Unnamed: 0 int64 0 41k | title stringlengths 4 274 | category stringlengths 5 18 | summary stringlengths 22 3.66k | theme stringclasses 8
values |
|---|---|---|---|---|
7,900 | Convergence to equilibrium in a class of interacting particle systems evolving in discrete time | nlin.CG | We conjecture that for a wide class of interacting particle systems evolving
in discrete time, namely conservative cellular automata with piecewise linear
flow diagram, relaxation to the limit set follows the same power law at
critical points. We further describe the structure of the limit sets of such
systems as union... | physics |
7,901 | Number conserving cellular automata: form decidability to dynamics | nlin.CG | We compare several definitions for number-conserving cellular automata that
we prove to be equivalent. A necessary and sufficient condition for \cas to be
number-conserving is proved. Using this condition, we give a linear-time
algorithm to decide number-conservation. The dynamical behavior of
number-conserving \cas is... | physics |
7,902 | Exact limiting solutions for certain deterministic traffic rules | nlin.CG | We analyze the steady-state flow as a function of the initial density for a
class of deterministic cellular automata rules (``traffic rules'') with
periodic boundary conditions [H. Fuks and N. Boccara, Int. J. Mod. Phys. C 9, 1
(1998)]. We are able to predict from simple considerations the observed,
unexpected cutoff o... | physics |
7,903 | Structure of Rule Table and Phase Diagram of One Dimensional Cellular Automata | nlin.CG | In addition to the $\lambda$ parameter, we have found another parameter which
characterize the class III, class II and class IV patterns more quantitatively.
It explains why the different classes of patterns coexist at the same
$\lambda$. With this parameter, the phase diagram for an one dimensional
cellular automata i... | physics |
7,904 | A New Kind of Science? | nlin.CG | Book Review for: "A New Kind of Science", by Stephen Wolfram (Wolfram Media,
Inc. Champaign IL 2002). | physics |
7,905 | The Mermin fixed point | nlin.CG | The most efficient known method for solving certain computational problems is
to construct an iterated map whose fixed points are by design the problem's
solution. Although the origins of this idea go back at least to Newton, the
clearest expression of its logical basis is an example due to Mermin. A
contemporary appli... | physics |
7,906 | Kinetic boundary conditions in the lattice Boltzmann method | nlin.CG | Derivation of the lattice Boltzmann method from the continuous kinetic theory
[X. He and L. S. Luo, {\it Phys. Rev. E} {\bf 55}, R6333 (1997); X. Shan and X.
He, {\it Phys. Rev. Lett.} {\bf 80}, 65 (1998)] is extended in order to obtain
boundary conditions for the method. For the model of a diffusively reflecting
movin... | physics |
7,907 | Headway distribution of the asymmetric simple exclusion model | nlin.CG | We present an exact solution of headway distribution of the asymmetric simple
exclusion model with open boundary conditions and compare it to the headway
distributions of the highway traffic. | physics |
7,908 | Headway statistics of public transport in Mexican cities | nlin.CG | We present a cellular automaton simulating the behavior of public bus
transport in several Mexican cities. The headway statistics obtained from the
model is compared to the measured time intervals between subsequent bus
arrivals to a given bus stop and to a spacing distribution resulting from a
random matrix theory. | physics |
7,909 | Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example | nlin.CG | Coarse timesteppers provide a bridge between microscopic / stochastic system
descriptions and macroscopic tasks such as coarse stability/bifurcation
computations. Exploiting this computational enabling technology, we present a
framework for designing observers and controllers based on microscopic
simulations, that can ... | physics |
7,910 | A class of cellular automata equivalent to deterministic particle systems | nlin.CG | We demonstrate that a local mapping f in a space of bisequences over {0,1}
which conserves the number of nonzero sites can be viewed as a deterministic
particle system evolving according to a local mapping in a space of increasing
bisequences over Z. We present an algorithm for determination of the local
mapping in the... | physics |
7,911 | Anomalous Diffusion in Infinite Horizon Billiards | nlin.CG | We consider the long time dependence for the moments of displacement < |r|^q
> of infinite horizon billiards, given a bounded initial distribution of
particles. For a variety of billiard models we find <|r|^q> ~ t^g(q) (up to
factors of log t). The time exponent, g(q), is piecewise linear and equal to
q/2 for q<2 and q... | physics |
7,912 | Long Time Algebraic Relaxation in Chaotic Billiards | nlin.CG | The long time algebraic relaxation process in spatially periodic billiards
with infinite horizon is shown to display a self-similar time asymptotic form.
