Completeness of dagger-categories and the complex numbers

The complex numbers are an important part of quantum theory, but are difficult to motivate from a theoretical perspective. We describe a simple formal framework for theories of physics, and show that if a theory of physics presented in this manner satisfies certain completeness properties, then it necessarily includes the complex numbers as a mathematical ingredient. Central to our approach are the techniques of category theory, and we introduce a new category-theoretical tool, called the dagger-limit, which governs the way in which systems can be combined to form larger systems. These dagger-limits can be used to characterize the dagger-functor on the category of finite-dimensional Hilbert spaces, and so can be used as an equivalent definition of the inner product. One of our main results is that in a nontrivial monoidal dagger-category with all finite dagger-limits and a simple tensor unit, the semiring of scalars embeds into an involutive field of characteristic 0 and orderable fixed field.Comment: 39 pages. Accepted for publication in the Journal of Mathematical Physic

Where do graduates Develop their Enterprise Skills? The Value of the Contribution of Higher Education Institutions’ Context

This study investigates the value of the contribution of HEIs’ context in developing graduates enterprise skills. HEIs are under pressure to develop more enterprising graduates, particularly with the increasing numbers of graduates seeking employment and the growing dissatisfaction of employers. This study explores where graduates develop enterprise skills through investigating the impact of HE and employment contexts on their development. The paper draws on a qualitative study in the social constructionist paradigm within the pharmacy context, where interviews were conducted with pharmacy academics and employers. Results show that ability to demonstrate skills in one context does not necessarily mean ability to demonstrate them in another since the development and demonstration of enterprise skills is impacted by the contexts in which they are developed and demonstrated. The study adds value by highlighting the significant role of both HE and employment contexts in developing enterprise skills, while emphasising that these skills become more transferable through exposure to more contexts

Class of Service in the High Performance Storage System

Quality of service capabilities are commonly deployed in archival mass storage systems as one or more client-specified parameters to influence physical location of data in multi-level device hierarchies for performance or cost reasons. The capabilities of new high-performance storage architectures and the needs of data-intensive applications require better quality of service models for modern storage systems. HPSS, a new distributed, high-performance, scalable, storage system, uses a Class of Service (COS) structure to influence system behavior. The authors summarize the design objectives and functionality of HPSS and describes how COS defines a set of performance, media, and residency attributes assigned to storage objects managed by HPSS servers. COS definitions are used to provide appropriate behavior and service levels as requested (or demanded) by storage system clients. They compare the HPSS COS approach with other quality of service concepts and discuss alignment possibilities

On the alleged simplicity of impure proof

Roughly, a proof of a theorem, is “pure” if it draws only on what is “close” or “intrinsic” to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is “extrinsic,” “extraneous,” “distant,” “remote,” “alien,” or “foreign” to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim

Enterprise Education Competitions: A Theoretically Flawed Intervention?

The demand for including enterprise in the education system, at all levels and for all pupils is now a global phenomenon. Within this context, the use of competitions and competitive learning activities is presented as a popular and effective vehicle for learning. The purpose of this chapter is to illustrate how a realist method of enquiry – which utilises theory as the unit of analysis – can shed new light on the assumed and unintended outcomes of enterprise education competitions. The case developed here is that there are inherent flaws in assuming that competitions will ‘work’ in the ways set out in policy and guidance. Some of the most prevalent stated outcomes – that competitions will motivate and reward young people, that they will enable the development of entrepreneurial skills, and that learners will be inspired by their peers – are challenged by theory from psychology and education. The issue at stake is that the expansion of enterprise education policy into primary and secondary education increases the likelihood that more learners will be sheep dipped in competitions, and competitive activities, without a clear recognition of the potential unintended effects. In this chapter, we employ a realist-informed approach to critically evaluate the theoretical basis that underpins the use of competitions and competitive learning activities in school-based enterprise education. We believe that our findings and subsequent recommendations will provide those who promote and practice the use of competitions with a richer, more sophisticated picture of the potential flaws within such activities.Peer reviewedFinal Published versio

Prevalence of diabetes mellitus and impaired glucose tolerance in a rural community of Angola

<p>Abstract</p> <p>Background</p> <p>To determine the prevalence of diabetes mellitus (DM) and impaired glucose tolerance (IGT) in a rural community (Bengo) of Angola.</p> <p>Methods</p> <p>A random sample of 421 subjects aged 30 to 69 years (30% men and 70% women) was selected from three villages of Bengo province. This cross-sectional home survey was conducted using a sampling design of stage conglomerates. First, clinical and anthropometric data were obtained and fasting capillary glucose level was determined. Subjects who screened positive (fasting capillary glucose ≥ 100 mg/dl and < 200 mg/dl) and each sixth consecutive subject who screened negative (fasting capillary glucose < 100 mg/dl) were submitted to the second phase of survey, consisting of the 75-g oral glucose tolerance test. Data was analyzed by the use of SAS statistical software.</p> <p>Results</p> <p>The prevalence rates of diabetes mellitus and IGT were 2.8% and 8.1%, respectively. The age group with the highest prevalence of diabetes was 60 to 69 years (42%). Impaired glucose tolerance prevalence was 38% in the 40 to 49 year age group and it increased with age, considering that the 50 to 59 and 60 to 69 year age groups as a whole represent 50% of all subjects with impaired glucose tolerance. The prevalence of diabetes mellitus did not differ significantly between men (3.2%) and women (2.7%) (p = 0.47). On the other hand, the prevalence of impaired glucose tolerance among women showed almost twice that found in men (9.1% vs. 5.6%, respectively). Overweight was present in 66.7% of the individuals with diabetes mellitus and 26.5% of individuals with impaired glucose tolerance showed overweight or obesity.</p> <p>Conclusions</p> <p>Although the prevalence of diabetes mellitus was low, the prevalence of impaired glucose tolerance is considered to be within an intermediary range, suggesting a future increase in the frequency of diabetes in this population.</p