Formal Contexts, Formal Concept Analysis, and Galois Connections

Formal concept analysis (FCA) is built on a special type of Galois connections called polarities. We present new results in formal concept analysis and in Galois connections by presenting new Galois connection results and then applying these to formal concept analysis. We also approach FCA from the perspective of collections of formal contexts. Usually, when doing FCA, a formal context is fixed. We are interested in comparing formal contexts and asking what criteria should be used when determining when one formal context is better than another formal context. Interestingly, we address this issue by studying sets of polarities.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455

Enriched Topology and Asymmetry

Mathematically modeling the question of how to satisfactorily compare, in many-valued ways, both bitstrings and the predicates which they might satisfy-a surprisingly intricate question when the conjunction of predicates need not be commutative-applies notions of enriched categories and enriched functors. Particularly relevant is the notion of a set enriched by a po-groupoid, which turns out to be a many-valued preordered set, along with enriched functors extended as to be variable-basis . This positions us to model the above question by constructing the notion of topological systems enriched by many-valued preorders, systems whose associated extent spaces motivate the notion of topological spaces enriched by many-valued preorders, spaces which are non-commutative when the underlying lattice-theoretic base is equipped with a non-commutative (semi-)tensor product. Of special interest are crisp and many-valued specialization preorders generated by many-valued topological spaces, orders having these consequences for many-valued spaces: they characterize the well-established L-T0 separation axiom, define the L-T1(1) separation axiom-logically equivalent under appropriate lattice-theoretic conditions to the L-T1 axiom of T. Kubiak, and define an apparently new L-T1(2) separation axiom. Along with the consequences of such ideas for many-valued spectra, these orders show that asymmetry has a home in many-valued topology comparable in at least some respects to its home in traditional topology

Relationships between Hereditary Sobriety, Sobriety, TD, T1, and Locally Hausdorff

This work augments the standard relationships between sobriety, T1, and Hausdorff by mixing in locally Hausdorff and the compound axioms sober + T1 and sober + TD. We show the latter compound condition characterizes hereditary sobriety, and that locally Hausdorff fits strictly between Hausdorff and sober + T1. Classes of examples are constructed, in part to show the non-reversibility of key implications

2015 KSU Concerto Competition Final Round

KSU School of Music presents 2015 KSU Concerto Competition Final Round.https://digitalcommons.kennesaw.edu/musicprograms/1169/thumbnail.jp

The Development of a Point of Care Clinical Guidelines Mobile Application Following a User-Centred Design Approach

This paper describes the development of a point of care clinical guidelines mobile application. A user-centred design approach was utilised to inform the design of a smartphone application, this included: Observations; a survey; focus groups and an analysis of popular apps utilised by clinicians in a UK NHS Trust. Usability testing was conducted to inform iterations of the application, which presents clinicians with a variety of integrated tools to aid in decision making and information retrieval. The study found that clinicians use a mixture of technology to retrieve information, which is often inefficient or has poor usability. It also shows that smartphone application development for use in UK hospitals needs to consider the variety of users and their clinical knowledge and work pattern. This study highlights the need for applying user-centred design methods in the design of information presented to clinicians and the need for clinical information delivery that is efficient and easy to use at the bedside

Investigation of relative risk estimates from studies of the same population with contrasting response rates and designs

Background: There is little empirical evidence regarding the generalisability of relative risk estimates from studies which have relatively low response rates or are of limited representativeness. The aim of this study was to investigate variation in exposure-outcome relationships in studies of the same population with different response rates and designs by comparing estimates from the 45 and Up Study, a population-based cohort study (self-administered postal questionnaire, response rate 18%), and the New South Wales Population Health Survey (PHS) (computer-assisted telephone interview, response rate ~60%). Methods: Logistic regression analysis of questionnaire data from 45 and Up Study participants (n = 101,812) and 2006/ 2007 PHS participants (n = 14,796) was used to calculate prevalence estimates and odds ratios (ORs) for comparable variables, adjusting for age, sex and remoteness. ORs were compared using Wald tests modelling each study separately, with and without sampling weights. Results: Prevalence of some outcomes (smoking, private health insurance, diabetes, hypertension, asthma) varied between the two studies. For highly comparable questionnaire items, exposure-outcome relationship patterns were almost identical between the studies and ORs for eight of the ten relationships examined did not differ significantly. For questionnaire items that were only moderately comparable, the nature of the observed relationships did not differ materially between the two studies, although many ORs differed significantly. Conclusions: These findings show that for a broad range of risk factors, two studies of the same population with varying response rate, sampling frame and mode of questionnaire administration yielded consistent estimates of exposure-outcome relationships. However, ORs varied between the studies where they did not use identical questionnaire items