Add lab session 4
Handed in on 10 Nov 2020.
Change-Id: Iac2b326e564a415d56c927b1900856d55fd6b9ed
diff --git a/p4/data/calculs.ods b/p4/data/calculs.ods
new file mode 100644
index 0000000..eea1392
--- /dev/null
+++ b/p4/data/calculs.ods
Binary files differ
diff --git a/p4/data/finaldata.dat b/p4/data/finaldata.dat
new file mode 100644
index 0000000..2da33eb
--- /dev/null
+++ b/p4/data/finaldata.dat
@@ -0,0 +1,6 @@
+# Y T I S=Y/(VI) delta S
+2.942 23.8 19.1 0.0770 0.08
+3 9.8 18.4 0.0815 0.09
+2.591 -0.2 18.7 0.0693 0.08
+3.117 -13.7 17.9 0.0871 0.10
+2.279 29.1 18.1 0.0630 0.07
diff --git a/p4/data/mesura1.dat b/p4/data/mesura1.dat
new file mode 100644
index 0000000..5a4e76e
--- /dev/null
+++ b/p4/data/mesura1.dat
@@ -0,0 +1,1193 @@
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diff --git a/p4/data/mesura1_deriva.dat b/p4/data/mesura1_deriva.dat
new file mode 100644
index 0000000..df6b32a
--- /dev/null
+++ b/p4/data/mesura1_deriva.dat
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diff --git a/p4/data/mesura2.dat b/p4/data/mesura2.dat
new file mode 100644
index 0000000..042f42a
--- /dev/null
+++ b/p4/data/mesura2.dat
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diff --git a/p4/data/mesura2_deriva.dat b/p4/data/mesura2_deriva.dat
new file mode 100644
index 0000000..878c274
--- /dev/null
+++ b/p4/data/mesura2_deriva.dat
@@ -0,0 +1,202 @@
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diff --git a/p4/data/mesura3.dat b/p4/data/mesura3.dat
new file mode 100644
index 0000000..ae33d45
--- /dev/null
+++ b/p4/data/mesura3.dat
@@ -0,0 +1,805 @@
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diff --git a/p4/data/mesura3_deriva.dat b/p4/data/mesura3_deriva.dat
new file mode 100644
index 0000000..a6891d1
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diff --git a/p4/data/mesura4.dat b/p4/data/mesura4.dat
new file mode 100644
index 0000000..3b9e34d
--- /dev/null
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diff --git a/p4/data/mesura4_deriva.dat b/p4/data/mesura4_deriva.dat
new file mode 100644
index 0000000..1c0affb
--- /dev/null
+++ b/p4/data/mesura4_deriva.dat
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diff --git a/p4/data/mesura5.dat b/p4/data/mesura5.dat
new file mode 100644
index 0000000..8934f53
--- /dev/null
+++ b/p4/data/mesura5.dat
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diff --git a/p4/data/mesura5_deriva.dat b/p4/data/mesura5_deriva.dat
new file mode 100644
index 0000000..f70f422
--- /dev/null
+++ b/p4/data/mesura5_deriva.dat
@@ -0,0 +1,187 @@
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diff --git a/p4/full_laboratori/practica4.pdf b/p4/full_laboratori/practica4.pdf
new file mode 100644
index 0000000..341e095
--- /dev/null
+++ b/p4/full_laboratori/practica4.pdf
Binary files differ
diff --git a/p4/graphs/finalgraph.gnu b/p4/graphs/finalgraph.gnu
new file mode 100755
index 0000000..dd9c4d4
--- /dev/null
+++ b/p4/graphs/finalgraph.gnu
@@ -0,0 +1,59 @@
+#!/usr/bin/env gnuplot -c
+# == DEFINICIONS ==