This form is identical for a class of such billiards, but can be different in
an important special case. | physics |
7,913 | A New Parameter $F$ to Classify Cellular Automata Rule Table Space and a Phase Diagram in $λ-F$ Plane | nlin.CG | It is shown that for the N-neighbor and K-state cellular automata, the class
II, class III and class IV patterns coexist at least in the range $\frac{1}{K}
\le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference
between the pattern classes at a fixed $\lambda$ is found, and it is studied
quantita... | physics |
7,914 | Non-deterministic density classification with diffusive probabilistic cellular automata | nlin.CG | We present a probabilistic cellular automaton (CA) with two absorbing states
which performs classification of binary strings in a non-deterministic sense.
In a system evolving under this CA rule, empty sites become occupied with a
probability proportional to the number of occupied sites in the neighborhood,
while occup... | physics |
7,915 | Quiescent String Dominance Parameter F and Classification of One-Dimensional Cellular Automata | nlin.CG | The mechanism which discriminates the pattern classes at the same $\lambda$,
is found. It is closely related to the structure of the rule table and
expressed by the numbers of the rules which break the strings of the quiescent
states. It is shown that for the N-neighbor and K-state cellular automata, the
class I, class... | physics |
7,916 | Sato-Crutchfield formulation for some Evolutionary Games | nlin.CG | The Sato-Crutchfield equations are studied analytically and numerically. The
Sato-Crutchfield formulation is corresponding to losing memory. Then
Sato-Crutchfield formulation is applied for some different types of games
including hawk-dove, prisoner's dilemma and the battle of the sexes games. The
Sato-Crutchfield form... | physics |
7,917 | Probabilistic cellular automata with conserved quantities | nlin.CG | We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can ... | physics |
7,918 | Complexity of Langton's Ant | nlin.CG | The virtual ant introduced by C. Langton has an interesting behavior, which
has been studied in several contexts. Here we give a construction to calculate
any boolean circuit with the trajectory of a single ant. This proves the
P-hardness of the system and implies, through the simulation of one dimensional
cellular aut... | physics |
7,919 | Universality and Decidability of Number-Conserving Cellular Automata | nlin.CG | Number-conserving cellular automata (NCCA) are particularly interesting, both
because of their natural appearance as models of real systems, and because of
the strong restrictions that number-conservation implies. Here we extend the
definition of the property to include cellular automata with any set of states
in $\Zse... | physics |
7,920 | On Conservative and Monotone One-dimensional Cellular Automata and Their Particle Representation | nlin.CG | Number-conserving (or {\em conservative}) cellular automata have been used in
several contexts, in particular traffic models, where it is natural to think
about them as systems of interacting particles. In this article we consider
several issues concerning one-dimensional cellular automata which are
conservative, monot... | physics |
7,921 | Coarse Projective kMC Integration: Forward/Reverse Initial and Boundary Value Problems | nlin.CG | In "equation-free" multiscale computation a dynamic model is given at a fine,
microscopic level; yet we believe that its coarse-grained, macroscopic dynamics
can be described by closed equations involving only coarse variables. These
variables are typically various low-order moments of the distributions evolved
through... | physics |
7,922 | Optimal switching policies using coarse timesteppers | nlin.CG | We present a computer-assisted approach to approximating coarse optimal
switching policies for systems described by microscopic/stochastic evolution
rules. The coarse timestepper constitutes a bridge between the underlying
kinetic Monte Carlo simulation and traditional, continuum numerical
optimization techniques formu... | physics |
7,923 | No production of entropy in the Euler fluid | nlin.CG | We derive the Euler equations as the hydrodynamic limit of a stochastic model
of a hard-sphere gas on a lattice. We show that the system does not produce
entropy. | physics |
7,924 | Towards a Noether-like conservation law theorem for one dimensional reversible cellular automata | nlin.CG | Evidence and results suggesting that a Noether--like theorem for conservation
laws in 1D RCA can be obtained. Unlike Noether's theorem, the connection here
is to the maximal congruences rather than the automorphisms of the local
dynamics.
