This work introduces a new class of image model which we call dynamic trees or DTs. A dynamic tree model specifies a prior over structures of trees, each of which is a forest of one or more tree-structured belief networks (TSBN). In the literature standard tree-structured belief network models were found to produce “blocky” segmentations when naturally occurring boundaries within an image did not coincide with those of the subtrees in the rigid fixed structure of the network. Dynamic trees have a flexible architecture which allows the structure to vary to accommodate configurations where the subtree and image boundaries align, and experimentation with the model showed significant improvements. They are also hierarchical in nature allowing a multi-scale representation and are constructed within a well founded Bayesian framework. For large models the number of tree configurations quickly becomes intractable to enumerate over, presenting a problem for exact inference. Techniques such as Gibbs sampling over trees are considered and search using simulated annealing finds high posterior probability trees on synthetic 2-d images generated from the model. However simulated annealing and sampling techniques are rather slow. Variational methods are applied to the model in an attempt to approximate the posterior by a simpler tractable distribution, and the simplest of these techniques, mean field, found comparable solutions to simulated annealing in the order of 100 times faster. This increase in speed goes a long way towards making real-time inference in the dynamic tree viable. Variational methods have the further advantage that by attempting to model the full posterior distribution it is possible to gain an indication as to the quality of the solutions found. An EM-style update based upon mean field inference is derived and the learned conditional probability tables (describing state transitions between a node and its parent) are compared with exact EM on small tractable fixed architecture models. The mean field approximation by virtue of its form is biased towards fully factorised solutions which tends to create degenerate CPTs, but despite this mean field learning still produces solutions whose log likelihood rivals exact EM. Development of algorithms for learning the probabilities of the prior over tree structures completes the dynamic tree picture. After discussion of the relative merits of certain representations for the disconnection probabilities and initial investigation on small model structures the full dynamic tree model is applied to a database of images of outdoor scenes where all of its parameters are learned. DTs are seen to offer significant improvement in performance over the fixed architecture TSBN and in a coding comparison the DT achieves 0 294 bits per pixel (bpp) compression compared to 0 378 bpp for lossless JPEG on images of 7 colours.

In this thesis we study string theory on orbifolds of AdS3. Non-extremal BTZ black holes have been shown to offer a good opportunity to study closed string tachyon condensation, as there are tachyons in the winding sector even in superstring theory. We study extremal BTZ black holes, both M = O and M = J from a world sheet perspective. The string spectrum is calculated within bosonic string theory and tachyons are identied within the spectrum. The at space limit of the M = 0 black hole is considered and an extension to superstring theory is discussed. In the second half of the thesis we discuss the self dual orbifold. The self dual orbifold is a simple example of a geometry which contains an AdS2 factor. AdS2 factors also appear in the near horizon limit of extremal Kerr and Reissner-Nordström black holes. Using the AdS/CFT correspondence we conjecture that the self dual orbifold is dual to a CFT on two distinct boundary regions and nd evidence to support this statement. We consider asymptotically self dual orbifold spacetimes, one of which is dual to a single copy of the groundstate of the CFT.

We investigate the convergence of infinite-centre Gibbons-Hawking metrics, in the contexts of four-dimensional gravitational instantons and their applications, Kaluza-Klein monopoles and vortices, gravitational calorons, analytical extensions of Majumdar-Papapetrou metrics to form extreme Reissner-Nordstrom black holes, and Kaluza-Klein black holes. We find that, in most cases, periodic arrangements of the sources give rise to divergent potentials. We investigate the consequences of various methods of ensuring convergence, particularly in terms of the appearance of naked singularities, and construct several new solutions of Einstein's equations.

No description available.

