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Presentations / Gambit / 07_05_2019 / mchrzasz.tex
@Marcin Chrzaszcz Marcin Chrzaszcz on 6 Aug 2019 26 KB large updatE
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  1. \documentclass[11 pt,xcolor={dvipsnames,svgnames,x11names,table}]{beamer}
  2.  
  3. \usepackage[english]{babel}
  4. \usepackage{polski}
  5.  
  6.  
  7. \usetheme[
  8. 	bullet=circle,		% Other option: square
  9. 	bigpagenumber,		% circled page number on lower right
  10. 	topline=true,			% colored bar at the top of the frame
  11. 	shadow=false,			% Shading for beamer blocks
  12. 	watermark=BG_lower,	% png file for the watermark
  13. 	]{Flip}
  14.  
  15. %\logo{\kern+1.em\includegraphics[height=1cm]{SHiP-3_LightCharcoal}}
  16.  
  17.  
  18. \usepackage[lf]{berenis}
  19. \usepackage[LY1]{fontenc}
  20. \usepackage[utf8]{inputenc}
  21.  
  22. \usefonttheme{professionalfonts}
  23. \usepackage[no-math]{fontspec}
  24. \defaultfontfeatures{Mapping=tex-text}	% This seems to be important for mapping glyphs properly
  25.  
  26. \setmainfont{Gillius ADF}			% Beamer ignores "main font" in favor of sans font
  27. \setsansfont{Gillius ADF}			% This is the font that beamer will use by default
  28. % \setmainfont{Gill Sans Light}		% Prettier, but harder to read
  29.  
  30. \setbeamerfont{title}{family=\fontspec{Gillius ADF}}
  31.  
  32. \input t1augie.fd
  33.  
  34. %\newcommand{\handwriting}{\fontspec{augie}} % From Emerald City, free font
  35. %\newcommand{\handwriting}{\usefont{T1}{fau}{m}{n}} % From Emerald City, free font
  36. % \newcommand{\handwriting}{}	% If you prefer no special handwriting font or don't have augie
  37.  
  38. %% Gill Sans doesn't look very nice when boldfaced
  39. %% This is a hack to use Helvetica instead
  40. %% Usage: \textbf{\forbold some stuff}
  41. %\newcommand{\forbold}{\fontspec{Arial}}
  42.  
  43. \usepackage{graphicx}
  44. \usepackage[export]{adjustbox}
  45.  
  46. \usepackage{amsmath}
  47. \usepackage{amsfonts}
  48. \usepackage{amssymb}
  49. \usepackage{bm}
  50. \usepackage{colortbl}
  51. \usepackage{mathrsfs} 			% For Weinberg-esque letters
  52. \usepackage{cancel}				% For "SUSY-breaking" symbol
  53. \usepackage{slashed}            % for slashed characters in math mode
  54. \usepackage{bbm}                % for \mathbbm{1} (unit matrix)
  55. \usepackage{amsthm}				% For theorem environment
  56. \usepackage{multirow}			% For multi row cells in table
  57. \usepackage{arydshln} 			% For dashed lines in arrays and tables
  58. \usepackage{siunitx}
  59. \usepackage{xhfill}
  60. \usepackage{grffile}
  61. \usepackage{textpos}
  62. \usepackage{subfigure}
  63. \usepackage{tikz}
  64.  
  65. %\usepackage{hepparticles}
  66. \usepackage[italic]{hepparticles}
  67.  
  68. \usepackage{hepnicenames}
  69.  
  70. % Drawing a line
  71. \tikzstyle{lw} = [line width=20pt]
  72. \newcommand{\topline}{%
  73.   \tikz[remember picture,overlay] {%
  74.     \draw[crimsonred] ([yshift=-23.5pt]current page.north west)
  75.              -- ([yshift=-23.5pt,xshift=\paperwidth]current page.north west);}}
  76.  
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  78.  
  79. % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % %
  80. \usepackage{tikzfeynman}		% For Feynman diagrams
  81. \usetikzlibrary{arrows,shapes}
  82. \usetikzlibrary{trees}
  83. \usetikzlibrary{matrix,arrows} 				% For commutative diagram
  84. % http://www.felixl.de/commu.pdf
  85. \usetikzlibrary{positioning}				% For "above of=" commands
  86. \usetikzlibrary{calc,through}				% For coordinates
  87. \usetikzlibrary{decorations.pathreplacing}  % For curly braces
  88. % http://www.math.ucla.edu/~getreuer/tikz.html
  89. \usepackage{pgffor}							% For repeating patterns
  90.  
