Cubature formulas, geometrical designs, reproducing kernels, and Markov operators

Cubature formulas and geometrical designs are described in terms of reproducing kernels for Hilbert spaces of functions on the one hand, and Markov operators associated to orthogonal group representations on the other hand. In this way, several known results for spheres in Euclidean spaces, involving cubature formulas for polynomial functions and spherical designs, are shown to generalize to large classes of finite measure spaces $(\Omega,\sigma)$ and appropriate spaces of functions inside $L^2(\Omega,\sigma)$. The last section points out how spherical designs are related to a class of reflection groups which are (in general dense) subgroups of orthogonal groups

A Social Learning Space Grid for MOOCs: Exploring a FutureLearn Case

Collaborative and social engagement promote active learning through knowledge intensive interactions. Massive Open Online Courses (MOOCs) are dynamic and diversified learning spaces with varying factors like flexible time frames, student count, demographics requiring higher engagement and motivation to continue learning and for designers to implement novel pedagogies including collaborative learning activities. This paper looks into available and potential collaborative and social learning spaces within MOOCs and proposes a social learning space grid that can aid MOOC designers to implement such spaces, considering the related requirements. Furthermore, it describes a MOOC case study incorporating three collaborative and social learning spaces and discusses challenges faced. Interesting lessons learned from the case give an insight on which spaces to be implemented and the scenarios and factors to be considered

Helping students connect: architecting learning spaces for experiential and transactional reflection

Given the complex and varied contexts that inform students’ consciousness and occasion their learning, learning spaces are more than physical and virtual spaces. Learning spaces are also a range of situations sedimented in our continuum of experiences that shape our philosophical orientations. As such, this article, written from the perspectives of two faculty members in an English department at a four-year public university, describes our efforts to do the following. First, to draw upon models of instructional design we have experienced in our own educational backgrounds; and equally importantly, to develop learning spaces that support learning that is continuous, situated, and personal. Specifically, we critique the ways in which learning has been segregated from the rest of our life contexts for us throughout our educational histories. The irony is that this de-segregation has motivated us to create diverse learning spaces that provide our students with a more realistic set of tools and techniques for integrative life-long learning

Suppressing decoherence of quantum algorithms by jump codes

The stabilizing properties of one-error correcting jump codes are explored under realistic non-ideal conditions. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly

Building sustainable learning environments that are ‘fit for the future’ with reference to Egypt

Perhaps there is no building type that has a more significant impact on our lives than the Kindergarten to high School (K-12). We continue to carry the memories of our early learning environments through the residue of our lives. It is the quality of those learning environments that play a crucial role in enhancing or hampering our learning experience. Learning spaces are complex spaces where the collective skills, knowledge, and practices of a culture are taught, shaped, encouraged, and transmitted. Comfortable/safe and creative learning spaces can inspire and motivate users, while ugly/unsafe spaces can oppress. Based on these two attitudes, the aims of this paper are to; firstly, developing Sustainable learning environments (SLE) in the Middle-East countries with reference to Egypt. Secondly, to reviewing and extending the planning and design of the internal, external and landscaping features of a proposed eco-class to collectively pass to the learners for enhancing the quality of learning space and thus education. After the Egyptian Revolution on the 25th of January, 2011 and the hopes and dreams this brings with it, for a major transformation in all life sectors, the Egyptian government needs to recognise the right of children and young people to learn in an environment which is safe, healthy and achieves the highest quality possible. We must all be committed to improving the quality, attractiveness and health of the learning and communal spaces in our schools. Environmental factors have significant effects on pupil and teacher wellbeing. In contrast, poor school and classroom design can affect concentration, creativity and general well-being; in addition, poor quality lighting, ventilation, acoustics and furniture all have a negative effect on student achievement and health. Nowadays, Egypt endure deterioration of education quality as a result of deficient learning spaces, high number of pupils in class, insufficient governmental expenditure and funding, and lack of proper research in education developmental strategies. Therefore, new learning spaces should be able to increase flexibility in order to support hands-on and outside-class learning activities. Furthermore, they intend to encourage extra-curricula activities beyond conventional learning times. Currently, these integral learning-components are crucial for socio-cultural sustainability and positive initiatives towards minimizing recent educational underachievement. Undoubtedly, comfortable, safe and creative learning spaces can inspire and motivate users, while ugly/unsafe spaces can depress. Therefore, well-designed learning spaces are able to support creative, productive and efficient learning processes on one hand. On the other hand, ecological design measures became increasingly major keystone for modern sustainable learning-spaces. Thus, learning-spaces’ design process, form, components, materials, features, and energy-saving technologies can generate well-educated, environmental-literate, energy-conscious, and innovative future-generations. (Continued