diff --git a/.gitignore b/.gitignore index bbb569f..90a62bc 100644 --- a/.gitignore +++ b/.gitignore @@ -4,3 +4,4 @@ *.pdf *.out *.bak +main.synctex.gz diff --git a/analysis.tex b/analysis.tex index d6136cd..2ec124c 100644 --- a/analysis.tex +++ b/analysis.tex @@ -34,7 +34,10 @@ For the next step, we show that the variance of an estimate is small.$$\var{\est &= \big(\estTwo\big)^2\\ &=\sum_{\substack{ \wVec_1, \wVec_2,\\ - \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} + \wVecPrime_1, \wVecPrime_2 \in \pw,\\ + \sketchHashParam{\wVec_1} = \sketchHashParam{\wVecPrime_1},\\ + \sketchHashParam{\wVec_2} = \sketchHashParam{\wVecPrime_2} + }}\wIndParam{\wVec_1} \cdot \wIndParam{\wVec_2}\cdot\polarFunc{\wVec_1}\cdot\polarFunc{\wVec_2}\cdot\polarFunc{\wVecPrime_1}\cdot\polarFunc{\wVecPrime_2} \end{align} diff --git a/macros.fdb_latexmk b/macros.fdb_latexmk new file mode 100644 index 0000000..31c23d4 --- /dev/null +++ b/macros.fdb_latexmk @@ -0,0 +1,13 @@ +# Fdb version 3 +["pdflatex"] 1559751491 "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex" "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.pdf" "macros" 1559751491 + "/etc/texmf/web2c/texmf.cnf" 1553542749 475 c0e671620eb5563b2130f56340a5fde8 "" + "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.aux" 1559750938 8 a94a2480d3289e625eea47cd1b285758 "" + "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex" 1559751491 12964 12dffb662fe2cb0b7979643f0a4f94fe "" + "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1551493644 34566 ab5be96bde1a5acfd4f881dbe566b5fb "" + "/usr/share/texmf/web2c/texmf.cnf" 1551493644 34566 ab5be96bde1a5acfd4f881dbe566b5fb "" + "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1557114040 4228722 ce598736682bfb26027b7c98b9d0ec51 "" + "macros.tex" 1559751491 12964 12dffb662fe2cb0b7979643f0a4f94fe "" + (generated) + "macros.log" + "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.pdf" + "/home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.log" diff --git a/macros.fls b/macros.fls new file mode 100644 index 0000000..74a229d --- /dev/null +++ b/macros.fls @@ -0,0 +1,7 @@ +PWD /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds +INPUT /etc/texmf/web2c/texmf.cnf +INPUT /usr/share/texmf/web2c/texmf.cnf +INPUT /usr/share/texlive/texmf-dist/web2c/texmf.cnf +INPUT /var/lib/texmf/web2c/pdftex/pdflatex.fmt +INPUT /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.tex +OUTPUT /home/okennedy/Cloud/Papers/Mimir-SketchingWorlds/macros.log diff --git a/macros.tex b/macros.tex index 0373bb3..ec91a71 100644 --- a/macros.tex +++ b/macros.tex @@ -1,3 +1,4 @@ +% -*- root: main.tex -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % NOTATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -32,12 +33,12 @@ \newcommand{\polarFuncSum}[1][]{\sum_{\substack{\wVecPrime ~|~ \\ \sketchHash\left[\wVecPrime\right] = j\\ {#1}}}\polarFunc{\wVecPrime}} -\newcommand{\estimate}{\sum_{j \in \sketchCols} \sketchIj \circ \polarFuncSum } +\newcommand{\estimate}{\sum_{j \in \sketchCols} \sketchIj \cdot \polarFuncSum } \newcommand{\estExpOne}{\sum_{\substack{j \in \sketchCols, \\ - \wVec \in \pw ~|~\sketchHash\left[\wVec\right] = j}} \wIndicator{t} \cdot\polarFunc{\wVec} \circ \polarFuncSum} + \wVec \in \pw ~|~\sketchHash\left[\wVec\right] = j}} \wIndicator{t} \cdot\polarFunc{\wVec} \cdot \polarFuncSum} \newcommand{\estTwo}{\sum_{\substack{j \in [B],\\ - \wVec \in \pw~|~ \sketchHash{i}[\wVec] = j,\\ - \wVec[w']\in \pw~|~ \sketchHash{i}[\wVec[w']] = j} } v_t[\wVec] \cdot s_i[\wVec] \cdot s_i[\wVec[w']]} + \wVec \in \pw~|~ \sketchHash{[\wVec]} = j,\\ + \wVec[w']\in \pw~|~ \sketchHash{[\wVec[w']]} = j} } v_t[\wVec] \cdot s_i[\wVec] \cdot s_i[\wVec[w']]} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % COMMENTS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -234,7 +235,7 @@ \newcommand{\zerosymbol}{\mathbbold{0}} 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