Which mathematics for the Information Society?

MathIS is a new project that aims to reinvigorate secondary- school mathematics by exploiting insights of the dynamics of algorithmic problem solving. This paper describes the main ideas that underpin the project. In summary, we propose a central role for formal logic, the development of a calculational style of reasoning, the emphasis on the algorithmic nature of mathematics, and the promotion of self-discovery by the students. These ideas are discussed and the case is made, through a number of examples that show the teaching style that we want to introduce, for their relevance in shaping mathematics training for the years to come. In our opinion, the education of software engineers that work effectively with formal methods and mathematical abstractions should start before university and would benefit from the ideas discussed here.Long-term collaboration with J. N. Oliveira on calculational approaches to mathematics is deeply acknowledged. We are also grateful to the anonymous referees for their valuable comments. This research was supported by FCT (the Portuguese Foundation for Science and Technology), in the context of the MATHIS Project under contract PTDC/EIA/73252/2006. The work of Joao F. Ferreira and AlexandraMendeswas further supported by FCT grants SFRH/BD/24269/2005 and SFRH/BD/29553/2006, respectively

Implications of non-feasible transformations among icosahedral hh orbitals

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

String cosmology from Poisson-Lie T-dual sigma models on supermanifolds

We generalize the formulation of Poisson-Lie T-dual sigma models on manifolds to supermanifolds. In this respect, we formulate 1+1 dimensional string cosmological models on the Lie supergroup C^3 and its dual (A_1,1 + 2A)^0_(1,0,0), which are coupled to two fermionic fields. Then, we solve the equations of motion of the models and show that there is a essential singularity for the metric of the original model and its dual.Comment: 17 pages, Appendix and three references have adde

Improving the Information Security Model by using TFI

In the context of information systems and information technology, information security is a concept that is becoming widely used. The European Network of Excellence INTEROP classifies information security as a nonfunctional aspect of interoperability and as such it is an integral part of the design process for interoperable systems. In the last decade, academics and practitioners have shown their interest in information security, for example by developing security models for evaluating products and setting up security specifications in order to safeguard the confidentiality, integrity, availability and accountability of data. Earlier research has shown that measures to achieve information security in the administrative or organisational level are missing or inadequate. Therefore, there is a need to improve information security models by including vital elements of information security. In this paper, we introduce a holistic view of information security based on a Swedish model combined with a literature survey. Furthermore we suggest extending this model using concepts based on semiotic theory and adopting the view of an information system as constituted of the technical, formal and informal (TFI) parts. The aim is to increase the understanding of the information security domain in order to develop a well-founded theoretical framework, which can be used both in the analysis and the design phase of interoperable systems. Finally, we describe and apply the Information Security (InfoSec) model to the results of three different case studies in the healthcare domain. Limits of the model will be highlighted and an extension will be proposed.In the context of information systems and information technology, information security is a concept that is becoming widely used. The European Network of Excellence INTEROP classifies information security as a nonfunctional aspect of interoperability and as such it is an integral part of the design process for interoperable systems. In the last decade, academics and practitioners have shown their interest in information security, for example by developing security models for evaluating products and setting up security specifications in order to safeguard the confidentiality, integrity, availability and accountability of data. Earlier research has shown that measures to achieve information security in the administrative or organisational level are missing or inadequate. Therefore, there is a need to improve information security models by including vital elements of information security. In this paper, we introduce a holistic view of information security based on a Swedish model combined with a literature survey. Furthermore we suggest extending this model using concepts based on semiotic theory and adopting the view of an information system as constituted of the technical, formal and informal (TFI) parts. The aim is to increase the understanding of the information security domain in order to develop a well-founded theoretical framework, which can be used both in the analysis and the design phase of interoperable systems. Finally, we describe and apply the Information Security (InfoSec) model to the results of three different case studies in the healthcare domain. Limits of the model will be highlighted and an extension will be proposed.Monograph's chapter

Inductive-Inductive Definitions

This article presents a new extension of inductive definitions, namely inductive-inductive definitions

The critical role of logarithmic transformation in Nernstian equilibrium potential calculations

