Related papers: Application of a renormalization group algorithm t…
We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small…
We apply the dinamically driven renormalization group to study the critical properties of the Domany-Kinzel probabilistic cellular automaton. To preserve the absorbing state clusters with at least one site occupied are renormalized into a…
We introduce a real-space renormalisation group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact…
This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the…
We introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium systems with steady-states: the Dynamically Driven Renormalization Group. We renormalize the time evolution…
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…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation…
Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…
We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution…
The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our…
A perturbative renormalization group method is used to obtain steady-state density profiles of a particle non-conserving asymmetric simple exclusion process. This method allows us to obtain a globally valid solution for the density profile…
We consider hexagonal cellular automata with immediate cell neighbourhood and three cell-states. Every cell calculates its next state depending on the integral representation of states in its neighbourhood, i.e. how many neighbours are in…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…
We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
There are few known universality classes of absorbing phase transitions in one dimension and most models fall in the well-known directed percolation (DP) class. Synchronization is a transition to an absorbing state and this transition is…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Global changes of states are of crucial importance in optimization algorithms. We review some heuristic algorithms in which global updates are realized by a sort of real-space renormalization group transformation. Emphasis is on the…