Uniformizing surfaces via discrete harmonic maps

We show that for any closed surface of genus greater than one and for any finite weighted graph filling the surface, there exists a hyperbolic metric which realizes the least Dirichlet energy harmonic embedding of the graph among a fixed homotopy class and all hyperbolic metrics on the surface. We give explicit examples of such hyperbolic surfaces through a new interpretation of the Nielsen realization problem for the mapping class groups.Comment: 31 pages, 5 figure

A massive disk galaxy at z>3 along the sightline of QSO 1508+5714

We have obtained deep images in the BVRIJHKs bands of the field centered on QSO 1508+5714 (z_{em} =4.28) with the Suprime camera, FOCAS and MOIRCS cameras on Subaru telescope. We report here the detection of a B-dropout galaxy, which is 3\secpoint 5 north-west of the QSO sightline. A photometric redshift analysis is presented to complement the color selection. Given the photometric properties of this object ($M = -22.2$, making $L\approx 3 L^{\ast}$, if placed at its photometric redshift $z\sim 3.5$), as well as the S$\acute{e}$rsic index ($n \sim 1$) derived from a 2-D imaging decomposition of the HST WFPC2 image taken in the $I_{F814}$ filter, the identified system is consistent with a massive disk galaxy at z>3. If confirmed, it would be one of the most distant massive disk galaxies known so far.Comment: 12 pages, 6 figures, accepted by PASJ, Vol.61/No.5, 200

Head-Trajectory-Tracking Control of a Snake Robot and Its Robustness Under Actuator Failure

This brief considers the problem of trajectory tracking of a planar snake robot without a lateral constraint. The reference trajectory of the head position and the orientation of link 1 are given, and torque control is determined to reduce tracking errors. The performance of the controller was tested in a number of simulations. The robustness during actuator failure was also studied. We assumed that one of the actuators was broken and the corresponding joint became passive. Furthermore, as a more realistic situation, we considered an instance when some of the states were not readily accessible from the sensor readings and needed to be estimated by an observer. The extended Kalman filter was employed for this purpose, and the performance of the closed-loop system with the observer was also tested in simulations