  91. \usetikzlibrary{decorations.pathmorphing}	% For Feynman Diagrams
  92. \usetikzlibrary{decorations.markings}
  93. \tikzset{
  94. 	% >=stealth', %%  Uncomment for more conventional arrows
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  112. 	bigvector/.style={decorate, decoration={snake,amplitude=4pt}, draw},
  113. }
  114.  
  115. % TIKZ - for block diagrams,
  116. % from http://www.texample.net/tikz/examples/control-system-principles/
  117. % \usetikzlibrary{shapes,arrows}
  118. \tikzstyle{block} = [draw, rectangle,
  119. minimum height=3em, minimum width=6em]
  120.  
  121.  
  122.  
  123.  
  124. \usetikzlibrary{backgrounds}
  125. \usetikzlibrary{mindmap,trees}	% For mind map
  126. \newcommand{\degree}{\ensuremath{^\circ}}
  127. \newcommand{\E}{\mathrm{E}}
  128. \newcommand{\TeV}{\mathrm{TeV}}
  129. \newcommand{\Var}{\mathrm{Var}}
  130. \newcommand{\Cov}{\mathrm{Cov}}
  131. \newcommand\Ts{\rule{0pt}{2.6ex}}       % Top strut
  132. \newcommand\Bs{\rule[-1.2ex]{0pt}{0pt}} % Bottom strut
  133.  
  134. \graphicspath{{images/}}	% Put all images in this directory. Avoids clutter.
  135.  
  136. % SOME COMMANDS THAT I FIND HANDY
  137. % \renewcommand{\tilde}{\widetilde} % dinky tildes look silly, dosn't work with fontspec
  138. \newcommand{\comment}[1]{\textcolor{comment}{\footnotesize{#1}\normalsize}} % comment mil	
  139. \newcommand{\Comment}[1]{\textcolor{Comment}{\footnotesize{#1}\normalsize}} % comment bold
  140. \newcommand{\COMMENT}[1]{\textcolor{COMMENT}{\footnotesize{#1}\normalsize}} % comment crazy bold
  141. \newcommand{\Alert}[1]{\textcolor{Alert}{#1}} % louder alert
  142. \newcommand{\ALERT}[1]{\textcolor{ALERT}{#1}} % loudest alert
  143. %% "\alert" is already a beamer pre-defined
  144. \newcommand*{\Scale}[2][4]{\scalebox{#1}{$#2$}}%
  145.  
  146. \def\Put(#1,#2)#3{\leavevmode\makebox(0,0){\put(#1,#2){#3}}}
  147.  
  148. \usepackage{gmp}
  149. \usepackage[final]{feynmp-auto}
  150.  
  151. \usepackage[backend=bibtex,style=numeric-comp,firstinits=true]{biblatex}
  152. \bibliography{bib}
  153. \setbeamertemplate{bibliography item}[text]
  154.  
  155. \makeatletter\let\frametextheight\beamer@frametextheight\makeatother
  156.  
  157. % suppress frame numbering for backup slides
  158. % you always need the appendix for this!
  159. \newcommand{\backupbegin}{
  160. 	\newcounter{framenumberappendix}
  161. 	\setcounter{framenumberappendix}{\value{framenumber}}
  162. }
  163. \newcommand{\backupend}{
  164. 	\addtocounter{framenumberappendix}{-\value{framenumber}}
  165. 	\addtocounter{framenumber}{\value{framenumberappendix}}
  166. }
  167.  
  168.  
  169. \definecolor{links}{HTML}{2A1B81}
  170. %\hypersetup{colorlinks,linkcolor=,urlcolor=links}
  171.  
