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  • 1.
    Gorreja, Frida
    et al.
    Örebro University, School of Medical Sciences.
    Rangel, Ignacio
    Örebro University, School of Medical Sciences.
    Rush, Stephen
    Örebro University, School of Medical Sciences.
    Wall, Rebecca
    Örebro University, School of Medical Sciences.
    De Vos, Willem M.
    Wageningen University & Research Centre, Wageningen, Netherlands; Department of Bacteriology and Immunology, University of Helsinki, Helsinki, Finland.
    Brummer, Robert Jan
    Örebro University, School of Medical Sciences.
    Double-blind cross-over trial reveals human mucosal transcriptome responses to variants of LGG administration in vivo2018In: Targeting microbiota: 6th World congress on targeting microbiota towards clinical revolution / [ed] Peter Konturek, Porto, Portugal: ISM , 2018, Vol. 5, article id 978-2-35609-010-2Conference paper (Other academic)
  • 2.
    Gorreja, Frida
    et al.
    Örebro University, School of Medical Sciences.
    Rush, Stephen
    Örebro University, School of Medical Sciences.
    Kasper, Dennis
    Department of Microbiology and Molecular Genetics, Boston, USA; Harvard Medical School, Boston, USA.
    Brummer, Robert Jan
    Örebro University, School of Medical Sciences.
    Meng, Di
    Harvard Medical School, Boston, USA; Mucosal Immunology Laboratory, Massachusetts General Hospital for Children, Boston, USA.
    Walker, W. Allan
    Harvard Medical School, Boston, USA; Mucosal Immunology Laboratory, Massachusetts General Hospital for Children, Boston, USA.
    Beneficial bacteria that affect Toll-like receptors in the gut immune system: the case of PSA on Bacteroides fragilis and transcription profile of developmentally-regulated genes2018Conference paper (Other academic)
  • 3.
    Gorreja, Frida
    et al.
    Örebro University, School of Medical Sciences.
    Rush, Stephen
    Örebro University, School of Medical Sciences.
    Marques, Tatiana M.
    Örebro University, School of Medical Sciences.
    Repsilber, Dirk
    Örebro University, School of Medical Sciences.
    Baker, Adam
    Örebro University, School of Medical Sciences. Head of Discovery, Microbiome and Human Health, Christian Hansen, Danimark.
    Wall, Rebecca
    Örebro University, School of Medical Sciences.
    Brummer, Robert Jan
    Örebro University, School of Medical Sciences.
    The impacts of probiotics and prebiotics on the gut mucosa and immune system through targeting inflammation and intestinal barrier function2018Conference paper (Other academic)
  • 4.
    Kim, Peter
    et al.
    Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada; Department of Pathology and Molecular Medicine, McMaster University, Hamilton, Ontario, Canada .
    Pinder, Shaun
    Department of Pathology and Molecular Medicine, McMaster University, Hamilton, Ontario, Canada .
    Rush, Stephen
    Department of Pathology and Molecular Medicine, McMaster University, Hamilton, Ontario, Canada .
    Fréchet analysis and the microbiome2014In: Journal of Statistical Planning and Inference, ISSN 0378-3758, E-ISSN 1873-1171, Vol. 145, p. 37-41Article in journal (Refereed)
    Abstract [en]

    The paper under discussion provides a detailed survey of the important developments in Fréchet analysis on manifolds or on stratified sample spaces. As it appears that data is now being realized over non-Euclidean spaces, such a paper is timely as such methods are called for in modern data analysis. In this discussion we explore this in the context of computational biology in general, and in particular for microbiome data which is gaining in popularity both in the scholarly and the popular presses. We will discuss the microbiome and metagenomics as well as outline how data is collected and strategies for data analysis. Finally we tie in how the microbiome data can be analyzed within the context of Fréchet analysis.

  • 5.
    Pereira, Rajesh
    et al.
    Department of Mathematics and Statistics, University of Guelph, Guelph ON, Canada.
    Rush, Stephen
    Department of Mathematics and Statistics, University of Guelph, Guelph ON, Canada.
    Wielandt's theorem, spectral sets, and Banach algebras2013In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 439, no 4, p. 852-855Article in journal (Refereed)
    Abstract [en]

    Let A be a complex unital Banach algebra and let a,b∈A. We give regions of the complex plane which contain the spectrum of a+b or ab using von Neumann spectral set theory. These results are a direct generalization of a theorem of Wielandt on the eigenvalues of the sum of two normal matrices.

