Graduate dissertations
Title: Background Connectivity: Understanding the brain's functional organization
Speaker: Mikayla Holmes, University of Victoria
Date and time:
19 May 2023,
10:00am -
11:00am
Location: David Strong Building C128
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Notice of the Final Oral Examination
for the Degree of Master of Science
of
MIKAYLA HOLMES
BSc (University of Victoria, 2021)
Background Connectivity:
Understanding the brain's functional organization
Department of Mathematics and Statistics
Friday, May 19, 2023 10:00 A.M.
David Strong Building Room C128
Supervisory Committee:
Dr. Michelle Miranda, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic (Member)
External Examiner:
Dr. Jodie Gawryluk, Department of Psychology, UVic
Chair of Oral Examination:
Dr. Raad Nashmi, Department of Biology, UVic
Abstract
Task-state fMRI (tfMRI) and rest-state fMRI (rfMRI) surface data from the Human
Connectome Project (HCP) was examined with the goal of better understanding the nature
of background activation signatures and how they compare to the functional connectivity of
a brain at rest. In this paper we use a hybrid-decomposition and seed-based approach to
calculate functional connectivity of both rfMRI data and the estimated residual data from a
Bayesian spatiotemporal model. This model accounts for local and global spatial correlations
within the brain by applying two levels of data decomposition methods. Moreover, long memory temporal correlations are taken into account by using the Haar discrete wavelet
transform. Motor task data from the HCP is modelled, followed by an analysis of the
residuals, which provide details regarding the brain's background functional connectivity.
These residual connectivity patterns are assessed using a manual procedure and through
studying the induced covariance matrix of the model's error term. When we compare these
activation signatures to those found for the same subject at rest we found that regions within
the subcortex displayed strong connections in both states. Regions associated with the
default mode network also displayed statistically significant connectivity while the subject
was at rest. In contrast, the pre-central ventral and mid-cingulate regions had strong
functional patterns in the background activation signatures that were not present in the rest-state data. This modelling technique combined with a hybrid approach to assessing
functional activation signatures provides valuable insights into the role background
connections play in the brain. Moreover, it is easily adaptable which allows for this research
to be extended across a variety of tasks and at a multi-subject level.
Title: Hierarchical Model for Evaluation of Physician Care in the ICU
Speaker: Jianping Yu, University of Victoria
Date and time:
26 Apr 2023,
10:00am -
11:00am
Location: via Zoom
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The Final Oral Examination
for the Degree of
Master of Science
(Department of Mathematics and Statistics)
Jianping Yu
Phd in Math, Chinese Academy of Sciences
“Hierarchical Model for Evaluation of Physician Care in the ICU”
April 26th, 2023
10:00am
On zoom
Supervisory Committee:
Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic
(Supervisor)
Dr.Farouk Nathoo, Department of Mathematics and Statistics, UVic
(Member)
Chair of Oral Examination:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic
Title: A Uniqueness Theorem for C*-algebras of Hausdorff Étale Groupoids
Speaker: Gavin Goerke, University of Victoria
Date and time:
18 Apr 2023,
10:00am -
11:00am
Location: David Strong Building C124
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Title: Convex Optimization Methods for Bounding Lyapunov Exponents
Speaker: Hans Oeri, University of Victoria
Date and time:
14 Apr 2023,
10:00am -
11:00am
Location: via Zoom
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Notice of the Final Oral Examination
for the Degree of Doctor of Philosophy
of
HANS OERI
MSc (Simon Fraser University, 2018)
BSc (Simon Fraser University, 2016)
“Convex Optimization Methods for Bounding Lyapunov Exponents”
Department of Mathematics and Statistics
Friday, April 14, 2023
10:00 A.M.
Virtual Defence
Supervisory Committee:
Dr. David Goluskin, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)
Dr. Nishant Mehta, Department of Computer Science, UVic (Outside Member)
External Examiner:
Dr. Milan Korda, Laboratoire d'analyse et d'architectures des systèmes,
Centre national de la recherche scientifique, France
Chair of Oral Examination:
Dr. Daniela Constantinescu, Department of Mechanical Engineering, UVic
Abstract
In dynamical systems, the stability of orbits is quantified by Lyapunov exponents, which are
computed from the average rate of divergence of trajectories. We develop techniques for
computing sharp upper bounds on the maximal LE using methods from convex optimization,
which have previously been used to compute sharp bounds on the time averages of scalar
quantities on bounded orbits of dynamical systems. For discrete-time dynamics we develop
an optimization-based approach for computing sharp bounds on the geometric mean of
scalar quantities. We therefore express LEs as infinite-time averages and as geometric
means in continuous-time systems and discrete-time systems, respectively, and then derive
optimization problems whose solutions give sharp bounds on LEs. When the system’s
dynamics is governed by a polynomial vector field, the problems can be relaxed to
computationally tractable SOS programs whose solutions also give sharp bounds on LEs.
