Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

ACVIM consensus statement on the diagnosis of immune-mediated hemolytic anemia in dogs and cats

Immune-mediated hemolytic anemia (IMHA) is an important cause of morbidity and mortality in dogs. IMHA also occurs in cats, although less commonly. IMHA is considered secondary when it can be attributed to an underlying disease, and as primary (idiopathic) if no cause is found. Eliminating diseases that cause IMHA may attenuate or stop immune-mediated erythrocyte destruction, and adverse consequences of long-term immunosuppressive treatment can be avoided. Infections, cancer, drugs, vaccines, and inflammatory processes may be underlying causes of IMHA. Evidence for these comorbidities has not been systematically evaluated, rendering evidence-based decisions difficult. We identified and extracted data from studies published in the veterinary literature and developed a novel tool for evaluation of evidence quality, using it to assess study design, diagnostic criteria for IMHA, comorbidities, and causality. Succinct evidence summary statements were written, along with screening recommendations. Statements were refined by conducting 3 iterations of Delphi review with panel and task force members. Commentary was solicited from several professional bodies to maximize clinical applicability before the recommendations were submitted. The resulting document is intended to provide clinical guidelines for diagnosis of, and underlying disease screening for, IMHA in dogs and cats. These should be implemented with consideration of animal, owner, and geographical factors

Characterization of Within-Host Plasmodium falciparum Diversity Using Next-Generation Sequence Data

Our understanding of the composition of multi-clonal malarial infections and the epidemiological factors which shape their diversity remain poorly understood. Traditionally within-host diversity has been defined in terms of the multiplicity of infection (MOI) derived by PCR-based genotyping. Massively parallel, single molecule sequencing technologies now enable individual read counts to be derived on genome-wide datasets facilitating the development of new statistical approaches to describe within-host diversity. In this class of measures the FWS metric characterizes within-host diversity and its relationship to population level diversity. Utilizing P. falciparum field isolates from patients in West Africa we here explore the relationship between the traditional MOI and FWS approaches. FWS statistics were derived from read count data at 86,158 SNPs in 64 samples sequenced on the Illumina GA platform. MOI estimates were derived by PCR at the msp-1 and -2 loci. Significant correlations were observed between the two measures, particularly with the msp-1 locus (P = 5.92×10−5). The FWS metric should be more robust than the PCR-based approach owing to reduced sensitivity to potential locus-specific artifacts. Furthermore the FWS metric captures information on a range of parameters which influence out-crossing risk including the number of clones (MOI), their relative proportions and genetic divergence. This approach should provide novel insights into the factors which correlate with, and shape within-host diversity

Too few staff, too many patients: A qualitative study of the impact on obstetric care providers and on quality of care in Malawi

Background: Shortages of staff have a significant and negative impact on maternal outcomes in low-income countries, but the impact on obstetric care providers in these contexts is less well documented. Despite the government of Malawi's efforts to increase the number of human resources for health, maternal mortality rates remain persistently high. Health workers' perceptions of insufficient staff or time to carry out their work can predict key variables concerning motivation and attrition, while the resulting sub-standard care and poor attitudes towards women dissuade women from facility-based delivery. Understanding the situation from the health worker perspective can inform policy options that may contribute to a better working environment for staff and improved quality of care for Malawi's women. Methods: A qualitative research design, using critical incident interviews, was used to generate a deep and textured understanding of participants' experiences. Eligible participants had performed at least one of the emergency obstetric care signal functions a in the previous three months and had experienced a demotivating critical incident within the same timeframe. Data were analysed using NVivo software. Results: Eighty-four interviews were conducted. Concerns about staff shortages and workload were key factors for over 40% of staff who stated their intention to leave their current post and for nearly two-thirds of the remaining health workers who were interviewed. The main themes emerging were: too few staff, too many patients; lack of clinical officers/doctors; inadequate obstetric skills; undermining performance and professionalism; and physical and psychological consequences for staff. Underlying factors were inflexible scheduling and staff allocations that made it impossible to deliver quality care. Conclusion: This study revealed the difficult circumstances under which maternity staff are operating and the professional and emotional toll this exacts. Systems failures and inadequate human resource management are key contributors to the gaps in provision of obstetric care and need to be addressed. Thoughtful strategies that match supply to demand, coupled with targeted efforts to support health workers, are necessary to mitigate the effects of working in this context and to improve the quality of obstetric care for women in Malawi

Do differences in understory light contribute to species distributions along a tropical rainfall gradient?