We take the results of Takesue and Hattori (1992) on the space of additive
cons... | physics |
7,925 | An Experimental Study of Robustness to Asynchronism for Elementary Cellular Automata | nlin.CG | Cellular Automata (CA) are a class of discrete dynamical systems that have
been widely used to model complex systems in which the dynamics is specified at
local cell-scale. Classically, CA are run on a regular lattice and with perfect
synchronicity. However, these two assumptions have little chance to truthfully
repres... | physics |
7,926 | On Markovian behaviour of $p$-adic random dynamical systems | nlin.CG | We study Markovian and non-Markovian behaviour of stochastic processes
generated by $p$-adic random dynamical systems. Given a family of $p$-adic
monomial random mappings generating a random dynamical system. Under which
conditions do the orbits under such a random dynamical system form Markov
chains? It is necessary t... | physics |
7,927 | Cellular Automata: Wolfram's Metaphors for Complex Systems | nlin.CG | A brief introduction to Wolfram's work on cellular automata. | physics |
7,928 | Advancing density waves and phase transitions in a velocity dependent randomization traffic cellular automaton | nlin.CG | Within the class of stochastic cellular automata models of traffic flows, we
look at the velocity dependent randomization variant (VDR-TCA) whose parameters
take on a specific set of extreme values. These initial conditions lead us to
the discovery of the emergence of four distinct phases. Studying the
transitions betw... | physics |
7,929 | Perturbing the topology of the Game of Life increases its robustness to asynchrony | nlin.CG | An experimental analysis of the asynchronous version of the "Game of Life" is
performed to estimate how topology perturbations modify its evolution. We focus
on the study of a phase transition from an "inactive-sparse phase" to a
"labyrinth phase" and produce experimental data to quantify these changes as a
function of... | physics |
7,930 | Cell-centric heuristics for the classification of cellular automata | nlin.CG | 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 novel entropy measures, one that is also based on inputs to the cells, the
othe... | physics |
7,931 | Dynamic Domains Networks | nlin.CG | We present a model for the description of the evolution of contacts among
individuals in a network. At each time step each individual is associated with
a domain or neighborhood of fully connected agents.The dynamics of this
changing neighborhood will later be translated into a situation where the links
between individ... | physics |
7,932 | An Equation-Free Approach to Nonlinear Control: Coarse Feedback Linearization With Pole-Placement | nlin.CG | We present an application of equation-free computation to the coarse-grained
feedback linearization problem of nonlinear systems described by
microscopic/stochastic simulators. Feedback linearization with pole placement
requires the solution of a functional equation involving the macroscopic
(coarse-grained) system mod... | physics |
7,933 | Two-state, Reversible, Universal Cellular Automata in Three Dimensions | nlin.CG | A novel two-state, Reversible Cellular Automata (RCA) is described. This
three-dimensional RCA is shown to be capable of universal computation.
Additionally, evidence is offered that this RCA Is capable of universal
construction. | physics |
7,934 | Motion representation of one-dimensional cellular automaton rules | nlin.CG | Generalizing the motion representation we introduced for number-conserving
rules, we give a systematic way to construct a generalized motion
representation valid for non-conservative rules using the expression of the
current, which appears in the discrete version of the continuity equation,
completed by the discrete an... | physics |
7,935 | Second order additive invariants in elementary cellular automata | nlin.CG | We investigate second order additive invariants in elementary cellular
automata rules. Fundamental diagrams of rules which possess additive invariants
are either linear or exhibit singularities similar to singularities of rules
with first-order invariant. Only rules which have exactly one invariants
exhibit singulariti... | physics |
7,936 | Two Cellular Automata for the 3x+1 Map | nlin.CG | Two simple Cellular Automata, which mimic the Collatz-Ulam iterated map (3x+1
map), are introduced. These Cellular Automata allow to test efficiently the
Collatz conjecture for very large numbers. | physics |
7,937 | On Reversible Cellular Automata with Triplet Local Rules | nlin.CG | Bijections between sets may be seen as discrete (or crisp) unitary
transformations used in quantum computations. So discrete quantum cellular
automata are cellular automata with reversible transition functions. This note
studies on 1d reversible cellular automata with triplet local rules. | physics |
7,938 | Spatial correlations in SIR epidemic models | nlin.CG | We investigate the role of global mixing in epidemic processes. We first
construct a simplified model of the SIR epidemic using a realistic population
distribution. Using this model, we examine possible mechanisms for destruction
of spatial correlations, in an attempt to produce correlation curves similar to
those repo... | physics |
7,939 | A Systems-Based Approach to Multiscale Computation: Equation-Free Detection of Coarse-Grained Bifurcations | nlin.CG | We discuss certain basic features of the equation-free (EF) approach to
