Events
All upcoming and recent events from the past six months:
Title: Studies on Math Education and Trigraph Homomorphisms
Speaker: Freddie Mullen, University of Victoria
Date and time:
14 Dec 2023,
3:30pm -
4:30pm
Location: via Zoom
Event type: Graduate dissertations
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Notice of the Final Oral Examination
for the Degree of Master of Science
of
FREDDIE MULLIN
BEd (University of Victoria, 2013)
BSc (University of Victoria, 2011)
BA (University of Victoria, 2011)
“Studies on Math Education and Trigraph Homomorphisms”
Department of Mathematics and Statistics
Thursday, December 14, 2023
3:30 P.M.
Virtual Defence
Supervisory Committee:
Dr. Gary MacGillivray, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Jane Butterfield, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Richard Brewster, Department of Mathematics and Statistics, UVic (Member)
External Examiner:
Dr. Jacobus Swarts, Mathematics Department, Vancouver Island University
Chair of Oral Examination:
Dr. Marlea Clarke, Department of Political Science, UVic
Abstract
This thesis is comprised of two parts: (i) a study of homomorphisms of weak trigraphs and
(ii) an analysis of the effectiveness of the University of Victoria (UVic) Department of
Mathematics and Statistics’ Pretest. In the first part of the thesis, we study homomorphisms
of weak trigraphs. Results analogous to those for graph homomorphisms are developed. In
particular, we determine the complexity of deciding whether there is a weak trigraph
homomorphism of a weak trigraph G to a weak trigraph H, the complexity of deciding whether
a given weak trigraph has a weak trigraph homomorphism to a proper subgraph (the
complexity of deciding whether it is not a core) and describe an efficient algorithm based on
Consistency Checking that determines whether there is a weak trigraph homomorphism from
a given cactus weak trigraph to a fixed weak trigraph H. In the second part of the thesis, we
analyse the effectiveness of the UVic Pretest. First we compare the current online UVic
Pretest with the past paper Pretest in terms of their respective effectiveness in identifying
students who are ready for Calculus I. We also analyse the current online UVic Pretest in
greater detail, to identify which precalculus skills are most likely to predict success on that
test itself. Finally, we use odd ratios to categorize each question on the online UVic Pretest
and identify questions that are particularly useful to the test.
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Title: PIMS Data Science Seminar: Artificial intelligence for data integration in biology and medicine
Speaker: Youlian Pan, National Research Council of Canada
Date and time:
14 Dec 2023,
2:30pm -
3:30pm
Location: David Strong Building C108 and Zoom
Event type: Statistics seminar
Read full description
Zoom link.
This is our 3rd talk of the PIMS Data Science Seminar Series. PIMS requests all seminar participants to complete the demographics form online.
Abstract:
In this data explosion era, machine learning has accelerated research in biology and medicine at an unprecedent speed and in multiple dimensions. The increased data volume and capacity for data aggregation and analytics power, along with decreasing costs of genome sequencing has spurred the growth in bioinformatics and need for novel tools to integrate the highly heterogenous data from multiple sources and of varying types, and extract meaningful patterns. The big data analytics and AI tools have already created significant impact in many fields of life sciences including medicine. However, the data complexity and multi-dimensionality have led to technical challenges in developing and validating AI solutions that generalize to diverse populations and imped the progress in their implementation in clinical practice due to imbalance in data distribution across population demography and data sparsity. This leads to the unconscious biases in the generated models and algorithms. In this talk, the speaker will discuss applications of AI in biology and medical research, advances and major challenges.
Short bio of the speaker:
Dr. Youlian Pan is an international expert in integrative pattern recognition from big data in Life Sciences. He has authored and co-authored over 80 refereed articles and created significant applications of data mining, machine learning, AI and bioinformatics in genomics, transcriptomics and systems biology with various medical applications, such as cancers, infectious diseases and neurodegenerative diseases. He also has extensive research interest in plants’ pathogenesis and embryogenesis, their interaction with environment, and biological oceanography specifically in marine pollution. Dr. Pan is a Senior Research Scientist at the National Research Council Canada and an Adjunct Professor at the University of Victoria and Brock University. He received his PhD in Biology and Master of Computer Science from Dalhousie University. He has served at various capacities in editorial board of six international journals, such as Journal of Computations & Modeling, Open Medical Informatics, and Frontiers in Genetics, Microbiology and Plant Sciences; and various national and international grant evaluation panels such as Natural Sciences and Engineering Research Council (NSERC) of Canada, National Science Foundation (NSF) of US.
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Title: Eternal Domination Problems
Speaker: Ethan Williams, Universiity of Victoria
Date and time:
13 Dec 2023,
10:30am -
11:30am
Location: DTB A203 and Zoom
Event type: Graduate dissertations
Read full description
Notice of the Final Oral Examination
for the Degree of Master of Science
of
J. ETHAN WILLIAMS
BSc (University of Victoria, 2021)
“Eternal Domination Problems”
Department of Mathematics and Statistics
Wednesday, December 13, 2023
10:30 A.M.
David Turpin Building
Room A203
Supervisory Committee:
Dr. Gary MacGillivray, Department of Mathematics and Statistics, University of Victoria
(Co-Supervisor)
Dr. Richard Brewster, Department of Mathematics and Statistics, UVic (Co-Supervisor)
External Examiner:
Dr. William Klostermeyer, School of Computing, University of North Florida
Chair of Oral Examination:
Dr. Matt Moffitt, Department of Chemistry, UVic
Abstract
Consider placing mobile guards on the vertices of a graph. The vertices are then attacked by an assailant, requiring you to move guards to the attacked vertices. What is the minimum number of guards you need in order to be able to defend against any sequence of attacks? This question is the basis for the eternal domination problem. In this thesis we investigate this problem and introduce new parameters related to it.
These new parameters arise from changing three of the assumptions made when defining the game. Specifically we assume that any number of guards can move when defending against an attack; only one attack needs to be defended against at a time; and that any number of guards can occupy a vertex. Changing these assumptions gives rise to the maneuver, invasion, and stacking numbers respectively. We investigate these parameters throughout this thesis, especially as they relate to trees.
Additionally, we tackle the related problem of eternal Roman domination, which is based on the topic which originally gave rise to the eternal domination problem. We establish a best possible upper bound for this parameter over all graphs. Finally, we present exponential time algorithms for solving all of these problems, as well as a host of other related problems.
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Title: Putnam math competition
Date:
02 Dec 2023
Location: DTB A102
Event type: Education and outreach
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Interested students, please contact Peter Dukes at dukes@uvic.ca for an invitation link.
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Title: The relationship between zero forcing and vertex covers
Speaker: Michael Young, Carnegie Mellon University
Date and time:
30 Nov 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
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Abstract: Zero forcing is a type of graph propagation based on the
color-change rule: Given graph $G$, if each vertex of $G$ is colored either
white or blue, and vertex $v$ is a blue vertex with only one white neighbor
$w$, then change the color of $w$ to blue. In this talk we prove a
conjecture formulated by the automated conjecturing program called
\emph{TxGraffiti}. The conjecture states that in a claw-free graph, the
vertex cover number of the graph is at least the zero forcing number of the
graph. We also prove a relationships about the zero forcing and independence
number of a connected subcubic graph.
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Title: PIMS Emergent Research PDF Seminar: Spaces of geodesic triangulations of surfaces
Speaker: Yanwen Luo, SFU and UVic
Date and time:
29 Nov 2023,
9:30am -
10:30am
Location: via Zoom registration required
Event type: PIMS lectures
Read full description
Register for Zoom link.
In 1962, Tutte proposed a simple method to produce a straight-line embedding of a planar graph in the plane, known as Tutte’s spring theorem. It leads to a surprisingly simple proof of a classical theorem proved by Bloch, Connelly, and Henderson in 1984, which states that the space of geodesic triangulations of a convex polygon is contractible. In this talk, I will introduce spaces of geodesic triangulations of surfaces, review Tutte’s spring theorem, and present this short proof. It time permits, I will briefly report the recent progress in identifying the homotopy types of spaces of geodesic triangulations of general surfaces.
