Probabilistic cellular automata

Persistent homology and the shape of evolutionary games

For nearly three decades, spatial games have produced a wealth of insights to the study of behavior and its relation to population structure. However, as different rules and factors are added or altered, the dynamics of spatial models often become increasingly complicated to interpret. To tackle this problem, we introduce persistent homology as a rigorous framework that can be used to both define and compute higher-order features of data in a manner which is invariant to parameter choices, robust to noise, and independent of human observation. Our work demonstrates its relevance for spatial games by showing how topological features of simulation data that persist over different spatial scales reflect the stability of strategies in 2D lattice games. To do so, we analyze the persistent homology of scenarios from two games: a Prisoner's Dilemma and a SIRS epidemic model. The experimental results show how the method accurately detects features that correspond to real aspects of the game dynamics. Unlike other tools that study dynamics of spatial systems, persistent homology can tell us something meaningful about population structure while remaining neutral about the underlying structure itself. Regardless of game complexity, since strategies either succeed or fail to conform to shapes of a certain topology there is much potential for the method to provide novel insights for a wide variety of spatially extended systems in biology, social science, and physics.

Source of Knowledge Dynamics-Transition from High School to University

The paper addresses the dynamics of education by using Markov chains, a powerful probabilistic model able to make predictions on how sources of knowledge either change or stabilize over adulthood. To this end, each student filled in a survey that rated, on a scale from 1 to 5, the utility of five different sources of knowledge. They completed this survey twice, once for their previous and once for their current education. The authors then fitted a Markov chain to these data—essentially, calculating transition probabilities from one ranking of sources of knowledge to another—and inferred the final maximum utility sources of knowledge via the stationary distribution. The overall conclusion is the following: even if the professor used to play a crucial role in early development, students have the tendency to become independent in their learning process, relying more on online materials and less on printed books and libraries.

The ulam Programming Language for Artificial Life

Traditional digital computing demands perfectly reliable memory and processing, so programs can build structures once then use them forever-but such deterministic execution is becoming ever more costly in large-scale systems. By contrast, living systems, viewed as computations, naturally tolerate fallible hardware by repairing and rebuilding structures even while in use-and suggest ways to compute using massive amounts of unreliable, merely best-effort hardware. However, we currently know little about programming without deterministic execution, in architectures where traditional models of computation-and deterministic ALife models such as the Game of Life-need not apply. This expanded article presents ulam, a language designed to balance concurrency and programmability upon best-effort hardware, using lifelike strategies to achieve robust and scalable computations. The article reviews challenges for traditional architecture, introduces the active-media computational model for which ulam is designed, and then presents the language itself, touching on its nomenclature and surface appearance as well as some broader aspects of robust software engineering. Several ulam examples are presented; then the article concludes with a brief consideration of the couplings between a computational model and its physical implementation.