Improved delineation of short cortical association fibers and gray/white matter boundary using whole-brain three-dimensional diffusion tensor imaging at submillimeter spatial resolution.

Recent emergence of human connectome imaging has led to a high demand on angular and spatial resolutions for diffusion magnetic resonance imaging (MRI). While there have been significant growths in high angular resolution diffusion imaging, the improvement in spatial resolution is still limited due to a number of technical challenges, such as the low signal-to-noise ratio and high motion artifacts. As a result, the benefit of a high spatial resolution in the whole-brain connectome imaging has not been fully evaluated in vivo. In this brief report, the impact of spatial resolution was assessed in a newly acquired whole-brain three-dimensional diffusion tensor imaging data set with an isotropic spatial resolution of 0.85 mm. It was found that the delineation of short cortical association fibers is drastically improved as well as the definition of fiber pathway endings into the gray/white matter boundary-both of which will help construct a more accurate structural map of the human brain connectome.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

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.

Normalisers, nest algebras and tensor products

We show that if $\cl A$ is the tensor product of finitely many continuous nest algebras, $\cl B$ is a CDCSL algebra and $\cl A$ and $\cl B$ have the same normaliser semi-group then either $\cl A = \cl B$ or $\cl A^* = \cl B$.

Tensor products of operator systems

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C*-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C*-algebra yet has the property that for every C*-algebra A, the minimal and maximal tensor product of S and A are equal.

Measurement of the full stress tensor in a crystal using photoluminescence from point defects: The example of nitrogen vacancy centers in diamond

We introduce a method for measuring the full stress tensor in a crystal utilising the properties of individual point defects. By measuring the perturbation to the electronic states of three point defects with C 3 v symmetry in a cubic crystal, sufficient information is obtained to construct all six independent components of the symmetric stress tensor. We demonstrate the method using photoluminescence from nitrogen-vacancy colour centers in diamond. The method breaks the inverse relationship between spatial resolution and sensitivity that is inherent to existing bulk strain measurement techniques, and thus, offers a route to nanoscale strain mapping in diamond and other materials in which individual point defects can be interrogated.

Operator Synthesis and Tensor Products

We show that Kraus' property $ S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $ \kappa \times \lambda $, where $ \kappa $ is a set of finite width while $ \lambda $ is operator synthetic, is, under a necessary restriction on the sets $ \lambda $, again operator synthetic. We show that property $ S_{\sigma }$ is preserved under spatial Morita subordinance.

Tensor products of subspace lattices and rank one density

We show that, if M is a subspace lattice with the property that the rank one subspace of its operator algebra is weak* dense, L is a commutative subspace lattice and P is the lattice of all projections on a separable Hilbert space, then L⊗M⊗P is reflexive. If M is moreover an atomic Boolean subspace lattice while L is any subspace lattice, we provide a concrete lattice theoretic description of L⊗M in terms of projection valued functions defined on the set of atoms of M . As a consequence, we show that the Lattice Tensor Product Formula holds for AlgM and any other reflexive operator algebra and give several further corollaries of these results.