A task-based metric for telerobotic performance assessment

A methodology is described for developing a task complexity index based on combining the six basic motion primitives (three translation, three orientation) with force control and accuracy requirements. The result of this development is a set of complexity values that can be assigned to the high-level task primitives derived from a relatively shallow top-down mission analysis. These values are then averaged to arrive at total average mission complexities, such as for the mission of exchanging the Hubble Space Telescope (HST) battery modules. Application of this metric to a candidate set of NASA Flight Telerobotic Servicer evaluation tasks is discussed using the HST battery module mission for an in-depth example

Implications of a DK Molecule at 2.32 GeV

We discuss the implications of a possible quasinuclear DK bound state at 2.32 GeV. Evidence for such a state was recently reported in D_s^+pi^o by the BaBar Collaboration. We first note that a conventional quark model c-sbar assignment is implausible, and then consider other options involving multiquark systems. An I=0 c sbar n nbar baryonium assignment is one possibility. We instead favor a DK meson molecule assignment, which can account for the mass and quantum numbers of this state. The higher-mass scalar c-sbar state expected at 2.48 GeV is predicted to have a very large DK coupling, which would encourage formation of an I=0 DK molecule. Isospin mixing is expected in hadron molecules, and a dominantly I=0 DK state with some I=1 admixture could explain both the narrow total width of the 2.32 GeV state as well as the observed decay to D_s^+ pi^o. Additional measurements that can be used to test this and related scenarios are discussed.Comment: 6 pages, 1 figur

On the measurement of frequency and of its sample variance with high-resolution counters

A frequency counter measures the input frequency $\bar{\nu}$ averaged over a suitable time $\tau$, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from $\smash{\sigma^2_\nu\propto1/\tau^2}$ to $\smash{\sigma^2_\nu\propto1/\tau^3}$. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance $\smash{\sigma^2_y(\tau)=\mathbb{E}\{\frac12(\bar{y}_{k+1}-\bar{y}_k) ^2\}}$ of the fractional frequency fluctuation $y$, the result is the \emph{modified} Allan variance mod $\sigma^2_y(\tau)$. But if a sufficient number of contiguous measures are averaged in order to get a longer $\tau$ and the data are fed into the same formula, the results is the (non-modified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood.Comment: 14 pages, 5 figures, 1 table, 18 reference

Vortex density fluctuations in quantum turbulence

We compute the frequency spectrum of turbulent superfluid vortex density fluctuations and obtain the same Kolmogorov scaling which has been observed in a recent experiment in Helium-4. We show that the scaling can be interpreted in terms of the spectrum of reconnecting material lines. The calculation is performed using a vortex tree algorithm which considerably speeds up the evaluation of Biot-Savart integrals.Comment: 7 Pages, 7 figure

Modeling Financial Volatility: Extreme Observations, Nonlinearities and Nonstationarities

This paper presents a selective survey of volatility topics, with emphasis on the measurement of volatility and a discussion of some of the most important time series models commonly employed in its modelling. In particular, the paper details the long memory characteristics of volatility, and discusses its possible origins and impact on option pricing. To conclude, the paper discusses statistical tools that discriminate between nonlinearity and nonstationarity.long memory; nonstationarity; nonlinearity; option pricing, volatility

Coordinate Confusion in Conformal Cosmology

A straight-forward interpretation of standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies is that objects move apart due to the expansion of space, and that sufficiently distant galaxies must be receding at velocities exceeding the speed of light. Recently, however, it has been suggested that a simple transformation into conformal coordinates can remove superluminal recession velocities, and hence the concept of the expansion of space should be abandoned. This work demonstrates that such conformal transformations do not eliminate superluminal recession velocities for open or flat matter-only FRLW cosmologies, and all possess superluminal expansion. Hence, the attack on the concept of the expansion of space based on this is poorly founded. This work concludes by emphasizing that the expansion of space is perfectly valid in the general relativistic framework, however, asking the question of whether space really expands is a futile exercise.Comment: 5 pages, accepted for publication in MNRAS Letter

Options for the SELEX state D_{s\J}^+(2632)

We consider possible assignments for the D_{s\J}^+(2632), which was recently reported in D$_s^+\eta$ and D$^0$K$^+$ final states by the SELEX Collaboration at Fermilab. The most plausible quark model assignment for this state is the first radial excitation ($2^3\S_1$) of the $c\bar s$ D$_s^*(2112)$, although the predicted mass and strong decay branching fractions for this assignment are not in agreement with the SELEX data. The reported dominance of D$_s\eta$ over DK appears especially problematic. An intriguing similarity to the K$^*(1414)$ is noted. $2^3\S_1$--^3\D_1 configuration mixing is also considered, and we find that this effect is unlikely to resolve the branching fraction discrepancy. Other interpretations as a $c\bar s$-hybrid or a two-meson molecule are also considered, but appear unlikely. Thus, if this state is confirmed, it will require reconsideration of the systematics of charmed meson spectroscopy and strong decays.Comment: 6 revtex4 pages, 2 eps figure

The Validity of the Adiabatic Contraction Approximation for Dark Matter Halos

We use high resolution numerical simulations to investigate the adiabatic contraction of dark matter halos with a Hernquist density profile. We test the response of the halos to the growth of additional axisymmetric disk potentials with various central concentrations and the spherically symmetric potential of a softened point mass. Adding the potentials on timescales that are long compared to the dynamical time scale of the halo, the contracted halos have density profiles that are in excellent agreement with analytical predictions based on the conservation of the adiabatic invariant $M(r)r$. This is surprising as this quantity is strictly conserved only for particles on circular orbits and in spherically symmetric potentials. If the same potentials are added on timescales that are short compared to the dynamical timescale, the result depends strongly on the adopted potential. The adiabatic approximation still works for disk potentials. It does, however, fail for the central potential.Comment: 7 pages, 3 figures, 1 table. Added reference. Accepted for publication in ApJ

On a q-analogue of the multiple gamma functions

A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.Comment: 8 pages, AMS-Late