Induced Dirac structures on isotropy-type manifolds

A new method of singular reduction is extended from Poisson to Dirac manifolds. Then it is shown that the Dirac structures on the strata of the quotient coincide with those of the only other known singular Dirac reduction metho

Dirac Optimal Reduction

The purpose of this paper is to generalize the (Poisson) Optimal Reduction Theorem in Ortega and Ratiu [Momentum Maps and Hamiltonian Reduction. Progress in Mathematics 222. Boston, MA: Birkhäuser. xxxiv, 497pp., 2004] to general proper Lie group actions on Dirac manifolds, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reductio

Double Lie algebroids and representations up to homotopy

We show that double Lie algebroids, together with a chosen linear splitting, are equivalent to pairs of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the tangent of a Lie algebroid

Induced Dirac structures on isotropy-type manifolds

A new method of singular reduction is extended from Poisson to Dirac manifolds. Then it is shown that the Dirac structures on the strata of the quotient coincide with those of the only other known singular Dirac reduction method

Dirac Optimal Reduction

The purpose of this paper is to generalize the (Poisson) Optimal Reduction Theorem in Ortega and Ratiu [Momentum Maps and Hamiltonian Reduction. Progress in Mathematics 222. Boston, MA: Birkhauser. xxxiv, 497pp., 2004] to general proper Lie group actions on Dirac manifolds, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution

Radioresistance of human glioma spheroids and expression of HSP70, p53 and EGFr

Background: Radiation therapy is routinely prescribed for high-grade malignant gliomas. However, the efficacy of this therapeutic modality is often limited by the occurrence of radioresistance, reflected as a diminished susceptibility of the irradiated cells to undergo cell death. Thus, cells have evolved an elegant system in response to ionizing radiation induced DNA damage, where p53, Hsp70 and/or EGFr may play an important role in the process. In the present study, we investigated whether the content of p53, Hsp70 and EGFr are associated to glioblastoma (GBM) cell radioresistance. Methods: Spheroids from U-87MG and MO59J cell lines as well as spheroids derived from primary culture of tumor tissue of one GBM patient (UGBM1) were irradiated (5, 10 and 20 Gy), their relative radioresistance were established and the p53, Hsp70 and EGFr contents were immunohistochemically determined. Moreover, we investigated whether EGFr-phospho-Akt and EGFr-MEK-ERK pathways can induce GBM radioresistance using inhibitors of activation of ERK (PD098059) and Akt (wortmannin). Results: At 5 Gy irradiation UGBM1 and U-87MG spheroids showed growth inhibition whereas the MO59J spheroid was relatively radioresistant. Overall, no significant changes in p53 and Hsp70 expression were found following 5 Gy irradiation treatment in all spheroids studied. The only difference observed in Hsp70 content was the periphery distribution in MO59J spheroids. However, 5 Gy treatment induced a significant increase on the EGFr levels in MO59J spheroids. Furthermore, treatment with inhibitors of activation of ERK (PD098059) and Akt (wortmannin) leads to radiosensitization of MO59J spheroids. Conclusions: These results indicate that the PI3K-Akt and MEK-ERK pathways triggered by EGFr confer GBM radioresistance