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Title: Random interlacement is a factor of i.i.d.
Speaker: Balazs Rath, Budapest University of Technology/ Renyi Institute
Date and time:
28 Nov 2023,
10:30am -
11:30am
Location: via Zoom
Event type: Probability and Dynamics seminar
Read full description
Zoom link.
Abstract: The random interlacement point process (introduced by Sznitman,
generalized by Teixeira) is a Poisson point process on the space of
labeled doubly infinite nearest neighbour trajectories modulo
time-shift on a transient graph G. We show that the random
interlacement point process on any transient transitive graph G is a
factor of i.i.d., i.e., it can be constructed from a family of i.i.d.
random variables indexed by vertices of the graph via an equivariant
measurable map. Our proof uses a variant of the soft local time method
(introduced by Popov and Teixeira) to construct the interlacement
point process as the almost sure limit of a sequence of finite-length
variants of the model with increasing length. We also discuss a more
direct method of proving that the interlacement point process is a
factor of i.i.d. which works if and only if G is non-unimodular.
Based on joint work with Márton Borbényi and Sándor Rokob.
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Title: The Heisenberg Spectral Triple and Associated Zeta Functions
Speaker: Brendan Steed, University of Victoria
Date and time:
27 Nov 2023,
10:00am -
11:00am
Location: David Turpin Building, Room A203
Event type: Graduate dissertations
Read full description
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Title: PIMS Data Science Seminar: A novel evolutionary, ensemble method for intrusion detection
Speaker: Belaid Moa, University of Victoria and Digital Research Alliance of Canada
Date and time:
24 Nov 2023,
2:00pm -
3:00pm
Location: Cornett A128 and Zoom
Event type: Statistics seminar
Read full description
Zoom link.
PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
Abstract: In this talk, we will share a new evolutionary but ensemble method, that enable us
to track different regimes of behavior and identify when the changes occurred.
As opposed to traditional methods that relies on statistical change tracking to detect intrusions,
we use the performance, and the predictive power of evolving models to detect when and which models can
or cannot describe the observations anymore. By doing so, we obtain a much fine-grain, more adaptive
outlier detection algorithm that can reliably model data while being robust to its variations.
The algorithm can be viewed as an evolutionary algorithm with growth and new generation capabilities,
but it is special in the sense that it includes ensemble of models with performance measures and
age decay corrections to evolve and compare models.
For some special cases, the algorithm can be related to Bayesian Change Point techniques.
Bio: Belaid Moa received the B.Sc. degree in electrical engineering from École Hassania
des Travaux Publics, Casablanca, Morocco, the M.Eng. degree in electronics and signal
processing from École Nationale Supérieure d'électronique, d'électrotechnique, d'informatique,
d'hydraulique et des Télécommunications, Toulouse, France, the DEA Diploma degree in Telecommunications
and Networks from the Institute National Polytechnique de Toulouse, Toulouse, and the Ph.D.
degree in computer science from the University of Victoria.
He is currently an adjunct faculty with ECE Dept., and Advanced Research Computing Specialist with the
Digital Research Alliance of Canada/BCDRI /University Systems, at the University of Victoria. He has
authored or co-authored many research articles and conference proceedings
in various journals and multi-disciplinary research areas
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Title: Innovative CVX-based Algorithms for Optimal Design Problems on Discretized Regions
Speaker: Hanan Abousaleh, University of Victoria
Date and time:
23 Nov 2023,
1:00pm -
2:00pm
Location: David Turpin Building, Room A203
Event type: Graduate dissertations
Read full description
Notice of the Final Oral Examination for the Degree of Master of Science
Hanan Abousaleh
BSc (University of Victoria, 2021)
Examining Committee
Supervisory Committee
Dr. Julie Zhou, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Michelle Miranda, Department of Mathematics and Statistics, UVic (Member)
External Examiner
Dr. Nilanjana Roy, Department of Economics, UVic
Chair of Oral Examination
Dr. Hong-Chuan Yang, Department of Electrical and Computer Engineering, UVic
Abstract
We focus on a class of optimization problems known as optimal design problems, where the goal is to select design points optimally with respect to some criterion of interest. For regression models, the optimality criterion is based on the statistical model itself and is often a function of the information matrix. We solve A-, D-, and EI-optimal design problems in this thesis. The CVX program in MATLAB is a modelling tool and solver for convex optimization problems. As with other numerical methods in the literature, formulating an optimal design problem in a CVX-compatible way requires a discrete design space. We develop a CVX-based algorithm to solve optimal design problems on large and irregular discrete spaces for multiple regression models. The algorithm uses innovative rules to add several design points at each iteration, and clusters nearby points together at the end of iteration. Furthermore, we provide useful guidelines for discretizing irregular regions. These are based on derived theoretical properties which relate optimal designs on continuous and discrete design spaces. Several numerical examples and their MATLAB codes are presented for A-, D-, and EI-optimal designs for both linear and generalized linear models. The optimal designs found via the CVX solver are better than those presented in the literature. In addition, our guidelines to discretizing design spaces improve the efficiency of optimal designs, especially over irregular regions. We find that our iterative procedure overcomes the bottlenecks of typical sequential and multiplicative algorithms.
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Title: Stacking Number for Eternal Domination
Speaker: Ethan Williams, University of Victoria
Date and time:
23 Nov 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: Eternal domination is a graph game where mobile guards are placed on vertices and then moved in order to defend against sequences of attacks. If only one guard is allowed to move in response to an attack, then it has been shown that there is no benefit to allowing multiple guards to occupy a vertex. It was conjectured that if all guards can move there would similarly be no benefit from multiple guards occupying a vertex. Finbow et al. showed this was untrue, and provided a construction demonstrating that there are graphs which need fewer guards when 2 guards are allowed on the same vertex. We extend these results to show that for any $k$ and $s$ there are $k$-connected graphs which need fewer guards when up to $s$ guards are allowed on any vertex.
This is joint work with Georgia Penner.
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Title: Clustering for Climate Science Insights
Speaker: Dr. John R.J. Thompson, UBC Okanagan
Date and time:
22 Nov 2023,
3:00pm -
4:00pm
Location: via Zoom registration required
Event type: Statistics seminar
Read full description
PCIC is pleased to announce an upcoming talk on Wednesday, November 22nd, titled, Clustering for Climate Science Insights, as part of our Pacific Climate Seminar Series.
This talk will be delivered by Dr. John R.J. Thompson, an Assistant Professor at the University of British Columbia (Okanagan campus) whose areas of expertise are nonparametric and applied statistics and machine learning. This talk will be held between 3 p.m. and 4 p.m. Pacific Time, via Zoom meetings. For more on this talk, including registration information and an abstract, see the talk’s page on our site.
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Title: PIMS Emergent Research PDF Seminar: Around Artin's primitive root conjecture
Speaker: Paul Péringuey, University of British Columbia
Date and time:
22 Nov 2023,
9:30am -
10:30am
Location: via Zoom registration required
Event type: PIMS lectures
Read full description
Register via Zoom
Abstract: In this talk we will first discuss this soon to be 100 years old conjecture, which states that the set of primes for which an integer $a$ different from $-1$ or a perfect square is a primitive root admits an asymptotic density among all primes. In 1967 Hooley proved this conjecture under the Generalized Riemann Hypothesis.
After that, we will look into a generalization of this conjecture, where we don't restrain ourselves to look for primes for which $a$ is a primitive root but instead elements of an infinite subset of $\N$ for which $a$ is a generalized primitive root. In particular, we will take this infinite subset to be either $\N$ itself or integers with few prime factors.
Speaker Biography: Paul Péringuey is a PIMS Postdoctoral fellow at the University of British Columbia where he is working with Prof. Greg Martin, under the sponsorship of the PIMS Collaborative Research Group "L-Functions in Analytic Number Theory". He obtained his PhD in 2022 at Université de Lorraine under the supervision of Cécile Dartyge. His area of research is in Analytic Number Theory, Comparative Prime Number Theory, as well as Additive Combinatorics.
Poster: The poster for the talk is available.