modeling and computation for complex/multiscale systems. We focus on links
between the equation-free approach and tools from systems and control theory
(design of experiments, data analysis, estimation, identification and
feedback). As our illustra... | physics |
7,940 | Cellular Automata under the influence of noise | nlin.CG | Noise in the local transition function is compared to fluctuations in the
updating times of the cells. Obtained results are shown to be quite different
in both cases. In this extended abstract we briefly explain the problem and
present results obtained and comment them. | physics |
7,941 | A Cellular Automata Model with Probability Infection and Spatial Dispersion | nlin.CG | In this article, we have proposed an epidemic model by using probability
cellular automata theory. The essential mathematical features are analyzed with
the help of stability theory. We have given an alternative modelling approach
for the spatiotemporal system which is more realistic and satisfactory from the
practical... | physics |
7,942 | Scale-invariant cellular automata and self-similar Petri nets | nlin.CG | Two novel computing models based on an infinite tessellation of space-time
are introduced. They consist of recursively coupled primitive building blocks.
The first model is a scale-invariant generalization of cellular automata,
whereas the second one utilizes self-similar Petri nets. Both models are
capable of hypercom... | physics |
7,943 | Cellular Automata Modeling of Continuous Stirred Tank Reactors | nlin.CG | The classical dynamical systems model of continuous stirred tank reactors
(CSTR) in which a first order chemical reaction takes place is reformulated in
terms of stochastic cellular automata by extending previous works of Seyborg
(1997) and Neuforth (2000) by including the feed flow of chemical reactants. We
show that ... | physics |
7,944 | Coalescing Cellular Automata | nlin.CG | We say that a Cellular Automata (CA) is coalescing when its execution on two
distinct (random) initial configurations in the same asynchronous mode (the
same cells are updated in each configuration at each time step) makes both
configurations become identical after a reasonable time. We prove coalescence
for two elemen... | physics |
7,945 | Dynamics of the Cellular Automaton Rule 142 | nlin.CG | We investigate dynamics of the cellular automaton rule 142. This rule
possesses additive invariant of the second order, namely it conserves the
number of blocks 10. Rule 142 can be alternatively described as an operation on
a binary string in which we simultaneously flip all symbols which have
dissenting right neighbou... | physics |
7,946 | Critical behavior of number-conserving cellular automata with nonlinear fundamental diagrams | nlin.CG | We investigate critical properties of a class of number-conserving cellular
automata (CA) which can be interpreted as deterministic models of traffic flow
with anticipatory driving. These rules are among the only known CA rules for
which the shape of the fundamental diagram has been rigorously derived. In
addition, the... | physics |
7,947 | Constructing the Critical Curve for the Two-Layer Potts Model Using Cellular Automata | nlin.CG | The critical points of the 3-states two-layer Potts model on square lattice
for different interlayer couplings (Kx, Ky,and Kz) are calculated with high
precision using probabilistic cellular automata with Glauber algorithm, where
Kx and Ky are the nearest-neighbor interactions within each layer in the x and
y direction... | physics |
7,948 | Local cause of coherence in Boolean networks | nlin.CG | We performed a numerical study on random Boolean networks with power-law rank
outdegree distributions to find local structural cause for the emergence of
high or low degree of coherence in binary state variables. The degree of
randomness and coherence of the binary sequence are measured by entropy and
mutual informatio... | physics |
7,949 | A "No-Go" Theorem for the Existence of an Action Principle for Discrete Invertible Dynamical Systems | nlin.CG | In this paper we study the problem of the existence of a least-action
principle for invertible, second-order dynamical systems, discrete in time and
space. We show that, when the configuration space is finite, a least-action
principle does not exist for such systems. We dichotomize discrete dynamical
systems with infin... | physics |
7,950 | Boolean Delay Equations: A simple way of looking at complex systems | nlin.CG | Boolean Delay Equations (BDEs) are semi-discrete dynamical models with
Boolean-valued variables that evolve in continuous time. Systems of BDEs can be
classified into conservative or dissipative, in a manner that parallels the
classification of ordinary or partial differential equations. Solutions to
certain conservati... | physics |
7,951 | Randomized Cellular Automata | nlin.CG | We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cell... | physics |
7,952 | Roles of hubs in Boolean networks | nlin.CG | We examined the effects of inhomogeneity on the dynamics and structural
properties using Boolean networks. Two different power-law rank outdegree
distributions were embedded to determine the role of hubs. The degree of
randomness and coherence of the binary sequence in the networks were measured
by entropy and mutual i... | physics |
7,953 | Asynchronism Induces Second Order Phase Transitions in Elementary Cellular Automata | nlin.CG | Cellular automata are widely used to model natural or artificial systems.
