March 14, 2010
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 | \documentclass [12pt,table]{beamer} \usepackage {hyperref} % For fancy math \usepackage {amsmath} % color theme \usetheme {psu} \usecolortheme [RGB={0,38,93}]{structure} \def \softness {0.4} \definecolor {softblue}{rgb}{ \softness , \softness ,1} \renewcommand { \emph }[1]{ \textit { \textcolor {softblue}{#1}}} \definecolor {darkgreen}{rgb}{0.2, 0.7, 0.5} \newcommand { \paper }[1]{ \textit { \textcolor {darkgreen}{#1}}} % For fancy footnotes \renewcommand { \thefootnote }{ \fnsymbol {footnote}} % For fancy fonts \usepackage {mathspec} \usepackage {fontspec} \defaultfontfeatures {Scale=MatchLowercase} \setmainfont [Mapping=tex-text]{Hoefler Text} %\setsansfont[Mapping=tex-text]{Candara} \setsansfont [Mapping=tex-text]{Myriad Pro} %\setsansfont[Mapping=tex-text]{Comic Sans MS} %\setmonofont{Courier} \setmonofont {Monaco} % For fancy picture \usepackage {tikz} %\usepackage{preamble} \usepackage {xspace} \newcommand { \LLL }{Lov \ 'asz Local Lemma \xspace } \begin {document} \title {A Constructive Proof of the Lov \ 'asz Local Lemma} \subtitle {Robin Moser, STOC 2009} \author {Youngtae Youn} \institute {CSE Dept. Penn State} \date {September 28, 2009} %%% \begin {frame} \frametitle { \LLL : Lov \ 'asz and Erd \H {o}s in 1975} \begin {itemize} \item What if bad events are \alert {not} independent? \begin {itemize} \item Bad events are \emph {mostly} independent from one another. \item Bad event are \alert {not} individually too likely to occur. \end {itemize} Still, $ \Pr [ \text {none of the bad events will occur}] & gt ; 0$. \end {itemize} \begin {block}{ \LLL (Symmetric Case)} \begin {enumerate} \item $ \Pr [bad_i] \leq \emph {p}$ for all $1 \leq i \leq n$. \item Each $bad_i$ depends on other \emph {$d$} bad events. \item $e \cdot p \cdot (d+1) \leq 1$ where $ \emph {e}=2.7182 \cdots $ \end {enumerate} \vspace {-4mm} \begin {center} Then, $ \Pr [ \text {none of the bad events will occur}] & gt ; 0$. \end {center} \end {block} \begin {itemize} \item dictionary definition of \emph {local}: affecting or limited to part of a whole. \item The bound in (3) is \alert {tight}. \item We will prove for the \emph {loose} bound $4pd \leq 1$. \end {itemize} \end {frame} \end {document} |
How to convert PDF into PNG
convert -density 600x600 -resize 800x600 -quality 90 myriad.pdf myriad.png |
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