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Recent whole brain imaging experiments on $\textit{C. elegans}$ has revealed that the neural population dynamics encode motor commands and stereotyped transitions between behaviors on low dimensional manifolds. Efforts to characterize the…

Quantitative Methods · Quantitative Biology 2020-04-15 Charles Fieseler , Manuel Zimmer , J. Nathan Kutz

Cellular automata are fully-discrete, spatially-extended dynamical systems that evolve by simultaneously applying a local update function. Despite their simplicity, the induced global dynamic produces a stunning array of richly-structured,…

Statistical Mechanics · Physics 2019-01-01 Adam Rupe , James P. Crutchfield

Multispectral images acquired by satellites are used to study phenomena on the Earth's surface. Unsupervised classification techniques analyze multispectral image content without considering prior knowledge of the observed terrain; this is…

Computer Vision and Pattern Recognition · Computer Science 2019-11-12 Wuilian Torres , Antonio Rueda-Toicen

In order to develop systems capable of modeling artificial life, 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…

Cellular Automata and Lattice Gases · Physics 2020-09-01 Barbora Hudcova , Tomas Mikolov

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…

Cellular Automata and Lattice Gases · Physics 2015-06-26 Navot Israeli , Nigel Goldenfeld

We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…

Dynamical Systems · Mathematics 2017-02-21 Martin Delacourt , Benjamin Hellouin de Menibus

The brain learns abstract representations of high-dimensional sensory input, but the plasticity rules that enable such learning are unknown. We study biologically plausible algorithms on the Random Hierarchy Model (RHM), an artificial…

Machine Learning · Computer Science 2026-05-19 Ariane Delrocq , Wu S. Zihan , Guillaume Bellec , Wulfram Gerstner

Owing to the advances in computational techniques and the increase in computational power, atomistic simulations of materials can simulate large systems with higher accuracy. Complex phenomena can be observed in such state-of-the-art…

Materials Science · Physics 2022-02-16 Ryo Tamura , Momo Matsuda , Jianbo Lin , Yasunori Futamura , Tetsuya Sakurai , Tsuyoshi Miyazaki

In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced…

Cellular Automata and Lattice Gases · Physics 2018-04-05 Norihito Toyota

We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…

Cellular Automata and Lattice Gases · Physics 2009-09-29 V. C. Barbosa , F. M. N. Miranda , M. C. M. Agostini

Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…

Cellular Automata and Lattice Gases · Physics 2021-04-05 Hugo Cisneros , Josef Sivic , Tomas Mikolov

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…

Pattern Formation and Solitons · Physics 2024-04-23 Alex D. Richardson , Tibor Antal , Richard A. Blythe , Linus J. Schumacher

Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the…

Optimization and Control · Mathematics 2020-06-30 Bharat Monga , Jeff Moehlis

The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…

Cellular automata (CA) are dynamical systems defined by a finite local rule but they are studied for their global dynamics. They can exhibit a wide range of complex behaviours and a celebrated result is the existence of (intrinsically)…

Discrete Mathematics · Computer Science 2009-02-10 Laurent Boyer , Guillaume Theyssier

We propose an alternative approach to construct an artificial learning system, which naturally learns in an unsupervised manner. Its mathematical prototype is a dynamical system, which automatically shapes its vector field in response to…

Adaptation and Self-Organizing Systems · Physics 2015-10-08 Natalia B. Janson , Christopher J. Marsden

We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recognizable patterns, usually in the form of second order recurrence equations with constant…

Cellular Automata and Lattice Gases · Physics 2013-05-29 Henryk Fukś

To celebrate Hans Frauenfelder's achievements, we examine energy(-like) "landscapes" for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some…

Quantitative Methods · Quantitative Biology 2021-10-18 Lars Koopmans , Hyun Youk

This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…

Discrete Mathematics · Computer Science 2013-05-20 Pablo Arrighi , Nicolas Schabanel , Guillaume Theyssier

Among the fundamental questions in computer science is that of the impact of synchronism/asynchronism on computations, which has been addressed in various fields of the discipline: in programming, in networking, in concurrence theory, in…

Cellular Automata and Lattice Gases · Physics 2024-03-13 Isabel Donoso Leiva , Eric Goles , Martín Ríos-Wilson , Sylvain Sené