208 research outputs found
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
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
On Sloane's persistence problem
We investigate the so-called persistence problem of Sloane, exploiting
connections with the dynamics of circle maps and the ergodic theory of
actions. We also formulate a conjecture concerning the
asymptotic distribution of digits in long products of finitely many primes
whose truth would, in particular, solve the persistence problem. The heuristics
that we propose to complement our numerical studies can be thought in terms of
a simple model in statistical mechanics.Comment: 5 figure
Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems
Most current methods for identifying coherent structures in
spatially-extended systems rely on prior information about the form which those
structures take. Here we present two new approaches to automatically filter the
changing configurations of spatial dynamical systems and extract coherent
structures. One, local sensitivity filtering, is a modification of the local
Lyapunov exponent approach suitable to cellular automata and other discrete
spatial systems. The other, local statistical complexity filtering, calculates
the amount of information needed for optimal prediction of the system's
behavior in the vicinity of a given point. By examining the changing
spatiotemporal distributions of these quantities, we can find the coherent
structures in a variety of pattern-forming cellular automata, without needing
to guess or postulate the form of that structure. We apply both filters to
elementary and cyclical cellular automata (ECA and CCA) and find that they
readily identify particles, domains and other more complicated structures. We
compare the results from ECA with earlier ones based upon the theory of formal
languages, and the results from CCA with a more traditional approach based on
an order parameter and free energy. While sensitivity and statistical
complexity are equally adept at uncovering structure, they are based on
different system properties (dynamical and probabilistic, respectively), and
provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv
requirements; write first author for higher-resolution version
Cellular Probabilistic Automata - A Novel Method for Uncertainty Propagation
We propose a novel density based numerical method for uncertainty propagation
under certain partial differential equation dynamics. The main idea is to
translate them into objects that we call cellular probabilistic automata and to
evolve the latter. The translation is achieved by state discretization as in
set oriented numerics and the use of the locality concept from cellular
automata theory. We develop the method at the example of initial value
uncertainties under deterministic dynamics and prove a consistency result. As
an application we discuss arsenate transportation and adsorption in drinking
water pipes and compare our results to Monte Carlo computations
Reliable Cellular Automata with Self-Organization
In a probabilistic cellular automaton in which all local transitions have
positive probability, the problem of keeping a bit of information indefinitely
is nontrivial, even in an infinite automaton. Still, there is a solution in 2
dimensions, and this solution can be used to construct a simple 3-dimensional
discrete-time universal fault-tolerant cellular automaton. This technique does
not help much to solve the following problems: remembering a bit of information
in 1 dimension; computing in dimensions lower than 3; computing in any
dimension with non-synchronized transitions.
Our more complex technique organizes the cells in blocks that perform a
reliable simulation of a second (generalized) cellular automaton. The cells of
the latter automaton are also organized in blocks, simulating even more
reliably a third automaton, etc. Since all this (a possibly infinite hierarchy)
is organized in ``software'', it must be under repair all the time from damage
caused by errors. A large part of the problem is essentially self-stabilization
recovering from a mess of arbitrary size and content. The present paper
constructs an asynchronous one-dimensional fault-tolerant cellular automaton,
with the further feature of ``self-organization''. The latter means that unless
a large amount of input information must be given, the initial configuration
can be chosen homogeneous.Comment: 166 pages, 17 figure
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