2008; Yeung 2008) between X and Y. The relations between the transmission, TXY, the joint entropy HXY and the marginal entropies of the variables, HX and HY, are (Shannon 1948)
In case of three random variables X, Y and Z (three dimensions), the relations between the system’s entropy, its transmission, the marginal entropies and the bilateral transmissions are given by (cf. (Abramson 1963; Theil 1972; Leydesdorff 2003):
The transmission power of a system is the fraction of the maximum value of the transmission devoted to information sharing in the system; it represents the share of the ‘total configurational information’ really produced in the system. In other words, it measures the efficiency of the mutual information.
For a three-dimensional system, Mêgnigbêto (2014a) distinguished two types of transmission power: the first one (τ1) when the transmission is negative and the second (τ2) when the transmission is positive:
The transmission power varies from 0 to 1; it is dimensionless and may be expressed as percentage (Mêgnigbêto 2014a).
Appendix 2
Search strategy within the local database
The CDS/ISIS search function operates mainly over the inverted file that contains ‘searchable terms’ as initially defined by the database administrator into a file called Field Selection Table (UNESCO 1989a). It admits the Boolean operators OR symbolised by the sign + (plus), AND symbolised by the character * (star) and NOT symbolised by the character ^ (circumflex). It also admits free search expression and parentheses to prioritise part of a search expression (UNESCO 1989a) and hashtag (#) to recall a previous search by its number. The following searches summarise the search strategy adopted (the example is based on the South Korean case):
#1:
UNIV-SOUTH KOREA selects all records with at least one South Korean-based university in affiliation;
#2:
INDU-SOUTH KOREA selects all records with at least one South Korean-based industry in affiliation;
#3:
GOV-SOUTH KOREA selects all records with at least one South Korean-based government in affiliation;
#4:
#1 * #2 selects all records with at least one South Korean-based university AND one South Korean-based industry in affiliation;
#5:
#1 * #3 selects all records with at least one South Korean-based university AND one South Korean-based government in affiliation;
#6:
#2 * #3 selects all records with at least one South Korean-based industry AND one South Korean-based government in affiliation;
#7:
#1 * #2 * #3 selects all records with at least one South Korean-based university AND one South Korean-based industry AND one South Korean-based government in affiliation.
The results of each stage were entered into a worksheet, and on a second worksheet, formulas were entered to compute university, industry and government sectorial output and other bilateral and trilateral collaboration data using the formulas,11 following the logical relations between sets in (1) U = [1] − [4] − [5] + [7], (2) I = [2] − [4] − [6] + [7], (3) G = [3] − [5] − [6] + [7], (4) UI = [4] − [7], (5) UG = [5] − [7], (6) IG = [6] − [7] and (7) UIG = [7].
This strategy was executed for each area at the three levels (domestic, foreign and global).12
Fig. 7
Cardinalities in a tri-dimensional system S = (U, I, G)
The West African region member states are, in alphabetic order: Benin, Burkina Faso, Cape Verde, Cote d’Ivoire, The Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, Mali, Nigeria, Niger, Senegal, Sierra Leone and Togo.
The search expression was (cu=benin or cu=Burkina faso or cu=cote ivoire or cu=cape verde or cu=gambia or cu=ghana or cu=guinea or cu=guinea bissau or cu=liberia or cu=mali or cu=niger or cu=nigeria or cu=senegal or cu=sierra leone or cu=togo) and (py=2001-2010). It also selected data of countries like Equatorial Guinea and Papua New Guinea due to the term guinea. The records of these two countries that did not result from collaboration with any West African countries were deleted from our local database.
The databases searched were Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Arts & Humanities Citation Index (A&HCI), Conference Proceedings Citation Index-Science (CPCI-S) and Conference Proceedings Citation Index-Social Science & Humanities (CPCI-SSH).
CDS/ISIS is a text database management software application developed and distributed by UNESCO (UNESCO 1989a) (http://www.unesco.org/isis) and mainly used for bibliographic management (de Smet 2008; de Smet and Dhamdhere 2010).
CDS/ISIS provides a programming language ‘designed to develop CDS/ISIS applications requiring functions which are not readily available in the standard package’ (UNESCO 1989b). This programming language enables users to extend functions of the standard package, to make it more robust and in order to meet users’ specific needs (Mêgnigbêto 1998).
Not categorised addresses were labelled ‘NC’; so the inverted file also contained NC-WEST AFRICA, NC-FOREIGN for the West African database and NC-KOREA, NC-FOREIGN for the Korean database.
UNESCO distinguished eight ECOWAS member states in three groups: those who have national STI policy (1), incomplete/nonfunctional out dated STI policies per sector (2) and, those without any STI policy (5) (Oti-Boateng 2010).
For South Korea for example, we conducted the following searches: (1) at domestic level: univ-korea, indu-korea, gov-korea and their bi and trilateral combinations; (2) at foreign level: univ-foreign, indu-foreign, gov-foreign and their bi or trilateral combinations; (3) at global level: univ-korea + univ-foreign, indu-korea + indu-foreign, gov-korea + gov-foreign and their bi and trilateral combinations.
