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IKI NO KOZO (The Structure of IKI), authored by Shuzo Kuki in 1930, has been an influential piece of work on Japanese culture with its emphasis on IKI as an aesthetical cultural entity. The present paper attempts to reformulate the structure of IKI depicted by Kuki in terms of a group theory in mathematics. By deriving various implications from a group-theoretic model of IKI, 1 want to show the significance of mathematical approaches to culture. [ABSTRACT FROM AUTHOR]

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points In this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions. In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor. Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept. Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their "best" requests and learn by experience. We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to "bolster" their own preference as much as possible. We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models. [ABSTRACT FROM AUTHOR]

Friendship networks usually show a certain degree or segmentation: subgroups of friends. The explanation of the emergence of such groups from initially dyadic pair friendships is a difficult but important problem. In this paper we attempt to provide a first contribution to the explanation of subgroup formation in friendship networks by using the LS set as a definition for a friendship group. We construct a dynamic individual oriented model of friendship formation and provide preliminary simulation results that give an idea of how to continue the process of explaining group formation. [ABSTRACT FROM AUTHOR]

A minimal social situation is a game-like situation in which there are two actors, each of them has two possible actions, and both evaluate the outcomes of their joint actions in terms of two categories (say, success and failure). By fixing actors and actions and varying payoffs the set of 256 'configurations' is obtained. This set decomposes into 43 'structural forms', or equivalence classes with respect to the relation of isoniorphism defined on it. This main theorem and other results concerning related configurations (minimal decision situations) are derived in this paper by means of certain tools of group theory. Some extensions to larger structures are proved in the Appendix. In the introductory section after a brief explanation of the meaning given to the terms structure and isomorphism in mathematics (Bourbaki) it is shown how these terms can be used to formalize the concept of social form. [ABSTRACT FROM AUTHOR]

The article is a reply by the author to his critique Martin Everett on his article "Algebraic Reinterpretation of IKI No Kozo." The author's aim in his article was twofolded. First, he attempted to show that different types of IKI, might be identified by means of mathematical formulation and some derivations. Second, he also wanted to show that there could be a variety of paths from any entity to any other entity. Or any entity, when combined with another entity, transforms itself to some another entity. According to the author, step one is to construct the permutation group using his original transformation. The next is to examine the orbits of IKI, which corresponds to each of the possible subgroups. Successive steps within a single theoretical framework will attain his twofolded aims. Anthropologists might claim that actual social organizations are too complex for this kind of formal analysis to be employed at all. Group theory seems to have enormous potentialities in its application in sociology and related fields of study.

The method of E-state structuralism provides dynamic models for the evolution and development of networks in small groups. Our interest lies in the kind of social networks that these models produce. We ask the question of whether such models produce "interesting" structure from a network point-of-view, in particular, from the perspective of Holland and Leinhardt who argue that any network that can be modeled adequately using only properties of nodes and dyads has no social structure. We show that E-state structuralism models are models of social structure in this technical sense because they assume a bystander mechanism in the creation of ties. [ABSTRACT FROM AUTHOR]