  • 6.
    Petrov, Pavel
    et al.
    MNP, Vancouver BC, Canada.
    Rush, Stephen
    Örebro University, School of Medical Sciences.
    Zhai, Zhichun
    Department of Mathematical and Statistical Sciences, University of Alberta, Canada.
    Lee, Christine H.
    Department of Microbiology, Royal Jubilee Hosptial, Victoria BC, Canada.
    Kim, Peter T.
    Department of Mathematics & Statistics, University of Guelph, Guelph Ontario, Canada.
    Heo, Giseon
    School of Dentistry, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada.
    Topological data analysis of Clostridioides difficile infection and fecal microbiota transplantationManuscript (preprint) (Other academic)
  • 7.
    Rush, Stephen
    et al.
    Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada.
    Lee, Christine
    Department of Pathology and Molecular Medicine, McMaster University, St Joseph's Healthcare, Hamilton, Ontario, Canada.
    Mio, Washington
    Department of Mathematics, Florida State University, Tallahassee, .
    Kim, Peter
    Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada; Department of Pathology and Molecular Medicine, McMaster University, St Joseph's Healthcare, Hamilton, Ontario, Canada.
    The phylogenetic LASSO and the microbiomeManuscript (preprint) (Other academic)
    Abstract [en]

    Scientific investigations that incorporate next generation sequencing involve analyses of high-dimensional data where the need to organize, collate and interpret the outcomes are pressingly important. Currently, data can be collected at the microbiome level leading to the possibility of personalized medicine whereby treatments can be tailored at this scale. In this paper, we lay down a statistical framework for this type of analysis with a view toward synthesis of products tailored to individual patients. Although the paper applies the technique to data for a particular infectious disease, the methodology is suciently rich to be expanded to other problems in medicine, especially those in which coincident `-omics' covariates and clinical responses are simultaneously captured.

  • 8.
    Rush, Stephen
    et al.
    Department of Mathematics and Statistics, University of Guelph, Guelph ON, Canada.
    Pinder, Shaun
    Department of Mathematics and Statistics, University of Guelph, Guelph ON, Canada.
    Costa, Marcio
    Department of Pathobiology, University of Guelph, Guelph ON, Canada.
    Kim, Peter
    Department of Mathematics and Statistics, University of Guelph, Guelph ON, Canada.
    A microbiology primer for pyrosequencing2012In: Quantitative Bio-Science, ISSN 2288-1344, Vol. 31, no 2, p. 53-81Article in journal (Refereed)
    Abstract [en]

    Metagenomic analysis is a very rich area for understanding the microbiology of organisms. Once the data has been assembled mathematical and statistical methods can be applied providing insights into biological properties that created the data in the first place. The foundations however, require some knowledge of microbiology which is not usually part of a mathematician’s nor a statistician’s training, and therefore, the data creation can itself be quite mysterious. In this paper we attempt to explain the microbiology to mathematicians and statisticians in a way that would hopefully provide insights into the data generating process. In particular our approach is specific to the open-source bioinformatics toolbox mothur. We will assume the reader has very little microbiology training but has some mathematical skills. It is the endeavor of this write-up to help bridge a needed gap.

  • 9.
    Rush, Stephen
    et al.
    Örebro University, School of Medical Sciences.
    Repsilber, Dirk
    Örebro University, School of Medical Sciences.
    Capturing context-specific regulation in molecular interaction networks2018In: BMC Bioinformatics, ISSN 1471-2105, E-ISSN 1471-2105, Vol. 19, no 1, article id 539Article in journal (Refereed)
    Abstract [en]

    Background: Molecular profiles change in response to perturbations. These changes are coordinated into functional modules via regulatory interactions. The genes and their products within a functional module are expected to be differentially expressed in a manner coherent with their regulatory network. This perspective presents a promising approach to increase precision in detecting differential signals as well as for describing differential regulatory signals within the framework of a priori knowledge about the underlying network, and so from a mechanistic point of view.

    Results: We present Coherent Network Expression (CoNE), an effective procedure for identifying differentially activated functional modules in molecular interaction networks. Differential gene expression is chosen as example, and differential signals coherent with the regulatory nature of the network are identified. We apply our procedure to systematically simulated data, comparing its performance to alternative methods. We then take the example case of a transcription regulatory network in the context of particle-induced pulmonary inflammation, recapitulating and proposing additional candidates to previously obtained results. CoNE is conveniently implemented in an R-package along with simulation utilities.

    Conclusion: Combining coherent interactions with error control on differential gene expression results in uniformly greater specificity in inference than error control alone, ensuring that captured functional modules constitute real findings.

  • 10.
    Sommerfeld, Max
    et al.
    Felix Bernstein Institute for Mathematical Statistics in the Biosciences, University of Göttingen, Göttingen, Germany.
    Heo, Giseon
    School of Dentistry, University of Alberta, Edmonton, Canada.
    Kim, Peter
    Department of Mathematics and Statistics, University of Guelph, Guelph, Canada.
    Rush, Stephen
    Örebro University, School of Medical Sciences.
    Marron, J. Steve
    Department of Mathematics and Statistics, University of Guelph, Guelph, Canada.
    Bump hunting by topological data analysis2017In: Stat, E-ISSN 2049-1573, Vol. 6, no 1, p. 462-471Article in journal (Refereed)
    Abstract [en]

    A topological data analysis approach is taken to the challenging problem of finding and validating the statistical significance of local modes in a data set. As with the SIgnificance of the ZERo (SiZer) approach to this problem, statistical inference is performed in a multi-scale way, that is, across bandwidths. The key contribution is a twoparameter approach to the persistent homology representation. For each kernel bandwidth, a sub-level set filtration of the resulting kernel density estimate is computed. Inference based on the resulting persistence diagram indicates statistical significance of modes. It is seen through a simulated example, and by analysis of the famous Hidalgo stamps data, that the new method has more statistical power for finding bumps than SiZer.

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