An approach for the practical implementation of a sequence of SOS feasibility problems
whose solutions converge to the maximal LE of discrete systems is provided. We explain
how symmetries can be used to simplify and generalize the optimization problems in both
continuous-time and discrete-time systems. We conclude by discussing the extension of the
techniques developed here to the problem of bounding the sum of the leading LEs. Tractable
SOS programs are derived for some special cases of this problem.
The applicability of all the techniques developed here is shown by applying them to various
explicit examples. For some systems we numerically compute sharp bounds that agree with
the the maximal LEs, and for some we prove analytic bounds on maximal LEs by solving the
optimization problems by hand.
Title: Supercritical Phase Transitions from Number Theory
Speaker: Tyler Schulz, University of Victoria
Date and time:
13 Apr 2023,
3:30pm -
4:30pm
Location: David Strong Building Room C128
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Title: Response to Improving abundance estimation by combining capture-recapture and presence-absence data: example with a large carnivore
Speaker: Jack Thomas, University of Victoria
Date and time:
11 Apr 2023,
9:30am -
10:30am
Location: David Strong Building C128
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The Final Oral Examination
for the Degree of
Master of Science
(Department of Mathematics and Statistics)
Jack THOMAS
BSc (University of Victoria, 2019)
"Response to Improving abundance estimation by combining
capture-recapture and presence-absence data: example with a large
carnivore"
Tuesday, April 11, 2023
9:30 A.M.
David Strong Building C128
Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Simon Bonner, Department of Statistical and Actuarial Sciences,
UWO (Co-Supervisor)
Chair of Oral Examination:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, UVic
Title: On linear models selected by the constrained minimum criterion
Speaker: Meifan Lin, University of Victoria
Date and time:
05 Apr 2023,
10:00am -
11:00am
Location: via Zoom
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The Final Oral Examination
for the Degree of
Master of Science
(Department of Mathematics and Statistics)
Meifan LIN
BMath, University of Waterloo, 2021
“On linear models selected by the constrained minimum criterion”
April 5th
10:00 a.m.
Conducted Virtually
Supervisory Committee:
Dr. Min Tsao, Department of Mathematics and Statistics, UVic
(Supervisor)
Dr. Julie Zhou, Department of Mathematics and Statistics, UVic
(Member)
Chair of Oral Examination:
Dr. Junling Ma, Department of Mathematics and Statistics, UVic
Title: Numerical Blowup Solutions for Boundary Value Models
Speaker: Duyeng Hoang, University of Victoria
Date and time:
13 Jan 2023,
2:00pm -
3:00pm
Location: DSB C114
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Notice of the Final Oral Examination for the Degree of Master of Science
Supervisory Committee
Dr. Slim Ibrahim, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Boualem Khouider, Department of Mathematics and Statistics, UVic (Co-Supervisor)
External Examiner
Dr. David Muraki, Department of Mathematics, Simon Fraser University
Chair of Oral Examination
Dr. Graham Voss, Department of Economics, UVic
Abstract
In this thesis, we discuss several numerical methods to approximate singular solutions for some partial differential equations such as Burgers’ equation, Prandtl’s equations, and the inviscid primitive equations. The numerical solutions we obtain for Burgers’ equation and Prandtl’s equations are compared with the existing analytical and numerical solutions in the literature. We observe the singularity formation in the numerical solutions to Burgers’ equation and Prandtl’s equations in finite time. For the inviscid primitive equations with the initial data are close to a suitable rescale of a smooth blowup profile proven by Collot, Ibrahim, and Lin, we compare the numerical solution to the theoretical blowup profile. The solution we obtain from the numerical scheme follows the profile, but the difference between the numerical and analytical profiles is quite significant closer to the blowup time. We then examine the stability of the numerical solutions by considering a small perturbation for the initial data. The gap between the perturbed and unperturbed solutions reduces as we choose smaller perturbation. However, this gap grows as it approaches the blowup time, and the stability of the numerical solutions remains in doubt.
Title: The i-Graph and Other Variations of the y-Graph
Speaker: Laura Teshima, University of Victoria
Date and time:
14 Dec 2022,
9:00am -
10:00am
Location: HHB 110 and Zoom
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Title: Algebraic Cycles on Products of Generically Smooth Quadrics
Speaker: Guangzhou Zhu, University of Victoria
Date and time:
09 Dec 2022,
10:00am -
11:00am
Location: David Strong Building C114
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