Invariant random subgroups of strictly diagonal limits of finite symmetric groups

We classify the ergodic invariant random subgroups of strictly diagonal limits of finite symmetric groups

Gauge Symmetry and Gravito-Electromagnetism

A tensor description of perturbative Einsteinian gravity about an arbitrary background spacetime is developed. By analogy with the covariant laws of electromagnetism in spacetime, gravito-electromagnetic potentials and fields are defined to emulate electromagnetic gauge transformations under substitutions belonging to the gauge symmetry group of perturbative gravitation. These definitions have the advantage that on a flat background, with the aid of a covariantly constant timelike vector field, a subset of the linearised gravitational field equations can be written in a form that is fully analogous to Maxwell's equations (without awkward factors of 4 and extraneous tensor fields). It is shown how the remaining equations in the perturbed gravitational system restrict the time dependence of solutions to these equations and thereby prohibit the existence of propagating vector fields. The induced gravito-electromagnetic Lorentz force on a test particle is evaluated in terms of these fields together with the torque on a small gyroscope. It is concluded that the analogy of perturbative gravity to Maxwell's description of electromagnetism can be valuable for (quasi-)stationary gravitational phenomena but that the analogy has its limitations.Comment: 29 pages no-fig

Engineering design applications of surrogate-assisted optimization techniques

The construction of models aimed at learning the behaviour of a system whose responses to inputs are expensive to measure is a branch of statistical science that has been around for a very long time. Geostatistics has pioneered a drive over the last half century towards a better understanding of the accuracy of such ‘surrogate’ models of the expensive function. Of particular interest to us here are some of the even more recent advances related to exploiting such formulations in an optimization context. While the classic goal of the modelling process has been to achieve a uniform prediction accuracy across the domain, an economical optimization process may aim to bias the distribution of the learning budget towards promising basins of attraction. This can only happen, of course, at the expense of the global exploration of the space and thus finding the best balance may be viewed as an optimization problem in itself. We examine here a selection of the state of-the-art solutions to this type of balancing exercise through the prism of several simple, illustrative problems, followed by two ‘real world’ applications: the design of a regional airliner wing and the multi-objective search for a low environmental impact hous

Integrating energy and environmental considerations into building design through use of a simplified thermal assessment method

New buildings and building refurbishments should be designed such that the best use is made of solar energy, and that fossil fuel based energy is not wasted. Because the thermal processes in a building are quite complex, the use of thermal assessment methods such as dynamic thermal simulation are generally recommended as part of the design process. These methods are intended to show building designers the effects of their building proposals on energy use, but are often too slow and difficult to use and do not really ‘fit’ into typical design practice. Therefore the job of energy assessment might be given to an engineer, but usually no assessment is done at all, or else the engineer is employed only to ‘rubber stamp’ the completed design. The method outlined in this paper is intended to give the building designer access to all the information in such a way that at early design stages the thermal characteristics of the building design can be quickly explored, in a parallel way to which designers explore issues of function and use, aesthetics, structure and cost. It is proposed that through use of such a method, considerations of energy and environment can be integrated into each project from the very start of the design process

A school in mind: an investigation of the stresses, pressures and challenges faced by Primary School Head Teachers in a context of organizational change in schools

This thesis is based on a research study conducted into the experiences of head teachers in their role of leaders in primary schools. Using biographical interviews, the study examines how participants have negotiated periods of change and challenge in their professional role. I will also consider how personal and professional biographies converge in participants’ understanding of role, leadership, organizational change and stress, and how wider organizational, political and social forces impacted upon those in role. The thesis will then go on to explore and attempt to extend some of the thinking related to the concept of the organization‐in‐the‐mind (Armstrong, 2005), which appeared, through the narratives of each participant to have considerable relevance to their understanding of professional role and indeed perhaps more significantly their performance in role

Distinguishability of infinite groups and graphs

The distinguishing number of a group G acting faithfully on a set V is the least number of colors needed to color the elements of V so that no non-identity element of the group preserves the coloring. The distinguishing number of a graph is the distinguishing number of its automorphism group acting on its vertex set. A connected graph Gamma is said to have connectivity 1 if there exists a vertex alpha \in V\Gamma such that Gamma \setminus \{\alpha\} is not connected. For alpha \in V, an orbit of the point stabilizer G_\alpha is called a suborbit of G. We prove that every nonnull, primitive graph with infinite diameter and countably many vertices has distinguishing number 2. Consequently, any nonnull, infinite, primitive, locally finite graph is 2-distinguishable; so, too, is any infinite primitive permutation group with finite suborbits. We also show that all denumerable vertex-transitive graphs of connectivity 1 and all Cartesian products of connected denumerable graphs of infinite diameter have distinguishing number 2. All of our results follow directly from a versatile lemma which we call The Distinct Spheres Lemma

Renewable versus non-renewable building fabric: A comparative study on the effect of material choice on the embodied energy and global warming potential of low energy dwellings

The built environment causes damaging environmental impacts through processes such as material extraction, manufacture, transport, construction, maintenance, demolition and disposal, and the operational energy of buildings. Building and fabric design is driven by statutory requirements to conserve operational energy in response to climate change mitigation. Very low energy in use building standards such as Passive House have been developed and these standards require careful and rigorous design incorporating heavily insulated fabric, solar heat gains, heat recovery, and non conventional heat distribution systems. This paper examines how material choice can contribute to overall thermal performance and also potentially sequester carbon within the building fabric which in turn might offset operational energy emissions. A house is modelled with two different specifications of fabric design, both achieving the Passive House standard. The implications of material choices on energy in use and the Embodied Energy and Global Warming Potential (both positive and negative) are explored