An introduction to quantum gravity

After an overview of the physical motivations for studying quantum gravity, we reprint THE FORMAL STRUCTURE OF QUANTUM GRAVITY, i.e. the 1978 Cargese Lectures by Professor B.S. DeWitt, with kind permission of Springer. The reader is therefore introduced, in a pedagogical way, to the functional integral quantization of gravitation and Yang-Mills theory. It is hoped that such a paper will remain useful for all lecturers or Ph.D. students who face the task of introducing (resp. learning) some basic concepts in quantum gravity in a relatively short time. In the second part, we outline selected topics such as the braneworld picture with the same covariant formalism of the first part, and spectral asymptotics of Euclidean quantum gravity with diffeomorphism-invariant boundary conditions. The latter might have implications for singularity avoidance in quantum cosmology.Comment: 68 pages, Latex file. Sections from 2 to 17 are published thanks to kind permission of Springe

Sampling and PCR method for detecting pathogenic Fusarium oxysporum strains in onion harvest

Fusarium basal rot is a worldwide disease problem in onions, and causes substantial losses in onion production, both during the growing season and in the storage. To minimize the post-harvest losses, a protocol for screening of latent infections with pathogenic Fusarium oxysporum strains from harvested onions was developed. This protocol is based on a dual PCR test with primers specific for the fungal species and new SIX3 primers specific for the onion-pathogenic F. oxysporum strains. A pooled sample containing pieces from 50 harvested symptomless onions was prepared for the dual PCR using microwave disruption of the filamentous Fusarium fungi and Whatman FTA(TM) filter paper matrix technology, or as a reference protocol, by extracting DNA with a commercial kit. The two sample preparation protocols gave consistent results with the tested onion samples. Detection limit of the dual PCR protocol was 100 pg of F. oxysporum DNA, in a mixture with onion DNA, when the FTA card was applied. The new protocol reported here is simple and sensitive enough for routine testing, enabling the detection of latent infections in harvest lots even at the infection levels under 10%. Significance and Impact of the Study Fusarium basal rot causes serious problems in onion production. To minimize post-harvest losses, a simple protocol based on FTA(TM) technology and a dual PCR test with Fusarium oxysporum species-specific and pathogenicity-specific primers was developed. By testing pooled onion samples using this method, latent infections with F. oxysporum can be screened from a representative sample of the harvest. This screening method could be a useful tool to manage the post-harvest losses caused by latent infections with F. oxysporum and, with modification of the PCR protocol, with other Fusarium species pathogenic to onion.Peer reviewe

A reliable Pade analytical continuation method based on a high accuracy symbolic computation algorithm

We critique a Pade analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a novel symbolic computation algorithm. As an example of this method in action we apply it to the problem of determining the spectral function of a one-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black magic label frequently attached to this procedure.Comment: 11 pages, 8 eps figs, revtex format; revised version includes reference to anonymous ftp site containing example codes (MapleVr5.1 worksheets) displaying the implementation of the algorithm, including the padematinv.m library packag

The Volume of a Local Nodal Domain

Let M either be a closed real analytic Riemannian manifold or a closed smooth Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball provided that this component enters the ball deeply enough.Comment: 21 pages; introduction improved putting the problem in a larger context

Restriction Properties of Annulus SLE

For $\kappa\in(0,4]$, a family of annulus SLE$(\kappa;\Lambda)$ processes were introduced in [14] to prove the reversibility of whole-plane SLE$(\kappa)$. In this paper we prove that those annulus SLE$(\kappa;\Lambda)$ processes satisfy a restriction property, which is similar to that for chordal SLE$(\kappa)$. Using this property, we construct $n\ge 2$ curves crossing an annulus such that, when any $n-1$ curves are given, the last curve is a chordal SLE$(\kappa)$ trace.Comment: 37 page

Large fluctuations in stochastic population dynamics: momentum space calculations

Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition then brings about an eigenvalue problem for a non-Hermitian linear differential operator. The ground-state eigenmode encodes the stationary distribution of the population size. For long-lived metastable populations which exhibit extinction or escape to another metastable state, the quasi-stationary distribution and the mean time to extinction or escape are encoded by the eigenmode and eigenvalue of the lowest excited state. If the average population size in the stationary or quasi-stationary state is large, the corresponding eigenvalue problem can be solved via WKB approximation amended by other asymptotic methods. We illustrate these ideas in several model examples.Comment: 20 pages, 9 figures, to appear in JSTA

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Geometric Aspects of the Moduli Space of Riemann Surfaces

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces with very good properties, study their curvatures and boundary behaviors in great detail. Based on the careful analysis of these new metrics, we have a good understanding of the Kahler-Einstein metric from which we prove that the logarithmic cotangent bundle of the moduli space is stable. Another corolary is a proof of the equivalences of all of the known classical complete metrics to the new metrics, in particular Yau's conjectures in the early 80s on the equivalences of the Kahler-Einstein metric to the Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes corrrecte

Early Category-Specific Cortical Activation Revealed by Visual Stimulus Inversion

Visual categorization may already start within the first 100-ms after stimulus onset, in contrast with the long-held view that during this early stage all complex stimuli are processed equally and that category-specific cortical activation occurs only at later stages. The neural basis of this proposed early stage of high-level analysis is however poorly understood. To address this question we used magnetoencephalography and anatomically-constrained distributed source modeling to monitor brain activity with millisecond-resolution while subjects performed an orientation task on the upright and upside-down presented images of three different stimulus categories: faces, houses and bodies. Significant inversion effects were found for all three stimulus categories between 70–100-ms after picture onset with a highly category-specific cortical distribution. Differential responses between upright and inverted faces were found in well-established face-selective areas of the inferior occipital cortex and right fusiform gyrus. In addition, early category-specific inversion effects were found well beyond visual areas. Our results provide the first direct evidence that category-specific processing in high-level category-sensitive cortical areas already takes place within the first 100-ms of visual processing, significantly earlier than previously thought, and suggests the existence of fast category-specific neocortical routes in the human brain