Regression-based motion planning

This thesis explores two novel approaches to sample-based motion planning that utilize regressions as continuous function approximations to reduce the memory cost of planning. The first approach, Field Search Trees (FST) provides a solution for single-start planning by iteratively building local regressions of the cost-to-arrive function. The second approach, the Regression Complex (RC), constructs a complex of cells with each cell containing a regression of the distance between any two points on its boundary, creating a useful data structure for any start and goal planning query. We provide formal definitions of both approaches and experimental results of running the algorithms on different simulated robot systems. We conclude that regression-based motion planning provides key advantages over traditional sample-based motion planning in certain cases, but more work is required to extend these approaches into higher dimensional configuration spaces

Abelian covers of surfaces and the homology of the level L mapping class group

We calculate the first homology group of the mapping class group with coefficients in the first rational homology group of the universal abelian $\Z / L \Z$-cover of the surface. If the surface has one marked point, then the answer is \Q^{\tau(L)}, where $\tau(L)$ is the number of positive divisors of $L$. If the surface instead has one boundary component, then the answer is \Q. We also perform the same calculation for the level $L$ subgroup of the mapping class group. Set $H_L = H_1(\Sigma_g;\Z/L\Z)$. If the surface has one marked point, then the answer is \Q[H_L], the rational group ring of $H_L$. If the surface instead has one boundary component, then the answer is \Q.Comment: 32 pages, 10 figures; numerous corrections and simplifications; to appear in J. Topol. Ana

Polymerized LB films imaged with a combined atomic force microscope-fluorescence microscope

The first results obtained with a new stand-alone atomic force microscope (AFM) integrated with a standard Zeiss optical fluorescence microscope are presented. The optical microscope allows location and selection of objects to be imaged with the high-resolution AFM. Furthermore, the combined microscope enables a direct comparison between features observed in the fluorescence microscope and those observed in the images obtained with the AFM, in air or under liquid. The cracks in polymerized Langmuir-Blodgett films of lO,l2-pentacosadiynoic acid as observed in the fluorescence microscope run parallel to one of the lattice directions of the crystal as revealed by molecular resolution images obtained with the AFM. The orientation of these cracks also coincides with the polarization direction of the fluorescent light, indicating that the cracks run along the polymer backbone. Ripple-like corrugations on a submicrometer scale have been observed, which may be due to mechanical stress created during the polymerization process

The Vela Cloud: A Giant HI Anomaly in the NGC 3256 Group

We present Australia Telescope Compact Array (ATCA) observations of a galaxy-sized intergalactic HI cloud (the Vela Cloud) in the NGC 3256 galaxy group. The group contains the prominent merging galaxy NGC 3256, which is surrounded by a number of HI fragments, the tidally disturbed galaxy NGC 3263, and several other peculiar galaxies. The Vela Cloud, with an HI mass of 3-5 * 10**9 solar masses, resides southeast of NGC 3256 and west of NGC 3263, within an area of 9' x 16' (100 kpc x 175 kpc for an adopted distance of 38 Mpc). In our ATCA data the Vela Cloud appears as 3 diffuse components and contains 4 density enhancements. The Vela Cloud's properties, together with its group environment, suggest that it has a tidal origin. Each density enhancement contains ~10**8 solar masses of HI gas which is sufficient material for the formation of globular cluster progenitors. However, if we represent the enhancements as Bonnor-Ebert spheres, then the pressure of the surrounding HI would need to increase by at least a factor of 6 in order to cause the collapse of an enhancement. Thus we do not expect them to form massive bound stellar systems like super star clusters or tidal dwarf galaxies. Since the HI density enhancements have some properties in common with High Velocity Clouds, we explore whether they may evolve to be identified with these starless clouds instead.Comment: 47 pages, 13 figures (incl. a & b), accepted by AJ, changes are minor additions, rearranging, and clarifications esp. in sections 6 &

The Metal-Enriched Outer Disk of NGC 2915

We present optical emission-line spectra for outlying HII regions in the extended neutral gas disk surrounding the blue compact dwarf galaxy NGC 2915. Using a combination of strong-line R23 and direct oxygen abundance measurements, we report a flat, possibly increasing, metallicity gradient out to 1.2 times the Holmberg radius. We find the outer-disk of NGC 2915 to be enriched to a metallicity of 0.4 Z_solar. An analysis of the metal yields shows that the outer disk of NGC 2915 is overabundant for its gas fraction, while the central star-foming core is similarly under-abundant for its gas fraction. Star formation rates derived from very deep ~14 ks GALEX FUV exposures indicate that the low-level of star formation observed at large radii is not sufficient to have produced the measured oxygen abundances at these galactocentric distances. We consider 3 plausible mechanisms that may explain the metal-enriched outer gaseous disk of NGC 2915: radial redistribution of centrally generated metals, strong galactic winds with subsequent fallback, and galaxy accretion. Our results have implications for the physical origin of the mass-metallicity relation for gas-rich dwarf galaxies.Comment: 11 pages, 4 figures, accepted to ApJ April 8th, 201