Accurate object reconstruction by statistical moments

Statistical moments can offer a powerful means for object description in object sequences. Moments used in this way provide a description of the changing shape of the object with time. Using these descriptions to predict temporal views of the object requires efficient and accurate reconstruction of the object from a limited set of moments, but accurate reconstruction from moments has as yet received only limited attention. We show how we can improve accuracy not only by consideration of formulation, but also by a new adaptive thresholding technique that removes one parameter needed in reconstruction. Both approaches are equally applicable for Legendre and other orthogonal moments to improve accuracy in reconstruction

Identifying candidates for targeted gait rehabilitation: better prediction through biomechanics-informed characterization

BACKGROUND: Walking speed has been used to predict the efficacy of gait training; however, poststroke motor impairments are heterogeneous and different biomechanical strategies may underlie the same walking speed. Identifying which individuals will respond best to a particular gait rehabilitation program using walking speed alone may thus be limited. The objective of this study was to determine if, beyond walking speed, participants' baseline ability to generate propulsive force from their paretic limbs (paretic propulsion) influences the improvements in walking speed resulting from a paretic propulsion-targeting gait intervention. METHODS: Twenty seven participants >6 months poststroke underwent a 12-week locomotor training program designed to target deficits in paretic propulsion through the combination of fast walking with functional electrical stimulation to the paretic ankle musculature (FastFES). The relationship between participants' baseline usual walking speed (UWSbaseline), maximum walking speed (MWSbaseline), and paretic propulsion (propbaseline) versus improvements in usual walking speed (∆UWS) and maximum walking speed (∆MWS) were evaluated in moderated regression models. RESULTS: UWSbaseline and MWSbaseline were, respectively, poor predictors of ΔUWS (R 2  = 0.24) and ΔMWS (R 2  = 0.01). Paretic propulsion × walking speed interactions (UWSbaseline × propbaseline and MWSbaseline × propbaseline) were observed in each regression model (R 2 s = 0.61 and 0.49 for ∆UWS and ∆MWS, respectively), revealing that slower individuals with higher utilization of the paretic limb for forward propulsion responded best to FastFES training and were the most likely to achieve clinically important differences. CONCLUSIONS: Characterizing participants based on both their walking speed and ability to generate paretic propulsion is a markedly better approach to predicting walking recovery following targeted gait rehabilitation than using walking speed alone

Adiabatic limit and the slow motion of vortices in a Chern-Simons-Schr\"odinger system

We study a nonlinear system of partial differential equations in which a complex field (the Higgs field) evolves according to a nonlinear Schroedinger equation, coupled to an electromagnetic field whose time evolution is determined by a Chern-Simons term in the action. In two space dimensions, the Chern-Simons dynamics is a Galileo invariant evolution for A, which is an interesting alternative to the Lorentz invariant Maxwell evolution, and is finding increasing numbers of applications in two dimensional condensed matter field theory. The system we study, introduced by Manton, is a special case (for constant external magnetic field, and a point interaction) of the effective field theory of Zhang, Hansson and Kivelson arising in studies of the fractional quantum Hall effect. From the mathematical perspective the system is a natural gauge invariant generalization of the nonlinear Schroedinger equation, which is also Galileo invariant and admits a self-dual structure with a resulting large space of topological solitons (the moduli space of self-dual Ginzburg-Landau vortices). We prove a theorem describing the adiabatic approximation of this system by a Hamiltonian system on the moduli space. The approximation holds for values of the Higgs self-coupling constant close to the self-dual (Bogomolny) value of 1. The viability of the approximation scheme depends upon the fact that self-dual vortices form a symplectic submanifold of the phase space (modulo gauge invariance). The theorem provides a rigorous description of slow vortex dynamics in the near self-dual limit.Comment: Minor typos corrected, one reference added and DOI give