  172. % For shapo's formulas:
  173. \def\lsi{\raise0.3ex\hbox{$<$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
  174. \def\gsi{\raise0.3ex\hbox{$>$\kern-0.75em\raise-1.1ex\hbox{$\sim$}}}
  175. \newcommand{\lsim}{\mathop{\lsi}}
  176. \newcommand{\gsim}{\mathop{\gsi}}
  177. \newcommand{\wt}{\widetilde}
  178. %\newcommand{\ol}{\overline}
  179. \newcommand{\Tr}{\rm{Tr}}
  180. \newcommand{\tr}{\rm{tr}}
  181. \newcommand{\eqn}[1]{&\hspace{-0.7em}#1\hspace{-0.7em}&}
  182. \newcommand{\vev}[1]{\rm{$\langle #1 \rangle$}}
  183. \newcommand{\abs}[1]{\rm{$\left| #1 \right|$}}
  184. \newcommand{\eV}{\rm{eV}}
  185. \newcommand{\keV}{\rm{keV}}
  186. \newcommand{\GeV}{\rm{GeV}}
  187. \newcommand{\im}{\rm{Im}}
  188. \newcommand{\disp}{\displaystyle}
  189. \def\be{\begin{equation}}
  190. \def\ee{\end{equation}}
  191. \def\ba{\begin{eqnarray}}
  192. \def\ea{\end{eqnarray}}
  193. \def\d{\partial}
  194. \def\l{\left(}
  195. \def\r{\right)}
  196. \def\la{\langle}
  197. \def\ra{\rangle}
  198. \def\e{{\rm e}}
  199. \def\Br{{\rm Br}}
  200. \def\fixme{FIXME}
  201.  
  202.  
  203.  
  204. \def\ARROW{{\color{JungleGreen}{$\Rrightarrow$}}\xspace}
  205. \def\ARROWR{{\color{WildStrawberry}{$\Rrightarrow$}}\xspace}
  206.  
  207. \author{Marcin Chrzaszcz (CERN)}
  208. \institute{UZH}
  209. \title[FlavBit update]{FlavBit update}
  210.  
  211.  
  212. \begin{document}
  213. \tikzstyle{every picture}+=[remember picture]
  214.  
  215. {
  216. \setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
  217. \begin{frame}[c]%{\phantom{title page}}
  218. \begin{center}
  219. \begin{center}
  220. 	\begin{columns}
  221. 		\begin{column}{0.15\textwidth}
  222. {~}
  223. 		\end{column}
  224. 		\begin{column}{0.02\textwidth}
  225.                   {~}
  226.                   \end{column}
  227. 		\begin{column}{0.73\textwidth}
  228. 			 \bfseries \Huge {FlavBit update}
  229. 		\end{column}
  230.                 \begin{column}{0.02\textwidth}
  231.                   {~}
  232.                   \end{column}
  233.  
  234. 	\end{columns}
  235. \end{center}
  236. 	\quad
  237. 	\vspace{3em}
  238. \begin{columns}
  239. \begin{column}{0.44\textwidth}
  240. \flushright \vspace{-2.8em} {Florian Bernlochner\\ Jihyun Bhom\\  Marcin Chrzaszcz\\ Nazila Mahmoudi\\ Pat Scott}
  241.  
  242. %\flushright \vspace{-2.8em} {  Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
  243.  
  244.  
  245. \end{column}
  246. \begin{column}{0.53\textwidth}
  247. \hspace{2.0cm}
  248. \includegraphics[height=1.6cm]{cern}{~}
  249. \includegraphics[height=1.6cm]{ifj.png}                                                                                                                        \\{~}{~}{~}
  250. \includegraphics[height=0.8cm]{imperial.png}                                                                                                                        
  251.  
  252. \end{column}
  253. \end{columns}
  254.  
  255. \vspace{1em}
  256. 	\vspace{1.4cm}
  257.  
  258. 	
  259. 	\textcolor{normal text.fg!50!Comment}{Gambit collaboration meeting, June 6, 2019}
  260. \end{center}
  261. \end{frame}
  262. }
  263.  
  264.  
  265.  
  266.  
  267.  
  268. \begin{frame}\frametitle{FlavBit: the past}
  269.  
  270. \begin{center}
  271.  
  272. \begin{columns}
  273. \column{0.5\textwidth}
  274. \ARROW Theory predictions calculated via SuperIso v2.3.\\
  275. \ARROW Theoretical errors hard-coded and scaled if needed.\\
  276.  
  277. \column{0.5\textwidth}
  278. \ARROW Experimental results are stored in YAML files and read by \texttt{Flav\_reader}.\\
  279. \ARROW The class also store theoretical errors.\\
  280. \ARROW Errors were symmetrized and other nasty assumptions were made.
