A String and M-theory Origin for the Salam-Sezgin Model

An M/string-theory origin for the six-dimensional Salam-Sezgin chiral gauged supergravity is obtained, by embedding it as a consistent Pauli-type reduction of type I or heterotic supergravity on the non-compact hyperboloid ${\cal H}^{2,2}$ times $S^1$. We can also obtain embeddings of larger, non-chiral, gauged supergravities in six dimensions, whose consistent truncation yields the Salam-Sezgin theory. The lift of the Salam-Sezgin (Minkowski)$_4\times S^2$ ground state to ten dimensions is asymptotic at large distances to the near-horizon geometry of the NS5-brane.Comment: Latex, 18 pages; minor correction

Footballs, Conical Singularities and the Liouville Equation

We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.Comment: 15 pages, Refs. added, minor changes. Typo in eq. 4.3 corrected. Version to be published in PR

A High-Performance Domain-Specific Language and Code Generator for General N-body Problems

General N-body problems are a set of problems in which an update to a single element in the system depends on every other element. N-body problems are ubiquitous, with applications in various domains ranging from scientific computing simulations in molecular dynamics, astrophysics, acoustics, and fluid dynamics all the way to computer vision, data mining and machine learning problems. Different N-body algorithms have been designed and implemented in these various fields. However, there is a big gap between the algorithm one designs on paper and the code that runs efficiently on a parallel system. It is time-consuming to write fast, parallel, and scalable code for these problems. On the other hand, the sheer scale and growth of modern scientific datasets necessitate exploiting the power of both parallel and approximation algorithms where there is a potential to trade-off accuracy for performance. The main problem that we are tackling in this thesis is how to automatically generate asymptotically optimal N-body algorithms from the high-level specification of the problem. We combine the body of work in performance optimizations, compilers and the domain of N-body problems to build a unified system where domain scientists can write programs at the high level while attaining performance of code written by an expert at the low level.In order to generate a high-performance, scalable code for this group of problems, we take the following steps in this thesis; first, we propose a unified algorithmic framework named PASCAL in order to address the challenge of designing a general algorithmic template to represent the class of N-body problems. PASCAL utilizes space-partitioning trees and user-controlled pruning/approximations to reduce the asymptotic runtime complexity from linear to logarithmic in the number of data points. In PASCAL, we design an algorithm that automatically generates conditions for pruning or approximation of an N-body problem considering the problem's definition. In order to evaluate PASCAL, we developed tree-based algorithms for six well-known problems: k-nearest neighbors, range search, minimum spanning tree, kernel density estimation, expectation maximization, and Hausdorff distance. We show that applying domain-specific optimizations and parallelization to the algorithms written in PASCAL achieves 10x to 230x speedup compared to state-of-the-art libraries on a dual-socket Intel Xeon processor with 16 cores on real-world datasets. Second, we extend the PASCAL framework to build PASCAL-X that adds support for NUMA-aware parallelization. PASCAL-X also presents insights on the influence of tuning parameters. Tuning parameters such as leaf size (influences the shape of the tree) and cut-off level (controls the granularity of tasks) of the space-partitioning trees result in performance improvement of up to 4.6x. A key goal is to generate scalable and high-performance code automatically without sacrificing productivity. That implies minimizing the effort the users have to put in to generate the desired high-performance code. Another critical factor is the adaptivity, which indicates the amount of effort that is required to extend the high-performance code generation to new N-body problems. Finally, we consider these factors and develop a domain-specific language and code generator named Portal, which is built on top of PASCAL-X. Portal's language design is inspired by the mathematical representation of N-body problems, resulting in an intuitive language for rapid implementation of a variety of problems. Portal's back-end is designed and implemented to generate optimized, parallel, and scalable implementations for multi-core systems. We demonstrate that the performance achieved by using Portal is comparable to that of expert hand-optimized code while providing productivity for domain scientists. For instance, using Portal for the k-nearest neighbors problem gains performance that is similar to the hand-optimized code, while reducing the lines of code by 68x. To the best of our knowledge, there are no known libraries or frameworks that implement parallel asymptotically optimal algorithms for the class of general N-body problems and this thesis primarily aims to fill this gap. Finally, we present a case study of Portal for the real-world problem of face clustering. In this case study, we show that Portal not only provides a fast solution for the face clustering problem with similar accuracy as the state-of-the-art algorithm, but also it provides productivity by implementing the face clustering algorithm in only 14 lines of Portal code

