Minisuperspace Models in M-theory

We derive the full canonical formulation of the bosonic sector of 11-dimensional supergravity, and explicitly present the constraint algebra. We then compactify M-theory on a warped product of homogeneous spaces of constant curvature, and construct a minisuperspace of scale factors. First classical behaviour of the minisuperspace system is analysed, and then a quantum theory is constructed. It turns out that there similarities with the "pre-Big Bang" scenario in String Theory.Comment: 35 pages, 2 figures, added additional discussion of gauge fixing and self-adjointness of the Hamiltonian, added reference

Quantum geometrodynamics for black holes and wormholes

The geometrodynamics of the spherical gravity with a selfgravitating thin dust shell as a source is constructed. The shell Hamiltonian constraint is derived and the corresponding Schroedinger equation is obtained. This equation appeared to be a finite differences equation. Its solutions are required to be analytic functions on the relevant Riemannian surface. The method of finding discrete spectra is suggested based on the analytic properties of the solutions. The large black hole approximation is considered and the discrete spectra for bound states of quantum black holes and wormholes are found. They depend on two quantum numbers and are, in fact, quasicontinuous.Comment: Latex, 32 pages, 5 fig

Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

We investigate the effects of competition between two complex, $\mathcal{PT}$-symmetric potentials on the $\mathcal{PT}$-symmetric phase of a "particle in a box". These potentials, given by $V_Z(x)=iZ\mathrm{sign}(x)$ and $V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$, represent long-range and localized gain/loss regions respectively. We obtain the $\mathcal{PT}$-symmetric phase in the $(Z,\xi)$ plane, and find that for locations $\pm a$ near the edge of the box, the $\mathcal{PT}$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $\mathcal{PT}$-symmetry will be restored by increasing the strength $\xi$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $\mathcal{PT}$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $\mathcal{PT}$-symmetric potentials show unique, unexpected properties.Comment: 7 pages, 3 figure

Using the Gibbs Function as a Measure of Human Brain Development Trends from Fetal Stage to Advanced Age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions

Using the gibbs function as a measure of human brain development trends from fetal stage to advanced age

We propose to use a Gibbs free energy function as a measure of the human brain development. We adopt this approach to the development of the human brain over the human lifespan: from a prenatal stage to advanced age. We used proteomic expression data with the Gibbs free energy to quantify human brain’s protein–protein interaction networks. The data, obtained from BioGRID, comprised tissue samples from the 16 main brain areas, at different ages, of 57 post-mortem human brains. We found a consistent functional dependence of the Gibbs free energies on age for most of the areas and both sexes. A significant upward trend in the Gibbs function was found during the fetal stages, which is followed by a sharp drop at birth with a subsequent period of relative stability and a final upward trend toward advanced age. We interpret these data in terms of structure formation followed by its stabilization and eventual deterioration. Furthermore, gender data analysis has uncovered the existence of functional differences, showing male Gibbs function values lower than female at prenatal and neonatal ages, which become higher at ages 8 to 40 and finally converging at late adulthood with the corresponding female Gibbs functions