A Resourceful Splitting Technique with Applications to Deterministic and Stochastic Multiscale Finite Element Methods

In this paper we use a splitting technique to develop new multiscale basis functions for the multiscale finite element method (MsFEM). The multiscale basis functions are iteratively generated using a Green's kernel. The Green's kernel is based on the first differential operator of the splitting. The proposed MsFEM is applied to deterministic elliptic equations and stochastic elliptic equations, and we show that the proposed MsFEM can considerably reduce the dimension of the random parameter space for stochastic problems. By combining the method with sparse grid collocation methods, the need for a prohibitive number of deterministic solves is alleviated. We rigorously analyze the convergence of the proposed method for both the deterministic and stochastic elliptic equations. Computational complexity discussions are also offered to supplement the convergence analysis. A number of numerical results are presented to confirm the theoretical findings.Comment: 32 pages, 22 figures; Multiscale Modeling and Simulation, 201

A Multiscale Enrichment Procedure for Nonlinear Monotone Operators

In this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and Y. Efendiev, SIAM Multiscale Model. Simul. 8 (2010) 1461–1483.] is extended to treat a class of nonlinear elliptic operators. The proposed method requires the solutions of (small dimension and local) nonlinear eigenvalue problems in order to systematically enrich the coarse solution space. Convergence of the method is shown to relate to the dimension of the coarse space (due to the enrichment procedure) as well as the coarse mesh size. In addition, it is shown that the coarse mesh spaces can be effectively used in two-level domain decomposition preconditioners. A number of numerical results are presented to complement the analysis

Engaging Sources: Information Literacy and theFreshman Research Paper (Part II)

The colonization of Ireland by mammals, has been the subject of extensive study using genetic methods, and forms a central problem in understanding the phylo-geography of European mammals after the Last Glacial Maximum. Ireland exhibits a de-pauperate mammal fauna relative to Great Britain and continental Europe, and a range of natural and anthropogenic processes have given rise to its modern fauna. Previous Europe-wide surveys of the European badger (Meles meles) have found conflicting microsatellite and mitochondrial DNA evidence in Irish populations, suggesting Irish badgers have arisen from admixture between human imported British and Scandinavian animals. . The extent and history of contact between British and Irish badger populations remains unclear. We use comprehensive genetic data from Great Britain and Ireland to demonstrate that badgers in Ireland’s northeastern and southeastern counties are genetically similar to contemporary British populations. Simulation analyses suggest this admixed population arose in Ireland 600-700 (CI 100-2600) years before present most likely through introduction of British badgers by people. These findings add to our knowledge of the complex colonization history of Ireland by mammals, and the central role of humans in facilitating it

Mathematics and Medicine: How mathematics, modelling and simulations can lead to better diagnosis and treatments

Starting with the discovery of X-rays by Röntgen in 1895, the progress in medical imaging has been extraordinary and immensely beneficial to diagnosis and therapy. Parallel to the increase of imaging accuracy, there is the quest of moving from qualitative to quantitative analysis and patient-tailored therapy. Mathematics, modelling and simulations are increasing their importance as tools in this quest. In this paper we give an overview of relations between mathematical modelling and imaging and focus particularly on the estimation of perfusion in the brain. In the forward model, the brain is treated as a porous medium and a two compartment model (arterial/venous) is used. Motivated by the similarity with techniques in reservoir modelling, we propose an ensemble Kalman filter to perform the parameter estimation and apply the method to a simple example as an illustrative example.acceptedVersio

Relative abundance of Mycobacterium bovis molecular types in cattle:a simulation study of potential epidemiological drivers

Background: The patterns of relative species abundance are commonly studied in ecology and epidemiology to provide insights into underlying dynamical processes. Molecular types (MVLA-types) of Mycobacterium bovis, the causal agent of bovine tuberculosis, are now routinely recorded in culture-confirmed bovine tuberculosis cases in Northern Ireland. In this study, we use ecological approaches and simulation modelling to investigate the distribution of relative abundances of MVLA-types and its potential drivers. We explore four biologically plausible hypotheses regarding the processes driving molecular type relative abundances: sampling and speciation; structuring of the pathogen population; historical changes in population size; and transmission heterogeneity (superspreading). Results: Northern Irish herd-level MVLA-type surveillance shows a right-skewed distribution of MVLA-types, with a small number of types present at very high frequencies and the majority of types very rare. We demonstrate that this skew is too extreme to be accounted for by simple neutral ecological processes. Simulation results indicate that the process of MVLA-type speciation and the manner in which the MVLA-typing loci were chosen in Northern Ireland cannot account for the observed skew. Similarly, we find that pathogen population structure, assuming for example a reservoir of infection in a separate host, would drive the relative abundance distribution in the opposite direction to that observed, generating more even abundances of molecular types. However, we find that historical increases in bovine tuberculosis prevalence and/or transmission heterogeneity (superspreading) are both capable of generating the skewed MVLA-type distribution, consistent with findings of previous work examining the distribution of molecular types in human tuberculosis. Conclusion: Although the distribution of MVLA-type abundances does not fit classical neutral predictions, our simulations show that increases in pathogen population size and/or superspreading are consistent with the pattern observed, even in the absence of selective pressures acting on the system