Duality is often most clearly manifest in supersymmetric theories, where the rigid mathematical structure affords good control over the behaviour of the system. In many real-world applications, and particularly in particle physics at the TeV scale, supersymmetry can only be present as a broken symmetry. In this thesis we explore various situations in which duality can continue be important when supersymmetry is broken spontaneously, or even explicitly. We first focus on the AdS/CFT correspondence, and consider the effect of instantons in a non-supersymmetric gauge theory obtained via a marginal deformation of N = 4 super Yang-Mills. This gauge theory is expected to be dual to type IIB string theory on a background that is the product of five-dimensional anti-de Sitter spacetime and a deformed five-sphere. By performing an instanton calculation in the deformed gauge theory we extract a prediction for the dilaton-axion field in dual string theory. In the limit of small deformations where the supergravity regime is valid, our instanton result reproduces the expression for the axio-dilaton of the supergravity solution originally found by Frolov, thus supporting the validity of the correspondence. We then go on to look at how supersymmetry breaking in a metastable vacuum allows one to build simple and concrete models of gauge mediation. In the prototypical model of Intriligator, Seiberg and Shih (ISS), Seiberg duality plays an important role in ensuring the longevity of the metastable vacuum. In a move to construct more realistic models we deform the ISS model by adding a baryon term to the superpotential. This simple deformation causes spontaneous breaking of the approximate R-symmetry of the metastable vacuum. We then gauge an SU(5) flavour group and identify it with the parent gauge symmetry of the supersymmetric Standard Model. This implements direct mediation of supersymmetry breaking without the need for an additional messenger sector. A reasonable choice of parameters leads to gaugino masses of the right order. To further explore the phenomenology of metastable susy breaking we distinguish different types of models by the manner in which R-symmetry is broken in the metastable vacuum. In general, there are two possible ways to break R-symmetry: explicitly or spontaneously. We find that the MSSM phenomenology can be greatly affected how this breaking occurs in the Hidden Sector. Explicit R-symmetry breaking models lead to fairly standard gauge mediation patterns, but we argue that in the context of ISS-type models this only makes sense if B = 0 at the mediation scale. This leads to high values of tan beta as a generic prediction. If on the other hand R-symmetry is broken spontaneously, then R-violating soft terms tend to be suppressed with respect to the R-symmetry preserving ones, and one is led to a scenario with large scalar masses. These models interpolate between standard gauge mediation and split SUSY models. We provide benchmark points for the two scenarios, which serve to demonstrate that the specific dynamics of the Hidden Sector - the underlying nature of supersymmetry and R-symmetry breaking - can considerably affect the mass spectrum of the MSSM.

Motivated by the holographic principle, within the context of the AdS/CFT Correspondence in the large t'Hooft limit, we investigate how the geometry of certain highly symmetric bulk spacetimes can be recovered given information of physical quantities in the dual boundary CFT. In particular, we use the existence of bulk-cone singularities (relating the location of operator insertion points of singular boundary correlation functions to the endpoints of boundary-to boundary null geodesics in the bulk spacetime) and the holographic entanglement entropy proposal (relating the entanglement entropy of certain subsystems on the boundary to the area of static minimal surfaces) to recover the bulk metric. Using null and zero-energy spacelike boundary-to-boundary geodesic probes, we show that for classes of static, spherically symmetric, asymptotically AdS spacetimes, one can find analytic expressions for extracting the metric functions given boundary data. We find that if the spacetime admits null circular orbits, the bulk geometry can only be recovered from the boundary, down to the radius of null circular orbits. We illustrate this for various analytic and numerical boundary functions of endpoint separation of null and spacelike geodesics. We then extend our analysis to higher dimensional minimal surface probes within a class of static, planar symmetric, asymptotically AdS spacetimes. We again find analytic and perturbative expressions for the metric function in terms of the entanglement entropy of straight belt and circular disk subsystems of the boundary theory respectively. Finally, we discuss how such extractions can be generalised.

