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arXiv2021

From Social to Epidemic Criticality and Back

We study the spread of a simulated epidemic in a network of individuals who may either contract a disease through sexual contact with an infected nearest neighbor or use safe sex practices under the influence of neighbors who are already adopting precautions. We show that both interaction between susceptible and infected individuals and the imitation of opinions concerning safe sex practices between individuals in favor of using such practices and those opposed to them leads to a phase transition. If the parameters of the epidemic are in the supercritical state, corresponding to an unlimited growth of infection, the interaction parameter of the sociological debate must also be in the supercritical state to control the spread of infection, and bring the system to criticality. Adopting a theoretical perspective like that of multilayer complex networks, we study the case where the epidemic network is under the influence of the above-mentioned sociological debate. We show that at criticality this debate generates clusters of individuals in favor of safe sex practices and clusters of individuals opposing their use. We study the influence of a sociological debate on whether to use safe sex or not, on the spreading of sexually transmitted infections. We show that due to this debate in the epidemic network a pattern mirroring the structures of the sociological network appears. Finally, we introduce a feedback of the epidemic network on the sociological network and prove that due to this feedback the sociological system undergoes a process of self-organization keeping it at criticality. We hope that these results have the effect of giving interesting suggestions to behavioral psychologists and information scientists actively involved in the analysis of the social debate on the moral issues connected to sexual activities.

physics.soc-ph↗

arXiv2022

Evolution of Symbiosis in the Game of Life: Three Characteristics of Successful Symbiotes

In past work, we developed a computational model of the evolution of symbiotic entities (Model-S), based on Conway's Game of Life. In this article, we examine three trends that biologists have observed in the evolution of symbiotes. (1) Management: If one partner is able to control the symbiotic relation, this control can reduce conflict; thus, evolutionary selection favours symbiotes that have a manager. (2) Mutualism: Although partners in a symbiote often have conflicting needs, evolutionary selection favours symbiotes in which partners are better off together inside the symbiote than they would be as individuals outside of the symbiote. (3) Interaction: Repeated interaction among partners in symbiosis tends to promote increasing fitness due to evolutionary selection. We have added new components to Model-S that allow us to observe these three trends in runs of Model-S. The new components are analogous to the practice of staining cells in biology research, to reveal patterns that are not usually visible. When we measure the fitness of a symbiote by making it compete with other symbiotes, we find that fitter symbiotes have significantly more management, mutualism, and interaction than less fit symbiotes. These results confirm the trends observed in nature by biologists. Model-S allows biologists to study these evolutionary trends and other characteristics of symbiosis in ways that are not tractable with living organisms.

cs.NE↗

arXiv2021

Dynamical properties of disjunctive Boolean networks

A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current configuration of states. In this paper, we are interested in disjunctive networks, where each local function is simply the disjunction of a set of variables. As such, this network is somewhat homogeneous, though the number of variables may vary from entity to entity, thus yielding a generalised cellular automaton. The aim of this paper is to review some of the main results, derive some additional fundamental results, and highlight some open problems, on the dynamics of disjunctive networks. We first review the different defining characteristics of disjunctive networks and several ways of representing them using graphs, Boolean matrices, or binary relations. We then focus on three dynamical properties of disjunctive networks: their image points, their periodic points, and their fixed points. For each class of points, we review how they can be characterised and study how many they could be. The paper finishes with different avenues for future work on the dynamics of disjunctive networks and how to generalise them.

math.CO↗

arXiv2021

Diameter mean equicontinuity and cellular automata

Mean and diam-mean equicontinuity are dynamical properties that have been of use in the study of non-periodic order. We show that the Pacman automaton is not almost diam-mean equicontinuous (it is already known that it is almost mean equicontinuous).

nlin.CG↗

arXiv2021

The Problem of Distributed Consensus: A Survey

A survey is given of approaches to the problem of distributed consensus, focusing particularly on methods based on cellular automata and related systems. A variety of new results are given, as well as a history of the field and an extensive bibliography. Distributed consensus is of current relevance in a new generation of blockchain-related systems.

