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Understanding the population dynamics of salmonids is important for both management and conservation purposes; however, their complex life history introduces challenges. In anadromous Dolly Varden (Salvelinus malma), growth is an important factor for understanding the survival and capture. To explore this relationship, we used a Bayesian multi-state capture-recapture framework to estimate survival and capture probabilities while modelling growth in four ways: (1) as an independent process, (2) linked to reproductive state transitions, (3) influenced by sex, and (4) influenced by both sex and reproductive state. We employed two approaches to modelling individual length—one incorporating the Von Bertalanffy growth model and another without it. We applied the models to Dolly Varden data collected from five river systems in the western Canadian Arctic. Our results reveal a consistent pattern—survival probability increases with length, while capture probability decreases. Moreover, length is found to be a significant predictor of both survival and capture across all models. This study invites discussion on the most suitable growth model for estimating demographic parameters of this Arctic fish, considering both biological realism and statistical fit.

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Long DNA and RNA molecules encode the genetic code of viruses and living organisms. We study the changes in DNA topology mediated by essential processes such as DNA packing and transcription of DNA into RNA. These processes are highly regulated, and even small structural changes can lead to catastrophic effects. We use techniques from knot theory and topology, aided by discrete and computational methods, to model these biological processes. Our emphasis is on the geometry and topology of DNA and RNA. In this lecture, I first discuss discrete methods in the study of biopolymers. The rest of the presentation will be devoted to the R-loop grammar, a formal grammar model that allows us to predict the formation and entanglement of DNA:RNA hybrids that arise during transcription. The presentation is accessible to students and suitable for a diverse interdisciplinary audience.

Abstract: Algebraic graph theory begins by associating a matrix to a graph and asking how the eigenvalues of the former relate to the structure of the latter. In the past fifteen or so years, horizons have broadened to include variants of graphs (such as signed graphs or directed graphs) which require variants of adjacency matrices such as signed or Hermitian adjacency matrices. I will focus on the topic of characterizing the graphs whose associated matrices have at most three distinct eigenvalues. I will discuss old results in the undirected and signed graph case and then present some new results for oriented graphs.

Based on joint work with S. Akbari, J. Aloni, B. Mohar and S. Xia.

Abstract: We consider nonlocal games (these will be introduced), but allow for quantum questions and answers living in quantum sets. It turns out the typical definitions from the nonlocal games literature can be extended and many of the typical results still hold in this quantum setting. The analogies to the typical setting can be seen clearly using string diagrams!

This talk contains many diagrams. Never fear: We begin by motivating the diagrams using multimatrix algebras. We use string diagrams to introduce extended definitions of games, correlations, and synchronicity. We show that perfect correlations and strategies for synchronous quantum games must be synchronous. Time permitting, as a key example: When the graph homomorphism game is extended to quantum graphs, we get a synchronous game, whose perfect correlations correspond to quantum graph homomorphisms! The talk is based on a preprint Quantum games and synchronicity. This work is inspired by Musto, Reutter, and Verdon's paper A compositional approach to quantum functions, and relies heavily on the reference Categories for Quantum Theory by Heunen and Vicary for string diagrams in quantum information.

ZOOM link .

Abstract: A fundamental problem in the theory of the Navier-Stokes equations is the uniqueness of solutions of the Cauchy problem. After discussing some of the recent progress in this area, we will describe a new approach to constructing solutions that exhibit non-uniqueness. As an application, we will show an example of non-unique Leray-Hopf solutions in a dyadic model of the 3D Navier-Stokes, with initial data in a sharp regularity class. Then we will present recent work with M. Coiculescu that uses a similar mechanism to construct non-unique solutions to the full Navier-Stokes whose data lies in a critical space.

Abstract: we consider the model in which uniform random points are added to the unit interval at a constant intensity and independently vanish each at rate 1. The stationary distribution is a Poisson point process. Our goal is to investigate the time until an atypically large gap appears, in the high-intensity limit. To do so we develop some theory that allows us to compute the hitting time of a rare set in a family of Markov chains in terms of the restriction of the stationary distribution to that set. By studying the stationary distribution, as well as sample paths of the counting processes that describe particle numbers on fixed intervals, we obtain an asymptotic formula for the expected time until the appearance of a large gap. A component of the theory involves generalizing the exponential limit of scaled geometric random variables to the case where the relevant Bernoulli sequence is one-dependent.

