Exponential factorizations of holomorphic maps

We show that any element of the special linear group $SL_2(R)$ is a product of two exponentials if the ring $R$ is either the ring of holomorphic functions on an open Riemann surface or the disc algebra. This is sharp: one exponential factor is not enough since the exponential map corresponding to $SL_2(\mathbb{C})$ is not surjective. Our result extends to the linear group $GL_2(R)$.Comment: 9 page

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

US imbalances: the role of technology and policy

This paper investigates the role of three likely factors in driving the steady deterioration of the US external balance: US technology developments, changes in the US government fiscal position and the Fed’s monetary policy. Estimating several Vector Autoregressions on US data over the period 1982:2 to 2005:4 we identify five structural shocks: a multi-factor productivity shock; an investment-specific technology shock; a monetary policy shock; and a fiscal revenue and spending shock. Together these shocks can account for the deterioration and subsequent reversal of the trade balance in the 1980s. Productivity improvements and fiscal and monetary policy easing also play an important role in the increase of the external deficit since 2000, but these structural shocks can not explain why the trade balance deteriorated in the second half of the 1990s. JEL Classification: F3, F4global imbalances, open economy, VARs

Neutron Star instabilities in full General Relativity using a Γ=2.75\Gamma=2.75 ideal fluid

We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $\Gamma=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change on the critical value of the instability parameter $\beta$ for the emergence of the instability when the adiabatic index $\Gamma$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness and give a precise quantification of the change in value of the critical parameter $\beta_c$. We also extend the analysis to lower values of $\beta$ and show that low-beta shear instabilities are present also in the case of matter described by a simple polytropic equation of state.Comment: 16 pages, 16 figure

Local causes, regional co-operation and global financing for environemntal problems: the case of Southeast Asian Haze pollution

Lack of action on cross-border environmental problems in developing countries is often ascribed to gaps in local capacity and resources, failure of regional cooperation, and lack of financial support from rich countries. Using the case of the Southeast Asian Haze pollution from forest and peat fires in Indonesia, we explore the challenges posed by environmental problems whose causes are closely linked to local development and livelihood strategies, and whose impacts are local, regional (haze) as well as global (carbon emissions). We assess whether there are real opportunities to implement effectively the recent Association of Southeast Asian Nations (ASEAN) Agreement on Transboundary Haze Pollution. To address the deep determinants behind haze pollution, we propose signatories to the Agreement refocus their efforts to controlling peat fires rather than strive for a zero-burning regime. We also recommend a new approach to financing sustainable development based on rules and incentives, with a regional pool of funds, contributed by rich countries through the Global Environment Facility and countries in Southeast Asia.ASEAN, climate change, fires, GEF, haze pollution, regional agreements

Dilute and dense axion stars

Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core $|\theta_0| \equiv |\theta(r=0)|$, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of $|\theta_0|$. For small $|\theta_0| \lesssim 1$, we reproduce results previously obtained in the literature, and we provide arguments for the stability of such configurations in terms of first principles. We compare qualitative analytical results with a numerical calculation. For large amplitudes $|\theta_0| \gtrsim 1$, the axion field probes the full non-harmonic QCD chiral potential and the axion star enters the {\it dense} branch. Our numerical solutions show that in this latter regime the axions are relativistic, and that one should not use a single frequency approximation, as previously applied in the literature. We employ a multi-harmonic expansion to solve the relativistic equation for the axion field in the star, and demonstrate that higher modes cannot be neglected in the dense regime. We interpret the solutions in the dense regime as pseudo-breathers, and show that the life-time of such configurations is much smaller than any cosmological time scale.Comment: 11 pages, 4 figures. v2: added references, matches published versio