Gauge Theories of Conformal Gravitation

In this thesis we investigate the locally scale-invariant theories of conformal and Weyl quadratic gravity, and the ensuing relationship between them. Using a Yang-Mills inspired gauge theory perspective, we derive the actions describing these theories and discuss their phenomenologies. Particular focus is put on the physically propagating degrees of freedom in each theory, as well as the cosmological implications of conformal gravity and the dimensional transmutation that occurs naturally in Weyl quadratic gravity. The issue of Ostrogradsky instabilities that arise from the fourth-order derivatives present in both theories is also discussed. Finally, using a process known as Ricci gauging, we find that conformal gravity can be viewed as gauged-fixed Weyl quadratic gravity, and we speculate on the existence of an alternative gauge fixing procedure that leads to a new theory which is dual to conformal gravity

Cross-correlation of CFHTLenS galaxy catalogue and Planck CMB lensing using the halo model prescription

I cross-correlate the galaxy counts from the Canada-France Hawaii Telescope Lensing Survey (CFHTLenS) galaxy catalogue and Cosmic Microwave Background (CMB) convergence from the Planck data release 1 (2013) and 2 (2015), following the work of Omori & Holder (2015). I improve their study by computing an analytic covariance from the Halo Model, implementing simulations to validate the theoretically estimated error bars and the reconstruction method, fitting both a galaxy bias and a cross-correlation amplitude using the joint cross and galaxy auto-correlation, and performing a series of null tests. Using a bayesian analysis, I find a galaxy bias $b=0.92_{-0.02}^{+0.02}$ and a cross-correlation amplitude $A=0.85_{-0.16}^{+0.15}$ for the 2015 release, whereas for the 2013 release I find $b=0.93_{-0.02}^{+0.02}$ and $A=1.05_{-0.15}^{+0.15}$. I thus confirm the difference between the two releases found by Omori & Holder (2015), although both values of the amplitude now appear to be compatible with the fiducial value $A=1$.Comment: 18 pages, 11 figure

Does the brain listen to the gut?

Transplanting gut bacteria from one mouse strain to another can override genetics and change behavior

Formal Dependability Engineering with MIOA

In this paper, we introduce MIOA, a stochastic process algebra-like specification language with datatypes, as well as a logic intSPDL, and its model checking algorithms. MIOA, which stands for Markovian input/output automata language, is an extension of Lynch's input/automata with Markovian timed transitions.MIOA can serve both as a fully fledged ``stand-alone'' specification language and the semantic model for the architectural dependability modelling and evaluation language Arcade. The logic intSPDL is an extension of the stochastic logic SPDL, to deal with the specialties of MIOA. intSPDL in the context of Arcade can be seen as the semantic model of abstract and complex dependability measures that can be defined in the Arcade framework. We define syntax and semantics of both MIOA and intSPDL, and show examples of applying MIOA and intSPDL in the realm of dependability modelling with Arcade

GCSRL - A Logic for Stochastic Reward Models with Timed and Untimed Behaviour

In this paper we define the logic GCSRL (generalised continuous stochastic reward logic) that provides means to reason about systems that have states which sojourn times are either greater zero, in which case this sojourn time is exponentially distributed (tangible states), or zero (vanishing states).\ud In case of generalised stochastic Petri nets (GSPNs) and stochastic process algebras it turned out that these vanishing states can be very useful when it comes to define system behaviour. In the same way these states are useful for defining system properties using stochastic logics. We extend both the semantic model and the semantics of CSRL such that it allows to attach impulse rewards to transitions emanating from vanishing states. We show by means of a small example how model checking GCSRL formulae works

SPDL Model Checking via Property-Driven State Space Generation

In this report we describe how both, memory and time requirements for stochastic model checking of SPDL (stochastic propositional dynamic logic) formulae can significantly be reduced. SPDL is the stochastic extension of the multi-modal program logic PDL.\ud SPDL provides means to specify path-based properties with or without timing restrictions. Paths can be characterised by so-called programs, essentially regular expressions, where the executability can be made dependent on the validity of test formulae. For model-checking SPDL path formulae it is necessary to build a product transition system (PTS)\ud between the system model and the program automaton belonging to the path formula that is to be verified.\ud In many cases, this PTS can be drastically reduced during the model checking procedure, as the program restricts the number of potentially satisfying paths. Therefore, we propose an approach that directly generates the reduced PTS from a given SPA specification and an SPDL path formula.\ud The feasibility of this approach is shown through a selection of case studies, which show enormous state space reductions, at no increase in generation time.\u

Many-body Green's function theory for thin ferromagnetic anisotropic Heisenberg films: treatment of the exchange anisotropy

The many-body Green's function theory developed in our previous work for treating the reorientation of the magnetization of thin ferromagnetic films is extended to include the exchange anisotropy. This leads to additional momentum dependencies which require some non-trivial changes in the formalism. The theory is developed for arbitrary spin values S and for multilayers. The effects of the exchange anisotropy and the single-ion anisotropy, which was treated in our earlier work, on the magnetic properties of thin ferromagnetic films are compared.Comment: 24 pages, 7 figures, accepted for publication in Eur. Phys. J.

Spacetime instability due to quantum gravity

We show that quantum gravity yields exponentially growing gravitational waves. Without a mechanism to stop these modes from growing, the universe would go through a gravitational collapse. For Minkowski background, we propose a solution by choosing an integration contour in Fourier space that does not enclose the problematic modes, thus preventing them from showing up in the effective theory. It turns out that this is only possible when the modes are removed altogether. For an expanding universe, we argue that the runaway modes can be managed accordingly to the dynamics of the Hubble constant, leading to important implications for astrophysics

Anisotropic susceptibilities of thin ferromagnetic films within many-body Green's function theory

Transverse and parallel static susceptibilities of in-plane uniaxial anisotropic ferromagnetic films are calculated within many-body Green's function theory on the basis of an Heisenberg model. The importance of collective magnetic excitations in particular in the paramagnetic regime are stressed by comparing with mean field calculations. The paper generalizes the work of Jensen et al. [1] to the multilayer case and to spins with S>1/2.Comment: 10 pages, 8 figures, submitted to Phys. Rev.