Although biologists discover and classify thousands of new species each year, an estimated 95% of the more than 20 million multicellular species on Earth remain unnamed and unclassified. Our research aligns with the long-term goals of the Planetary Biodiversity Mission—to map all multicellular life by 2045 —and with the challenge of deciphering the "Rosetta Stone" of genomics, by understanding the mathematical structure underlying genomic sequences.

In this talk, I discuss mathematical representations of DNA sequences and their integration with supervised machine learning and unsupervised deep learning techniques for ultrafast, accurate, and scalable genome classification across all taxonomic levels. I also present our recent findings, which provide compelling evidence that adaptations to extreme temperatures and pH leave a distinct environmental imprint on the genomic signatures of microbial extremophiles. Notably, our use of unsupervised learning on unlabelled DNA sequences has identified several instances of extremophile microbes that, despite their significant evolutionary divergence, share similar genomic signatures linked to the extreme environments they inhabit.

Abstract: The peaceable queens problem asks to determine the maximum number $a(n)$ such that there is a placement of $a(n)$ white queens and $a(n)$ black queens on an $n \times n$ chessboard so that no queen can capture any queen of the opposite color.

We consider the peaceable queens problem and its variant on the toroidal board. For the regular board, we show that $a(n) \leq 0.1716n^2$, for all sufficiently large $n$. This improves on the bound $a(n) \leq 0.25n^2$ of van Bommel and MacEachern.

For the toroidal board, we provide new upper and lower bounds. Somewhat surprisingly, our bounds show that there is a sharp contrast in behaviour between the odd torus and the even torus. Our lower bounds are given by explicit constructions. For the upper bounds, we formulate the problem as a non-linear optimization problem with at most 100 variables, regardless of the size of the board. We solve our non-linear program exactly using modern optimization software.

We also provide a local search algorithm and a software implementation which converges very rapidly to solutions which appear optimal. Our algorithm is sufficiently robust that it works on both the regular and toroidal boards. For example, for the regular board, the algorithm quickly finds the so-called Ainley construction.

This is joint work with Katie Clinch, Matthew Drescher, and Abdallah Saffidine.

Zoom link.

Abstract: Driven by an outdated problem in aerodynamics, we discovered a new principle in fluid physics. The Euler equation does not possess a unique solution for the flow over a multiply connected domain. This problem has serious repercussions in aerodynamics; it implies that the inviscid aero-hydrodynamic lift force over a two-dimensional object cannot be determined from first principles; a closure condition must be provided. The Kutta condition has been ubiquitously considered for such a closure in the literature, even in cases where it is not applicable. In this talk, I will present a special variational principle in analytical mechanics: Hertz’ principle of least curvature. Using this principle, we developed a variational formulation of Euler’s dynamics of ideal fluids that is different from the previously developed variational formulations based on Hamilton’s principle of least action. Applying this new variational formulation to the century-old problem of the ideal flow over an airfoil, we developed a general (dynamical) closure condition that is, unlike the Kutta condition, derived from first principles. In contrast to the classical theory, the proposed variational theory is not confined to sharp edged airfoils; i.e., it allows, for the first time, theoretical computation of lift over arbitrarily smooth shapes, thereby generalizing the century-old lift theory of Kutta and Zhukovsky. Moreover, the new variational condition reduces to the Kutta condition in the special case of a sharp-edged airfoil, which challenges the widely accepted wisdom about the viscous nature of the Kutta condition.

We also generalized this variational principle to Navier-Stokes’ via Gauss’ principle of least constraint, thereby presenting the fundamental quantity that Nature minimizes in every incompressible flow. We proved that the magnitude of the pressure gradient over the field is minimum at every instant! We call it the Principle of Minimum Pressure Gradient (PMPG). It is straightforward to prove that the Navier-Stokes’ equation is the first-order necessary condition for minimizing the pressure gradient cost subject to the continuity constraint. Hence, the PMPG turns a fluid mechanics problem into a minimization one where fluid mechanicians need not to apply Navier-Stokes’ equations, but minimize the pressure gradient cost. We close by posing two conjectures: one on nonlinear hydrodynamic stability and another on the mathematical problem of the inviscid limit of Navier-Stokes.