Genomic epidemiology of Mycobacterium bovis infection in sympatric badger and cattle populations in Northern Ireland

Bovine tuberculosis (bTB) is a costly, epidemiologically complex, multi-host, endemic disease. Lack of understanding of transmission dynamics may undermine eradication efforts. Pathogen whole-genome sequencing improves epidemiological inferences, providing a means to determine the relative importance of inter- and intra-species host transmission for disease persistence. We sequenced an exceptional data set of 619 Mycobacterium bovis isolates from badgers and cattle in a 100 km2 bTB 'hotspot' in Northern Ireland. Historical molecular subtyping data permitted the targeting of an endemic pathogen lineage, whose long-term persistence provided a unique opportunity to study disease transmission dynamics in unparalleled detail. Additionally, to assess whether badger population genetic structure was associated with the spatial distribution of pathogen genetic diversity, we microsatellite genotyped hair samples from 769 badgers trapped in this area. Birth death models and TransPhylo analyses indicated that cattle were likely driving the local epidemic, with transmission from cattle to badgers being more common than badger to cattle. Furthermore, the presence of significant badger population genetic structure in the landscape was not associated with the spatial distribution of M. bovis genetic diversity, suggesting that badger-to-badger transmission is not playing a major role in transmission dynamics. Our data were consistent with badgers playing a smaller role in transmission of M. bovis infection in this study site, compared to cattle. We hypothesize, however, that this minor role may still be important for persistence. Comparison to other areas suggests that M. bovis transmission dynamics are likely to be context dependent, with the role of wildlife being difficult to generalize.ISSN:2057-585

Genetic evidence further elucidates the history and extent of badger introductions from Great Britain into Ireland

This is the final version. Available from Royal Society via the DOI in this record. The colonization of Ireland by mammals has been the subject of extensive study using genetic methods and forms a central problem in understanding the phylogeography of European mammals after the Last Glacial Maximum. Ireland exhibits a depauperate mammal fauna relative to Great Britain and continental Europe, and a range of natural and anthropogenic processes have given rise to its modern fauna. Previous Europe-wide surveys of the European badger (Meles meles) have found conflicting microsatellite and mitochondrial DNA evidence in Irish populations, suggesting Irish badgers have arisen from admixture between human imported British and Scandinavian animals. The extent and history of contact between British and Irish badger populations remains unclear. We use comprehensive genetic data from Great Britain and Ireland to demonstrate that badgers in Ireland's northeastern and southeastern counties are genetically similar to contemporary British populations. Simulation analyses suggest this admixed population arose in Ireland 600-700 (CI 100-2600) years before present most likely through introduction of British badgers by people. These findings add to our knowledge of the complex colonization history of Ireland by mammals and the central role of humans in facilitating it.DAERA-NINER

Genomic epidemiology of Mycobacterium bovis infection in sympatric badger and cattle populations in Northern Ireland

Publication history: Accepted - 29 March 2023; Published - 25 May 2023.Bovine tuberculosis (bTB) is a costly, epidemiologically complex, multi-host, endemic disease. Lack of understanding of transmission dynamics may undermine eradication efforts. Pathogen whole-genome sequencing improves epidemiological inferences, providing a means to determine the relative importance of inter- and intra-species host transmission for disease persistence. We sequenced an exceptional data set of 619 Mycobacterium bovis isolates from badgers and cattle in a 100 km2 bTB 'hotspot' in Northern Ireland. Historical molecular subtyping data permitted the targeting of an endemic pathogen lineage, whose long-term persistence provided a unique opportunity to study disease transmission dynamics in unparalleled detail. Additionally, to assess whether badger population genetic structure was associated with the spatial distribution of pathogen genetic diversity, we microsatellite genotyped hair samples from 769 badgers trapped in this area. Birth death models and TransPhylo analyses indicated that cattle were likely driving the local epidemic, with transmission from cattle to badgers being more common than badger to cattle. Furthermore, the presence of significant badger population genetic structure in the landscape was not associated with the spatial distribution of M. bovis genetic diversity, suggesting that badger-to-badger transmission is not playing a major role in transmission dynamics. Our data were consistent with badgers playing a smaller role in transmission of M. bovis infection in this study site, compared to cattle. We hypothesize, however, that this minor role may still be important for persistence. Comparison to other areas suggests that M. bovis transmission dynamics are likely to be context dependent, with the role of wildlife being difficult to generalize.This work was funded by the Department of Agriculture, Environment and Rural Affairs for Northern Ireland (DAERA-NI) through its Evidence and Innovation programme – project no. 15/3/07. Additional funding was provided by the UK’s Biotechnology and Biological Sciences Research Council (BBSRC) – grant numbers BB/P0105598 and BB/M01262X. A. A. is supported by a Bolashak International Scholarship