Cholinergic and GABAergic pathways in fly motion vision

BACKGROUND: The fly visual system is a highly ordered brain structure with well-established physiological and behavioral functions. A large number of interneurons in the posterior part of the third visual neuropil, the lobula plate tangential cells (LPTCs), respond to visual motion stimuli. In these cells the mechanism of motion detection has been studied in great detail. Nevertheless, the cellular computations leading to their directionally selective responses are not yet fully understood. Earlier studies addressed the neuropharmacological basis of the motion response in lobula plate interneurons. In the present study we investigated the distribution of the respective neurotransmitter receptors in the fly visual system, namely nicotinic acetylcholine receptors (nAChRs) and GABA receptors (GABARs) demonstrated by antibody labeling. RESULTS: The medulla shows a laminar distribution of both nAChRs and GABARs. Both receptor types are present in layers that participate in motion processing. The lobula also shows a characteristic layering of immunoreactivity for either receptor in its posterior portion. Furthermore, immunostaining for nAChRs and GABARs can be observed in close vicinity of lobula plate tangential cells. Immunostaining of GABAergic fibers suggests that inhibitory inputs from the medulla are relayed through the lobula to the lobula plate rather than through direct connections between medulla and lobula plate. CONCLUSIONS: The interaction of excitatory and inhibitory pathways is essential for the computation of visual motion responses and discussed in the context of the Reichardt model for motion detection

Quantum general relativity and Hawking radiation

In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around a black hole, and show that in the WKB approximation, the wave-functional describes an eternal black hole in equilibrium with a thermal bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para following Eqn. (10). Revised version to appear in Phys. Rev.

Semiclassical Black Hole States and Entropy

We discuss semiclassical states in quantum gravity corresponding to Schwarzschild as well as Reissner Nordstr\"om black holes. We show that reduced quantisation of these models is equivalent to Wheeler-DeWitt quantisation with a particular factor ordering. We then demonstrate how the entropy of black holes can be consistently calculated from these states. While this leads to the Bekenstein-Hawking entropy in the Schwarzschild and non-extreme Reissner-Nordstr\"om cases, the entropy for the extreme Reissner-Nordstr\"om case turns out to be zero.Comment: Revtex, 15 pages, some clarifying comments and additional references included, to appear in Phys. Rev.

Microcanonical statistics of black holes and bootstrap condition

The microcanonical statistics of the Schwarzschild black holes as well as the Reissner-Nordstr$\sf \ddot{o}$m black holes are analyzed. In both cases we set up the inequalities in the microcanonical density of states. These are then used to show that the most probable configuration in the gases of black holes is that one black hole acquires all of the mass and all of the charge at high energy limit. Thus the black holes obey the statistical bootstrap condition and, in contrast to the other investigation, we see that U(1) charge does not break the bootstrap property.Comment: 16 pages. late

On Modular Invariance and 3D Gravitational Instantons

We study the modular transformation properties of Euclidean solutions of 3D gravity whose asymptotic geometry has the topology of a torus. These solutions represent saddle points of the grand canonical partition function with an important example being the BTZ black hole, and their properties under modular transformations are inherited from the boundary conformal field theory encoding the asymptotic dynamics. Within the Chern Simons formulation, classical solutions are characterised by specific holonomies describing the wrapping of the gauge field around cycles of the torus. We find that provided these holonomies transform in an appropriate manner, there exists an associated modular invariant grand canonical partition function and that the spectrum of saddle points naturally includes a thermal bath in $AdS_3$ as discussed by Maldacena and Strominger. Indeed, certain modular transformations can naturally be described within classical bulk dynamics as mapping between different foliations with a "time" coordinate along different cycles of the asymptotic torus.Comment: 14 pages, RevTeX, typos corrected, to appear in Phys. Rev.

A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenvalue equation for the ADM mass of the hole, from the point of view of a distant observer at rest, is obtained. Our eigenvalue equation implies that the ADM mass and the electric charge spectra of the hole are discrete, and the mass spectrum is bounded below. Moreover, the spectrum of the quantity $M^2-Q^2$ is strictly positive when an appropriate self-adjoint extension is chosen. The WKB analysis yields the result that the large eigenvalues of the quantity $\sqrt{M^2-Q^2}$ are of the form $\sqrt{2n}$, where $n$ is an integer. It turns out that this result is closely related to Bekenstein's proposal on the discrete horizon area spectrum of black holes.Comment: 37 pages, Plain TeX, no figure

Topology Change in Canonical Quantum Cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^{\i}tre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.Comment: 23 pages, LaTex file. We added in the conclusion some comments about path integral formalism and corrected litle misprinting

Must Quantum Spacetimes Be Euclidean?

The Bohm-de Broglie interpretation of quantum mechanics is applied to canonical quantum cosmology. It is shown that, irrespective of any regularization or choice of factor ordering of the Wheeler-DeWitt equation, the unique relevant quantum effect which does not break spacetime is the change of its signature from lorentzian to euclidean. The other quantum effects are either trivial or break the four-geometry of spacetime. A Bohm-de Broglie picture of a quantum geometrodynamics is constructed, which allows the investigation of these latter structures. For instance, it is shown that any real solution of the Wheeler-De Witt equation yields a generate four-geometry compatible with the strong gravity limit of General Relativity and the Carroll group. Due to the more detailed description of quantum geometrodynamics given by the Bohm-de Broglie interpretation, some new boundary conditions on solutions of the Wheeler-DeWitt equation must be imposed in order to preserve consistency of this finer view.Comment: 42 pages LaTeX, last version with minor corrections, being the most importants on pages 0, 6, 11, 21, 23, and 30 . The new title does not change our conclusion

Quantum Scalar Field on the Massless (2+1)-Dimensional Black Hole Background

The behavior of a quantum scalar field is studied in the metric ground state of the (2+1)-dimensional black hole of Ba\~nados, Teitelboim and Zanelli which contains a naked singularity. The one-loop BTZ partition function and the associate black hole effective entropy, the expectation value of the quantum fluctuation as well as the renormalized expectation value of the stress tensor are explicitly computed in the framework of the $\zeta$-function procedure. This is done for all values of the coupling with the curvature, the mass of the field and the temperature of the quantum state. In the massless conformally coupled case, the found stress tensor is used for determining the quantum back reaction on the metric due to the scalar field in the quantum vacuum state, by solving the semiclassical Einstein equations. It is finally argued that, within the framework of the 1/N expansion, the Cosmic Censorship Hypothesis is implemented since the naked singularity of the ground state metric is shielded by an event horizon created by the back reaction.Comment: 18 pages, RevTeX, no figures, minor changes, final version accepted for publication in Phys. Rev.

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to appear in Foundations of Physic