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  • Which graphs are rigid in lpd? 

    Dewar, Sean; Kitson, Derek; Nixon, Anthony (Springer, 2021-03-13)
    We present three results which support the conjecture that a graph is minimally rigid in d-dimensional ℓp-space, where p∈(1,∞) and p≠2, if and only if it is (d, d)-tight. Firstly, we introduce a graph bracing operation ...
  • Constructing isostatic frameworks for the l1 and l infinity plane (Pre-published) 

    Clinch, Katie; Kitson, Derek (Electronic Journal of Combinatorics, 2020-06-12)
    We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G = (V,E) has a partition into two spanning trees T1 and T2 then there is a map p : V → R2, p(v) = (p(v)1,p(v)2), such that ...
  • Graph rigidity for unitarily invariant matrix norms (Pre-published) 

    Kitson, Derek; Levene, Rupert H (Elsevier, 2020-11-15)
    A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant matrix norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks ...
  • Symbol functions for symmetric frameworks (Pre-published) 

    Kitson, Derek; Kastis, Eleftherios; McCarthy, John E (Elsevier, 2021-05-15)
    We prove a variant of the well-known result that intertwiners for the bilateral shift on ℓ2(Z) are unitarily equivalent to multiplication operators on L2(T). This enables us to unify and extend fundamental aspects of ...
  • Symmetric frameworks in normed spaces 

    Kitson, Derek; Nixon, Anthony; Schulze, Bernd (Elsevier, 2020-12-15)
    We develop a combinatorial rigidity theory for symmetric bar-joint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwell-type sparsity counts are identified for a ...
  • Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope 

    O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)
    The slope of the best-fit line y h x x 0 1  ( )    from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four which has exactly two real roots, one positive and ...
  • An investigation of the performance of five different estimators in the measurement error regression model 

    O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)
    In a comprehensive paper by Riggs et al.(1978) the authors analyse the performances of numerous estimators for the regression slope in the measurement error model with positive measurement error variances >0 0 for X and ...
  • On moduli stacks of G-bundles over a curve (Pre-published version) 

    Hoffmann, Norbert (Springer, 2010)
    Let C be a smooth projective curve over an algebraically closed eld k of arbitrary characteristic. Given a linear algebraic group G over k, let MG be the moduli stack of principal G-bundles on C. We determine the set of ...
  • Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Pre-published version) 

    Hoffmann, Norbert (Springer, 2010)
    Let C be a connected smooth projective curve of genus g ≥ 2 over an algebraically closed field k. Consider the coarse moduli scheme Bunr,d (resp. Bunr,L) of stable vector bundles on C with rank r and degree d ∈ Z (resp. ...
  • On semistable vector bundles over curves (Pre-published version) 

    Hoffmann, Norbert; Biswas, Indranil; Hein, Georg (Elsevier, 2008)
    Let X be a geometrically irreducible smooth projective curve de ned over a eld k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X; F E) = 0 for i = 0; ...
  • Poincaré families and automorphisms of principal bundles on a curve (Pre-published version) 

    Hoffmann, Norbert; Biswas, Indranil (Elsevier, 2009)
    Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized ...
  • A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras 

    Flatley, Ronan (Scientific Advances Publishers, 2014)
    Let K be a field with characteristic different from 2 and let S be a symbol algebra over K. We compute the symmetric powers of hyperbolic quadratic forms over K. Also, we compute the symmetric powers of the quadratic trace ...
  • Generalized vector bundles on curves (Pre-published version) 

    Hoffmann, Norbert; Stuhler, Ulrich; Jahnel, Joerg (de Gruyter, 1998)
    In their paper [14] G. Harder and M.S. Narasimhan (and independently D. Quillen) have constructed a canonical flag of subbundles on any vector bundle on a complete smooth algebraic curve over a field. This flag measures ...
  • Moduli schemes of generically simple Azumaya modules 

    Hoffmann, Norbert; Stuhler, Ulrich (Documenta Mathematica, 2005)
    Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion ...
  • Mitigating collinearity in linear regression models using ridge, surrogate and raised estimators 

    O'Driscoll, Diarmuid; Ramirez, Donald E. (Cogent OA, 2016)
    Collinearity in the design matrix is a frequent problem in linear regression models, for example, with economic or medical data. Previous standard procedures to mitigate the effects of collinearity included ridge regression ...
  • Response surface designs using the generalized variance inflation factors 

    O'Driscoll, Diarmuid; Ramirez, Donald E. (Cogent OA, 2015)
    We study response surface designs using the generalized variance inflation factors for subsets as an extension of the variance inflation factors.
  • Ireland's participation in the 50th international mathematical olympiad 

    Kreussler, Bernd (Irish Mathematical Society, 2009)
    The 50th International Mathematical Olympiad (IMO) took place in Bremen (Germany) from 12th July until 22nd July 2009. With 565 participants (59 of whom were girls) from 104 countries, this was the IMO with the largest ...
  • Minimizing oblique errors for robust estimating 

    O'Driscoll, Diarmuid; Ramirez, Donald E.; Schmitz, Rebecca (Irish Mathematical Society, 2008)
    The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show ...
  • Analytic moduli spaces of simple sheaves on families of integral curves (Pre-print version) 

    Kreussler, Bernd (Wiley, 2013)
    We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, ...
  • Solving cubic equations in two variables 

    Kreussler, Bernd (Irish Mathematical Society, 2007)
    After recalling a geometric construction of all Pythagorean triples of integers, the same idea is applied to find rational solutions of cubic equations in two variables. This leads to the definition of the Mordell-Weil ...

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