(2,m,n)-groups with Euler characteristic equal to −2asb-2^as^b

We study those $(2, m, n)$-groups which are almost simple and for which the absolute value of the Euler characteristic is a product of two prime powers. All such groups which are not isomorphic to $PSL_2 (q)$ or $PGL_2(q)$ are completely classified

World. An anthropological examination (part 2)

This paper is the second of a two-part essay that aims to examine anthropologically the category “world.” The first part argued in favor of a single-world approach and for the unavoidable centrality of personhood in the human condition. In this second part of the essay, I address the metaphysical implications of the category “world” and relate them to the process of “worlding,” thus defending the continued heuristic value of the old anthropological category of worldview. I suggest that a consideration of the Ontological Proof of God’s existence, developed by St. Anselm of Canterbury in the late eleventh century, helps us develop a comparative theory of personhood by showing how the experience of transcendence is inherent in personal ontogenesis

Finite scattering amplitudes in field theory

In this thesis we explore the infrared problem perturbatively in massless field theory. We review the current conventional methods and theorems that are applied in the calculation of QCD jet observables and then discuss the formulation of an alternative approach called the Asymptotic Interaction Picture (AIP). The AIP is based on a unitary transformation such that long-ranged interactions are present in the asymptotic Lagrangian and thus the states associated with this picture are no longer free Fock states but are asymptotic states containing soft and collinear interactions. Under the guidance of the AIP we are led to modifying conventional perturbation theory, cutting up amplitudes in a manner that allows for the construction of infrared finite amplitudes that are in correspondence with the asymptotic states of the AIP. We apply this formalism to several NLO corrections to QCD observables and construct dressed states who's amplitudes are finite in all regions of phase space. Using these amplitudes we compute several observables and show agreement with the conventional calculations in infrared safe regions. Higher-order calculations are then investigated in ϕ (^3)theory and the infrared pole structure is shown to behave as expected such that NNLO corrections to dressed states are obtained. Finally we present part of the NNLO correction to the dressed two-parton amplitude in QCD and show that, with several provisos, this approach may potentially be applied to the precision calculations of observables at the International Linear Collider (ILC). We therefore give a possible alternative to current subtraction methods at NNLO when no initial state radiation is present

Collaborative Development of Open Educational Resources for Open and Distance Learning

Open and distance learning (ODL) is mostly characterised by the up front development of self study educational resources that have to be paid for over time through use with larger student cohorts (typically in the hundreds per annum) than for conventional face to face classes. This different level of up front investment in educational resources, and increasing pressures to utilise more expensive formats such as rich media, means that collaborative development is necessary to firstly make use of diverse professional skills and secondly to defray these costs across institutions. The Open University (OU) has over 40 years of experience of using multi professional course teams to develop courses; of working with a wide range of other institutions to develop educational resources; and of licensing use of its educational resources to other HEIs. Many of these arrangements require formal contracts to work properly and clearly identify IPR and partner responsibilities. With the emergence of open educational resources (OER) through the use of open licences, the OU and other institutions has now been able to experiment with new ways of collaborating on the development of educational resources that are not so dependent on tight legal contracts because each partner is effectively granting rights to the others to use the educational resources they supply through the open licensing (Lane, 2011; Van Dorp and Lane, 2011). This set of case studies examines the many different collaborative models used for developing and using educational resources and explain how open licensing is making it easier to share the effort involved in developing educational resources between institutions as well as how it may enable new institutions to be able to start up open and distance learning programmes more easily and at less initial cost. Thus it looks at three initiatives involving people from the OU (namely TESSA, LECH-e, openED2.0) and contrasts these with the Peer-2-Peer University and the OER University as exemplars of how OER may change some of the fundamental features of open and distance learning in a Web 2.0 world. It concludes that while there may be multiple reasons and models for collaborating on the development of educational resources the very openness provided by the open licensing aligns both with general academic values and practice but also with well established principles of open innovation in businesses

Perfect countably infinite Steiner triple systems

We use a free construction to prove the existence of perfect Steiner triple systems on a countably infinite point set. We use a specific countably infinite family of partial Steiner triple systems to start the construction, thus yielding 2ℵ0 non-isomorphic perfect systems

Searching and ranking ontologies on the Semantic Web

The number of ontologies available online is increasing constantly. Tools that are capable of searching, retrieving, and ranking ontologies are becoming crucial to facilitate ontology search and reuse. In this document, we describe OntoSearch, which is a tool for capturing and searching ontologies on the Semantic web. We also briefly describe AKTiveRank which is used to rank OWL ontologies based on certain ontology-structure analysis.

