Waterloo Research
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Pure Pairs. IX. Transversal Trees
(Society for Industrial and Applied Mathematics, 2024)Fix k>0, and let G be a graph, with vertex set partitioned into k subsets ("blocks") of approximately equal size. An induced subgraph of G is "transversal" (with respect to this partition) if it has exactly one vertex in ... 
Around the closure of the set of commutators of idempotents in B(H): Biquasitriangularity and factorisation
(Elsevier, 20230415)In this paper, we continue our study of the normclosure of the set CEof bounded linear operators acting on a complex, infinitedimensional, separable Hilbert space Hwhich may be expressed as the commutator of two idempotent ... 
Five Hilbert Space Problems in Operator Algebras
(Springer, 20221103)A number of questions which have been solved over the years in the theory of single operators acting on Hilbert space have interesting analogues when recast in the setting of elements of C*algebras. We list five of these, ... 
A note on the structure of matrix *subalgebras with scalar diagonals
(EleMath, 2021)We characterize those unital, selfadjoint algebras of complex n x n matrices that are simultaneously unitarily similar to algebras in which every member has a scalar diagonal. 
On *similarity in C*algebras
(Instytut Matematyczny, 2020)Two subsets X and Y of a unital C algebra A are said to be similar via s 2 A1 if Y = s1Xs and Y = s1X s. We show that this relation imposes a certain structure on the sets X and Y, and that under certain natural ... 
Quasidiagonal weighted shifts on directed trees
(Instytut Matematyczny, 2023)We investigate quasidiagonality of weighted shifts on directed trees. We concentrate mainly on a subclass of weighted shifts operators called adjacency operators. In particular, we provide equivalent conditions for ... 
On Specht's Theorem in UHF C*algebras
(Elsevier, 20210101)Specht’s Theorem states that two matrices Aand Bin Mn(C)are unitarily equivalent if and only if tr(w(A, A∗)) =tr(w(B, B∗))for all words w(x, y)in two noncommuting variables xand y. In this article we examine to what extent ... 
Triangular Operator Algebras and Simultaneous Triangularisation
(American Mathematical Society, 2023)We consider the question of whether every collection of compact operators that is contained in a triangular operator algebra (in the sense of Kadison and Singer) must be simultaneously triangularisable. The answer is shown ... 
On NormLimits of Algebraic Quasidiagonal Operators
(Theta Foundation, 2020)It is still an open question to know whether or not every quasidiagonal operator can be expressed as a normlimit of algebraic quasidiagonal operators. In this note, we provide an alternative characterization of those ... 
On the spectrum of the SylvesterRosenblum operator acting on triangular algebras
(EleMath, 2020)Let A and B be algebras and M be an A Bbimodule. For A ∈ A , B ∈B, we define the SylvesterRosenblum operator τA,B :M →M via τA,B(M) = AM+MB for all M ∈ M . We investigate the spectrum of τA,B in three settings, namely: ... 
Expansion und Dynastische Politik in Pontos: Zwei neue Ären unter Pharnakes I.
(Steiner Verlag, Stuttgart, Germany, 20220101)The most heated debates on earlyPontic history surround the treaty of alliance made between Pharnakes I and the citizens of Chersonesos in year 157 (IOSPE I2 402 = III3 103). About a half of the present generation of ... 
The Chronology of the Asylia Dossier from Kos Revisited in Light of Some Recent Epigraphic Discoveries
(Kabalcı, Istanbul, Türkiye, 20211231)While the Third Syrian War was raging, the Koans deployed substantial diplomatic efforts to have the asylia of their Asklepieion and the panhellenic penteteric games recognized throughout the Mediterranean world. In the ... 
Cavitation threshold evaluation of porcine cerebrospinal fluid using a Polymeric Split Hopkinson Pressure BarConfinement chamber apparatus
(Elsevier, 201912)Studies investigating mild Traumatic Brain Injury (mTBI) in the military population using experimental head surrogates and Finite Element (FE) head models have demonstrated the existence of transient negative pressures ... 
Polynomial Bounds for Chromatic Number. IV: A Nearpolynomial Bound for Excluding the Fivevertex Path
(Springer, 20230915)A graph G is H free if it has no induced subgraph isomorphic to H. We prove that a P5free graph with clique number ω ≥ 3 has chromatic number at most ωlog2(ω). The best previous result was an exponential upper bound ... 
Pure Pairs. V. Excluding Some Long Subdivision.
(Springer, 20230616)A \pure pair" in a graph G is a pair A;B of disjoint subsets of V (G) such that A is complete or anticomplete to B. Jacob Fox showed that for all " > 0, there is a comparability graph G with n vertices, where n is large, ... 
Strengthening Rodl's theorem
(Elsevier, 202311)What can be said about the structure of graphs that do not contain an induced copy of some graph H? Rödl showed in the 1980s that every Hfree graph has large parts that are very sparse or very dense. More precisely, ... 
My data collection is complete, now what? Connecting researchers to Data Repositories that can support Cold Regions Researchers
(University of Waterloo, 20201127)The natural climate variability of the cold regions, together with the relatively sparse observational data sets and difficult terrain can make data collection which supports key science challenging. Notwithstanding, ... 
Role of Artificial Intelligence in Theranostics: Toward Routine Personalized Radiopharmaceutical Therapies
(Elsevier, 202110)KEY POINTS AI has shown promising applications in quantitative imaging required for dosimetry. Segmentation of organs and tumors, the most time consuming task in the dosimetry workflow, can be automated using AI. ... 
Clinical Applications of Artificial Intelligence in positron emission tomography of Lung Cancer
(Elsevier, 202201)The ability of a computer to perform tasks normally requiring human intelligence or artificial intelligence (AI) is not new. However, until recently, practical applications in medical imaging were limited, especially in ... 
Induced subgraphs and tree decompositions II. Toward walls and their line graphs in graphs of bounded degree.
(Elsevier, 202401)This paper is motivated by the following question: what are the unavoidable induced subgraphs of graphs with large treewidth? Aboulker et al. made a conjecture which answers this question in graphs of bounded maximum ...