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![Plot of the predictability index (11) of the different cells along the n-interval [1, 50] for a partition of N ¼ 200 elements. From zero to one, the value of the predictability index is represented by a degradation of color from black to light gray.](profile/Gian-Luigi-Forti/publication/257448351/figure/fig2/AS:880586621210626@1586959619402/Plot-of-the-predictability-index-11-of-the-different-cells-along-the-n-interval-1-50.png)
Plot of the predictability index (11) of the different cells along the n-interval [1, 50] for a partition of N ¼ 200 elements. From zero to one, the value of the predictability index is represented by a degradation of color from black to light gray.
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The present work elaborates on predictability and information aspects of dynamical systems, in connection with the connectivity features of their network representation. The basic idea underlying this work is to map the set of coarse-grained states of a dynamical system onto a set of network nodes and transitions between them onto a set of network...
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Context 1
... the right hand side of (20) can be identified as the stretching factor of the nth iterate of the map j@ x T ðnÞ ðxÞj ¼ 2 n . Fig. 2 depicts the behavior of the PI's (11) as a function of n. Due to the steep growth in the number of outgoing connections, a low value of n suffices for the different PI of all the cells to undergo a rapid transition, that leads from limited to zero predictability. Such a transition is characterized by the appearance of a fine structure ...
Context 2
... of the PI's (11) as a function of n. Due to the steep growth in the number of outgoing connections, a low value of n suffices for the different PI of all the cells to undergo a rapid transition, that leads from limited to zero predictability. Such a transition is characterized by the appearance of a fine structure in the profile of PI values (see Fig. 2). The latter clearly reflects the increasingly complex connectivity patterns that arise as n increases (see the plots in panels (c) and (d) of Fig. 1). From a fine-grained perspective, the loss of predictability observed in Fig. 2 with increasing n is characterized by the Lyapunov time (10) of the nth iterate of the ...
Context 3
... Such a transition is characterized by the appearance of a fine structure in the profile of PI values (see Fig. 2). The latter clearly reflects the increasingly complex connectivity patterns that arise as n increases (see the plots in panels (c) and (d) of Fig. 1). From a fine-grained perspective, the loss of predictability observed in Fig. 2 with increasing n is characterized by the Lyapunov time (10) of the nth iterate of the ...
Context 4
... order to understand better the sharp increase of uncertainty exhibited in Fig. 2 and its dependence on N, let us turn to quantity AI (14), as obtained by using the invariant measure of cells (19). Fig. 3 depicts the plot of the AI for different values of n and N. As can be seen, AI exhibits a steep linear decrease as the number of outgoing connections increases with n. The latter constitutes a signature of a short ...
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... This measure is shown to be useful for the detection of stable manifolds and local transport barriers as well as being closely related to finite-time Lyapunov exponents. Related measures of transitional complexity based on node centrality have been used to quantify divergence of trajectories in chaotic attractors [13] and as an index of predictability for discrete processes [15]. Recently, Unakafov et al. proposed a direct and logical extension to permutation entropy which they called the conditional entropy of ordinal patterns, henceforth referred to in this paper as conditional permutation entropy. ...
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El monitoreo de carga no intrusivo es un conjunto de técnicas
cuyo objetivo es la identificación de los electrodomésticos
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Disaggregation Data Set (REDD) de acceso gratuito y que
contiene información detallada del consumo eléctrico de
artefactos de varios hogares. El presente trabajo tuvo como
objetivo utilizar herramientas de la teoría de la información y
del análisis de señales para generar un espacio de
características como conjunto de entrenamiento para un
modelo de Machine Learning supervisado (SVM); para
formular así una clasificación satisfactoria de
electrodomésticos. Los resultados obtenidos muestran una
precisión lo suficientemente elevada como para alentar la
continuación de esta línea de investigación.
We consider a PageRank model of opinion formation on Ulam networks, generated
by the intermittency map and the typical Chirikov map. The Ulam networks
generated by these maps have certain similarities with such scale-free networks
as the World Wide Web (WWW), showing an algebraic decay of the PageRank
probability. We find that the opinion formation process on Ulam networks have
certain similarities but also distinct features comparing to the WWW. We
attribute these distinctions to internal differences in network structure of
the Ulam and WWW networks. We also analyze the process of opinion formation in
the frame of generalized Sznajd model which protects opinion of small
communities.