Classically they are run with perfect synchrony, i.e., the local rule is
applied to each cell at each time step. A possible modification of the updating
scheme consists in applying the rule with a fixed probability, called the
synchrony rate. For... | physics |
7,954 | Analysis of random Boolean networks using the average sensitivity | nlin.CG | In this work we consider random Boolean networks that provide a general model
for genetic regulatory networks. We extend the analysis of James Lynch who was
able to proof Kauffman's conjecture that in the ordered phase of random
networks, the number of ineffective and freezing gates is large, where as in
the disordered... | physics |
7,955 | Determining a regular language by glider-based structures called phases fi_1 in Rule 110 | nlin.CG | Rule 110 is a complex elementary cellular automaton able of supporting
universal computation and complicated collision-based reactions between
gliders. We propose a representation for coding initial conditions by means of
a finite subset of regular expressions. The sequences are extracted both from
de Bruijn diagrams a... | physics |
7,956 | On the Dynamical Behaviour of Cellular Automata | nlin.CG | In this paper we study the dynamics of 1- and 2- dimensional cellular
automata, using a 2-adic representation of the states, we give a simple
graphical technique for finding periodic solutions. We also study the
continuity properties of the associated 2-adic system and show how to compute
the entropy. | physics |
7,957 | Capillary filling using Lattice Boltzmann Equations: the case of multi-phase flows | nlin.CG | We present a systematic study of capillary filling for multi-phase flows by
using mesoscopic lattice Boltzmann models describing a diffusive interface
moving at a given contact angle with respect to the walls. We compare the
numerical results at changing the density ratio between liquid and gas phases
and the ratio bet... | physics |
7,958 | Pattern Formation without Favored Local Interactions | nlin.CG | Individual cellular automata rules are attractive models for a range of
biological and physical self-assembling systems. While coexpression and
coevolution are common in such systems, ensembles of cellular automata rules
remain poorly understood. Here we report the first known analysis of the
equally weighted ensemble ... | physics |
7,959 | When--and how--can a cellular automaton be rewritten as a lattice gas? | nlin.CG | Both cellular automata (CA) and lattice-gas automata (LG) provide finite
algorithmic presentations for certain classes of infinite dynamical systems
studied by symbolic dynamics; it is customary to use the term `cellular
automaton' or `lattice gas' for the dynamic system itself as well as for its
presentation. The two ... | physics |
7,960 | A realistic interpretation of quantum mechanics. Asymmetric random walks in a discrete spacetime | nlin.CG | In this paper, I propose a realistic interpretation (RI) of quantum
mechanics, that is, an interpretation according to which a particle follows a
definite path in spacetime. The path is not deterministic but it is rather a
random walk. However, the probability of each step of the walk is found to
depend from some avera... | physics |
7,961 | Catalan numbers and power laws in cellular automaton rule 14 | nlin.CG | We discuss example of an elementary cellular automaton for which the density
of ones decays toward its limiting value as a power of the number of iterations
$n$. Using the fact that this rule conserves the number of blocks 10 and that
preimages of some other blocks exhibit patterns closely related to patterns
observed ... | physics |
7,962 | Enumeration of number-conserving cellular automata rules with two inputs | nlin.CG | We show that there exists a one-to-one correspondence between the set of
number-conserving cellular automata (CA) with $q$ inputs and the set of
balanced sequences with $q$ terms. This allows to enumerate number-conserving
CA. We also show that number-conserving rules are becoming increasingly rare as
the number of sta... | physics |
7,963 | Phase diagram and edge effects in the ASEP with bottlenecks | nlin.CG | We investigate the totally asymmetric simple exclusion process (TASEP) in the
presence of a bottleneck, i.e. a sequence of consecutive defect sites with
reduced hopping rate. The influence of such a bottleneck on the phase diagram
is studied by computer simulations and a novel analytical approach. We find a
clear depen... | physics |
7,964 | Coalescing Cellular Automata -- Synchronizing CA by Common Random Source and Varying Asynchronicity | nlin.CG | We say that a Cellular Automata (CA) is coalescing when its execution on two
distinct (random) initial configurations in the same asynchronous mode (the
same cells are updated in each configuration at each time step) makes both
configurations become identical after a reasonable time.
