Related papers: Supervised and unsupervised learning with numerica…
We demonstrate how to explore phase diagrams with automated and unsupervised machine learning to find regions of interest for possible new phases. In contrast to supervised learning, where data is classified using predetermined labels, we…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
Classification of quantum phases is one of the most important areas of research in condensed matter physics. In this work, we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning. Firstly, we choose two…
Neural population activity often exhibits regime-dependent non-stationarity in the form of switching dynamics. Learning accurate switching dynamical system models can reveal how behavior is encoded in neural activity. Existing switching…
Motivated by questions in biology and distributed computing, we investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. We investigate what sort of self-stabilising…
We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
The use of fluorescent molecules to create long sequences of low-density, diffraction-limited images enables highly-precise molecule localization. However, this methodology requires lengthy imaging times, which limits the ability to view…
A digit function is presented which provides the $i$th-digit in base $p$ of any real number $x$. By means of this function, formulated within $\mathcal{B}$-calculus, the local, nonlocal and global dynamical behaviors of cellular automata…
We consider the problem of finding response curves for a class of binary two-dimensional cellular automata with $L$-shaped neighbourhood. We show that the dependence of the density of ones after an arbitrary number of iterations, on the…
Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal…
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…
Resource allocation and transceivers in wireless networks are usually designed by solving optimization problems subject to specific constraints, which can be formulated as variable or functional optimization. If the objective and constraint…
We introduce a simple, fast, and easy to implement unsupervised learning algorithm for detecting different local environments on a single-particle level in colloidal systems. In this algorithm, we use a vector of standard bond-orientational…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
There is a vast literature on representation learning based on principles such as coding efficiency, statistical independence, causality, controllability, or symmetry. In this paper we propose to learn representations from sequence data by…