Darwinian Selection and Non-existence of Nash Equilibria

We study selection acting on phenotype in a collection of agents playing local games lacking Nash equilibria. After each cycle one of the agents losing most games is replaced by a new agent with new random strategy and game partner. The network generated can be considered critical in the sense that the lifetimes of the agents is power law distributed. The longest surviving agents are those with the lowest absolute score per time step. The emergent ecology is characterized by a broad range of behaviors. Nevertheless, the agents tend to be similar to their opponents in terms of performance.Comment: 4 pages, 5 figure

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure

The Exchange Gate in Solid State Spin Quantum Computation: The Applicability of the Heisenberg Model

Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external magnetic field. Using exact diagonalization we obtain the regime of validity of the adiabatic approximation. We also find qualitative corrections to the Heisenberg model at high magnetic fields and in looped arrays of spins. Looped geometries of localized spins generate flux dependent, multi-spin terms which go beyond the basic Heisenberg model.Comment: 13 pages, 8 figure

Inversion improves the recognition of facial expression in thatcherized images

The Thatcher illusion provides a compelling example of the face inversion effect. However, the marked effect of inversion in the Thatcher illusion contrasts to other studies that report only a small effect of inversion on the recognition of facial expressions. To address this discrepancy, we compared the effects of inversion and thatcherization on the recognition of facial expressions. We found that inversion of normal faces caused only a small reduction in the recognition of facial expressions. In contrast, local inversion of facial features in upright thatcherized faces resulted in a much larger reduction in the recognition of facial expressions. Paradoxically, inversion of thatcherized faces caused a relative increase in the recognition of facial expressions. Together, these results suggest that different processes explain the effects of inversion on the recognition of facial expressions and on the perception of the Thatcher illusion. The grotesque perception of thatcherized images is based on a more orientation-sensitive representation of the face. In contrast, the recognition of facial expression is dependent on a more orientation-insensitive representation. A similar pattern of results was evident when only the mouth or eye region was visible. These findings demonstrate that a key component of the Thatcher illusion is to be found in orientation-specific encoding of the features of the face

First phylogenetic analyses of galaxy evolution

The Hubble tuning fork diagram, based on morphology, has always been the preferred scheme for classification of galaxies and is still the only one originally built from historical/evolutionary relationships. At the opposite, biologists have long taken into account the parenthood links of living entities for classification purposes. Assuming branching evolution of galaxies as a "descent with modification", we show that the concepts and tools of phylogenetic systematics widely used in biology can be heuristically transposed to the case of galaxies. This approach that we call "astrocladistics" has been first applied to Dwarf Galaxies of the Local Group and provides the first evolutionary galaxy tree. The cladogram is sufficiently solid to support the existence of a hierarchical organization in the diversity of galaxies, making it possible to track ancestral types of galaxies. We also find that morphology is a summary of more fundamental properties. Astrocladistics applied to cosmology simulated galaxies can, unsurprisingly, reconstruct the correct "genealogy". It reveals evolutionary lineages, divergences from common ancestors, character evolution behaviours and shows how mergers organize galaxy diversity. Application to real normal galaxies is in progress. Astrocladistics opens a new way to analyse galaxy evolution and a path towards a new systematics of galaxies

Scale-free networks are not robust under neutral evolution

Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution. The guiding principle for this is robustness in the resulting phenotype. The numerical results show that a power-law distribution is not stable under such an evolution, and the network approaches a homogeneous form where the overall distribution of connectivities is given by a Poisson distribution.Comment: Submitted for publicatio

Chirality in Quantum Computation with Spin Cluster Qubits

We study corrections to the Heisenberg interaction between several lateral, single-electron quantum dots. We show, using exact diagonalization, that three-body chiral terms couple triangular configurations to external sources of flux rather strongly. The chiral corrections impact single qubit encodings utilizing loops of three or more Heisenberg coupled quantum dots.Comment: 5 pages, 2 figure

Kerr black hole lensing for generic observers in the strong deflection limit

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review

Tidal coupling of a Schwarzschild black hole and circularly orbiting moon

We describe the possibility of using LISA's gravitational-wave observations to study, with high precision, the response of a massive central body to the tidal gravitational pull of an orbiting, compact, small-mass object. Motivated by this application, we use first-order perturbation theory to study tidal coupling for an idealized case: a massive Schwarzschild black hole, tidally perturbed by a much less massive moon in a distant, circular orbit. We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment in the hole's external gravitational field at large radii. In the limit that the moon is static, we find, in Schwarzschild coordinates and Regge-Wheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon's tidal field. As a partial analog of a result derived long ago by Hartle for a spinning hole and a stationary distant companion, we show that the orbiting moon's tidal field induces a tidal bulge on the hole's horizon, and that the rate of change of the horizon shape leads the perturbing tidal field at the horizon by a small angle.Comment: 14 pages, 0 figures, submitted to Phys. Rev.

Dynamical Diffraction Theory for Wave Packet Propagation in Deformed Crystals

We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a correction to geometrical optics. The trajectory of the wave packet has a shift of the center position due to a crystal deformation. Remarkably, in the vicinity of the Bragg condition, the shift is enhanced by a factor $\omega /\Delta \omega$ ($\omega$: frequency of an x ray, $\Delta\omega$: gap frequency induced by the Bragg reflection). Comparison with the conventional dynamical diffraction theory is also made.Comment: 4 pages, 2 figures. Title change