Metric dimension of dual polar graphs

A resolving set for a graph $\Gamma$ is a collection of vertices $S$, chosen so that for each vertex $v$, the list of distances from $v$ to the members of $S$ uniquely specifies $v$. The metric dimension $\mu(\Gamma)$ is the smallest size of a resolving set for $\Gamma$. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over $\mathbb{R}$ of the incidence matrix of the corresponding polar space. We then compute this rank to give an explicit upper bound on the metric dimension of dual polar graphs.Comment: 8 page

On the metric dimension of Grassmann graphs

The {\em metric dimension} of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph $G_q(n,k)$ (whose vertices are the $k$-subspaces of $\mathbb{F}_q^n$, and are adjacent if they intersect in a $(k-1)$-subspace) for $k\geq 2$, and find a constructive upper bound on its metric dimension. Our bound is equal to the number of 1-dimensional subspaces of $\mathbb{F}_q^n$.Comment: 9 pages. Revised to correct an error in Proposition 9 of the previous versio

Empirical line lists and absorption cross sections for methane at high temperature

Hot methane is found in many "cool" sub-stellar astronomical sources including brown dwarfs and exoplanets, as well as in combustion environments on Earth. We report on the first high-resolution laboratory absorption spectra of hot methane at temperatures up to 1200 K. Our observations are compared to the latest theoretical spectral predictions and recent brown dwarf spectra. The expectation that millions of weak absorption lines combine to form a continuum, not seen at room temperature, is confirmed. Our high-resolution transmittance spectra account for both the emission and absorption of methane at elevated temperatures. From these spectra, we obtain an empirical line list and continuum that is able to account for the absorption of methane in high temperature environments at both high and low resolution. Great advances have recently been made in the theoretical prediction of hot methane, and our experimental measurements highlight the progress made and the problems that still remain.Comment: 9 pages, 5 figures and 3 tables. For associated online data see http://dx.doi.org/10.1088/0004-637X/813/1/1

Kinematically redundant arm formulations for coordinated multiple arm implementations

Although control laws for kinematically redundant robotic arms were presented as early as 1969, redundant arms have only recently become recognized as viable solutions to limitations inherent to kinematically sufficient arms. The advantages of run-time control optimization and arm reconfiguration are becoming increasingly attractive as the complexity and criticality of robotic systems continues to progress. A generalized control law for a spatial arm with 7 or more degrees of freedom (DOF) based on Whitney's resolved rate formulation is given. Results from a simulation implementation utilizing this control law are presented. Furthermore, results from a two arm simulation are presented to demonstrate the coordinated control of multiple arms using this formulation