Open inflation and the singulary boundary

The singularity in the Hawking-Turok model of open inflation has some appealing properties, such as the fact that its action is integrable. Also, if one thinks of the singularity as the boundary of spacetime, then the Gibbons-Hawking term is nonvanishing and finite. Here, we consider a model where the gravitational and scalar fields are coupled to a dynamical membrane. The singular instanton can then be obtained as the limit of a family of no-boundary solutions where both the geometry and the scalar field are regular. Using this procedure, the contribution of the singularity to the Euclidean action is just 1/3 of the Gibbons-Hawking term. Unrelated to this issue, we also point out that the singularity acts as a reflecting boundary for scalar perturbations and gravity waves. Therefore, the quantization of cosmological perturbations seems to be well posed in this background.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Self-similarity of complex networks and hidden metric spaces

We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.

Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Best approach regions for potential spaces

We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Some spectral properties of the canonical solution operator to $\bar\partial$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\overline{\partial}$ acting on $L^2(e^{-2\phi})$, where $\phi$ is a subharmonic function with $\Delta\phi$ a doubling measure. The obtained characterization is in terms of $\Delta\phi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\phi})$

Evaporation and coarsening dynamics with open boundaries

We present a study of the evaporation dynamics of a substance undergoing a coarsening process. The system is modeled by the Cahn-Hilliard equation with absorbing boundaries. We have found that the dynamics, although of a diffusive nature, is much slower than the usual one without coarsening. Analytical and simulation results are in reasonable agreement.

Open licensing's impact on higher education resources colombian and catalan approaches

A new initiative has sprung on the path created by the Open Access (OA) movement: Open Education (OE). The initiative's aim is to open up all educational resources at all learning levels. In order to achieve this goal, several international institutions, like UNESCO and the OECD, have published reports, surveys and documents to help educational institutions in this endeavor. This global initiative needs a legal framework; as a result, efforts thus far have usually resorted to Open Licensing (OL), especially Creative Commons (CC) licensing. In fact, as a response to this new movement, Creative Commons launched a new program, ccLearn , which recognizes open licensing's impact on education and directly supports the idea of open educational resources (OER). However, there still remain a good amount of open questions: What is happening locally with OL in higher education? How are educational institutions receiving the initiative? How is it that the OL initiative relates to educational resources? Are there local examples of open educational resources (OER)? How do these local instances incorporate CC into their educational frameworks?. To this effect, this analysis aims to focus on the legal approach and specifically on the way the educational sector is using open licenses outside the English speaking world. It will do so by looking at the current situation in two specific scenarios, the Colombian and the Catalan experiences with open educational projects at the higher education level.

Copyright issues related to the implementation of Open Access policies

The presentation provides an overview of the copyright issues related to the implementation of Open Access policies. It focuses on the need to obtain permission to reproduce and disseminate a copy of any published paper taking into account any copyright transfer signed by authors. This permission is needed to implement Green Open Access policies through repositories. Moreover it explores the use of open content licenses in repositories and journals to move to the Gold Open Access model that offers not only free access to full text but full reuse of contributions.

Explaining Open Courseware Europe

Since two years ago, five European universities are working together with Creative Commons and the Open Courseware Consortium in an EU funded project aimed at supporting student virtual mobility on the basis of OCW. During those two years, there have been several workshops dedicated to different topics and some documents have been produced, among them about the use of CC licenses. The final goal of the project is to establish an European branch of the OCW Consortium as the existing ones in other regions. More information about the project: http://opencourseware.eu/

La situació de l'Open Access a la Universitat de Barcelona

Comunicació presentada a: II Setmana Internacional de l'Accés Obert a la Universitat de Barcelona. Universitat de Barcelona, del 18 al 22 d'octubre de 2010