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.

'A Job in Politics is not for Woman': Analysing Barriers to Women's Political Representation in CEE

This article discusses women’s political representation in Central and Eastern Europe in the fifteen years after the fall of the Berlin Wall and the adoption of liberal democratic political systems in the region. It highlights the deepseated gender stereotypes that define women primarily as wives and mothers, with electoral politics seen as an appropriate activity for men, but less so for women. The article explores the ways in which conservative attitudes on gender roles hinders the supply of, and demand for, women in the politics of Central and Eastern Europe. It also discusses the manner in which the internalisation of traditional gender norms affects women’s parliamentary behaviour, as few champion women’s rights in the legislatures of the region. The article also finds that links between women MPs and women’s organisations are weak and fragmented, making coalition-building around agendas for women’s rights problematic.

Quantum teleportation via mixed two-mode squeezed states in the coherent-state representation

Quantum teleportation for continuous variables is generally described in phase space by using the Wigner functions. We study quantum teleportation via a mixed two-mode squeezed state in Hilbert-Schmidt space by using the coherent-state representation and operators. This shows directly how the teleported state is related to the original state.

Time operators and shift representation of dynamical systems

We introduce and characterise time operators for unilateral shifts and exact endomorphisms. The associated shift representation of evolution is related to the spectral representation by a generalized Fourier transform. We illustrate the results for a simple exact system, namely the Renyi map.