Doubt in sim_mean and ground truth

[cakeinspace]

The muscat bioconductor page says that

Where $\lambda_c$ is a cell dependent parameter. Now for each cell that we simulate the sim_mean for a gene should be different however when i look at the metadata(sim)$gene_info. It appears that each gene in each cluster and each sample has only one sim_mean values. Shouldn't it be different for each cell. Or is $\lambda_c$ chosen once for each cluster.

[cakeinspace]

After some digging around in the code base. What i think is happening is that the counts are simulated using $\mu_{gc}$ above. so each cell has its own $\mu_{gc}$. Then finally we average all the $\mu_{gc}$ for a cluster over the cells to report the $\mu_g$ for each gene in a cluster. Is this correct