Abstract: The mixing time and spectral gap of a random walk on the symmetric group can sometimes be understood in terms of its low dimensional representations (e.g., Aldous' spectral gap conjecture). It turns out that under a mild degree condition involving the step of the group, the same holds for nilpotent groups w.r.t. their one dimensional representations: the spectral gap and the epsilon total variation mixing time of the walk on G are determined by those of the projection of the walk to the abelianization G/[G,G]. We'll discuss some applications concerning the cutoff phenomenon (= abrupt convergence to equilibrium) and the dependence (or lack of!) of the spectral gap and the mixing time on the choice of generators.

As time permits we shall discuss a related result, confirming in the nilpotent setup a conjecture of Aldous and Diaconis concerning the occurrence of cutoff when a diverging number of generators are picked uniformly at random. Joint work with Zoe Huang.

Selection acts upon genes tied together on chromosomes. This physical association reduces the efficiency of evolution because, in the absence of sex, alleles must rise and fall together in frequency with the genome in which they are found.  In this talk, I introduce the concept of selective interference, describe the role that sex and recombination play in reducing this interference, and provide evidence from both theoretical and empirical studies that sex and recombination may have evolved and be maintained to reduce this interference, thereby increasing the efficiency of evolution.

Abstract: A phase transition is a phenomenon in physics, chemistry, and other related fields where the macroscopic behavior of a system changes qualitatively when the tuning parameter (such as temperature) that governs local interactions is varied by a small amount through a critical value. A familiar example of a phase transition is the evaporation of water into steam when the temperature reaches the boiling point.

In statistical mechanics, percolation is a simple model that undergoes a phase transition. At the critical threshold, percolation exhibits fractal properties that prove to be a rich area of research. In this talk, I will give a high-level introduction to the dimension-dependence of critical phenomena for percolation on Euclidean lattices.

Abstract:
School timetabling is a complex problem in combinatorial optimization, requiring the best possible assignment of course sections to teachers, timeslots, and classrooms.

For educational institutions, the Master Timetable dictates to every single teacher and student where they need to be at each hour of the school day. Given its importance, school administrators spend weeks or months constructing the annual Master Timetable, often using Post-it notes or wall magnets to assign a teacher, classroom, and timeslot to each section of a course.

When timetables are constructed by hand, the process is often 10% mathematics and 90% politics, leading to errors, inefficiencies, and resentment among teachers and students.

To address these concerns, a field of Discrete Mathematics known as "automated timetabling" has emerged, to create mathematically-optimal timetables for schools.

Over the past five years, I have had the privilege of creating over 50 Master Timetables for various high schools across Canada, including all three of Victoria's independent schools. In this informal interactive talk, I will describe how I create these timetables by modelling the school's constraints as an Integer Linear Program.

Abstract: We begin by characterizing the KMS states of the Toeplitz C*-algebra of the ax+b monoid in terms of a class of probability measures on the unit circle satisfying a 'subconformal' property. We then give explicit formulas for the atomic subconformal measures and prove a 'multiplicative' version of Wiener's lemma that implies that Lebesgue measure is the only nonatomic one.

ZOOM link: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09

Abstract: The stability of shear flows in the fluid mechanics is an old problem dating back to the famous Reynolds experiments in 1883. The question is to quantify the size of the basin of attraction of equilibria of the Navier-Stokes equations depending on the viscosity parameters, giving rise to the so-called stability threshold. In the case of a three-dimensional homogeneous fluid, it is known that the Couette flow has a stability threshold proportional to the viscosity, and this is sharp in view of a linear instability mechanism known as the lift-up effect. In this talk, I will explain how to exploit certain physical mechanisms to improve this bound: these can be identified with stratification (i.e. non-homogeneity in the fluid density) or rotation (i.e. Coriolis force). Either mechanism gives rise to oscillations which suppress the lift-effect. This can be captured at the linear level in an explicit manner, and at the nonlinear level by combining sharp energy estimates with suitable dispersive estimates.

This Alternative Math Education event will present fun methods of teaching math and computer science concepts to children (and adults!) using games and art. 

Lots of hands-on activities!

Including: 

• A Sorting Network 

• An Impossible Balancing Act

• Mathematical Puzzles 

• The Guessing Game 

• Sudoku• The Penny Game• The Set Game• And many more!

For more information please contact the school or Kristina McKinnon, PIMS University of Victoria Site at:

T: 250-472-4271

E: pims@uvic.ca

Join Zoom Meeting https://uvic.zoom.us/j/89270000801
Meeting ID: 892 7000 0801

This seminar will focus on aspects of the ecology of animal home ranges in which empirically derived movement tracks are viewed as realizations of continuous time, continuous space stochastic processes. Topics will include the distinctions between occurrence distributions and range distributions, data thresholds for effective statistical estimation, estimation of behavioral change points following animals’ release from captivity, population-level inference, and the estimation of population ranges.

