Urszula A. Strawinska-Zanko

Capital in the First Century: The Evolution of Inequality in Ancient Maya Society

We investigated the evolution of inequality in ancient Maya society using the sizes of houses as a proxy for household wealth. We used several mathematical and statistical methods to study the distribution of wealth at four major archaeological sites in the Maya lowlands: Komchen, Palenque, Sayil, and Mayapan. We calculated the Gini coefficient and the probability density function of the distribution of the house sizes as a measure of the wealth distribution at each site. We found that the wealth distributions had some characteristics of an approximate power law at all the sites, yet the exact distributions were statistically different from each other. The results indicate that the evolution of Maya culture across these sites cannot be understood as simply dependent on a monotonic evolution of the wealth distribution with time but should rather be explained by the historical circumstances surrounding each community. Specifically, the analyses show that, before the evolution of urban, state-level society, significant inequality existed in the Late Preclassic period, but a Pareto distribution either had not emerged or was incipient. In the Late and Terminal Classic periods, economic inequality became increasingly pronounced, while in the succeeding Postclassic period inequality ameliorated, although it seems that poverty prevailed.

Future Directions in the Mathematical Modeling of Social Relationships

New methods of computational modeling and new areas of their application will expand the importance of the mathematical modeling of social relationships. To take full advantage, these new methods may require interdisciplinary teams of scientists.

Introduction to the Mathematical Modeling of Social Relationships

Mathematics has been used to describe the assumptions and determine their consequences in the physical sciences over the last three centuries. More recently, mathematics has been used to develop a deeper understanding of complex biological phenomena and data. We are now witnessing the expansion of mathematical methods into the social sciences. In this chapter, we trace that trail of mathematics from the physical sciences, to the biological sciences, to the social sciences and review mathematical methods that provide new tools to understand social relationships.

Modeling Psychotherapy Encounters: Rupture and Repair

In this chapter, we present an extension of the mathematical model of the therapeutic relationship developed by Liebovitch and Peluso by investigating relationship ruptures. We present a simulation work that models a repair to relationship ruptures and investigates its potential impact on the success of the therapy. This new model suggests that an intervention of the therapist to repair the relationship with client is an effective way of preventing the client from falling into negative affective states that the therapist considers detrimental to the therapy process.

A Dynamical Approach to Conflict Management in Teams

In this chapter, we argue for the relevance and application of the dynamical systems framework in the study of conflict management processes in work teams and present some preliminary research that explores three key questions: First, can meaningful, distinct patterns of conflict management approaches – cooperation, competition, and avoidance – emerge within and across intact work teams and in ways that distinguish higher-performing teams from lower-performing ones? Can some fundamental dynamical properties, such as time evolution, self-organization, and attractor states, be observed in the phenomenon of team conflict management? And finally, how do temporal patterns of team conflict management dynamics change and vary in relation to external influences or critical junctures over the course of team interaction? Based on our preliminary research, we observed that a critical difference between high- and low-performing teams may lie in the consistent yet flexible (or attractor-like) reliance of both highly cooperative and avoidant strategies relative to competitive strategies over time; further, an adaptive use of competitive strategies around critical junctures in the team’s life span also appeared particularly crucial to team success. We also discuss implications of our tentative findings, limitations of the current study, and possible directions in future research in the chapter.