2,444 research outputs found
The Ideal Storage Cellular Automaton Model
We have implemented and investigated a spatial extension of the orig-
inal ideal storage model by embedding it in a 2D cellular automaton with
a diffusion-like coupling between neighboring cells. The resulting ideal
storage cellular automaton model (ISCAM) generates many interesting
spatio-temporal patterns, in particular spiral waves that grow and com-
pete" with each other. We study this dynamical behavior both mathemat-
ically and computationally, and compare it with similar patterns observed
in actual chemical processes. Remarkably, it turned out that one can use
such CA for modeling all sorts of complex processes, from phase transition
in binary mixtures to using them as a metaphor for cancer onset caused
by only one short pulse of \u27tissue dis-organzation\u27 (changing e.g. for only
one single time step the diffusion coefficient) as hypothesized in recent
papers questioning the current gene/genome centric view on cancer onset
by AO Ping et al
The Kinetic Basis of Self-Organized Pattern Formation
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that
different spatio-temporal patterns can arise due to instability of the
homogeneous state in reaction-diffusion systems, but at least two species are
necessary to produce even the simplest stationary patterns. This paper is aimed
to propose a novel model of the analog (continuous state) kinetic automaton and
to show that stationary and dynamic patterns can arise in one-component
networks of kinetic automata. Possible applicability of kinetic networks to
modeling of real-world phenomena is also discussed.Comment: 8 pages, submitted to the 14th International Conference on the
Synthesis and Simulation of Living Systems (Alife 14) on 23.03.2014, accepted
09.05.201
Memristive excitable cellular automata
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 incoming links. A link can be one 'conductive' or
'non-conductive' states. States of every link are updated depending on states
of cells the link connects. Every cell of a memristive automaton takes three
states: resting, excited (analog of positive polarity) and refractory (analog
of negative polarity). A cell updates its state depending on states of its
closest neighbours which are connected to the cell via 'conductive' links. We
study behaviour of memristive automata in response to point-wise and spatially
extended perturbations, structure of localised excitations coupled with
topological defects, interfacial mobile excitations and growth of information
pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011
When--and how--can a cellular automaton be rewritten as a lattice gas?
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 kinds of presentation share many traits but also display
profound differences on issues ranging from decidability to modeling
convenience and physical implementability.
Following a conjecture by Toffoli and Margolus, it had been proved by Kari
(and by Durand--Lose for more than two dimensions) that any invertible CA can
be rewritten as an LG (with a possibly much more complex ``unit cell''). But
until now it was not known whether this is possible in general for
noninvertible CA--which comprise ``almost all'' CA and represent the bulk of
examples in theory and applications. Even circumstantial evidence--whether in
favor or against--was lacking.
Here, for noninvertible CA, (a) we prove that an LG presentation is out of
the question for the vanishingly small class of surjective ones. We then turn
our attention to all the rest--noninvertible and nonsurjective--which comprise
all the typical ones, including Conway's `Game of Life'. For these (b) we prove
by explicit construction that all the one-dimensional ones are representable as
LG, and (c) we present and motivate the conjecture that this result extends to
any number of dimensions.
The tradeoff between dissipation rate and structural complexity implied by
the above results have compelling implications for the thermodynamics of
computation at a microscopic scale.Comment: 16 page
The origin of life: chemical evolution of a metabolic system in a mineral honeycomb?
For the RNA-world hypothesis to be ecologically feasible, selection mechanisms acting on replicator communities need to be invoked and the corresponding scenarios of molecular evolution specified. Complementing our previous models of chemical evolution on mineral surfaces, in which selection was the consequence of the limited mobility of macromolecules attached to the surface, here we offer an alternative realization of prebiotic group-level selection: the physical encapsulation of local replicator communities into the pores of the mineral substrate. Based on cellular automaton simulations we argue that the effect of group selection in a mineral honeycomb could have been efficient enough to keep prebiotic ribozymes of different specificities and replication rates coexistent, and their metabolic cooperation protected from extensive molecular parasitism. We suggest that mutants of the mild parasites persistent in the metabolic system can acquire useful functions such as replicase activity or the production of membrane components, thus opening the way for the evolution of the first autonomous protocells on Earth
25 Years of Self-Organized Criticality: Solar and Astrophysics
Shortly after the seminal paper {\sl "Self-Organized Criticality: An
explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has
been applied to solar physics, in {\sl "Avalanches and the Distribution of
Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics took
place, where the SOC concept was initially applied to solar flares, stellar
flares, and magnetospheric substorms, and later extended to the radiation belt,
the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar
glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and
boson clouds. The application of SOC concepts has been performed by numerical
cellular automaton simulations, by analytical calculations of statistical
(powerlaw-like) distributions based on physical scaling laws, and by
observational tests of theoretically predicted size distributions and waiting
time distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated also
vigorous debates about the discrimination between SOC models, SOC-like, and
non-SOC processes, such as phase transitions, turbulence, random-walk
diffusion, percolation, branching processes, network theory, chaos theory,
fractality, multi-scale, and other complexity phenomena. We review SOC studies
from the last 25 years and highlight new trends, open questions, and future
challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized
Criticality and Turbulence" (2012, 2013, Bern, Switzerland
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