A Recursive Restricted Total Least-squares Algorithm

We show that the generalized total least squares (GTLS) problem with a singular noise covariance matrix is equivalent to the restricted total least squares (RTLS) problem and propose a recursive method for its numerical solution. The method is based on the generalized inverse iteration. The estimation error covariance matrix and the estimated augmented correction are also characterized and computed recursively. The algorithm is cheap to compute and is suitable for online implementation. Simulation results in least squares (LS), data least squares (DLS), total least squares (TLS), and RTLS noise scenarios show fast convergence of the parameter estimates to their optimal values obtained by corresponding batch algorithms

Are HI Supershells the Remnants of Gamma-Ray Bursts?

Gamma-Ray Bursts (GRBs) are thought to originate at cosmological distances from the most powerful explosions in the Universe. If GRBs are not beamed then the distribution of their number as a function of Gamma-ray flux implies that they occur once per (0.3-40) million years per bright galaxy and that they deposit >10^{53} ergs into their surrounding interstellar medium. The blast wave generated by a GRB explosion would be washed out by interstellar turbulence only after tens of millions of years when it finally slows down to a velocity of 10 km/s. This rather long lifetime implies that there could be up to several tens of active GRB remnants in each galaxy at any given time. For many years, radio observations have revealed the enigmatic presence of expanding neutral-hydrogen (HI) supershells of kpc radius in the Milky Way and in other nearby galaxies. The properties of some supershells cannot be easily explained in terms of conventional sources such as stellar winds or supernova explosions. However, the inferred energy and frequency of the explosions required to produce most of the observed supershells agree with the above GRB parameters. More careful observations and analysis might reveal which fraction of these supershells are GRB remnants. We show that if this link is established, the data on HI supershells can be used to constrain the energy output, the rate per galaxy, the beaming factor, and the environment of GRB sources in the Universe.Comment: 8 pages, final version, ApJ Letters, in pres

Twist operator correlation functions in O(n) loop models

Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

Dislocation core structures in Si-doped GaN

Aberration-corrected scanning transmission electron microscopy was used to investigate the core structures of threading dislocations in plan-view geometry of GaN films with a range of Si-doping levels and dislocation densities ranging between (5 ± 1) × 108 and (10 ± 1) × 109 cm−2. All a-type (edge) dislocation core structures in all samples formed 5/7-atom ring core structures, whereas all (a + c)-type (mixed) dislocations formed either double 5/6-atom, dissociated 7/4/8/4/9-atom, or dissociated 7/4/8/4/8/4/9-atom core structures. This shows that Si-doping does not affect threading dislocation core structures in GaN. However, electron beam damage at 300 keV produces 4-atom ring structures for (a + c)-type cores in Si-doped GaN.This work was funded in part by the Cambridge Commonwealth trust, St. John's College, British Federation of Women Graduates and the EPSRC. M.A.M. acknowledges the support from the Royal Society through a University Research Fellowship. Additional support was provided by the EPSRC through the UK National Facility for Aberration-Corrected STEM (SuperSTEM).This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.493745

AGC 226067: A possible interacting low-mass system

We present Arecibo, GBT, VLA and WIYN/pODI observations of the ALFALFA source AGC 226067. Originally identified as an ultra-compact high velocity cloud and candidate Local Group galaxy, AGC 226067 is spatially and kinematically coincident with the Virgo cluster, and the identification by multiple groups of an optical counterpart with no resolved stars supports the interpretation that this systems lies at the Virgo distance (D=17 Mpc). The combined observations reveal that the system consists of multiple components: a central HI source associated with the optical counterpart (AGC 226067), a smaller HI-only component (AGC 229490), a second optical component (AGC 229491), and extended low surface brightness HI. Only ~1/4 of the single-dish HI emission is associated with AGC 226067; as a result, we find M_HI/L_g ~ 6 Msun/Lsun, which is lower than previous work. At D=17 Mpc, AGC 226067 has an HI mass of 1.5 x 10^7 Msun and L_g = 2.4 x 10^6 Lsun, AGC 229490 (the HI-only component) has M_HI = 3.6 x 10^6 Msun, and AGC 229491 (the second optical component) has L_g = 3.6 x 10^5 Lsun. The nature of this system of three sources is uncertain: AGC 226067 and AGC 229490 may be connected by an HI bridge, and AGC 229490 and AGC 229491 are separated by only 0.5'. The current data do not resolve the HI in AGC 229490 and its origin is unclear. We discuss possible scenarios for this system of objects: an interacting system of dwarf galaxies, accretion of material onto AGC 226067, or stripping of material from AGC 226067.Comment: Accepted for publication in A&A. 6 pages, 4 figure

Three-Axis Fiber-Optic Body Force Sensor for Flexible Manipulators

This paper proposes a force/torque sensor structure that can be easily integrated into a flexible manipulator structure. The sensor's ring-like structure with its hollow inner section provides ample space for auxiliary components, such as cables and tubes, to be passed through and, hence, is very suitable for integration with tendon-driven and fluid-actuated manipulators. The sensor structure can also accommodate the wiring for a distributed sensor system as well as for diagnostic instruments that may be incorporated in the manipulator. Employing a sensing approach based on optical fibers as done here allows for the creation of sensors that are free of electrical currents at the point of sensing and immune to magnetic fields. These sensors are inherently safe when used in the close vicinity of humans and their measuring performance is not impaired when they are operated in or nearby machines, such as magnetic resonance imaging scanners. This type of sensor concept is particularly suitable for inclusion in instruments and robotic tools for minimally invasive surgery. This paper summarizes the design, integration challenges, and calibration of the proposed optical three-axis force sensor. The experimental results confirm the effectiveness of our optical sensing approach and show that after calibrating its stiffness matrix, force and momentum components can be determined accurately