Fuzzy Results for Finitely Supported Structures

We present a survey of some results published recently by the authors regarding the fuzzy aspects of finitely supported structures. Considering the notion of finite support, we introduce a new degree of membership association between a crisp set and a finitely supported function modelling a degree of membership for each element in the crisp set. We define and study the notions of invariant set, invariant complete lattices, invariant monoids and invariant strong inductive sets. The finitely supported (fuzzy) subgroups of an invariant group, as well as the L-fuzzy sets on an invariant set (with L being an invariant complete lattice) form invariant complete lattices. We present some fixed point results (particularly some extensions of the classical Tarski theorem, Bourbaki–Witt theorem or Tarski–Kantorovitch theorem) for finitely supported self-functions defined on invariant complete lattices and on invariant strong inductive sets; these results also provide new finiteness properties of infinite fuzzy sets. We show that apparently, large sets do not contain uniformly supported, infinite subsets, and so they are invariant strong inductive sets satisfying finiteness and fixed-point properties.

Neural encoding of phrases and sentences in spoken language comprehension

Speech stands out in the natural world as a biological signal that communicates formally-specifiable complex meanings. However, the acoustic and physical dynamics of speech do not injectively mark the linguistic structure and meaning that we perceive. Linguistic structure must therefore be inferred through the human brain’s endogenous mechanisms, which remain poorly understood. Using electroencephalography, we investigated the neural response to synthesized spoken phrases and sentences that were closely physically-matched but differed in syntactic structure, under either linguistic or non-linguistic task conditions. Differences in syntactic structure were well-captured in theta band (~ 2 to 7 Hz) phase coherence, phase connectivity degree at low frequencies (< ~ 2 Hz), and in both intensity and degree of power connectivity of induced neural response in the alpha band (~ 7.5 to 13.5 Hz). Theta-gamma phase-amplitude coupling was found when participants listened to speech, but it did not discriminate between syntactic structures. Spectral-temporal response function modelling suggested different encoding states in both temporal and spectral dimensions as a function of the amount and type of linguistic structure perceived, over and above the acoustically-driven neural response. Our findings provide a comprehensive description of how the brain separates linguistic structures in the dynamics of neural responses, and imply that phase synchronization and strength of connectivity can be used as readouts for constituent structure, providing a novel basis for future neurophysiological research on linguistic structure in the brain.

Neurovascular coupling and oxygenation are decreased in hippocampus compared to neocortex because of microvascular differences

The hippocampus is essential for spatial and episodic memory but is damaged early in Alzheimer’s disease and is very sensitive to hypoxia. Understanding how it regulates its oxygen supply is therefore key for designing interventions to preserve its function. However, studies of neurovascular function in the hippocampus in vivo have been limited by its relative inaccessibility. Here we compared hippocampal and visual cortical neurovascular function in awake mice, using two photon imaging of individual neurons and vessels and measures of regional blood flow and haemoglobin oxygenation. We show that blood flow, blood oxygenation and neurovascular coupling were decreased in the hippocampus compared to neocortex, because of differences in both the vascular network and pericyte and endothelial cell function. Modelling oxygen diffusion indicates that these features of the hippocampal vasculature may restrict oxygen availability and could explain its sensitivity to damage during neurological conditions, including Alzheimer’s disease, where the brain’s energy supply is decreased.

Harmonisation of PET/CT contrast recovery performance for brain studies

Purpose In order to achieve comparability of image quality, harmonisation of PET system performance is imperative. In this study, prototype harmonisation criteria for PET brain studies were developed. Methods Twelve clinical PET/CT systems (4 GE, 4 Philips, 4 Siemens, including SiPM-based “digital” systems) were used to acquire 30-min PET scans of a Hoffman 3D Brain phantom filled with ~ 33 kBq·mL−1 [18F]FDG. Scan data were reconstructed using various reconstruction settings. The images were rigidly coregistered to a template (voxel size 1.17 × 1.17 × 2.00 mm3) onto which several volumes of interest (VOIs) were defined. Recovery coefficients (RC) and grey matter to white matter ratios (GMWMr) were derived for eroded (denoted in the text by subscript e) and non-eroded grey (GM) and white (WM) matter VOIs as well as a mid-phantom cold spot (VOIcold) and VOIs from the Hammers atlas. In addition, left-right hemisphere differences and voxel-by-voxel differences compared to a reference image were assessed. Results Systematic differences were observed for reconstructions with and without point-spread-function modelling (PSFON and PSFOFF, respectively). Normalising to image-derived activity, upper and lower limits ensuring image comparability were as follows: for PSFON, RCGMe = [0.97–1.01] and GMWMre = [3.51–3.91] for eroded VOI and RCGM = [0.78–0.83] and GMWMr = [1.77–2.06] for non-eroded VOI, and for PSFOFF, RCGMe = [0.92–0.99] and GMWMre = [3.14–3.68] for eroded VOI and RCGM = [0.75–0.81] and GMWMr = [1.72–1.95] for non-eroded VOI. Conclusions To achieve inter-scanner comparability, we propose selecting reconstruction settings based on RCGMe and GMWMre as specified in “Results”. These proposed standards should be tested prospectively to validate and/or refine the harmonisation criteria.