We prove coalescence for two elem... | physics |
7,965 | Lattice Boltzmann simulations of capillary filling: finite vapour density effects | nlin.CG | Numerical simulations of two-dimensional capillary filling using the
pseudo-potential lattice Boltzmann model for multiphase fluids are presented,
with special emphasis on the role of finite-vapour density effects. It is shown
that whenever the density of the light-phase exceeds about ten percent of the
dense phase, th... | physics |
7,966 | Capillary filling using Lattice Boltzmann Equations: the case of multi-component fluids | nlin.CG | We present a systematic study of capillary filling for a binary fluid by
using mesoscopic a lattice Boltzmann model describing a diffusive interface
moving at a given contact angle with respect to the walls. We compare the
numerical results at changing the ratio the typical size of the capillary, H,
and the wettability... | physics |
7,967 | Model dynamics on a multigrid across multiple length and time scales | nlin.CG | Most methods for modelling dynamics posit just two time scales: a fast and a
slow scale. But many applications, including many in continuum mechanics,
possess a wide variety of space-time scales; often they possess a continuum of
space-time scales. I discuss an approach to modelling the discretised dynamics
of advectio... | physics |
7,968 | Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors | nlin.CG | The rapid developing area of compressed sensing suggests that a sparse vector
lying in an arbitrary high dimensional space can be accurately recovered from
only a small set of non-adaptive linear measurements. Under appropriate
conditions on the measurement matrix, the entire information about the original
sparse vecto... | physics |
7,969 | Predictability of the large relaxations in a cellular automaton model | nlin.CG | A simple one-dimensional cellular automaton model with threshold dynamics is
introduced. The cumulative distribution of the size of the relaxations is
analytically computed and behaves as a power law with an exponent equal to -1.
This coincides with the phenomenological Gutenberg-Richter behavior observed in
Seismology... | physics |
7,970 | Universal Cellular Automata Based on the Collisions of Soft Spheres | nlin.CG | Fredkin's Billiard Ball Model (BBM) is a continuous classical mechanical
model of computation based on the elastic collisions of identical
finite-diameter hard spheres. When the BBM is initialized appropriately, the
sequence of states that appear at successive integer time-steps is equivalent
to a discrete digital dyna... | physics |
7,971 | An order-preserving property of additive invariant for Takesue-type reversible cellular automata | nlin.CG | We show that, for a fairly large class of reversible, one-dimensional
cellular automata, the set of additive invariants exhibits an algebraic
structure. More precisely, if $f$ and $g$ are one-dimensional, reversible
cellular automata of the kind considered by Takesue, we show that there is a
binary operation on these a... | physics |
7,972 | Issues on drawing the State Transition Diagram for arbitrary Cellular Automata | nlin.CG | This paper proposes several algorithms and their Cellular Automata Machine
(CAM) for drawing the State Transition Diagram (STD) of an arbitrary Cellular
Automata (CA) Rule (any neighborhood, uniform/ hybrid and null/ periodic
boundary) and length of the CA n. It also discusses the novelty, hardware cost
and the complex... | physics |
7,973 | Isomorphisms of Additive Cellular Automata on Finite Groups | nlin.CG | We study sources of isomorphisms of additive cellular automata on finite
groups (called index-group). It is shown that many isomorphisms (called
regular) of automata are reducible to the isomorphisms of underlying algebraic
structures (such as the index-group, monoid of automata rules, and its subgroup
of reversible el... | physics |
7,974 | Outer-totalistic cellular automata on graphs | nlin.CG | We present an intuitive formalism for implementing cellular automata on
arbitrary topologies. By that means, we identify a symmetry operation in the
class of elementary cellular automata. Moreover, we determine the subset of
topologically sensitive elementary cellular automata and find that the overall
number of comple... | physics |
7,975 | Flexible Time and the Evolution of One-Dimensional Cellular Automata | nlin.CG | Here I describe a view of the evolution of cellular automata that allows to
operate on larger structures. Instead of calculating the next state of all
cells in one step, the method here developed uses a time slice that can proceed
at different places differently. This allows to "jump" over the evolution of
known struct... | physics |
7,976 | Solutions on 1D and 2D Density Classification Problem Using Programmable Cellular Automata | nlin.CG | This paper presents solutions to Density Classification Task (DCT) using a
variant of Cellular Automata (CA) called Programmable Cellular Automata (PCA).
