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- Kim, Peter, et al.
(författare)
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Fréchet analysis and the microbiome
- 2014
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Ingår i: Journal of Statistical Planning and Inference. - : Elsevier. - 0378-3758 .- 1873-1171. ; 145, s. 37-41
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Pereira, Rajesh, et al.
(författare)
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Wielandt's theorem, spectral sets, and Banach algebras
- 2013
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 439:4, s. 852-855
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Rush, Stephen, 1989-, et al.
(författare)
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A microbiology primer for pyrosequencing
- 2012
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Ingår i: Quantitative Bio-Science. - Daegu, Korea : Natural Science Institute, College of Natural Sciences, Keimyung University. - 2288-1344. ; 31:2, s. 53-81
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Rush, Stephen, 1989-, et al.
(författare)
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Capturing context-specific regulation in molecular interaction networks
- 2018
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Ingår i: BMC Bioinformatics. - : BioMed Central. - 1471-2105. ; 19:1
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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- Rush, Stephen, 1989-, et al.
(författare)
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The phylogenetic LASSO and the microbiome
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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- Sommerfeld, Max, et al.
(författare)
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Bump hunting by topological data analysis
- 2017
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Ingår i: Stat. - : John Wiley & Sons. - 2049-1573. ; 6:1, s. 462-471
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Tidskriftsartikel (refereegranskat)abstract
- 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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