Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

Effect of neoadjuvant chemotherapy on low-density lipoprotein (LDL) receptor and LDL receptor-related protein 1 (LRP-1) receptor in locally advanced breast cancer

Low-density lipoprotein (LDL) receptors are overexpressed in most neoplastic cell lines and provide a mechanism for the internalization and concentration of drug-laden nanoemulsions that bind to these receptors. The aim of the present study was to determine whether the administration of standard chemotherapeutic schemes can alter the expression of LDL and LDL receptor-related protein 1 (LRP-1) receptors in breast carcinoma. Fragments of tumoral and normal breast tissue from 16 consecutive volunteer women with breast cancer in stage II or III were obtained from biopsies before the beginning of neoadjuvant chemotherapy and after chemotherapy, from fragments excised during mastectomy. Tissues were analyzed by immunohistochemistry for both receptors. Because complete response to treatment was achieved in 4 patients, only the tumors from 12 were analyzed. Before chemotherapy, there was overexpression of LDL receptor in the tumoral tissue compared to normal breast tissue in 8 of these patients. LRP-1 receptor overexpression was observed in tumors of 4 patients. After chemotherapy, expression of both receptors decreased in the tumors of 6 patients, increased in 4 and was unchanged in 2. Nonetheless, even when chemotherapy reduced receptors expression, the expression was still above normal. The fact that chemotherapy does not impair LDL receptors expression supports the use of drug carrier systems that target neoplastic cells by the LDL receptor endocytic pathway in patients on conventional chemotherapy.