This thesis consists of an investigation into supersymmetry and its breaking. Emphasis is placed on the question of metastability and the role of non-topological solitons in the hidden sector. A desirable feature in models employing direct gauge mediation is that of tree level metastability, in order to generate large enough gaugino masses. An explicit realisation of this idea is constructed via a simple deformation of SQCD that is well motivated and needs no fine tuning. Any viable metastable supersymmetry breaking vacuum must also be stable enough to survive until the present day. Non-topological solitons, or Q-balls, are supported in all such vacua where there is a conserved, global U(1) symmetry and no massless, charged scalars. It is shown that for a broad class of models Q-balls are extremely influential on the vacuum lifetime and make seemingly viable vacua catastrophically short lived. Even when there is no effect on vacuum stability flat directions charged under an R-symmetry are a ubiquitous feature of O’Raifeartaigh models. Non-topological solitons associated with this symmetry, R-balls, are likely to form through the fragmentation of a condensate. Their cosmology is studied and it is found that they can have significant observable effects, from acting as a good dark matter candidate to providing the primary source of reheating in the early universe.

In this thesis we are going to investigate the behaviour of geodesics in a metric with a singularity known as the ``Mixmaster Universe''. This was motivated from previous work done, where the now well-known AdS/CFT correspondence was used to extract information about an AdS Schwarzschild black hole singularity beyond the horizon by studying correlators on the boundary that correspond to spacelike geodesics which bounce off the singularity. It was then shown that when the singularity was a cosmological one (in this case a Friedmann Robertson Walker cosmology with a Big Crunch), this was no longer possible as it is impossible for spacelike geodesics to bounce off this kind of singularity. This raises the question of whether, when an example of a more general singularity (the ``Mixmaster Universe'') is considered, it is possible for the spacelike geodesics to bounce away from this kind of singularity. This would enable us to potentially extract information about the singularity from the boundary correlators. Unfortunately, it will be shown that bouncing of such geodesics is extremely unlikely (if not impossible) and thus we would be unable to extract information about the singularity in the mixmaster universe using such a technique. We also discuss another aspect of the evolution of the mixmaster universe which shows that it does indeed have a very complicated evolution.

The major purpose of this work is to combine the minimal-hidden-photon model with Large Extra Dimensions (LED). This involves confining the Standard- Model photon to a 3-brane, whilst allowing the hidden photon and graviton to occupy the higher-dimensional bulk. After integrating out the extra dimensions both the hidden photon and graviton obtain a tower of massive Kaluza-Klein (KK) modes. The Standard-Model photon obtains no KK modes, in accordance with experiment. The work begins with a discussion of the minimal hidden photon with- out KK modes, including the current constraints. In most cases existing con- straints are simply quoted or rederived, but for some experiments original con- straints are produced. For example new constraints from atomic spectra are produced. Significant modifications are also made to the published constraint from the SN1987a energy-loss experiment. This means properly accounting for the plasma mass of the electron, and also accounting for the modification of the kinetic-mixing parameter in a plasma. Finally constraints are produced for the minimal-hidden-photon model with KK modes.

The non-perturbative behaviour of the non-Abelian gauge theory of strong interactions, namely QCD, is investigated using the Schwinger-Dyson equations. Using an approximation based on solving the Slavnov-Taylor identities, we derive a closed integral equation for the full gluon propagator. We numerically solve this equation, finding a consistent solution which is as singular as 1/p(^4) the momentum p(^2) → 0, whilst at large momenta the gluon propagates like a free particle. This infra-red behaviour can be seen as a signal for the confinement of quarks and gluons, implying, for example, that the Wilson loop operator behaves an 'axea law'. We then derive an equation for the full massless quark propagator. Using our solution for the gluon, we find the quark propagator to be suppressed at low momentum, to such an extent that the physical particle pole is removed, and free quarks cannot propagate. This is just what we might expect of a confining theory. The inclusion of quarks means we must study their dynamical effects via closed fermion loops in the gluon propagator equation. This couples the two equations together. We solve the two equations simultaneously, finding that the previous infra-red behaviour still holds. As we introduce more flavours of fermions, however, the infra-red enhancement of the gluon propagator is diminished, and this in turn means that the quark propagator is less suppressed. This exhibits the dynamical importance of quarks. These physically realistic results demonstrate the importance and validity of the Schwinger-Dyson equations as a valuable tool for investigating the non-perturbative features of gauge theories.