RSS 1.0Department of Mathematics and Computer Studies
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Groups of singular alternating sign matrices
(International Linear Algebra Society, 2025-05-20)We investigate multiplicative groups consisting entirely of singular alternating sign matrices (ASMs) and present several constructions of such groups. It is shown that every finite group is isomorphic to a group of ... -
Weighted projections of alternating sign matrices: Latin-like squares and the ASM polytope
(Electronic Journal of Combinatorics, 2024-01-12)The weighted projection of an alternating sign matrix (ASM) was introduced by Brualdi and Dahl (2018) as a step towards characterising a generalisation of Latin squares they defined using alternating sign hypermatrices. ... -
Alternating signed bipartite graphs and difference-1 colourings
(Elsevier, 2020-07-13)We investigate a class of 2-edge coloured bipartite graphs known as alternating signed bipartite graphs (ASBGs) that encode the information in alternating sign matrices. The central question is when a given bipartite ... -
Alternating sign hypermatrix decompositions of Latin-like squares
(Elsevier, 2020-08-14)To any n × n Latin square L, we may associate a unique sequence of mutually orthogonal permutation matrices P = P1, P2, ..., Pn such that L = L(P ) = ∑ kPk . Brualdi and Dahl (2018) described a generalisation of a Latin ... -
Alternating sign matrices of finite multiplicative order
(Elsevier, 2022-07-08)We investigate alternating sign matrices that are not permuta- tion matrices, but have finite order in a general linear group. We classify all such examples of the form P + T , where P is a permutation matrix and T has ... -
Markovianity and the Thompson Group F (Pre-published version)
(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)
(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)
(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)
(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)
(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)
(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 ... -
The stability space of the derived category of holomorphic triples and further investigations
(2021-04-14)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 (Pre-published)
(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)
(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)
(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
(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 ... -
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 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
(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)
(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 ...