  281.  
  282.  
  283. \end{columns}
  284.  
  285. \begin{exampleblock}{Future}
  286. Each of the elements of the code is there and we just need to put them together inside Gambit.
  287. \end{exampleblock}
  288.  
  289.  
  290. \end{center}
  291. \end{frame}
  292.  
  293.  
  294.  
  295.  
  296.  
  297. \begin{frame}\frametitle{FlavBit: present and future}
  298.  
  299. \begin{center}
  300.  
  301. \begin{columns}
  302. \column{0.5\textwidth}
  303. \ARROW Theory predictions calculated via SuperIso v3+.\\
  304. \ARROW Program can calculate theoretical errors for each scanning point.\\
  305.  
  306. \column{0.5\textwidth}
  307. \ARROW Experimental results are stored in YAML files and read by external program called \texttt{HEPLike}.\\
  308. \ARROW Very nice features included.
  309.  
  310. \end{columns}
  311.  
  312. \end{center}
  313. \end{frame}
  314.  
  315.  
  316.  
  317.  
  318. \iffalse
  319.  
  320.  
  321.  
  322.  
  323. \begin{frame}\frametitle{HEP results}
  324. \ARROW How do we publish results?
  325. \begin{columns}
  326. \column{0.35\textwidth}
  327. \includegraphics[width=0.95\textwidth]{images/arxiv.png}\\
  328. \pause
  329. \begin{align*}
  330. R_K=0.846^{+0.060 +0.016}_{-0.054 - 0.014}
  331. \end{align*}
  332.  
  333. \pause
  334. \column{0.65\textwidth}
  335. \begin{center}
  336. \includegraphics[angle=-90,width=0.5\textwidth]{images/FigS8.pdf}\\
  337. \pause
  338. \includegraphics[width=0.75\textwidth]{images/hepdata.png}
  339. \end{center}
  340.  
  341.  
  342. \end{columns}
  343.  
  344.  
  345. \end{frame}
  346.  
  347.  
  348.  
  349.  
  350.  
  351. \begin{frame}\frametitle{HEP results}
  352. \ARROW How are the results used?
  353. \begin{columns}
  354. \column{0.5\textwidth}
  355.  
  356. \ARROWR Correlations are neglected
  357. \includegraphics[width=0.75\textwidth]{{images/Table_12}.pdf}
  358.  
  359.  
  360. \ARROWR Non Linear effects are forgotten
  361. \includegraphics[angle=-90,width=0.75\textwidth]{{images/example}.pdf}
  362.  
  363.  
  364.  
  365. \column{0.5\textwidth}
  366.  
  367. \ARROWR Errors are being symmetrized
  368. \includegraphics[angle=-90,width=0.75\textwidth]{{images/Fig62aS}.pdf}
  369.  
  370. {~}\\{~}\\
  371. \end{columns}
  372.  
  373.  
  374. \end{frame}
  375.  
  376.  
  377. \begin{frame}\frametitle{HEP results}
  378. \ARROW How are the results used?\\{~}\\
  379.  
  380. \ARROWR Interpreting Upper limits [HLFAV, 90\% UL]:
  381. \begin{align*}
  382. \mathcal{B} (\tau \to \mu \mu e) < 9.9 \times 10^{-9}
  383. \end{align*}
  384. \ARROW People interpret this assuming it's a gaussian centered around $0$ and width $\frac{9.9\times 10^{-9}}{1.64} $.\\
  385. \ARROW Usually a full p-value scan is published: 
  386. \begin{columns}
  387. \column{0.5\textwidth}
  388. \includegraphics[width=0.75\textwidth]{{images/180}.png}
  389.  
  390. \column{0.5\textwidth}
  391. \includegraphics[width=0.75\textwidth]{{images/dupa}.png}
  392.  
  393.  
  394. \end{columns}
  395. \ARROW The examples go on and on...
  396.  
  397.  
  398. \end{frame}
  399.  
  400.  
  401.  
  402.  
  403.  
  404. \begin{frame}\frametitle{The idea}
  405. \ARROW The theory and experimental community need to work together about proper interpretation.
