Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems

We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized. Standard methods for these problems, such as central finite differences, lead to system matrices that are positive definite. The direct solvers of choice for such systems are based on Cholesky factorisation. However, as observed by MacLachlan and Madden (SIAM J. Sci. Comput. 35-5 (2013), pp. A2225-A2254), these solvers may exhibit poor performance for singularly perturbed problems. We provide an analysis of the distribution of entries in the factors based on their magnitude that explains this phenomenon, and give bounds on the ranges of the perturbation and discretization parameters where poor performance is to be expected.Comment: 9 pages, 2 figure

A curious property of oscillatory FEM solutions of one-dimensional convection-diffusion problems

summary:Song, Yin and Zhang (Int. J. Numer. Anal. Model. 4: 127-140, 2007) discovered a remarkable property of oscillatory finite element solutions of one-dimensional convection-diffusion problems that leads to a novel numerical method for the solution of such problems. In the present paper this property is described using several figures, then a simple proof of the phenomenon is given which is much more intuitive than the technical analysis of Song et al

Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information

We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) that incorporate \emph{a posteriori} solution information. There are numerous studies on the development of parameter robust numerical methods for SPDEs that depend on the layer-adapted mesh of Bakhvalov. In~\citep{HiMa2021}, a novel MPDE-based approach for constructing a generalisation of these meshes was proposed. Like with most layer-adapted mesh methods, the algorithms in that article depended on detailed derivations of \emph{a priori} bounds on the SPDE's solution and its derivatives. In this work we extend that approach so that it instead uses \emph{a posteriori} computed estimates of the solution. We present detailed algorithms for the efficient implementation of the method, and numerical results for the robust solution of two-parameter reaction-convection-diffusion problems, in one and two dimensions. We also provide full FEniCS code for a one-dimensional example.Comment: 15 pages, 5 figures, FEniCS cod

Yuwaya Ngarra-li Community Briefing Report: Key Findings from the Food and Water Security Surveys in Walgett

This Briefing Report summarises the key findings and recommendations from the Food and Water for Life Project's survey of food and water security in Walgett, NSW

Measuring reliable change in cognition using the Edinburgh Cognitive and Behavioural ALS Screen (ECAS)

doi:https://doi.org/10.1080/21678421.2017.1407794Background: Cognitive impairment affects approximately 50% of people with amyotrophic lateral sclerosis (ALS). Research has indicated that impairment may worsen with disease progression. The Edinburgh Cognitive and Behavioural ALS Screen (ECAS) was designed to measure neuropsychological functioning in ALS, with its alternate forms (ECAS-A, B, and C) allowing for serial assessment over time. Objective: The aim of the present study was to establish reliable change scores for the alternate forms of the ECAS, and to explore practice effects and test-retest reliability of the ECAS?s alternate forms. Method: Eighty healthy participants were recruited, with 57 completing two and 51 completing three assessments. Participants were administered alternate versions of the ECAS serially (A-B-C) at four-month intervals. Intra-class correlation analysis was employed to explore test-retest reliability, while analysis of variance was used to examine the presence of practice effects. Reliable change indices (RCI) and regression-based methods were utilized to establish change scores for the ECAS alternate forms. Results: Test-retest reliability was excellent for ALS Specific, ALS Non-Specific, and ECAS Total scores of the combined ECAS A, B, and C (all?>?.90). No significant practice effects were observed over the three testing sessions. RCI and regression-based methods produced similar change scores. Conclusion: The alternate forms of the ECAS possess excellent test-retest reliability in a healthy control sample, with no significant practice effects. The use of conservative RCI scores is recommended. Therefore, a change of ?8, ?4, and ?9 for ALS Specific, ALS Non-Specific, and ECAS Total score is required for reliable chang

MHC Class I Bound to an Immunodominant Theileria parva Epitope Demonstrates Unconventional Presentation to T Cell Receptors

T cell receptor (TCR) recognition of peptide-MHC class I (pMHC) complexes is a crucial event in the adaptive immune response to pathogens. Peptide epitopes often display a strong dominance hierarchy, resulting in focusing of the response on a limited number of the most dominant epitopes. Such T cell responses may be additionally restricted by particular MHC alleles in preference to others. We have studied this poorly understood phenomenon using Theileria parva, a protozoan parasite that causes an often fatal lymphoproliferative disease in cattle. Despite its antigenic complexity, CD8+ T cell responses induced by infection with the parasite show profound immunodominance, as exemplified by the Tp1214–224 epitope presented by the common and functionally important MHC class I allele N*01301. We present a high-resolution crystal structure of this pMHC complex, demonstrating that the peptide is presented in a distinctive raised conformation. Functional studies using CD8+ T cell clones show that this impacts significantly on TCR recognition. The unconventional structure is generated by a hydrophobic ridge within the MHC peptide binding groove, found in a set of cattle MHC alleles. Extremely rare in all other species, this feature is seen in a small group of mouse MHC class I molecules. The data generated in this analysis contribute to our understanding of the structural basis for T cell-dependent immune responses, providing insight into what determines a highly immunogenic p-MHC complex, and hence can be of value in prediction of antigenic epitopes and vaccine design

