6.1 Data collection
The elaboration of the Triple Helix thesis lays on the collaboration between the university, industry and government. Of course, collaboration may cover several aspects and not all collaboration yields publications. In this paper, however, we focus on research collaboration understood as co-authorship. We downloaded West African scientific publication data from Thomson Reuters' Web of Science over a 10-year period (2001 to 2010). The databases selected were Science Citation Index Expanded (SCI-EXPANDED), Conference Proceedings Citation Index-Science (CPCI-S), Conference Proceedings Citation Index- Social Science & Humanities (CPCI-SSH) and Index Chemicus (IC). The search expression was cu = benin or cu = cote ivoire or cu = niger or cu = senegal or cu = cape verde or cu = gambia or cu = ghana or cu = nigeria or cu = togo or cu = mali or cu = liberia or cu = sierra leone or cu = guinea or cu = burkina faso or cu = guinea-bissau. The 28,380 resulting records were downloaded and imported into a bibliographic database managed with the CDS/ISISc software application. Based on Leydesdorff's (2003) method for label assignment to addresses, we coded a Pascal CDS/ISISd programme that assigned each address the label ‘university’ (abbreviated UNIV), ‘industry’ (abbreviated INDU) or ‘government’ (abbreviated GOV) to each address. A record may contain many addresses; therefore, one record may have two or more different labels. The CDS/ISIS programme was also instructed to read the countries' name from the addresses and automatically add the associated two characters ISO codes to the label. Non-West African countries were given unique identifiers ZZ. Therefore, in the inverted file, a university in Benin appears under the label UNIV-BJ, and an enterprise in a non-West African country appears under ZZ-INDU.
The CDS/ISIS search function operates mainly over the inverted file that contains ‘searchable terms’ as previously defined by the database administrator upon a field. It admits the Boolean operators OR symbolized by the sign + (plus), AND symbolized by the character * (star) and NOT symbolized by the character ^ (circumflex). We run searches over the CDS/ISIS database using keywords composed of each country names and Triple Helix actors' codes. For example, the search expressions (1) to (7) were conducted for Benin:
-
(1)
UNIV-BJ: retrieves all records the university in Benin authored;
-
(2)
INDU-BJ: retrieves all records the industry in Benin authored;
-
(3)
GOV-BJ: retrieves all records the government in Benin authored;
-
(4)
UNIV-BJ * INDU-BJ retrieves all records the university and industry in Benin co-authored;
-
(5)
UNIV-BJ * GOV-BJ retrieves all records the university and industry in Benin co-authored;
-
(6)
INDU-BJ * GOV-BJ retrieves all records the industry and government in Benin co-authored;
-
(7)
UNIV-BJ * INDU-BJ * GOV-BJ retrieves all records the university, industry and government in Benin co-authored;
Finally, the contribution of each actor was computed as follows (according to the Venn diagram in Figure 2):
U = (1) − (4) − (5) + (7): number of publications university only authored;
I = (2) − (4) − (6) + (7): number of publications industry only authored;
G = (3) − (5) − (6) + (7): number of publications government only authored;
UI = (4) − (7): number of publications university and industry only co-authored;
UG = (5) − (7): number of publications university and government only co-authored;
IG = (6) − (7): number of publications industry and government only co-authored;
UIG = (7): number of publications university, industry and government co-authored.
Such searches and computation were run for individual countries and then for the whole region.
6.2 Entropy, mutual information, efficiency and transmission power
Shannon (1948) defined the entropy of an event that occurs with the probability p as
(1)
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, …, x
n
) is a random variable and its components occur with the probabilities p1, p2, …, p
n
, respectively, then the entropy generated by X is (Shannon 1948; Shannon and Weaver 1949)
(2)
An information source is a random variable that produces symbols (Shannon 1948; Cover and Thomas 2006; Mori 2006; Le Boudec et al. 2013). An information source may also be composed of two or more random variables. For two random variables X and Y (two dimensions), if H
X
is the entropy of X and H
Y
that of Y, the joint entropy H
XY
of the two variables is equal to the entropy H
X
plus H
Y
minus the entropy of the overlay of X and Y. The latter is called ‘rate of transmission’ (Shannon 1948) or mutual information (Yeung 2001, 2008; Leydesdorff 2003; Cover and Thomas 2006; Mori 2006) between X and Y. The relations between the transmission, T
XY
, the joint entropy, H
XY
, and the marginal entropies of the variables, H
X
and H
Y
, are (Shannon 1948)
(3)
and
(4)
In case of three random variables X, Y and Z (three dimensions), Leydesdorff (2003) and Leydesdorff and Ivanova (2014), citing McGill (1954), Theil (1972) and Abramson (1963), demonstrated that the relations between the system's entropy, its transmission, the marginal entropies and the bilateral transmissions are given by
(5)
and
(6)
Transmission or mutual information may be used as innovation indicator. According to Leydesdorff (2003), in more than two dimensions, if the transmission is negative, it indicates the level of synergy or information flow between variables; if it is positive, it indicates how centrally controlled is the system. A null transmission means an absence of interactions between variables. However, Krippendorff (2009a, [b]) claims that mutual information does not measure the unique interactions in a complex system and a null transmission could not be interpreted as the absence of interaction within a system.
Mêgnigbêto (2014b) defined the efficiency of a system as the fraction of its information production capacity that is really produced, relative unused capacity is the complement to 1 of the efficiency, and 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. All the three indicators vary from 0 to 1; they all are dimensionless and may be expressed as percentage.
In a tri-dimensional one, two types of transmission power are distinguished (Mêgnigbêto 2014b): the first one (τ1) when the transmission is negative and the second (τ2) when the transmission is positive:
(7)