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>\[f{\rm{(r) = }}\frac{{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}{{{\rm{ 1 + }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}} + {\rm{ }}\sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} }}\]</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>
 
<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>
 
<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>
 
  <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)})\\
 
  <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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<span class="middle">\[Max\left\{ {Ave(A),Ave(B),Ave(C),Ave(D)...} \right\} \]</span>
 
<span class="middle">\[Max\left\{ {Ave(A),Ave(B),Ave(C),Ave(D)...} \right\} \]</span>
  
−
<span>\[{{\rm{R}}_{{\rm{j + 1}}}}(i) = \left\{ \begin{array}{l} - 1,\begin{array}{*{20}{c}}{}&{}&{}&{}&{}&{}&{}&{}&{}&{}&{}\end{array}{{\rm{P}}_{\rm{j}}}(i) =  - 1\\T(i,{\rm{reactant,product),}}\begin{array}{*{20}{c}}{}&{}&{}\end{array}{{\rm{P}}_{\rm{j}}}(i) \ne  - 1\end{array} \right.\]</span>
 
 
</body>
 
</body>
 
</html>
 
</html>

Revision as of 15:44, 13 October 2018

Get the power of blast

Where:

$$X=[x_1,\ x_2,\ x_3,\ ...,\ x_n]^T$$ $$W=[w_1,\ w_2,\ w_3,\ ...,\ w_n]^T$$ $$\varepsilon=[\varepsilon_1,\ \varepsilon_2,\ \varepsilon_3,\ ...,\ \varepsilon_n]^T$$

  The aim is to search for the best W that minimize the mean of e.

\[{e^{-\Delta{r}{G^{'\circ}}/RT}}\] $$\hat p=\sigma(\theta^T \cdot x_b)=\frac{1}{1+\mathbf{e}^{-{\theta^{T \cdot x_b}}}}$$ \[f(r)= \frac{{e^{-\Delta{r}{G^{'\circ}}/RT}}}{1 + {e^{-\Delta{r}{G^{'\circ}}/RT}} + \sum {{r^'} \in {R_N}\backslash {{\left\{ r \right\}}^{{\rm{ }}{{\rm{e}}^{ - {\Delta _r}{G^{' \circ /RT}}}}}}} \] \[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}}}}} $$J(\theta)=-\frac{1}{m}\displaystyle\sum_{i=1}^m y^{(i)}\log(\hat p^{(i)})+(1-y^{(i)})\log(1-\hat p^{(i)})\\ =-\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))\\ \[f(r) = \frac{e^{-\Delta{r}{G^{'\circ}}/RT}}{{{1+}{e^{-\Delta{r}{G^{'\circ}}/RT}}+\sum r^'\in {R_N}\backslash{{\left\{r \right\}}^{{e^{-\Delta{r}{G^{'\circ}}/RT}}}} }}\] \[Max\left\{ {Ave(A),Ave(B),Ave(C),Ave(D)...} \right\} \]