432 research outputs found

    Equivariant K-theory classes of matrix orbit closures

    Get PDF
    The group G = \GL_r(k) \times (k^\times)^n acts on A˚r×n\AA^{r \times n}, the space of rr-by-nn matrices: \GL_r(k) acts by row operations and (k×)n(k^\times)^n scales columns. A matrix orbit closure is the Zariski closure of a point orbit for this action. We prove that the class of such an orbit closure in GG-equivariant KK-theory of A˚r×n\AA^{r \times n} is determined by the matroid of a generic point. We present two formulas for this class. The key to the proof is to show that matrix orbit closures have rational singularities

    Green Care: a Conceptual Framework. A Report of the Working Group on the Health Benefits of Green Care

    Get PDF
    ‘Green Care’ is a range of activities that promotes physical and mental health and well-being through contact with nature. It utilises farms, gardens and other outdoor spaces as a therapeutic intervention for vulnerable adults and children. Green care includes care farming, therapeutic horticulture, animal assisted therapy and other nature-based approaches. These are now the subject of investigation by researchers from many different countries across the world

    EQUIVARIANT CHOW CLASSES OF MATRIX ORBIT CLOSURES

    Get PDF
    Let GG be the product GLr(C)×(C×)nGL_r(C) \times (C^\times)^n. We show that the GG-equivariant Chow class of a GG orbit closure in the space of rr-by-nn matrices is determined by a matroid. To do this, we split the natural surjective map from the GG equvariant Chow ring of the space of matrices to the torus equivariant Chow ring of the Grassmannian. The splitting takes the class of a Schubert variety to the corresponding factorial Schur polynomial, and also has the property that the class of a subvariety of the Grassmannian is mapped to the class of the closure of those matrices whose row span is in the variety.Comment: 11 pages. Theorem 3.5 here proves a version of the main result of arXiv:1306.1810v5, the proof of which contained an erro

    Critical groups of graphs with reflective symmetry

    Full text link

    Dyslexia and password usage:accessibility in authentication design

    Get PDF
    Governments and businesses are moving online with alacrity, driven by potential cost savings, changing consumer and citizen expectations, and the momentum towards general digital provision. Services are legally required to be inclusive and accessible. Now consider that almost every online service, where people have to identify themselves, requires a password. Passwords seem to be accessible, until one considers specific disabilities, one of which can lead to many challenges: dyslexia being a case in point. Dyslexia is associated with word processing and retention difficulties, and passwords are essentially words, phrases or alphanumeric combinations. We report on a literature review conducted to identify extant research into the impact of dyslexia on password usage, as well as any ameliorations that have been proposed. We discovered a relatively neglected field. We conclude with recommendations for future research into the needs of a large population of dyslexics who seem to struggle with passwords, in a world where avoiding passwords has become almost impossible. The main contribution of this paper is to highlight the difficulties dyslexics face with passwords, and to suggest some avenues for future research in this area

    Matrix Orbit Closures

    Get PDF
    Let GG be the group \GL_r(\CC) \times (\CC^\times)^n. We conjecture that the finely-graded Hilbert series of a GG orbit closure in the space of rr-by-nn matrices is wholly determined by the associated matroid. In support of this, we prove that the coefficients of this Hilbert series corresponding to certain hook-shaped Schur functions in the \GL_r(\CC) variables are determined by the matroid, and that the orbit closure has a set-theoretic system of ideal generators whose combinatorics are also so determined. We also discuss relations between these Hilbert series for related matrices
    corecore