288 research outputs found
Expressing the entropy of lattice systems as sums of conditional entropies
Whether a system is to be considered complex or not depends on how one
searches for correlations. We propose a general scheme for calculation of
entropies in lattice systems that has high flexibility in how correlations are
successively taken into account. Compared to the traditional approach for
estimating the entropy density, in which successive approximations builds on
step-wise extensions of blocks of symbols, we show that one can take larger
steps when collecting the statistics necessary to calculate the entropy density
of the system. In one dimension this means that, instead of a single sweep over
the system in which states are read sequentially, one take several sweeps with
larger steps so that eventually the whole lattice is covered. This means that
the information in correlations is captured in a different way, and in some
situations this will lead to a considerably much faster convergence of the
entropy density estimate as a function of the size of the configurations used
in the estimate. The formalism is exemplified with both an example of a free
energy minimisation scheme for the two-dimensional Ising model, and an example
of increasingly complex spatial correlations generated by the time evolution of
elementary cellular automaton rule 60
Topology regulates pattern formation capacity of binary cellular automata on graphs
We study the effect of topology variation on the dynamic behavior of a system
with local update rules. We implement one-dimensional binary cellular automata
on graphs with various topologies by formulating two sets of degree-dependent
rules, each containing a single parameter. We observe that changes in graph
topology induce transitions between different dynamic domains (Wolfram classes)
without a formal change in the update rule. Along with topological variations,
we study the pattern formation capacities of regular, random, small-world and
scale-free graphs. Pattern formation capacity is quantified in terms of two
entropy measures, which for standard cellular automata allow a qualitative
distinction between the four Wolfram classes. A mean-field model explains the
dynamic behavior of random graphs. Implications for our understanding of
information transport through complex, network-based systems are discussed.Comment: 16 text pages, 13 figures. To be published in Physica
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
Empiricism and stochastics in cellular automaton modeling of urban land use dynamics
An increasing number of models for predicting land use change in regions of rapidurbanization are being proposed and built using ideas from cellular automata (CA)theory. Calibrating such models to real situations is highly problematic and to date,serious attention has not been focused on the estimation problem. In this paper, wepropose a structure for simulating urban change based on estimating land usetransitions using elementary probabilistic methods which draw their inspiration fromBayes' theory and the related ?weights of evidence? approach. These land use changeprobabilities drive a CA model ? DINAMICA ? conceived at the Center for RemoteSensing of the Federal University of Minas Gerais (CSR-UFMG). This is based on aneight cell Moore neighborhood approach implemented through empirical land useallocation algorithms. The model framework has been applied to a medium-size townin the west of São Paulo State, Bauru. We show how various socio-economic andinfrastructural factors can be combined using the weights of evidence approach whichenables us to predict the probability of changes between land use types in differentcells of the system. Different predictions for the town during the period 1979-1988were generated, and statistical validation was then conducted using a multipleresolution fitting procedure. These modeling experiments support the essential logicof adopting Bayesian empirical methods which synthesize various information aboutspatial infrastructure as the driver of urban land use change. This indicates therelevance of the approach for generating forecasts of growth for Brazilian citiesparticularly and for world-wide cities in general
Outer-totalistic cellular automata on graphs
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 complex patterns decreases under increasing neighborhood size in
regular graphs. As exemplary applications, we apply the formalism to complex
networks and compare the potential of scale-free graphs and metabolic networks
to generate complex dynamics.Comment: 5 pages, 4 figures, 1 table. To appear in Physics Letters
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