A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie

Constants of motion associated with alternative Hamiltonians

It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then the determinant and the trace of any power of a certain matrix formed by the Poisson brackets of the $Q_{i}, P_{i}$ with respect to $q_{i}, p_{i}$, are constants of motion

Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

A proposal for the Hamilton-Jacobi theory in the context of the covariant formulation of Hamiltonian systems is done. The current approach consists in applying Dirac's method to the corresponding action which implies the inclusion of second-class constraints in the formalism which are handled using the procedure of Rothe and Scholtz recently reported. The current method is applied to the nonrelativistic two-dimensional isotropic harmonic oscillator employing the various symplectic structures for this dynamical system recently reported.Comment: 17 pages, no figure

Local continuity laws on the phase space of Einstein equations with sources

Local continuity equations involving background fields and variantions of the fields, are obtained for a restricted class of solutions of the Einstein-Maxwell and Einstein-Weyl theories using a new approach based on the concept of the adjoint of a differential operator. Such covariant conservation laws are generated by means of decoupled equations and their adjoints in such a way that the corresponding covariantly conserved currents possess some gauge-invariant properties and are expressed in terms of Debye potentials. These continuity laws lead to both a covariant description of bilinear forms on the phase space and the existence of conserved quantities. Differences and similarities with other approaches and extensions of our results are discussed.Comment: LaTeX, 13 page

Drug Discovery of Novel Targeted Therapeutics for Metastatic Breast Cancer

Metastatic disease is the primary cause of breast cancer mortality, due to the lack of effective therapy. The Rho GTPase Rac is integral for the promotion of cancer cell migration/invasion, proliferation, and survival. Since metastatic breast cancers often overexpress or exhibit high Rac activity, inhibition of Rac is a viable strategy against metastatic cancer. Recently, we characterized EHop-016, a small molecule that inhibits Rac activity of metastatic breast cancer cells more efficiently than previously available Rac inhibitors (IC50 of 1µM). EHop-016 inhibits the activity of the Rac downstream effector p21 activated kinase and cell migration of metastatic breast cancer cells. We also reported that EHop-016 at ≥ 25mg/kg body weight significantly reduced tumor growth and metastasis in mice. However, our recent pharmacokinetic study of EHop-016 in a mouse model demonstrated that the bioavailability of Ehop-016 needs to be improved for pharmacological development. The hypothesis is that improvement of the EHop-016 structure will provide probes with increased potency against Rac and, therefore, increased bioavailability. Several Ehop-016 derivatives have been tested for their effects on breast cancer cell viability using the MTT assay. We found one compound, HV-107, which at concentrations ≥1µM inhibits the viability of metastatic breast cancer cell lines MDA-MB-231 and MDA-MB-435 by 45%. The effects of HV-107 on the inhibition of Rac activation were tested by pulldown assays. At 250nM, HV-107 inhibits Rac activation by 55% in MDA-MB-231 and MDA-MB-435 cells. Taken together, our findings suggest HV-107 has potential as an anti-metastatic agent and should, therefore, be further characterized