Self-Dual Supergravity from N=2 Strings

A new heterotic N=2 string with manifest target space supersymmetry is constructed by combining a conventional N=2 string in the right-moving sector and a Green-Schwarz-Berkovits type string in the left-moving sector. The corresponding sigma model is then obtained by turning on background fields for the massless excitations. We compute the beta functions and we partially check the OPE's of the superconformal algebra perturbatively in $\alpha'$, all in superspace. The resulting field equations describe N=1 self-dual supergravity.Comment: 32 pages, Latex, discussion in pages 10, 11 revised so that it is compatible with the complex structure chosen in Appendix A. Appendix A slightly expanded. Final versio

Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold

We quantize the superstring on the AdS_2 x S^2 background with Ramond-Ramond flux using a PSU(1,1|2)/U(1) x U(1) sigma model with a WZ term. One-loop conformal invariance of the model is guaranteed by a general mechanism which holds for coset spaces G/H where G is Ricci-flat and H is the invariant locus of a Z_4 automorphism of G. This mechanism gives conformal theories for the PSU(1,1|2) x PSU(2|2)/SU(2) x SU(2) and PSU(2,2|4)/SO(4,1) x SO(5) coset spaces, suggesting our results might be useful for quantizing the superstring on AdS_3 x S^3 and AdS_5 x S^5 backgrounds.Comment: 34 pages, 4 figures, harvmac big mode ; typos corrected, clarified the choice of the real form

Solving promise equations over monoids and groups

We give a complete complexity classification for the problem of finding a solution to a given system of equations over a fixed finite monoid, given that a solution over a more restricted monoid exists. As a corollary, we obtain a complexity classification for the same problem over groups

Algorithms and VLSI architectures for parametric additive synthesis

A parametric additive synthesis approach to sound synthesis is advantageous as it can model sounds in a large scale manner, unlike the classical sinusoidal additive based synthesis paradigms. It is known that a large body of naturally occurring sounds are resonant in character and thus fit the concept well. This thesis is concerned with the computational optimisation of a super class of form ant synthesis which extends the sinusoidal parameters with a spread parameter known as band width. Here a modified formant algorithm is introduced which can be traced back to work done at IRCAM, Paris. When impulse driven, a filter based approach to modelling a formant limits the computational work-load. It is assumed that the filter's coefficients are fixed at initialisation, thus avoiding interpolation which can cause the filter to become chaotic. A filter which is more complex than a second order section is required. Temporal resolution of an impulse generator is achieved by using a two stage polyphase decimator which drives many filterbanks. Each filterbank describes one formant and is composed of sub-elements which allow variation of the formant’s parameters. A resource manager is discussed to overcome the possibility of all sub- banks operating in unison. All filterbanks for one voice are connected in series to the impulse generator and their outputs are summed and scaled accordingly. An explorative study of number systems for DSP algorithms and their architectures is investigated. I invented a new theoretical mechanism for multi-level logic based DSP. Its aims are to reduce the number of transistors and to increase their functionality. A review of synthesis algorithms and VLSI architectures are discussed in a case study between a filter based bit-serial and a CORDIC based sinusoidal generator. They are both of similar size, but the latter is always guaranteed to be stable

Non-local Hamiltonian structures and applications to the theory of integrable systems I

We develop a rigorous theory of non-local Hamiltonian structures, built on the notion of a non-local Poisson vertex algebra. As an application, we find conditions that guarantee applicability of the Lenard-Magri scheme of integrability to a pair of compatible non-local Hamiltonian structures.Comment: 55 page

Design and implementation of high-radix arithmetic systems based on the SDNR/RNS data representation

This project involved the design and implementation of high-radix arithmetic systems based on the hybrid SDNRIRNS data representation. Some real-time applications require a real-time arithmetic system. An SDNR/RNS arithmetic system provides parallel, real-time processing. The advantages and disadvantages of high-radix SDNR/RNS arithmetic, and the feasibility of implementing SDNR/RNS arithmetic systems in CMOS VLSI technology, were investigated in this project. A common methodological model, which included the stages of analysis, design, implementation, testing, and simulation, was followed. The combination of the SDNR and RNS transforms potential complex logic networks into simpler logic blocks. It was found that when constructing a SDNRIRNS adder, factors such as the radix, digit set, and moduli must be taken into account. There are many avenues still to explore. For example, implementing other arithmetic systems in the same CMOS VLSI technology used in this project and comparing them to equivalent SDNR/RNS systems would provide a set of benchmarks. These benchmarks would be useful in addressing issues relating to relative performance

Techniques for power system simulation using multiple processors

The thesis describes development work which was undertaken to improve the speed of a real-time power system simulator used for the development and testing of control schemes. The solution of large, highly sparse matrices was targeted because this is the most time-consuming part of the current simulator. Major improvements in the speed of the matrix ordering phase of the solution were achieved through the development of a new ordering strategy. This was thoroughly investigated, and is shown to provide important additional improvements compared to standard ordering methods, in reducing path length and minimising potential pipeline stalls. Alterations were made to the remainder of the solution process which provided more flexibility in scheduling calculations. This was used to dramatically ease the run-time generation of efficient code, dedicated to the solution of one matrix structure, and also to reduce memory requirements. A survey of the available microprocessors was performed, which concluded that a special-purpose design could best implement the code generated at run-time, and a design was produced using a microprogrammable floating-point processor, which matched the code produced by the earlier work. A method of splitting the matrix solution onto parallel processors was investigated, and two methods of producing network splits were developed and their results compared. The best results from each method were found to agree well, with a predicted three-fold speed-up for the matrix solution of the C.E.G.B. transmission system from the use of six processors. This gain will increase for the whole simulator. A parallel processing topology of the partitioned network and produce the necessary structures for the remainder of the solution process