On the existence of Killing vector fields

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra

Detection of fixed points in spatiotemporal signals by clustering method

We present a method to determine fixed points in spatiotemporal signals. A 144-dimensioanl simulated signal, similar to a Kueppers-Lortz instability, is analyzed and its fixed points are reconstructed.Comment: 3 pages, 3 figure

Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies

It is shown that during expanding phases of flat homogeneous cosmologies all small enough non-linear perturbations decay exponentially. This result holds for a large class of perfect fluid equations of state, but notably not for very ``stiff'' fluids as the pure radiation case

The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions

We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary dimensions. We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case.Comment: 83 pages, 1 figur

Depression, School Performance, and the Veridicality of Perceived Grades and Causal Attributions

An external criterion was assessed to test whether depressives have distorted perceptions of covariation information and whether their attributions are consistent with this information. Students’ actual and self-perceived grades, depression status, and attributions for failures were assessed. Furthermore, partici pants estimated average grades. Generally, self-perceived own past grades were inflated. Depressed students and those with low grades distorted their own grades (but not the average grade) more to their favor than individuals low in depression and those with high grades. Depression went along with lower actual grades and with internal, stable, and global failure attributions. Mood differences in attributions were not due to differences in previous grades. Depressed individuals drew (unrealistically) more depressogenic causal inferences when they perceived average grades to be low than when average grades were perceived to be high. However, they (realistically) attributed failure more in a depressogenic fashion than did nondepressives when their own grade history was low

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Fano Lineshapes Revisited: Symmetric Photoionization Peaks from Pure Continuum Excitation

In a photoionization spectrum in which there is no excitation of the discrete states, but only the underlying continuum, we have observed resonances which appear as symmetric peaks, not the commonly expected window resonances. Furthermore, since the excitation to the unperturbed continuum vanishes, the cross section expected from Fano's configuration interaction theory is identically zero. This shortcoming is removed by the explicit introduction of the phase shifted continuum, which demonstrates that the shape of a resonance, by itself, provides no information about the relative excitation amplitudes to the discrete state and the continuum.Comment: 4 pages, 3 figure

Physics of brain dynamics: Fokker-Planck analysis reveals changes in EEG delta-theta interactions in anaesthesia

We use drift and diffusion coefficients to reveal interactions between different oscillatory processes underlying a complex signal and apply the method to EEG delta and theta frequencies in the brain. By analysis of data recorded from rats during anaesthesia, we consider the stability and basins of attraction of fixed points in the phase portrait of the deterministic part of the retrieved stochastic process. We show that different classes of dynamics are associated with deep and light anaesthesia, and we demonstrate that the predominant directionality of the interaction is such that theta drives delt

Complementary Sensory and Associative Microcircuitry in Primary Olfactory Cortex

The three-layered primary olfactory (piriform) cortex is the largest component of the olfactory cortex. Sensory and intracortical inputs converge on principal cells in the anterior piriform cortex (aPC).Wecharacterize organization principles of the sensory and intracortical microcircuitry of layer II and III principal cells in acute slices of rat aPC using laser-scanning photostimulation and fast two-photon population Ca²⁺ imaging. Layer II and III principal cells are set up on a superficial-to-deep vertical axis. We found that the position on this axis correlates with input resistance and bursting behavior. These parameters scale with distinct patterns of incorporation into sensory and associative microcircuits, resulting in a converse gradient of sensory and intracortical inputs. In layer II, sensory circuits dominate superficial cells, whereas incorporation in intracortical circuits increases with depth. Layer III pyramidal cells receive more intracortical inputs than layer II pyramidal cells, but with an asymmetric dorsal offset. This microcircuit organization results in a diverse hybrid feedforward/recurrent network of neurons integrating varying ratios of intracortical and sensory input depending on a cell’s position on the superficial-to-deep vertical axis. Since burstiness of spiking correlates with both the cell’s location on this axis and its incorporation in intracortical microcircuitry, the neuronal output mode may encode a given cell’s involvement in sensory versus associative processing

Influence of the Particles Creation on the Flat and Negative Curved FLRW Universes

We present a dynamical analysis of the (classical) spatially flat and negative curved Friedmann-Lameitre-Robertson-Walker (FLRW) universes evolving, (by assumption) close to the thermodynamic equilibrium, in presence of a particles creation process, described by means of a realiable phenomenological approach, based on the application to the comoving volume (i. e. spatial volume of unit comoving coordinates) of the theory for open thermodynamic systems. In particular we show how, since the particles creation phenomenon induces a negative pressure term, then the choice of a well-grounded ansatz for the time variation of the particles number, leads to a deep modification of the very early standard FLRW dynamics. More precisely for the considered FLRW models, we find (in addition to the limiting case of their standard behaviours) solutions corresponding to an early universe characterized respectively by an "eternal" inflationary-like birth and a spatial curvature dominated singularity. In both these cases the so-called horizon problem finds a natural solution.Comment: 14 pages, no figures, appeared in Class. Quantum Grav., 18, 193, 200