k-Color Multi-Robot Motion Planning

We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multi-robot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots and polygonal robots translating in the plane. We show that the algorithm successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a simplified version of this algorithm, that can be viewed as an extension of a prevalent sampling-based algorithm for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a well established implementation of PRM for the standard multi-robot problem, in which each robot has a distinct color.Comment: 2

TE Wave Measurement and Modeling

In the TE wave method, microwaves are coupled into the beam-pipe and the effect of the electron cloud on these microwaves is measured. An electron cloud (EC) density can then be calculated from this measurement. There are two analysis methods currently in use. The first treats the microwaves as being transmitted from one point to another in the accelerator. The second more recent method, treats the beam-pipe as a resonant cavity. This paper will summarize the reasons for adopting the resonant TE wave analysis as well as give examples from CESRTA and DA{\Phi}NE of resonant beam-pipe. The results of bead-pull bench measurements will show some possible standing wave patterns, including a cutoff mode (evanescent) where the field decreases exponentially with distance from the drive point. We will outline other recent developments in the TE wave method including VORPAL simulations of microwave resonances, as well as the simulation of transmission in the presence of both an electron cloud and magnetic fields.Comment: Presented at ECLOUD'12: Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects, La Biodola, Isola d'Elba, Italy, 5-9 June 2012; CERN-2013-002, pp. 193-20

Random field Ising systems on a general hierarchical lattice: Rigorous inequalities

Random Ising systems on a general hierarchical lattice with both, random fields and random bonds, are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These inequalities lead to upper bounds on the crossover exponents $\{\phi_i\}$.Comment: LaTeX, 13 pages, figs. 1a,1b,2. To be published in PR

The Induced Magnetic Field of the Moon: Conductivity Profiles and Inferred Temperature

Electromagnetic induction in the moon driven by fluctuations of the interplanetary magnetic field is used to determine the lunar bulk electrical conductivity. The present data clearly show the north-south and east-west transfer function difference as well as high frequency rollover. The difference is shown to be compatible over the mid-frequency range with a noise source associated with the compression of the local remanent field by solar wind dynamic pressure fluctuations. Models for two, three, and four layer; current layer, double current layer, and core plus current layer moons are generated by inversion of the data using a theory which incorporates higher order multipoles. Core radii conductivities generally are in the range 1200 to 1300 km and 0.001 to 0.003 mhos/m; and for the conducting shell 1500 to 1700 km with 0.0001 to 0.0007 mhos/m with an outer layer taken as nonconducting. Core temperature based on available olivine data is 700 to 1000 C

Precision of the calibration of the AXAF engineering test article (VETA) mirrors

Measurements of the VETA encircled energies have been performed at 5 energies within 16 radii ranging from 0.05 to 200 arcseconds. We report here on the analysis of the accuracy of those measurements. A common 'error tree' structure applies, and we present representative numbers for the larger terms. At 0.277, 1.5, and 2.07 keV, and for radii of 3 arcsec and larger, our measurements have estimated 1 sigma errors of 0.6 to 1.5 percent. Effects of measurement statistics and of the VETA test mount limit the accuracy at smaller angles, and modulation by the counter window support structure together with the imperfect position repeatability limit the accuracy for the 0.93 and 2.3 keV energies. We expect to mitigate these limitations when calibrating the complete AXAF flight mirror assembly

Efficient Multi-Robot Motion Planning for Unlabeled Discs in Simple Polygons

We consider the following motion-planning problem: we are given $m$ unit discs in a simple polygon with $n$ vertices, each at their own start position, and we want to move the discs to a given set of $m$ target positions. Contrary to the standard (labeled) version of the problem, each disc is allowed to be moved to any target position, as long as in the end every target position is occupied. We show that this unlabeled version of the problem can be solved in $O(n\log n+mn+m^2)$ time, assuming that the start and target positions are at least some minimal distance from each other. This is in sharp contrast to the standard (labeled) and more general multi-robot motion-planning problem for discs moving in a simple polygon, which is known to be strongly NP-hard

Age-related changes in the relationship between alcohol use and violence from early adolescence to young adulthood

BACKGROUND: Despite the accumulation of studies examining the link between alcohol use and violence, no studies to our knowledge have systematically set out to detect age-related differences in these relationships. This limitation inhibits important insights into the stability of the relationship between alcohol use and violence among youth across varying ages. METHOD: Study findings are based on repeated, cross-sectional data collected annually as part of the National Survey on Drug Use and Health between 2002 and 2013. We combined a series of nationally representative cross-sections to provide a multi-year string of data that, in effect, reflects a nationally representative non-traditional cohort. We conducted logistic regression analyses to examine the cross-sectional association between non-binge and binge drinking and violent attacks among youth between ages 12 (2002) and 24/25 (2013). RESULTS: With respect to the association between non-binge alcohol use and violence, the only significant relationship identified—while controlling for sociodemographic and drug use factors—was for youth at age 13 (2003; OR = 1.97, 95% CI = 1.04–3.72). For binge drinking, we identified a distinct pattern of results. Controlling for sociodemographic, drug use factors, and school enrollment, binge drinking was significantly associated with violence between ages 13 (2003) and 20 (2010) with the largest odds ratios observed during the early adolescent period. CONCLUSIONS: Non-binge drinking is associated with violent behavior at age 13. Binge drinking was found to be associated with violence among youth through age 20; however, the relationship dissipates when youth arrive at the legal drinking age of 21

Critical Behavior of the 3d Random Field Ising Model: Two-Exponent Scaling or First Order Phase Transition?

In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the random fields it is found that the correlation length $\xi$ diverges with an exponent $\nu=1.1\pm0.2$ at the critical temperature and that $\chi\sim\xi^{2-\eta}$ with $\eta=0.50\pm0.05$ for the connected susceptibility and $\chi_{\rm dis}\sim\xi^{4-\bar{\eta}}$ with $\bar{\eta}=1.03\pm0.05$ for the disconnected susceptibility. Together with the amplitude ratio $A=\lim_{T\to T_c}\chi_{\rm dis}/\chi^2(h_r/T)^2$ being close to one this gives further support for a two exponent scaling scenario implying $\bar{\eta}=2\eta$. The magnetization behaves discontinuously at the transition, i.e. $\beta=0$, indicating a first order transition. However, no divergence for the specific heat and in particular no latent heat is found. Also the probability distribution of the magnetization does not show a multi-peak structure that is characteristic for the phase-coexistence at first order phase transition points.Comment: 14 pages, RevTeX, 11 postscript figures (fig9.ps and fig11.ps should be printed separately

SCD Patterns Have Singular Diffraction

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part, that they have a uniformly discrete pure point part on the z-axis, and that they are otherwise supported on a set of concentric cylinder surfaces around this axis. For SCD tilings with additional properties, more detailed results are given.Comment: 11 pages, 2 figures; Accepted for Journal of Mathematical Physic