+outputfile = "../output/finalgraph" # Nom de la imatge resultant (sense extensió)
+datafile = "../data/finaldata.dat" # Nom del fitxer de dades que es vol usar
+error_sist_b = 0.11 # Error sistemàtic en
+
+# == CONFIGURACIÓ DE L'OUTPUT PEL LATEX ==
+set terminal cairolatex size 10cm, 7cm
+set output outputfile.'.tex'
+
+# == CONFIGURACIÓ DEL PLOT ==
+set xlabel "$T \\, (\\si{\\celsius})$"
+set ylabel "$S \\, (\\si{\\per\\ampere})$"
+
+# Opcions per la llegenda:
+set key above
+set key spacing 1.5
+
+# == CONFIGURACIÓ DEL FIT ==
+set fit quiet
+
+f(x) = a*x + b # Funció a fitar
+fit f(x) datafile u 2:4 via a, b # Fem el fit de les dades
+
+# Això s'usa per obtenir el valor del coeficient de correlació "r", que estarà
+# guardat a la var. "STATS_correlation"
+stats datafile u 2:4 name "STATS" nooutput
+
+# Funció per obtenir els dígits significatius d'una expressió
+f_sd(n, i) = (int(n) == 0 ? f_sd(n*10, i+1) : (int(n) == 1 ? i+1 : i))
+significant_digits(n) = f_sd(n - 10*int(n/10), 0)
+
+significant_digits_r(n) = (n == 1 ? 0 : significant_digits(1 - n))
+
+error_a = STATS_slope_err
+sd_error_a = significant_digits(error_a)
+error_b = sqrt(STATS_slope_err + error_sist_b)
+sd_error_b = significant_digits(error_b)
+r = STATS_correlation
+sd_r = significant_digits_r(r)
+
+print("=== ".datafile." ===")
+print(sprintf('delta(a) = %.'.sd_error_a.'f, sd=%.0f', error_a, sd_error_a))
+print(sprintf('delta(b) = %.'.sd_error_b.'f, sd=%.0f', error_b, sd_error_b))
+
+# Aquesta funció escriu, a partir dels valors del paràmetres a, b i r,
+# l'equació de la regressió:
+title_f(a, b, r) = sprintf('$S(T) = %.'.sd_error_a.'f T + %.'.sd_error_b.'f$, $r = %.'.sd_r.'f$', a, b, r);
+
+plot datafile u 2:4:(0.1):5 t "Dades experimentals" w xyerr, f(x) t title_f(a, b, r)
+
+# == CONFIGURACIÓ DE L'OUTPUT PER SVG ==
+# Això ho uso per generar també una imatge de previsualització que puc carregar
+# a l'ordinador per veure més o menys com a sortit el plot sense haver
+# d'inserir-ho al LaTeX per veure-ho.
+set terminal svg dashed size 600, 600 font "Computer Modern,Tinos,Helvetica,15"
+set output outputfile.'.svg'
+
+replot
diff --git a/p4/graphs/generate.bash b/p4/graphs/generate.bash
new file mode 100644
index 0000000..b53e10b
--- /dev/null
+++ b/p4/graphs/generate.bash
@@ -0,0 +1,8 @@
+#!/usr/bin/env bash
+mkdir -p ../output
+
+for i in 1 2 3 4 5; do
+ ./graph.gnu "../data/mesura${i}.dat" "../data/mesura${i}_deriva.dat" "../output/mesura${i}" "../output/mesura${i}_wd"
+done
+
+./finalgraph.gnu
diff --git a/p4/graphs/graph.gnu b/p4/graphs/graph.gnu
new file mode 100755
index 0000000..80f1931
--- /dev/null
+++ b/p4/graphs/graph.gnu
@@ -0,0 +1,95 @@
+#!/usr/bin/env gnuplot -c
+# == DEFINICIONS ==
+outputfile = ARG3 # Nom de la imatge resultant (sense extensió)
+outputfile2 = ARG4 # Nom de la imatge resultant 2 (sense extensió)
+datafile = ARG1 # Nom del fitxer de dades que es vol usar
+derivafile = ARG2 # Nom del fitxer de dades que es vol usar
+error_sist_b = 0.001 # Error sistemàtic en l'eix y
+
+# Set to 0 for quadratic fitting.
