Formulation and performance of variational integrators for rotating bodies

Variational integrators are obtained for two mechanical systems whose configuration spaces are, respectively, the rotation group and the unit sphere. In the first case, an integration algorithm is presented for Euler’s equations of the free rigid body, following the ideas of Marsden et al. (Nonlinearity 12:1647–1662, 1999). In the second example, a variational time integrator is formulated for the rigid dumbbell. Both methods are formulated directly on their nonlinear configuration spaces, without using Lagrange multipliers. They are one-step, second order methods which show exact conservation of a discrete angular momentum which is identified in each case. Numerical examples illustrate their properties and compare them with existing integrators of the literature

Longitudinal associations between paternal mental health and child behavior and cognition in middle childhood

IntroductionPaternal mental health has been associated with adverse consequences on offspring psychosocial development, and family environmental factors may partly explain those associations. To clarify this, we need comprehensive prospective studies, particularly in middle-childhood when the child enters school and is expected to make use of behavioral and cognitive skills as part of their interactions and learning.MethodUsing data from a sub-sample of the prospective 3D birth cohort study comprised of mother-father-child triads, and a follow-up of the parents and the children at 6–8 years of age (n = 61; 36 boys, 25 girls), we examined whether paternal anxious and depressive symptoms measured during the pregnancy period (i.e., prenatally) or concurrently when the child was assessed at 6–8 years old were associated with children's cognition/behavior.ResultsIn contrast to our hypotheses, we found that greater prenatal paternal depressive symptoms predicted fewer child behavioral difficulties; and that greater concurrent childhood paternal depression or anxiety symptoms were associated with higher child full-scale IQ, controlling for the equivalent maternal mental health assessment and parental education. Father parenting perception did not mediate these associations, nor were they moderated by maternal mental health at the concurrent assessment, or paternal ratings of marital relationship quality.DiscussionThese findings suggest that higher symptoms of paternal mental health symptoms are associated with fewer child behavioral difficulties and higher cognitive performance in middle childhood. Potential clinical implications and future research directions are discussed

Modeling Robustness Tradeoffs in Yeast Cell Polarization Induced by Spatial Gradients

Cells localize (polarize) internal components to specific locations in response to external signals such as spatial gradients. For example, yeast cells form a mating projection toward the source of mating pheromone. There are specific challenges associated with cell polarization including amplification of shallow external gradients of ligand to produce steep internal gradients of protein components (e.g. localized distribution), response over a broad range of ligand concentrations, and tracking of moving signal sources. In this work, we investigated the tradeoffs among these performance objectives using a generic model that captures the basic spatial dynamics of polarization in yeast cells, which are small. We varied the positive feedback, cooperativity, and diffusion coefficients in the model to explore the nature of this tradeoff. Increasing the positive feedback gain resulted in better amplification, but also produced multiple steady-states and hysteresis that prevented the tracking of directional changes of the gradient. Feedforward/feedback coincidence detection in the positive feedback loop and multi-stage amplification both improved tracking with only a modest loss of amplification. Surprisingly, we found that introducing lateral surface diffusion increased the robustness of polarization and collapsed the multiple steady-states to a single steady-state at the cost of a reduction in polarization. Finally, in a more mechanistic model of yeast cell polarization, a surface diffusion coefficient between 0.01 and 0.001 µm2/s produced the best polarization performance, and this range is close to the measured value. The model also showed good gradient-sensitivity and dynamic range. This research is significant because it provides an in-depth analysis of the performance tradeoffs that confront biological systems that sense and respond to chemical spatial gradients, proposes strategies for balancing this tradeoff, highlights the critical role of lateral diffusion of proteins in the membrane on the robustness of polarization, and furnishes a framework for future spatial models of yeast cell polarization

