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arXiv2024

Block approximations for probabilistic mixtures of elementary cellular automata

Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied, making the study of their phase diagrams particularly interesting. The block approximation method, also known in this context as the local structure approach, is a powerful tool for studying the main features of these diagrams, improving upon Mean Field results. This work considers systems with multiple stationary states, aiming to understand how their interactions give rise to the structure of the phase diagram. Additionally, it shows how a simple algorithmic implementation of the block approximation allows for the effective study of the phase diagram even in the presence of several absorbing states.

nlin.CG↗

arXiv2024

Biological arrow of time: Emergence of tangled information hierarchies and self-modelling dynamics

We study open-ended evolution by focusing on computational and information-processing dynamics underlying major evolutionary transitions. In doing so, we consider biological organisms as hierarchical dynamical systems that generate regularities in their phase-spaces through interactions with their environment. These emergent information patterns can then be encoded within the organism's components, leading to self-modelling "tangled hierarchies". Our main conjecture is that when macro-scale patterns are encoded within micro-scale components, it creates fundamental tensions (computational inconsistencies) between what is encodable at a particular evolutionary stage and what is potentially realisable in the environment. A resolution of these tensions triggers an evolutionary transition which expands the problem-space, at the cost of generating new tensions in the expanded space, in a continual process. We argue that biological complexification can be interpreted computation-theoretically, within the Gödel--Turing--Post recursion-theoretic framework, as open-ended generation of computational novelty. In general, this process can be viewed as a meta-simulation performed by higher-order systems that successively simulate the computation carried out by lower-order systems. This computation-theoretic argument provides a basis for hypothesising the biological arrow of time.

q-bio.PE↗

arXiv2024

Never Mind The No-Ops: Faster and Less Volatile Simulation Modelling of Co-Evolutionary Species Interactions via Spatial Cyclic Games

Issues in co-evolutionary population dynamics have long been studied via computationally intensive simulations of minimally simple agent-based models, known as Evolutionary Spatial Cyclic Games (ESCGs), involving multiple interacting biological species in which each agent has its own unique spatial location in a cell on a regular lattice, and can move from cell to cell over time. Many papers have been published exploring the dynamics of ESCGs where competitive inter-species predator/prey relationships are modelled via the cyclic game Rock-Paper-Scissors (RPS) for three species, or Rock-Paper-Scissors-Lizard-Spock (RPSLS) for five. At the core of these simulations is the "Elementary Step" (ES), in which one or two agents are chosen at random to either compete to the death, or to reproduce, or to move location. ESCG studies typically involve executing trillions of ESs and hence the computational efficiency of the core ES algorithm is a key concern. In this paper I demonstrate that the de facto standard "Original ES" (OES) algorithm is computationally inefficient both in time and in space due to the implicit execution of many "no-op" commands (i.e., commands that do nothing) and because at steady state large numbers of cells can be empty, and yet empty cells serve no purpose. I present a new "Revised ES" (RES) algorithm which eliminates these inefficiencies, and I show empirically that ESCGs with RES exhibit qualitatively the same characteristics as those with OES, and are also markedly more stable. The more stable dynamics of RES-based simulations means that they can be run with smaller lattices than when using OES, leading to reductions in total simulation times of 85% or more. Python source code developed for the experiments reported here is freely available on GitHub.

q-bio.PE↗

arXiv2024

An open problem: Why are motif-avoidant attractors so rare in asynchronous Boolean networks?

Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular in systems biology due to their ability to model long-term biological phenotypes within a qualitative, predictive framework. Boolean networks model phenotypes as attractors, which are closely linked to minimal trap spaces (inescapable hypercubes in the system's state space). In biological applications, attractors and minimal trap spaces are typically in one-to-one correspondence. However, this correspondence is not guaranteed: motif-avoidant attractors (MAAs) that lie outside minimal trap spaces are possible. MAAs are rare and (despite recent efforts) poorly understood. Here we summarize the current state of knowledge regarding MAAs and present several novel observations regarding their response to node deletion reductions and linear extensions of edges. We conduct large-scale computational studies on an ensemble of 14,000 models derived from published Boolean models of biological systems, and more than 100 million Random Boolean Networks. Our findings quantify the rarity of MAAs (in particular, we found no MAAs in the biological models), but highlight the role of network reduction in introducing MAAs into the dynamics. We also show that MAAs are fragile to linear extensions: in sparse networks, even a single linear node can disrupt virtually all MAAs. Motivated by this observation, we improve the upper bound on the number of delays needed to disrupt a motif-avoidant attractor.

q-bio.MN↗

arXiv2024

Touching Loop Patterns with Cellular Automata

The objective is the design of a Cellular Automata rule that can form patterns with 'touching' loops. A loop is defined as a closed path of 1-cells in a 2D grid on a zero background and with a zero border. A path cell is connected with two of its adjacent neighbors. In touching loops a path cell is also allowed to touch another on a diagonal. A CA rule was designed that can evolve stable touching loop patterns. The rule tries to cover the 2D space by overlapping tiles. The rule uses so-called templates, 5 x 5 matching patterns which are systematically derived from the given set of 3 x 3 tiles. The rule checks the pattern being evolved against a list of templates. If the outer neighbors of a template match, then the cell's state is set to the template's center value. Noise is injected if there is no matching template, or the tiles are not properly assembled. Thereby the evolution is driven to the desired loop patterns.

nlin.CG↗

arXiv2024

Conways game of life as an analogue to a habitable world Livingness beyond the biological

Conways Game of Life is a cellular automaton noted for its rich, complex, and emergent behavior, which seems qualitatively lifelike it exists within a wider space of different rule-sets of cellular automata none of which have been found to display behaviors that seem as rich as Conways selected example We present here a set of three quantitative tests for lifelike behavior based on the critical brain theory Shannons theory of information entropy and integrated information theory all of which are successfully able to select Conways Game of Life as an outlier within this set which is a nonbiological analogue to the selection of a habitable planet or universe among a wider space of similar settings that cannot support the same kinds of living systems

nlin.CG↗

arXiv2024

Physics of collective transport and traffic phenomena in biology: progress in 20 years

Enormous progress have been made in the last 20 years since the publication of our review \cite{csk05polrev} in this journal on transport and traffic phenomena in biology. In this brief article we present a glimpse of the major advances during this period. First, we present similarities and differences between collective intracellular transport of a single micron-size cargo by multiple molecular motors and that of a cargo particle by a team of ants on the basis of the common principle of load-sharing. Second, we sketch several models all of which are biologically motivated extensions of the Asymmetric Simple Exclusion Process (ASEP); some of these models represent the traffic of molecular machines, like RNA polymerase (RNAP) and ribosome, that catalyze template-directed polymerization of RNA and proteins, respectively, whereas few other models capture the key features of the traffic of ants on trails. More specifically, using the ASEP-based models we demonstrate the effects of traffic of RNAPs and ribosomes on random and `programmed' errors in gene expression as well as on some other subcellular processes. We recall a puzzling empirical result on the single-lane traffic of predatory ants {\it Leptogenys processionalis} as well as recent attempts to account for this puzzle. We also mention some surprising effects of lane-changing rules observed in a ASEP-based model for 3-lane traffic of army ants. Finally, we explain the conceptual similarities between the pheromone-mediated indirect communication, called stigmergy, between ants on a trail and the floor-field-mediated interaction between humans in a pedestrian traffic. For the floor-field model of human pedestrian traffic we present a major theoretical result that is relevant from the perspective of all types of traffic phenomena.

