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A study of thematic areas in economy by a measure of similarities based on a Kernel/Un estudio de areas tematicas en economia con una medida de similitude basada en la teoria de los nucleos/Um estudo de areas tematicas em economia com uma medida de similaridade baseada na teoria dos nucleos.


Some results on the similarities among thirteen subjects in the Economy area between 1990 and 2003 are presented and a virtual analysis of their interrelations is carried out. To this end, an intuitive interpretation of the similarity measure between two sets based on the Kernel method is defined, which provides a useful graphical representation. Several tables are considered that show the potentiality of this similarity index.

KEYWORDS / Kernel / Scientific Production / Similarity / SSCI /


Presentamos en este trabajo resultados interesantes acerca de las similitudes existentes entre trece topicos dentro del ambito de la Economia entre los anos 1990 y 2003, asi como las interrelaciones existentes entre ellas. Para ello, introducimos una medida de similitud intuitiva entre dos conjuntos, basada en la teoria de los nucleos, que nos permite dar una representacion grafica muy util. Consideramos ademas varias tablas en las que se muestra la potencialidad futura del indice de similitud introducido.


Apresentam-se resultados sobre as similaridade existentes entre treze topicos dentro do ambito da Economia entre os anos 1990 e 2003, assim como as interrelacoes existentes entre eles. Para isto, se introduz uma medida de similaridade intuitiva entre dois conjuntos, baseada na teoria dos nucleos, que permite dar uma representacao grafica util. Se consideram alem disso varias tabelas nas que se mostra a potencialidade do indice de similaridade introduzido.


The first stage of research or innovation in any scientific research is having up-to-date knowledge of previous works on the subject. Nowadays there are many databases available for consultation and, thus, it is easy to obtain up-to-date information. An inexperienced researcher may have doubts when selecting a research field, and about choosing the most appropriate subject to achieve the best possible results. His supervisors can obviously help him, although if he can obtain up-to-date information about the interrelation between different subjects, and about how productive they are currently in the research world, he will have stronger reasons to choose one of them. This is true not only for a new researcher, but for all researchers in any subject, since it is always essential to know the thematic relations between distinct areas. One subject can be strongly related to another; that is, they can be similar and evolve together; or, they can be dissimilar in the sense of gradually becoming more distant from each other. It seems that this question can be solved by analyzing absolute values, such as for instance the number of works which are simultaneously referred to two particular subjects. But this localized view does not allow to see all the relations between every subject from a global perspective, and for this reason it is necessary to build a certain bounded measure that will enable to decide whether two subjects are close to each other or disconnected. It would be also helpful to know how this similarity has developed over time, and how it is expected to change in the near future.

This kind of problems have already been treated and have given rise to the development of a wide range of multivariate analysis tools and visual procedures that have been adapted to disciplines such as Sciencemetry (Callon et al., 1986; Coulter et al, 1998), Informetry (Egghe and Rousseau, 1990; Wolfram, 2000), Bibliometry (Noyons et al., 2002; Buter and Noyons, 2002; Mijac and Ryder, 2009) or Webometry (Almind and Ingwersen, 1997; Rousseau, 1997; Larson, 1996), in order to analyze the documental databases from a visual perspective. These methods are known as "procedures of dimension reduction" and their common characteristic is to transform the available information and store it in a two- or three-dimensional space where it is easier to analyze. These procedures of dimension reduction are used in all disciplines related to the treatment of scientific information and can be classified into neuronal and statistical procedures. The neuronal procedures are based on the learning capacity of the neuronal networks, such as Kohonen's net (Lin and Marchionini, 1991; Kohonen, 1998; Kohonen et al., 2000), in order to achieve a dimensional reduction for the bibliometric data, and the statistical procedures include clustering as one of these techniques. There is a wide variety of statistical tools used to reduce the bibliometric data dimension (Kinnucan et al., 1987), and among them we can highlight the multidimensional scaling (Deus, 2001; Klock and Buhman, 1999), whose development began in the psycho-psychic area.

