Discrete and continuum third quantization of Gravity

We give a brief introduction to matrix models and the group field theory (GFT) formalism as realizations of the idea of a third quantization of gravity, and present in some more detail the idea and basic features of a continuum third quantization formalism in terms of a field theory on the space of connections, building up on the results of loop quantum gravity that allow to make the idea slightly more concrete. We explore to what extent one can rigorously define such a field theory. Concrete examples are given for the simple case of Riemannian GR in 3 spacetime dimensions. We discuss the relation between GFT and this formal continuum third quantized gravity, and what it can teach us about the continuum limit of GFTs.Comment: 21 pages, 5 eps figures; submitted as a contribution to the proceedings of the conference "Quantum Field Theory and Gravity Conference Regensburg 2010" (28 September - 1 October 2010, Regensburg/Bavaria); v2: preprint number include

Loop Quantum Gravity a la Aharonov-Bohm

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.Comment: 19 pages, 1 figure; v2: corrected typos, section 4 expanded

Using molecular data for epidemiological inference: assessing the prevalence of Trypanosoma brucei rhodesiense in Tsetse in Serengeti, Tanzania

Background: Measuring the prevalence of transmissible Trypanosoma brucei rhodesiense in tsetse populations is essential for understanding transmission dynamics, assessing human disease risk and monitoring spatio-temporal trends and the impact of control interventions. Although an important epidemiological variable, identifying flies which carry transmissible infections is difficult, with challenges including low prevalence, presence of other trypanosome species in the same fly, and concurrent detection of immature non-transmissible infections. Diagnostic tests to measure the prevalence of T. b. rhodesiense in tsetse are applied and interpreted inconsistently, and discrepancies between studies suggest this value is not consistently estimated even to within an order of magnitude. Methodology/Principal Findings: Three approaches were used to estimate the prevalence of transmissible Trypanosoma brucei s.l. and T. b. rhodesiense in Glossina swynnertoni and G. pallidipes in Serengeti National Park, Tanzania: (i) dissection/microscopy; (ii) PCR on infected tsetse midguts; and (iii) inference from a mathematical model. Using dissection/microscopy the prevalence of transmissible T. brucei s.l. was 0% (95% CI 0–0.085) for G. swynnertoni and 0% (0–0.18) G. pallidipes; using PCR the prevalence of transmissible T. b. rhodesiense was 0.010% (0–0.054) and 0.0089% (0–0.059) respectively, and by model inference 0.0064% and 0.00085% respectively. Conclusions/Significance: The zero prevalence result by dissection/microscopy (likely really greater than zero given the results of other approaches) is not unusual by this technique, often ascribed to poor sensitivity. The application of additional techniques confirmed the very low prevalence of T. brucei suggesting the zero prevalence result was attributable to insufficient sample size (despite examination of 6000 tsetse). Given the prohibitively high sample sizes required to obtain meaningful results by dissection/microscopy, PCR-based approaches offer the current best option for assessing trypanosome prevalence in tsetse but inconsistencies in relating PCR results to transmissibility highlight the need for a consensus approach to generate meaningful and comparable data

Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry

We deform the action and the supersymmetry transformations of the d = 10 and d = 4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d = 6 vector branes related to chiral (2,0) supergravity, which we denote as 'Vp-branes'. We use a space-filling V5 superbrane for the d = 6 model and a V3 superbrane for the d = 4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d = 10 and 4, and half-maximal 8+8 supersymmetries in d = 6 and 4.</p

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Phenology of Scramble Polygyny in a Wild Population of Chrysolemid Beetles: The Opportunity for and the Strength of Sexual Selection

