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Creators/Authors contains: "Cummings, Joseph"

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  1. ; ; ; (, Numerical Algorithms)
    Abstract A standard question in real algebraic geometry is to compute the number of connected components of a real algebraic variety in affine space. This manuscript provides algorithms for computing the number of connected components, the Euler characteristic, and deciding the connectivity between two points for a smooth manifold arising as the complement of a real hypersurface of a real algebraic variety. When considering the complement of the set of singular points of a real algebraic variety, this yields an approach for determining smooth connectivity in a real algebraic variety. The method is based upon gradient ascent/descent paths on the real algebraic variety inspired by a method proposed by Hong, Rohal, Safey El Din, and Schost for complements of real hypersurfaces. Several examples are included to demonstrate the approach. 
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  2. ; (, Geometriae Dedicata)
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  3. ; ; (, Advances in Applied Mathematics)
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  4. ; ; ; ; ; ; ; ; ; ; et al (, microPublication biology)
    In Drosophila melanogaster genetic screens are often used to identify genes associated with different biological processes. Here, we have utilized the Flp/FRT system to generate mitotic clones within the developing eye. These clones were screened for mutations that disrupt cell division, organ patterning, and cell growth. One such mutation from this screen, mutant M.3.2, resulted in an expansion of the cuticle within the area normally covered by ommatidium as well as an overall smaller eye size. Genetic and molecular mapping revealed this mutation to be in the gene, tout-velu (ttv). 
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    Free, publicly-accessible full text available January 1, 2026