Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

Mainstreaming zero carbon : lessons for built-environment education and training

Education and training are identified as a key means of reducing carbon emissions from buildings to help address the climate emergency. Institutional, industry and organisational responses are shown to be failing in this regard. This editorial introduces the themes and individual papers in the special issue and then explores the current state of the art through pedagogy, theory, training, policy, practice and standards. These areas are interrogated through three fundamental questions. How can education and training be rapidly changed to ensure the creation of zero-carbon built environments? How can this transition be implemented successfully? What positive examples and models can be drawn upon or adapted? In proposing an agenda for change, a new approach to education is set out which combines learning outcomes with new standards and personal values within a continual questioning and holding to account of all stakeholders involved through evidenced outcomes. This draws on evidence from the special issue and Capability Theory which allies competency with personhood to create capability through agency. The process to make this change requires: (1) government intervention, to ensure that the lowest common denominator is zero-carbon best practice within a negotiated, holistic approach to developing the built environment sustainably; (2) new ethical, interdisciplinary and collective educational working practices underpinned by new pedagogical theory and accreditation processes; and (3) rapid auditing and upskilling in climate literacy to bring pressure to bear on governments and institutions to carry out reforms

Spectral index of the H2O-maser emitting planetary nebula IRAS 17347-3139

We present radio continuum observations of the planetary nebula (PN) IRAS 17347-3139 (one of the only two known to harbour water maser emission), made to derive its spectral index and the turnover frequency of the emission. The spectrum of the source rises in the whole frequency range sampled, from 2.4 to 24.9 GHz, although the spectral index seems to decrease at the highest frequencies (0.79+-0.04 between 4.3 and 8.9 GHz, and 0.64+-0.06 between 16.1 and 24.9 GHz). This suggests a turnover frequency around 20 GHz (which is unusual among PNe, whose radio emission usually becomes optically thin at frequencies < 10 GHz), and a relatively high emission measure (1.5 x 10^9 cm^{-6} pc). The radio continuum emission has increased by a factor of ~1.26 at 8.4 GHz in 13 years, which can be explained as expansion of the ionized region by a factor of ~1.12 in radius with a dynamical age of ~120 yr and at an expansion velocity of ~5-40 km/s. These radio continuum characteristics, together with the presence of water maser emission and a strong optical extinction suggest that IRAS 17347-3139 is one of the youngest PNe known, with a relatively massive progenitor star.Comment: Five pages, 2 figures, accepted by MNRA

Identity and Function of a Cardiac Mitochondrial Small Conductance Ca2+-Activated K+ Channel Splice Variant

We provide evidence for location and function of a small conductance, Ca2+-activated K+ (SKCa) channel isoform 3 (SK3) in mitochondria (m) of guinea pig, rat and human ventricular myocytes. SKCa agonists protected isolated hearts and mitochondria against ischemia/reperfusion (IR) injury; SKCa antagonists worsened IR injury. Intravenous infusion of a SKCa channel agonist/antagonist, respectively, in intact rats was effective in reducing/enhancing regional infarct size induced by coronary artery occlusion. Localization of SK3 in mitochondria was evidenced by Western blot of inner mitochondrial membrane, immunocytochemical staining of cardiomyocytes, and immunogold labeling of isolated mitochondria. We identified a SK3 splice variant in guinea pig (SK3.1, aka SK3a) and human ventricular cells (SK3.2) by amplifying mRNA, and show mitochondrial expression in mouse atrial tumor cells (HL-1) by transfection with full length and truncated SK3.1 protein. We found that the N-terminus is not required for mitochondrial trafficking but the C-terminus beyond the Ca2+ calmodulin binding domain is required for Ca2+ sensing to induce mK+ influx and/or promote mitochondrial localization. In isolated guinea pig mitochondria and in SK3 overexpressed HL-1 cells, mK+ influx was driven by adding CaCl2. Moreover, there was a greater fall in membrane potential (ΔΨm), and enhanced cell death with simulated cell injury after silencing SK3.1 with siRNA. Although SKCa channel opening protects the heart and mitochondria against IR injury, the mechanism for favorable bioenergetics effects resulting from SKCa channel opening remains unclear. SKCa channels could play an essential role in restraining cardiac mitochondria from inducing oxidative stress-induced injury resulting from mCa2+ overload

Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin-film with Patterned Nanostructures

We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.Comment: To appear in Phys. Rev. Let

Efficacy of tofacitinib monotherapy in methotrexate-naive patients with early or established rheumatoid arthritis.

