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1. Skew Orthogonal Convolutions

   Singla, S; Feizi, S. (January 2021, International Conference on Machine Learning (ICML))
2. texas-skew-update-2021

   https://doi.org/10.18738/T8/SVLCOQ  

   Cleveland, Theodore G.; null (January 2021, Texas Data Repository)

   A permanent copy of a data repository resulting from project 0-6977 Update Texas Skew Coefficients, including interim reports and the final report (as pdf and source) When the data are final this sentence will be deleted 

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3. Skew and sphere fibrations

   https://doi.org/10.1090/tran/8953  

   Harrison, Michael (July 2023, Transactions of the American Mathematical Society)

   A great sphere fibration is a sphere bundle with total space S n S^n and fibers which are great k k -spheres. Given a smooth great sphere fibration, the central projection to any tangent hyperplane yields a nondegenerate fibration of R n \mathbb {R}^n by pairwise skew, affine copies of R k \mathbb {R}^k (though not all nondegenerate fibrations can arise in this way). Here we study the topology and geometry of nondegenerate fibrations, we show that every nondegenerate fibration satisfies a notion of Continuity at Infinity, and we prove several classification results. These results allow us to determine, in certain dimensions, precisely which nondegenerate fibrations correspond to great sphere fibrations via the central projection. We use this correspondence to reprove a number of recent results about sphere fibrations in the simpler, more explicit setting of nondegenerate fibrations. For example, we show that every germ of a nondegenerate fibration extends to a global fibration, and we study the relationship between nondegenerate line fibrations and contact structures in odd-dimensional Euclidean space. We conclude with a number of partial results, in hopes that the continued study of nondegenerate fibrations, together with their correspondence with sphere fibrations, will yield new insights towards the unsolved classification problems for sphere fibrations. 

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4. Iterating skew evolutes and skew involutes: a linear analog of the bicycle kinematics

   Tabachnikov, Serge (December 2023, Moscow mathematical journal)
5. SkewIT: The Skew Index Test for large-scale GC Skew analysis of bacterial genomes

   https://doi.org/10.1371/journal.pcbi.1008439  

   Lu, Jennifer; Salzberg, Steven L. (December 2020, PLOS Computational Biology)

   Rzhetsky, Andrey (Ed.)

   GC skew is a phenomenon observed in many bacterial genomes, wherein the two replication strands of the same chromosome contain different proportions of guanine and cytosine nucleotides. Here we demonstrate that this phenomenon, which was first discovered in the mid-1990s, can be used today as an analysis tool for the 15,000+ complete bacterial genomes in NCBI’s Refseq library. In order to analyze all 15,000+ genomes, we introduce a new method, SkewIT (Skew Index Test), that calculates a single metric representing the degree of GC skew for a genome. Using this metric, we demonstrate how GC skew patterns are conserved within certain bacterial phyla, e.g. Firmicutes, but show different patterns in other phylogenetic groups such as Actinobacteria. We also discovered that outlier values of SkewIT highlight potential bacterial mis-assemblies. Using our newly defined metric, we identify multiple mis-assembled chromosomal sequences in previously published complete bacterial genomes. We provide a SkewIT web app https://jenniferlu717.shinyapps.io/SkewIT/ that calculates SkewI for any user-provided bacterial sequence. The web app also provides an interactive interface for the data generated in this paper, allowing users to further investigate the SkewI values and thresholds of the Refseq-97 complete bacterial genomes. Individual scripts for analysis of bacterial genomes are provided in the following repository: https://github.com/jenniferlu717/SkewIT . 

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