The kernel Kalman rule: efficient nonparametric inference with recursive least squares

Nonparametric inference techniques provide promising tools for probabilistic reasoning in high-dimensional nonlinear systems. Most of these techniques embed distributions into reproducing kernel Hilbert spaces (RKHS) and rely on the kernel Bayes’ rule (KBR) to manipulate the embeddings. However, the computational demands of the KBR scale poorly with the number of samples and the KBR often suffers from numerical instabilities. In this paper, we present the kernel Kalman rule (KKR) as an alternative to the KBR. The derivation of the KKR is based on recursive least squares, inspired by the derivation of the Kalman innovation update. We apply the KKR to filtering tasks where we use RKHS embeddings to represent the belief state, resulting in the kernel Kalman filter (KKF). We show on a nonlinear state estimation task with high dimensional observations that our approach provides a significantly improved estimation accuracy while the computational demands are significantly decreased

Learning robust policies for object manipulation with robot swarms

Swarm robotics investigates how a large population of robots with simple actuation and limited sensors can collectively solve complex tasks. One particular interesting application with robot swarms is autonomous object assembly. Such tasks have been solved successfully with robot swarms that are controlled by a human operator using a light source. In this paper, we present a method to solve such assembly tasks autonomously based on policy search methods. We split the assembly process in two subtasks: generating a high-level assembly plan and learning a low-level object movement policy. The assembly policy plans the trajectories for each object and the object movement policy controls the trajectory execution. Learning the object movement policy is challenging as it depends on the complex state of the swarm which consists of an individual state for each agent. To approach this problem, we introduce a representation of the swarm which is based on Hilbert space embeddings of distributions. This representation is invariant to the number of agents in the swarm as well as to the allocation of an agent to its position in the swarm. These invariances make the learned policy robust to changes in the swarm and also reduce the search space for the policy search method significantly. We show that the resulting system is able to solve assembly tasks with varying object shapes in multiple simulation scenarios and evaluate the robustness of our representation to changes in the swarm size. Furthermore, we demonstrate that the policies learned in simulation are robust enough to be transferred to real robots

Robust learning of object assembly tasks with an invariant representation of robot swarms

— Swarm robotics investigates how a large population of robots with simple actuation and limited sensors can collectively solve complex tasks. One particular interesting application with robot swarms is autonomous object assembly. Such tasks have been solved successfully with robot swarms that are controlled by a human operator using a light source. In this paper, we present a method to solve such assembly tasks autonomously based on policy search methods. We split the assembly process in two subtasks: generating a high-level assembly plan and learning a low-level object movement policy. The assembly policy plans the trajectories for each object and the object movement policy controls the trajectory execution. Learning the object movement policy is challenging as it depends on the complex state of the swarm which consists of an individual state for each agent. To approach this problem, we introduce a representation of the swarm which is based on Hilbert space embeddings of distributions. This representation is invariant to the number of agents in the swarm as well as to the allocation of an agent to its position in the swarm. These invariances make the learned policy robust to changes in the swarm and also reduce the search space for the policy search method significantly. We show that the resulting system is able to solve assembly tasks with varying object shapes in multiple simulation scenarios and evaluate the robustness of our representation to changes in the swarm size. Furthermore, we demonstrate that the policies learned in simulation are robust enough to be transferred to real robots

Hydrodynamical evolution near the QCD critical end point

Hydrodynamical calculations have been successful in describing global observables in ultrarelativistic heavy ion collisions, which aim to observe the production of the quark-gluon plasma. On the other hand, recently, a lot of evidence that there exists a critical end point (CEP) in the QCD phase diagram has been accumulating. Nevertheless, so far, no equation of state with the CEP has been employed in hydrodynamical calculations. In this paper, we construct the equation of state with the CEP on the basis of the universality hypothesis and show that the CEP acts as an attractor of isentropic trajectories. We also consider the time evolution in the case with the CEP and discuss how the CEP affects the final state observables, such as the correlation length, fluctuation, chemical freezeout, kinetic freezeout, and so on. Finally, we argue that the anomalously low kinetic freezeout temperature at the BNL Relativistic Heavy Ion Collider suggests the possibility of the existence of the CEP.Comment: 13 pages, 12 figures, accepted for publication in Physical Review

The Spin of M87 as measured from the Rotation of its Globular Clusters

We revisit the kinematical data for 204 globular clusters in the halo of M87. Beyond 3 r_eff along the major axis of the galaxy light, these globular clusters exhibit substantial rotation (~ 300 +/- 70 km/s) that translates into an equally substantial spin (lambda ~ 0.18). The present appearance of M87 is most likely the product of a single major merger, since this event is best able to account for so sizable a spin. A rotation this large makes improbable any significant accretion of material after this merger, since that would have diluted the rotation signature. We see weak evidence for a difference between the kinematics of the metal-poor and metal-rich population, in the sense that the metal-poor globular clusters appear to dominate the rotation. If, as we suspect, the last major merger event of M87 was mainly dissipationless and did not trigger the formation of a large number of globular clusters, the kinematic difference between the two could reflect their orbital properties in the progenitor galaxies; these differences would be compatible with these progenitors having formed in dissipational mergers. However, to put strong kinematic constraints on the origin of the globular clusters themselves is difficult, given the complex history of the galaxy and its last dominant merger event.Comment: 20 pages (AAS two column style, including 1 table and 7 figures) accepted in the AJ (November issue), also available at http://www.ucolick.org/~mkissler

On Shape Transformations and Shape Fluctuations of Cellular Compartments and Vesicles

