349 research outputs found
Simply modified GKL density classifiers that reach consensus faster
The two-state Gacs-Kurdyumov-Levin (GKL) cellular automaton has been a staple
model in the study of complex systems due to its ability to classify binary
arrays of symbols according to their initial density. We show that a class of
modified GKL models over extended neighborhoods, but still involving only three
cells at a time, achieves comparable density classification performance but in
some cases reach consensus more than twice as fast. Our results suggest the
time to consensus (relative to the length of the CA) as a complementary measure
of density classification performance.Comment: Short note, 3 pages, 1 table, 2 composite figures, 18 reference
Ergodicity versus non-ergodicity for Probabilistic Cellular Automata on rooted trees
In this article we study a class of shift-invariant and positive rate
probabilistic cellular automata (PCA) on rooted d-regular trees .
In a first result we extend the results of [10] on trees, namely we prove
that to every stationary measure of the PCA we can associate a space-time
Gibbs measure on
. Under certain assumptions on the dynamics
the converse is also true.
A second result concerns proving sufficient conditions for ergodicity and
non-ergodicity of our PCA on d-ary trees for and
characterizing the invariant product Bernoulli measures.Comment: 17 page
Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata
We give new sufficient ergodicity conditions for two-state probabilistic
cellular automata (PCA) of any dimension and any radius. The proof of this
result is based on an extended version of the duality concept. Under these
assumptions, in the one dimensional case, we study some properties of the
unique invariant measure and show that it is shift-mixing. Also, the decay of
correlation is studied in detail. In this sense, the extended concept of
duality gives exponential decay of correlation and allows to compute
explicitily all the constants involved
Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
In this article we review classical and recent results in anomalous diffusion
and provide mechanisms useful for the study of the fundamentals of certain
processes, mainly in condensed matter physics, chemistry and biology. Emphasis
will be given to some methods applied in the analysis and characterization of
diffusive regimes through the memory function, the mixing condition (or
irreversibility), and ergodicity. Those methods can be used in the study of
small-scale systems, ranging in size from single-molecule to particle clusters
and including among others polymers, proteins, ion channels and biological
cells, whose diffusive properties have received much attention lately.Comment: Review article, 20 pages, 7 figures. arXiv admin note: text overlap
with arXiv:cond-mat/0201446 by other author
Aspects of algorithms and dynamics of cellular paradigms
Els paradigmes cel·lulars, com les xarxes neuronals cel·lulars (CNN, en anglès) i els autòmats cel·lulars (CA, en anglès), són una eina excel·lent de cà lcul, al ser equivalents a una mà quina universal de Turing. La introducció de la mà quina universal CNN (CNN-UM, en anglès) ha permès desenvolupar hardware, el nucli computacional del qual funciona segons la filosofia cel·lular; aquest hardware ha trobat aplicació en diversos camps al llarg de la darrera dècada. Malgrat això, encara hi ha moltes preguntes a obertes sobre com definir els algoritmes d'una CNN-UM i com estudiar la dinà mica dels autòmats cel·lulars. En aquesta tesis es tracten els dos problemes: primer, es demostra que es possible acotar l'espai dels algoritmes per a la CNN-UM i explorar-lo grà cies a les tècniques genètiques; i segon, s'expliquen els fonaments de l'estudi dels CA per mitjà de la dinà mica no lineal (segons la definició de Chua) i s'il·lustra com aquesta tècnica ha permès trobar resultats innovadors.Los paradigmas celulares, como las redes neuronales celulares (CNN, eninglés) y los autómatas celulares (CA, en inglés), son una excelenteherramienta de cálculo, al ser equivalentes a una maquina universal deTuring. La introducción de la maquina universal CNN (CNN-UM, eninglés) ha permitido desarrollar hardware cuyo núcleo computacionalfunciona según la filosofÃa celular; dicho hardware ha encontradoaplicación en varios campos a lo largo de la ultima década. Sinembargo, hay aun muchas preguntas abiertas sobre como definir losalgoritmos de una CNN-UM y como estudiar la dinámica de los autómatascelular. En esta tesis se tratan ambos problemas: primero se demuestraque es posible acotar el espacio de los algoritmos para la CNN-UM yexplorarlo gracias a técnicas genéticas; segundo, se explican losfundamentos del estudio de los CA por medio de la dinámica no lineal(según la definición de Chua) y se ilustra como esta técnica hapermitido encontrar resultados novedosos.Cellular paradigms, like Cellular Neural Networks (CNNs) and Cellular Automata (CA) are an excellent tool to perform computation, since they are equivalent to a Universal Turing machine. The introduction of the Cellular Neural Network - Universal Machine (CNN-UM) allowed us to develop hardware whose computational core works according to the principles of cellular paradigms; such a hardware has found application in a number of fields throughout the last decade. Nevertheless, there are still many open questions about how to define algorithms for a CNN-UM, and how to study the dynamics of Cellular Automata. In this dissertation both problems are tackled: first, we prove that it is possible to bound the space of all algorithms of CNN-UM and explore it through genetic techniques; second, we explain the fundamentals of the nonlinear perspective of CA (according to Chua's definition), and we illustrate how this technique has allowed us to find novel results
The dynamics of iterated transportation simulations
Iterating between a router and a traffic micro-simulation is an increasibly
accepted method for doing traffic assignment. This paper, after pointing out
that the analytical theory of simulation-based assignment to-date is
insufficient for some practical cases, presents results of simulation studies
from a real world study. Specifically, we look into the issues of uniqueness,
variability, and robustness and validation. Regarding uniqueness, despite some
cautionary notes from a theoretical point of view, we find no indication of
``meta-stable'' states for the iterations. Variability however is considerable.
By variability we mean the variation of the simulation of a given plan set by
just changing the random seed. We show then results from three different
micro-simulations under the same iteration scenario in order to test for the
robustness of the results under different implementations. We find the results
encouraging, also when comparing to reality and with a traditional assignment
result.
Keywords: dynamic traffic assignment (DTA); traffic micro-simulation;
TRANSIMS; large-scale simulations; urban planningComment: 24 pages, 7 figure
A method for inferring hierarchical dynamics in stochastic processes
Complex systems may often be characterized by their hierarchical dynamics. In
this paper do we present a method and an operational algorithm that
automatically infer this property in a broad range of systems; discrete
stochastic processes. The main idea is to systematically explore the set of
projections from the state space of a process to smaller state spaces, and to
determine which of the projections that impose Markovian dynamics on the
coarser level. These projections, which we call Markov projections, then
constitute the hierarchical dynamics of the system. The algorithm operates on
time series or other statistics, so a priori knowledge of the intrinsic
workings of a system is not required in order to determine its hierarchical
dynamics. We illustrate the method by applying it to two simple processes; a
finite state automaton and an iterated map.Comment: 16 pages, 12 figure
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