Dimensional analysis using toric ideals: Primitive invariants

© 2014 Atherton et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units M, L, T etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive basis in a well-defined sense, which typically has more terms than the standard Buckingham approach. Some textbook examples are revisited and the full set of primitive invariants found. First, a worked example based on convection is introduced to recall the Buckingham method, but using computer algebra to obtain an integer K matrix from the initial integer A matrix holding the exponents for the derived quantities. The K matrix defines the dimensionless variables. But, rather than this integer linear algebra approach it is shown how, by staying with the power product representation, the full set of invariants (dimensionless groups) is obtained directly from the toric ideal defined by A. One candidate for the set of invariants is a simple basis of the toric ideal. This, although larger than the rank of K, is typically not unique. However, the alternative Graver basis is unique and defines a maximal set of invariants, which are primitive in a simple sense. In addition to the running example four examples are taken from: a windmill, convection, electrodynamics and the hydrogen atom. The method reveals some named invariants. A selection of computer algebra packages is used to show the considerable ease with which both a simple basis and a Graver basis can be found.The third author received funding from Leverhulme Trust Emeritus Fellowship (1-SST-U445) and United Kingdom EPSRC grant: MUCM EP/D049993/1

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Despite the enthusiastic rhetoric about the so called \emph{collective intelligence}, conspiracy theories -- e.g. global warming induced by chemtrails or the link between vaccines and autism -- find on the Web a natural medium for their dissemination. Users preferentially consume information according to their system of beliefs and the strife within users of opposite narratives may result in heated debates. In this work we provide a genuine example of information consumption from a sample of 1.2 million of Facebook Italian users. We show by means of a thorough quantitative analysis that information supporting different worldviews -- i.e. scientific and conspiracist news -- are consumed in a comparable way by their respective users. Moreover, we measure the effect of the exposure to 4709 evidently false information (satirical version of conspiracy theses) and to 4502 debunking memes (information aiming at contrasting unsubstantiated rumors) of the most polarized users of conspiracy claims. We find that either contrasting or teasing consumers of conspiracy narratives increases their probability to interact again with unsubstantiated rumors.Comment: misinformation, collective narratives, crowd dynamics, information spreadin

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Steps towards online monitoring systems and interoperability

In the health area, there is, on a daily basis, an enormous amount of data being produced and disseminated. The fast-growing amount of collected data and the rich knowledge, possibly life-saving, that could be extracted from these data has demanded the search of new ways to ensure the reliability and availability of the information with an emphasis on the efficient use of information technology tools. Although the main focus of the information systems is the health professionals who contact directly with the patient, it is also imperative to have tools for the background of the health units (information services, managers of systems, etc.). The main purpose of this work is the development of an innovative and interactive web platform for the daily monitoring of the web services activities of a Portuguese hospital, Centro Hospitalar do Porto (CHP). This platform is a web application developed in React that aims to ensure the correct functioning of the web services, that are responsible for numerous tasks within the hospital environment, and which failure could result in disastrous consequences, both for the health institution and for the patients. The development of the web application followed the six stages of the Design Science Research (DSR) methodology and was submitted to the Strengths Weaknesses Opportunities and Threats (SWOT) analysis, which results were considered optimistic.This work has been supported by FCT – Fundação para a Ciência e Tecnologia within the Project Scope: UID/CEC/00319/201

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Sustainable development is a commonly quoted goal for decision making and supports a large number of other discourses. Sustainability appraisal has a stated goal of supporting decision making for sustainable development. We suggest that the inherent flexibility of sustainability appraisal facilitates outcomes that often do not adhere to the three goals enshrined in most definitions of sustainable development: economic growth, environmental protection and enhancement, and the wellbeing of the human population. Current practice is for sustainable development to be disenfranchised through the interpretation of sustainability, whereby the best alternative is good enough even when unsustainable. Practitioners must carefully and transparently review the frameworks applied during sustainability appraisal to ensure that outcomes will meet the three goals, rather than focusing on a discourse that emphasises one or more goals at the expense of the other(s)