The associated words method (Braam et al., 1991; Callon et al., 1991; Courtial, 1994; Grivel and Francois, 1995: Banos and Contreras, 1998; Coulter et al., 1998) is one of the best-known statistical techniques for establishing hierarchic order. This method is based on a graph where the key words are represented by knots and the arches refer to how frequently the related key words appear. From these graphs, such techniques can find and represent centers of interest concealed in the documents; that is, zones strongly related and consistent networks, susceptible of being interpreted as "hot points" or "attraction poles" of powerful informative intensity (Banos and Contreras, 1998; de la Rosa et al., 2005).

In contrast with the previous ones, a new procedure was described in Gonzalez et al. (2005), based on a study of frequencies and having its foundations in the Statistical Learning Theory (Li et al., 2007; Srebro, 2007; Vapnik, 1998; Burrell, 2005; Clara, 2006: Zhang and Fu, 2006: Stentiford, 2007; Gonzalez-Abril et al., 2009a, b). The measure of similarity described in Gonzalez et al. (2005) is used to measure the connections between several subjects. Nevertheless, this measure has several drawbacks, because it depends on the weights of each set with respect to the rest. So, it does not provide a unified scale and does not allow to make comparisons. For this reason, a new similarity index is defined in this paper, which allows for the solving of these inconveniences.

This method could be applied to any field of knowledge. The reason why attention is driven to economics relies on the high concern that the problems stemming from a crisis produce, not only because of the current situation, but also because there has always been a tendency for crises to arise throughout history. In addition, it seems interesting to know which are the latest topics in the field of economics, and the relationships between them. Thus, research can be redirected toward policies that attempt to cushion the effects of the successive crises.

The following section presents the new similarity index and an application of this index is given thereafter, by calculating the similarity between a set of lines in the economy area. The last section is devoted to conclusions and future work, with some ideas about various fields where it seems possible to develop this index.

Similarities Between Events

Similarity must be understood, initially, as a measure between two elements in a set X, which provides a numerical value to quantify how analogous they are. An important kind of similarity measures are dot products. In order to be able to use a dot product as a similarity measure in X, this domain must be embedded into some dot product space H. To this end, a map is used [phi]: X [right arrow] H. Thus, a particular similarity measure in X, called Mercer kernel, is defined as

k: X x X [right arrow] R (x,x') [right arrow] k (x.x') = [([phi])(x), [phi])(x')).sub.H]

where dot product in H is denoted by (*,*). The idea of a kernel generalizes the dot product in the space X and provides a descriptive language used by the learning machine to see the data. Kernels offer a solution for projecting a dataset in a large feature space, which also increases the ability to generalize the various training algorithms. On the other hand, kernels can be interpreted as a similarity measure and this is the way they will be used in this paper. Hence, a kernel on a probabilistic space is to be considered.

Let us consider two events A and B on a ([OMEGA],A,P) probabilistic space. The similarity between them, denoted by k(A,B) is defined Gonzalez et al. (2005) as

k(A,B) = P(A,B)-P(A)P(B)

This similarity can take positive and negative values, and has interesting properties, as can be seen in Gonzalez et al. (2005). Nevertheless, it is worth noting that this similarity has a great drawback, since k(A,B) [less than or equal to] k(A,A)= P(A)(1-P(A)) and, therefore, if P(A) is small, then k(A,B) will be small for any B. Thus, for example, if P(A)= 0.01 and P(B)= 0.5, then k(A,A)= 0.009 and k(B,B)= 0.25. That is, B is approximately 28 times more similar to B than A to A and this result is not logical. To avoid this drawback, a new index is considered:

[k.sup.*] (A,B)= k(A,B)/[square root of k(A,A)k(B,B)]

