Given a regulatory pathway system consisting of a set of proteins, can we predict which pathway class it belongs to? Such a problem is closely related to the biological function of the pathway in cells and hence is quite fundamental and essential in systems biology and proteomics. This is also an extremely difficult and challenging problem due to its complexity. To address this problem, a novel...

In this paper first of all we introduce Property $U$-($G$-$PWP$) of acts, which is an extension of Condition $(G$-$PWP)$ and give some general properties. Then we give a characterization of monoids when this property of acts implies some others. Also we show that the strong (faithfulness, $P$-cyclicity) and ($P$-)regularity of acts imply the property $U$-($G$-$PWP$). Finally, we give a necessar...