Revisited: the inertia tensor as a proprioceptive invariant in humans

A multitude of tasks that we perform on a daily basis require precise information about the orientation of our limbs with respect to the environment and the objects located within it. Recent studies have suggested that the inertia tensor, a physical property whose values are time- and co-ordinate-indepenclent, may be an important informational invariant used by the proprioceptive system to control the movements of our limbs (Pagano et al., Ecol. Psychol. 8 (1996) 43; Pagano and Turvey, Percept. Psychophys. 52 (1992) 617; Pagano and Turvey, J. Exp. Psychol. Hum. Percept. Perform. 21 (1995) 1070). We tested this hypothesis by recording the angular errors made by subjects when pointing to virtual targets in the dark. Close examination of the pointing errors made did not show any significant effects of the inertia tensor modifications on pointing accuracy. The kinematics of the pointing movements did not indicate that any on-line adjustments were being made to compensate for the inertia tensor changes. The implications of these findings with respect to the functioning of the proprioceptive system are discussed.

Is perception of upper body orientation based on the inertia tensor? Normogravity versus microgravity conditions

During lateral leg raising, a synergistic inclination of the supporting leg and trunk in the opposite direction to the leg movement is performed in order to preserve equilibrium. As first hypothesized by Pagano and Turvey (J Exp Psychol Hum Percept Perform, 1995, 21:1070-1087), the perception of limb orientation could be based on the orientation of the limb's inertia tensor. The purpose of this study was thus to explore whether the final upper body orientation (trunk inclination relative to vertical) depends on changes in the trunk inertia tensor. We imposed a loading condition, with total mass of 4 kg added to the subject's trunk in either a symmetrical or asymmetrical configuration. This changed the orientation of the trunk inertia tensor while keeping the total trunk mass constant. In order to separate any effects of the inertia tensor from the effects of gravitational torque, the experiment was carried out in normo- and microgravity. The results indicated that in normogravity the same final upper body orientation was maintained irrespective of the loading condition. In microgravity, regardless of loading conditions the same (but different from the normogravity) orientation of the upper body was achieved through different joint organizations: two joints (the hip and ankle joints of the supporting leg) in the asymmetrical loading condition, and one (hip) in the symmetrical loading condition. In order to determine whether the different orientations of the inertia tensor were perceived during the movement, the interjoint coordination was quantified by performing a principal components analysis (PCA) on the supporting and moving hips and on the supporting ankle joints. It was expected that different loading conditions would modify the principal component of the PCA. In normogravity, asymmetrical loading decreased the coupling between joints, while in microgravity a strong coupling was preserved whatever the loading condition. It was concluded that the trunk inertia tensor did not play a role during the lateral leg raising task because in spite of the absence of gravitational torque the final upper body orientation and the interjoint coupling were not influenced.

On subspace lattices I. Closedness type properties and tensor products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.

Hamiltonian Tomography in an Access-Limited Setting without State Initialization

We propose a scheme for the determination of the coupling parameters in a chain of interacting spins. This requires only time-resolved measurements over a single particle, simple data postprocessing and no state initialization or prior knowledge of the state of the chain. The protocol fits well into the context of quantum-dynamics characterization and is efficient even when the spin chain is affected by general dissipative and dephasing channels. We illustrate the performance of the scheme by analyzing explicit examples and discuss possible extensions.

Roche tomography of cataclysmic variables - IV. Star-spots and slingshot prominences on BV Cen

We present Roche tomograms of the G5-G8 IV/V secondary star in the long-period cataclysmic variable BV Cen reconstructed from Magellan Inamori Kyocera Echelle spectrograph echelle data taken on the Magellan Clay 6.5-m telescope. The tomograms show the presence of a number of large, cool star-spots on BV Cen for the first time. In particular, we find a large high-latitude spot which is deflected from the rotational axis in the same direction as seen on the K3-K5 IV/V secondary star in the cataclysmic variable AE Aqr. BV Cen also shows a similar relative paucity of spots at latitudes between 40° and 50° when compared with AE Aqr. Furthermore, we find evidence for an increased spot coverage around longitudes facing the white dwarf which supports models invoking star-spots at the L1 point to explain the low states observed in some cataclysmic variables. In total, we estimate that some 25 per cent of the Northern hemisphere of BV Cen is spotted. We also find evidence for a faint, narrow, transient emission line with characteristics reminiscent of the peculiar low-velocity emission features observed in some outbursting dwarf novae. We interpret this feature as a slingshot prominence from the secondary star and derive a maximum source size of 75000 km and a minimum altitude of 160000 km above the orbital plane for the prominence. The entropy landscape technique was applied to determine the system parameters of BV Cen. We find M1 = 1.18 +/-0.280.16Msolar and M2 = 1.05 +/-0.230.14Msolar and an orbital inclination of i = 53° +/- 4° at an optimal systemic velocity of ? = -22.3 km s-1. Finally, we also report on the previously unknown binarity of the G5IV star HD 220492.