cs.DC↗

arXiv2021

A strongly universal cellular automaton with four states

In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tesselllation {5,3,4} of the hyperbolic 3D space, with four states but, it is not rotation invariant as the automaton of arXiv:2104.01561 is with five states. The present paper is not an improvement of arXiv:2104.01561. The reduction to four states of the automaton of the present paper results from a relaxation of the condition of rotation invariance. However, the relaxation is not complete: the rules are invariant with respect to rotations of the dodecahedron which leave it globally invariant which also leave invariant a couple of opposite faces of the dodecahedron. As there are twenty five such rotations, it can be considered that the reduction to four states is significant although the relaxation it implied.

nlin.CG↗

arXiv2021

The Ameyalli-Rule: Logical Universality in a 2D Cellular Automaton

We present a new spontaneously emergent glider-gun in a 2D Cellular Automaton and build the logical gates NOT, AND and OR required for logical universality. The Ameyalli-rule is not based on survival/birth logic but depends on 102 isotropic neighborhood groups making an iso-rule, which can drive an interactive input-frequency histogram for visualising iso-group activity and dependent functions for filtering and mutation. Neutral inputs relative to logical gates are identified which provide an idealized striped-down form of the iso-rule.

nlin.CG↗

arXiv2021

Non-trivial Lyapunov spectrum from fractal quantum cellular automata

A generalized set of Clifford cellular automata, which includes all Clifford cellular automata, result from the quantization of a lattice system where on each site of the lattice one has a $2k$-dimensional torus phase space. The dynamics is a linear map in the torus variables and it is also local: the evolution depends only on variables in some region around the original lattice site. Moreover it preserves the symplectic structure. These are classified by $2k\times 2k$ matrices with entries in Laurent polynomials with integer coefficients in a set of additional formal variables. These can lead to fractal behavior in the evolution of the generators of the quantum algebra. Fractal behavior leads to non-trivial Lyapunov exponents of the original linear dynamical system. The proof uses Fourier analysis on the characteristic polynomial of these matrices.

cond-mat.stat-mech↗

arXiv2021

Application of Artificial Neural Network in the Control and Optimization of Distillation Tower

Distillation is a unit operation with multiple input parameters and multiple output parameters. It is characterized by multiple variables, coupling between input parameters, and non-linear relationship with output parameters. Therefore, it is very difficult to use traditional methods to control and optimize the distillation column. Artificial Neural Network (ANN) uses the interconnection between a large number of neurons to establish the functional relationship between input and output, thereby achieving the approximation of any non-linear mapping. ANN is used for the control and optimization of distillation tower, with short response time, good dynamic performance, strong robustness, and strong ability to adapt to changes in the control environment. This article will mainly introduce the research progress of ANN and its application in the modeling, control and optimization of distillation towers.

physics.chem-ph↗

arXiv2021

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

We present a new 3D lattice Boltzmann (LB) algorithm based on central moments for the D3Q27 lattice using a cuboid grid, which is parameterized by two grid aspect ratios that are related to the ratios of the particle speeds with respect to that along a reference coordinate direction. The use of the cuboid lattice grid enables the method to compute flows having different characteristic length scales in different directions more efficiently. It is constructed to simulate the Navier-Stokes equations consistently via introducing counteracting corrections to the second order moment equilibria obtained via a Chapman-Enskog analysis that eliminate the errors associated with the grid anisotropy and the non-Galilean invariant terms. The implementation is shown to be compact and modular, with an interpretation based on special matrices, admitting ready extension of the standard algorithm for the cubic lattice to the cuboid lattice via appropriate scaling of moments based on grid aspect ratios before and after collision step and equilibria corrections. The resulting formulation is general in that the same grid corrections developed for the D3Q27 lattice for recovering the correct viscous stress tensor is applicable for other lattice subsets, and a variety of collision models, including those based on the relaxation of raw moments, central moments and cumulants, as well as their special case involving the distribution functions. The cuboid central moment LBM is validated against a variety of benchmark flows, and when used in lieu of the corresponding raw moment formulation for simulating shear flows, we show that it results in significant improvements in numerical stability. Finally, we demonstrate that our cuboid LB approach is efficient in simulating anisotropic shear flow problems with significant savings in computational cost and memory storage when compared to that based on the cubic lattice.