The most important property of k* is that it is the correlation between two random variables, k* (A,B)= corr([I.sub.A], [I.sub.B]), where [I.sub.A] and [I.sub.B] are the indicator functions of A and B, respectively, and corr stands for correlation. This result is straightforward to prove, since k(A,B)= cov([I.sub.A], [I.sub.B]), where cov is the covariance (Gonzalez et al., 2005). Therefore -1 [less than or equal to] k*(A,B) [less than or equal to] and bounds are attained with B = [bar.A] and B=A. Hence, -1 = k* (A, [bar.A]) [less than or equal to] k*(A,B) [less than or equal to] k*(A,B) [less than or equal to] 1 for any A and B; that is, the most similar event to A is the same A, and the most dissimilar event to A is the complementary event of A ([bar.A]). Therefore, [k.sup.*] does not have the drawback of k and this is also normalized. On the other hand, it is well-known that the correlation is a dot product (Scholkopf and Smola, 2002) and therefore, k* is a kernel.

Similarities Among Several Research Lines in Economics

The research lines shown in Table I have been obtained from the SSCI (Social Science Citation index) database in the ISI (Institute for Scientific Information) web of Knowledge (Thompson, 1945-2008). The years from 1990 to 2003, both included, have been selected for this study.

Preliminary study

A total of N = 372805 different papers have been found after a thorough search, each of them related to at least one of the 13 research lines considered. Table II shows the values obtained for [n.sub.ij], the number of papers appearing simultaneously in lines Ai and Aj for the period considered, 1990-2003. Also, the papers published yearly for each of the 13 research lines from 1990 to 2003 have been depicted in Figure 1.




It can be observed from Table II and Figure 1 that Development ([A.sub.7]) is the line with the most published papers, with a total of 114487, whereas Social Science ([A.sub.10]), with 2783, is the line with the fewest published papers. Furthermore, it can be seen that Development has always been the most published line, year after year, and that Social Science is the fewest published line year after year except in 1992 when it was Finance.

Figure 1 also shows that the order of research lines change in time when they are sorted according to the amount of published papers. The published paper's average for each research line is shown in Figure 2, where they are ordered from the smallest to the greatest in the period of study. It can be seen that Social Sciences is the line with fewest papers (on average) with a value of 198.77, while the line with most papers is Development, with an average of 8177.64.

Another aspect to emphasize is the different weights for each research line according to their amount of published papers; that is, the proportion of each line with respect to the total number of published papers expressed over 1. These weights are shown in Figure 3 for every year. Hence, for example, Development takes in 1990 a value of 0.2508, resulting from the fact that this year Development has 2909 out of 11601 papers. Figure 3 shows clearly that some line weights change through the years, such as, for instance, happens with Family Studies and Management. Family Studies is above Management from 1990 to 1994, both are very close between 1995 and 1997 and from 1998 Management overtakes the other line.

Nevertheless, in this preliminary study, the hypothetical similarities among the research lines do not appear clearly, in the sense that it is not known how are the relations between lines. Thus, a study of

similarities is carried out.

Study of the similarities

It is worth noting that Table II reflects the relations between [A.sub.i] and [A.sub.j] in absolute values ([n.sub.ij] for i [not equal to] j), but it does not show if there is any similarity or dissimilarity between them. Thus, the relationship between the research lines shown in Table I is studied according to the similarity measure k*.

To link the data from Table II to the construction of similarities, keeping in mind that the number of data available is sufficiently large, a frequency-based interpretation of probability is considered. Hence, assuming that

P([A.sub.i] [intersection] [A.sub.j]) = [n.sub.ij]/N

where N = [summation over (i,j)] [n.sub.ij], k* is used as in Eq. 1 to

calculate the similarity between lines. These calculations are shown in Table III, and their similarities are depicted in Figure 4, where the positions for each item is shown with respect to the others using the values when [k.sup.*](Ai) [Aj] goes from i = 1 to 13 (see Table I). Hence, it can be seen that the similarities between the different lines are negative, except in some specific cases. This was expected because if two lines are very similar it means that both lines share many papers and they should be considered as the same line. The greatest value of the similarity index in the whole period is [k.sup.*]([A.sub.8], [A.sub.9])=0.02942, linking Transportation and Urban Studies. The greatest similarity value for each year is depicted in Figure 5, where it can be seen that the greatest similarity value is given for the similarity between Planning and Transportation in 2003 (k*([A.sub.6], [A.sub.8])=0.04893).

