Home page of Edward R. Vrscay
Edward R. Vrscay
Professor Emeritus and Adjunct
Department of Applied Mathematics
Faculty of Mathematics
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
e-mail: ervrscay "at" uwaterloo.ca
Faculty of Mathematics Award for Distinction in Teaching - September 2019
In July, 1986, I joined the Department of Applied Mathematics, UW, as an NSERC University Research Fellow and Assistant Professor.
On January 1, 2023, I retired from my
position as full-time and tenured Professor in Applied Mathematics. I am now
an Adjunct Professor in the Department of Applied Mathematics.
Table of Contents
The last two years of my employment at UW, i.e., 2021-22,
were quite "eventful" because of
my refusal to submit
mandatory COVID-19 vaccination policy.
Indeed, I came very close to being "dismissed with cause" (i.e., fired) in April 2022.
and its enforcement over the years
2021-2022, represent a very dark period at the University of Waterloo.
At least 50 UW employees (49 staff members and one faculty member) were fired for
"noncompliance" to the mandate.
In contrast, no employees were fired at Wilfred Laurier University,
down the street from us.
I believe that UW's "Requirement" created wounds on this campus that may never
fully heal. For this reason, I am posting here the closing remarks of a document
which I wrote in December 2022 as part of the arbitration process for
two grievances that I had
filed against the University of Waterloo (following guidelines
contained in the Memorandum of
Agreement between the University of Waterloo and the Faculty Association of the
University of Waterloo). These remarks are of a general nature
and are most certainly non-confidential. I think that it is most appropriate
that they be seen not only by the entire UW campus community but
also by the world-at-large.
The motives of my two grievances lie not in the University of Waterloo’s “Requirement” itself but in the ways in which the “Requirement” was enforced. Firstly, as pointed out in these grievances, the University unnecessarily resorted to falsehoods (i.e., that it was compelled to adopt a vaccination mandate) and deception (two “Requirements”) to justify its mandate.
Secondly, my grievances are concerned about how those deemed “noncompliant” with respect to the “Requirement” were treated by UW’s administration, both at the local level, i.e., Deans, as well as the higher level, i.e., President and Vice President Academic and Provost. Indeed, I conclude this document with an expression of sympathy and greatest respect for the fifty (to my knowledge) UW employees who were fired because of “noncompliance”. Why these fifty people were fired, while no employees were fired at our sister institution, Wilfrid Laurier University, remains a mystery. One can only pray that the truth will someday be revealed. The authoritarian behaviour of the UW administration in its imposition and enforcement of the “Requirement” suggests a new and more appropriate motto for the University of Waterloo, namely,
Concordia cum falsitate per coercionem (In harmony with falsehood by coercion)
A tragic stain on an institution which I used to consider, with pride, as my “home”.
I cannot help but think that the Faculty Association of the University of Waterloo (FAUW),
by "sleeping at the wheel" (or perhaps "looking the other way")
must share some responsibility with the UW administration for this stain,
which includes the firing of
Dr. Michael Palmer - to the best of my knowledge, the only firing of a full-time,
tenured faculty member at a Canadian university for "noncompliance" to a vaccine mandate.
How much responsibility? Time will tell.
letter to the FAUW Board on this matter.)
A brief history of the UW vaccine mandate "imbroglio" is presented
at the bottom of this
A more detailed history of the UW vaccine mandate "imbroglio" and the
people affected, along with the many letters that I wrote during
the "imbroglio", is presented
I think it fitting, as a warning, to conclude
this section with the final paragraph, plus references, of a
letter that I wrote
during the "imbroglio":
That being said, I fear that if this "vaccine imbroglio" is but an initial
glimpse of where and how this administration wishes to lead our institution,
especially with its dedication to the "great reset" [1,2], then "this kind does not go
out except by prayer and fasting" (Matthew 17:21). Those familiar with the Bible
will know the message contained in this quote. Others may wish to do a little "digging".
Those not at all interested, however, can simply continue to be silent, enjoy
the ride on the good ship SS UWaterloo and faithfully support the UW administration
without question in its relentless drive for coerced compliance. The penalty
for noncompliance is exclusion (interestingly, a product of colonialism ) but you
can rest assured that "everyone feels a sense of belonging at this institution,
and can achieve their full potential" .
 UW President Vivek Goel's Installation Address
 COVID-19: The Great Reset, by Klaus Schwab and
Thierry Malleret. World Economic Forum Publishing (2020). Is this the unofficial "textbook"
being adopted by government, NGOs and universities, including our own?
Final examination question:
Do you think that any of the fifty UW employees fired for "noncompliance"
felt a sense of belonging at UW,
or were able to achieve their full potential (at UW)?
- Mathematical imaging:
Nonlocal image processing: theory and applications.
