A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Kinematic models of interseismic deformation from inversion of GPS and InSAR measurements to estimate fault parameters and coupling degree

We have used kinematic models in two Italian regions to reproduce surface interseismic velocities obtained from InSAR and GPS measurements. We have considered a Block modeling, BM, approach to evaluate which fault system is actively accommodating the occurring deformation in both considered areas. We have performed a study for the Umbria-Marche Apennines, obtaining that the tectonic extension observed by GPS measurements is explained by the active contribution of at least two fault systems, one of which is the Alto Tiberina fault, ATF. We have estimated also the interseismic coupling distribution for the ATF using a 3D surface and the result shows an interesting correlation between the microseismicity and the uncoupled fault portions. The second area analyzed concerns the Gargano promontory for which we have used jointly the available InSAR and GPS velocities. Firstly we have attached the two datasets to the same terrestrial reference frame and then using a simple dislocation approach, we have estimated the best fault parameters reproducing the available data, providing a solution corresponding to the Mattinata fault. Subsequently we have considered within a BM analysis both GPS and InSAR datasets in order to evaluate if the Mattinata fault may accommodate the deformation occurring in the central Adriatic due to the relative motion between the North-Adriatic and South-Adriatic plates. We obtain that the deformation occurring in that region should be accommodated by more that one fault system, that is however difficult to detect since the poor coverage of geodetic measurement offshore of the Gargano promontory. Finally we have performed also the estimate of the interseismic coupling distribution for the Mattinata fault, obtaining a shallow coupling pattern. Both of coupling distributions found using the BM approach have been tested by means of resolution checkerboard tests and they demonstrate that the coupling patterns depend on the geodetic data positions.

Numerical and semi-analytical models of sliding masses: application to the 1783 Scilla tsunamigenic landslide

The Scilla rock avalanche occurred on 6 February 1783 along the coast of the Calabria region (southern Italy), close to the Messina Strait. It was triggered by a mainshock of the Terremoto delle Calabrie seismic sequence, and it induced a tsunami wave responsible for more than 1500 casualties along the neighboring Marina Grande beach. The main goal of this work is the application of semi-analtycal and numerical models to simulate this event. The first one is a MATLAB code expressly created for this work that solves the equations of motion for sliding particles on a two-dimensional surface through a fourth-order Runge-Kutta method. The second one is a code developed by the Tsunami Research Team of the Department of Physics and Astronomy (DIFA) of the Bologna University that describes a slide as a chain of blocks able to interact while sliding down over a slope and adopts a Lagrangian point of view. A wide description of landslide phenomena and in particular of landslides induced by earthquakes and with tsunamigenic potential is proposed in the first part of the work. Subsequently, the physical and mathematical background is presented; in particular, a detailed study on derivatives discratization is provided. Later on, a description of the dynamics of a point-mass sliding on a surface is proposed together with several applications of numerical and analytical models over ideal topographies. In the last part, the dynamics of points sliding on a surface and interacting with each other is proposed. Similarly, different application on an ideal topography are shown. Finally, the applications on the 1783 Scilla event are shown and discussed.

Cartilage, bone and synovial histomorphometry in animal models of osteoarthritis

http://www.ncbi.nlm.nih.gov/pubmed/20864016

Life history, ecology and the biogeography of strong genetic breaks among 15 species of PaciWc rockWsh, Sebastes

Strong genetic change over short spatial scales is surprising among marine species with high dispersal potential. Concordant breaks among several species signals a role for geographic barriers to dispersal. Along the coast of California, such breaks have not been seen across the biogeographic barrier of Point Conception, but other potential geographic boundaries have been surveyed less often.;We tested for strong-population structure in 11 species of Sebastes sampled across two regions containing potential dispersal barriers, and conducted a meta-analysis including four additional species. We show two strong breaks north of Monterey Bay, spanning an oceanographic gradient and an upwelling jet. Moderate genetic structure is just as common in the north as it is in the south, across the biogeographic break at Point Conception. Gene Xow is generally higher among deep-water species, but these conclusions are confounded by phylogeny. Species in the subgenus Sebastosomus have higher structure than those in the subgenus;Pteropodus, despite having larvae with longer pelagic phases. DiVerences in settlement behavior in the face of ocean currents might help explain these diVerences. Across similar species across the same coastal environment, we document a wide variety of patterns in gene Xow, suggesting that interaction of individual species traits such as settlement behavior with environmental factors such as;oceanography can strongly impact population structure

Metabolomics reveals attenuation of the SLC6A20 kidney transporter in nonhuman primate and mouse models of type 2 diabetes mellitus

To enhance understanding of the metabolic indicators of type 2 diabetes mellitus (T2DM) disease pathogenesis and progression, the urinary metabolomes of well characterized rhesus macaques (normal or spontaneously and naturally diabetic) were examined. High-resolution ultra-performance liquid chromatography coupled with the accurate mass determination of time-of-flight mass spectrometry was used to analyze spot urine samples from normal (n = 10) and T2DM (n = 11) male monkeys. The machine-learning algorithm random forests classified urine samples as either from normal or T2DM monkeys. The metabolites important for developing the classifier were further examined for their biological significance. Random forests models had a misclassification error of less than 5%. Metabolites were identified based on accurate masses (<10 ppm) and confirmed by tandem mass spectrometry of authentic compounds. Urinary compounds significantly increased (p < 0.05) in the T2DM when compared with the normal group included glycine betaine (9-fold), citric acid (2.8-fold), kynurenic acid (1.8-fold), glucose (68-fold), and pipecolic acid (6.5-fold). When compared with the conventional definition of T2DM, the metabolites were also useful in defining the T2DM condition, and the urinary elevations in glycine betaine and pipecolic acid (as well as proline) indicated defective re-absorption in the kidney proximal tubules by SLC6A20, a Na(+)-dependent transporter. The mRNA levels of SLC6A20 were significantly reduced in the kidneys of monkeys with T2DM. These observations were validated in the db/db mouse model of T2DM. This study provides convincing evidence of the power of metabolomics for identifying functional changes at many levels in the omics pipeline.