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Wolfram Summer SchoolFounded in 2003

16th Annual Wolfram Summer School, held at Bentley University June 24–July 13, 2018


Rubens de Almeida Zimbres

Class of 2006


From 1987 to 1992 Rubens studied dentistry at Universidade de São Paulo. He was a lieutenant of the Brazilian Air Force for five years, and then had his personal dental office for two years. During the year 2000, Rubens spent ten months in Los Angeles studying and visiting dental offices. Rubens got his title of Master in Business Administration at Universidade Presbiteriana Mackenzie, with the dissertation "Formation and Evolution of Business Networks in Dentistry," where he used cellular automata to model evolution of the opinions of 304 dentists located in a social network regarding their partner selection criteria, evaluating flow (rule 234), interruption of information (rule 204), and strength of ties between them. Today Rubens is enrolled in a doctorate program at Universidade Presbiteriana Mackenzie. His interests are social networks, cellular automata, agent-based modeling, strategic management, complexity, evolutionary theory, game theory, competitive advantage, alliances, partner selection, innovation, services, and cognitive sciences.

Project: Effects of Changes in the Neighborhood and Initial State in the Flow of Information in Social Networks

There is an increasing academic interest in networks, especially social ones. Social networks are created by interactions between actors, and as time goes on connections appear. These connections are called ties. There are strong and weak ties. Strong ties are related to trust and spatial closeness between agents. There is a convergence of opinions in this case. Weak ties are related to diversity. Individuals connected to others through strong ties tend to be in closed communities and are usually refractory to external influences. Weak ties connect different networks and are a source of diversity. As an abstraction, I will use CA neighborhoods to understand how information flows, appears, and fades away from the network.

This project explores the influences of the rule, initial condition, and the neighborhood in the evolution of one- and two-dimensional cellular automata. We will analyze how the neighborhood influences the density and information flow in the network. This will be done by comparing differences in the regular neighborhood CA and the modified neighborhood CA. Preliminary results with the 255 rules in 1D CA show that the number of 1's (i.e., the number of cells that did not change their values) corresponded to 50% of the cells, and white and black (0 and 2) had 25% each in most cases. We are doing an exhaustive search to see how each rule behaves according to the change in neighborhood. Measurements are being made, and we have found that rules may be classified regarding their stability when submitted to changes in the neighborhood. Figures show changes applied to neighborhood in one-dimensional and two-dimensional CA.

Favorite Four-Color, Radius-1/2 Rule

Rule chosen: 661856526