3-Branes and Uniqueness of the Salam-Sezgin Vacuum

We prove the uniqueness of the supersymmetric Salam-Sezgin (Minkowski)_4\times S^2 ground state among all nonsingular solutions with a four-dimensional Poincare, de Sitter or anti-de Sitter symmetry. We construct the most general solutions with an axial symmetry in the two-dimensional internal space, and show that included amongst these is a family that is non-singular away from a conical defect at one pole of a distorted 2-sphere. These solutions admit the interpretation of 3-branes with negative tension.Comment: Latex, 12 pages; typos corrected, discussion of brane tensions amende

A Conical Tear Drop as a Vacuum-Energy Drain for the Solution of the Cosmological Constant Problem

We propose a partial solution to the cosmological constant problem by using the simple observation that a three-brane in a six-dimensional bulk is flat. A model is presented in which Standard Model vacuum energy is always absorbed by the transverse space. The latter is a tear-drop like space with a conical singularity, which preserves bulk supersymmetry and gives rise to conventional macroscopic 4D gravity with no cosmological constant. Its cone acts like a drain, depleting vacuum energy from the three-brane to the tear drop increasing its volume. We stress that although gravity is treated classically, Standard Model is handled quantum-field theoretically and the model is robust against Standard Model corrections and particular details. The price paid is the presence of boundaries which are nevertheless physically harmless by appropriate boundary conditions.Comment: 14 pages, 1 fig. As appeared in Phys. lett.

New D=6, N=(1,1) Gauged Supergravity with Supersymmetric (Minkowski)_4 X S^2 Vacuum

We obtain a new gauged D=6, N=(1,1) pure supergravity by a generalised consistent Kaluza-Klein reduction of M-theory on K3 \times R. The reduction requires a conspiratory gauging of both the Cremmer-Julia type global (rigid) symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion. The gauged supergravity is different from the Romans D=6 gauged supergravity in that the four vector fields in our new theory are all abelian. We show that it admits a supersymmetric (Minkowski)_4\times S^2 vacuum, which can be lifted to D=11 where it becomes the near-horizon geometry of two intersecting M5-branes wrapping on a supersymmetric two-cycle of K3.Comment: latex, 13 pages, typo correcte

Brane Gravitational Interactions from 6D Supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincare symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.Comment: 13 pages, 4 figure

Hypomineralisation or hypoplasia?

Enamel hypomineralisation is a qualitative defect, with reduced mineralisation resulting in discoloured enamel in a tooth of normal shape and size. Because the enamel is weaker, teeth can undergo post eruptive breakdown, resulting in missing enamel. Enamel hypoplasia is a quantitative defect of the enamel presenting as pits, grooves, missing enamel or smaller teeth. It can sometimes be difficult to differentiate between the two. In this review paper, we aim to explain the importance of differentiating between the two conditions, and how to manage patients presenting with enamel defects

The 6D SuperSwirl

We present a novel supersymmetric solution to a nonlinear sigma model coupled to supergravity. The solution represents a static, supersymmetric, codimension-two object, which is different to the familiar cosmic strings. In particular, we consider 6D chiral gauged supergravity, whose spectrum contains a number of hypermultiplets. The scalar components of the hypermultiplet are charged under a gauge field, and supersymmetry implies that they experience a simple paraboloid-like (or 2D infinite well) potential, which is minimised when they vanish. Unlike conventional vortices, the energy density of our configuration is not localized to a string-like core. The solutions have two timelike singularities in the internal manifold, which provide the necessary boundary conditions to ensure that the scalars do not lie at the minimum of their potential. The 4D spacetime is flat, and the solution is a continuous deformation of the so-called ``rugby ball'' solution, which has been studied in the context of the cosmological constant problem. It represents an unexpected class of supersymmetric solutions to the 6D theory, which have gravity, gauge fluxes and hyperscalars all active in the background.Comment: 26 pages, 2 figures, JHEP3 class. Typos corrected, analysis expanded, references adde

Brane Universes and the Cosmological Constant

The cosmological constant problem and brane universes are reviewed briefly. We discuss how the cosmological constant problem manifests itself in various scenarios for brane universes. We review attempts - and their difficulties - that aim at a solution of the cosmological constant problem.Comment: corrected typos, added references, 13 pages, accepted by MPLA as brief revie