notes: use native div syntax
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@ -43,7 +43,7 @@ The proper distribution of $\theta$ is obtained by applying a transform
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to a variable $x$ with uniform distribution in $[0, 1)$,
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easily generated by the GSL function `gsl_rng_uniform()`.
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<div id="fig:compare">
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::: { id=fig:compare }
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![Uniformly distributed points with $\theta$ evenly distributed between
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0 and $\pi$.](images/3-histo-i-u.pdf){width=50%}
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![Points uniformly distributed on a spherical
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@ -56,7 +56,7 @@ easily generated by the GSL function `gsl_rng_uniform()`.
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Examples of samples. On the left, points with $\theta$ evenly distributed
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between 0 and $\pi$; on the right, points with $\theta$ properly distributed.
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</div>
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:::
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The transformation can be found by imposing the angular PDF to be a constant:
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\begin{align*}
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@ -594,7 +594,7 @@ amplitude changes: it always gives the same outcome, which would be exactly the
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original signal, if the floating point precision would not affect the result. In
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fact, the FFT is the analytical result of the deconvolution.
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<div id="fig:rounds-noiseless">
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::: {id=fig:rounds-noiseless}
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![](images/6-nonoise-rounds-0.1.pdf){#fig:rless-0.1}
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![](images/6-nonoise-rounds-0.5.pdf){#fig:rless-0.5}
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@ -604,9 +604,9 @@ fact, the FFT is the analytical result of the deconvolution.
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EMD as a function of RL rounds for different kernel $\sigma$ values. The
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average is shown in red and the standard deviation in grey. Noiseless results
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shown.
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</div>
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:::
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<div id="fig:emd-noiseless">
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::: {id="fig:emd-noiseless"}
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![$\sigma = 0.1 \, \Delta \theta$](images/6-nonoise-emd-0.1.pdf){#fig:eless-0.1}
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![$\sigma = 0.5 \, \Delta \theta$](images/6-nonoise-emd-0.5.pdf){#fig:eless-0.5}
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@ -617,7 +617,7 @@ EMD distributions for different kernel $\sigma$ values. The plots on the left
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show the results for the FFT deconvolution, the central column the results for
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the RL deconvolution and the third one shows the EMD for the convolved signal.
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Noiseless results.
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</div>
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:::
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For this reason, the EMD obtained with the FFT can be used as a reference point
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against which to compare the EMDs measured with RL.
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@ -706,7 +706,7 @@ However, in real world applications the measures are affected by (possibly
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unknown) noise and the signal can only be partially reconstructed by either
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method.
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<div id="fig:rounds-noise">
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::: {id=fig:rounds-noise}
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![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005}
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![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01}
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@ -716,9 +716,9 @@ method.
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EMD as a function of RL rounds for different noise $\sigma_N$ values with the
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kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the
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standard deviation in grey. Noisy results.
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</div>
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:::
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<div id="fig:emd-noisy">
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::: {id=fig:emd-noisy}
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![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005}
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![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01}
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@ -729,4 +729,4 @@ EMD distributions for different noise $\sigma_N$ values. The plots on the left
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show the results for the FFT deconvolution, the central column the results for
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the RL deconvolution and the third one shows the EMD for the convolved signal.
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Noisy results.
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</div>
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:::
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