This paper deals with the state and input observability analysis for structured linear systems with unknown inputs. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. Using a particular decomposition of the systems into two subsystems, we express, in simple graphic terms, necessary and sufficient conditions for the generic state and input observability. These conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph. Therefore, our approach is suited to study large scale systems.
This paper deals with the partial state and input observability analysis for structured linear systems with an application to distributed systems. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. More precisely, we express, in simple graphic terms, necessary and sufficient conditions for the strong observability of a state or an input component. These results are then directly applied to study the observability of a distributed system in some different configurations. In fact, we define two configurations called decentralized interconnected observation scheme and decentralized autonomous observation scheme, for which we check whether or not any given part of the states or the inputs of a considered subsystem is strongly observable. All the provided conditions are easy to verify because they are based on comparison of integers and on finding paths in a digraph.
Estrogen receptor alpha 36 (ERα36) is a variant of the canonical estrogen receptor alpha (ERα66), widely expressed in hormone sensitive cancer cells and whose high expression level correlates with a poor survival prognosis for breast cancer patients. While ERα36 activity have been related to breast cancer progression or acquired resistance to treatment, expression level and location of ERα36 are poorly documented in the normal mammary gland. Therefore, we explored the consequences of a ERα36 overexpression in vitro in MCF-10A normal mammary epithelial cells and in vivo in a unique model of MMTV-ERα36 transgenic mouse strain wherein ERα36 mRNA was specifically expressed in the mammary gland. By a combination of bioinformatics and computational analyses of microarray data, we identified hierarchical gene networks, downstream of ERα36 and modulated by the JAK2/STAT3 signaling pathway. Concomitantly, ERα36 overexpression lowered proliferation rate but enhanced migration potential and resistance to staurosporin-induced apoptosis of the MCF-10A cell line. In vivo, ERα36 expression led to duct epithelium thinning and disruption in adult but not in prepubescent mouse mammary gland. These phenotypes correlated with a loss of E-cadherin expression. Here, we show that an enhanced expression of ERα36 is sufficient, by itself, to disrupt normal breast epithelial phenotype in vivo and in vitro through a dominant-positive effect on nongenomic estrogen signaling pathways. These results also suggest that, in the presence of adult endogenous steroid levels, ERα36 overexpression in vivo contributes to alter mammary gland architecture which may support pre-neoplastic lesion and augment breast cancer risk.
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