• Markovianity and the Thompson Group F (Pre-published version) 

  Koestler, Claus; Krishnan, Arundhathi (2022-10-27)

  We show that representations of the Thompson group F in the automorphisms of a noncommutative probability space yield a large class of bilateral stationary noncommutative Markov processes. As a partial converse, bilateral ...

• Pseudospectrum of an element of a Banach algebra (Pre-published version) 

  Kulkarni, S H; Krishnan, Arundhathi (Element Publishing House, 2017-03)

  The ε -pseudospectrum Λε (a) of an element a of an arbitrary Banach algebra A is studied. Its relationships with the spectrum and numerical range of a are given. Characterizations of scalar, Hermitian and Hermitian idempotent ...

• Pseudospectra of elements of reduced Banach algebras (Pre-published version) 

  Kulkarni, S H; Krishnan, Arundhathi (Springer, 2017)

  Let A be a Banach algebra with identity 1 and p ∈ A be a non-trivial idempotent. Then q = 1−p is also an idempotent. The subalgebras pAp and qAq are Banach algebras, called reduced Banach algebras, with identities p and q ...

• Markovianity and the Thompson monoid F+ (Pre-published version) 

  Koestler, Claus; Krishnan, Arundhathi; Wills, Stephen (Elsevier, 2023-03-13)

  We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid F+ in noncommutative probability spaces. We show that a partially ...

• Pseudospectra of elements of reduced Banach algebras II (Pre-published version) 

  Kulkarni, S H; Krishnan, Arundhathi (Faculty of Sciences and Mathematics, University of Nis, Serbia, 2018-06)

  Let A be a Banach algebra with identity 1 and p ∈ A be a non-trivial idempotent. Then q = 1 − p is also an idempotent. The subalgebras pAp and qAq are Banach algebras, called reduced Banach algebras, with identities p and ...

• Which graphs are rigid in lpd? (Pre-published) 

  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 ...

• Rigidity 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 ...

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