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Title: Some results on Levy spin glasses
Speaker: Arnab Sen, University of Minnesota
Date and time:
21 Nov 2023,
2:30pm -
3:30pm
Location: Zoom
Event type: Probability and Dynamics seminar
Read full description
Zoom link
.
Abstract. We study a mean-field spin glass model whose coupling distribution has a power-law tail with exponent \alpha \in (0, 2). This is known as Levy spin glasses in literature. Though it is a fully connected model, many of its important characteristics are driven by the presence of strong bonds that have a sparse structure. In this sense, the Levy model sits between the widely studied Sherrington-Kirkpatrick model (with Gaussian couplings) and diluted spin glass models, which are more realistic but harder to understand. In this talk, I will report a number of rigorous results on the Levy model. For example, when 1< \alpha < 2, in the high-temperature regime, we obtain the limit and the fluctuation of the free energy. Also, we can determine the behaviors of the site and bond overlaps at the high temperature. Furthermore, we establish a variational formula of the limiting free energy that holds at any temperature. Interestingly, when 0< \alpha < 1, the effect of the strong bonds becomes more pronounced, which significantly changes the behavior of the model. For example, the free energy requires a different normalization (N^{1/\alpha} vs N), and its limit has a simple description via a Poisson point process at any temperature.
This is a joint work with Wei-Kuo Chen and Heejune Kim.
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Title: PIMS Network-wide Colloquium: AI4Crypto
Speaker: Kristin Lauter, Meta
Date and time:
16 Nov 2023,
1:30pm -
2:30pm
Location: via Zoom registration required
Event type: PIMS lectures
Read full description
Speaker Bio:
Kristin Lauter is an American mathematician and cryptographer whose research interest is broadly in application of number theory and algebraic geometry in cryptography. She is particularly known for her work in the area of elliptic curve cryptography. She was a researcher at Microsoft Research in Redmond, Washington, from 1999 - 2021, and the head of the Cryptography Group from 2008 - 2021; her group developed Microsoft SEAL. In April 2021, Lauter joined Facebook AI Research (FAIR) as the West Coast Head of Research Science. She became the President-Elect of the Association for Women in Mathematics in February 2014 and served as President from 2015 - 2017.
Registration:
Participants register once on Zoom and can attend any of the Colloquium talks. Please remember to download the calendar information to save the dates on your calendar. PIMS will resend the confirmation from Zoom prior to the event date.
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Title: Ramsey numbers of bounded degree trees versus general graphs
Speaker: Matias Pavez-Signe, University of Chile
Date and time:
09 Nov 2023,
10:00am -
11:00am
Location: via Zoom and Clearihue C111
Event type: Discrete math seminar
Read full description
Zoom link.
Abstract: For every $k\ge 2$ and $\Delta$, we prove that there exists a constant $C_{\Delta,k}$ such that the following holds. For every graph $H$ with $\chi(H)=k$ and every tree with at least $C_{\Delta,k}|H|$ vertices and maximum degree at most $\Delta$, the Ramsey number $R(T,H)$ is $(k-1)(|T|-1)+\sigma(H)$, where $\sigma(H)$ is the size of a smallest colour class across all proper $k$-colourings of $H$. This is tight up to the value of $C_{\Delta,k}$, and confirms a conjecture of Balla, Pokrovskiy, and Sudakov.
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Title: Dimers on a Riemann surface and compactified free field
Speaker: Mikhail Basok, University of Helsinki
Date and time:
07 Nov 2023,
9:30am -
10:30am
Location: via Zoom
Event type: Probability and Dynamics seminar
Read full description
Abstract: In this talk I will be speaking about the dimer model sampled on a general Riemann surface. Dimer model on a graph consists of sampling a random perfect matching with the probability proportional to the product of edge weights. In the case when the graph is planar, perfect matchings are in correspondence with their height functions defined on faces of the graph. Given a sequence of graphs approximating a given planar domain in a small mesh size, one can ask whether the underlying sequence of dimer height functions has a scaling limit and how to describe it. The landmark result of Kenyon asserts that in the case of a simply-connected domain approximated by Temperley polygons on the square grid the fluctuations of the height functions around their means converge to the (properly normalized) Gaussian free field in the target domain. The same result in the case of general Temperley graphs was established by Berestycki, Laslier and Ray 15 years later.
The dimer height function can still be defined when the graph is not planar, but is embedded into a general Riemann surface. In this case the height function becomes additively multivalued and is expected to converge to the compactified free field on the surface in the scaling limit. Recently, this problem was studied by Berestycki, Laslier and Ray in the case of general Temperley graphs embedded into the Riemann surface. Using soft probabilistic methods they proved the scaling limit exists, is conformally invariant and does not depend on a particular sequence of graphs. However, its identification with the compactified free field was missing. My goal is to fill this gap by studying the same problem from the perspective of discrete complex analysis. For this I consider graphs embedded into locally flat Riemann surfaces with conical singularities and satisfying certain geometric assumptions with respect to the local Euclidean structure. Using various analytic methods (both discrete and continuous counterparts are non-trivial) I obtain convergence to the compactified free field when the Riemann surface is chosen generically. Moreover, I am able to prove that the tightness of the underlying height fluctuations always implies their convergence to the compactified free field.
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Title: Coast Combinatorics Conference
Date:
04 Nov 2023
Location: Clearihue Building, Room A127
Event type: Conferences and workshops
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The Coast Combinatorics Conferences are informal, low-key meetings that welcome 30-minute (or so) talks on any topic in discrete mathematics and/or theoretical computer science. There is no registration fee, no main speaker, and you may on your own for coffee etc. at a nearby cafe. There is often an informal social event at the end of the day.
Everyone is welcome to attend the CCC. Please let us know if you are coming by sending email to Gary MacGillivray: gmacgill at UVic dot ca. It makes planning easier.
For more information and a schedule see the conference website.
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Title: Using auxiliary information for estimation with left truncated data
Speaker: Leilei Zeng, University of Waterloo
Date and time:
03 Nov 2023,
2:00pm -
3:00pm
Location: Cornett A128 and Zoom
Event type: Statistics seminar
Read full description
This talk is co-sponsored by Pacific Institute for the Mathematical Sciences (PIMS).
This seminar will be in person and available through Zoom.
PIMS requests all seminar participants to complete the demographics form online at https://ubc.ca1.qualtrics.com/jfe/form/SV_6QcNr2rQcIlQGyy
.
Abstract:
In life history studies one often encounters situations where individuals in a population are eligible to enroll only if the response time does not exceed an associated censoring time, which leads to the so called left truncated lifetime data. While auxiliary information for the truncated individuals from the same or similar cohorts may be available, challenges arise due to the practical issue of accessibility of individual-level data and taking account of various sampling conditions for different cohorts. We propose a likelihood-based method for incorporating auxiliary data to eliminate the bias due to left-truncation and improve efficiency. Simulation results and an application to data from a longitudinal study of aging are given.
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Title: Counting unit area and unit perimeter triangles
Speaker: Kenneth Moore, University of British Columbia
Date and time:
02 Nov 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: A broad class of problems in extremal geometry can be characterized as follows. Fix a positive integer k and a property of k-tuples of points in R^2. The problem is then to determine how many k-tuples in an n-point set in R^2 can have the chosen property. One of the most famous instances of this form of problem is the unit distance problem, asked by Erdős in 1946. Here, the special property is pairs of points being precisely distance one apart. Another pair of well-studied open problems is to determine the maximum number of triples that determine a triangle of unit area or unit perimeter. In this presentation we will discuss recent progress on these triangle problems, particularly our new bounds on the number of unit perimeter triangles from earlier this year.
This talk is based on a joint work with Ritesh Goenka and Ethan White.
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Title: How the Tulips get their Stripes
Speaker: Thomas Hillen, University of Alberta
Date and time:
01 Nov 2023,
2:30pm -
3:30pm
Location: DTB A203
Event type: Applied math seminar
Read full description
Zoom link: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09
Abstract: Tulips have captivated human interest for centuries, with their vibrant colors and unique shapes. Particularly striped tulips have been highly popular, leading to the “tulipomania” in the Dutch Golden Age. But how do the tulips get their stripes? Maybe Turing can help?