cs.CE↗

arXiv2021

Generating Boolean Functions on Totalistic Automata Networks

We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are updated in parallel following a local totalistic rule, i.e., depending only on the sum of active states. Four families of totalistic rules are considered: linear or matrix defined rules (a node takes state 1 if each of its neighbours is in state 1), threshold rules (a node takes state 1 if the sum of its neighbours exceed a threshold), isolated rules (a node takes state 1 if the sum of its neighbours equals to some single number) and interval rule (a node takes state 1 if the sum of its neighbours belong to some discrete interval). We focus in studying the simulation capabilities of the dynamics of each of the latter classes. In particular, we show that totalistic automata networks governed by matrix defined rules can only implement constant functions and other matrix defined functions. In addition, we show that t by threshold rules can generate any monotone Boolean functions. Finally, we show that networks driven by isolated and the interval rules exhibit a very rich spectrum of boolean functions as they can, in fact, implement any arbitrary Boolean functions. We complement this results by studying experimentally the set of different Boolean functions generated by totalistic rules on random graphs.

cs.CC↗

arXiv2021

Classification of Discrete Dynamical Systems Based on Transients

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 systems. The method is based on classifying the asymptotic behavior of the average computation time in a given system before entering a loop. We were able to identify a critical region of behavior that corresponds to a phase transition from ordered behavior to chaos across various classes of dynamical systems. To show that our approach can be applied to many different computational systems, we demonstrate the results of classifying cellular automata, Turing machines, and random Boolean networks. Further, we use this method to classify 2D cellular automata to automatically find those with interesting, complex dynamics. We believe that our work can be used to design systems in which complex structures emerge. Also, it can be used to compare various versions of existing attempts to model open-ended evolution (Ray (1991), Ofria et al. (2004), Channon (2006)).

cs.AI↗

arXiv2026

Universal principles of cell population growth follow from local contact inhibition

Cancer cell populations often exhibit remarkably similar growth laws despite their heterogeneity. Explanations of universal cell population growth remain partly unresolved to this day. Here, we present a growth-law unification by investigating the connection between microscopic assumptions and the expected contact inhibition, which leads to five classical tumor growth laws: exponential, radial growth, fractal growth, generalized logistic, and Gompertzian growth. All five can be seen as manifestations of a single microscopic model. Agent-based simulations substantiate our theory, and we can explain differences in growth curves in experimental data from em in vitro cancer cell population growth. Thus, our framework offers a possible explanation for many mean-field laws used to empirically capture seemingly unrelated cancer or microbial growth dynamics. Our results highlight that the interplay between contact inhibition and other assumptions (e.g., well-mixed) can influence our quantitative understanding of how cancer cells grow and, in turn, how they may interact.

q-bio.PE↗

arXiv2022

Information dynamics and the arrow of time

Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and restricting to a macroscopic view, we are left with a stochastic PCA (SPCA). When the underlying PCA's dynamics are reversible, the corresponding SPCA serves as a model of emergent time-reversal asymmetry. Specifically, we prove that its transition probabilities are homogeneous in space and time, as well as Markov relative to a Pearlean causal graph with timelike future-directed edges. Consequently, SPCAs satisfy generalizations of the second law of thermodynamics, which we term the Resource and Memory Laws. By subjecting information-processing agents (e.g., human experimenters) to these laws, we clarify issues regarding the Past Hypothesis, Landauer's principle, Boltzmann brains, scientific induction, and the so-called psychological arrow of time. Finally, by describing a theoretical agent powered by data compression, we argue that the algorithmic entropy takes conceptual precedence over both the Shannon-Gibbs and Boltzmann entropies.