Aspects of holographic string theory

In this thesis we study several aspects of gauge/gravity dualities. We start by analyzing the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be canceled out by choosing the boundary condition of the string appropriately. Our results, together with the result of [15], where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analyzed, allow us to conclude that Legendre transform is at best capable of canceling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancelation of the leading linear divergences generally and find that many well-known super gravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N = 1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be canceled away with the Legendre transform. Moreover, our results indicate that the finiteness of the expectation value of the Wilson loop does not depend on the supersymmetry. In the next chapter, we propose a definition of the Wilson loop operator in the N = 1 ß-deformed supersymmetric Yang-Mills theory. Although the operator is not BPS, it has a finite expectation value, result that come from the work in the previous chapter but also from the field theory calculations at least up to order (9(^2)N)(^2). We also derive the general form of the boundary condition satisfied by the dual string worldsheet and find that it is deformed. Finiteness of the expectation value of the Wilson loop, together with some rather remarkable properties of the Lunin-Maldacena metric and the B-field, fixes the boundary condition to be one which is characterized by the vielbein of the deformed supergravity metric. The Wilson loop operators provide natural candidates as dual descriptions to some of the existing D-brane configurations in the Lunin-Maldacena background. We also construct the string dual configuration for a near-1/4 BPS circular Wilson loop operator. The string lies on a deformed three-sphere instead of a two-sphere as in the undeformed case. The expectation value of the Wilson loop operator is computed using the AdS/CFT correspondence and is found to be independent of the deformation. In the next chapter we focus on a different topic, and find point-like and classical string solutions on the AdS(_5) x X(^5), where are the 5-dimensional Sasaki-Einstein manifolds Y(^p,q) and L(^p.q.r). The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. We find the energy-spin relations of the above solutions and see that they depend on the parameters of the Sasaki-Einstein manifolds. A discussion on BPS solutions is presented as well. In the last chapter we present a general discussion on topics which related closely to all previous chapters. Among other things we also give some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory

Simulation of packet and cell-based communication networks

This thesis investigates, using simulation techniques, the practical aspects of implementing a novel mobility protocol on the emerging Broadband Integrated Services Digital Network standard. The increasing expansion of telecommunications networks has meant that the demand for simulation has increased rapidly in recent years; but conventional simulators are slow and developments in the communications field are outstripping the ability of sequential uni-processor simulators. Newer techniques using distributed simulation on a multi-processor network are investigated in an attempt to make a cell-level simulation of a non-trivial B.-I.S.D.N. network feasible. The current state of development of the Asynchronous Transfer Mode standard, which will be used to implement a B.-I.S.D.N., is reviewed and simulation studies of the Orwell Slotted Ring protocol were made in an attempt to devise a simpler model for use in the main simulator. The mobility protocol, which uses a footprinting technique to simplify hand- offs by distributing information about a connexion to surrounding base stations, was implemented on the simulator and found to be functional after a few 'special case' scenarios had been catered for

On the synthesis and processing of high quality audio signals by parallel computers

This work concerns the application of new computer architectures to the creation and manipulation of high-quality audio bandwidth signals. The configuration of both the hardware and software in such systems falls under consideration in the three major sections which present increasing levels of algorithmic concurrency. In the first section, the programs which are described are distributed in identical copies across an array of processing elements; these programs run autonomously, generating data independently, but with control parameters peculiar to each copy: this type of concurrency is referred to as isonomic}The central section presents a structure which distributes tasks across an arbitrary network of processors; the flow of control in such a program is quasi- indeterminate, and controlled on a demand basis by the rate of completion of the slave tasks and their irregular interaction with the master. Whilst that interaction is, in principle, deterministic, it is also data-dependent; the dynamic nature of task allocation demands that no a priori knowledge of the rate of task completion be required. This type of concurrency is called dianomic? Finally, an architecture is described which will support a very high level of algorithmic concurrency. The programs which make efficient use of such a machine are designed not by considering flow of control, but by considering flow of data. Each atomic algorithmic unit is made as simple as possible, which results in the extensive distribution of a program over very many processing elements. Programs designed by considering only the optimum data exchange routes are said to exhibit systolic^ concurrency. Often neglected in the study of system design are those provisions necessary for practical implementations. It was intended to provide users with useful application programs in fulfilment of this study; the target group is electroacoustic composers, who use digital signal processing techniques in the context of musical composition. Some of the algorithms in use in this field are highly complex, often requiring a quantity of processing for each sample which exceeds that currently available even from very powerful computers. Consequently, applications tend to operate not in 'real-time' (where the output of a system responds to its input apparently instantaneously), but by the manipulation of sounds recorded digitally on a mass storage device. The first two sections adopt existing, public-domain software, and seek to increase its speed of execution significantly by parallel techniques, with the minimum compromise of functionality and ease of use. Those chosen are the general- purpose direct synthesis program CSOUND, from M.I.T., and a stand-alone phase vocoder system from the C.D.P..(^4) In each case, the desired aim is achieved: to increase speed of execution by two orders of magnitude over the systems currently in use by composers. This requires substantial restructuring of the programs, and careful consideration of the best computer architectures on which they are to run concurrently. The third section examines the rationale behind the use of computers in music, and begins with the implementation of a sophisticated electronic musical instrument capable of a degree of expression at least equal to its acoustic counterparts. It seems that the flexible control of such an instrument demands a greater computing resource than the sound synthesis part. A machine has been constructed with the intention of enabling the 'gestural capture' of performance information in real-time; the structure of this computer, which has one hundred and sixty high-performance microprocessors running in parallel, is expounded; and the systolic programming techniques required to take advantage of such an array are illustrated in the Occam programming language

Trinity symmetry and kaleidoscopic regular maps

A cellular embedding of a connected graph (also known as a map) on an orientable surface has trinity symmetry if it is isomorphic to both its dual and its Petrie dual. A map is regular if for any two incident vertex-edge pairs there is an automorphism of the map sending the first pair onto the second. Given a map M with all vertices of the same degree d, for any e relatively prime to d the power map Me is formed from M by replacing the cyclic rotation of edges at each vertex on the surface with the e th power of the rotation. A map is kaleidoscopic if all of its power maps are pairwise isomorphic. In this paper, we present a covering construction that gives infinite families of kaleidoscopic regular maps with trinity symmetry