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The array

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has an interesting feature: its columns are each vectors satisfying the linear relation 3x + 4y + 5z = 0, and its rows are permutations of each other. Are there arrays of integers like this for other simple linear relations? This question was raised by Chris Smyth in 1986 in connection with an audacious conjecture in algebraic number theory about linear relations between Galois conjugates. We explain how to prove Smyth's conjecture, and what it has to do with eigenvalues of sums of permutation matrices, weightings on hypergraphs, and (depending on time and audience indulgence) a local-to-global principle for equations in random variables.

Joint work with Will Hardt.

Abstract: Combinatorial Configurations lay between block designs and hypergraphs. When these incidence structures can be embedded in the plane, we call them Geometric Configurations. In this talk, we will explore several results in the study of configurations, including an extension of Erdős and Kelly's result on the minimal regular graph containing a given graph, applied to linear hypergraphs.

Abstract: I will begin by describing the Toeplitz C*-algebra of the ax+b monoid over the natural numbers introduced in recent joint work with an Huef and Raeburn, and then compute the equilibrium states for inverse temperature below 1 by first transforming the problem into the computation of probability measures on the unit circle that satisfy a certain subconformal property. This is joint work with Tyler Schulz.

The Math and Stats EDI committee is organizing two events in February 2025 to celebrate Black History Month. The events consist of the screening of two documentary films from the series Journeys of Black Mathematicians on Feb 13 and Feb 25, 2025 from 3:30 to 5:00 pm, in room C118 of the David Strong Building. Free popcorn will be provided to all those attending, thanks to the generosity of the Math and Stats Department.

Abstract:
The stabilized automorphism group of a dynamical system (X,T) is the group of all self-homeomorphisms of X that commute with some power of T. In this talk, we will describe the stabilized automorphism group of minimal systems. The main result we will prove is that if two minimal systems have isomorphic stabilized automorphism groups and each has at least one non-trivial rational eigenvalue, then the systems have the same rational eigenvalues.

Location: Zoom (link
Meeting ID: 893 7295 9263 Password: 033409)

Join Zoom Meeting: https://uvic.zoom.us/j/89270000801
Meeting ID: 892 7000 0801

Network control theory is a whole-brain framework for characterizing the macro-scale dynamics of the brain, incorporating the structural and functional connectome. Existing network models of the brain are sometimes limited in the hypotheses that can be tested. The brain is modeled as a controllable linear dynamical system constrained by white matter structure. Model specification, control strategies, and use in interventional studies are covered.

Abstract: Depth and width parameters of graphs, e.g., tree-width, path-width and tree-depth, play a crucial role in algorithmic and structural graph theory. These notions are of fundamental importance in the theory of graph minors, fixed parameter complexity and combinatorial sparsity.

In this talk, we will survey structural and algorithmic results concerning width and depth parameters of matroids. We will view matroids as purely combinatorial objects and discuss their structural properties related to depth and width decompositions. As an algorithmic application, we will present matroid based algorithms that can uncover a hidden Dantzig-Wolfe-like structure of instances of integer programs (if such structure is present).

The most recent results presented in the talk are based on joint work with Marcin Briański, Jacob Cooper, Timothy F. N. Chan, Martin Koutecký, Ander Lamaison, Kristýna Pekárková and Felix Schröder.

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Meeting ID: 864 4690 5312
Password: 003745

Abstract: Comparative genomics offers valuable insights into evolutionary biology, uncovering patterns such as whole-genome duplications, gene retention, and gene loss. Polyploidization, a widespread evolutionary process, plays a pivotal role in shaping the genomes of plants and certain animal species. This talk examines the mechanisms of polyploidization and its evolutionary impact, including processes like gene retention, divergence, and adaptive evolution. By utilizing metrics such as gene pair similarity and synonymous substitution rates (Ks), alongside advanced tools like synteny analysis, we investigate methods to differentiate ancient and recent whole-genome duplication (WGD) events. The presentation also outlines potential future directions, emphasizing the integration of statistical mathematics, data science, and bioinformatics to address questions in evolutionary biology.

