Informal learning recognition through a cloud ecosystem

Learning and teaching processes, like all human activities, can be mediated through the use of tools. Information and communication technologies are now widespread within education. Their use in the daily life of teachers and learners affords engagement with educational activities at any place and time and not necessarily linked to an institution or a certificate. In the absence of formal certification, learning under these circumstances is known as informal learning. Despite the lack of certification, learning with technology in this way presents opportunities to gather information about and present new ways of exploiting an individual’s learning. Cloud technologies provide ways to achieve this through new architectures, methodologies, and workflows that facilitate semantic tagging, recognition, and acknowledgment of informal learning activities. The transparency and accessibility of cloud services mean that institutions and learners can exploit existing knowledge to their mutual benefit. The TRAILER project facilitates this aim by providing a technological framework using cloud services, a workflow, and a methodology. The services facilitate the exchange of information and knowledge associated with informal learning activities ranging from the use of social software through widgets, computer gaming, and remote laboratory experiments. Data from these activities are shared among institutions, learners, and workers. The project demonstrates the possibility of gathering information related to informal learning activities independently of the context or tools used to carry them out.

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C1+ conjugacy classes of C1+H Cantor exchange systems that are C1+H fixed points of renormalization and (ii) C1+ conjugacy classes of C1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. However, we prove that there is no C1+alpha Cantor exchange system, with bounded geometry, that is a C1+alpha fixed point of renormalization with regularity alpha greater than the Hausdorff dimension of its invariant Cantor set.

Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.