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Title: Lie-Poisson Neural Networks (LPNets): Data-Based Computing of Hamiltonian Systems with Symmetries
Speaker: Vakhtang Putkaradze, University of Alberta
Date and time:
30 Oct 2023,
2:30pm -
3:30pm
Location: DTB A-203
Event type: Applied math seminar
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Abstract: Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The idea of PINNs is to approximate the equations and boundary and initial conditions through a loss function for a neural network. PINNs combine the efficiency of data-based prediction with the accuracy and insights provided by the physical models. However, applications of these methods to predict the long-term evolution of systems with little friction, such as many systems encountered in space exploration, oceanography/climate, and many other fields, need extra care as the errors tend to accumulate, and the results may quickly become unreliable.
We provide a solution to the problem of data-based computation of Hamiltonian systems utilizing symmetry methods. Many Hamiltonian systems with symmetry can be written as a Lie-Poisson system, where the underlying symmetry defines the Poisson bracket. For data-based computing of such systems, we design the Lie-Poisson neural networks (LPNets). We consider the Poisson bracket structure primary and require it to be satisfied exactly, whereas the Hamiltonian, only known from physics, can be satisfied approximately. By design, the method preserves all special functions of the bracket (Casimirs) to machine precision. LPNets yield an efficient and promising computational method for many particular cases, such as rigid body or satellite motion (the case of SO(3) group), Kirchhoff's equations for an underwater vehicle (SE(3) group), and others.
Joint work with Chris Eldred (Sandia National Lab), Francois Gay-Balmaz (CNRS and ENS, France), and Sophia Huraka (U Alberta). The work was partially supported by an NSERC Discovery grant.
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Title: imii: an automated workflow for plant virus diagnostics using high-throughput genome sequencing data
Speaker: Haochen Ning, University of Victoria
Date and time:
27 Oct 2023,
2:00pm -
3:00pm
Location: Cornett A128
Event type: Statistics seminar
Read full description
Abstract:
Plant virus infection causes enormous economic loss, $350 billion worldwide in 2021. We focus on grapevine viruses, which caused Canadian grape growers’ annual loss of over $23 million. Once infected by a virus, the grapevine remains infected for life and must be replaced, since no therapeutic treatments are available. So, diagnosis of virus infection is critical for disease control. Collaborating with researchers from CFIA and other institutes, we are developing a genomic-sequencing-based diagnostic test to detect virus infections of grapevines. More information about this project can be found at https://www.bloomberg.com/press-releases/2020-10-27/-10m-in-funding-coming-to-bc-researchers-for-improved-grapevine-and-cannabis-management.
My role is to support the method/software development to decide if a sample is infected by any virus (from a list of ~1000 viruses) based on its genomic sequencing data. In this talk, I will briefly discuss our recent research results from this project.
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Title: The distributive absorption method in Latin squares
Speaker: Alp Muyesser, University of College London
Date and time:
26 Oct 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
A Latin square is an n by n grid filled with n symbols so that each symbol appears exactly once in every row and column. A transversal in a Latin square is a selection of entries with no row, column, or symbol repetition. The study of transversals in Latin squares is as old as combinatorics, going back to Euler's work in the 18th century. A lot of exciting progress has been made in this area in the past few years. In 2020, Kwan proved that, with high probability, a random Latin square contains a full transversal (hitting each row and column). In the other extreme, in 2022, Müyesser and Pokrovskiy characterised the "algebraic" Latin squares which contain full transversals. Very recently, Montgomery proved that all Latin squares contain a transversal hitting all but one row. A key technique that is used in each of these results is the "distributive absorption method", introduced in 2014 by Montgomery to find spanning trees in random graphs. In this talk, we will give a gentle introduction to this technique.
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Title: C*-algebras of submonoids of the Thompson group F, Part 2
Speaker: Marcelo Laca, Universiity of Victoria
Date and time:
25 Oct 2023,
3:30pm -
4:30pm
Location: CLE A 326
Event type: Operator theory seminar
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Abstract: We consider monoids M_k generated by the first k+1 generators of the infinite presentation of the Thompson group F
F=⟨x0,x1,x2,…∣ xjxi=xixj+1 for j>i⟩.
The standard normal form for F breaks down for these monoids and we develop a new reduced form that works in F and every Mk and allows us to analyze their constructible right ideal structure. We show that there exist embeddings Mk↪Mk+1 for which the associated Toeplitz algebras are functorial, and then we study the directed system of Toeplitz algebras λ(Mk)↪λ(Mk+1). We characterize faithful representations and show that the boundary quotients are purely infinite simple.
This is joint work in progress with A. an Huef, B. Nucinkis, I. Raeburn and C. Sehnem.
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Title: Weyl's law for Liouville quantum gravity
Speaker: Mo Dick Wong, Durham UK
Date and time:
24 Oct 2023,
10:30am -
11:30am
Location: via Zoom
Event type: Probability and Dynamics seminar
Read full description
Abstract: The Liouville quantum gravity (LQG) surface, formally defined as a 2-dimensional Riemannian manifold with conformal factor being the exponentiation of a Gaussian free field, is closely related to random planar geometry as well as scaling limits of models from statistical mechanics. In this talk we consider the bounded, simply connected setting, and explain the Weyl's law for the asymptotics of the eigenvalues of the (random) Laplace-Beltrami operator. We also discuss a few open problems about the spectral geometry of LQG. This is a joint work with Nathanael Berestycki.
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Title: PIMS Network-wide Colloquium: Surface sums and Yang-Mills gauge theory
Speaker: Scott Sheffield, MIT
Date and time:
19 Oct 2023,
1:30pm -
2:30pm
Location: via Zoom registration required
Event type: PIMS lectures
Read full description
Register for talk series.
Constructing and understanding the basic properties of Euclidean Yang-Mills theory is a fundamental problem in physics. It is also one of the Clay Institute's famous Millennium Prize problems in mathematics. The basic problem is not hard to understand. You can begin by describing a simple random function from a set of lattice edges to a group of matrices. Then you ask whether you can construct/understand a continuum analog of this object in one way or another. In addition to a truly enormous physics literature, this topic has inspired research within many major areas of mathematics: representation theory, random matrix theory, probability theory, differential geometry, stochastic partial differential equations, low-dimensional topology, graph theory and planar-map combinatorics.
Attempts to understand this problem in the 1970's and 1980's helped inspire the study of "random surfaces" including Liouville quantum gravity surfaces. Various relationships between Yang-Mills theory and random surface theory have been obtained over the years, but many of the most basic questions have remained out of reach. I will discuss our own recent work in this direction, as contained in two long recent papers relating "Wilson loop expectations" (the fundamental objects in Yang-Mills gauge theory) to "sums over spanning surfaces."
1. Wilson loop expectations as sums over surfaces on the plane (joint with Minjae Park, Joshua Pfeffer, Pu Yu)
2. Random surfaces and lattice Yang-Mills (joint with Sky Cao, Minjae Park)
The first paper explains how in 2D (where Yang-Mills theory is more tractable) one can interpret continuum Wilson loop expectations purely in terms of flat surfaces. The second explains a general-dimensional interpretation of the Wilson loop expectations in lattice Yang-Mills theory in terms of discrete-and not-necessarily-flat surfaces, a.k.a. embedded planar maps.
Speaker Biography:
Scott Sheffield is the Leighton Family Professor of Mathematics at MIT. He is a leading figure at the interface of mathematical physics and probability. He has held positions at Microsoft Research, Berkeley, the Institute for Advanced Study and New York University. He received the Rollo Davidson and Loève prizes in probability and has twice spoken at the International Congress of Mathematicians
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Title: Stability analysis of a single-species logistic model with time delay and constant inflow
Speaker: Yasuhiro Takeuchia, Aoyama Gakuin University, Kanagawa, Japan
Date and time:
19 Oct 2023,
11:30am -
12:30pm
Location: DSB C114
Event type: Applied math seminar
Read full description
We consider a single-species system with distributed delay and constant inflow. First, we consider the case with time delay in which the constant inflow does not exist. The condition of Hopf bifurcation for the delay order of k = 2 is known, but is not given clearly for the delay order of k ≥ 3. We have obtained the relationship among systems parameters for Hopf bifurcation. Next, we consider the case in which the constant inflow exists. In this case, the positive equilibrium changes to be unstable from being stable first, and return to be stable again by increasing with average time delay T for small intrinsic growth rate r. It is found that there exists important difference between the delay orders k = 2 and k ≥ 3. For k = 2, the equilibrium can be stable for large T and any r(> 0), but for k ≥ 3, the equilibrium is unstable for large T and r .
