Opinion Dynamics and Social Influence

A Mathematical Theory of Communication

In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.

Statistical physics of human cooperation

Impurity Problem in the Ising Model

Progress of Theoretical Physics Vol. 49 No. 1 (1973) pp. 83-88 Critical Properties of Ising Models Containing Dilute Impurities Takeo Osawa and Katuro Sawada Progress of Theoretical Physics Vol. 50 No. 4 (1973) pp. 1232-1239 Critical Properties of Ising Models Containing Dilute Impurities. II Katuro Sawada and Takeo Osawa

Equivalence of<i>s</i>-<i>d</i>Exchange, Anderson and Wolff Models

Fumiaki Shibata, Kazushige Machida, Hiroshi Mamada; Equivalence of s-d Exchange, Anderson and Wolff Models, Progress of Theoretical Physics, Volume 45, Iss