  406. \pause
  407. \begin{center}
  408. \includegraphics[width=0.95\textwidth]{{images/kim}.jpg}
  409. \end{center}
  410.  
  411.  
  412.  
  413.  
  414.  
  415. \end{frame}
  416.  
  417. \fi
  418.  
  419. \begin{frame}\frametitle{HEPLike}
  420.  
  421. \ARROW High Energy Physics Likelihood (HEPLike).
  422. \begin{itemize}
  423. \item Open source software.
  424. \item With separate database of measurements.
  425. \item Statistics library.
  426. \item Can be interfaced with existing codes.
  427. \end{itemize}
  428. \ARROW It constructs the experimental likelihoods for you!\\
  429. \ARROW Does work with both the $\chi^2$ and (log-)likelihood fits.\\
  430. \ARROW Useful utilities for creating citations and database search.
  431. \end{frame}
  432.  
  433.  
  434. \begin{frame}\frametitle{HEPLike}
  435.  
  436. \ARROW The are couple of measurement types:
  437. \begin{itemize}                                                                                                                                                                                                                                                                                                                
  438. \item Upper limits,                                                                                                                                                                                                                                                                                                            
  439. \item Single measurement with symmetric uncertainty,                                                                                                                                                                                                                                                                           
  440. \item Single measurement with asymmetric uncertainty,                                                                                                                                                                                                                                                                          
  441. \item Multiple measurements with symmetric uncertainty,                                                                                                                                                                                                                                                                        
  442. \item Multiple measurements with asymmetric uncertainty,                                                                                                                                                                                                                                                                       
  443. \item One dimensional likelihood function,                                                                                                                                                                                                                                                                                     
  444. \item n-dimensional likelihood function.                                                                                                                                                                                                                                                                                       
  445. \end{itemize}                                                                                                                                                                                                                                                                                                                  
  446.                                                                      
  447.  
  448. \begin{alertblock}{Bonus}
  449. In addition we provide a way for the future that the experiments can publish the dataset.
  450. \end{alertblock}
  451.  
  452. \end{frame}
  453.  
  454.  
  455. \begin{frame}\frametitle{HEPLike - code structure}
  456.  
  457. \begin{center}
  458. \includegraphics[width=0.99\textwidth]{images/diagram.png}                                                                                                                                                                                                                                                                       
  459.  
  460. \end{center}
  461.  
  462.  
  463.  
  464. \end{frame}
  465.  
  466.  
  467.  
  468.  
  469.  
  470.  
  471. \begin{frame}\frametitle{Measurement encoding, \texttt{Hl\_Data}}
  472.  
  473. \ARROW Measurements are stored in \texttt{YAML} file:
  474. \includegraphics[width=0.9\textwidth]{images/yaml.png}    \\                                                   
  475. \includegraphics[width=0.9\textwidth]{images/yaml2.png}                                                       
  476.  
  477.  
  478. \end{frame}
  479.  
  480.  
  481.  
  482.  
  483. \begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
  484.  
  485. \ARROW Example of published p-value scans:\\
  486. \begin{columns}
  487.  
  488. \column{0.4\textwidth}
  489.  
  490. \includegraphics[angle=-90,width=0.95\textwidth]{images/Bs2tautau.pdf}                                                                                                                                                                                                                                                                    
  491.  
  492. \column{0.6\textwidth}
  493. \ARROW Information coded as:
  494. \includegraphics[width=0.95\textwidth]{images/yaml3.png}
  495.  
  496. \end{columns}
  497.  
  498.  
  499.  
  500. \end{frame}
  501.  
  502.  
  503.  
  504. \begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
  505.  
