Boris Atenas

This chapter explores agent-based models (ABMs) as computational tools for simulating complex systems through autonomous agents and their interactions. We discuss the foundational principles of ABMs and their connection to dynamic systems theory. Applications across socio-physics, such as opinion dynamics, civil unrest, fake news, urban transportation policies, and education, illustrate how micro-level interactions lead to macro-level societal patterns, including Pareto’s laws. In biology, ABMs have proven valuable in modeling medical treatments, such as magnetic fluid hyperthermia, as well as in simulating the spread of diseases like COVID-19. Additionally, dynamical systems such as Lotka-Volterra, when combined with ABMs, can offer complementary insights into complex interactions. Finally, in the economics section, we examine market behaviors, wealth distribution, and strategic interactions, such as the Minority Game. We expect that with these examples, the reader will gain a deeper understanding of how ABMs provide a powerful framework for capturing the emergent behaviors of complex systems across diverse fields.

A physical model, based on energy balances, is proposed to describe the fractures in solid structures such as stelae, tiles, glass, and others. We applied the model to investigate the transition of the Rosetta Stone from the original state to the final state with three major fractures. We consider a statistical corner-breaking model with cutting rules. We obtain a probability distribution as a function of the area and the number of vertices. Our generic results are consistent with the current state of the Rosetta Stone and, additionally, predictions related to a fourth fracture are declared. The loss of information on such heritage pieces is considered through entropy production. The explicit quantification of this concept in information theory stays examined.