It should be pointed out that the graphical scales in Figure 4 are different. In the y-axis the maximum depicted for each line is 0.08, 0.05, 0.08, 0.15, 0.20, 0.08, 0.25, 0.012, 0.08, 0.008, 0.06, 0.15 and 0.02, and it must be taken into account that each of these representations refers to one particular line.

Looking again at Table III and Figure 4, the following conclusions can be drawn about the similarity between each research line and its links to the others:

[A.sub.1] has positive similarity with [A.sub.13] (0.00739) and is dissimilar to the others. The most dissimilar items to [A.sub.1] are [A.sub.4] and [A.sub.12], with analogous dissimilarity levels. The remaining dissimilarities are quite small.

[A.sub.2] has positive similarity with [A.sub.13] and [A.sub.10] and is dissimilar to the rest. The greatest similarity is related to [A.sub.7].

[A.sub.3] has dissimilarities with all the other lines. The most dissimilar is [A.sub.12].

[A.sub.4] has dissimilarities with all the other lines. The most dissimilar is [A.sub.7].


[A.sub.5] has dissimilarities with all the other lines. The most dissimilar is [A.sub.12].

[A.sub.6] has positive similarity with [A.sub.8] (0.02679) and [A.sub.9] (0.02281). The other lines are all dissimilar and the most dissimilar is [A.sub.12].

[A.sub.7] shows negative similarity to the other lines, being [A.sub.12] the most dissimilar.

[A.sub.8] has positive similarity with [A.sub.6] (0.02679). It is dissimilar to the other lines, and [A.sub.12] is the most dissimilar line.

[A.sub.9] has positive similarity with [A.sub.6] (0.02281) and [A.sub.8] (0.02679). [A.sub.12] is the most dissimilar.

[A.sub.10] has positive similarity with [A.sub.2] (0.00682) and also with [A.sub.13] (0.00280) and [A.sub.7] is its most similar line.

[A.sub.11] has negative similarity with each of the other lines and [A.sub.7] is the most dissimilar line.


[A.sub.12] has negative similarity with the other lines, as in the previous case, being [A.sub.7] the most dissimilar.

[A.sub.13] by symmetry with [A.sub.1], [A.sub.2] and [A.sub.10] has positive similarity with all them and is dissimilar to the others. [A.sub.4] is the most similar line.

As it can be seen, [A.sub.7] (Development) is the most dissimilar one to the other research lines. This point shall be brought up later, after explaining the construction of Table IV. It should be remarked that the main deficiency of Figure 4 is the use of so many figures as studied items. It would be much more practical to have only one representation to gather all the previous graphic information. To fulfill this aim, the following graphical construction is proposed:


