Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues

This article is concerned with the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals which implement, respectively, the exact Bayesian Model Averaging (BMA) estimator and the Weighted Average Least Squares (WALS) estimator developed by Magnus et al. (2010). Unlike standard pretest estimators which are based on some preliminary diagnostic test, these model averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to a number practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model averaging estimation.Model uncertainty;Model averaging;Bayesian analysis;Exact computation

A Bayesian framework for optimal motion planning with uncertainty

Modeling robot motion planning with uncertainty in a Bayesian framework leads to a computationally intractable stochastic control problem. We seek hypotheses that can justify a separate implementation of control, localization and planning. In the end, we reduce the stochastic control problem to path- planning in the extended space of poses x covariances; the transitions between states are modeled through the use of the Fisher information matrix. In this framework, we consider two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two correct and complete algorithms are presented. The first is the direct extension of classical graph-search algorithms in the extended space. The second one is a back-projection algorithm: uncertainty constraints are propagated backward from the goal towards the start state

Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of Low Mass X-ray Binaries around Sgr A* are very likely to be seen by future X-ray interferometry missions.Comment: 19 pages, 9 figures, published on Phys. Rev.

Out-of-plane magnetic domain structure in a thin film of La0.67Sr0.33MnO3 on SrTiO3 (001) observed by magnetic force microscopy

The room temperature out-of-plane magnetization of epitaxial thin films of La0.67Sr0.33MnO3 on SrTiO3 (001) has been investigated with magnetic force microscopy, using magnetic tips with very small coercivity, relative to the film. A clear magnetic pattern in the form of a checkerboard, with domain dimensions of a few hundred nanometers, was found for the thin, coherently strained films, which is approximately aligned along the maximum strain [110] and [1[overline 1]0] directions in the film. With increasing in-plane applied magnetic field, the magnetic contrast reduces, reflecting the rotation of the magnetization vector into the plane of the film. This process is reversible with the field. The out-of-plane magnetic pattern is not sensitive to rotation of the in-plane field. We attribute the observed out-of-plane magnetization component to an out-of-plane magnetic anisotropy, which is a remainder of the [111] magnetic easy axis in bulk La0.67Sr0.33MnO3 single crystal

Conformations Of A Model Protein Revealed By An Aggregating Cuᴵᴵ Porphyrin: Sensing The Difference

Aggregated t-CuP binds to poly-L-glutamate through supramolecular interactions, revealing itself to be an extremely sensitive probe for the major conformations of the polymeric scaffold

Beyond divide and rule: weak dictators, natural resources and civil conflict

We propose a model where an autocrat rules over an ethnically divided society. The dictator selects the tax rate over domestic production and the nation's natural resources to maximize his rents under the threat of a regime-switching revolution. We show that a weak ruler may let the country plunge in civil war to increase his personal rents. Inter-group fighting weakens potential opposition to the ruler, thereby allowing him to increase fiscal pressure. We show that the presence of natural resources exacerbatesthe incentives of the ruler to promote civil conflict for his own profit, especially if the resources are unequally distributed across ethnic groups. We validate the main predictions of the model using cross-country data over the period 1960-2007, and show that our empirical results are not likely to be driven by omitted observable determinants of civil war incidence or by unobservable country-specific heterogeneity.

Holographic duals of 6d RG flows

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements $\mu_\mathrm{L,R}$ in $G$. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for $G=\mathrm{SU}(k)$, where AdS$_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS$_7$ vacua, determined by two nilpotent elements, which are naturally interpreted as IIA AdS$_7$ solutions. The BPS equations for domain walls connecting two such vacua can be solved analytically, up to a Nahm equation with certain boundary conditions. The latter admit a solution connecting two vacua if and only if the corresponding nilpotent elements are related by the natural partial ordering, in agreement with the field theory conjecture.Comment: 33 pages, 2 figure

Quantum spin Hall effect in bound states in continuum

Moving the polarization of the incident wave along a meridian of the Poincaré sphere, experimentally we show that the coupling with the fundamental Bloch's surface waves of the mode, provide a spatially coherent, macroscopic spinmomentum locked propagation along the symmetry axes of the PhCM. This novel mechanism of light-spin manipulation enables a versatile implementation of spin-optical structures that may pave the way to novel strategies for light spin technology and photonic multiplatform implementations

The Ineludible non-Gaussianity of the Primordial Black Hole Abundance

We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one based on peak theory and the other on threshold statistics. Our results show that the unavoidable non-Gaussian nature of the inhomogeneities in the energy density makes it harder to generate PBHs. We provide simple (semi-)analytical expressions to calculate the non-Gaussian abundances of the primordial black holes and show that for both narrow and broad power spectra the gaussian case from threshold statistics is reproduced by increasing the amplitude of the power spectrum by a factor ${\cal O}(2\div 3)$.Comment: 26 pages, 10 figures, matching published versio