The membrane potential, arising from uneven distribution of ions across cell membranes containing selectively permeable ion channels, is of fundamental importance to cell signaling. The necessity of maintaining the membrane potential may be appreciated by expressing Ohm’s law as current = voltage/resistance and recognizing that no current flows when voltage = 0, i.e., transmembrane voltage gradients, created by uneven transmembrane ion concentrations, are an absolute requirement for the generation of currents that precipitate the action and synaptic potentials that consume >80% of the brain’s energy budget and underlie the electrical activity that defines brain function. The concept of the equilibrium potential is vital to understanding the origins of the membrane potential. The equilibrium potential defines a potential at which there is no net transmembrane ion flux, where the work created by the concentration gradient is balanced by the transmembrane voltage difference, and derives from a relationship describing the work done by the diffusion of ions down a concentration gradient. The Nernst equation predicts the equilibrium potential and, as such, is fundamental to understanding the interplay between transmembrane ion concentrations and equilibrium potentials. Logarithmic transformation of the ratio of internal and external ion concentrations lies at the heart of the Nernst equation, but most undergraduate neuroscience students have little understanding of the logarithmic function. To compound this, no current undergraduate neuroscience textbooks describe the effect of logarithmic transformation in appreciable detail, leaving the majority of students with little insight into how ion concentrations determine, or how ion perturbations alter, the membrane potential

Pointfree factorization of operation refinement

The standard operation refinement ordering is a kind of “meet of op- posites”: non-determinism reduction suggests “smaller” behaviour while increase of definition suggests “larger” behaviour. Groves’ factorization of this ordering into two simpler relations, one per refinement concern, makes it more mathe- matically tractable but is far from fully exploited in the literature. We present a pointfree theory for this factorization which is more agile and calculational than the standard set-theoretic approach. In particular, we show that factorization leads to a simple proof of structural refinement for arbitrary parametric types and ex- ploit factor instantiation across different subclasses of (relational) operation. The prospect of generalizing the factorization to coalgebraic refinement is discussedFundação para a Ciência e a Tecnologia (FCT) - PURE Project (Program Understanding and Re-engineering: Calculi and Applications), contract POSI/ICHS/44304/2002

Prevalence and microbiological characteristics of clinically infected foot-ulcers in patients with rheumatoid arthritis: A retrospective exploratory study

Background: The prevalence of foot ulcers in patients with rheumatoid arthritis (RA) has been reported at almost 10 %. These foot ulcers often occur at multiple sites and are reoccurring, with the potential risk of infection increased due to RA diagnosis and disease modifying medications. The objective of this study was to estimate the prevalence of clinical infection in foot-ulcers of patients with RA; describe the microbiological characteristics and investigate risk factors. Methods: Retrospective clinical data was collected for all patients attending a rheumatology foot ulcer clinic between 1st May 2012 and 1st May 2013: wound swab data was collected from those with clinical infection. Results: Twenty-eight patients with RA and foot-ulcers were identified; eight of these patients had clinical infection and wound swabs taken (29 %). Of these eight patients there were equal men and women, with median age 74 years, and average disease duration 22 years. Cardiovascular disease/peripheral-vascular disease (CVD/PVD) were reported in six patients, diabetes in two patients. Six patients were treated with disease-modifying anti-rheumatic drugs (DMARDs); three were on biologic medications and two on steroids. Five wound swabs cultured skin flora, one staphylococcus aureus, one had no growth after culture; and one was rejected due to labelling error. Conclusion: Almost a third of people with RA and foot ulcers attending clinic over one year had clinical infection, however microbiological analysis failed to isolate pathogens in six of seven wound swabs. This may be due to inaccurate diagnosis of ulcer infection or to issues with sampling, collection, transport, analysis or reporting. There was insufficient data to relate risk of clinical infection with risk factors. Further research is required to identify the most appropriate techniques for infection diagnosis, wound sampling and processing. Trial registration: Ethical approval was obtained from University of Leeds, Faculty of Medicine and Health (Reference number: SHREC/RP/349)