The translation property as well as the density preserving property of
fundamental CA rules in 1D and 2D, and the advantage of PCA are embedded
together to obtain the... | physics |
7,977 | A hybrid of the optimal velocity and the slow-to-start models and its ultradiscretization | nlin.CG | Through an extension of the ultradiscretization for the optimal velocity (OV)
model, we introduce an ultradiscretizable traffic flow model, which is a hybrid
of the OV and the slow-to-start (s2s) models. Its ultradiscrete limit gives a
generalization of a special case of the ultradiscrete OV (uOV) model recently
propos... | physics |
7,978 | Computing Naturally in the Billiard Ball Model | nlin.CG | Fredkin's Billiard Ball Model (BBM) is considered one of the fundamental
models of collision-based computing, and it is essentially based on elastic
collisions of mobile billiard balls. Moreover, fixed mirrors or reflectors are
brought into the model to deflect balls to complete the computation. However,
the use of fix... | physics |
7,979 | Growth and Decay in Life-Like Cellular Automata | nlin.CG | We propose a four-way classification of two-dimensional semi-totalistic
cellular automata that is different than Wolfram's, based on two questions with
yes-or-no answers: do there exist patterns that eventually escape any finite
bounding box placed around them? And do there exist patterns that die out
completely? If bo... | physics |
7,980 | Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow | nlin.CG | We introduce density dependence of the cell size in cellular-automaton models
for traffic flow, which allows a more precise correspondence between real-world
phenomena and what observed in simulation. Also, we give an explicit
calibration of the particle density particularly for the asymmetric simple
exclusion process ... | physics |
7,981 | Cellular Automata Networks | nlin.CG | 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 type of cellular automata networks uses local rules with a fraction of
long-rang... | physics |
7,982 | Characterization of Multispecies Living Ecosystems With Cellular Automata | nlin.CG | A multispecies artificial ecosystem is formulated using cellular automata
with species interactions and food chain hierarchy. The constructed finite
state automaton can simulate the complexity and self-organized characteristics
of the evolving multispecies living ecosystems. Numerical experiments show that
a small pert... | physics |
7,983 | Probabilistic initial value problem for cellular automaton rule 172 | nlin.CG | We consider the problem of computing a response curve for binary cellular
automata -- that is, the curve describing the dependence of the density of ones
after many iterations of the rule on the initial density of ones. We
demonstrate how this problem could be approached using rule 130 as an example.
For this rule, pre... | physics |
7,984 | Discrete analogue computing with rotor-routers | nlin.CG | Rotor-routing is a procedure for routing tokens through a network that can
implement certain kinds of computation. These computations are inherently
asynchronous (the order in which tokens are routed makes no difference) and
distributed (information is spread throughout the system). It is also possible
to efficiently c... | physics |
7,985 | Gliders and Ether in Rule 54 | nlin.CG | This is a study of the one-dimensional elementary cellular automaton rule 54
in the new formalism of "flexible time". We derive algebraic expressions for
groups of several cells and their evolution in time. With them we can describe
the behaviour of simple periodic patterns like the ether and gliders in an
efficient wa... | physics |
7,986 | Two-lane traffic-flow model with an exact steady-state solution | nlin.CG | We propose a stochastic cellular-automaton model for two-lane traffic flow
based on the misanthrope process in one dimension. The misanthrope process is a
stochastic process allowing for an exact steady-state solution; hence we have
an exact flow-density diagram for two lane traffic. In addition, we introduce
two param... | physics |
7,987 | Chaos control in random Boolean networks by reducing mean damage percolation rate | nlin.CG | Chaos control in Random Boolean networks is implemented by freezing part of
the network to drive it from chaotic to ordered phase. However, controlled
nodes are only viewed as passive blocks to prevent perturbation spread. This
paper proposes a new control method in which controlled nodes can exert an
active impact on ... | physics |
7,988 | A Language for Particle Interactions in One-dimensional Cellular Automata | nlin.CG | This is a study of localised structures in one-dimensional cellular automata,
with the elementary cellular automaton Rule 54 as a guiding example.
