Waterloo Research
http://hdl.handle.net/10012/9972
20220522T05:19:34Z

On Specht's Theorem in UHF C⁎algebras
http://hdl.handle.net/10012/18308
On Specht's Theorem in UHF C⁎algebras
Marcoux, Laurent W.; Zhang, Yuanhang
Specht's Theorem states that two matrices A and B in 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 x and y. In this article we examine to what extent this trace condition characterises approximate unitary equivalence in uniformly hyper nite (UHF) C algebras. In particular, we show that given two elements a; b of the universal UHF algebra Q which generate C algebras satisfying the UCT, they are approximately unitarily equivalent if and only if (w(a; a )) = (w(b; b )) for all words w(x; y) in two noncommuting variables (where denotes the unique tracial state on Q), while there exist two elements a; b in the UHFalgebra M21 which fail to be approximately unitarily equivalent despite the fact that they satisfy the trace condition. We also examine a consequence of these results for ampliations of matrices.
The final publication is available at Elsevier via https://doi.org/10.1016/j.jfa.2020.108778 © 2020. This manuscript version is made available under the CCBYNCND 4.0 license
20210101T00:00:00Z

Analysis of a pressurerobust hybridized discontinuous Galerkin method for the stationary NavierStokes equations
http://hdl.handle.net/10012/18285
Analysis of a pressurerobust hybridized discontinuous Galerkin method for the stationary NavierStokes equations
Kirk, Keegan L.A.; Rhebergen, Sander
We present wellposedness and an a priori error analysis of the hybridized discontinuous Galerkin
method for the stationary form of the NavierStokes problem proposed in (J Sci Comput, 76(3):1484{
1501, 2018). This scheme was shown to result in an approximate velocity eld that is pointwise
divergencefree and divergenceconforming. As a consequence we show that the velocity error estimate
is independent of the pressure. Furthermore, we show that estimates for both the velocity
and pressure are optimal. Numerical examples demonstrate pressurerobustness and optimality of
the scheme.
20190830T00:00:00Z

Dispersing representations of semisimple subalgebras of complex matrices
http://hdl.handle.net/10012/18284
Dispersing representations of semisimple subalgebras of complex matrices
Marcoux, Laurent W.; Radjavi, Heydar; Zhang, Yuanhang
In this paper we consider the problem of determining the maximum dimension
of P?(A!B)P, where A and B are unital, semisimple subalgebras of the set Mn of n⇥n
complex matrices, and P 2 M2n is a projection of rank n. We exhibit a number of
equivalent formulations of this problem, including the one which occupies the majority of
the paper, namely: determine the minimum dimension of the space A\ S−1BS, where S
is allowed to range over the invertible group GL(n,C) of Mn. This problem in turn is seen
to be equivalent to the problem of finding two automorphisms ↵ and " of Mn for which
the dimension of ↵(A)+"(B) is maximised. It is this phenomenon which gives rise to the
title of the paper.
The final publication is available at Elsevier via https://doi.org/10.1016/j.laa.2022.02.017 © 2021. This manuscript version is made available under the CCBYNCND 4.0 license
20220601T00:00:00Z

Linebased deep learning method for tree branch detection from digital images
http://hdl.handle.net/10012/18260
Linebased deep learning method for tree branch detection from digital images
Silva, Rodrigo; Marcato Junior, José; Almeida, Laisa; Gonçalves, Diogo; Zamboni, Pedro; Fernandes, Vanessa; Silva, Jonathan; Matsubara, Edson; Batista, Edson; Ma, Lingfei; Li, Jonathan; Gonçalves, Wesley
Preventive maintenance of power lines, including cutting and pruning of tree branches, is essential to avoid interruptions in the energy supply. Automatic methods can support this risky task and also reduce time consuming. Here, we propose a method in which the orientation and the grasping positions of tree branches are estimated. The proposed method firstly predicts the straight line (representing the tree branch extension) based on a convolutional neural network (CNN). Secondly, a Hough transform is applied to estimate the direction and position of the line. Finally, we estimate the grip point as the pixel point with the highest probability of belonging to the line. We generated a dataset based on internet searches and annotated 1868 images considering challenging scenarios with different tree branch shapes, capture devices, and environmental conditions. Tenfold crossvalidation was adopted, considering 90% for training and 10% for testing. We also assessed the method under corruptions (gaussian and shot) with different severity levels. The experimental analysis showed the effectiveness of the proposed method reporting F1score of 96.78%. Our method outperformed stateoftheart Deep Hough Transform (DHT) and Fully Convolutional Line Parsing (FClip).
The final publication is available at Elsevier via https://doi.org/10.1016/j.jag.2022.102759. © 2021. This manuscript version is made available under the CCBYNCND 4.0 license
20220601T00:00:00Z