Giu/analistica
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

sections: fix and add a lot of things

Browse Source
This commit is contained in:
Giù Marcer 2020-06-10 18:48:17 +02:00 committed by rnhmjoj
parent 2ea9b8d36f
commit 4ea618d8ee
3 changed files with 81 additions and 10 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
slides/sections/2.md
View File

@ -4,7 +4,7 @@
## Landau PDF
:::: {.columns}
::: {.column width=50% .c}
::: {.column width=50% align=center}
$$
L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
dt \, e^{-t \ln(t) -xt} \sin (\pi t)

32
slides/sections/3.md
View File

@ -83,6 +83,17 @@ Defined by $F(m) = \frac{1}{2}$ or $m = Q \left( \frac{1}{2} \right)$:
\text{erf}^{-1} \left( \frac{1}{2} \right) \right]
\end{align*}
\setbeamercovered{}
\begin{center}
\begin{tikzpicture}[overlay]
\pause
\node [opacity=0.5, xscale=0.55, yscale=0.4 ] at (1.85,1.1) {\includegraphics{images/high.png}};
\end{tikzpicture}
\end{center}
\setbeamercovered{transparent}
## Moyal mode
Peak of the PDF:
@ -99,6 +110,16 @@ $$
\partial_x M_{\mu \sigma}(x) = 0 &\thus \mu_M\ex = \mu \\
\end{align*}
\setbeamercovered{}
\begin{center}
\begin{tikzpicture}[overlay]
\pause
\node [opacity=0.5, xscale=0.18, yscale=0.25 ] at (2.4,1.8) {\includegraphics{images/high.png}};
\end{tikzpicture}
\end{center}
\setbeamercovered{transparent}
## Moyal FWHM
@ -129,3 +150,14 @@ $$
M_{\mu \sigma}(x)
&\thus w_M^{\text{exp}} = \sigma \cdot a \\
\end{align*}
\setbeamercovered{}
\begin{center}
\begin{tikzpicture}[overlay]
\pause
\node [opacity=0.5, xscale=0.2, yscale=0.25 ] at (1.9,1.9) {\includegraphics{images/high.png}};
\end{tikzpicture}
\end{center}
\setbeamercovered{transparent}

53
slides/sections/4.md
View File

@ -133,14 +133,56 @@ $$
Kernel Density Estimation
- empirical PDF construction:
:::: {.columns}
::: {.column width=50% .c}
- empirical PDF construction:
$$
$$
f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N
G \left( \frac{x-x_i}{\varepsilon} \right)
$$
$$
The parameter $\varepsilon$ controls the strength of the smoothing
The parameter $\varepsilon$ controls the strength of the smoothing
:::
::: {.column width=50%}
\setbeamercovered{}
\begin{center}
\begin{tikzpicture}
% points
\draw [blue, fill=blue] (-2,-0.1) rectangle (-1.8,0.1);
\draw [blue, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1);
\draw [blue, fill=blue] (1.3,-0.1) rectangle (1.5,0.1);
\draw [blue, fill=blue] (0.7,-0.1) rectangle (0.9,0.1);
\pause
% lines
\draw [cyclamen, dashed] (-1.9,0.1) -- (-1.9,1);
\draw [cyclamen, dashed] (0,0.1) -- (0,1);
\draw [cyclamen, dashed] (1.4,0.1) -- (1.4,1);
\draw [cyclamen, dashed] (0.8,0.1) -- (0.8,1);
% Gaussians
\draw[domain=-3.4:-0.4, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x + 1.9)*(\x + 1.9)) + 0.1});
\draw[domain=-1.5:1.5, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-\x*\x + 0.1});
\draw[domain=-0.1:2.9, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 1.4)*(\x - 1.4)) + 0.1});
\draw[domain=-0.7:2.3, smooth, variable=\x, cyclamen, very thick]
plot ({\x}, {exp(-(\x - 0.8)*(\x - 0.8)) + 0.1});
\pause
% sum
\draw [fill=white, white, opacity=0.5] (-3.5,0.1) rectangle (3,1.3);
\draw[domain=-3.4:3.4, smooth, variable=\x, blue, very thick]
plot ({\x}, {exp(-(\x + 1.9)*(\x + 1.9)) +
exp(-\x*\x) +
exp(-(\x - 1.4)*(\x - 1.4)) +
exp(-(\x - 0.8)*(\x - 0.8)) + 0.1});
\end{tikzpicture}
\end{center}
\setbeamercovered{transparent}
:::
::::
## Sample FWHM
@ -148,9 +190,6 @@ The parameter $\varepsilon$ controls the strength of the smoothing
Silverman's rule of thumb:
$$
f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N
G \left( \frac{x-x_i}{\varepsilon} \right)
\with
\varepsilon = 0.88 \, S_N
\left( \frac{d + 2}{4}N \right)^{-1/(d + 4)}
$$