Some Implications on Amorphic Association Schemes

AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition

Some Implications on Amorphic Association Schemes

AMS classifications: 05E30, 05B20;

Using geometric algebra to interactively model the geometry of Euclidean and non-Euclidean spaces.

This research interprets and develops the 'conformal model of space' in a way appropriate for a graphics developer interested in the design of interactive software for exploring 2-dimensional non-Euclidean spaces. The conformal model of space extends the standard projective model – instead of adding just one extra dimension to standard Euclidean space, a second one is added that results in a Minkowski space similar to that of relativistic spacetime. Also, standard matrix algebra is replaced by geometric ( i.e. Clifford) algebra. The key advantage of the conformal model is that both Euclidean and non- Euclidean spaces are accommodated within it. Transformations in conformal space are generated by bivectors which are special elements of the geometric algebra. These induce geometric transformations in the embedded non Euclidean spaces. However, the relationship between the bivector generated transformations of the Minkowski modelling space and the geometric transformations they induce is extremely obscure. This thesis provides new analytical tools for determining the nature of this relationship. Their derivation was motivated by the need to successfully solve key implementation problems relating to navigation and in-scene mouse interaction. The analytic approaches developed not only successfully solved these problems but pointed the way to implementing other unplanned features. These include facilities for dynamically altering on-screen geometry as well as using multiple viewports to allow the user to interact with the same objects embedded in different geometries. These new analytical approaches could be powerful tools for solving future and as yet unforeseen implementation problems

Partial geometric designs and difference families

We examine the designs produced by different types of difference families. Difference families have long been known to produce designs with well behaved automorphism groups. These designs provide the elegant solutions desired for applications. In this work, we explore the following question: Does every (named) design have a difference family analogue? We answer this question in the affirmative for partial geometric designs

ADVANCES IN QUANTUM PARAMETER ESTIMATION AND OTHER TOPICS

The first half of this thesis deals with the problem of parameter estimation in a quantum system. In quantum parameter estimation theory, the quantum Fisher information is usually considered as the ultimate precision limit, beyond which no further improvement is possible due to the inherent stochasticity of quantum measurements. On the other hand, in this thesis we will show that a better precision is achievable than predicted by a quantum Fisher information analysis. This is true if some regularity assumptions about the underlying quantum parametric model are relaxed. In such situations, the quantum Fisher information does not completely capture the best possible performance of quantum measurements, and a different approach must be followed. In the second part of the thesis, we will focus on some applications of orthogonal array theory to two notable quantum information problems: the problem of multipartite entanglement classification and the quantum marginal problem. Introduced by Rao in 1947, orthogonal arrays have been usefully applied to different fields, from cryptography and coding theory to the statistical design of experiments, software testing and quality control. Remarkably, orthogonal arrays have also found application in quantum information and, in particular, in the study of quantum entanglement. We will employ tools from orthogonal array theory to study a toy version of the multipartite entanglement classification problem. Finally, we will show how orthogonal arrays can be employed to build constructive solutions to low-dimensional quantum marginal problems

J. N. Srivastava and experimental design

J. N. Srivastava was a tremendously productive statistical researcher for five decades. He made significant contributions in many areas of statistics, including multivariate analysis and sampling theory. A constant throughout his career was the attention he gave to problems in discrete experimental design, where many of his best known publications are found. This paper focuses on his design work, tracing its progression, recounting his key contributions and ideas, and assessing its continuing impact. A synopsis of his design-related editorial and organizational roles is also included

Using geometric algebra to interactively model the geometry of Euclidean and non-Euclidean spaces

This research interprets and develops the 'conformal model of space' in a way appropriate for a graphics developer interested in the design of interactive software for exploring 2-dimensional non-Euclidean spaces. The conformal model of space extends the standard projective model – instead of adding just one extra dimension to standard Euclidean space, a second one is added that results in a Minkowski space similar to that of relativistic spacetime. Also, standard matrix algebra is replaced by geometric ( i.e. Clifford) algebra. The key advantage of the conformal model is that both Euclidean and non- Euclidean spaces are accommodated within it. Transformations in conformal space are generated by bivectors which are special elements of the geometric algebra. These induce geometric transformations in the embedded non Euclidean spaces. However, the relationship between the bivector generated transformations of the Minkowski modelling space and the geometric transformations they induce is extremely obscure. This thesis provides new analytical tools for determining the nature of this relationship. Their derivation was motivated by the need to successfully solve key implementation problems relating to navigation and in-scene mouse interaction. The analytic approaches developed not only successfully solved these problems but pointed the way to implementing other unplanned features. These include facilities for dynamically altering on-screen geometry as well as using multiple viewports to allow the user to interact with the same objects embedded in different geometries. These new analytical approaches could be powerful tools for solving future and as yet unforeseen implementation problems.EThOS - Electronic Theses Online ServiceGBUnited Kingdo