Firstly, the events {[A.sub.1], [A.sub.2], ..., [A.subu.13]} are ordered by their probabilities; that is, 0 [less than or equal to] P([A.sub.1]) [less than or equal to] P([A.sub.2]) ... [less than or equal to] P([A.sub.13]) and these probabilities are represented on the x-axis. The similarities are represented on the y-axis in the following way: first, for the event [A.sub.1] the set of similarities {-k([A.sub.1],[A.sub.1]), k([A.sub.1],[A.sub.2]), ..., k([A.sub.1],[A.sub.13]), k([A.sub.1],[A.sub.1])} is represented on the abscissa P([A.sub.1]), and then for the event [A.sub.2] the set of similarities {-k([A.sub.2],[A.sub.2]), k([A.sub.2],[A.sub.3]), ..., k([A.sub.2],[A.sub.13]), k([A.sub.2],[A.sub.2])} is represented on the abscissa P([A.sub.2]), and so on up to the event [A.sub.13]. The graphical representation, following this procedure applied to the 13 lines of research related to Economy may be seen in Figure 6. To determine which lines are most similar (or dissimilar) to the others, Table IV has been built, where similarity is represented in columns in increasing order; then, for instance, in the [A.sub.1] column, [A.sub.4] is the most dissimilar one to it, followed by [A.sub.12] and so on up to [A.sub.13] where the maximum similarity is found (the first picture in Figure 4 shows this situation). Nevertheless, the order obtained does not match with the absolute values of Table II and, for instance, line [A.sub.10] is the first in the [A.sub.1] column in Table II in relation to the number [n.sub.ij], although [A.sub.10] is in the 9th position in that column in Table IV, and [A.sub.4] is situated in the 5th position in Table II and in the first place in Table IV. It is remarkable that [A.sub.12] is in the 11th place in Table II and the second in Table IV. This fact can be explained since the considered values in Table IV are relative but not absolute values as in Table II. Hence, Table IV gives a more suitable order relation according to the affinity among the topics.

Table IV has some aspects that are shown in Table V. On the first row of Table IV it can be seen, that the [A.sub.7] appears six times, [A.sub.12] five times, and [A.sub.4] twice. These numbers appear in this order in the second column of Table V, indicating that they are in the first dissimilarity position. So, this is the order of the topics in the first column. Analogously, in the second row of Table IV [A.sub.7] appears twice, [A.sub.12] four times, [A.sub.4] four times, and [A.sub.5] three times, and these appear in the third column of Table V. That is, Table V indicates the dissimilarity of each topic in relation with the others, not taking into account the similarity values, but the order. To be able to make comparisons a weighted sum is carried out, where the weights are the order positions from the first row, and the results are written in the antepenultimate column. In this way, if for instance [A.sub.12] is considered, the result 5x1+4x2+1x3+1x4+1x6+1x13= 39 is obtained and placed in the antepenultimate column of Table V. After dividing into 13, the weight of the topic is found, referred to its dissimilarity with respect to the other ones.

In the case of [A.sub.11], the weighted sum is 87. Arranging the table according to the last column Table V is constructed, where the topics are sorted from lower to higher similarity. From this Table it can be seen that the item more related to the others is [A.sub.8], followed by [A.sub.10] and finishing with [A.sub.12] and [A.sub.7], respectively. This Table shows that the strongest subjects are [A.sub.7], [A.sub.12], [A.sub.4] and [A.sub.5], in the sense of being the most published and because they are in the first rows of Table V, thus having more dissimilarity with the others. This result indicates that they share little with the other lines and seem to be self-sufficient. Table V has a complementary column where average rank by year is calculated.

It was stated before that the lines with highest similarity for the whole period were [A.sub.8] and [A.sub.9], with a value of 0.02942, and it can be questioned whether this situation holds for every year. Figure 5 provides a representation of the maximum similarities in the 1990-2003 period. These similarities have followed an increasing trend, although the lines are not always the same. Table VI shows the lines for which the similarities are maximal each year. Line [A.sub.8] appears in 11 years, [A.sub.9] appears in 8 years, [A.sub.6] in seven years and [A.sub.13] and [A.sub.1] once each. Also, the pair formed by [A.sub.8] and [A.sub.9] appears six times, [A.sub.6] with As five times, [A.sub.6] with [A.sub.9] twice, and, finally, [A.sub.1] with [A.sub.13] once. This means that [A.sub.8] and [A.sub.9] are really the lines with the highest similarity between them. Figure 7 shows the similarities between [A.sub.8] and [A.sub.9] in the 1990-2003 period. As it is possible to see in this Figure, in 1991 the similarity is negative, changing to positive in 1992. The trend is ascendant, with slight punctual variations in some years.