+# Set to 1 for linear fitting.
+linear = 0
+
+# == CONFIGURACIÓ DE L'OUTPUT PEL LATEX ==
+set terminal cairolatex size 7.4cm, 6cm
+set output outputfile.'.tex'
+
+# == CONFIGURACIÓ DEL PLOT ==
+set xlabel "$t \\, (\\si{\\second})$"
+set ylabel "$V \\, (\\si{\\milli\\volt})$"
+set xtics 200
+
+# Opcions per la llegenda:
+set key above
+set key spacing 1.5
+
+# == CONFIGURACIÓ DEL FIT ==
+set fit quiet
+
+if (linear == 1) {
+ f(x) = a*x + b # Funció a fitar
+ fit f(x) derivafile u 1:2 via a, b # Fem el fit de les dades
+
+ # Això s'usa per obtenir el valor del coeficient de correlació "r", que estarà
+ # guardat a la var. "STATS_correlation"
+ stats derivafile u 1:2 name "STATS" nooutput
+
+ # Funció per obtenir els dígits significatius d'una expressió
+ f_sd(n, i) = (int(n) == 0 ? f_sd(n*10, i+1) : (int(n) == 1 ? i+1 : i))
+ significant_digits(n) = f_sd(n - 10*int(n/10), 0)
+
+ significant_digits_r(n) = (n == 1 ? 0 : significant_digits(1 - n))
+
+ error_a = STATS_slope_err
+ sd_error_a = significant_digits(error_a)
+ error_b = sqrt(STATS_slope_err + error_sist_b)
+ sd_error_b = significant_digits(error_b)
+ r = STATS_correlation
+ sd_r = significant_digits_r(r)
+
+ print("=== ".derivafile." ===")
+ print("* Linear fit")
+ print(sprintf('delta(a) = %.'.sd_error_a.'f, sd=%.0f', error_a, sd_error_a))
+ print(sprintf('delta(b) = %.'.sd_error_b.'f, sd=%.0f', error_b, sd_error_b))
+
+ # Aquesta funció escriu, a partir dels valors del paràmetres a, b i r,
+ # l'equació de la regressió:
+ title_f(a, b, r) = sprintf('$Deriva d(t) = %.'.sd_error_a.'f t + (%.'.sd_error_b.'f)$, $r = %.'.sd_r.'f$', a, b, r);
+
+ plot [0:] datafile u 1:2 t "Senyal calorimètric" w p pt 7 ps 0.35, f(x) t title_f(a, b, r)
+} else {
+ print("=== ".derivafile." ===")
+ print("* Quadratic fit")
+
+ f(x) = a*x*x + b*x + c # Funció a fitar
+ fit f(x) derivafile u 1:2 via a, b, c # Fem el fit de les dades
+
+ title_f(a, b, c) = sprintf('$d(t) = %.1e t^2 + %.1e t + %.1e t$', a, b, c);
+
+ plot [0:] datafile u 1:2 t "Senyal calorimètric" w p pt 7 ps 0.35, f(x) t "Línia base"
+}
+
+stats datafile u (column(1) < 100 ? 0 : column(2) - f(column(1))) name "CORRECTED_STATS" nooutput
+
+print(sprintf("Y = %.3f", CORRECTED_STATS_max))
+
+# == CONFIGURACIÓ DE L'OUTPUT PER SVG ==
+# Això ho uso per generar també una imatge de previsualització que puc carregar
+# a l'ordinador per veure més o menys com a sortit el plot sense haver
+# d'inserir-ho al LaTeX per veure-ho.
