Related papers: A New Class of Cellular Automata for Reaction-Diff…
In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a…
The advantage of Cellular Potts Model (CPM) is due to its ability for introducing cell-cell interaction based on the well known statistical model i.e. the Potts model. On the other hand, Lattice gas Cellular Automata (LGCA) can simulate…
We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students…
We investigate number conserving cellular automata with up to five inputs and two states with the goal of comparing their dynamics with diffusion. For this purpose, we introduce the concept of decompression ratio describing expansion of…
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
Quantum cellular automata are alternative quantum-computing paradigms to quantum Turing machines and quantum circuits. Their working mechanisms are inherently automated, therefore measurement free, and they act in a translation invariant…
We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work…
We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to…
We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem:…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
Despite considerable success, large Denoising Diffusion Models (DDMs) with UNet backbone pose practical challenges, particularly on limited hardware and in processing gigapixel images. To address these limitations, we introduce two Neural…
We concern with a special class of binary cellular automata, i.e., the so-called particle cellular automata (PCA) in the present paper. We first propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic operations of the…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the…
We investigate one-dimensional Probabilistic Cellular Automata, called Diploid Elementary Cellular Automata (DECA), obtained as random mixture of two different Elementary Cellular Automata rules. All the cells are updated synchronously and…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g.…
To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule,…