Conclusions and Future Work

A new index of similarity is presented, improving the one presented by Gonzalez et al. (2005). In addition, it has been shown that the similarity between events can be used to detect that, although the output of papers in some research areas of Economy seems to be high, this is not the case in other areas in the same field. In the present paper it has been shown that lines such as Development ([A.sub.7]), with 114487 published papers in the 1990-2003 period, do not have great similarity with the other lines. This is because the number of work coincidences with other areas is proportionally very small. This also holds for other important lines in relation to the amount of published papers, such as History ([A.sub.12]), Management ([A.sub.5]) and Family Studies ([A.sub.4]). Throughout all this work it is seen that these lines are quite independent. It has been stated, in another way, that Social Science ([A.sub.10]) is the line with fewest papers in Table II but, however, it holds a good relationship with the other lines, and thus its position in Table V is logical.

The different lines can also be sorted according to the dissimilarities (similarities), indicating which ones are most similar to the others.

Several lines of work are planned for the near future. One of them will consist on using the science databases as documental information to carry out a similar study into different subjects in areas of interest. Another work line will consist on making a dynamic study about the relative growth of each subtopic and the existing temporal similarities between topics and subtopics.

It is also envisaged to find out the similarities between the relevant groups of research in certain areas, sub-areas or research lines on the web. In this paper, it has been attempted to highlight some of the applications that can be developed with the mathematical method of Gonzalez (2002) and Gonzalez et al. (2005), briefly presented above. This gives an idea of the power of this similarity index, whose potential possibilities are being extended to real intervals and to time series, also allowing the study of similarities in cases such as economic series, radio or television audiences, etc.


This work has been partially financed by the PAI-2009/00001200, PAI-2008/00000607, P06-TIC-02141 help, provided by the Junta de Andalucia, and by the Science and Technology Ministerial Department under project TIN2009-14378-C02-01.

Received: 03/13/2009. Modified: 02/26/2010. Accepted: 03/01/2010.


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Francisco Velasco Morente. Ph.D. in Mathematics, Faculty of Mathematics, University of Seville (US) Spain. Lecturer, Department of Applied Economics I, US. Spain Address: FCCEE, Department of Applied Economics I, Avenida Ramon y Cajal, 1, Sevilla, Espana. e-mail:

Luis Gonzalez-Abril. Ph.D. in Economics, US, Spain. Lecturer, Department of Applied Economics I, US. Spain. e-mail:

Juan Antonio Ortega Ramirez. Ph.D. in Computer Science, US, Spain. Lecturer, Department of Computing System and Languages, US, Spain. e-mail:

Juan Antonio Alvarez Garcia. Ph.D. in Computer Science, US, Spain. Lecturer, Department of Computing System and Languages, e-mail:

Notation     Research Lines

[A.sub.1]    Business
[A.sub.2]    Economics
[A.sub.3]    Environmental Studies
[A.sub.4]    Family Studies
[A.sub.5]    Management
[A.sub.6]    Planning
[A.sub.7]    Development
[A.sub.8]    Transportation
[A.sub.9]    Urban Studies
[A.sub.10]   Social Sciences
[A.sub.11]   Labor
[A.sub.12]   History
[A.sub.13]   Finance


             [A.sub.1]   [A.sub.2]   [A.sub.3]   [A.sub.4]   [A.sub.5]

[A.sub.1]        25545         754         766         623        4519
[A.sub.2]                    17741         973         321        1234
[A.sub.3]                                30699        1660        3925
[A.sub.4]                                            60360        2961
[A.sub.5]                                                        66333

             [A.sub.6]   [A.sub.7]   [A.sub.8]   [A.sub.9]

[A.sub.1]          976        3708         153         520
[A.sub.2]          282        1745         107         341
[A.sub.3]         1473        5437         284        1442
[A.sub.4]         3026        6603         142        2006
[A.sub.5]         3960       10203         434        1550
[A.sub.6]        24366        5081         542        2260
[A.sub.7]                   114487         544        4711
[A.sub.8]                                 4273         601
[A.sub.9]                                            26337