  506. \begin{equation}                                                                                                                                                                                                                                                                                                               
  507. pdf(x) = \frac{1}{2^{1/2} \Gamma(1/2)} x^{1/2 -1} e ^{-x/2},                                                                                                                                                                                                                                                                   
  508. \end{equation}                                                                                                                                                                                                                                                                                                                 
  509. which had the cumulative distribution function defined as:                                                                                                                                                                                                                                                                     
  510. \begin{equation}                                                                                                                                                                                                                                                                                                               
  511. cdf(x)=\frac{1}{\Gamma(1/2) } \gamma(1/2,x/2).                                                                                                                                                                                                                                                                                 
  512. \end{equation}                                           
  513. In the above equations the $\Gamma(x)$ and $\gamma(k,x)$ correspond to Gamma and incomplete gamma functions.                                                                                                                                                                                                                   
  514. By revering the $cdf(x)$ one can obtain the $\chi^2$ value:                                                                                                                                                                                                                                                                      
  515. \begin{equation}                                                                                                                                                                                                                                                                                                               
  516. \chi^2=cdf^{-1}(1-p),                                                                                                                                                                                                                                                                                                          
  517. \end{equation}                                                                          
  518. and if needed the log-likelihood:
  519. \begin{equation}                                                                                                                                                                                                                                                                                                               
  520. -\log(\mathcal{L})= \frac{1}{2}\chi^2, \label{eq:wilks}                                                                                                                                                                                                                                                                        
  521. \end{equation}     
  522. \end{frame}
  523.  
  524.  
  525.  
  526.  
  527. \begin{frame}\frametitle{Single measurement, symmetric error, \texttt{HL\_Gaussian}}
  528.  
  529. \ARROW Well this is as simple as:
  530. \begin{center}
  531. \includegraphics[width=0.6\textwidth]{images/yaml4.png}
  532. \end{center}
  533. \ARROW The $\chi^2$ is simple:
  534. \begin{equation}                                                                                                                                                                                                                               
  535. \chi^2 = \frac{(x_{obs}-x)^{2}}{  \sigma_{stat}^{2}+ \sigma_{syst}^{2} },                                                                                                                                                                      
  536. \end{equation}                                                               
  537.  
  538. \ARROW Wilks theorem can be used to translate to (log-)likelihood.
  539.  
  540.    
  541. \end{frame}
  542.  
  543.  
  544.  
  545. \begin{frame}\frametitle{Single measurement, symmetric error, \texttt{HL\_Gaussian}}
  546.  
  547. \ARROW Well this is as simple as:
  548. \begin{center}
  549. \includegraphics[width=0.6\textwidth]{images/yaml4.png}
  550. \end{center}
  551. \ARROW The $\chi^2$ is simple:
  552. \begin{equation}                                                                                                                                                                                                                               
  553. \chi^2 = \frac{(x_{obs}-x)^{2}}{  \sigma_{stat}^{2}+ \sigma_{syst}^{2} },                                                                                                                                                                      
  554. \end{equation}                                                               
  555.  
  556. \ARROW Wilks theorem can be used to translate to (log-)likelihood.
  557.  
  558.    
  559. \end{frame}
  560.  
  561.  
  562.  
  563.  
  564. \begin{frame}\frametitle{Multiple measurement, symmetric error, \texttt{HL\_nDimGaussian}}
  565.  
  566. \ARROW You need to pass two arguments:
  567. \begin{center}
  568. \includegraphics[width=0.6\textwidth]{images/yaml5.png}
  569. \end{center}
  570. \ARROW From this one constructs the covariance matrix, and evaluates the $\chi^2$:                                                        
  571. \begin{align}                                                                                                                                                                                                                                  
  572. \chi^2 =  V^{T} {\rm Cov}^{-1} V,\label{eq:chi2ndim}                                                                                                                                                                                           
  573. \end{align}                                            
  574.  
  575.    
  576. \end{frame}
  577.  
  578.  
  579. \begin{frame}\frametitle{Measurement, asymmetric error, \texttt{HL\_BifurGaussian}, \texttt{HL\_ndimBifurGaussian}}
  580.  
  581. \ARROW You need to pass two arguments:
  582. \begin{center}
  583. \includegraphics[width=0.6\textwidth]{images/yaml6.png}
  584. \end{center}   
  585.  
  586. \ARROW We choose to interpret this as Bifurcated Gaussian:
  587.  
  588.    \begin{align}                                                                                                        
  589. {\rm Cov}_{i,j}=                                                                                                     
  590. \begin{cases}                                                                                                        
  591. {\rm Corr}_{i,j}~\sigma^{i}_+ \sigma^{j}_+, & \text{if } x^i \geq x^i_{obs} \text{ and }  x^j \geq x^j_{obs} \\      
  592. {\rm Corr}_{i,j}~\sigma^{i}_+ \sigma^{j}_-, & \text{if } x^i \geq x^i_{obs} \text{ and }  x^j < x^j_{obs} \\         
  593. {\rm Corr}_{i,j}~\sigma^{i}_- \sigma^{j}_+, & \text{if } x^i < x^i_{obs} \text{ and }  x^j \geq x^j_{obs} \\         
  594. {\rm Corr}_{i,j}~\sigma^{i}_- \sigma^{j}_-, & \text{if } x^i < x^i_{obs} \text{ and }  x^j < x^j_{obs} \\            
  595. \end{cases}                                                                                                          
  596. \end{align}                                                                                                          
  597.  