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Title: Structural Ramsey theory and group actions
Speaker: Chris Eagle, University of Victoria
Date and time:
19 Oct 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: Structural Ramsey theory generalizes classical Ramsey theory by considering classes of finite sets with additional structure (such as finite groups or finite partial orders) and colourings of their substructures. When the class satisfies an appropriate amalgamation condition it is possible to assemble all of the structures in the class into a countably infinite structure, which is known as the Fraisse limit of the class. The goal of this talk is to describe a deep connection (due to Kechris, Pestov, and Todorcevic) between the structural Ramsey theory of a class of finite structures and the actions of the automorphism group of the class' Fraisse limit. This connection will be illustrated with a Ramsey theorem for finite-dimensional algebras of matrices.
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Title: C*-algebras of submonoids of the Thompson group F
Speaker: Marcelo Laca, University of Victoria
Date and time:
18 Oct 2023,
3:30pm -
4:45pm
Location: CLE A 326
Event type: Operator theory seminar
Read full description
Abstract: We consider monoids M_k generated by the first k+1 generators of the infinite presentation of the Thompson group F
F=⟨x0,x1,x2,…∣ xjxi=xixj+1 for j>i⟩.
The standard normal form for F breaks down for these monoids and we develop a new reduced form that works in F and every Mk and allows us to analyze their constructible right ideal structure. We show that there exist embeddings Mk↪Mk+1 for which the associated Toeplitz algebras are functorial, and then we study the directed system of Toeplitz algebras λ(Mk)↪λ(Mk+1). We characterize faithful representations and show that the boundary quotients are purely infinite simple.
This is joint work in progress with A. an Huef, B. Nucinkis, I. Raeburn and C. Sehnem.
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Title: Some Trees are Always More Plentiful than Others
Speaker: Jon Noel, University of Victoria
Date and time:
17 Oct 2023,
2:30pm -
3:20pm
Location: DSB C130
Event type: Probability and Dynamics seminar
Read full description
Abstract: The homomorphism density of a graph H in a graph G is the probability that a random function from the vertex set of H to the vertex set of G is a graph homomorphism. A natural question studied by Leontovich and Sidorenko back in the 80s and 90s is: given two trees, say H and T, under what conditions does the homomorphism density function of H dominate the homomorphism density function of T? We apply a beautiful information-theoretic approach of Kopparty and Rossman to reduce this problem to solving a particular linear program. We then use this perspective to answer the question for various pairs H and T of trees. Roughly speaking, short bushy trees tend to be more numerous than tall skinny ones, but there are exceptions. Joint work with Natalie Behague, Gabriel Crudele and Lina M. Simbaqueba.
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Title: Multivariate Point Process Frameworks for Simultaneously Recorded Neural Spike Trains
Speaker: Reza Ramezan, University of Waterloo
Date and time:
13 Oct 2023,
1:30pm -
2:30pm
Location: CLE A320
Event type: Statistics seminar
Read full description
Abstract:
Neural spike trains are sequences of consecutive electrochemical waves generated by the nerve cells through which they communicate. These waves are localized in time hence called spikes. Statistical analysis of simultaneously recorded neural spike trains from an ensemble of neurons is a challenging problem from both statistical and computational points of view. I will discuss some biologically inspired multivariate point process models for such data, namely- Skellam Process with Resetting (SPR) and a generalization of it under a continuous-time latent factor model (LFM). To the best of our knowledge, this generalization of the SPR is the first continuous-time multivariate LFM for studying neuronal interactions and functional connectivity. Leveraging the computational efficacy of approximate Bayesian inference, we show that our model can handle larger neuronal ensembles compared to alternative approaches. Using experimental data from a classical conditioning study on the prefrontal cortex in rats, we shed light on our understanding of cue and outcome value encoding.
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Title: Borel line graphs
Speaker: Anton Bernshteyn, Georgia Institute of Technology
Date and time:
12 Oct 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: The line graph of a graph $G$ is the graph $L$ with vertex set $E(G)$ in which two vertices are adjacent if and only if the corresponding edges of $G$ share an endpoint. A famous theorem of Beineke characterizes the class of line graphs by a list of 9 forbidden induced subgraphs. In this talk we will be interested in the following question: Given an "explicit description" of a line graph $L$, when does the underlying graph $G$ also have an "explicit description"? To use the precise terminology (which I will define in the talk), when is a Borel graph $L$ a line graph of a Borel graph $G$? It turns out that to answer this question, we need to expand Beineke's list to include a tenth forbidden subgraph. This is joint work with James Anderson.
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Title: Fibre-Dirac classes for discrete group actions on manifolds
Speaker: Heath Emerson, University of Victoria
Date and time:
11 Oct 2023,
3:30pm -
5:00pm
Location: CLE A326
Event type: Operator theory seminar
Read full description
Abstract: I discuss a modest framework for doing Noncommutative Geometry for
certain examples of `noncommutative manifolds,' namely crossed products
of discrete groups acting smoothly on manifolds. The analogue of the
`fundamental class' in topology for these C*-algebras is something I call a `fibre class.'
I will discuss the numerous examples of these fibre classes, and explain why the definition is
so great.
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Title: Convex optimization for statistical mechanics
Speaker: Minjae Cho, Princeton
Date and time:
11 Oct 2023,
2:30pm -
3:30pm
Location: DTB A203
Event type: Applied math seminar
Read full description
Abstract: In this talk, we will discuss how convex optimization can be used to study statistical mechanics, with a focus on the example of the lattice Ising model. After introducing the Gibbs measure that describes the system, we will explain how convex optimization produces results that asymptotically converge to the Gibbs measure. If time permits, we will also explore the relationship between Markov chain Monte-Carlo and convex optimization for the Ising model.
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Title: Characterizing the law of branching diffusion by minimizing relative entropy
Speaker: Nitya Gadhiwala , University of British Columbia
Date and time:
10 Oct 2023,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
Read full description
Abstract: Recent advances in single cell sequencing has led to the availability of gene expression data. We model the trajectories of cells in gene expression space using a diffusion and gradient drift process that also undergoes branching. In this talk, we show that one can recover the law of this process given time marginals using an entropy minimization problem. The optimization is over the set of all processes with the same branching mechanism and given marginals. We prove that among these the one which minimizes the relative entropy with respect to a reference branching Brownian motion is the ground truth. We conclude this talk with a general result showing that the solution to a entropy minimization problem with respect to a Markov reference measure with given marginals is also Markov.
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Title: Proper rainbow saturation
Speaker: Andrew Lane, University of Victoria
Date and time:
05 Oct 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract (plain text):
Given a graph H, say that a graph G is properly rainbow H-saturated if there exists a rainbow H-free proper edge-colouring of G and, for any non-edge e of G, every proper edge-colouring of G+e contains a rainbow copy of H. The proper rainbow saturation number is the minimum number of edges in a properly rainbow H-saturated graph on n vertices. This is a natural variant of the graph saturation problem based on the rainbow extremal number. In this talk, we will prove bounds on the proper rainbow saturation number for specific classes of graphs, and we will prove general bounds on the proper rainbow saturation number using related saturation numbers.
Joint work with Natasha Morrison.