+set terminal svg dashed size 600, 600 font "Computer Modern,Tinos,Helvetica,15"
+set output outputfile.'.svg'
+
+replot
+
+# Fem el plot del segon gràfic
+
+set terminal cairolatex size 7.4cm, 6cm
+set output outputfile2.'.tex'
+
+plot [0:] datafile u 1:(column(2) - f(column(1))) t "Senyal calor. corregit" w p pt 7 ps 0.35
+
+set terminal svg dashed size 600, 600 font "Computer Modern,Tinos,Helvetica,15"
+set output outputfile2.'.svg'
+
+replot
diff --git a/p4/informe/p4.pdf b/p4/informe/p4.pdf
new file mode 100644
index 0000000..016f377
--- /dev/null
+++ b/p4/informe/p4.pdf
Binary files differ
diff --git a/p4/informe/p4.tex b/p4/informe/p4.tex
new file mode 100644
index 0000000..aebdff6
--- /dev/null
+++ b/p4/informe/p4.tex
@@ -0,0 +1,197 @@
+\documentclass[11pt,a4paper]{article}
+\usepackage[utf8x]{inputenc}
+\usepackage[catalan]{babel}
+\usepackage{fancyhdr}
+\usepackage{graphicx}
+\usepackage[labelfont=bf]{caption}
+\usepackage{siunitx}
+\usepackage{geometry}
+\geometry{top=25mm}
+\usepackage{amsmath}
+\usepackage{booktabs}
+\usepackage{chemformula}
+\usepackage{multicol}
+%\usepackage{hyperref} % @TODO: Remove when generating the PDF
+
+\usepackage{pgfplotstable}
+\pgfplotsset{compat=1.16}
+\pgfplotstableset{
+empty cells with={--}, % replace empty cells with ’--’
+every head row/.style={before row=\toprule,after row=\midrule},
+every last row/.style={after row=\bottomrule}%,
+%every even row/.style={
+%before row={\rowcolor[gray]{0.9}}}, % Add this for stylish tables ;)
+%begin table=\begin{longtable},
+%end table=\end{longtable}
+}
+
+\setlength{\parskip}{1em}
+
+\pagestyle{fancy}
+\fancyhf{}
+\rhead{Adrià Vilanova Martínez}
+\lhead{Pràctica 4}
+\rfoot{\thepage}
+
+%%%% Title %%%%
+\title{\vspace{-2ex}Pràctica 4. Mesura de la calor: calibratge d'un calorímetre\vspace{-2ex}}
+\author{Adrià Vilanova Martínez (T1B)\vspace{-2ex} }
+\date{Tardor 2020}
+
+\begin{document}
+ \maketitle
+
+ \section{Objectiu de la pràctica}
+
+ L'objectiu de la pràctica és calibrar el calorímetre B, és a dir, determinar quina és la sensibilitat del calorímetre depenent de la temperatura. Per això un tercer ha realitzat al laboratori l'experiment 4 descrit al guió de pràctiques de Termodinàmica, i en aquest informe s'analitzaran els resultats obtinguts.
+
+ En aquest cas el calorímetre és un calorímetre diferencial, que és un aparell experimental que permet mesurar la diferència de calor que existeix entre dos sistemes termodinàmics. Calibrar-lo és necessari per poder realitzar aquestes mesures. En el futur el calibratge realitzat en aquesta pràctica s'usarà per usar el mateix calorímetre en una altra pràctica.
+
+ \section{Gràfiques}
+
+ L'experiment s'ha realitzat 5 vegades. S'han graficat 2 gràfiques per cada vegada: les gràfiques de les figures 1-5 mostren el senyal calorimètric mesurat i la línia base, i les de les figures 6-10 mostren el senyal calorimètric corregit restant-li la deriva, a partir de la línia base.
