A Sound and Complete Axiomatization of Majority-n Logic

Manipulating logic functions via majority operators recently drew the attention of researchers in computer science. For example, circuit optimization based on majority operators enables superior results as compared to traditional logic systems. Also, the Boolean satisfiability problem finds new solving approaches when described in terms of majority decisions. To support computer logic applications based on majority a sound and complete set of axioms is required. Most of the recent advances in majority logic deal only with ternary majority (MAJ- 3) operators because the axiomatization with solely MAJ-3 and complementation operators is well understood. However, it is of interest extending such axiomatization to n-ary majority operators (MAJ-n) from both the theoretical and practical perspective. In this work, we address this issue by introducing a sound and complete axiomatization of MAJ-n logic. Our axiomatization naturally includes existing majority logic systems. Based on this general set of axioms, computer applications can now fully exploit the expressive power of majority logic.Comment: Accepted by the IEEE Transactions on Computer

Developing Mathematics Enrichment Workshops for Middle School Students: Philosophy and Sample Workshops

This paper describes our approach to organizing enrichment activities using advanced mathematics topics for diverse audiences of middle school students. We discuss our philosophy and approaches for the structure of these workshops, and then provide sample schedules and resource materials. The workshops cover activities on the following topics: Graphing Calculators; The Chaos Game; Statistical Sampling; CT Scans–the reconstruction problem; The Platonic and Archimedean solids; The Shape of Space; Symmetry; The Binary Number System and the game of NIM; Graph Theory: Proof by Counterexample

The uses of qualitative data in multimethodology:Developing causal loop diagrams during the coding process

In this research note we describe a method for exploring the creation of causal loop diagrams (CLDs) from the coding trees developed through a grounded theory approach and using computer aided qualitative data analysis software (CAQDAS). The theoretical background to the approach is multimethodology, in line with Minger’s description of paradigm crossing and is appropriately situated within the Appreciate and Analyse phases of PSM intervention. The practical use of this method has been explored and three case studies are presented from the domains of organisational change and entrepreneurial studies. The value of this method is twofold; (i) it has the potential to improve dynamic sensibility in the process of qualitative data analysis, and (ii) it can provide a more rigorous approach to developing CLDs in the formation stage of system dynamics modelling. We propose that the further development of this method requires its implementation within CAQDAS packages so that CLD creation, as a precursor to full system dynamics modelling, is contemporaneous with coding and consistent with a bridging strategy of paradigm crossing

Is an Environmental Management System able to influence environmental and competitive performance? The case of the Eco-Management and Audit Scheme (EMAS) in the European Union

The EMAS Regulation (Reg 761/01 EC) is an EU scheme for the implementation of an Environmental Management System (EMS) by any organization, implemented by the European Commission since the year 1993. The EMS has been originally proposed both by the European Commission and by ISO as the frontrunner of a series of policy tools that were conceived to enable companies to simultaneously pursue environmental objectives and competitive targets (in a synergetic way). Based on the unique dataset of the EVER project, this paper investigates whether or not an EMS implemented within the EMAS Regulation has an effect on firm performance both from an environmental and a competitive point of view. The econometric analysis shows a positive impact of well-designed environmental management system on environmental performance and, as a consequence, on technical and organizational innovations. Effects on other competitive variable as market performance, resource productivity and intangible asset are not strongly supported

Limits on Fundamental Limits to Computation

An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit scaling, we review fundamental limits to computation: in manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, we recall how some limits were circumvented, compare loose and tight limits. We also point out that engineering difficulties encountered by emerging technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl

Exploring the Use of Virtual Worlds as a Scientific Research Platform: The Meta-Institute for Computational Astrophysics (MICA)

We describe the Meta-Institute for Computational Astrophysics (MICA), the first professional scientific organization based exclusively in virtual worlds (VWs). The goals of MICA are to explore the utility of the emerging VR and VWs technologies for scientific and scholarly work in general, and to facilitate and accelerate their adoption by the scientific research community. MICA itself is an experiment in academic and scientific practices enabled by the immersive VR technologies. We describe the current and planned activities and research directions of MICA, and offer some thoughts as to what the future developments in this arena may be.Comment: 15 pages, to appear in the refereed proceedings of "Facets of Virtual Environments" (FaVE 2009), eds. F. Lehmann-Grube, J. Sablating, et al., ICST Lecture Notes Ser., Berlin: Springer Verlag (2009); version with full resolution color figures is available at http://www.mica-vw.org/wiki/index.php/Publication

The impact of professional learning on the teaching identities of higher education lecturers

Higher Education is currently undergoing some of the most profound changes in its history. Against a backdrop of increasing marketization, rising levels of student debt and far greater fully online offerings, the higher education lecturer is grappling with new ways of working and high expectations of teaching quality. This 3 year qualitative study based in The Open University UK investigates the ways in which HE distance learning lecturers are approaching professional development and learning, identifying what type of learning may be most effective in creating and sustaining an online teaching identity. The study also examines ways in which resistance discourse is shaping these identities and practices revealing emerging re- conceptualisations of what it means to be an effective and well-motivated distance learning lecturer. The investigation uses a framework for identity analysis which analyses professional identity via the expression of hegemonies, phenomenological, narrative articulations of identity, and a post-modern, constructivist view of identity which is shaped by social interactions and communities of practice. It highlights the importance of personal agency in identity formation. The results revealed a number of insights into the ways in which a combination of resistance discourse, professional learning and reflections from student interactions are shaping new understandings of professional knowledge in this context