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

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

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

Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging

We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of these individuals, we assume that the characteristic is stochastic and depends on its ancestors' only through the mother's characteristic. The dependency structure may be described by a transition probability $P(x,dy dz)$ which gives the probability that the pair of daughters' characteristics is around $(y,z)$, given that the mother's characteristic is $x$. Note that $y$, the characteristic of the daughter of type 0, and $z$, that of the daughter of type 1, may be conditionally dependent given $x$, and their respective conditional distributions may differ. We then speak of bifurcating Markov chains. We derive laws of large numbers and central limit theorems for such stochastic processes. We then apply these results to detect cellular aging in Escherichia Coli, using the data of Stewart et al. and a bifurcating autoregressive model.Comment: Published in at http://dx.doi.org/10.1214/105051607000000195 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Indirect detection of Dark Matter with antimatter: Demystifying the clumpiness boost factors

The hierarchical scenario of structure formation, in the frame of the $\Lambda$-CDM cosmology, predicts the existence of dark matter (DM) sub-halos down to very small scales, of which the minimal size depends on the microscopic properties of the DM. In the context of annihilating DM, such substructures are expected to enhance the primary cosmic ray (CR) fluxes originating from DM annihilation in the Galaxy. This enhancement has long been invoked to allow predictions of imprints of DM annihilation on the antimatter CR spectra. Taking advantage of the method developed by Lavalle et al (2007b), we (Lavalle et al, 2007a) accurately compute the boost factors for positrons and anti-protons, as well as the associated theoretical and statistical errors. To this aim, we use a compilation of the latest results of cosmological N-body simulations and the theoretical insights found in the literature. We find that sub-halos are not likely to significantly boost the exotic production of antimatter CRs.Comment: Proceeding of the SciNeGHE07 workshop (Frascati, Italy, June 2007

TASI Lectures on Cosmological Perturbations

We present a self-contained summary of the theory of linear cosmological perturbations. We emphasize the effect of the six parameters of the minimal cosmological model, first, on the spectrum of Cosmic Microwave Background temperature anisotropies, and second, on the linear matter power spectrum. We briefly review at the end the possible impact of a few non-minimal dark matter and dark energy models.Comment: TASI 2013 lecture note

Two Pinning Models with Markov disorder

Disordered pinning models deal with the (de)localization tran- sition of a polymer in interaction with a heterogeneous interface. In this paper, we focus on two models where the inhomogeneities at the interface are not independent but given by an irreducible Markov chain on a finite state space. In the first model, using Markov renewal tools, we give an expression for the annealed critical curve in terms of a Perron-Frobenius eigenvalue, and provide examples where exact computations are possible. In the second model, the transition matrix vary with the size of the system so that, roughly speaking, disorder is more and more correlated. In this case we are able to give the limit of the averaged quenched free energy, therefore providing the full phase diagram picture, and the number of critical points is related to the number of states of the Markov chain. We also mention that the question of pinning in correlated disorder appears in the context of DNA denaturation