Ptolemy groupoids, shear coordinates and the augmented Teichmuller space

We start by describing how ideal triangulations on a surface degenerate under pinching of a multicurve. We use this process to construct a homomorphism from the Ptolemy groupoid of a surface to that of a pinched surface which is natural with respect to the action of the mapping class group. We then apply this construction to the study of shear coordinates and their extension to the augmented Teichm\"uller space. In particular, we give an explicit description of the action of the mapping class group on the augmented Teichm\"uller space in terms of shear coordinates.Comment: 21 pages, 13 figures. v2: minor corrections, added the once-punctured torus as an exampl

Quantization of the Laplacian operator on vector bundles I

Let $(E,h)$ be a holomorphic Hermitian vector bundle over a polarized manifold. We provide a canonical quantization of the Laplacian operator acting on sections of the bundle of Hermitian endomorphisms of $E$. If $E$ is simple we obtain an approximation of the eigenvalues and eigenspaces of the Laplacian

IMF lending and geopolitics

There is growing awareness that the distribution of IMF facilities may not be influenced only by the economic needs of the borrowers. This paper focuses on the fact that the IMF may favour geopolitically important countries in the distribution of IMF loans, differentiating between concessional and nonconcessional facilities. To carry out the empirical analysis, we construct a new database that compiles proxies for geopolitical importance for 107 IMF countries over 1990–2003, focusing on emerging and developing economies. We use a factor analysis to capture the common underlying characteristic of countries' geopolitical importance as well as a potential analysis since we also want to account for the geographical situation of the loan recipients. While controlling for economic and political determinants, our results show that geopolitical factors influence notably lending decisions when loans are nonconcessional, whereas results are less robust and in opposite direction for concessional loans. This study provides empirical support to the view that geopolitical considerations are an important factor in shaping IMF lending decisions, potentially affecting the institution's effectiveness and credibility. JEL Classification: F33, H77, O19factor analysis, geopolitics, International Monetary Fund, potential analysis

Formality of derived intersections

We study derived intersections of smooth analytic cycles, and provide in some cases necessary and sufficient conditions for this intersection be formal. In particular, if X is a complex submanifold of a complex manifold Y, we prove that X can be quantized if and only if the derived intersection of XxX and \Delta_Y is formal in D(XxX).Comment: A mistake has been corrected in Section

Towards Teaching a Robot to Count Objects

We present here an example of incremental learning between two computational models dealing with different modalities: a model allowing to switch spatial visual attention and a model allowing to learn the ordinal sequence of phonetical numbers. Their merging via a common reward signal allows anyway to produce a cardinal counting behaviour that can be implemented on a robot