Lattice Gas Automata for Reactive Systems

Reactive lattice gas automata provide a microscopic approachto the dynamics of spatially-distributed reacting systems. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a simple physical picture to show how an automaton can be constructed to capture the essentials of a reactive molecular dynamics scheme. The statistical mechanical theory of the automaton is then developed for diffusive transport and for reactive processes, and a general algorithm is presented for reactive LGA. The method is illustrated by considering applications to bistable and excitable media, oscillatory behavior in reactive systems, chemical chaos and pattern formation triggered by Turing bifurcations. The reactive lattice gas scheme is contrasted with related cellular automaton methods and the paper concludes with a discussion of future perspectives.Comment: to appear in PHYSICS REPORTS, 81 revtex pages; uuencoded gziped postscript file; figures available from [email protected] or [email protected]

Identification of binary cellular automata from spatiotemporal binary patterns using a fourier representation

The identification of binary cellular automata from spatio-temporal binary patterns is investigated in this paper. Instead of using the usual Boolean or multilinear polynomial representation, the Fourier transform representation of Boolean functions is employed in terms of a Fourier basis. In this way, the orthogonal forward regression least-squares algorithm can be applied directly to detect the significant terms and to estimate the associated parameters. Compared with conventional methods, the new approach is much more robust to noise. Examples are provided to illustrate the effectiveness of the proposed approach

Isolating and Quantifying the Role of Developmental Noise in Generating Phenotypic Variation

Genotypic variation, environmental variation, and their interaction may produce variation in the developmental process and cause phenotypic differences among individuals. Developmental noise, which arises during development from stochasticity in cellular and molecular processes when genotype and environment are fixed, also contributes to phenotypic variation. While evolutionary biology has long focused on teasing apart the relative contribution of genes and environment to phenotypic variation, our understanding of the role of developmental noise has lagged due to technical difficulties in directly measuring the contribution of developmental noise. The influence of developmental noise is likely underestimated in studies of phenotypic variation due to intrinsic mechanisms within organisms that stabilize phenotypes and decrease variation. Since we are just beginning to appreciate the extent to which phenotypic variation due to stochasticity is potentially adaptive, the contribution of developmental noise to phenotypic variation must be separated and measured to fully understand its role in evolution. Here, we show that variation in the component of the developmental process corresponding to environmental and genetic factors (here treated together as a unit called the LALI-type) versus the contribution of developmental noise, can be distinguished for leopard gecko (Eublepharis macularius) head color patterns using mathematical simulations that model the role of random variation (corresponding to developmental noise) in patterning. Specifically, we modified the parameters of simulations corresponding to variation in the LALI-type to generate the full range of phenotypic variation in color pattern seen on the heads of eight leopard geckos. We observed that over the range of these parameters, variation in color pattern due to LALI-type variation exceeds that due to developmental noise in the studied gecko cohort. However, the effect of developmental noise on patterning is also substantial. Our approach addresses one of the major goals of evolutionary biology: to quantify the role of stochasticity in shaping phenotypic variation

Emergence of diverse epidermal patterns by integrating Turing pattern model and majority voting model

The Turing pattern model is one type of reaction-diffusion (RD) model. The first identification of pattern formation by the Turing pattern model in an actual animal was made in the 1990s with the observation of patterns in the sea anemone. But can we assume that all epidermal patterns in animals can be explained by the Turing pattern model? Even for fish, there are some fish that are clearly not Turing patterns, differing significantly from the patterns that can be generated by RD models. For example, the body pattern of the ornamental carp Nishiki goi produced in Japan varies randomly from individual to individual, and it is difficult to predict the pattern of the offspring from that of the parent fish. A model in which these fish patterns are formed randomly is the majority voting model. From this, it can be inferred that the epidermal pattern of fish can be explained by either the Turing pattern model or the majority voting model. But how do fish use these two different models? It is hard to imagine that completely different epidermal formation mechanisms are used among species of the same family. For this reason, there may be a more basic model that can produce patterns for either model. In this study, the Turing pattern model and the majority voting model were represented by cellular automata, and then a new model integrating these two models was proposed. By adjusting the parameters, this integrated model was able to create patterns that are equivalent to both the Turing pattern model and the majority voting model. By setting the intermediate parameters values of these two models, it was possible to create a variety of patterns that were more diverse than those created by each single model. Although this model is simpler than previously proposed models, it was able to confirm that it can create a variety of patterns

Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and simulate the model with NetLogo to observe pattern formation. The model examination is focused on the two parameters for stability analysis. The results show that if there is a pattern formation in the model, the system is unstable, and if the patches are smaller and lighter patches, it is stable. Furthermore, the analysis for the choice of particle density and adhesion coefficient displayed that they are the main decision-mechanisms for general structure

Modeling pattern formation in communities by using information particles

Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the distributed behavior model. The information particle drives competition or coordination among species. Therefore, a traverse of information particles in a social system makes it possible to express four different classes of patterns (i.e. "stationary", "competitive-equilibrium", "chaotic", and "periodic"). Remarkably, "competitive equilibrium" well expresses the complex dynamics that is equilibrium macroscopically and non-equilibrium microscopically. Although it is a fundamental phenomenon in pattern formation in nature, it has not been obtained by conventional models. Furthermore, the pattern transitions across the classes depending only on parameters of system, namely, the number of species (vertices in network) and distance (edges) between species. It means that one information-particle model successfully develops the patterns with an in-situ computation under various environments.Comment: 12 pages and 6 figure

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Adversarial Turing Patterns from Cellular Automata

State-of-the-art deep classifiers are intriguingly vulnerable to universal adversarial perturbations: single disturbances of small magnitude that lead to misclassification of most in-puts. This phenomena may potentially result in a serious security problem. Despite the extensive research in this area,there is a lack of theoretical understanding of the structure of these perturbations. In image domain, there is a certain visual similarity between patterns, that represent these perturbations, and classical Turing patterns, which appear as a solution of non-linear partial differential equations and are underlying concept of many processes in nature. In this paper,we provide a theoretical bridge between these two different theories, by mapping a simplified algorithm for crafting universal perturbations to (inhomogeneous) cellular automata,the latter is known to generate Turing patterns. Furthermore,we propose to use Turing patterns, generated by cellular automata, as universal perturbations, and experimentally show that they significantly degrade the performance of deep learning models. We found this method to be a fast and efficient way to create a data-agnostic quasi-imperceptible perturbation in the black-box scenario. The source code is available at https://github.com/NurislamT/advTuring.Comment: Published as a conference paper at AAAI 2021 (camera-ready version