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notes: use native div syntax

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Michele Guerini Rocco 2020-06-02 00:22:27 +02:00
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commit 0585b80009
2 changed files with 10 additions and 10 deletions
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4
notes/sections/3.md
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@ -43,7 +43,7 @@ The proper distribution of $\theta$ is obtained by applying a transform
to a variable $x$ with uniform distribution in $[0, 1)$, to a variable $x$ with uniform distribution in $[0, 1)$,
easily generated by the GSL function `gsl_rng_uniform()`. easily generated by the GSL function `gsl_rng_uniform()`.
<div id="fig:compare"> ::: { id=fig:compare }
![Uniformly distributed points with $\theta$ evenly distributed between ![Uniformly distributed points with $\theta$ evenly distributed between
0 and $\pi$.](images/3-histo-i-u.pdf){width=50%} 0 and $\pi$.](images/3-histo-i-u.pdf){width=50%}
![Points uniformly distributed on a spherical ![Points uniformly distributed on a spherical
@ -56,7 +56,7 @@ easily generated by the GSL function `gsl_rng_uniform()`.
Examples of samples. On the left, points with $\theta$ evenly distributed Examples of samples. On the left, points with $\theta$ evenly distributed
between 0 and $\pi$; on the right, points with $\theta$ properly distributed. between 0 and $\pi$; on the right, points with $\theta$ properly distributed.
</div> :::
The transformation can be found by imposing the angular PDF to be a constant: The transformation can be found by imposing the angular PDF to be a constant:
\begin{align*} \begin{align*}

16
notes/sections/6.md
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@ -594,7 +594,7 @@ amplitude changes: it always gives the same outcome, which would be exactly the
original signal, if the floating point precision would not affect the result. In original signal, if the floating point precision would not affect the result. In
fact, the FFT is the analytical result of the deconvolution. fact, the FFT is the analytical result of the deconvolution.
<div id="fig:rounds-noiseless"> ::: {id=fig:rounds-noiseless}
![](images/6-nonoise-rounds-0.1.pdf){#fig:rless-0.1} ![](images/6-nonoise-rounds-0.1.pdf){#fig:rless-0.1}
![](images/6-nonoise-rounds-0.5.pdf){#fig:rless-0.5} ![](images/6-nonoise-rounds-0.5.pdf){#fig:rless-0.5}
@ -604,9 +604,9 @@ fact, the FFT is the analytical result of the deconvolution.
EMD as a function of RL rounds for different kernel $\sigma$ values. The EMD as a function of RL rounds for different kernel $\sigma$ values. The
average is shown in red and the standard deviation in grey. Noiseless results average is shown in red and the standard deviation in grey. Noiseless results
shown. shown.
</div> :::
<div id="fig:emd-noiseless"> ::: {id="fig:emd-noiseless"}
![$\sigma = 0.1 \, \Delta \theta$](images/6-nonoise-emd-0.1.pdf){#fig:eless-0.1} ![$\sigma = 0.1 \, \Delta \theta$](images/6-nonoise-emd-0.1.pdf){#fig:eless-0.1}
![$\sigma = 0.5 \, \Delta \theta$](images/6-nonoise-emd-0.5.pdf){#fig:eless-0.5} ![$\sigma = 0.5 \, \Delta \theta$](images/6-nonoise-emd-0.5.pdf){#fig:eless-0.5}
@ -617,7 +617,7 @@ EMD distributions for different kernel $\sigma$ values. The plots on the left
show the results for the FFT deconvolution, the central column the results for show the results for the FFT deconvolution, the central column the results for
the RL deconvolution and the third one shows the EMD for the convolved signal. the RL deconvolution and the third one shows the EMD for the convolved signal.
Noiseless results. Noiseless results.
</div> :::
For this reason, the EMD obtained with the FFT can be used as a reference point For this reason, the EMD obtained with the FFT can be used as a reference point
against which to compare the EMDs measured with RL. against which to compare the EMDs measured with RL.
@ -706,7 +706,7 @@ However, in real world applications the measures are affected by (possibly
unknown) noise and the signal can only be partially reconstructed by either unknown) noise and the signal can only be partially reconstructed by either
method. method.
<div id="fig:rounds-noise"> ::: {id=fig:rounds-noise}
![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005} ![](images/6-noise-rounds-0.005.pdf){#fig:rnoise-0.005}
![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01} ![](images/6-noise-rounds-0.01.pdf){#fig:rnoise-0.01}
@ -716,9 +716,9 @@ method.
EMD as a function of RL rounds for different noise $\sigma_N$ values with the EMD as a function of RL rounds for different noise $\sigma_N$ values with the
kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the kernel $\sigma = 0.8 \Delta \theta$. The average is shown in red and the
standard deviation in grey. Noisy results. standard deviation in grey. Noisy results.
</div> :::
<div id="fig:emd-noisy"> ::: {id=fig:emd-noisy}
![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005} ![$\sigma_N = 0.005$](images/6-noise-emd-0.005.pdf){#fig:enoise-0.005}
![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01} ![$\sigma_N = 0.01$](images/6-noise-emd-0.01.pdf){#fig:enoise-0.01}
@ -729,4 +729,4 @@ EMD distributions for different noise $\sigma_N$ values. The plots on the left
show the results for the FFT deconvolution, the central column the results for show the results for the FFT deconvolution, the central column the results for
the RL deconvolution and the third one shows the EMD for the convolved signal. the RL deconvolution and the third one shows the EMD for the convolved signal.
Noisy results. Noisy results.
</div> :::