             [A.sub.10]   [A.sub.11]   [A.sub.12]   [A.sub.13]

[A.sub.1]            51         1036          726          475
[A.sub.2]           179          629          725          302
[A.sub.3]            98          356         1483          111
[A.sub.4]            57         1631         6027          120
[A.sub.5]           120         1386         1946          530
[A.sub.6]            44          252          739          133
[A.sub.7]           343         1646         5306          746
[A.sub.8]             4          129           85           44
[A.sub.9]            50          832         1238          202
[A.sub.10]         2783           29          241           11
[A.sub.11]                     21926          873          156
[A.sub.12]                                  61234          129
[A.sub.13]                                                5687


                  P        [A.sub.1]   [A.sub.2]   [A.sub.3]

[A.sub.1]      0.0685          1         0.023      -0.052
[A.sub.2]      0.0476                      1        -0.022
[A.sub.3]      0.0823                                  1
[A.sub.4]      0.1619
[A.sub.5]      0.1779
[A.sub.6]      0.0654
[A.sub.7]      0.3071
[A.sub.8]      0.0115
[A.sub.9]      0.0703
[A.sub.10]     0.0075
[A.sub.11]     0.0588
[A.sub.12]     0.1643
[A.sub.13]     0.0153

             [A.sub.4]   [A.sub.5]   [A.sub.6]   [A.sub.7]   [A.sub.8]

[A.sub.1]      0.101      -0.001      -0.030      -0.095      -0.014
[A.sub.2]     -0.087      -0.063      -0.045      -0.101      -0.011
[A.sub.3]     -0.088      -0.039      -0.021      -0.084      -0.006
[A.sub.4]        1        -0.148      -0.027      -0.188      -0.037
[A.sub.5]                    1        -0.011      -0.155      -0.022
[A.sub.6]                                1        -0.057      0.0268
[A.sub.7]                                            1        -0.042
[A.sub.8]                                                        1

             [A.sub.9]   [A.sub.10]   [A.sub.11]   [A.sub.12]

[A.sub.1]     -0.053       -0.017       -0.021       -0.099
[A.sub.2]     -0.045       0.0068       -0.022       -0.074
[A.sub.3]     -0.028       -0.015       -0.060       -0.094
[A.sub.4]     -0.064       -0.033       -0.059       -0.076
[A.sub.5]     -0.086       -0.031       -0.075       -0.169
[A.sub.6]     0.0228       -0.017       -0.055       -0.096
[A.sub.7]     -0.076       -0.035       -0.126       -0.212
[A.sub.8]     0.0294       -0.008       -0.013       -0.042
[A.sub.9]        1         -0.018       -0.032       -0.087
[A.sub.10]                   1          -0.018       -0.018
[A.sub.11]                                1          -0.084
[A.sub.12]                                             1


[A.sub.1]      0.0074
[A.sub.2]      0.0032
[A.sub.3]      -0.028
[A.sub.4]      -0.048
[A.sub.5]      -0.028
[A.sub.6]      -0.021
[A.sub.7]      -0.047
[A.sub.8]      -0.004
[A.sub.9]      -0.017
[A.sub.10]     0.0028
[A.sub.11]     -0.016
[A.sub.12]     -0.048
[A.sub.13]       1


     [A.sub.1]    [A.sub.2]    [A.sub.3]    [A.sub.4]    [A.sub.5]