- Fractal image coding (a particular example of nonlocal image processing) and
the self-similarity of images.
- The use of fractal-based coding methods in image processing: compression,
Image quality measures -- in particular, the ``structural similarity'' measure
(originally due to Prof. Z. Wang, my collaborator from E&CE, UW).
Novel spaces of image functions and their applications: Most recently: (i) measure-valued image mappings and (ii) function-valued image mappings. The latter are ideally suited for the representation of hyperspectral images and diffusion MRI images.
Intensity-based metrics for image functions, including those that
accommodate Weber's models of perception.
- "Diagnostically lossless" medical image compression.
- Fractal-based methods of analysis and approximation: Iterated function systems,
"generalized fractal transforms" over various metric spaces, inverse problems of
approximation using fractal-based methods (e.g., "collage method for contraction mappings").
- For a brief and quite readable introduction to the ideas behind
fractal image coding, please
consult A Hitchhiker's Guide to Fractal Image Coding
(Admittedly, it's an old document (1996), but people still find it helpful.)
Dynamical systems and their applications, e.g., iteration of rational mappings
in the complex plane, chaotic dynamics.
Design of a new generation
of conformable high-pressure vessels for gaseous fuels in automotive
This work was
supported by a Natural Sciences and Engineering Research
Council Collaborative Research and Development (CRD) with Chrysler Canada Inc.
-- now Fiat Chrysler Automotive Canada (FCA Canada)--
as industrial sponsor during the years 2014-2018.
(The heading of this section
is the title of the CRD Grant.)
In collaboration with FCA, we were engaged in
developing a framework
for the design of compressed gaseous fuel vessels that will occupy
arbitrary geometries. Our goal was to develop
algorithms for fitting a network of tubes with a range of diameters into
an arbitrary three-dimensional region.
A tubular network constructed during the early period of our project
The following three faculty members were involved in this project:
This research was highly interdisciplinary in nature, involving
various aspects of optimization, fluid mechanics, solid mechanics,
software design and computing. Both theory and application played important
Edward R. Vrscay, Dept. of Applied Mathematics, UW
Sean Peterson, Dept. of Mechanical and Mechatronics Engineering, UW.
Franklin Mendivil, Dept. of Mathematics and Statistics, Acadia
University, Wolfville, NS.
Three M.Math. students, one M.Sc. student and one
Postdoctoral Research worked
on this project (see below).
I was originally approached by Chrysler Canada because of our
Waterloo Fractal Coding and Analysis Group website. Our project would eventually involve very little
fractal content, except for the important idea of branching.
Nevertheless, the entire exercise was
a very good opportunity for me, and others as well, to
``expand our horizons'' by learning new ideas and methods. For example,
one of the important components of our project and subsequent
algorithms was circle packing, which was used to pack tubes
Here are two slide presentations on our work
delivered at the AMMCS-CAIMS 2015 meeting, June 7-12, 2015,
held at Wilfrid Laurier University, Waterloo, Ontario, Canada.
Here is a set of notes on an early method of circle
packing for arbitrary polygonal regions which I developed
a little later in the project (and for which I
wrote some primitive code) in collaboration with my colleagues
Sean Peterson (UW) and Franklin Mendivil:
Mathematical physics, in particular quantum theory. At one time, this
represented a major research activity of mine. However, as time progressed
and my activities in mathematical imaging were expanding,
there was less and less time (and energy!) available to supervise
graduate students in this area. As a result, I decided in 2007 that I would not
take any new graduate students. It was a difficult decision for a number of reasons:
Here is a brief list of areas of quantum mechanics in which I have worked,
arranged chronologically from past to most recent:
I enjoyed very much the later work on the de Broglie-Bohm causal interpretation
of quantum mechanics with my students Caroline Colijn (Ph.D.) and Jeff Timko (M.Math.),
I was still receiving many requests from potential students to supervise them in the
area of foundations of quantum theory, especially "Bohmian mechanics",
I am still very much interested in the foundations (or lack thereof!) of quantum theory.
Quantum mechanical perturbation theory and summability of divergent perturbation expansions:
Continued fraction representations of divergent series
Coherent states in quantum mechanics
Classical limit of quantum mechanics, including classical limits of perturbation expansions
The de Broglie-Bohm causal interpretation of quantum mechanics
D. La Torre (Milan), F. Mendivil (Acadia), H. Kunze (Guelph): We
Waterloo Fractal Coding and Analysis Group .
We have been interested in various aspects
of fractal analysis including: iterated function systems, fractal image coding,
generalized fractal transforms and the inverse problem of approximation using fixed
points of contraction mappings. Here is a photo of our book, Fractal Based Methods in Analysis (Springer Verlag 2012).
You can read about it at the Springer website for the book.
