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Demonstrates the value of mathematical modeling in social movement research, particularly for investigating collective action. Eight fundamental principles in generating & analyzing formal mathematical models are outlined & some strengths & weaknesses of mathematical modeling & simulation approaches are identified. Some specialized computer programs ideally suited to working with these models & simulations are reviewed. For the nonmathematically inclined, some principles are offered to guide the evaluation of formal models used in others' research. 1 Figure, 1 Appendix, 51 References. K. Hyatt Stewart

ObjectivesThis article examines the comparative effectiveness of different types of social ties used by a job seeker and proposes an explanation for the inconsistency in empirical evidence for strength‐of‐weak‐ties hypothesis.MethodsGranovetter's strength‐of‐weak‐ties hypothesis predicted that in a job search, weak ties (acquaintances) are a more valuable source of information as compared to strong ties (close friends or relatives). However, subsequent empirical research has provided ambiguous support for this hypothesis. To sort out the conflicting results, a mathematical model of the transmission of job information through a contact network has been constructed. Along with the strength of tie, a widely used characteristic of contact, the model also incorporates the work relation of tie.ResultsThe model has numerous implications with strong empirical support, as well as propositions going beyond the findings of prior empirical work, which can be evaluated in subsequent studies. It is shown that the effectiveness of a certain type of contact depends on both the ego's status (weak and work‐related contacts are more advantageous for higher‐status workers) and the composition of the ego's network (work‐related contacts promote the effectiveness of weak ties, while strong‐tie contacts hinder the effectiveness of work‐related ties). In particular, it implies that the inconsistency in empirical evidence for the strength‐of‐weak‐ties hypothesis can be explained by the differences in status or the proportion of work‐related contacts in the samples examined.ConclusionWork‐related ties play a significant role in the analysis of informal job‐search methods; their incorporation into the model allows one to account for a number of previously unexplained empirical results.

The definition of place utility from potential theory shows that a preference and orthogonal indifference field can influence a decisionmaker, which suggests the operation of behavioural forces. Learning energy is defined to be a major behavioural force and a statistical model is proposed for its distribution over an assembly of decisionmakers. An attitude system is derived for a social network where the decisionmaker can be in a unitary state of utility or disutility. The resulting partition function shows that the learning energy of the assembly is derived from nearest-neighbour interactions and the operation of an external place utility preference field. A positive linear relationship is proposed between learning energy and environmental stress. The critical stress in social interaction is determined and a variety of behaviours in urban sociology are predicted. The model is then applied to a Markov learning system and the results discussed.

Mathematical models describing relationships in a group of individuals are known for a long time. The basic idea underlying these models can be described as follows. There are affective (emotionally colored) not necessarily symmetrical relationships between any two members of the group. In general, these relationships vary over time and can be described by numerical functions of time. The value of the corresponding function is positive if the first individual has a positive attitude toward the second one and negative if the attitude is negative. While interacting, two individuals share their views on other members of the group. It affects the dynamics of group relationships. At the same time, the model uses principles such as "if the person whom I dislike says something unpleasant about a third person then I improve my opinion of this third person." This paper also deals with the modeling of group interactions, with the difference that the considered interactions have features of mass (not paired) communications, i.e., the opinion of each individual is equally available to all the others (at the same time, affective relations are paired). This situation occurs, for example, in communities of users of internet forums and blogging platforms. Another important difference is due to the fact that individuals do not discuss other members of the group, but discuss various issues on the topic (e.g., political) of interest to all members of the group. The results of numerical experiments for the system are presented and a number of substantial conclusions are formulated. DOI:10.5901/mjss.2013.v4n10p380