Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.Comment: 10 pages, 4 figure

The Czech Economic Transition: Exploring Options Using a Macrosectoral Model

The processes that will drive the next stage of the Czech transition are likely to be similar to those promoting real convergence in the EU cohesion countries. We draw on previous modelling research on the cohesion economies to construct and calibrate a small macrosectoral model of the Czech Republic that serves to highlight key policy issues facing CEE-country decision-makers. Four scenarios are then explored by simulation: the first projects the current pattern of disequilibrium wage setting into the future, while a second looks at the consequences of labour market reform. The other scenarios highlight some of the differences between policy strategies based on indigenous versus FDI-driven export-led growth.

THE LECTOTYPE AND TYPE LOCALITY OF CANDOIA CARINATA (REPTILIA, SERPENTES)

The lectotype of Boa carinata Schneider, 1801, has been rediscovered and is now ZMFK35503, having been transferred in 1977 from the Göttingen Museum, its original location. Its typelocality has not been reported previously, but is indicated as “Amboina” on a label with the lectotype.The specimen is redescribed and fi gured, and conforms with expectations for material from the vicinityof the type locality. A brief history of Schneider and of the syntypes of Boa carinata, now Candoiacarinata, is reviewed

Depilating Global Charge From Thermal Black Holes

At a formal level, there appears to be no difficulty involved in introducing a chemical potential for a globally conserved quantum number into the partition function for space-time including a black hole. Were this possible, however, it would provide a form of black hole hair, and contradict the idea that global quantum numbers are violated in black hole evaporation. We demonstrate dynamical mechanisms that negate the formal procedure, both for topological charge (Skyrmions) and complex scalar-field charge. Skyrmions collapse to the horizon; scalar-field charge fluctuates uncontrollably

Obtaining Maxwell's equations heuristically

Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light together with Galileo invariance of the Lorentz force allows us to introduce arbitrary electrodynamic units naturally.Comment: 11 page

CNO abundances in the globular clusters NGC 1851 and NGC 6752

We measure the C+N+O abundance sum in red giant stars in two Galactic globular clusters, NGC 1851 and NGC 6752. NGC 1851 has a split subgiant branch which could be due to different ages or C+N+O content while NGC 6752 is representative of the least complex globular clusters. For NGC 1851 and NGC 6752, we obtain average values of A(C+N+O) = 8.16 ± 0.10 (σ = 0.34) and 7.62 ± 0.02 (σ = 0.06), respectively. When taking into account the measurement errors, we find a constant C+N+O abundance sum in NGC 6752. The C+N+O abundance dispersion is only 0.06 dex, and such a result requires that the source of the light element abundance variations does not increase the C+N+O sum in this cluster. For NGC 1851, we confirm a large spread in C+N+O. In this cluster, the anomalous RGB has a higher C+N+O content than the canonical RGB by a factor of 4 (∼0.6 dex). This result lends further support to the idea that the two subgiant branches in NGC 1851 are roughly coeval, but with different CNO abundances

Effects of the Tax Cuts and Jobs Act on State Individual Income Taxes

This article considers how the changes in the federal tax code will affect states whose tax codes link to the federal tax code. The article first summarizes the different parts of the federal code state tax codes link to, most importantly by linking to the definition of income. The article then describes the provisions of the Tax Cuts and Jobs Act that will have the biggest effect on state taxes. The article then uses four sample states (Missouri, Colorado, Utah and New York) and the District of Columbia to analyze how the changes contained in the Tax Cut and Jobs Act will affect: 1) the revenue collected by these jurisdictions; and 2) the state tax incidence across different income groups

B852: Organic Wild Blueberry Production

Recent research carried out under the auspices of a USDA organic transition grant resulted in a better understanding of the interaction of wild blueberry production tactics such as pruning method, soil pH reduction by sulfur (S) application, and organic fertilizer rates on wild blueberry growth, development, and yield. This bulletin is the product of what we have learned over the past four years of this research project.https://digitalcommons.library.umaine.edu/aes_bulletin/1002/thumbnail.jp