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Scaling and universality of the complexity of analog computation
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10.1063/1.2194471
/content/aip/journal/chaos/16/2/10.1063/1.2194471
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/2/10.1063/1.2194471
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

is plotted as a function of , for the bimodal distribution (for ). The number of instances used in the simulation is 39 732 for the case, 46 583 for the case and 47 169 for the case. The number of converging instances for each case is 5000.

Image of FIG. 2.
FIG. 2.

is plotted as a function of for the bimodal distribution for the instances of Fig. 1 .

Image of FIG. 3.
FIG. 3.

is plotted as a function of for the instances of Fig. 1 .

Image of FIG. 4.
FIG. 4.

is plotted as a function of for the instances of Fig. 1 .

Image of FIG. 5.
FIG. 5.

is plotted as a function of for the instances of Fig. 1 .

Image of FIG. 6.
FIG. 6.

is plotted as a function of for the instances of Fig. 1 .

Image of FIG. 7.
FIG. 7.

is plotted as a function of for the diluted bimodal distribution, where . As before, . The number of instances used in the simulation is 54 951 for the case, 41 107 for the case and 50 863 for the case. The number of converging instances for each case is 5000.

Image of FIG. 8.
FIG. 8.

is plotted as a function of for the diluted bimodal distribution, where . As before, . The number of instances used in the simulation is 54 620 for the case, 37 697 for the case, and 65 367 for the case. The number of converging instances for these cases were, respectively, 4980, 3725, and 5921.

Image of FIG. 9.
FIG. 9.

is plotted as a function of for the uniform distribution. As before, . The number of instances used in the simulation is 121 939 for the case, 91 977 for the case and 112 206 for the case. The number of converging instances for each case is 20 000.

Image of FIG. 10.
FIG. 10.

as a function of (for and ). The graphs are scaled to fit the theoretical Gaussian result by appropriate choice of the factors .

Image of FIG. 11.
FIG. 11.

as a function of for all the distributions checked (for and ), where the scale factors were found by least squares fit to the distribution for the Gaussian ensemble, which was found numerically as well.

Image of FIG. 12.
FIG. 12.

as a function of for all the distributions checked (for and ). The scale factors were found by least squares fit to the distribution for the Gaussian ensemble, which was found numerically as well.

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/content/aip/journal/chaos/16/2/10.1063/1.2194471
2006-05-11
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Scaling and universality of the complexity of analog computation
http://aip.metastore.ingenta.com/content/aip/journal/chaos/16/2/10.1063/1.2194471
10.1063/1.2194471
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