A framework for human microbiome research

A variety of microbial communities and their genes (the microbiome) exist throughout the human body, with fundamental roles in human health and disease. The National Institutes of Health (NIH)-funded Human Microbiome Project Consortium has established a population-scale framework to develop metagenomic protocols, resulting in a broad range of quality-controlled resources and data including standardized methods for creating, processing and interpreting distinct types of high-throughput metagenomic data available to the scientific community. Here we present resources from a population of 242 healthy adults sampled at 15 or 18 body sites up to three times, which have generated 5,177 microbial taxonomic profiles from 16S ribosomal RNA genes and over 3.5 terabases of metagenomic sequence so far. In parallel, approximately 800 reference strains isolated from the human body have been sequenced. Collectively, these data represent the largest resource describing the abundance and variety of the human microbiome, while providing a framework for current and future studies

Structure, function and diversity of the healthy human microbiome

Author Posting. © The Authors, 2012. This article is posted here by permission of Nature Publishing Group. The definitive version was published in Nature 486 (2012): 207-214, doi:10.1038/nature11234.Studies of the human microbiome have revealed that even healthy individuals differ remarkably in the microbes that occupy habitats such as the gut, skin and vagina. Much of this diversity remains unexplained, although diet, environment, host genetics and early microbial exposure have all been implicated. Accordingly, to characterize the ecology of human-associated microbial communities, the Human Microbiome Project has analysed the largest cohort and set of distinct, clinically relevant body habitats so far. We found the diversity and abundance of each habitat’s signature microbes to vary widely even among healthy subjects, with strong niche specialization both within and among individuals. The project encountered an estimated 81–99% of the genera, enzyme families and community configurations occupied by the healthy Western microbiome. Metagenomic carriage of metabolic pathways was stable among individuals despite variation in community structure, and ethnic/racial background proved to be one of the strongest associations of both pathways and microbes with clinical metadata. These results thus delineate the range of structural and functional configurations normal in the microbial communities of a healthy population, enabling future characterization of the epidemiology, ecology and translational applications of the human microbiome.This research was supported in part by National Institutes of Health grants U54HG004969 to B.W.B.; U54HG003273 to R.A.G.; U54HG004973 to R.A.G., S.K.H. and J.F.P.; U54HG003067 to E.S.Lander; U54AI084844 to K.E.N.; N01AI30071 to R.L.Strausberg; U54HG004968 to G.M.W.; U01HG004866 to O.R.W.; U54HG003079 to R.K.W.; R01HG005969 to C.H.; R01HG004872 to R.K.; R01HG004885 to M.P.; R01HG005975 to P.D.S.; R01HG004908 to Y.Y.; R01HG004900 to M.K.Cho and P. Sankar; R01HG005171 to D.E.H.; R01HG004853 to A.L.M.; R01HG004856 to R.R.; R01HG004877 to R.R.S. and R.F.; R01HG005172 to P. Spicer.; R01HG004857 to M.P.; R01HG004906 to T.M.S.; R21HG005811 to E.A.V.; M.J.B. was supported by UH2AR057506; G.A.B. was supported by UH2AI083263 and UH3AI083263 (G.A.B., C. N. Cornelissen, L. K. Eaves and J. F. Strauss); S.M.H. was supported by UH3DK083993 (V. B. Young, E. B. Chang, F. Meyer, T. M. S., M. L. Sogin, J. M. Tiedje); K.P.R. was supported by UH2DK083990 (J. V.); J.A.S. and H.H.K. were supported by UH2AR057504 and UH3AR057504 (J.A.S.); DP2OD001500 to K.M.A.; N01HG62088 to the Coriell Institute for Medical Research; U01DE016937 to F.E.D.; S.K.H. was supported by RC1DE0202098 and R01DE021574 (S.K.H. and H. Li); J.I. was supported by R21CA139193 (J.I. and D. S. Michaud); K.P.L. was supported by P30DE020751 (D. J. Smith); Army Research Office grant W911NF-11-1-0473 to C.H.; National Science Foundation grants NSF DBI-1053486 to C.H. and NSF IIS-0812111 to M.P.; The Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231 for P.S. C.; LANL Laboratory-Directed Research and Development grant 20100034DR and the US Defense Threat Reduction Agency grants B104153I and B084531I to P.S.C.; Research Foundation - Flanders (FWO) grant to K.F. and J.Raes; R.K. is an HHMI Early Career Scientist; Gordon&BettyMoore Foundation funding and institutional funding fromthe J. David Gladstone Institutes to K.S.P.; A.M.S. was supported by fellowships provided by the Rackham Graduate School and the NIH Molecular Mechanisms in Microbial Pathogenesis Training Grant T32AI007528; a Crohn’s and Colitis Foundation of Canada Grant in Aid of Research to E.A.V.; 2010 IBM Faculty Award to K.C.W.; analysis of the HMPdata was performed using National Energy Research Scientific Computing resources, the BluBioU Computational Resource at Rice University