Tight polynomial worst-case bounds for loop programs

In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple programming language - representing non-deterministic imperative programs with bounded loops, and arithmetics limited to addition and multiplication - it is possible to decide precisely whether a program has certain growth-rate properties, in particular whether a computed value, or the program's running time, has a polynomial growth rate. A natural and intriguing problem was to move from answering the decision problem to giving a quantitative result, namely, a tight polynomial upper bound. This paper shows how to obtain asymptotically-tight, multivariate, disjunctive polynomial bounds for this class of programs. This is a complete solution: whenever a polynomial bound exists it will be found. A pleasant surprise is that the algorithm is quite simple; but it relies on some subtle reasoning. An important ingredient in the proof is the forest factorization theorem, a strong structural result on homomorphisms into a finite monoid

Transience of Simple Random Walks With Linear Entropy Growth

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at a vertex $x_0$, if the entropy after $n$ steps, $E_n$ is at least $Cn$ where the $C$ is independent of $x_0$, then the random walk is transient. We also give an example which demonstrates that the condition of $C$ being independent of $x_0$ is necessary.Comment: 8 pages, 1 figur

Interventions at the end of life – a taxonomy for ‘overlapping consensus’

Context: Around the world there is increasing interest in end of life issues. An unprecedented number of people dying in future decades will put new strains on families, communities, services and governments. It will also have implications for representations of death and dying within society and for the overall orientation of health and social care. What interventions are emerging in the face of these challenges? Methods: We conceptualize a comprehensive taxonomy of interventions, defined as ‘organized responses to end of life issues’. Findings: We classify the range of end of life interventions into 10 substantive categories: policy, advocacy, educational, ethico-legal, service, clinical, research, cultural, intangible, self-determined. We distinguish between two empirical aspects of any end of life intervention: the ‘locus’ refers to the space or spaces in which it is situated; the ‘focus’ captures its distinct character and purpose. We also contend that end of life interventions can be seen conceptually in two ways – as ‘frames’ (organized responses that primarily construct a shared understanding of an end of life issue) or as ‘instruments’ (organized responses that assume a shared understanding and then move to act in that context). Conclusions: Our taxonomy opens up the debate about end of life interventions in new ways to provide protagonists, activists, policy makers, clinicians, researchers and educators with a comprehensive framework in which to place their endeavours and more effectively to assess their efficacy. Following the inspiration of political philosopher John Rawls, we seek to foster an ‘overlapping consensus’ on how interventions at the end of life can be construed, understood and assessed

Organised crime in Scotland and the Criminal Justice Response

A chapter exploring the nature and extent of organised crime in Scotland and charting developments and innovation in policing and criminal justice responses and policy. 

Low cost, SPF aluminum cryogenic tank structure for ALS

Past production work has shown that cryogenic tank structure for the Shuttle Booster Rockets and the Titan system have very high life cycle costs for the fuel tank structure. The tanks are machined stiffener-skin combination that are subsequently formed into the required contour after machining. The material scrap rate for these configurations are usually high, and the loss of a tank panel due to forming or heat treatment problems is very costly. The idea of reducing the amount of scrap material and scrapped structural members has prompted the introduction of built-up structure for cryogenic tanks to be explored on the ALS program. A build-up structure approach that has shown improvements in life cycle cost over the conventional built-up approach is the use of superplastically formed (SPF) stiffened panels (reducing the overall part count and weight for the tank) resistance spot welded (RSW) to outer tank skin material. The stiffeners provide for general stability of the tank, while the skin material provides hoop direction continuity for the loads

Faculty String Quartet

Kemp Recital Hall Thursday Evening April 16, 1998 8:00 p.m