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This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
Adaptive voter models (AVMs) are simple mechanistic systems that model the emergence of mesoscopic structure from local networked processes driven by conflict and homophily. AVMs display rich behavior, including a phase transition from a…
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…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Volumetry is one of the principal downstream applications of 3D medical image segmentation, for example, to detect abnormal tissue growth or for surgery planning. Conformal Prediction is a promising framework for uncertainty quantification,…
Calibration is defined as the ratio of the average predicted click rate to the true click rate. The optimization of calibration is essential to many online advertising recommendation systems because it directly affects the downstream bids…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
The Integrated Information Theory provides a quantitative approach to consciousness and can be applied to neural networks. An embodied agent controlled by such a network influences and is being influenced by its environment. This involves,…
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…
Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself…
The field of Multi-Agent System (MAS) is an active area of research within Artificial Intelligence, with an increasingly important impact in industrial and other real-world applications. Within a MAS, autonomous agents interact to pursue…
A consensus-based optimization (CBO) algorithm, which enables derivative and mesh-free optimization, is presented to localize a bioluminescent source. The light propagation is modeled by the radiative transfer equation approximated by…
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…