On the Influence of Amplitude on the Connectivity between Phases

In recent studies, functional connectivities have been reported to display characteristics of complex networks that have been suggested to concur with those of the underlying structural, i.e., anatomical, networks. Do functional networks always agree with structural ones? In all generality, this question can be answered with “no”: for instance, a fully synchronized state would imply isotropic homogeneous functional connections irrespective of the “real” underlying structure. A proper inference of structure from function and vice versa requires more than a sole focus on phase synchronization. We show that functional connectivity critically depends on amplitude variations, which implies that, in general, phase patterns should be analyzed in conjunction with the corresponding amplitude. We discuss this issue by comparing the phase synchronization patterns of interconnected Wilson–Cowan models vis-à-vis Kuramoto networks of phase oscillators. For the interconnected Wilson–Cowan models we derive analytically how connectivity between phases explicitly depends on the generating oscillators’ amplitudes. In consequence, the link between neurophysiological studies and computational models always requires the incorporation of the amplitude dynamics. Supplementing synchronization characteristics by amplitude patterns, as captured by, e.g., spectral power in M/EEG recordings, will certainly aid our understanding of the relation between structural and functional organizations in neural networks at large

Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory

Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others

The effects of visual feedback during a rhythmic weight-shifting task in patients with Parkinson's disease

Augmented visual feedback (VF) may offer benefits similar to those of rhythmic external cues in alleviating some mobility-related difficulties in individuals with Parkinson’s disease (PD). However, due to an impaired ability to reweigh sensory information under changing circumstances, subjects with PD may be rather vulnerable to incongruity of visual information. In the present study, we investigatedwhether VF is indeed effective in improving motor functioning in a weight-shifting task during upright stance, and whether subjects with PD are affected more by incongruent VF than healthy controls. Participants performed sideways swaying motions based on tracking of real-time and delayed VF – the first providing congruent, and hence more accurate, visual information than the latter. We analyzed center-of-pressure signals patterns for 28 individuals with PD and 16 healthy, age- and gender-matched controls by estimating task accuracy, movement pattern variability, and normalized movement amplitude. For conditions without feedback and with real-time feedback, subjects with PD performed lateral swaying motions with greater error (F(1, 42) = 12.065, p = .001) and with more variablemovement patterns than healthy controls (F(1, 24) = 113.086, p < .001). Error change scores revealed that patients with PD were nevertheless still able to use VF to improve tracking performance (t(24) = 2.366, p = .026). However, whereas controls were able to adapt to a certain amount of visual incongruity, patients with PD were not. Instead, movement amplitude was significantly reduced in this group (F(1.448, 60.820) = 17.639, p < .001). By reducing movement amplitude, subjects with PD appear to resort to a ‘conservative’ strategy to minimize performance breakdown

Tightening Up the Control of Treadmill Walking: Effects of Maneuverability Range and Acoustic Pacing on Stride-to-Stride Fluctuations

The correlational structure of stride-to-stride fluctuations differs between healthy and pathological gait. Uncorrelated and anti-persistent stride-to-stride fluctuations are believed to indicate pathology whereas persistence represents healthy functioning. However, this reading can be questioned because the correlational structure changes with task constraints, like acoustic pacing, signifying the tightness of control over particular gait parameters. We tested this “tightness-of-control interpretation” by varying the maneuverability range during treadmill walking (small, intermediate, and large walking areas), with and without acoustic pacing. Stride-speed fluctuations exhibited anti-persistence, suggesting that stride speeds were tightly controlled, with a stronger degree of anti-persistence for smaller walking areas. Constant-speed goal-equivalent-manifold decompositions revealed simultaneous control of stride times and stride lengths, especially for smaller walking areas to limit stride-speed fluctuations. With acoustic pacing, participants followed both constant-speed and constant-stride-time task goals. This was reflected by a strong degree of anti-persistence around the stride-time by stride-length point that uniquely satisfied both goals. Our results strongly support the notion that anti-persistence in stride-to-stride fluctuations reflect the tightness of control over the associated gait parameter, while not tightly regulated gait parameters exhibit statistical persistence. We extend the existing body of knowledge by showing quantitative changes in anti-persistence of already tightly regulated stride-speed fluctuations

Local Hidden Variables Underpinning of Entanglement and Teleportation

Entangled states whose Wigner functions are non-negative may be viewed as being accounted for by local hidden variables (LHV). Recently, there were studies of Bell's inequality violation (BIQV) for such states in conjunction with the well known theorem of Bell that precludes BIQV for theories that have LHV underpinning. We extend these studies to teleportation which is also based on entanglement. We investigate if, to what extent, and under what conditions may teleportation be accounted for via LHV theory. Our study allows us to expose the role of various quantum requirements. These are, e.g., the uncertainty relation among non-commuting operators, and the no-cloning theorem which forces the complete elimination of the teleported state at its initial port.Comment: 24 pages, 1 figure, accepted Found. Phy

Persistent fluctuations in stride intervals under fractal auditory stimulation

Copyright @ 2014 Marmelat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.Commission of the European Community and the Netherlands Organisation for Scientific Research

Optimising Psychoeducation for Transient Ischaemic Attack and Minor Stroke Management (OPTIMISM): Protocol for a feasibility randomised controlled trial

Background: A transient ischaemic attack (TIA) and minor stroke are medical emergencies and often a warning sign of future strokes if remain untreated. Few studies have investigated the long-term psychosocial effects of TIA and minor stroke. Secondary prevention and medical management are often the primary focus with limited access offered for further psychosocial support. Psychoeducational interventions can provide education and advice to people with physical health conditions and, with suitable tailoring, could be appropriate for people after TIA and minor stroke. This study aims to develop a group psychoeducational intervention for people after TIA and minor stroke and to test whether it is acceptable and feasible. Methods: This mixed-methodology study involves two phases: Phase 1) A qualitative study to determine the content of a suitable intervention; Phase 2) A single-centre feasibility randomised controlled trial to evaluate the acceptability of this intervention. The overall study has ethical approval. Stroke survivors have been involved in designing and monitoring the trial. The aim is to recruit 30-40 participants from a Stroke/TIA Service, within 6 months following their diagnosis. Participants will be randomly allocated to either the usual care control group or the intervention group (psychoeducational programme). The programme will consist of six group sessions based on providing education, psychological and social support. The primary outcomes will relate to the feasibility aims of the study. Outcomes will be collected at 3 and 6 months to assess mood, quality of life, knowledge and satisfaction, and resource use. Discussion: There is a need to develop and evaluate effective interventions that enhance the education provided to people after TIA and minor stroke and to promote their psychosocial wellbeing. Findings will indicate the acceptability of the intervention and parameters needed to conduct a definitive trial

Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequency-specific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequency-specific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated in-silico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical resting-state MEG data obtained from healthy subjects and reconstructed two-layered networks consisting of either alpha-to-beta or theta-to-gamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by one-to-one interactions for both alpha-to-beta band and theta-to-gamma band networks. For theta-gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the one-to-one connections. Our work is an stepping stone towards the identification of interdependencies across frequency-specific networks. Our results lay the ground for the use of the promising multilayer framework in this field with more-informed and justified interlayer connections