1    [A.sub.4]    [A.sub.7]    [A.sub.12]   [A.sub.7]    [A.sub.12]
2    [A.sub.12]   [A.sub.4]    [A.sub.14]   [A.sub.5]    [A.sub.7]
3    [A.sub.7]    [A.sub.12]   [A.sub.7]    [A.sub.1]    [A.sub.4]
4    [A.sub.9]    [A.sub.5]    [A.sub.11]   [A.sub.3]    [A.sub.9]
5    [A.sub.3]    [A.sub.9]    [A.sub.1]    [A.sub.2]    [A.sub.11]
6    [A.sub.6]    [A.sub.6]    [A.sub.5]    [A.sub.12]   [A.sub.2]
7    [A.sub.2]    [A.sub.1]    [A.sub.13]   [A.sub.9]    [A.sub.3]
8    [A.sub.11]   [A.sub.3]    [A.sub.9]    [A.sub.11]   [A.sub.10]
9    [A.sub.10]   [A.sub.11]   [A.sub.2]    [A.sub.13]   [A.sub.13]
10   [A.sub.8]    [A.sub.8]    [A.sub.6]    [A.sub.8]    [A.sub.8]
11   [A.sub.5]    [A.sub.13]   [A.sub.10]   [A.sub.10]   [A.sub.6]
12   [A.sub.13]   [A.sub.10]   [A.sub.6]    [A.sub.6]    [A.sub.1]


             1    2    3    4    5    6    7    8    9    10   11

[A.sub.7]    6    2    4    --   --   --   --   --   --   --   --
[A.sub.12]   5    4    1    1    --   1    --   --   --   --   --
[A.sub.4]    2    4    2    1    1    1    --   1    --   --   --
[A.sub.5]    --   3    3    2    1    1    --   --   --   1    1
[A.sub.11]   --   --   1    2    2    1    2    3    1    --   --
[A.sub.3]    --   --   --   3    2    --   2    3    2    --   --
[A.sub.1]    --   --   2    --   4    1    1    1    1    --   --
[A.sub.9]    --   --   --   2    1    2    3    2    --   --   1
[A.sub.2]    --   --   --   1    2    2    2    1    2    --   1
[A.sub.6]    --   --   --   1    --   4    1    --   1    1    3
[A.sub.13]   --   --   --   --   --   --   2    --   2    4    3
[A.sub.10]   --   --   --   --   --   --   --   2    3    2    2
[A.sub.8]    --   --   --   --   --   --   --   --   1    5    2

             12   13   Sum   Average      Av.

[A.sub.7]    --   1    35      2.7        2.6
[A.sub.12]   --   1    39      3.0        3.2
[A.sub.4]    --   1    52      4.0        4.1
[A.sub.5]    --   1    68      5.2        5.2
[A.sub.11]   --   1    87      6.7        6.5
[A.sub.3]    --   1    91      7.0        7.0
[A.sub.1]    2    1    93      7.2        7.3
[A.sub.9]    1    1    98      7.5        7.6
[A.sub.2]    1    1    102     7.8        7.8
[A.sub.6]    1    1    112     8.6        8.6
[A.sub.13]   1    1    130    10.0       10.0
[A.sub.10]   3    1    134    10.3       10.3
[A.sub.8]    4    1    142    10.9       10.7

THE 1990-2003 PERIOD

Year   Similarity   Pos.          Lines

1990    0.009015     1     [A.sub.8]-[A.sub.9]
1991    0.000782     1     [A.sub.6]-[A.sub.8]
1992    0.036096     6     [A.sub.1]-[A.sub.3]
1993    0.030621     7     [A.sub.8]-[A.sub.9]
1994    0.030535     5     [A.sub.8]-[A.sub.9]
1995    0.035925     5     [A.sub.8]-[A.sub.9]
1996    0.032662     6     [A.sub.6]-[A.sub.9]
1997    0.036425     6     [A.sub.8]-[A.sub.9]
1998    0.033272     5     [A.sub.8]-[A.sub.9]
1999    0.027378     6     [A.sub.6]-[A.sub.9]
2000    0.046976     6     [A.sub.6]-[A.sub.8]
2001    0.035831     7     [A.sub.6]-[A.sub.8]
2002    0.046076     5     [A.sub.6]-[A.sub.9]
2003    0.048929     5     [A.sub.6]-[A.sub.8]
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Author:Velasco, Francisco; Gonzalez-Abril, Luis; Ortega, Juan Antonio; Alvarez, Juan Antonio
Date:Mar 1, 2010
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