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In many settings, machine learning models may be used to inform decisions that impact individuals or entities who interact with the model. Such entities, or agents, may game model decisions by manipulating their inputs to the model to…
John H. Conway's Game of Life, as well as cellular automata in the larger family of Life-like CA, are discrete: the cells have a binary state space and the birth and survival transition rules are 9-bits apiece. Inspired by Life, several…
In this paper we review previous work and present new work concerning the relationship between dynamical systems theory and computation. In particular, we review work by Langton \cite{Langton90} and Packard \cite{Packard88} on the…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
According to cognitive psychology and related disciplines, the development of complex problem-solving behaviour in biological agents depends on hierarchical cognitive mechanisms. Hierarchical reinforcement learning is a promising…
The process of evolutionary emergence of purposeful adaptive behavior is investigated by means of computer simulations. The model proposed implies that there is an evolving population of simple agents, which have two natural needs: energy…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
Because combat environments change over time and technology upgrades are widespread for ground vehicles, a large number of vehicles and equipment become quickly obsolete. A possible solution for the U.S. Army is to develop fleets of modular…
We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model where agents who make decisions using either automatic or…
Advanced reasoning models with agentic capabilities (AI agents) are deployed to interact with humans and to solve sequential decision-making problems under (approximate) utility functions and internal models. When such problems have…
A cellular automaton in which cells represent agents playing the Prisoner's Dilemma (PD) game following the simple "win-stay, loose-shift" strategy is studied. Individuals with binary behavior, such as they can either cooperate (C) or…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
The problem of multi-agent learning and adaptation has attracted a great deal of attention in recent years. It has been suggested that the dynamics of multi agent learning can be studied using replicator equations from population biology.…
Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within…
Contemporary machine learning paradigm excels in statistical data analysis, solving problems that classical AI couldn't. However, it faces key limitations, such as a lack of integration with planning, incomprehensible internal structure,…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
We analyse the long term behaviour of the measure-valued solutions of a class of linear renewal equations modelling physiologically structured populations. The renewal equations that we consider are characterised by a regularisation…