Related papers: Partial differential equations versus cellular aut…
We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…
Search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
A new class of deterministic dynamical systems, termed semipredictable dynamical systems, is presented. The spatiotemporal evolution of these systems have both predictable and unpredictable traits, as found in natural complex systems. We…
Modeling social interactions based on individual behavior has always been an area of interest, but prior literature generally presumes rational behavior. Thus, such models may miss out on capturing the effects of biases humans are…
Autonomous artificial agents must be able to learn behaviors in complex environments without humans to design tasks and rewards. Designing these functions for each environment is not feasible, thus, motivating the development of intrinsic…
We describe a map-based model which reproduces many of the behaviors seen in partial differential equations (PDE's). Like PDE's, we show that this model can support an infinite number of stationary solutions, traveling solutions, breathing…
We argue that an explainable artificial intelligence must possess a rationale for its decisions, be able to infer the purpose of observed behaviour, and be able to explain its decisions in the context of what its audience understands and…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…
In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and…
Multi-agent reinforcement learning (MARL) has received increasing attention for its applications in various domains. Researchers have paid much attention on its partially observable and cooperative settings for meeting real-world…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Common computational problems, such as parameter estimation in dynamic models and PDE constrained optimization, require data fitting over a set of auxiliary parameters subject to physical constraints over an underlying state. Naive…
Recent advances in neurosciences and psychology have provided evidence that affective phenomena pervade intelligence at many levels, being inseparable from the cognitionaction loop. Perception, attention, memory, learning, decisionmaking,…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
With humans interacting with AI-based systems at an increasing rate, it is necessary to ensure the artificial systems are acting in a manner which reflects understanding of the human. In the case of humans and artificial AI agents operating…
Artificially intelligent agents deployed in the real-world will require the ability to reliably \textit{cooperate} with humans (as well as other, heterogeneous AI agents). To provide formal guarantees of successful cooperation, we must make…
Mathematical models are vital interpretive and predictive tools used to assist in the understanding of cell migration. There are typically two approaches to modelling cell migration: either micro-scale, discrete or macro-scale, continuum.…