We found correlation between reduced scattering coefficient and total hemoglobin concentration measured on muscles by the frequency-domain spectroscopy during venous occlusion protocol. This can be a useful parameter, which can be employed in clinical studies.

We review our most recent results on near-IR studies of human brain activity, which have been evolving in two directions: detection of neuronal signals and measurements of functional hemodynamics. We discuss results obtained so far, describing in detail the techniques we developed for detecting neuronal activity, and presenting results of a study that, as we believe, confirms the feasibility of neuronal signal detection. We review our results on near-IR measurements of cerebral hemodynamics, which are performed simultaneously with functional magnetic resonance imaging (MRI) These results confirm the cerebral origin of hemodynamic signals measured by optical techniques on the surface of the head. We also show how near-IR methods can be used to study the underlying physiology of functional MRI signals.

In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on which an exponential solvable Lie group acts transitively by isometries. The bounded isometries are proved to be of constant displacement. Their characterization gives further evidence for the author’s 1962 conjecture on homogeneous Riemannian quotient manifolds. That conjecture suggests that if Γ \ M is a Riemannian quotient of a connected simply connected homogeneous Riemannian manifold M, then Γ \ M is homogeneous if and only if each isometry γ∈ Γ is of constant displacement. The description of bounded isometries in this paper gives an alternative proof of an old result of J. Tits on bounded automorphisms of semisimple Lie groups. The topic of constant displacement isometries has an interesting history, starting with Clifford’s use of quaternions in non-Euclidean geometry, and we sketch that in a historical note.

In a recent paper we found conditions for a nilpotent Lie group N to have a filtration by normal subgroups whose successive quotients have square integrable representations, and such that these square integrable representations fit together nicely to give an explicit construction of Plancherel for almost all representations of N. The prototype for this sort of group is the group of upper triangular real matrices with 1’s down the diagonal. More generally, this class of groups contains the nilradicals of minimal parabolic subgroups of all (finite-dimensional) reductive real or complex Lie groups, in other words, all groups N in Iwasawa decompositions of reductive real or complex Lie groups. The construction of stepwise square integrable representations resulted in explicit character formulae, Plancherel formulae and multiplicity formulae. Here we extend those results to direct limits of stepwise square integrable nilpotent Lie groups. There are two keys to this extension. The first is to set up the corresponding direct system so that it respects the construction at every finite level. In the case of simple (or more generally reductive) groups this means that the restricted root Dynkin diagrams increase in a particular manner. The second is to follow Schwartz space theory through the direct limit process, develop a Schwartz space theory for certain direct limit nilpotent groups, and use it to study stepwise square integrability for coefficients of direct limits of stepwise square integrable nilpotent Lie groups. This leads to the main result, an explicit Fourier inversion formula for that class of infinite-dimensional Lie groups. One important consequence is the Fourier inversion formula for nilradicals of classical minimal parabolic subgroups of finitary real reductive Lie groups such as GL(∞; ℝ), Sp(∞; ℂ) and SO(∞, ∞).

Based on prior research, multiple discriminable dimensions of interoception have been defined: awareness, accuracy and sensibility. Some investigators defined interoceptive awareness as metacognitive awareness of interoceptive accuracy, assessed as correspondence between subjective confidence in and objective accuracy of one's heartbeat detection. However, metacognitive awareness has been understood quite differently: 'a cognitive set in which negative thoughts/feelings are experienced as mental events, rather than as the self' or as 'error awareness'. Interoceptive sensibility, defined as self-reported interoception, distinguishes self-reported interoception from objective interoceptive accuracy, but does not differentiate between anxiety-driven and mindful attention styles towards interoceptive cues, a distinction of key clinical importance: one attention style is associated with somatization and anxiety disorders; the other has been viewed as healthy, adaptive, resilience-enhancing. The self-report Multidimensional Assessment of Interoceptive Awareness was developed to differentiate these attention styles. It has been translated into 16 languages and applied in cross-sectional and longitudinal studies. Findings from these applications suggest that differentiating interoceptive sensibility according to attention style and regulatory aspects (i) provides insights into the psychology of interoceptive awareness, (ii) differentiates between clinically maladaptive and beneficial interoceptive attention, and (iii) helps elucidate therapeutic approaches that claim to provide health benefits by training mindful styles of bodily awareness.This article is part of the themed issue 'Interoception beyond homeostasis: affect, cognition and mental health'.