Planck 2015 results. XVIII. Background geometry and topology of the Universe

Maps of cosmic microwave background (CMB) temperature and polarization from the 2015 release of Planck data provide the highestquality full-sky view of the surface of last scattering available to date. This enables us to detect possible departures from a globally isotropic cosmology. We present the first searches using CMB polarization for correlations induced by a possible non-trivial topology with a fundamental domain that intersects, or nearly intersects, the last-scattering surface (at comoving distance χrec), both via a direct scan for matched circular patterns at the intersections and by an optimal likelihood calculation for specific topologies. We specialize to flat spaces with cubic toroidal (T3) and slab (T1) topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology with a scale below the diameter of the last-scattering surface. The limits on the radius ℛi of the largest sphere inscribed in the fundamental domain (at log-likelihood ratio Δlnℒ > −5 relative to a simply-connected flat Planck best-fit model) are: ℛi > 0.97 χrec for the T3 cubic torus; and ℛi > 0.56 χrec for the T1 slab. The limit for the T3 cubic torus from the matched-circles search is numerically equivalent, ℛi > 0.97 χrec at 99% confidence level from polarization data alone. We also perform a Bayesian search for an anisotropic global Bianchi VIIh geometry. In the non-physical setting, where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component with a Bayes factor of at least 2.3 units of log-evidence. However, the cosmological parameters that generate this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to the Planck data requires an amplitude of −0.10 ± 0.04 compared to the value of + 1 if the model were to be correct. In the physically motivated setting, where the Bianchi parameters are coupled and fitted simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VIIh cosmology and constrain the vorticity of such models to (ω/H)0 < 7.6 × 10-10 (95% CL)

Developmental variation in testosterone: Cortisol ratio alters cortical- and amygdala-based cognitive processes

Testosterone (T) and cortisol (C) are the end products of neuroendocrine axes that interact with the process of shaping brain structure and function. Relative levels of T:C (TC ratio) may alter prefrontal-amygdala functional connectivity in adulthood. What remains unclear is whether TC-related effects are rooted to childhood and adolescence. We used a healthy cohort of 4-22-year-olds to test for associations between TC ratios, brain structure (amygdala volume, cortical thickness (CTh), and their coordinated growth), as well as cognitive and behavioral development. We found greater TC ratios to be associated with the growth of specific brain structures: 1) parietal CTh; 2) covariance of the amygdala with CTh in visual and somatosensory areas. These brain parameters were in turn associated with lower verbal/executive function and higher spatial working memory. In sum, individual TC profiles may confer a particular brain phenotype and set of cognitive strengths and vulnerabilities, prior to adulthood

Phenylalanine-544 plays a key role in substrate and inhibitor binding by providing a hydrophobic packing point at the active site of insulin-regulated aminopeptidase

Inhibitors of insulin-regulated aminopeptidase (IRAP) improve memory and are being developed as a novel treatment for memory loss. In this study, the binding of a class of these inhibitors to human IRAP was investigated using molecular docking and site-directed mutagenesis. Four benzopyran-based IRAP inhibitors with different affinities were docked into a homology model of the catalytic site of IRAP. Two 4-pyridinyl derivatives orient with the benzopyran oxygen interacting with the Zn2+ ion and a direct parallel ring-stack interaction between the benzopyran rings and Phe544. In contrast, the two 4-quinolinyl derivatives orient in a different manner, interacting with the Zn2+ ion via the quinoline nitrogen, and Phe544 contributes an edge-face hydrophobic stacking point with the benzopyran moiety. Mutagenic replacement of Phe544 with alanine, isoleucine, or valine resulted in either complete loss of catalytic activity or altered hydrolysis velocity that was substrate-dependent. Phe544 is also important for inhibitor binding, because these mutations altered the Ki in some cases, and docking of the inhibitors into the corresponding Phe544 mutant models revealed how the interaction might be disturbed. These findings demonstrate a key role of Phe544 in the binding of the benzopyran IRAP inhibitors and for optimal positioning of enzyme substrates during catalysis. <br /