Both Corticospinal and Reticulospinal Tracts Control Force of Contraction

The control of contraction strength is a key part of movement control. In primates, both corticospinal and reticulospinal cells provide input to motoneurons. Corticospinal discharge is known to correlate with force, but there are no previous reports of how reticular formation (RF) activity modulates with different contractions. Here we trained two female macaque monkeys (body weight 5.9-6.9kg) to pull a handle which could be loaded with 0.5-6kg weights, and recorded from identified pyramidal tract neurons (PTNs) in primary motor cortex and RF cells during task performance. Population-averaged firing rate increased monotonically with higher force for the RF, but showed a complex profile with little net modulation for PTNs. This reflected a more heterogeneous profile of rate modulation across the PTN population, leading to cancellation in the average. Linear discriminant analysis (LDA) classified the force based on the time course of rate modulation equally well for PTNs and RF cells. Peak firing rate had significant linear correlation with force for 43/92 (46.7%) PTNs and 21/46 (43.5%) RF cells. For almost all (20/21) RF cells the correlation coefficient was positive; similar numbers of PTNs (22 vs 21) had positive vs negative coefficients. Considering the timing of force representation, similar fractions (PTNs: 61.2%; RF cells: 55.5%) commenced coding before the onset of muscle activity. We conclude that both corticospinal and reticulospinal tracts contribute to control of contraction force; the reticulospinal tract seems to specify an overall signal simply related to force, whereas corticospinal cell activity would be better suited for fine-scale adjustments.SIGNIFICANCE STATEMENTFor the first time, we compare coding of force for corticospinal and reticular formation cells in awake behaving monkeys, over a wide range of contraction strengths likely to come close to maximum voluntary contraction. Both cortical and brainstem systems coded similarly well for force, but whereas reticular formation cells carried a simple uniform signal, corticospinal neurons were more heterogenous. This may reflect a role in gross specification of a coordinated movement, versus more fine-grained adjustments around individual joints

Detection of Dense Molecular Gas in Inter-Arm Spurs in M51

Spiral arm spurs are prominent features that have been observed in extinction and 8$\mu$m emission in nearby galaxies. In order to understand their molecular gas properties, we used the Owens Valley Radio Observatory to map the CO(J=1--0) emission in three spurs emanating from the inner northwestern spiral arm of M51. We report CO detections from all three spurs. The molecular gas mass and surface density are M$_{H2} \sim3\times10^6$ M_{\sun} and $\Sigma_{H2} \sim$50 M_{\sun} pc$^{-2}$. Thus, relative to the spiral arms, the spurs are extremely weak features. However, since the spurs are extended perpendicular to the spiral arms for $\sim$500 pc and contain adequate fuel for star formation, they may be the birthplace for observed inter-arm HII regions. This reduces the requirement for the significant time delay that would be otherwise needed if the inter-arm star formation was initiated in the spiral arms. Larger maps of galaxies at similar depth are required to further understand the formation and evolution of these spurs and their role in star formation - such data should be forthcoming with the new CARMA and future ALMA telescopes and can be compared to several recent numerical simulations that have been examining the evolution of spiral arm spurs.Comment: 6 pages, 3 figures, emulate-apj format, accepted in Ap

Gauged vortices in a background

We discuss the statistical mechanics of a gas of gauged vortices in the canonical formalism. At critical self-coupling, and for low temperatures, it has been argued that the configuration space for vortex dynamics in each topological class of the abelian Higgs model approximately truncates to a finite-dimensional moduli space with a Kaehler structure. For the case where the vortices live on a 2-sphere, we explain how localisation formulas on the moduli spaces can be used to compute explicitly the partition function of the vortex gas interacting with a background potential. The coefficients of this analytic function provide geometrical data about the Kaehler structures, the simplest of which being their symplectic volume (computed previously by Manton using an alternative argument). We use the partition function to deduce simple results on the thermodynamics of the vortex system; in particular, the average height on the sphere is computed and provides an interesting effective picture of the ground state.Comment: Final version: 22 pages, LaTeX, 1 eps figur

Binary Black-Hole Mergers in Magnetized Disks: Simulations in Full General Relativity

We present results from the first fully general relativistic, magnetohydrodynamic (GRMHD) simulations of an equal-mass black hole binary (BHBH) in a magnetized, circumbinary accretion disk. We simulate both the pre and post-decoupling phases of a BHBH-disk system and both "cooling" and "no-cooling" gas flows. Prior to decoupling, the competition between the binary tidal torques and the effective viscous torques due to MHD turbulence depletes the disk interior to the binary orbit. However, it also induces a two-stream accretion flow and mildly relativistic polar outflows from the BHs. Following decoupling, but before gas fills the low-density "hollow" surrounding the remnant, the accretion rate is reduced, while there is a prompt electromagnetic (EM) luminosity enhancement following merger due to shock heating and accretion onto the spinning BH remnant. This investigation, though preliminary, previews more detailed GRMHD simulations we plan to perform in anticipation of future, simultaneous detections of gravitational and EM radiation from a merging BHBH-disk system.Comment: 5 pages, 5 figure

Conservation Laws in a First Order Dynamical System of Vortices

Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear and angular momenta as low moments of vorticity. The conservation laws are compared with those obtained in the moduli space approximation for vortex dynamics.Comment: LaTex file, 16 page