Mathematics (Faculty of)
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A spatial version of Wedderburn’s Principal Theorem
(Taylor & Francis, 2015)In this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector ... -
Universal bounds for positive matrix semigroups
(Polish Academy of Sciences, 2016)We show that any compact semigroup of positive n×n matrices is similar (via a positive diagonal similarity) to a semigroup bounded by n√. We give examples to show this bound is best possible. We also consider the effect ... -
Reducibility of operator semigroups and values of vector states
(Springer, 2017-08-01)Let S be a multiplicative semigroup of bounded linear operators on a complex Hilbert space H, and let Ω be the range of a vector state on S so that Ω = {⟨Sξ, ξ⟩ : S ∈ S} for some fixed unit vector ξ ∈ H. We study the ... -
Compact ideals and rigidity of representations for amenable operator algebras
(Polish Academy of Sciences, 2019)We examine rigidity phenomena for representations of amenable operator algebras which have an ideal of compact operators. We establish that a generalized version of Kadison’s conjecture on completely bounded homomorphisms ... -
Residual finite dimensionality and representations of amenable operator algebras
(Elsevier, 2019-04-15)We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable ... -
Abelian, amenable operator algebras are similar to C∗ -algebras
(Duke University Press, 2016-12)Suppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if 𝒜⊆ℬ(H) is ... -
Ranges of vector states on irreducible operator semigroups
(Springer, 2016)Let 𝜑 be a linear functional of rank one acting on an irreducible semigroup S of operators on a finite- or infinite-dimensional Hilbert space. It is a well-known and simple fact that the range of 𝜑 cannot be a singleton. ... -
On selfadjoint extensions of semigroups of partial isometries
(American Mathematical Society, 2016)Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists ... -
Linear preservers of polynomial numerical hulls of matrices
(Elsevier, 2019-08-15)Let Mn be the algebra of all n × n complex matrices, 1 ≤ k ≤ n − 1 be an integer, and φ : Mn −→ Mn be a linear operator. In this paper, it is shown that φ preserves the polynomial numerical hull of order k if and only if ... -
Computing lower rank approximations of matrix polynomials
(Elsevier, 2020-05)Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of ... -
Incentivizing evaluation with peer prediction and limited access to ground truth
(Elsevier, 2019-10)In many settings, an effective way of evaluating objects of interest is to collect evaluations from dispersed individuals and to aggregate these evaluations together. Some examples are categorizing online content and ... -
The number of valid factorizations of Fibonacci prefixes
(Elsevier, 2019-07-05)We establish several recurrence relations and an explicit formula for V(n), the number of factorizations of the length-n prefix of the Fibonacci word into a (not necessarily strictly) decreasing sequence of standard Fibonacci ... -
Critical exponents of infinite balanced words
(Elsevier, 2019-07-19)Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2 + root2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent (5 + root5)/4. Over larger ... -
Subword complexity and power avoidance
(Elsevier, 2019-11-05)We begin a systematic study of the relations between subword complexity of infinite words and their power avoidance. Among other things, we show that –the Thue–Morse word has the minimum possible subword complexity over ... -
Complexity of proper prefix-convex regular languages
(Elsevier, 2019-10-01)A language L over an alphabet Σ is prefix-convex if, for any words x,y,z ∈ Σ*, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefix-closed, and prefix-free languages, which were ... -
Multistate analysis from cross-sectional and auxiliary samples
(Wiley, 2020-02-20)Epidemiological studies routinely involve cross‐sectional sampling of a population comprised of individuals progressing through life history processes. We consider features of a cross‐sectional sample in terms of the ... -
Design of cancer trials based on progression-free survival with intermittent assessment
(Wiley, 2018-03-26)Therapeutic advances in cancer mean that it is now impractical to performed phase III randomized trials evaluating experimental treatments on the basis of overall survival. As a result, the composite endpoint of progression-free ... -
A new perspective on loss to follow-up in failure time and life history studies
(Wiley, 2019-07-24)A framework is proposed for the joint modeling of life history and loss to follow-up (LTF) processes in cohort studies. This framework provides a basis for discussing independence conditions for LTF and censoring and ... -
Style Recognition in Music with Context Free Grammars and Kolmogorov Complexity
(University of Waterloo, 2020-03-11)The Kolmogorov Complexity of an object is incomputable. But built in its structure is a way to specify description methods of an object that is computable in some sense. Such a description method then can be exploited ... -
Constrained-CNN losses for weakly supervised segmentation
(Elsevier, 2019-05)Weakly-supervised learning based on, e.g., partially labelled images or image-tags, is currently attracting significant attention in CNN segmentation as it can mitigate the need for full and laborious pixel/voxel annotations. ...
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