Roche tomography of cataclysmic variables - III. Star-spots on AE Aqr

We present a Roche tomography reconstruction of the secondary star in the cataclysmic variable AE Aqr. The tomogram reveals several surface inhomogeneities that are due to the presence of large, cool star-spots. In addition to a number of lower latitude spots, the maps also show the presence of a large, high-latitude spot similar to that seen in Doppler images of rapidly rotating isolated stars, and a relative paucity of spots at a latitude of 40 degrees. In total, we estimate that some 18 per cent of the Northern hemisphere of AE Aqr is spotted.

Roche tomography of the secondary stars in CVs

The secondary stars in cataclysmic variables (CVs) are key to our understanding of the origin, evolution and behaviour of this class of interacting binary. In seeking a fuller understanding of these objects, the challenge for observers is to obtain images of the secondary star. This goal can be achieved through Roche tomography, an indirect imaging technique that can be used to map the Roche-lobe-filling secondary. The review begins with a description of the basic principles that underpin Roche tomography, including methods for determining the system parameters. Finally, we conclude with a look at the main scientific highlights to date, including the first unambiguous detection of starspots on AE Aqr B, and consider the future prospects of this technique.

Stokes imaging, Doppler mapping and Roche tomography of the AM Herculis system V834 Cen

We report on new simultaneous phase-resolved spectroscopic and polarimetric observations of the polar (AM Herculis star) V834 Cen during a high state of accretion. Strong emission lines and high levels of variable circular and linear polarization are observed over the orbital period. The polarization data are modelled using the Stokes imaging technique of Potter et al. The spectroscopic emission lines are investigated using the Doppler tomography technique of Marsh and Horne and the Roche tomography technique of Dhillon and Watson. Up to now, all three techniques have been used separately to investigate the geometry and accretion dynamics in cataclysmic variables. For the first time, we apply all three techniques to simultaneous data for a single system. This allows us to compare and test each of the techniques against each other and hence to derive a better understanding of the geometry, dynamics and system parameters of V834 Cen.

Roche tomography of cataclysmic variables - II. Images of the secondary stars in AM Her, QQ Vul, IP Peg and HU Aqr

We present a set of Roche tomography reconstructions of the secondary stars in the cataclysmic variables AM Her, QQ Vul, IP Peg and HU Aqr. The image reconstructions show distinct asymmetries in the irradiation pattern for all four systems that can be attributed to shielding of the secondary star by the accretion stream/column in AM Her, QQ Vul and HU Aqr, and increased irradiation by the bright-spot in IP Peg. We use the entropy landscape technique to derive accurate system parameters (M-1, M-2, i and gamma) for the four binaries. In principle, this technique should provide the most reliable mass determinations available, since the intensity distribution across the secondary star is known. We also find that the intensity distribution can systematically affect the value of gamma derived from circular orbit fits to radial velocity variations.

Roche tomography of cataclysmic variables - I. Artefacts and techniques

Roche tomography is a technique used for imaging the Roche-lobe-filling secondary stars in cataclysmic variables (CVs). In order to interpret Roche tomograms correctly, one must determine whether features in the reconstruction are real, or the result of statistical or systematic errors. We explore the effects of systematic errors using reconstructions of simulated data sets, and show that systematic errors result in characteristic distortions of the final reconstructions that can be identified and corrected. In addition, we present a new method of estimating statistical errors on tomographic reconstructions using a Monte Carlo bootstrapping algorithm, and show this method to be much more reliable than Monte Carlo methods which 'jiggle' the data points in accordance with the size of their error bars.