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Title: High-dimension expansion of the critical intensity of the random connection model
Speaker: Mathew Dickson, UBC
Date and time:
03 Oct 2023,
2:30pm -
3:30pm
Location: via Zoom
Event type: Probability and Dynamics seminar
Read full description
Abstract: The random connection model (RCM) is a random graph model where the vertices are given by a Poisson point process with a given intensity, $\lambda>0$, and the edges exist independently with a probability that depends upon the relative positions of the two vertices in question. A standard example would be the Gilbert disc model. As we vary $\lambda$, we observe a percolation phase transition at a critical intensity $\lambda_c>0$. Finding $\lambda_c$ is only possible in very exceptional cases, so here we investigate a high-dimension asymptotic expansion for the critical intensity that applies for a great variety of RCMs. This is based on arXiv:2309.08830 with Markus Heydenreich (Universität Augsburg).
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Title: Lansdowne Lecture: Development and evaluation of statistical methodology - Lessons from genome-wide association studies
Speaker: Dr. Shelley Bull, Lunenfeld-Tanenbaum Research Institute
Date and time:
28 Sep 2023,
4:00pm -
5:00pm
Location: Clearihue C112
Read full description
As a statistical scientist working in epidemiology and biostatistics, Dr. Shelley Bull has been recognized for her research in medicine, public health, genetics, epidemiology and statistical methodology as well as her leadership, supervision and mentorship, by awards from the Statistical Society of Canada and the International Genetic Epidemiology Society.
Using a research project in statistical methods for region-level analysis of genome-wide association studies as an illustration, this statistically oriented talk will explain the motivation and development of an alternative approach to GWAS data analysis, and consider criteria and techniques for method evaluation.
See poster (PDF file).
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Title: The number of distinct eigenvalues realized by a symmetric matrix with a given graph
Speaker: Shahla Nasserasr, Rochester Institute of Technology
Date and time:
28 Sep 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
For a simple graph $G$ on $n$ vertices, let $\mathcal{S}(G)$ be the set of all $n\times n$ real symmetric matrices $A=[a_{i,j}]$ with $a_{i,j}\neq 0$ if and only if $\{i,j\}$ is an edge of $G$. There are no restrictions on the diagonal entries of $A$. The inverse eigenvalue problem for a graph $G$ (IEP-G) seeks to determine all possible spectra of matrices in $\mathcal{S}(G)$.
One of the relaxations of the IEP-G is to determine the minimum number of distinct eigenvalues of a matrix in $\mathcal{S}(G)$ for a given graph $G$. This parameter is denoted by $q(G)$ and it is called the minimum number of distinct eigenvalues of $G$.
In this presentation, we will review some of the results and the techniques from recent developments about $q(G)$.
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Title: Fokas Diagonalization
Speaker: Dave Smith, Yale-NUS
Date and time:
27 Sep 2023,
2:30pm -
3:20pm
Location: DTB A203
Event type: Applied math seminar
Read full description
Abstract: We describe a new form of diagonalization for linear two point constant coefficient differential operators with arbitrary linear boundary conditions. Although the diagonalization is in a weaker sense than that usually employed to solve initial boundary value problems (IBVP), we show that it is sufficient to solve IBVP whose spatial parts are described by such operators. We argue that the method described may be viewed as a reimplementation of the Fokas transform method for linear evolution equations on the finite interval. The results are extended to multipoint and interface operators, including operators defined on networks of finite intervals, in which the coefficients of the differential operator may vary between subintervals, and arbitrary interface and boundary conditions may be imposed; differential operators with piecewise constant coefficients are thus included.
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Title: UVic Math Competition
Date and time:
26 Sep 2023,
4:30pm -
6:30pm
Location: DSB C130
Event type: Education and outreach
Read full description
The UVic Mathematics Competition is held annually in the fall. The competition will be held on Tuesday, September 26, 2023 between 4:30-6:30 pm in DSB C130. There are monetary prizes. To participate, just show up.
Here are some recent question papers: 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006.
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Title: Lansdowne Lecture: Genome-wide association studies: How molecular technology, biology, epidemiology, and statistical genetics came together
Speaker: Dr. Shelley Bull, Lunenfeld-Tanenbaum Research Institute
Date and time:
26 Sep 2023,
3:30pm -
5:20pm
Location: Cornett A225
Read full description
As a statistical scientist working in epidemiology and biostatistics, Dr. Shelley Bull has been recognized for her research in medicine, public health, genetics, epidemiology and statistical methodology as well as her leadership, supervision and mentorship, by awards from the Statistical Society of Canada and the International Genetic Epidemiology Society.
In this general audience lecture, Bull will talk about how genome-wide studies and methods have evolved, highlight landmark papers, and give examples of key contributions from statistical methodology. The talk will close with comments on recent developments in biobanks, multi-omics and global population studies.
See poster (PDF file).
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Title: Monomer-Dimer Models in the Disordered Setting
Speaker: Kesav Krishnan, University of Victoria
Date and time:
26 Sep 2023,
2:30pm -
3:20pm
Location: DSB C130
Event type: Probability and Dynamics seminar
Read full description
Abstract: I will introduce the Monomer-Dimer model, a Gibbs probability measure on the space of (not necessarily perfect) weighted matchings on a graph. I will recap some known results of Heilmann and Lieb which establish the absence of a phase transition. I will then describe how many of these results carry over when we consider iid random weights to the edges and vertices. In certain special cases, we show how laws of large numbers and central limit theorems can be established for partition function as well as statistics such as the number of unpaired vertices.
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Title: Investigating the Relationship between Bayes Factors and Credible Intervals
Speaker: Zoe Lyu, University of Victoria
Date and time:
22 Sep 2023,
2:00pm -
3:00pm
Location: via Zoom
Event type: Graduate dissertations
Read full description
The Final Oral Examination for the Degree of
Master of Science
(Department of Mathematics and Statistics)
ZIYI LYU
University of Waterloo, 2021 (B.Math)
Investigating the Relationship between Bayes Factors and Credible Intervals
Friday, September 22nd, 2023 2:00 P.M
Online
Supervisory Committee:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Member)
Chair of Oral Examination:
Dr. Ryan Budney, Department of Mathematics and Statistics, UVic
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Title: PIMS Network-Wide Colloquium - Understanding arithmetic and geometry through cutting and pasting
Speaker: Ravi Vakil, Stanford University
Date and time:
21 Sep 2023,
1:30pm -
2:30pm
Location: via Zoom registration required
Event type: PIMS lectures
Read full description
Register for talk.
Euler’s famous formula tells us that (with appropriate caveats), a map on the sphere with f countries (faces), e borders (edges), and v border-ends (vertices) will satisfy v-e+f=2. And more generally, for a map on a surface with g holes, v-e+f=2-2g. Thus we can figure out the genus of a surface by cutting it into pieces (faces, edges, vertices), and just counting the pieces appropriately. This is an example of the topological maxim “think globally, act locally”. A starting point for modern algebraic geometry can be understood as the realization that when geometric objects are actually algebraic, then cutting and pasting tells you far more than it does in “usual” geometry. I will describe some easy-to-understand statements (with hard-to-understand proofs), as well as easy-to-understand conjectures (some with very clever counterexamples, by M. Larsen, V. Lunts, L. Borisov, and others). I may also discuss some joint work with Melanie Matchett Wood.
Speaker Biography: Ravi Vakil is a Professor of Mathematics and the Robert K. Packard University Fellow at Stanford University, and was the David Huntington Faculty Scholar. He received the Dean's Award for Distinguished Teaching, an American Mathematical Society Centennial Fellowship, a Frederick E. Terman fellowship, an Alfred P. Sloan Research Fellowship, a National Science Foundation CAREER grant, the presidential award PECASE, and the Brown Faculty Fellowship. Vakil also received the Coxeter-James Prize from the Canadian Mathematical Society, and the AndrÉ-Aisenstadt Prize from the CRM in MontrÉal. He was the 2009 Earle Raymond Hedrick Lecturer at Mathfest, and a Mathematical Association of America's Pólya Lecturer 2012-2014. The article based on this lecture has won the Lester R. Ford Award in 2012 and the Chauvenet Prize in 2014. In 2013, he was a Simons Fellow in Mathematics.