physics.bio-ph↗

arXiv2025

A gradient model for the Bernstein polynomial basis

We introduce a symmetric, gradient exclusion process within the class of non-cooperative kinetically constrained lattice gases, modelling a non-linear diffusivity in which the exchange of occupation values between two neighbouring sites depends on the local density in specific boxes surrounding the pair. The existence of such a model satisfying the gradient property is the main novelty of this work, filling a gap in the literature regarding the types of diffusivities attainable within this class of models. The resulting dynamics exhibits similarities with the Bernstein polynomial basis and generalises the Porous Media Model. We also introduce an auxiliary collection of processes, which extend the Porous Media Model in a different direction and are related to the former process via an inversion formula.

math.PR↗

arXiv2026

Temporally Non-Uniform Cellular Automata: Surjectivity, Reversibility and Cyclic Behavior

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as infinite lattices, are considered in this work. Surjectivity and injectivity of the t-NUCAs are studied. The reversibility of the t-NUCAs is also explored here. Finally, a study on the cyclic behavior of finite t-NUCAs is presented.

cs.FL↗

arXiv2025

Multiresolution relaxation times lattice Boltzmann schemes with projection

We propose to extend the multiresolution relaxation times lattice Boltzmann schemes with an additional projection step. For the explicit example of the D2Q9 scheme, we define this extended method. We prove that in general the projection step does not change the asymptotic partial differential equations at second order. We present four numerical test cases. One concerns linear stability with a Fourier analysis with a single-vertex scheme. Three bidimensional fluid flows with a coarse mesh have been tested: the Minion and Brown sheared flow, the Ghia, Ghia and Shin lid-driven cavity and an unsteady acoustic wave. Our results indicate that the bulk viscosity can be dramatically reduced with a better stability than the initial scheme.

nlin.CG↗

arXiv2024

Non-reciprocal interactions preserve the universality class of Potts model

We study the $q$-state Potts model on a square lattice with directed nearest-neighbor spin-spin interactions that are inherently non-reciprocal. Both equilibrium and non-equilibrium dynamics are investigated. Analytically, we demonstrate that non-reciprocal interactions do not alter the critical exponents of the model under equilibrium dynamics. In contrast, numerical simulations with selfish non-equilibrium dynamics reveal distinctive behavior. For $q=2$ (non-reciprocal non-equilibrium Ising model), the critical exponents remain consistent with those of the equilibrium Ising universality class. However, for $q=3$ and $q=4$, the critical exponents vary continuously. Remarkably, a super-universal scaling function -- Binder cumulant as a function of $ξ_2/ξ_0$, where $ξ_2$ is the second moment correlation length and $ξ_0$ its maximum value -- remains identical to that of the equilibrium $q=3,4$ Potts models. These findings indicate that non-reciprocal Potts models belong to the superuniversality class of their respective equilibrium counterparts.

cond-mat.stat-mech↗

arXiv2025

A Novel Approach to Real-Time Short-Term Traffic Prediction based on Distributed Fiber-Optic Sensing and Data Assimilation with a Stochastic Cell-Automata Model

This paper demonstrates real-time short-term traffic flow prediction through distributed fiber-optic sensing (DFOS) and data assimilation with a stochastic cell-automata-based traffic model. Traffic congestion on expressways is a severe issue. To alleviate its negative impacts, it is necessary to optimize traffic flow prior to becoming serious congestion. For this purpose, real-time short-term traffic flow prediction is promising. However, conventional traffic monitoring apparatus used in prediction methods faces a technical issue due to the sparsity in traffic flow data. To overcome the issue for realizing real-time traffic prediction, this paper employs DFOS, which enables to obtain spatially continuous and real-time traffic flow data along the road without dead zones. Using mean velocities derived from DFOS data as a feature extraction, this paper proposes a real-time data assimilation method for the short-term prediction. As the theoretical model, the stochastic Nishinari-Fukui-Schadschneider model is adopted. Future traffic flow is simulated with the optimal values of model parameters estimated from observed mean velocities and the initial condition estimated as the latest microscopic traffic state. This concept is validated using two congestion scenarios obtained in Japanese expressways. The results show that the mean absolute error of the predicted mean velocities is 10-15 km/h in the prediction horizon of 30 minutes. Furthermore, the prediction error in congestion length and travel time decreases by 40-84% depending on congestion scenarios when compared with conventional methods with traffic counters. This paper concludes that real-time data assimilation using DFOS enables an accurate short-term traffic prediction.

