4,689 research outputs found
From quantum cellular automata to quantum lattice gases
A natural architecture for nanoscale quantum computation is that of a quantum
cellular automaton. Motivated by this observation, in this paper we begin an
investigation of exactly unitary cellular automata. After proving that there
can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in
one dimension, we weaken the homogeneity condition and show that there are
nontrivial, exactly unitary, partitioning cellular automata. We find a one
parameter family of evolution rules which are best interpreted as those for a
one particle quantum automaton. This model is naturally reformulated as a two
component cellular automaton which we demonstrate to limit to the Dirac
equation. We describe two generalizations of this automaton, the second of
which, to multiple interacting particles, is the correct definition of a
quantum lattice gas.Comment: 22 pages, plain TeX, 9 PostScript figures included with epsf.tex
(ignore the under/overfull \vbox error messages); minor typographical
corrections and journal reference adde
Can geocomputation save urban simulation? Throw some agents into the mixture, simmer and wait ...
There are indications that the current generation of simulation models in practical,
operational uses has reached the limits of its usefulness under existing specifications.
The relative stasis in operational urban modeling contrasts with simulation efforts in
other disciplines, where techniques, theories, and ideas drawn from computation and
complexity studies are revitalizing the ways in which we conceptualize, understand,
and model real-world phenomena. Many of these concepts and methodologies are
applicable to operational urban systems simulation. Indeed, in many cases, ideas from
computation and complexity studies—often clustered under the collective term of
geocomputation, as they apply to geography—are ideally suited to the simulation of
urban dynamics. However, there exist several obstructions to their successful use in
operational urban geographic simulation, particularly as regards the capacity of these
methodologies to handle top-down dynamics in urban systems.
This paper presents a framework for developing a hybrid model for urban geographic
simulation and discusses some of the imposing barriers against innovation in this
field. The framework infuses approaches derived from geocomputation and
complexity with standard techniques that have been tried and tested in operational
land-use and transport simulation. Macro-scale dynamics that operate from the topdown
are handled by traditional land-use and transport models, while micro-scale
dynamics that work from the bottom-up are delegated to agent-based models and
cellular automata. The two methodologies are fused in a modular fashion using a
system of feedback mechanisms. As a proof-of-concept exercise, a micro-model of
residential location has been developed with a view to hybridization. The model
mixes cellular automata and multi-agent approaches and is formulated so as to
interface with meso-models at a higher scale
Causal graph dynamics
We extend the theory of Cellular Automata to arbitrary, time-varying graphs.
In other words we formalize, and prove theorems about, the intuitive idea of a
labelled graph which evolves in time - but under the natural constraint that
information can only ever be transmitted at a bounded speed, with respect to
the distance given by the graph. The notion of translation-invariance is also
generalized. The definition we provide for these "causal graph dynamics" is
simple and axiomatic. The theorems we provide also show that it is robust. For
instance, causal graph dynamics are stable under composition and under
restriction to radius one. In the finite case some fundamental facts of
Cellular Automata theory carry through: causal graph dynamics admit a
characterization as continuous functions, and they are stable under inversion.
The provided examples suggest a wide range of applications of this mathematical
object, from complex systems science to theoretical physics. KEYWORDS:
Dynamical networks, Boolean networks, Generative networks automata, Cayley
cellular automata, Graph Automata, Graph rewriting automata, Parallel graph
transformations, Amalgamated graph transformations, Time-varying graphs, Regge
calculus, Local, No-signalling.Comment: 25 pages, 9 figures, LaTeX, v2: Minor presentation improvements, v3:
Typos corrected, figure adde
Astrobiological Complexity with Probabilistic Cellular Automata
Search for extraterrestrial life and intelligence constitutes one of the
major endeavors in science, but has yet been quantitatively modeled only rarely
and in a cursory and superficial fashion. We argue that probabilistic cellular
automata (PCA) represent the best quantitative framework for modeling
astrobiological history of the Milky Way and its Galactic Habitable Zone. The
relevant astrobiological parameters are to be modeled as the elements of the
input probability matrix for the PCA kernel. With the underlying simplicity of
the cellular automata constructs, this approach enables a quick analysis of
large and ambiguous input parameters' space. We perform a simple clustering
analysis of typical astrobiological histories and discuss the relevant boundary
conditions of practical importance for planning and guiding actual empirical
astrobiological and SETI projects. In addition to showing how the present
framework is adaptable to more complex situations and updated observational
databases from current and near-future space missions, we demonstrate how
numerical results could offer a cautious rationale for continuation of
practical SETI searches.Comment: 37 pages, 11 figures, 2 tables; added journal reference belo
Modeling the Heart as a Communication System
Electrical communication between cardiomyocytes can be perturbed during
arrhythmia, but these perturbations are not captured by conventional
electrocardiographic metrics. We developed a theoretical framework to quantify
electrical communication using information theory metrics in 2-dimensional cell
lattice models of cardiac excitation propagation. The time series generated by
each cell was coarse-grained to 1 when excited or 0 when resting. The Shannon
entropy for each cell was calculated from the time series during four
clinically important heart rhythms: normal heartbeat, anatomical reentry,
spiral reentry, and multiple reentry. We also used mutual information to
perform spatial profiling of communication during these cardiac arrhythmias. We
found that information sharing between cells was spatially heterogeneous. In
addition, cardiac arrhythmia significantly impacted information sharing within
the heart. Entropy localized the path of the drifting core of spiral reentry,
which could be an optimal target of therapeutic ablation. We conclude that
information theory metrics can quantitatively assess electrical communication
among cardiomyocytes. The traditional concept of the heart as a functional
syncytium sharing electrical information cannot predict altered entropy and
information sharing during complex arrhythmia. Information theory metrics may
find clinical application in the identification of rhythm-specific treatments
which are currently unmet by traditional electrocardiographic techniques.Comment: 26 pages (including Appendix), 6 figures, 8 videos (not uploaded due
to size limitation
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