Related papers: Cyclic Network Automata and Cohomological Waves
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…
We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological…
Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
Complex systems in the real world can be modeled as a network of connected components. The human brain, as a network of neurons among which the interactions cause perception, is a complex network. Synchronization is a dynamical phenomenon…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
Wireless sensor networks are normally characterized by resource challenged nodes. Since communication costs the most in terms of energy in these networks, minimizing this overhead is important. We consider minimum length node scheduling in…
Although random cell complexes occur throughout the physical sciences, there does not appear to be a standard way to quantify their statistical similarities and differences. The various proposals in the literature are usually motivated by…
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least a threshold number of successor colors in a prescribed…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
This paper addresses analytical aspects of deterministic, continuous-time dynamical systems defined on networks. The goal is to model and analyze certain phenomena which must be framed beyond the context of networked dynamical systems,…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
We relate structurally dynamic cellular networks, a class of models we developed in fundamental space-time physics, to SDCA, introduced some time ago by Ilachinski and Halpern. We emphasize the crucial property of a non-linear interaction…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We introduce a very general approach to the analysis of signals from their noisy measurements from the perspective of Topological Data Analysis (TDA). While TDA has emerged as a powerful analytical tool for data with pronounced topological…