cond-mat.stat-mech↗

arXiv2025

Evolution of Spots and Stripes in Cellular Automata

Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of Life, which is a universal computer. It belongs to a family of cellular automata with 262,144 members. Playing the Game of Life generally involves engineering; that is, assembling a device composed of various parts that are combined to achieve a specific intended result. Instead of engineering cellular automata, we propose evolving cellular automata. Evolution applies mutation and selection to a population of organisms. If a mutation increases the fitness of an organism, it may have many descendants, displacing the less fit organisms. Unlike engineering, evolution does not work towards an imagined goal. Evolution works towards increasing fitness, with no expectations about the specific form of the final result. Mutation, selection, and fitness yield structures that appear to be more organic and life-like than engineered structures. In our experiments, the patterns resulting from evolving cellular automata look much like the spots on leopards and the stripes on tigers.

nlin.CG↗

arXiv2025

Quantum Circuits for Elementary Cellular Automata

In this paper we identify full list of Elementary Cellular Automata rules which can be simulated using a quantum circuit (there are 22 such rules). For every such rule we present quantum circuit implementing it with $O(N)$ gates.

quant-ph↗

arXiv2025

Elementary Cellular Automata as Multiplicative Automata

Elementary cellular automata (ECA) are converted into multiplicative versions by using permuted n-dim Galois fields and octonion multiplication tables as binary pointers to each rule's Wolfram code truth table. This enables an extension of the binary ECA to complex numbers, identity solutions are found, produces a polynomial, and is implemented in Java.

nlin.CG↗

arXiv2025

Kinetic modelling of economic markets with individual and collective transactions

Two kinetic exchange models are proposed to explore the dynamics of closed economic markets characterized by random exchanges, saving propensities, and collective transactions. Model I simulates a system where individual transactions occur among agents with saving tendencies, along with collective transactions between groups. Model II restricts individual transactions to agents within the same group, but allows for collective transactions between groups. A three-step trading process--comprising intergroup transactions, intragroup redistribution, and individual exchanges--is developed to capture the dual-layered market dynamics. The saving propensity is incorporated using the Chakraborti-Chakrabarti model, applied to both individual and collective transactions. Results reveal that collective transactions increase wealth inequality by concentrating wealth within groups, as indicated by higher Gini coefficients and Kolkata indices. In contrast, individual transactions across groups mitigate inequality through more uniform wealth redistribution. The interplay between saving propensities and collective transactions governs deviation degree and entropy, which display inverse trends. Higher saving propensities lead to deviations from the Boltzmann-Gibbs equilibrium, whereas specific thresholds result in collective transaction dominance, producing notable peaks or troughs in these metrics. These findings underscore the critical influence of dual-layered market interactions on wealth distribution and economic dynamics.

nlin.CG↗

arXiv2025

Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for nonlinear problems remains a significant challenge. We introduce a novel node-level ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer. This approach combines the advantages of the lattice Boltzmann method, which offers low-dimensional representation, and lattice gas cellular automata, which provide linear collision treatment. Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality. We validated the algorithm through comprehensive simulations of benchmark cases, including vortex-pair merging and decaying turbulence on $2048^2$ computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work offers valuable insights into developing quantum algorithms for other nonlinear problems, and potentially advances the application of quantum computing across various transport phenomena in engineering.

physics.flu-dyn↗

arXiv2025

Extended Cellular Automata

In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful in studying complex systems involving two related phenomena and provide a way to their co-study.

nlin.CG↗