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Which graphs are rigid in lpd? (Prepublished)
(Springer, 20210313)We present three results which support the conjecture that a graph is minimally rigid in ddimensional ℓpspace, where p∈(1,∞) and p≠2, if and only if it is (d, d)tight. Firstly, we introduce a graph bracing operation ... 
The stability space of the derived category of holomorphic triples and further investigations
(20210414)In this thesis we give a complete description of the Bridgeland stability space for the bounded derived category of holomorphic triples over a smooth projective curve of genus one as a connected, four dimensional complex ... 
Constructing isostatic frameworks for the l1 and l infinity plane (Prepublished)
(Electronic Journal of Combinatorics, 20200612)We use a new coloured multigraph constructive method to prove that if the edgeset 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 (Prepublished)
(Elsevier, 20201115)A rigidity theory is developed for barjoint 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 (Prepublished)
(Elsevier, 20210515)We prove a variant of the wellknown 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
(Elsevier, 20201215)We develop a combinatorial rigidity theory for symmetric barjoint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwelltype sparsity counts are identified for a ... 
Symmetric powers of trace forms on symbol algebras
(Université D'Artois, 2013) 
Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope
(Athens Institute for Education and Research, 2015)The slope of the bestfit 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
(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 Gbundles over a curve (Prepublished version)
(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 Gbundles on C. We determine the set of ... 
Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Prepublished version)
(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 (Prepublished version)
(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 (Prepublished version)
(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 Gbundles on C, for the existence of Poincaré families parameterized ... 
Moment estimation of measurement errors
(NEDETAS, 2011)The slope of the bestfit line from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four. We use second order and fourth order moment equations to estimate the ratio ... 
Revisiting some design criteria
(Athens Institute for Education and Research, 2015)We address the problem that the A (trace) design criterion is not scale invariant and often is in disagreement with the D (determinant) design criterion. We consider the canonical moment matrix CM and use the trace of its ... 
Limitations of the least squares estimators; a teaching perspective
(Athens Institute for Education and Research, 2016)The standard linear regression model can be written as Y = Xβ+ε with X a full rank n × p matrix and L(ε) = N(0, σ2In). The least squares estimator is = (X΄X)−1XY with variancecovariance matrix Coυ( ) = σ2(X΄X)−1, where ... 
A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras
(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 (Prepublished version)
(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
(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
(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 ...