IntroductionTofacitinib is an oral Janus kinase inhibitor for the treatment of rheumatoid arthritis (RA). Tofacitinib monotherapy was previously shown to inhibit structural damage, reduce clinical signs and symptoms of RA, and improve physical functioning over 24 months in methotrexate (MTX)-naive adult patients with RA. In this post hoc analysis, we compared efficacy and safety of tofacitinib in patients with early (disease duration &lt;1 year) versus established (≥1 year) RA.MethodsMTX-naive patients ≥18 years with active RA received tofacitinib monotherapy (5 or 10 mg two times a day, or MTX monotherapy, in a 24-month Phase 3 trial.ResultsOf 956 patients (tofacitinib 5 mg two times a day, n=373; tofacitinib 10 mg two times a day, n=397; MTX, n=186), 54% had early RA. Baseline disease activity and functional disability were similar in both groups; radiographic damage was greater in patients with established RA. At month 24, clinical response rates were significantly greater in patients with early versus established RA in the tofacitinib 5 mg two times a day group. Both tofacitinib doses had greater effects on clinical, functional and radiographic improvements at 1 and 2 years compared with MTX, independent of disease duration. No new safety signals were observed.ConclusionsTreatment response was generally similar in early and established RA; significantly greater improvements were observed at month 24 with tofacitinib 5 mg two times a day in early versus established RA. Tofacitinib 5 and 10 mg two times a day demonstrated greater efficacy versus MTX irrespective of disease duration. No difference in safety profiles was observed between patients with early or established RA.Trial registration numberNCT01039688; Results

Postnatal maturation of the spinal-bulbo-spinal loop: brainstem control of spinal nociception is independent of sensory input in neonatal rats

The rostroventral medial medulla (RVM) is part of a rapidly acting spino-bulbo-spinal loop that is activated by ascending nociceptive inputs and drives descending feedback modulation of spinal nociception. In the adult rat, the RVM can facilitate or inhibit dorsal horn neuron inputs but in young animals descending facilitation dominates. It is not known whether this early life facilitation is part of a feedback loop. We hypothesized that the newborn RVM functions independently of sensory input, before the maturation of feedback control. We show here that noxious hind paw pinch evokes no fos activation in the RVM or the periaqueductal gray at postnatal day (P) 4 or P8, indicating a lack of nociceptive input at these ages. Significant fos activation was evident at P12, P21, and in adults. Furthermore, direct excitation of RVM neurons with microinjection of DL-homocysteic acid did not alter the net activity of dorsal horn neurons at P10, suggesting an absence of glutamatergic drive, whereas the same injections caused significant facilitation at P21. In contrast, silencing RVM neurons at P8 with microinjection of lidocaine inhibited dorsal horn neuron activity, indicating a tonic descending spinal facilitation from the RVM at this age. The results support the hypothesis that early life descending facilitation of spinal nociception is independent of sensory input. Since it is not altered by RVM glutamatergic receptor activation, it is likely generated by spontaneous brainstem activity. Only later in postnatal life can this descending activity be modulated by ascending nociceptive inputs in a functional spinal-bulbo-spinal loop

Assessing results after distal radius fracture treatment: a comparison of objective and subjective tools

Objectives: Functional outcomes following distal radius fractures are directly influenced by the choice of outcome assessment instruments used. Our objective was to compare scoring systems in measuring patient functional outcomes and to determine which scoring system compared most favorably with the widely used Disabilities of the Arm, Shoulder, and Hand (DASH) questionnaire. Methods: In all, 108 patients between May 2004 and November 2006 were treated operatively following distal radius fractures. Follow-up was at 3 months, 6 months, 1 year, and 2 years postsurgery, during which anatomical and functional assessments were performed. Patient outcomes were recorded using DASH, Green and O’Brien system, Gartland and Werley system, and Sarmiento radiological scoring system. Results: There was a stronger correlation between the Green and O’Brien scoring system and DASH (r = −.54) than Gartland and Werley and DASH (r = .44). The Green and O’Brien scoring system was more demanding so patients rated “excellent” or “good” had better functional outcome than those bearing the same grade in the Gartland and Werley system. Nonetheless, the Green and O’Brien score and Gartland and Werley score showed good correlation with each other (r = .66). The Sarmiento radiological score had no significant correlation with any of the other scoring systems. Significant predictors of the DASH score were function (r = .42), power grip (r = .41), pain (r = .37), and range of motion (r = .28). Conclusion: The Green and O’Brien scoring system correlated most strongly with the DASH score. Radiological scoring (reflecting anatomical deformity) was not significantly correlated with functional outcome. While subjective parameters “pain” and “function” are influenced by psychosocial factors and thus highly variable, it is paramount to include subjective tools in outcome assessment in future studies on wrist fractures.postprin