A formalism for particles on a periodic background is derived, applicable to
all one-dimensional cellular automata. One can compute which particles collide
and in how many... | physics |
7,989 | Algebraic approach to directed stochastic avalanches | nlin.CG | A two-dimensional directed stochastic sandpile model is studied analytically
with the use of directed Abelian algebras recently introduced by Alcaraz and V.
Rittenberg [Phys. Rev. E {\bf 78}, 041126 (2008)]. Exact expressions for the
probabilities of all possible toppling events which follow the transfer of
arbitrary n... | physics |
7,990 | Excitable Delaunay triangulations | nlin.CG | In an excitable Delaunay triangulation every node takes three states
(resting, excited and refractory) and updates its state in discrete time
depending on a ratio of excited neighbours. All nodes update their states in
parallel. By varying excitability of nodes we produce a range of phenomena,
including reflection of e... | physics |
7,991 | Can anything from Noether's theorem be salvaged for discrete dynamical systems? | nlin.CG | The dynamics of a physical system is linked to its phase-space geometry by
Noether's theorem, which holds under standard hypotheses including continuity.
Does an analogous theorem hold for discrete systems? As a testbed, we take the
Ising spin model with both ferromagnetic and antiferromagnetic bonds. We show
that---an... | physics |
7,992 | Cellular automaton supercolliders | nlin.CG | Gliders in one-dimensional cellular automata are compact groups of
non-quiescent and non-ether patterns (ether represents a periodic background)
translating along automaton lattice. They are cellular-automaton analogous of
localizations or quasi-local collective excitations travelling in a spatially
extended non-linear... | physics |
7,993 | A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata | nlin.CG | Cellular automata are both computational and dynamical systems. We give a
complete classification of the dynamic behaviour of elementary cellular
automata (ECA) in terms of fundamental dynamic system notions such as
sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not
chaotic and not eventually... | physics |
7,994 | Response Curves and Preimage Sequences of Two-Dimensional Cellular Automata | nlin.CG | 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 initial density of ones, can be calculated for a fairly large number of
rules by co... | physics |
7,995 | Response curves for cellular automata in one and two dimensions - an example of rigorous calculations | nlin.CG | We consider the problem of computing a response curve for binary cellular
automata -- that is, the curve describing the dependence of the density of ones
after many iterations of the rule on the initial density of ones. We
demonstrate how this problem could be approached using rule 130 as an example.
For this rule, pre... | physics |
7,996 | Uncertainty principle for single particle lattice gas cellular automata models | nlin.CG | We present an uncertainty ... | physics |
7,997 | Cooperative game in a two-lane traffic flow | nlin.CG | We use cellular automata model to study the cooperation between cyclists. In
the two-lane model, cyclists can change lanes. Even there is someone on the
back they will take a cooperative attitude. It means that they will be in a
same lattice. Simulation carried out under the open borders. Simulation results
show that t... | physics |
7,998 | Generalization of Conway's "Game of Life" to a continuous domain - SmoothLife | nlin.CG | We present what we argue is the generic generalization of Conway's "Game of
Life" to a continuous domain. We describe the theoretical model and the
explicit implementation on a computer. | physics |
7,999 | Memristive excitable cellular automata | nlin.CG | The memristor is a device whose resistance changes depending on the polarity
and magnitude of a voltage applied to the device's terminals. We design a
minimalistic model of a regular network of memristors using
structurally-dynamic cellular automata. Each cell gets info about states of its
closest neighbours via incomi... | physics |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.