Z. Wang, Department of Electrical and Computer Engineering, UW.
H. Tizhoosh, Department of Systems Design Engineering, UW.
D. Koff, Chair, Department of Radiology, McMaster University.
W. Wallace, Agfa HealthCare, Waterloo, Ontario.
O. Michailovich, Department of Electrical and Computer Engineering, UW.
M.Math., in progress
A. Kunze, Mathematical properties of image metrics designed to accommodate the human visual system.
Postdoctoral Research Associate, completed
F. Ghasempour, Design and analysis of conformable tubular networks
which occupy arbitrary regions in (2015-2017)
co-supervision with S. Peterson, UW and F. Mendivil, Acadia/UW)
A.K. Cheeseman, "A Critical Examination of Two Specific Approaches Used to
Characterize Medical Images: (i) Projection-based Descriptors for Image Retrieval
and (ii) Estimating Fractal Dimensions of Discrete Sets" (2022).
D. Otero, "Function-valued mappings and SSIM-based optimization in imaging" (2015) (co-supervision with O. Michailovich, UW)
I. Kowalik-Urbaniak, "The quest for 'diagnostically lossless' medical
image compression using objective image quality measures" (2015)
(co-supervision with Z. Wang, UW)
J. Vass, "On the Geometry of IFS Fractals and its Applications" (2014)
D. Brunet, "A study of the structural similarity image quality measure
with applications to image processing" (2012)
(co-supervision with Z. Wang, UW)
N. Portman, "The modelling of biological growth using a pattern theoretic approach"
(2009) (co-supervision with U. Grenander, Brown University)
G.S. Mayer, "Resolution enhancement in magnetic resonance imaging by frequency extrapolation"
M. Ebrahimi Kahrizsangi, "Inverse problems and self-similarity in imaging" (2008)
S.K. Alexander, "Multiscale methods in image modelling and image processing" (2005)
C. Colijn, "The de Broglie-Bohm causal interpretation of quantum mechanics
and its application to some simple systems" (2003)
D. Li, A Novel Class of Intensity-based Metrics for Image Functions
which Accommodate a Generalized Weber's Model of Perception (2020)
M. Miao, Monte Carlo Simulation of Diffusion Magnetic Resonance
J. Liang, Design of an Automatic Facial Expression Detector (2018)
H. Wang, A Novel Diffusion-based Empirical Mode Decomposition Algorithm
for Signal and Image Analysis (2018)
(co-supervision with R. Mann, Cheriton School of Computer Science, UW)
E. Maki, "Iterated function systems with place-dependent
probabilities and the inverse
problem of measure approximation using moments" (2017)
T. Qiao, "Design of tubular network systems using circle packing and discrete optimization" (2016)
co-supervision with F. Mendivil, Acadia/UW)
W. Jiang, "Construction of optimal tubular networks in arbitrary regions
in " (2015)
co-supervision with S. Peterson, UW)
I.-T. Ho, "Improvements on circle packing algorithms in two-dimensional cross-sectional areas " (2015)
co-supervision with S. Peterson, UW)
J. Ladan, "An analysis of Stockwell transforms, with applications to
image processing" (2014)
D. Glew, "Self-similarity of images, nonlocal image processing and image quality metrics" (2011)
C. Antonio Sanchez, "Dynamic magnetic resonance elastography: Improved direct methods
of shear modulus estimation" (2009)
J. Timko, "Bohmian trajectories of the two-electron helium atom" (2007)
Y. Li, "Determining NMR relaxation times for porous media: Theory, measurement
and the inverse problem" (2007)
S.K. Alexander, "Two- and three-dimensional coding schemes for wavelet
and fractal-wavelet image compression (2001)
Undergraduate RA, in progress
Undergraduate RA, completed
H. Chen, Investigating the self-similarity of images
(Physics 437 research project, Fall 2019, Winter 2020)
D. Li, A novel class of metrics for image functions designed
to accommodate Weber's model of perception
(Physics 437 research project, Fall 2017, Winter 2018)
A. Cheeseman, Methods of predicting the severity
of degradation of image blocks by JPEG and JPEG2000 compression methods
(Physics 437 research project, Fall 2014, Winter 2015)
P. Bendevis, Construction and analysis of a family of higher-order structural similarity
rational functions (URA, Fall 2013, Winter 2014)
A. Akulov, Indexing images by means of their fractal codes (NSERC USRA, Spring 2011)
Below are links to my lecture or supplementary notes for some
courses taught recently -- and not so recently.
The "Spirit of Calculus"
details of the "imbroglio" and the people it affected, please visit the following website:
REQUESTS TO REPEAL UW's MANDATORY
VACCINATION AND TESTING POLICY
On August 26, 2021, an Open Letter, signed by 32 people -
faculty (including myself), staff, students and parents of students - was sent to the
UW administration asking it to repeal its vaccination and testing mandate.