+
+ \begin{center}
+ \begin{minipage}{\textwidth}
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura1.tex}
+ \captionof{figure}{Experiment 1.}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura2.tex}
+ \captionof{figure}{Experiment 2.}
+ \end{center}
+ \end{multicols}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura3.tex}
+ \captionof{figure}{Experiment 3.}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura4.tex}
+ \captionof{figure}{Experiment 4.}
+ \end{center}
+ \end{multicols}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura5.tex}
+ \captionof{figure}{Experiment 5.}
+ \end{center}
+
+ \columnbreak
+
+ \begin{center}
+ \end{center}
+ \end{multicols}
+ \end{minipage}
+ \end{center}
+
+ \begin{center}
+ \begin{minipage}{\textwidth}
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura1_wd.tex}
+ \captionof{figure}{Experiment 1.}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura2_wd.tex}
+ \captionof{figure}{Experiment 2.}
+ \end{center}
+ \end{multicols}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura3_wd.tex}
+ \captionof{figure}{Experiment 3.}
+ \end{center}
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura4_wd.tex}
+ \captionof{figure}{Experiment 4.}
+ \end{center}
+ \end{multicols}
+
+ \begin{multicols}{2}
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/mesura5_wd.tex}
+ \captionof{figure}{Experiment 5.}
+ \end{center}
+
+ \columnbreak
+
+ \begin{center}
+ \end{center}
+ \end{multicols}
+ \end{minipage}
+ \end{center}
+
+ \section{Taula de dades}
+
+ \begin{center}
+ \centering
+ \pgfplotstabletypeset[
+ columns/0/.style={column name=$Y \, (\si{\milli\volt})$, fixed, fixed zerofill, precision=2},
+ columns/1/.style={column name=$T \, (\si{\celsius})$, fixed, fixed zerofill, precision=1},
+ columns/2/.style={column name=$I \, (\si{\milli\ampere})$, fixed, fixed zerofill, precision=1},
+ columns/3/.style={column name=$S \, (\si{\milli\meter})$, fixed, fixed zerofill, precision=2},
+ columns/4/.style={column name=$\delta(S) \, (\si{\per\ampere})$, fixed, fixed zerofill, precision=2}
+ ]
+ {../data/finaldata.dat}
+
+ \captionof{table}{Dades experimentals recollides i càlcul de $S$ i la seva incertesa.}
+ \end{center}
+
+ L'error relatiu d'S s'ha calculat de la següent manera: \[ \varepsilon_{S} = \varepsilon_{Y} + \varepsilon_{V^{-1}} + \varepsilon_{I^{-1}} = \varepsilon_{Y} + \varepsilon_{V} + \varepsilon_{I} \implies \delta(S) = |s| ( \varepsilon_{Y} + \varepsilon_{V} + \varepsilon_{I} ) \] on $\delta(x)$ és l'error absolut de $x$ i $\varepsilon_{x}$ és l'arror relatiu de $x$.
+
+ Finalment s'han fitat els valors $(T, S)$ de la taula per obtenir una expressió de $S$ depenent de $T$: \[ S(T) = a T + b \]
+
+ \begin{center}
+ \centering
+ \vspace{-2em}
+ \input{../output/finalgraph.tex}
+ \captionof{figure}{Relació entre $S$ i $T$.}
+ \end{center}
+
+ Del fit s'han obtingut els següents valors d'$a$ i $b$: \[ \begin{cases}
+ a = (0.0004 \pm 0.0002) \, \si{\per\celsius\per\ampere} \\
+ b = (0.1 \pm 0.3) \, \si{\per\ampere}
+ \end{cases} \]
+
+ \newpage
+
+ \section{Conclusió}
+ S'ha determinat que $S(T) = -0.0004 T + 0.1$. No obstant, s'ha de tenir en compte que $r = -0.6$, i per tant les dades no estan molt correlacionades. Per aquest motiu, la regressió lineal trobada no és una bona aproximació i per tant la calibració del calorímetre trobada no és suficientment bona.
+
+ Això és degut al fet que no es pot trobar amb exactitud la línia base de les dades del senyal calorimètric, ja que per un motiu desconegut les línies base del principi i el final d'algunes de les vegades que s'han realitzat els experiments no es poden aproximar bé per un polinomi, i per tant la correcció de la deriva no es pot realitzar correctament.
