Second order splitting of a class of fourth order PDEs with point constraints

We formulate a well-posedness and approximation theory for a class of generalised saddle point problems with a specific form of constraints. In this way we develop an approach to a class of fourth order elliptic partial differential equations with point constraints using the idea of splitting into coupled second order equations. An approach is formulated using a penalty method to impose the constraints. Our main motivation is to treat certain fourth order equations involving the biharmonic operator and point Dirichlet constraints for example arising in the modelling of biomembranes on curved and flat surfaces but the approach may be applied more generally. The theory for well-posedness and approximation is presented in an abstract setting. Several examples are described together with some numerical experiments

Cardiovascular MRI in clinical trials: expanded applications through novel surrogate endpoints

Recent advances in cardiovascular magnetic resonance (CMR) now allow the accurate and reproducible measurement of many aspects of cardiac and vascular structure and function, with prognostic data emerging for several key imaging biomarkers. These biomarkers are increasingly used in the evaluation of new drugs, devices and lifestyle modifications for the prevention and treatment of cardiovascular disease. This review outlines a conceptual framework for the application of imaging biomarkers to clinical trials, highlights several important CMR techniques which are in use in randomised studies, and reviews certain aspects of trial design, conduct and interpretation in relation to the use of CMR

Long-term complications of continent catheterizable channels: a problem for transitional urologists.

A majority of the transitional urology patient population have neurogenic bladder and many of these patients have undergone creation of continent catheterizable channels (CCCs) to facilitate bladder emptying. Transitional urologists will be faced with revision of these channels due to a variety of possible complications. We performed a comprehensive literature review to the data regarding the incidence, timing, and predisposing factors that lead to complications of CCCs as well as surgical revision techniques and their outcomes. Long-term channel complications and related revisions are common (25-30%) and likely underestimated. While many predictors for revision have been posited, the only predictor that has been significant in robust multivariable analysis is channel type, with appendicovesicostomies having a lower chance of requiring revision compared to Monti channels. Channels created in adults have high likelihood of requiring revision, even within a relatively short follow-up period. We review techniques for management of channel complications and their outcomes. As patients with congenital urologic conditions requiring CCCs are gaining longer lifespans, transitional urologists will be faced with revision and/or replacement of these channels. While some of these patients may require supravesical diversion in the future, data show that revision is feasible with good outcomes. Longer-term follow-up data is needed to understand the life-span and best practices of new CCCs created among the transitional population

Many-body localization and mobility edge in a disordered Heisenberg spin ladder

We examine the interplay of interaction and disorder for a Heisenberg spin ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the quantum phase transition at a critical random field strength $h_c \sim 8.5\pm 0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuation of the bipartite magnetization show distinct probability distributions which characterize different quantum phases. Furthermore, we show that for weaker $h$, energy eigenstates with higher energy density are delocalized while states at lower energy density are localized. This defines a mobility edge and a mobility gap separating these two phases. By following the evolution of low energy eigenstates, we observe that the mobility gap grows with increasing the random field strength, which drives the system to the phase of the full many-body localization with increasing disorder strength.Comment: 6 pages, 4 figure

Crystal structure of Schmallenberg orthobunyavirus nucleoprotein-RNA complex reveals a novel RNA sequestration mechanism

Schmallenberg virus (SBV) is a newly emerged orthobunyavirus (family Bunyaviridae) that has caused severe disease in the offspring of farm animals across Europe. Like all orthobunyaviruses, SBV contains a tripartite negative-sense RNA genome that is encapsidated by the viral nucleocapsid (N) protein in the form of a ribonucleoprotein complex (RNP). We recently reported the three-dimensional structure of SBV N that revealed a novel fold. Here we report the crystal structure of the SBV N protein in complex with a 42-nt-long RNA to 2.16 Å resolution. The complex comprises a tetramer of N that encapsidates the RNA as a cross-shape inside the protein ring structure, with each protomer bound to 11 ribonucleotides. Eight bases are bound in the positively charged cleft between the N- and C-terminal domains of N, and three bases are shielded by the extended N-terminal arm. SBV N appears to sequester RNA using a different mechanism compared with the nucleoproteins of other negative-sense RNA viruses. Furthermore, the structure suggests that RNA binding results in conformational changes of some residues in the RNA-binding cleft and the N- and C-terminal arms. Our results provide new insights into the novel mechanism of RNA encapsidation by orthobunyaviruses