Recent debate has highlighted the importance of estimating both the strength of sexual selection on phenotypic traits, and the opportunity for sexual selection. We describe seasonal fluctuations in mating dynamics of Leptinotarsa undecimlineata (Coleoptera: Chrysomelidae). We compared several estimates of the opportunity for, and the strength of, sexual selection and male precopulatory competition over the reproductive season. First, using a null model, we suggest that the ratio between observed values of the opportunity for sexual selections and their expected value under random mating results in unbiased estimates of the actual nonrandom mating behavior of the population. Second, we found that estimates for the whole reproductive season often misrepresent the actual value at any given time period. Third, mating differentials on male size and mobility, frequency of male fighting and three estimates of the opportunity for sexual selection provide contrasting but complementary information. More intense sexual selection associated to male mobility, but not to male size, was observed in periods with high opportunity for sexual selection and high frequency of male fights. Fourth, based on parameters of spatial and temporal aggregation of female receptivity, we describe the mating system of L. undecimlineata as a scramble mating polygyny in which the opportunity for sexual selection varies widely throughout the season, but the strength of sexual selection on male size remains fairly weak, while male mobility inversely covaries with mating success. We suggest that different estimates for the opportunity for, and intensity of, sexual selection should be applied in order to discriminate how different behavioral and demographic factors shape the reproductive dynamic of populations

The genetic mating system of a sea spider with male-biased sexual size dimorphism: evidence for paternity skew despite random mating success

Male-biased size dimorphism is usually expected to evolve in taxa with intense male–male competition for mates, and it is hence associated with high variances in male mating success. Most species of pycnogonid sea spiders exhibit female-biased size dimorphism, and are notable among arthropods for having exclusive male parental care of embryos. Relatively little, however, is known about their natural history, breeding ecology, and mating systems. Here we first show that Ammothella biunguiculata, a small intertidal sea spider, exhibits male-biased size dimorphism. Moreover, we combine genetic parentage analysis with quantitative measures of sexual selection to show that male body size does not appear to be under directional selection. Simulations of random mating revealed that mate acquisition in this species is largely driven by chance factors, although actual paternity success is likely non-randomly distributed. Finally, the opportunity for sexual selection (Is), an indirect metric for the potential strength of sexual selection, in A. biunguiculata males was less than half of that estimated in a sea spider with female-biased size dimorphism, suggesting the direction of size dimorphism may not be a reliable predictor of the intensity of sexual selection in this group. We highlight the suitability of pycnogonids as model systems for addressing questions relating parental investment and sexual selection, as well as the current lack of basic information on their natural history and breeding ecology

The Spin Foam Approach to Quantum Gravity

This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The models are motivated by a suitable implementation of the path integral quantization of the Plebanski formulation of gravity on a simplicial regularization. The article also includes a self-contained treatment of the 2+1 gravity. The simple nature of the latter provides the basis and a perspective for the analysis of both conceptual and technical issues that remain open in four dimensions.Comment: To appear in Living Reviews in Relativit

Sex-specific Trans-regulatory Variation on the Drosophila melanogaster X Chromosome

The X chromosome constitutes a unique genomic environment because it is present in one copy in males, but two copies in females. This simple fact has motivated several theoretical predictions with respect to how standing genetic variation on the X chromosome should differ from the autosomes. Unmasked expression of deleterious mutations in males and a lower census size are expected to reduce variation, while allelic variants with sexually antagonistic effects, and potentially those with a sex-specific effect, could accumulate on the X chromosome and contribute to increased genetic variation. In addition, incomplete dosage compensation of the X chromosome could potentially dampen the male-specific effects of random mutations, and promote the accumulation of X-linked alleles with sexually dimorphic phenotypic effects. Here we test both the amount and the type of genetic variation on the X chromosome within a population of Drosophila melanogaster, by comparing the proportion of X linked and autosomal trans-regulatory SNPs with a sexually concordant and discordant effect on gene expression. We find that the X chromosome is depleted for SNPs with a sexually concordant effect, but hosts comparatively more SNPs with a sexually discordant effect. Interestingly, the contrasting results for SNPs with sexually concordant and discordant effects are driven by SNPs with a larger influence on expression in females than expression in males. Furthermore, the distribution of these SNPs is shifted towards regions where dosage compensation is predicted to be less complete. These results suggest that intrinsic properties of dosage compensation influence either the accumulation of different types of trans-factors and/or their propensity to accumulate mutations. Our findings document a potential mechanistic basis for sex-specific genetic variation, and identify the X as a reservoir for sexually dimorphic phenotypic variation. These results have general implications for X chromosome evolution, as well as the genetic basis of sex-specific evolutionary change