On the existence of identifiable reparametrizations for linear compartment models

The parameters of a linear compartment model are usually estimated from experimental input-output data. A problem arises when infinitely many parameter values can yield the same result; such a model is called unidentifiable. In this case, one can search for an identifiable reparametrization of the model: a map which reduces the number of parameters, such that the reduced model is identifiable. We study a specific class of models which are known to be unidentifiable. Using algebraic geometry and graph theory, we translate a criterion given by Meshkat and Sullivant for the existence of an identifiable scaling reparametrization to a new criterion based on the rank of a weighted adjacency matrix of a certain bipartite graph. This allows us to derive several new constructions to obtain graphs with an identifiable scaling reparametrization. Using these constructions, a large subclass of such graphs is obtained. Finally, we present a procedure of subdividing or deleting edges to ensure that a model has an identifiable scaling reparametrization

The Arabidopsis thaliana SOMATIC EMBRYOGENESIS RECEPTOR-LIKE KINASES1 and 2 control male sporogenesis

The Arabidopsis thaliana SOMATIC EMBRYOGENESIS RECEPTOR-LIKE KINASE (SERK) family of plasma membrane receptors consists of five closely related members. The SERK1 and SERK2 genes show a complex expression pattern throughout development. Both are expressed in anther primordia up to the second parietal division. After this point, expression ceases in the sporocytes and is continued in the tapetum and middle layer precursors. Single knockout mutants of SERK1 and SERK2 show no obvious phenotypes. Double mutants of SERK1 and SERK2 are completely male sterile due to a failure in tapetum specification. Fertility can be restored by a single copy of either gene. The SERK1 and SERK2 proteins can form homodimers or heterodimers in vivo, suggesting they are interchangeable in the SERK1/SERK2 signaling comple