cond-mat.stat-mech↗

arXiv2021

The negative dependence of evacuation time on group size under a binding mechanism

This paper initiates the analysis of the relation between evacuation time and group size by applying an extended floor field cellular automaton model. Agents with various speeds, a group structure containing leaders and followers, and a dynamic field dependent on local population density are implemented all together in the model. Most importantly, a complete binding mechanism which includes leaders waiting for followers is brought up for the first time. A counterintuitive negative relation between evacuation time and group size is discovered in simulations. An entropy like quantity, namely the mixing index, is constructed to analyze the cause of that relation. It is found that under the binding mechanism, the higher degree of group mixing, the longer the evacuation time will be. Moreover, through a constant scale transformation, it is shown that the mixing index can be a key indicator that contains useful information about the evacuation system.

nlin.CG↗

arXiv2021

On the feasibility of dynamical analysis of network models of biochemical regulation

A recent article by Weidner et al. [2021] presents a method to extract graph properties that are predictive of the dynamical behavior of multivariate, discrete models of biochemical regulation. In other words, a method that uses only features from the structure of network interactions to predict which nodes are most involved in automata network dynamics. However, the authors claim that dynamical analysis of large automata network models is "not even feasible." To make sure that others are not discouraged from working on this problem, it is important to clarify that effective dynamical analysis of automata network models, to the contrary, is feasible. Unlike what is suggested in the article, graph-based analysis of static features is not the only analytical avenue for large systems biology models of regulation and signaling dynamics because there are dynamical methods that are, indeed, scalable.

q-bio.QM↗

arXiv2025

The maximum distinctness of physical systems

The limited distinctness of physical systems is roughly expressed by uncertainty relations. Here we show distinctness is a finite resource we can exactly count to define basic physical quantities, limits to the resolution of space and time, and informational foundations for classical mechanics. Our analysis generalizes quantum speed limits: we count the distinct (orthogonal) states that can occur in a finite length of unitary change. As in Nyquist's bound on distinct signal values in classical waves, widths of superpositions bound the distinct states per unit length -- and basic conserved quantities are widths. Maximally distinct unitary evolution is effectively discrete -- and this characterizes classical systems. [see also Popular Summary in arxiv ancillary files]

quant-ph↗

arXiv2022

Grand-potential-based phase-field model of dissolution/precipitation: lattice Boltzmann simulations of counter term effect on porous medium

Most of the lattice Boltzmann methods simulate an approximation of the sharp interface problem of dissolution and precipitation. In such studies the curvature-driven motion of interface is neglected in the Gibbs-Thomson condition. In order to simulate those phenomena with or without curvature-driven motion, we propose a phase-field model which is derived from a thermodynamic functional of grand-potential. Compared to the free energy, the main advantage of the grand-potential is to provide a theoretical framework which is consistent with the equilibrium properties such as the equality of chemical potentials. The model is composed of one equation for the phase-field ϕ coupled with one equation for the chemical potential μ. In the phase-field method, the curvature-driven motion is always contained in the phase-field equation. For canceling it, a counter term must be added in the ϕ-equation. For reason of mass conservation, the μ-equation is written with a mixed formulation which involves the composition c and the chemical potential. The closure relationship between c and μ is derived by assuming quadratic free energies of bulk phases. The anti-trapping current is also considered in the composition equation for simulations with null solid diffusion. The lattice Boltzmann schemes are implemented in LBM_saclay, a numerical code running on various High Performance Computing architectures. Validations are carried out with analytical solutions representative of dissolution and precipitation. Simulations with or without counter term are compared on the shape of porous medium characterized by microtomography. The computations have run on a single GPU-V100.

cs.CE↗