Edits from meetings
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*.pdf
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*.pdf
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*.out
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*.bak
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*.bak
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main.synctex.gz
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@ -34,7 +34,10 @@ For the next step, we show that the variance of an estimate is small.$$\var{\est
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&= \big(\estTwo\big)^2\\
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&= \big(\estTwo\big)^2\\
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&=\sum_{\substack{
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&=\sum_{\substack{
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\wVec_1, \wVec_2,\\
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\wVec_1, \wVec_2,\\
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\wVecPrime_1, \wVecPrime_2 \in \pw}}\wIndParam{\wVec_1} \cdot \wIndParam{\wVec_2}\cdot\polarFunc{\wVec_1}\cdot\polarFunc{\wVec_2}\cdot\polarFunc{\wVecPrime_1}\cdot\polarFunc{\wVecPrime_2}
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\wVecPrime_1, \wVecPrime_2 \in \pw,\\
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\sketchHashParam{\wVec_1} = \sketchHashParam{\wVecPrime_1},\\
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\sketchHashParam{\wVec_2} = \sketchHashParam{\wVecPrime_2}
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}}\wIndParam{\wVec_1} \cdot \wIndParam{\wVec_2}\cdot\polarFunc{\wVec_1}\cdot\polarFunc{\wVec_2}\cdot\polarFunc{\wVecPrime_1}\cdot\polarFunc{\wVecPrime_2}
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\end{align}
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\end{align}
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# Fdb version 3
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["pdflatex"] 1559751491 "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex" "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.pdf" "macros" 1559751491
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"/etc/texmf/web2c/texmf.cnf" 1553542749 475 c0e671620eb5563b2130f56340a5fde8 ""
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.aux" 1559750938 8 a94a2480d3289e625eea47cd1b285758 ""
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex" 1559751491 12964 12dffb662fe2cb0b7979643f0a4f94fe ""
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"/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1551493644 34566 ab5be96bde1a5acfd4f881dbe566b5fb ""
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"/usr/share/texmf/web2c/texmf.cnf" 1551493644 34566 ab5be96bde1a5acfd4f881dbe566b5fb ""
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"/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1557114040 4228722 ce598736682bfb26027b7c98b9d0ec51 ""
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"macros.tex" 1559751491 12964 12dffb662fe2cb0b7979643f0a4f94fe ""
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(generated)
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"macros.log"
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.pdf"
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.log"
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macros.fls
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PWD /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds
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INPUT /etc/texmf/web2c/texmf.cnf
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INPUT /usr/share/texmf/web2c/texmf.cnf
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INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf
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INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt
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INPUT /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex
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OUTPUT /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.log
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macros.tex
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% -*- root: main.tex -*-
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% NOTATION
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% NOTATION
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\polarFuncSum}[1][]{\sum_{\substack{\wVecPrime ~|~ \\
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\newcommand{\polarFuncSum}[1][]{\sum_{\substack{\wVecPrime ~|~ \\
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\sketchHash\left[\wVecPrime\right] = j\\
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\sketchHash\left[\wVecPrime\right] = j\\
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{#1}}}\polarFunc{\wVecPrime}}
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{#1}}}\polarFunc{\wVecPrime}}
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\newcommand{\estimate}{\sum_{j \in \sketchCols} \sketchIj \circ \polarFuncSum }
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\newcommand{\estimate}{\sum_{j \in \sketchCols} \sketchIj \cdot \polarFuncSum }
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\newcommand{\estExpOne}{\sum_{\substack{j \in \sketchCols, \\
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\newcommand{\estExpOne}{\sum_{\substack{j \in \sketchCols, \\
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\wVec \in \pw ~|~\sketchHash\left[\wVec\right] = j}} \wIndicator{t} \cdot\polarFunc{\wVec} \circ \polarFuncSum}
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\wVec \in \pw ~|~\sketchHash\left[\wVec\right] = j}} \wIndicator{t} \cdot\polarFunc{\wVec} \cdot \polarFuncSum}
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\newcommand{\estTwo}{\sum_{\substack{j \in [B],\\
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\newcommand{\estTwo}{\sum_{\substack{j \in [B],\\
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\wVec \in \pw~|~ \sketchHash{i}[\wVec] = j,\\
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\wVec \in \pw~|~ \sketchHash{[\wVec]} = j,\\
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\wVec[w']\in \pw~|~ \sketchHash{i}[\wVec[w']] = j} } v_t[\wVec] \cdot s_i[\wVec] \cdot s_i[\wVec[w']]}
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\wVec[w']\in \pw~|~ \sketchHash{[\wVec[w']]} = j} } v_t[\wVec] \cdot s_i[\wVec] \cdot s_i[\wVec[w']]}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% COMMENTS
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% COMMENTS
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\newcommand{\zerosymbol}{\mathbbold{0}}
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\newcommand{\zerosymbol}{\mathbbold{0}}
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\newcommand{\multsymb}{\otimes}
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\newcommand{\addsymbol}{\oplus}
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\newcommand{\addormultsymbol}{\bigcirc}
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\newcommand{\monsymbol}{\ominus}
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\newcommand{\kDom}{K}
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# Fdb version 3
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/main.pdf"
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"/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/main.log"
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PWD /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/fxlri-5letters.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/fxlri-7letters.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxmi.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/rtxmi7.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/rtxr.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/txexs.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txsyb.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/txfonts/txsyc.pfb
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INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/txsys.pfb
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|
INPUT /usr/share/texlive/texmf-dist/fonts/type1/public/newtx/zxlri.pfb
|
BIN
main.synctex.gz
BIN
main.synctex.gz
Binary file not shown.
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Reference in a new issue