Related papers: Reversible Causal Graph Dynamics
We develop a rigorous topological theory of anomalies on the lattice, which are obstructions to gauging global symmetries and the existence of trivial symmetric states. We also construct $\Omega$-spectra of a class of invertible states and…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…
An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…
We study self-similarity in one-dimensional probabilistic cellular automata (PCA) using the renormalization technique. We introduce a general framework for algebraic construction of renormalization groups (RG) on cellular automata and apply…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
For any infinite transitive sofic shift $X$ we construct a reversible cellular automaton (i.e. an automorphism of the shift $X$) which breaks any given finite point of the subshift into a finite collection of gliders traveling into opposing…
While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…
While the disciplines of physics and engineering sciences in many cases have taken advantage from accurate time-series prediction of system behaviour by applying ordinary differential equation systems upon precise basic physical laws such…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
Various kinds of spread of influence occur in real world social and virtual networks. These phenomena are formulated by activation processes and irreversible dynamic monopolies in combinatorial graphs representing the topology of the…
Understanding causal relations between temporal variables is a central challenge in time series analysis, particularly when the full causal structure is unknown. Even when the full causal structure cannot be fully specified, experts often…
The evolution of spin network states in loop quantum gravity can be described by introducing a time variable, defined by the surfaces of constant value of an auxiliary scalar field. We regulate the Hamiltonian, generating such an evolution,…
Causal reasoning has been an indispensable capability for humans and other intelligent animals to interact with the physical world. In this work, we propose to endow an artificial agent with the capability of causal reasoning for completing…
In many application areas---lending, education, and online recommenders, for example---fairness and equity concerns emerge when a machine learning system interacts with a dynamically changing environment to produce both immediate and…
We present a sound and complete algorithm, called iterative causal discovery (ICD), for recovering causal graphs in the presence of latent confounders and selection bias. ICD relies on the causal Markov and faithfulness assumptions and…
Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…
Extending the work of Godsil and others, we investigate the notion of the inverse of a graph (specifically, of bipartite graphs with a unique perfect matching). We provide a concise necessary and sufficient condition for the invertibility…