The age of imagination: imagining play and invention: implications for creative development

This paper presents findings from The Irish Neighbourhood Play Study; a national, cross-border research project which recorded children’s play patterns in Ireland during 2012. The study incorporated 1688 families across 240 communities. Data was established on the play choices of children aged from birth to 14 years. Multiple differentials were explored including socio-economic and geographical environments. This paper focuses on the findings within imaginary play patterns for the full cohort. As such, it presents the play patterns for imaginary play in children aged birth-14 years. The findings are discussed in the context of developmental patterns with particular emphasis on the relationship between imaginary play and the development of creativity. Creativity is a key concept within contemporary education. Its central nexus is problem solving in the face of uncertainty. Within a rapidly changing world, it is a key skill requirement for today’s children as they grow towards efficacy within instability. The relationship between the development of creativity and children’s engagement with imaginary play practices are explored in this paper. ©IATED (2017). Reproduced in Research Online with permission

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546