On September 2, 2021, this Open Letter was sent by e-mail to all faculty, staff and
students on the UW campus. Eventually, 155 people signed the Letter.
Here is my letter of September 27, 2021 in which I formally state, with reasons,
my refusal to submit to the UW vaccine mandate.
Starting in January 2022, the UW administration began subjecting, to my knowledge,
five faculty "mandate resisters"
(including myself as well as a young Canada Research
Chair) to a series of "disciplinary measures",
with the ultimate goal of terminating their positions.
(Note: There may have been others of whom I was unaware.
I also knew of a couple of other faculty "resisters" who were on medical
leave at the time.)
At that time, it was unknown how many students - undergraduate
or graduate - were not allowed to
either begin or continue their academic programs at UW because of
the vaccine mandate.
Later, a few of us (three faculty members plus three staff members)
were interviewed by Robert Williams of the Waterloo Region Record newspaper.
This led to the following article by Mr. Williams which appeared in the
March 2, 2022 issue of the Record:
UW has terminated staff not complying with policy, professors begin unpaid
Here is another Record article by Mr. Williams (March 10, 2022)
on the subject of how
students requesting religious accommodations were being treated by UW:
Waterloo students barred from campus question criteria used for
The UW ADMINISTRATION ACHIEVES AN ALL-TIME LOW:
On March 21, 2022,
Professor Michael Palmer
(Chemistry, UW) was fired for "noncompliance" with UW's vaccine mandate.
UW fires professor over vaccine mandate
A critical examination of UW's COVID-19 "vaccination requirement"
by John Turri (Philosophy, UW).
Past articles include:
The University of Waterloo's "vaccination requirement" was not legally
required. But the university lied by saying it was. (March 25, 2022)
The University of Waterloo keeps changing what its "vaccination requirement"
requires. A hallmark of arbitrary and authoritarian governance. (March 25, 2022)
The University of Waterloo's "vaccination requirement" violates its own
compulsory policy on health and safety. This makes the requirement illegitimate.
(March 27, 2022)
The University of Waterloo's own data show that its "vaccination requirement"
failed to make the campus safer. But its President now says that compliance,
not safety, was the true goal. (March 28, 2022)
The University of Waterloo defies public health authorities by maintaining
its "vaccination requirement". Because punishment is an end in itself.
(March 29, 2022)
The University of Waterloo broke its promise to end its "vaccination requirement".
Now it might be breaking the law. (March 30, 2022)
The University of Waterloo's "vaccination requirement" and the COVID-19 Immunity
Task Force. UW President Vivek Goel's undisclosed conflict of interest.
(April 1, 2022)
Coercion quantified: The University of Waterloo's "Vaccination Requirement".
(April 5, 2022)
The University of Waterloo's dishonest and manipulative accomodations program.
Designed to achieve "maximum compliance". (April 6, 2022)
COVID-19 disinformation at the University of Waterloo.
UW relies on fake claims to make bad decisions. (April 8, 2022)
The University of Waterloo spreads COVID-19 disinformation.
And they won't correct it. (April 10, 2022)
The University of Waterloo spreads more COVID-19 disinformation. This time about
the stated purpose and history of COVID-19 "vaccines". (April 12, 2022)
The hypocrisy of the University of Waterloo's "vaccination requirement".
Privacy for me but not for thee. (April 16, 2022)
In this episode of the Children's Health Defense "Tea Time" series, Michael Palmer, MD - yes, the Michael Palmer who was fired by UW (see above) - discusses mRNA vaccines, spike proteins, heart and lung health, vaccine-related deaths and more. Dr. Palmer exposes the dangers of mRNA technology and how the body reacts negatively to it. Viewer discretion is advised.
Dr. Palmer has been a member of Doctors for COVID Ethics (D4CE) since its inception in April 2021.
At the D4CE site, you will be able to find much information on
COVID-19 vaccines which is contrary to
that being peddled by the mainstream media, government, established
health agencies, and, yes, academia.
A MOMENTOUS EVENT IN CANADIAN HISTORY: THE "TRUCKERS' FREEDOM CONVOY" TO OTTAWA
On Thursday, January 27, 2022, the portion of the convoy which began in
Sarnia passed by Kitchener on Highway 401 East. Here are a couple of photos of
the convoy which I took from the Conestoga College walkover bridge at 2:30 p.m.
Here is a short video of the convoy taken from the bridge
There are many wonderful photos and videos to be found of the Convoy during its
procession to Ottawa and during the peaceful protest of the "fringe minority"
in our nation's capital. This photo is perhaps the nearest and dearest to my heart
because to me, "it says it all".
GOD KEEP OUR LAND GLORIOUS AND FREE!