We discuss the shape formation and shape transitions of simple bilayer vesicles in context with their role in biology. In the first part several classes of shape changes of vesicles of one lipid component are described and it is shown that these can be explained in terms of the bending energy concept in particular augmented by the bilayer coupling hypothesis. In the second part shape changes and vesicle fission of vesicles composed of membranes of lipid mixtures are reported. These are explained in terms of coupling between local curvature and phase separation

Spatially resolved simulation of a radio frequency driven micro atmospheric pressure plasma jet and its effluent

Radio frequency driven plasma jets are frequently employed as efficient plasma sources for surface modification and other processes at atmospheric pressure. The radio-frequency driven micro atmospheric pressure plasma jet ($\mu$APPJ) is a particular variant of that concept whose geometry allows direct optical access. In this work, the characteristics of the $\mu$APPJ operated with a helium-oxygen mixture and its interaction with a helium environment are studied by numerical simulation. The density and temperature of the electrons, as well as the concentration of all reactive species are studied both in the jet itself and in its effluent. It is found that the effluent is essentially free of charge carriers but contains a substantial amount of activated oxygen (O, O$_3$ and O$_2(^1\Delta)$). The simulation results are verified by comparison with experimental data

UBVI Surface Photometry of the Spiral Galaxy NGC 300 in the Sculptor Group

We present UBVI surface photometry for 20.'5 X 20.'5 area of a late-type spiral galaxy NGC 300. In order to understand the morphological properties and luminosity distribution characteristics of NGC 300, we have derived isophotal maps, surface brightness profiles, ellipticity profiles, position angle profiles, and color profiles. By merging the I-band data of our surface brightness measurements with those of Boeker et al. (2002) based on Hubble Space Telescope observations, we have made combined I-band surface brightness profiles for the region of 0."02 < r < 500" and decomposed the profiles into three components: a nucleus, a bulge, and an exponential disk.Comment: 16 pages(cjaa209.sty), Accepted by the Chinese J. Astron. Astrophys., Fig 2 and 8 are degraded to reduce spac

Hubble Space Telescope Evidence for an Intermediate-Mass Black Hole in the Globular Cluster M15: II. Kinematical Analysis and Dynamical Modeling

We analyze HST/STIS spectra (see Paper I) of the central region of the dense globular cluster M15. We infer the velocities of 64 individual stars, two-thirds of which have their velocity measured for the first time. This triples the number of stars with measured velocities in the central 1 arcsec of M15 and doubles the number in the central 2 arcsec. Combined with existing ground-based data we obtain the radial profiles of the projected kinematical quantities. The RMS velocity sigma_RMS rises to 14 km/s in the central few arcsec, somewhat higher than the values of 10-12 km/s inferred previously from ground-based data. To interpret the results we construct dynamical models based on the Jeans equation, which imply that M15 must have a central concentration of non-luminous material. If this is due to a single black hole, then its mass is M_BH = (3.9 +/- 2.2) x 10^3 solar masses. This is consistent with the relation between M_BH and sigma_RMS that has been established for galaxies. Also, the existence of intermediate-mass black holes in globular clusters is consistent with several scenarios for globular cluster evolution proposed in the literature. Therefore, these results may have important implications for our understanding of the evolution of globular clusters, the growth of black holes, the connection between globular cluster and galaxy formation, and the nature of the recently discovered `ultra-luminous' X-ray sources in nearby galaxies. Instead of a single black hole, M15 could have a central concentration of dark remnants (e.g., neutron stars) due to mass segregation. However, the best-fitting Fokker-Planck models that have previously been constructed for M15 do not predict a central mass concentration that is sufficient to explain the observed kinematics.[ABRIDGED]Comment: 43 pages, LaTeX, with 14 PostScript figures. Astronomical Journal, in press (Dec 2002). Please note that the results reported here are modified by the Addendum available at astro-ph/0210158 (Astronomical Journal, in press, Jan 2003). This second version submitted to astro-ph is identical to first, with the exception of the preceeding remar

SuperMassive Black Holes in Bulges

We present spatially extended gas kinematics at parsec-scale resolution for the nuclear regions of four nearby disk galaxies, and model them as rotation of a gas disk in the joint potential of the stellar bulge and a putative central black hole. The targets were selected from a larger set of long-slit spectra obtained with the Hubble Space Telescope as part of the Survey of Nearby Nuclei with STIS (SUNNS). They represents the 4 galaxies (of 24) that display symmetric gas velocity curves consistent with a rotating disk. We derive the stellar mass distribution from the STIS acquisition images adopting the stellar mass-to-light ratio normalized so as to match ground-based velocity dispersion measurements over a large aperture. Subsequently, we constrain the mass of a putative black hole by matching the gas rotation curve, following two distinct approaches. In the most general case we explore all the possible disk orientations, alternatively we constrain the gas disk orientation from the dust-lane morphology at similar radii. In the latter case the kinematic data indicate the presence of a central black hole for three of the four objects, with masses of 10^7 - 10^8 solar masses, representing up to 0.025 % of the host bulge mass. For one object (NGC2787) the kinematic data alone provide clear evidence for the presence of a central black hole even without external constraints on the disk orientation. These results illustrate directly the need to determine black-hole masses by differing methods for a large number of objects, demonstrate that the variance in black hole/bulge mass is much larger than previously claimed, and reinforce the recent finding that the black-hole mass is tightly correlated with the bulge stellar velocity dispersion.Comment: 26 pages, 11 Postscript figures, accepted for publication on Ap