Classification of extensions of principal bundles and transitive Lie groupoids with prescribed kernel and cokernel

The equivalence of principal bundles with transitive Lie groupoids due to Ehresmann is a well known result. A remarkable generalisation of this equivalence, due to Mackenzie, is the equivalence of principal bundle extensions with those transitive Lie groupoids over the total space of a principal bundle, which also admit an action of the structure group by automorphisms. This paper proves the existence of suitably equivariant transition functions for such groupoids, generalising consequently the classification of principal bundles by means of their transition functions, to extensions of principal bundles by an equivariant form of \v{C}ech cohomology.Comment: 23 page

Failure Processes in Embedded Monolayer Graphene under Axial Compression

Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of –0.60% corresponding to a yield stress up to -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1–2 nm. These results were compared with DFT computations performed on analogue coronene/PMMA oligomers and a reasonable agreement was obtained

A torque-based method demonstrates increased rigidity in Parkinson’s disease during low-frequency stimulation

Low-frequency oscillations in the basal ganglia are prominent in patients with Parkinson’s disease off medication. Correlative and more recent interventional studies potentially implicate these rhythms in the pathophysiology of Parkinson’s disease. However, effect sizes have generally been small and limited to bradykinesia. In this study, we investigate whether these effects extend to rigidity and are maintained in the on-medication state. We studied 24 sides in 12 patients on levodopa during bilateral stimulation of the STN at 5, 10, 20, 50, 130 Hz and in the off-stimulation state. Passive rigidity at the wrist was assessed clinically and with a torque-based mechanical device. Low-frequency stimulation at ≤20 Hz increased rigidity by 24 % overall (p = 0.035), whereas high-frequency stimulation (130 Hz) reduced rigidity by 18 % (p = 0.033). The effects of low-frequency stimulation (5, 10 and 20 Hz) were well correlated with each other for both flexion and extension (r = 0.725 ± SEM 0.016 and 0.568 ± 0.009, respectively). Clinical assessments were unable to show an effect of low-frequency stimulation but did show a significant effect at 130 Hz (p = 0.002). This study provides evidence consistent with a mechanistic link between oscillatory activity at low frequency and Parkinsonian rigidity and, in addition, validates a new method for rigidity quantification at the wrist

The effect of salient stimuli on neural oscillations, isometric force, and their coupling.

Survival in a suddenly-changing environment requires animals not only to detect salient stimuli, but also to promptly respond to them by initiating or revising ongoing motor processes. We recently discovered that the large vertex brain potentials elicited by sudden supramodal stimuli are strongly coupled with a multiphasic modulation of isometric force, a phenomenon that we named cortico-muscular resonance (CMR). Here, we extend our investigation of the CMR to the time-frequency domain. We show that (i) both somatosensory and auditory stimuli evoke a number of phase-locked and non-phase-locked modulations of EEG spectral power. Remarkably, (ii) some of these phase-locked and non-phase-locked modulations are also present in the Force spectral power. Finally, (iii) EEG and Force time-frequency responses are correlated in two distinct regions of the power spectrum. An early, low-frequency region (∼4 Hz) reflects the previously-described coupling between the phase-locked EEG vertex potential and force modulations. A late, higher-frequency region (beta-band, ∼20 Hz) reflects a second coupling between the non-phase-locked increase of power observed in both EEG and Force. In both time-frequency regions, coupling was maximal over the sensorimotor cortex contralateral to the hand exerting the force, suggesting an effect of the stimuli on the tonic corticospinal drive. Thus, stimulus-induced CMR occurs across at least two different types of cortical activities, whose functional significance in relation to the motor system should be investigated further. We propose that these different types of corticomuscular coupling are important to alter motor behaviour in response to salient environmental events