We provide a pipeline for data preprocessing, biomarker selection, and classification of liquid chromatography–mass spectrometry (LCMS) serum samples to generate a prospective diagnostic test for Lyme disease. We utilize tools of machine learning (ML), e.g., sparse support vector machines (SSVM), iterative feature removal (IFR), and k-fold feature ranking to select several biomarkers and build a discriminant model for Lyme disease. We report a 98.13% test balanced success rate (BSR) of our model based on a sequestered test set of LCMS serum samples. The methodology employed is general and can be readily adapted to other LCMS, or metabolomics, data sets.
This paper introduces a pathway expression framework as an approach for constructing derived biomarkers. The pathway expression framework incorporates the biological connections of genes leading to a biologically relevant model. Using this framework, we distinguish between shedding subjects post-infection and all subjects pre-infection in human blood transcriptomic samples challenged with various respiratory viruses: H1N1, H3N2, HRV (Human Rhinoviruses), and RSV (Respiratory Syncytial Virus). Additionally, pathway expression data is used for selecting discriminatory pathways from these experiments. The classification results and selected pathways are benchmarked against standard gene expression based classification and pathway ranking methodologies. We find that using the pathway expression data along with selected pathways, which have minimal overlap with high ranking pathways found by traditional methods, improves classification rates across experiments.
For each fundamental and widely used ordinary second-order linear homogeneous differential equation of mathematical physics, we derive a family of associated differential equations that share the same “degenerate” canonical form. These equations can be solved easily if the original equation is known to possess analytic solutions, otherwise their properties and the properties of their solutions are de facto known as they are comparable to those already deduced for the fundamental equation. We analyze several particular cases of new families related to some of the famous differential equations applied to physical problems, and the degenerate eigenstates of the radial Schrödinger equation for the hydrogen atom in N dimensions.
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