Jürgen Klüver and Christina Stoica (2003)
Simulations of Group Dynamics with Different Models
Journal of Artificial Societies and Social Simulation
vol. 6, no. 4
<http://jasss.soc.surrey.ac.uk/6/4/8.html>
To cite articles published in the Journal of Artificial Societies and Social Simulation, please reference the above information and include paragraph numbers if necessary
Received: 13-Jul-2003 Accepted: 13-Jul-2003 Published: 31-Oct-2003
A | B | C | |
A | 1 | 1 | 1 |
B | 0 | 1 | 0 |
C | 0 | 0 | 0 |
A | B | C | |
A | 0 | 4 | 5 |
B | 4 | 0 | 1 |
C | 5 | 1 | 0 |
S_{A} = S v(A,X)/n, |
Where n is the number of non-empty cells in the Moore neighbourhood. The Moreno matrix consists, as mentioned above, only of values v(A,X) = 1, 0 or -1.
S_{AU} > S_{A}. |
Sy = symm.rel./all rel. |
In our case of n = 30 members so we have n^{2} -n relations between the members, if one does not count the relations (A, A), and therefore 870 relations.
The "normal" behaviour of our Moreno-CA, i.e., the behaviour generated from the majority of Moreno-matrices with a reasonable degree of symmetry and from all different ranges of observation is the generation of point attractors after rather short preperiods. Only low values of Sy combined with the largest range of observation generate a more complex behaviour, i.e., the generation of attractors with periods significantly larger than 1.
A | B | C | |
A | 0 | 1 | 1 |
B | 1 | 0 | 0 |
C | 0 | 0 | 0 |
A - B - C |
with equal distances d(A,B) and d(B,C), but with a significantly greater distance d(A,C). The Ritter-Kohonen KFM generates a grid where the units A, B, C ... are placed in artificial cells rather similar to the grids of CA; the distance d(A,B) is then simply the number of cells between A and B.
A_{j} = Σ_{i} A_{i} *w_{ij}, |
if A_{j} is the activation state of the receiving neuron j, A_{i} is the activation state of the sending neurons i and w_{ij} is the "weight" of the connections between the neurons j and i. Weight means a numerical value that decides to which degree the connections between i and j are inhibiting or reinforcing the information flow between them. The KFM usually operates with the same linear activation rule although other non-linear activation functions are possible.
Ev_{j} = Σ_{ i} w_{ji}. |
The emotional value of a subgroup k is then
Ev_{k} = Σ_{ j} Ev_{j} /n |
for the n members j of the subgroup k. The emotional value for the whole group m, i.e., the combination of disjoint subgroups is obtained by
Ev_{m} = Σ_{ k} Ev_{k} /r |
for all r subgroups k of the group m. In other words, the better the emotional relations of the members are with respect to the other members of their subgroup, the better is the emotional value of the subgroups and of the whole group.
V_{1} = (3, 0, 4, 0, 1, 0, 0, 6, ... . , 1). |
This means that the first component of the vector that represents the first group member is placed into subgroup 1 (regardless in which subgroup he was before); the second member stays in his subgroup, the third member is placed into subgroup 4, the fourth member stays in his subgroup, the fifth member is placed into subgroup 1, the next two members stay in their respective subgroups, the eighth member is placed into subgroup 6 and so on. In other words, the components of these vectors represent the new subgroups the members will be placed into. A 0 means that no changing of the according member will take place.
The models we discussed can be obtained from us at: http://www.cobasc.de
^{2} We deliberately use the term of prototype in the meaning of the well known prototype theory of Rosch (cf. e.g. Lakoff 1987). The clusters of a KFM as the result of its operations are the logical equivalent of the semantic clusters which are constructed around cognitive prototypes.
^{3} This version of the Moreno-KFM was implemented by Rouven Malecki
^{4} To be more exact: if the cells of the Moore neighbourhoods that were occupied with group members were subsets of the clusters.
^{5} The absolute spatial order is always a result of the particular initial configurations of the CA; these were generated at random. That is so because this CA is a deterministic system.
KAUFFMAN, S (1993), The Origins of Order. Oxford: Oxford University Press
KLÜVER J (2002), An Essay Concerning Sociocultural Evolution. Theoretical Principles and Mathematical Models. Dordrecht: Kluwer Academic Publishers
KLÜVER, J and Schmidt, J (1999): Control Parameters in Cellular Automata and Boolean Networks Revisited. From a Logical and a Sociological Point of View. In: Complexity 5, No. 1, pp. 45 - 52
KLÜVER, J (2000): The Dynamics and Evolution of Social Systems. New Foundations of a Mathematical Sociology, Dordrecht: Kluwer Academic Publishers
KLÜVER, J, Stoica, C and Schmidt, J (2003): Formal models, social theory and computer simulations: some methodological reflections. In: JASSS - Journal for Social Simulation and Artificial Societies http://jasss.soc.surrey.ac.uk/6/2/8.html
LAKOFF, G (1987): Women, Fire and Dangerous Things. What Categories reveal about the Mind. Chicago-London: University of Chicago Press
MORENO, J L (1934): Who Shall Survive. Nervous and Mental Disease Monograph 58. Washington DC
RITTER, H and Kohonen, T (1989): Self-Organizing Semantic Maps. In: Biological Cybernetics 61, pp. 241 - 254
STOICA, C (2000): Die Vernetzung sozialer Einheiten. Hybride Interaktive Neuronale Netze in den Kommunikations- und Sozialwissenschaften. Wiesbaden: Deutscher Universitätsverlag
WOLFRAM, S (2002): A New Kind of Science. Champaign (IL): Wolfram Media
Return to Contents of this issue
© Copyright Journal of Artificial Societies and Social Simulation, [2003]