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Title: Nowhere-zero 8-flows in 3-edge-connected signed graphs
Speaker: Kathryn Nurse, Simon Fraser University
Date and time:
21 Sep 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: In 1954, Tutte made a conjecture that every graph without a cut-edge has a nowhere-zero 5-flow. A parallel conjecture to this, but for signed graphs is Bouchet’s Conjecture (1983) that every signed graph without the obvious obstruction has a nowhere-zero 6-flow. We prove that Bouchet’s Conjecture holds in the special case of 3-edge-connected graphs when 6 is replaced with 8.
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Title: Ramsey theory of random graphs: On the Kohayakawa-Kreuter conjecture
Speaker: Joseph Hyde, Universiity of Victoria
Date and time:
19 Sep 2023,
2:30pm -
3:20pm
Location: DSB C130
Event type: Probability and Dynamics seminar
Read full description
Abstract: For graphs $G, H_1,\dots,H_r$, write $G \to (H_1, \ldots, H_r)$ to denote the property that whenever we $r$-colour the edges of $G$, there is a monochromatic copy of $H_i$ in colour $i$ for some $i \in \{1,\dots,r\}$.
Mousset, Nenadov and Samotij proved an upper bound on the threshold function for the property that $G_{n,p} \to (H_1,\dots,H_r)$, thereby resolving the 1-statement of the Kohayakawa--Kreuter conjecture.
We reduce the 0-statement of the Kohayakawa--Kreuter conjecture to a natural deterministic colouring problem and resolve this problem for almost all cases,
which in particular includes (but is not limited to)
when $H_2$ is strictly 2-balanced and either has density greater than 2 or is not bipartite.
In addition, we extend our reduction to hypergraphs, proving the colouring problem in almost all cases there as well.
Joint work with Candida Bowtell (University of Warwick) and Robert Hancock (Universität Heidelberg)
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Title: Recent progress on the eternal eviction game
Speaker: Virgelot Virgile, Universiity of Victoria
Date and time:
14 Sep 2023,
10:00am -
11:00am
Location: Clearihue C111
Event type: Discrete math seminar
Read full description
Abstract: In the eternal eviction game, a set of guards placed on the vertices of (a dominating set of) a graph G must move to defend the graph against attacks on those of its vertices that contain guards, while maintaining a dominating set of G. The eternal eviction number of G is the minimum number of guards required to defend G against any sequence of attacks. In this talk, we will present some recent progress on the game. In particular, we will show that for any integer $k \geq 1$, there exists $f(k)$ such that any graph with independence number at most $k$ has eviction number at most $f(k)$.
This is joint work with Gary MacGillivray and Kieka Mynhardt.
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Title: The Oseledets Theorem and AF-algebras
Speaker: Ian Putnam, University of Victoria
Date and time:
13 Sep 2023,
3:30pm -
4:30pm
Location: CLE A326
Event type: Operator theory seminar
Read full description
Abstract: I will begin with some basics about Approximately Finite
dimensional C*-algebras or AF-algebras. These have played a fundamental
role in many aspects of the theory and I will mention some special
classes of interest. I will briefly describe the Oseledets or
Multiplicative Ergodic Theorem (warning! I am not an expert) and how
this can be used to create a broad class of AF-algebras with interesting
features.
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Title: A walk with relative equilibria from the plane to the sphere S2
Speaker: Ernesto Prerez Chavela, ITAM Mexico
Date and time:
13 Sep 2023,
2:30pm -
3:30pm
Location: ECS 130
Event type: Applied math seminar
Read full description
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Title: Approximate Marginal Likelihood Inference in Mixed Models for Grouped Data
Speaker: Alex Stringer, University of Waterloo
Date and time:
12 Sep 2023,
2:30pm -
3:30pm
Location: DSB C130
Event type: Statistics seminar
Read full description
Abstract: I introduce a method for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contributions are (a) an algorithm for computing the exact gradient of the approximate log marginal likelihood and (b) a useful parameterization of the multivariate Gaussian. The former leads to efficient quasi-Newton optimization of the marginal likelihood that is several times faster than established methods; the latter gives Wald confidence intervals for random effects variances that attain nominal coverage and low bias if enough quadrature points are used. The Laplace approximation is a special case of the method and is shown in simulations to perform exceptionally poorly for binary random slopes models, but this is mitigated by just adding more quadrature points.
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Title: Some results on linear dynamical systems
Speaker: George Lee, University of Victoria
Date and time:
24 Aug 2023,
9:00am -
10:00am
Location: David Strong Building, Room C126
Event type: Graduate dissertations
Read full description
Reviewers
Supervisory Committee
Dr. Anthony Quas, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Christopher Bose, Department of Mathematics and Statistics, UVic (Member)
Dr. Sean Chester, Department of Computer Science, UVic (Outside Member)
External Examiner
Dr. Ian Morris, School of Mathematical Sciences, Queen Mary University of London
Chair of Oral Examination
Dr. Michel Lefebvre, Department of Physics and Astronomy, UVic
Abstract
A linear cocycle is an object that arises naturally in the study of dynamical systems and statistics. Oseledets’ theorem [21] guarantees a decomposition of X into fast and slow subspaces. This dissertaton is a study of strongly measurable cocycles over an invertible ergodic system acting on a separable Banach space, including a proof of this theorem in this infinite dimensional setting.
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Title: A meta-analysis of genome-wide associations with body mass index
Speaker: Guojun Ma, University of Victoria
Date and time:
21 Aug 2023,
2:00pm -
3:00pm
Location: via Zoom
Event type: Graduate dissertations
Read full description
The Final Oral Examination
for the Degree of
Master of Science
(Department of Mathematics and Statistics)
Guojun Ma
2020 University of Alberta B.Sc.
A meta-analysis of genome-wide associations with body mass index
August 21, 2023
2:00pm
Online
Supervisory Committee:
Dr. Yu-Ting Chen, Department of Mathematics and Statistics, UVic
(Supervisor)
Dr. Xuekui Zhang, Department of Mathematics and Statistics, UVic
(Co-Supervisor)
Chair of Oral Examination:
Dr. Trefor Bazett, Department of Mathematics and Statistics, UVic
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Title: Iimi: A novel automated workflow for plant virus diagnostics from high-throughput sequencing data
Speaker: Haochen Ning, University of Victoria
Date and time:
18 Aug 2023,
3:00pm -
4:00pm
Location: David Strong Building, Room C130
Event type: Graduate dissertations
Read full description
Reviewers
Supervisory Committee
Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Li Xing, Department of Mathematics and Statistics, UVic (Member)
External Examiner
Dr. Ibrahim Numanagic, Department of Computer Science, UVic
Chair of Oral Examination
Dr. Catherine Leéger, Department of French, UVic
Abstract
Several workflows have been developed for the diagnostic testing of plant viruses using high-throughput sequencing methods. Most of these workflows require considerable expertise and input from the analyst to perform and interpret the data when deciding on a plant’s disease status. The most common detection methods use workflows based on de novo assembly and/or read mapping. Existing virus detection software mainly uses simple deterministic rules for decision-making, requiring a certain level of understanding of virology when interpreting the results. This can result in inconsistencies in data interpretation between analysts which can have serious ramifications.
To combat these challenges, we developed an automated workflow using machine-learning methods, decreasing human interaction while increasing recall, precision, and consistency. Our workflow involves sequence data mapping, feature extraction, and machine learning model training. Using real data, we compared the performance of our method with other popular approaches and showed that our approach increases recall and precision while decreasing the detection time for most types of sequencing data.
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Title: Some underrated facts about solenoids
Speaker: Rodrigo Trevino, University of Maryland
Date and time:
15 Aug 2023,
3:30pm -
4:30pm
Location: David Strong Building C130
Event type: Probability and Dynamics seminar
Read full description
Flat Wieler solenoids are inverse limits of locally expanding affine maps. They appear in several contexts in dynamical systems, for example as tiling spaces of self-similar tilings, and they are very interesting because they are not manifolds but have an interesting local product structure. I will talk about several geometric and dynamical properties of these spaces, emphasizing the interplay between intrinsic topological properties and renormalization. This talk is for everyone as no prior knowledge of inverse limits will be assumed.
