Difference between revisions of "Team:Tongji-Software/Template:Example Math"

 
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<span>$$\hat p=\sigma(\theta^T \cdot x_b)=\frac{1}{1+\mathbf{e}^{-{\theta^{T \cdot x_b}}}}$$</span>
 
<span>$$\hat p=\sigma(\theta^T \cdot x_b)=\frac{1}{1+\mathbf{e}^{-{\theta^{T \cdot x_b}}}}$$</span>
  
<span>\[f(r)= \frac{{e^{-\Delta{r}{G^{'\circ}}/RT}}}{1 + {e^{-\Delta{r}{G^{'\circ}}/RT}} + \sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} \]</span>
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<span>\[{\sum\nolimits_{{r^'}} {{{\rm{e}}^{ - {\Delta _{{r^'}}}{G^{' \circ /RT}}}}} }\]</span>
<span class="equation">\[f{(r)=}\frac{{e}}^{-{\Delta_r}{G^{'\circ/RT}}}{{{{1+}}{{{e}}^{-{\Delta _r}{G^{'\circ/RT}}}}+\sum{{r^'}\in{R_N}\backslash{{\left\{r\right\}}^{{{}}{{{e}}^{-{\Delta _r{G^{'\circ/RT}}}}}</span>
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<span>$$J(\theta)=-\frac{1}{m}\displaystyle\sum_{i=1}^m y^{(i)}\log(\hat p^{(i)})+(1-y^{(i)})\log(1-\hat p^{(i)})\\
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=-\frac{1}{m}\displaystyle\sum_{i=1}^m y^{(i)}\log(\sigma(-X_b^{(i)}\theta))+(1-y^{(i)})\log(1-\sigma(-X_b^{(i)}\theta))\\
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<span class="equation">\[f(r) = \frac{e^{-\Delta{r}{G^{'\circ}}/RT}}{{{1+}{e^{-\Delta{r}{G^{'\circ}}/RT}}+\sum r^'\in {R_N}\backslash{{\left\{r \right\}}^{{e^{-\Delta{r}{G^{'\circ}}/RT}}}} }}\]</span>
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<span class="middle">\[Max\left\{ {Ave(A),Ave(B),Ave(C),Ave(D)...} \right\} \]</span>
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Latest revision as of 17:00, 13 October 2018