Commit f9b5b4f4 by xiaotong

updates of section 3

parent 19badf54
......@@ -112,13 +112,13 @@
% CHAPTERS
%----------------------------------------------------------------------------------------
\include{Chapter1/chapter1}
\include{Chapter2/chapter2}
%\include{Chapter1/chapter1}
%\include{Chapter2/chapter2}
\include{Chapter3/chapter3}
\include{Chapter4/chapter4}
\include{Chapter5/chapter5}
\include{Chapter6/chapter6}
\include{ChapterAppend/chapterappend}
%\include{Chapter4/chapter4}
%\include{Chapter5/chapter5}
%\include{Chapter6/chapter6}
%\include{ChapterAppend/chapterappend}
......
......@@ -3824,7 +3824,7 @@ s.t. $\forall t_y: \sum_{s_x} f(s_x|t_y) =1 $ & \\
\begin{eqnarray}
\frac{\partial L(f,\lambda)}{\partial f(s_u|t_v)} & = & \frac{\partial \big[ \frac{\epsilon}{(l+1)^{m}} \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i) \big]}{\partial f(s_u|t_v)} - \nonumber \\
& & \frac{\partial \big[ \sum_{t_y} \lambda_{t_y} (\sum_{s_x} f(s_x|t_y) -1) \big]}{\partial f(s_u|t_v)} \nonumber \\
& = & \frac{\epsilon}{(l+1)^{m}} \cdot \frac{\partial \big[ \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_{a_j}) \big]}{\partial f(s_u|t_v)} - \lambda_{t_v} \nonumber
& = & \frac{\epsilon}{(l+1)^{m}} \cdot \frac{\partial \big[ \prod\limits_{j=1}^{m} \sum\limits_{i=0}^{l} f(s_j|t_i) \big]}{\partial f(s_u|t_v)} - \lambda_{t_v} \nonumber
\end{eqnarray}
\vspace{-0.3em}
......
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