Probabilistic abstract argumentation: An investigation with Boltzmann machines

In page 189, concerning random variables:

• $\{\{\mathit{l}\}\in \mathrm{\Omega }\mid {\mathit{L}}_{\mathit{A}\mathrm{,}\mathsf{on}}\mathrm{(}\mathit{l}\mathrm{)}=1\}$ should be $\{\mathit{l}\in \mathrm{\Omega }\mid {\mathit{L}}_{\mathit{A}\mathrm{,}\mathsf{on}}\mathrm{(}\mathit{l}\mathrm{)}=1\}$ or $\{\mathit{l}\in \mathrm{\Omega }\mid \mathit{l}\mathrm{(}\mathit{A}\mathrm{)}=\mathsf{on}\}$ ;

• $\{\{\mathit{l}\}\in \mathrm{\Omega }\mid {\mathit{L}}_{\mathit{A}}\mathrm{(}\mathit{l}\mathrm{)}=\mathsf{on}\}$ should be $\{\mathit{l}\in \mathrm{\Omega }\mid {\mathit{L}}_{\mathit{A}}\mathrm{(}\mathit{l}\mathrm{)}=\mathsf{on}\}$ or $\{\mathit{l}\in \mathrm{\Omega }\mid \mathit{l}\mathrm{(}\mathit{A}\mathrm{)}=\mathsf{on}\}$ .

In page 194, the Lagrangian can be written as follows: $$\begin{array}{c}\mathit{L}=\mathit{S}-\mathit{\beta }·\mathrm{(}{\displaystyle \sum }_{\mathit{i}}{\mathit{P}}_{\mathit{i}}·{\mathit{Q}}_{\mathit{i}}-\mathit{Q}\mathrm{)}-\mathrm{(}\mathit{\alpha }-1\mathrm{)}\mathrm{(}{\displaystyle \sum }_{\mathit{i}}{\mathit{P}}_{\mathit{i}}-1\mathrm{)}.\end{array}$$