+
+ A part, és destacable també el fet que les barres d'error corresponents a $S$ són molt grans, i això tampoc permet garantir que la regressió lineal sigui una bona calibració del calorímetre. Es podrien rebaixant les fites de les incerteses quan es calcula la propagació d'errors de variables independents, però tot i així les barres d'error continuarien sent igual de grans.
+
+ Així doncs, s'hauria de repetir l'experiment un altre cop i analitzar les dades de nou per tal d'obtenir una calibració correcta del calorímetre B.
+
+\end{document}
diff --git a/p4/rawdata/IMPORTANT LLEGIR PRIMER.txt b/p4/rawdata/IMPORTANT LLEGIR PRIMER.txt
new file mode 100644
index 0000000..115bfb0
--- /dev/null
+++ b/p4/rawdata/IMPORTANT LLEGIR PRIMER.txt
@@ -0,0 +1,12 @@
+Aquí teniu mesures pel calibratge de tres tres calorimetres, etiquetats de A a C. Heu d'escollir un dels tres i analitzar les dades.
+
+Cada carpeta conté 5 mesures a temperatures gradualment més baixes. Així, per exemple, "Mesura 1 - T=24_8 - I=19_2.xls" correspon a la primera mesura, i on s'ha desconnectat la potència sumministrada a la resistència en el règim estacionari amb l'amperímetre marcant 19.2 mA i el termòmetre 24.8 ºC.
+
+Recordeu que, en el calibratge, el voltatge sumministrat és sempre V=2V. La intensitat oscil·la lleugerament però és propera a 20 mA.
+
+Preneu 0.1 mA com a incertesa en intensitat, i 0.001 mV com incertesa en senyal calorimètric.
+
+SOBRE ELS FITXERS EXCEL:
+És possible que el vostre ordinador us demani d'instal·lar macros quan obriu els fitxers. Ignoreu el missatge o cancel·leu l'acció. Del fitxer Excel només voleu les dades, que estan en una pestanya "Dades" a la part inferior-esquerra.
+
+
diff --git "a/p4/rawdata/Mesura 1 - T=23_8 - I=19_1 \0501\051.xls" "b/p4/rawdata/Mesura 1 - T=23_8 - I=19_1 \0501\051.xls"
new file mode 100644
index 0000000..c9aeab9
--- /dev/null
+++ "b/p4/rawdata/Mesura 1 - T=23_8 - I=19_1 \0501\051.xls"
Binary files differ
diff --git a/p4/rawdata/Mesura 2 - T=9_8 - I=18_4.xls b/p4/rawdata/Mesura 2 - T=9_8 - I=18_4.xls
new file mode 100644
index 0000000..ffa2052
--- /dev/null
+++ b/p4/rawdata/Mesura 2 - T=9_8 - I=18_4.xls
Binary files differ
diff --git a/p4/rawdata/Mesura 3 - T=-0_2 - I=18_7.xls b/p4/rawdata/Mesura 3 - T=-0_2 - I=18_7.xls
new file mode 100644
index 0000000..61ef8a9
--- /dev/null
+++ b/p4/rawdata/Mesura 3 - T=-0_2 - I=18_7.xls
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diff --git a/p4/rawdata/Mesura 4 - T=-13_7 - I=17_9.xls b/p4/rawdata/Mesura 4 - T=-13_7 - I=17_9.xls
new file mode 100644
index 0000000..159061c
--- /dev/null
+++ b/p4/rawdata/Mesura 4 - T=-13_7 - I=17_9.xls
Binary files differ
diff --git a/p4/rawdata/Mesura 5 - T=-29_1 - I=18_1.xls b/p4/rawdata/Mesura 5 - T=-29_1 - I=18_1.xls
new file mode 100644
index 0000000..6dd3d99
--- /dev/null
+++ b/p4/rawdata/Mesura 5 - T=-29_1 - I=18_1.xls
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