Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling.

We introduce two new lowest order methods, a mixed method, and a hybrid discontinuous Galerkin method, for the approximation of incompressible flows. Both methods use divergence-conforming linear Brezzi-Douglas-Marini space for approximating the velocity and the lowest order Raviart-Thomas space for approximating the vorticity. Our methods are based on the physically correct viscous stress tensor of the fluid, involving the symmetric gradient of velocity (rather than the gradient), provide exactly divergence-free discrete velocity solutions, and optimal error estimates that are also pressure robust. We explain how the methods are constructed using the minimal number of coupling degrees of freedom per facet. The stability analysis of both methods are based on a Korn-like inequality for vector finite elements with continuous normal component. Numerical examples illustrate the theoretical findings and offer comparisons of condition numbers between the two new methods.

The influence of androstadienone during psychosocial stress is modulated by gender, trait anxiety and subjective stress: An fMRI study.

Androstadienone (ANDR), a bodily secreted steroid compound, is a socially relevant chemosignal that modulates subjective and (neuro)physiological responses, predominantly in females. The impact of ANDR on stress responses in males and females has not been explored. Therefore, this fMRI study aimed to examine psychosocial stress reactions induced by mental arithmetic and social evaluation on behavioral and hormonal levels (46 participants: 15 naturally cycling females in their early follicular phase (EF), 15 females on hormonal contraceptives (HC) and 16 males); and on a neural level (40 participants: 13 EF-females, 13 HC-females and 14 males) in an ANDR and placebo treatment repeated-measures design. While no gender differences emerged in subjective ratings and performance during stress, neural activation patterns differed significantly. Besides, ANDR attenuated the post-stress increase of negative mood in all participants. Region of interest analyses showed that irrespective of treatment, males showed stronger activation of the dorsolateral prefrontal cortex (DLPFC) than females. At the whole brain level, gender differences emerged indicating stronger fronto-parietal activation in males compared to HC-females on both treatments. Males showed stronger visual and fusiform activation than EF-females under ANDR. Both female groups did not show stronger activation than males. Further, error ratio in the ANDR-stress condition was positively associated with their post-stress cortisol level and increase in subjective stress in males; and male DLPFC activity in the ANDR-stress condition was negatively associated with trait anxiety. Surprisingly, compared to HC-females, EF-female only showed stronger activation of arousal-related areas under placebo treatment. Taken together, these findings suggest that the male stress reaction under social evaluative threat was stronger than female stress reactions as a function of ANDR. More specifically, this effect on behavioral and neural stress reactions seems to depend on trait anxiety in males only. The study highlights the significance of a chemosignal in enhancing social threat that may facilitate adaptive stress responses.

Transdiagnostic commonalities and differences in resting state functional connectivity of the default mode network in schizophrenia and major depression.

Schizophrenia and depression are prevalent psychiatric disorders, but their underlying neural bases remains poorly understood. Neuroimaging evidence has pointed towards the relevance of functional connectivity aberrations in default mode network (DMN) hubs, dorso-medial prefrontal cortex and precuneus, in both disorders, but commonalities and differences in resting state functional connectivity of those two regions across disorders has not been formally assessed. Here, we took a transdiagnostic approach to investigate resting state functional connectivity of those two regions in 75 patients with schizophrenia and 82 controls from 4 scanning sites and 102 patients with depression and 106 controls from 3 sites. Our results demonstrate common dysconnectivity patterns as indexed by a significant reduction of functional connectivity between precuneus and bilateral superior parietal lobe in schizophrenia and depression. Furthermore, our findings highlight diagnosis-specific connectivity reductions of the parietal operculum in schizophrenia relative to depression. In light of evidence that points towards the importance of the DMN for social cognitive abilities and well documented impairments of social interaction in both patient groups, it is conceivable that the observed transdiagnostic connectivity alterations may contribute to interpersonal difficulties, but this could not be assessed directly in our study as measures of social behavior were not available. Given the operculum's role in somatosensory integration, diagnosis-specific connectivity reductions may indicate a pathophysiological mechanism for basic self-disturbances that is characteristic of schizophrenia, but not depression.