Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in \cite{ge09_1} where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high and low conductivity inclusions

Randomized oversampling for generalized multiscale finite element methods

In this paper, we develop efficient multiscale methods for ows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approxi- mates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the random- ized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed

Gaps in knowledge and future directions for the use of faecal microbiota transplant in the treatment of inflammatory bowel disease

Faecal microbiota transplant (FMT) has now been established into clinical guidelines for the treatment of recurrent and refractory Clostridioides difficile infection (CDI). Its therapeutic application in inflammatory bowel disease (IBD) is currently at an early stage. To date there have been four randomised controlled trials for FMT in IBD and a multitude of observational studies. However significant gaps in our knowledge regarding optimum methods for FMT preparation, technical and logistics of its administration, as well as mechanistic underpinnings, still remain. This article aims to highlight these gaps by reviewing evidence and makes key recommendations on the direction of future studies in this field. In addition, we provide an overview of the current evidence of potential mechanistics of FMT in IBD

Reanalysis and Simulation Suggest a Phylogenetic Microarray Does Not Accurately Profile Microbial Communities

The second generation (G2) PhyloChip is designed to detect over 8700 bacteria and archaeal and has been used over 50 publications and conference presentations. Many of those publications reveal that the PhyloChip measures of species richness greatly exceed statistical estimates of richness based on other methods. An examination of probes downloaded from Greengenes suggested that the system may have the potential to distort the observed community structure. This may be due to the sharing of probes by taxa; more than 21% of the taxa in that downloaded data have no unique probes. In-silico simulations using these data showed that a population of 64 taxa representing a typical anaerobic subterranean community returned 96 different taxa, including 15 families incorrectly called present and 19 families incorrectly called absent. A study of nasal and oropharyngeal microbial communities by Lemon et al (2010) found some 1325 taxa using the G2 PhyloChip, however, about 950 of these taxa have, in the downloaded data, no unique probes and cannot be definitively called present. Finally, data from Brodie et al (2007), when re-examined, indicate that the abundance of the majority of detected taxa, are highly correlated with one another, suggesting that many probe sets do not act independently. Based on our analyses of downloaded data, we conclude that outputs from the G2 PhyloChip should be treated with some caution, and that the presence of taxa represented solely by non-unique probes be independently verified

Artificial Gravity Reveals that Economy of Action Determines the Stability of Sensorimotor Coordination

Background: When we move along in time with a piece of music, we synchronise the downward phase of our gesture with the beat. While it is easy to demonstrate this tendency, there is considerable debate as to its neural origins. It may have a structural basis, whereby the gravitational field acts as an orientation reference that biases the formulation of motor commands. Alternatively, it may be functional, and related to the economy with which motion assisted by gravity can be generated by the motor system

Reanalysis and simulation suggest the phylogenetic microarray does not accurately profile microbial communities

The second generation (G2) PhyloChip is designed to detect over 8700 bacteria and archaeal and has been used over 50 publications and conference presentations. Many of those publications reveal that the PhyloChip measures of species richness greatly exceed statistical estimates of richness based on other methods. An examination of probes downloaded from Greengenes suggested that the system may have the potential to distort the observed community structure. This may be due to the sharing of probes by taxa; more than 21% of the taxa in that downloaded data have no unique probes. In-silico simulations using these data showed that a population of 64 taxa representing a typical anaerobic subterranean community returned 96 different taxa, including 15 families incorrectly called present and 19 families incorrectly called absent. A study of nasal and oropharyngeal microbial communities by Lemon et al (2010) found some 1325 taxa using the G2 PhyloChip, however, about 950 of these taxa have, in the downloaded data, no unique probes and cannot be definitively called present. Finally, data from Brodie et al (2007), when re-examined, indicate that the abundance of the majority of detected taxa, are highly correlated with one another, suggesting that many probe sets do not act independently. Based on our analyses of downloaded data, we conclude that outputs from the G2 PhyloChip should be treated with some caution, and that the presence of taxa represented solely by non-unique probes be independently verified