Central sets and substitutive dynamical systems

In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Central sets, first introduced by Furstenberg using notions from topological dynamics, constitute a special class of subsets of \nats possessing strong combinatorial properties: Each central set contains arbitrarily long arithmetic progressions, and solutions to all partition regular systems of homogeneous linear equations. We give an equivalent reformulation of the strong coincidence condition in terms of central sets and minimal idempotent ultrafilters in the Stone-\v{C}ech compactification \beta \nats . This provides a new arithmetical approach to an outstanding conjecture in tiling theory, the Pisot substitution conjecture. The results in this paper rely on interactions between different areas of mathematics, some of which had not previously been directly linked: They include the general theory of combinatorics on words, abstract numeration systems, tilings, topological dynamics and the algebraic/topological properties of Stone-\v{C}ech compactification of \nats.Comment: arXiv admin note: substantial text overlap with arXiv:1110.4225, arXiv:1301.511

Maximal equicontinuous factors and cohomology for tiling spaces

We study the homomorphism induced on cohomology by the maximal equicontinuous factor map of a tiling space. We will see that this map is injective in degree one and has torsion free cokernel. We show by example, however, that the cohomology of the maximal equicontinuous factor may not be a direct summand of the tiling cohomology

Firm R&D units and outsourcing partners: A matching story

We present a theory that examines the optimal match between firm R&D units and external partners for projects that involve problem solving. We have a firm selecting an external partner conditional on the learning costs of its internal R&D unit. We show that there exists a matching equilibrium with property that external partners with low learning costs for a project work with R\&D units that also have low learning costs for the same project. Empirically, we use a dataset of Spanish R\&D firms and relate their share of R&D outsourcing to universities to the composition of their R&D units, described by the presence of staff with a PhD. Our main finding is that, controlling for endogeneity, firms that employ R\&D staff with a PhD outsource relatively more to universities than to firms. We interpret this result as evidence that R&D units with relatively low learning costs for basic projects tend to match with external partners, universities, with relatively low learning costs for the same projects.

Investigating an open methodology for designing domain-specific language collections

With this research and design paper, we are proposing that Open Educational Resources (OERs) and Open Access (OA) publications give increasing access to high quality online educational and research content for the development of powerful domain-specific language collections that can be further enhanced linguistically with the Flexible Language Acquisition System (FLAX, http://flax.nzdl.org). FLAX uses the Greenstone digital library system, which is a widely used open-source software that enables end users to build collections of documents and metadata directly onto the Web (Witten, Bainbridge, & Nichols, 2010). FLAX offers a powerful suite of interactive text-mining tools, using Natural Language Processing and Artificial Intelligence designs, to enable novice collections builders to link selected language content to large pre-processed linguistic databases. An open methodology trialed at Queen Mary University of London in collaboration with the OER Research Hub at the UK Open University demonstrates how applying open corpus-based designs and technologies can enhance open educational practices among language teachers and subject academics for the preparation and delivery of courses in English for Specific Academic Purposes (ESAP)

Developing indicators to measure Technology Institutes` performance

Technology institutes (TIs) are non-profit innovation and technology organisations aimed to encourage competitiveness of firms. They are a key organisation in the Spanish National Innovation System because of their size and closeness to the productive sector. Despite this, there is a lack of studies trying to measure their performance and its determinants. This work sheds some light on this. We study the influence of operative, financial, organisational, relational and general variables on three measures of results: selffinance, impact and added value. Our conclusions show the relevance of this approach and are confirmed by grouping TIs according to their service supply characteristics.Publicad