  598.    
  599. \end{frame}
  600.  
  601.  
  602.  
  603.  
  604. \begin{frame}\frametitle{Likelihoods, \texttt{HL\_ProfLikelihood}, \texttt{HL\_nDimLikelihood}}
  605.    
  606. \ARROW Here we add just the location of \texttt{ROOT} object.\\
  607. \begin{columns}
  608. \column{0.7\textwidth}
  609.   \begin{center}
  610. \includegraphics[width=0.9\textwidth]{images/yaml7.png}\\
  611. \includegraphics[width=0.9\textwidth]{images/yaml8.png}
  612. \end{center}  
  613.  
  614. \ARROW This is the best way to publish results!!!\\
  615. \ARROW The problem is in what way one should publish the higher dim likelihoods?
  616.  
  617.    
  618. \column{0.3\textwidth}
  619. \includegraphics[angle=-90,width=0.95\textwidth]{images/Fig2-S.pdf}\\
  620. \includegraphics[angle=-90,width=0.95\textwidth]{images/Fig21.pdf}
  621. \end{columns}   
  622.    
  623.    
  624.    
  625.    
  626.    
  627. \end{frame}
  628.  
  629.  
  630.  
  631.  
  632.  
  633. \begin{frame}\frametitle{Publishing data \texttt{HL\_ExpData}}
  634.    
  635. \ARROW The \texttt{YAML} entry:
  636.  
  637.   \includegraphics[width=0.5\textwidth]{images/yaml9.png}\\
  638.    \ARROW Set the PDF you want to fit:\\ \texttt{double (*fun)(vector<double> par , vector<double> point)}\\
  639.    \ARROW The program will evaluate the (log-)likelihood on the whole dataset for given parameters.\\
  640.    \ARROW You only need a scanning tools and you are done.
  641.    
  642.    
  643. \end{frame}
  644.  
  645.  
  646. \begin{frame}\frametitle{Useful functions}
  647.  
  648.  
  649.    
  650. \ARROW Search for measurement you need:
  651. \begin{center}
  652. \includegraphics[width=0.9\textwidth]{images/example.png}
  653. \end{center}
  654.  
  655.  
  656.    
  657. \ARROW Create citation file:
  658. \begin{center}
  659. \includegraphics[width=0.9\textwidth]{images/example2.png}
  660. \end{center}
  661.  
  662.    
  663. \end{frame}
  664.  
  665.  
  666. \begin{frame}\frametitle{Other things in the pipeline, a bit lost but need to reactivated}
  667.  
  668. \ARROW Backending \texttt{flavio}.\\
  669. \ARROW Backending \texttt{EOS}.\\
  670.  
  671.  
  672.    
  673. \end{frame}
  674.  
  675.  
  676.  
  677.  
  678. \iffalse
  679. \begin{frame}\frametitle{Check it out}
  680.  
  681. \ARROW The HEPLike code:\\
  682. \url{https://github.com/mchrzasz/HEPLike}
  683.   
  684. \ARROW The HEPLike database:\\
  685. \url{https://github.com/mchrzasz/HEPLikeData}
  686.   
  687. \begin{alertblock}{}
  688. Don't be shy! Give it a spin. Feedback is welcomed.
  689. \end{alertblock}
  690.   \pause
  691.   
  692.   
  693.   \begin{exampleblock}{}
  694.   \begin{center}
  695.     Thank you for your attention
  696.  
  697.   \end{center}
  698.   
  699.   \end{exampleblock}
  700.   
  701.    
  702. \end{frame}
  703. \fi
  704.  
  705. \backupbegin
  706.  
  707. \begin{frame}\frametitle{Backup}
  708. \topline
  709.  
  710. \end{frame}
  711.  
  712. \backupend
  713.  
  714. \end{document}