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Title: Estimating the Size of the COVID-19 Population in British Columbia Using the Stratified Petersen Estimator
Speaker: Tuan Viet Dao, University of Victoria
Date and time:
14 Aug 2023,
10:00am -
11:00am
Location: virtual defence
Event type: Graduate dissertations
Read full description
Notice of the Final Oral Examination
for the Degree of Master of Science
of
TUAN VIET DAO
BA (Gustavus Adolphus College, 2017)
“Estimating the Size of the COVID-19 Population in British Columbia
Using the Stratified Petersen Estimator”
Department of Mathematics and Statistics
Monday, August 14, 2023
10:00 A.M.
Virtual Defence
Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Junling Ma, Department of Mathematics and Statistics, UVic (Co-Supervisor)
External Examiner:
Dr. Lloyd Elliott, Department of Statistics and Actuarial Science, Simon Fraser University
Chair of Oral Examination:
Dr. Tim Pelton, Department of Curriculum and Instruction, UVic
Abstract
The presence of undetected COVID-19 cases is a known phenomenon. Mathematical
modelling techniques, such as capture-recapture, provide a reliable method for estimating
the true size of the infected population. Treating a positive SARS-CoV-2 diagnostic test result
as the initial capture and a hospital admission with a COVID-19-related diagnosis code as
the recapture, we developed a Lincoln-Petersen model with temporal stratification, taking
into account factors that influence the occurrence of captures. Applying this model to
repeated patient encounter data collected at the provincial level in British Columbia, we
estimated the number of COVID-19 cases among males aged 35 or older during the first
week of March 2021. Our analysis revealed that the true number of cases ranged from 4.94
to 9.18 times greater than the number of detected cases.
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Title: The Edwards–Sokal Coupling for the Potts Higher Lattice Gauge Theory on Z^d
Speaker: Yakov Shklarov, University of Victoria
Date and time:
09 Aug 2023,
9:30am -
10:30am
Location: DSB C108
Event type: Graduate dissertations
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Title: Saturation Problems on Graphs
Speaker: Shannon Ogden, University of Victoria
Date and time:
19 Jul 2023,
10:00am -
11:00am
Location: David Strong Building, Room C108
Event type: Graduate dissertations
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BSc (University of Victoria, 2021)
Notice of the Final Oral Examination for the Degree of Master of Science
Topic: Saturation Problems on Graphs
Mathematics and Statistics
Date and location:
Wednesday, July 19, 2023 10:00 A.M.
David Strong Building Room C108
Reviewers
Supervisory Committee
Dr. Natasha Morrison, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Kieka Mynhardt, Department of Mathematics and Statistics, UVic (Co-Supervisor)
External Examiner
Dr. Antonio Girão, Mathematical Institute, University of Oxford
Chair of Oral Examination
Dr. Tao Lu, Department of Electrical and Computer Engineering, UVic
Abstract
In this thesis, we consider two variations on classical saturation problems in extremal graph theory: rainbow saturation and weak saturation.
An edge-coloured graph G is rainbow if every edge in G receives a distinct colour. Given a graph H, an edge-coloured graph G is H-rainbow-saturated if G does not contain a rainbow copy of H, but the addition of any non-edge to G, in any colour from , creates a rainbow copy of H. The rainbow saturation number of H, denoted by rsat(n,H), is the minimum number of edges in an H-rainbow saturated graph on n vertices. In Chapter 2, we prove that, like ordinary saturation numbers, the rainbow saturation number of every graph H is linear in n. This result confirms a conjecture of Girão, Lewis, and Popielarz.
In Chapter 3, we consider a specific type of weak saturation known as r-bond bootstrap percolation. In the r-bond bootstrap percolation process on a graph G, we start with a set of initially infected edges of G, and consider all other edges in G to be healthy. At each subsequent step in the process, the infection spreads to a healthy edge if at least one of its endpoints is incident with at least r infected edges. Once an edge is infected, it remains infected indefinitely. If a set of initially infected edges will eventually infect all of E(G), we refer to it as an r-percolating set of G. Define me(G, r) to be the minimum number of edges in an r-percolating set of G.
Recently, Hambardzumyan, Hatami, and Qian introduced a clever new polynomial method, which they used to provide recursive formulas for me(G, r) when G is either a d-dimensional torus or a d-dimensional grid. We push this polynomial method further, in order to determine me(G, r) for certain other graphs G. In particular, we provide recursive formulas for me(G, r) when G is a Cartesian product of stars or a Cartesian product of joined cycles (cycles with a single chord). We also give upper and lower bounds on me(G, r) when G is a Cartesian product of a tree with any graph H, and examine the conditions under which these bounds match.
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Title: Cross-Sperner Systems
Speaker: Akina Kuperus, University of Victoria
Date and time:
18 Jul 2023,
10:00am -
11:00am
Location: David Strong Building, Room C108
Event type: Graduate dissertations
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BSc (University of Regina, 2021)
Notice of the Final Oral Examination for the Degree of Master of Science
Topic: Cross-Sperner Systems
Department of Mathematics and Statistics
Date and location
Tuesday, July 18, 2023
10:00 A.M.
David Strong Building, Room C108
Reviewers
Supervisory Committee
Dr. Natasha Morrison, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Kieka Mynhardt, Department of Mathematics and Statistics, UVic (Member)
External Examiner
Dr. Karen Meagher, Department of Mathematics and Statistics, University of Regina
Chair of Oral Examination
Dr. Shemine Gulamhusein, School of Child and Youth Care, UVic
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Title: Topological Data Analysis: Persistent Homology of Uniformly Distributed Points
Speaker: Ranjit Sohal, University of Victoria
Date and time:
05 Jul 2023,
9:00am -
10:00am
Location: David Strong Building C126
Event type: Graduate dissertations
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Title: A New Numerical Approach to Solve 1D Viscous Plastic Sea Ice Momentum Equation
Speaker: Fahim Alam, University of Victoria
Date and time:
26 Jun 2023,
9:30am -
10:30am
Location: via Zoom
Event type: Graduate dissertations
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Fahim Alam
BSc (Shahjalal University of Science and Technology, Bangladesh, 2017)
Notice of the Final Oral Examination for the Degree of Master of Science
Topic
A New Numerical Approach to Solve 1D Viscous Plastic Sea Ice Momentum Equation
Department of Mathematics and Statistics
Date and location
Monday, June 26, 2023
9:30 A.M.
David Strong Building, Room C128
Supervisory Committee
Dr. Boualem Khouider, Department of Mathematics and Statistics, University of Victoria(Supervisor)
Dr. David Goluskin, Department of Mathematics and Statistics, UVic (Member)
External Examiner
Dr. Alex Bihlo, Department of Mathematics and Statistics, Memorial University ofNewfoundland
Chair of Oral Examination
Dr. Randy Scharien, Department of Geography, UVic
Abstract
While there has been a colossal effort in the ongoing decades, the ability to simulate ocean icehas fallen behind various parts of the climate system and most Earth System Models areunable to capture the observed adversities of Arctic sea ice, which is, as it were, attributed toour frailty to determine sea ice dynamics. Viscous Plastic rheology is the most by and largerecognized model for sea ice dynamics and it is expressed as a set of partial differentialequations that are hard to tackle numerically. Using the 1D sea ice momentum equation as aprototype, we use the method of lines based on Euler’s backward method. This results in anonlinear PDE in space only. At that point, we apply the Damped Newton’s method which hasbeen introduced in Looper and Rapetti et al. and used and generalized to 2D in Saumier et al.to solve the Monge-Ampere equation. However, in our case, we need to solve 2nd order linearequation with discontinuous coeffi cients during Newton iteration. To overcome this diffi culty,we use the Finite element method to solve the linear PDE at each Newton iteration. In thispaper, we show that with the adequate smoothing and re-scaling of the linear equation,convergence can be guaranteed and the numerical solution indeed converges effi ciently to thecontinuum solution unlike other numerical approaches that typically solve an alternate set ofequations and avoid the diffi culty of the Newton method for a large nonlinear algebraicsystem. The fi nite element solver failed to converge when the original setting of the smoothedSIME with a smoothing constant K = 2.8 x 108
was used. A much smaller constant of K=100 wasnecessary. The large smoothing constant K leads to an ill conditioned mass matrix.
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