Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.Comment: v2: 38 pages; completely rewritten. The crucial difference with respect to the first version is that in the present one the quantum four-sphere, the base space of the fibration, is NOT a quantum homogeneous space. This has important consequences and led to very drastic changes to the paper. To appear in CM

Evaluation of the usefulness of a computer‐based learning program to support student learning in pharmacology

This study aims to evaluate the effectiveness of a computer‐based teaching program in supporting and enhancing traditional teaching methods. The program covers the pharmacology of inflammation and has been evaluated with a group of second‐year medical students at a UK university. The study assessed subject‐specific knowledge using a pre‐ and post‐test and surveyed, by questionnaire, students’ perceptions of the usefulness of the program to support learning before and after use. The use of computers for learning amongst this cohort of students was widespread. The results demonstrated an increase in students ‘ knowledge of the pharmacology of inflammation, coupled with a positive attitude towards the CBL program they had used and the advantages that this mode of study may provide in enabling students to manage their own learning. However, students did not feel that the program could substitute for traditional teaching (lectures)

The ADHM Construction of Instantons on Noncommutative Spaces

We present an account of the ADHM construction of instantons on Euclidean space-time $\mathbb{R}^4$ from the point of view of noncommutative geometry. We recall the main ingredients of the classical construction in a coordinate algebra format, which we then deform using a cocycle twisting procedure to obtain a method for constructing families of instantons on noncommutative space-time, parameterised by solutions to an appropriate set of ADHM equations. We illustrate the noncommutative construction in two special cases: the Moyal-Groenewold plane $\mathbb{R}^4_\hbar$ and the Connes-Landi plane $\mathbb{R}^4_\theta$.Comment: Latex, 40 page

Focal Ca2+ Transient Detection in Smooth Muscle

Ca2+ imaging of smooth muscle provides insight into cellular mechanisms that may not result in changes of membrane potential, such as the release of Ca2+ from internal stores, and allows multiple cells to be monitored simultaneously to assess, for example, coupling in syncytial tissue. Subcellular Ca2+ transients are common in smooth muscle, yet are difficult to measure accurately because of the problems caused by their stochastic occurrence, over an often wide field of view, in an organ that it prone to contract. To overcome this problem, we've developed a series of imaging protocols and analysis routines to acquire and then analyse, in an automated fashion, the frequency, location and amplitude of such events. While this approach may be applied in other contexts, our own work involves the detection of local purinergic Ca2+ transients for locating transmitter release with submicron resolution

Competition for Andersen\u27s Clients

We examine competition for Andersen’s public clients during and after its failure in 2002. This setting provides a natural experiment to examine audit market dynamics at the local level. We construct a database documenting Big4 purchases of local Andersen offices. After exploring the factors associated with office purchases, we examine the impact of office purchases on public client market share gains and changes in audit fees. We find that three Big4 firms – Deloitte, Ernst & Young, and KPMG – purchased approximately 60% of Andersen’s offices while PricewaterhouseCoopers did not purchase any. The probability that a firm purchased a specific office is greater in markets where the acquiring firm: 1) already had a presence, 2) had a lower ratio of local Andersen clients to the purchaser’s clients, and 3) had already acquired relatively more local former Andersen public clients than other firms prior to the purchase. Our fee analysis expands the United States Government Accountability Office (GAO) post-Andersen audit market study by documenting that the former Andersen clients’ change in audit fees is associated with the differences in client acquisition method

Simulated kinetic effects of the corona and solar cycle on high altitude ion transport at Mars

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/99008/1/jgra50358.pd

On the origin of aurorae on Mars

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95268/1/grl20829.pd

Quantisation of twistor theory by cocycle twist

We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra form which we can then `quantise' by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor space CP^3, compactified Minkowski space CMh and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we show that the pull-back of the tautological bundle on CMh pulls back to the basic instanton on S^4\subset CMh and that this observation quantises to obtain the Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the tautological bundle on our \theta-deformed CMh. We likewise quantise the fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae for classical and quantum CP^