In tropical forests, regional differences in annual rainfall correlate with differences in plant species composition. Although water availability is clearly one factor determining species distribution, other environmental variables that covary with rainfall may contribute to distributions. One such variable is light availability in the understory, which decreases towards wetter forests due to differences in canopy density and phenology. We established common garden experiments in three sites along a rainfall gradient across the Isthmus of Panama in order to measure the differences in understory light availability, and to evaluate their influence on the performance of 24 shade-tolerant species with contrasting distributions. Within sites, the effect of understory light availability on species performance depended strongly on water availability. When water was not limiting, either naturally in the wetter site or through water supplementation in drier sites, seedling performance improved at higher light. In contrast, when water was limiting at the drier sites, seedling performance was reduced at higher light, presumably due to an increase in water stress that affected mostly wet-distribution species. Although wetter forest understories were on average darker, wet-distribution species were not more shade-tolerant than dry-distribution species. Instead, wet-distribution species had higher absolute growth rates and, when water was not limiting, were better able to take advantage of small increases in light than dry-distribution species. Our results suggest that in wet forests the ability to grow fast during temporary increases in light may be a key trait for successful recruitment. The slower growth rates of the dry-distribution species, possibly due to trade-offs associated with greater drought tolerance, may exclude these species from wetter forests

Specific Receptor Usage in Plasmodium falciparum Cytoadherence Is Associated with Disease Outcome

Our understanding of the basis of severe disease in malaria is incomplete. It is clear that pathology is in part related to the pro-inflammatory nature of the host response but a number of other factors are also thought to be involved, including the interaction between infected erythrocytes and endothelium. This is a complex system involving several host receptors and a major parasite-derived variant antigen (PfEMP1) expressed on the surface of the infected erythrocyte membrane. Previous studies have suggested a role for ICAM-1 in the pathology of cerebral malaria, although these have been inconclusive. In this study we have examined the cytoadherence patterns of 101 patient isolates from varying clinical syndromes to CD36 and ICAM-1, and have used variant ICAM-1 proteins to further characterise this adhesive phenotype. Our results show that increased binding to CD36 is associated with uncomplicated malaria while ICAM-1 adhesion is raised in parasites from cerebral malaria cases

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

Parsimonious Higher-Order Hidden Markov Models for Improved Array-CGH Analysis with Applications to Arabidopsis thaliana

Array-based comparative genomic hybridization (Array-CGH) is an important technology in molecular biology for the detection of DNA copy number polymorphisms between closely related genomes. Hidden Markov Models (HMMs) are popular tools for the analysis of Array-CGH data, but current methods are only based on first-order HMMs having constrained abilities to model spatial dependencies between measurements of closely adjacent chromosomal regions. Here, we develop parsimonious higher-order HMMs enabling the interpolation between a mixture model ignoring spatial dependencies and a higher-order HMM exhaustively modeling spatial dependencies. We apply parsimonious higher-order HMMs to the analysis of Array-CGH data of the accessions C24 and Col-0 of the model plant Arabidopsis thaliana. We compare these models against first-order HMMs and other existing methods using a reference of known deletions and sequence deviations. We find that parsimonious higher-order HMMs clearly improve the identification of these polymorphisms. Moreover, we perform a functional analysis of identified polymorphisms revealing novel details of genomic differences between C24 and Col-0. Additional model evaluations are done on widely considered Array-CGH data of human cell lines indicating that parsimonious HMMs are also well-suited for the analysis of non-plant specific data. All these results indicate that parsimonious higher-order HMMs are useful for Array-CGH analyses. An implementation of parsimonious higher-order HMMs is available as part of the open source Java library Jstacs (www.jstacs.de/index.php/PHHMM)