Brief Bio: Dr. Yue Zhang is an Assistant Professor in the Department of Mathematics and Statistics at Thompson Rivers University. Holding a Ph.D. in mathematics from the University of Ottawa, specializing in comparative genomics within bioinformatics, Dr. Zhang’s research spans computational biology, data science, and evolutionary genomics. Dr. Zhang previously worked as a research associate at the Michael Smith Genome Sciences Centre. Her work focuses on developing computational methods to analyze whole-genome duplication events, gene divergence, and retention patterns in polyploid genomes. Dr. Zhang has guided multiple student research projects and has received internal and external grants, including NSERC Discovery Grant, to advance research in genome evolution. With a interest in addressing biological questions, Dr. Zhang seeks to advance bioinformatics research and foster connections between related fields.

Starting with one red ball and one black ball in an urn, repeat the following - choose a ball from the urn at random, observe the colour, put it back in the urn together with an additional ball of the same colour. This simple model is called Polya’s urn and is an example of a random process with 'reinforcement' (e.g. if red is selected first then after this first iteration we have 2 red balls and 1 black ball in the urn, so red is more likely to be selected again in the second iteration).

Beginning with Polya’s urn, this talk will take a tour through some of the weird and wonderful behaviour that has been observed or conjectured for various random processes with reinforcement.

The Math and Stats EDI committee is organizing two events in February 2025 to celebrate Black History Month. The events consist of the screening of two documentary films from the series Journeys of Black Mathematicians on Feb 13 and Feb 25, 2025 from 3:30 to 5:00 pm, in room C118 of the David Strong Building. Free popcorn will be provided to all those attending, thanks to the generosity of the Math and Stats Department.

Abstract: Let $G$ be a countable discrete group, and let $\mu$ be a probability measure on $G$ with finite (Shannon) entropy. We initiate the study of several related concepts associate to a probability measure $\mu$ and exploit their relations. First, we look at the concept of {\it Lyapunov exponent} of $\mu$ with respect to weights on $G$ and build a framework that connects it to the entropy of $\mu$ in $G$. This is done by introducing a generalization of Avez entropy $h(G,\mu)$, taking into account the given weight, and investigating in details their relations together as well as to the actions of $G$ on measurable stationary spaces.

As a byproduct of our techniques, we show that for a large class of groups (e.g. groups with rapid decay) and probability measures on them, the weak containment of the representation $\pi_X$ of $G$ on a $\mu$-stationary space $(X,\xi)$ implies that

$$h(G,\mu)=h_\mu(X,\xi),$$

where $h_\mu(X,\xi)$ is the Furstenberg entropy of $(X,\xi)$.

This implies that these types of stationary spaces are precisely measure-preserving extension of the Poisson boundary of $(G,\mu)$. In particular, $(X,\xi)$ is an amenable $(G,\mu)$-space if and only if it is a measure-preserving extension of the Poisson boundary of $(G,\mu)$.

This is a join work with Benjamin Anderson-Sackaney, Tim de Laat, and Matthew Wiersma.

Join Zoom Meeting https://uvic.zoom.us/j/89270000801
Meeting ID: 892 7000 0801

Cooperative hunting describes predators hunting prey in a group and sharing the resulting kill. This form of cooperation may expand predators’ access to food by allowing them to hunt prey they could not catch alone, but the catch is that they have to share. Many predators that exert enormous influence over their ecosystems are cooperative hunters, such as wolves and orcas, but it is not well understood how prey availability and prey choice selects for group sizes, nor how cooperative hunting influences the population dynamics of predator and prey. We model a predator population hunting two types of prey-- big prey that is best hunted in groups and small prey that is best hunted alone. In conjunction, we track the dynamics of the distribution of group sizes in the predator population. We find that groups form if the big prey is very available and very beneficial – i.e., very large – but that groups do not grow very large. Furthermore, if big prey is too difficult to catch, requiring at least three predators to be caught, then groups almost never form. Our results indicate that the occurrence of very large predator groups are likely not just explained by the availability of big prey, but on a feedback with other social mechanisms.

Abstract: A classical problem in combinatorial geometry, posed by Erdős in 1946, asks to determine the maximum number of unit segments in a set of n points in the plane. Since then a great variety of extremal problems in finite planar point sets have been studied. In this talk, we examine several such problems, all of which have in common that they can be reduced to the study of the independence number of an auxiliary hypergraph.

1) What is the size of the largest subset of the n x n grid whose points determine distinct slopes?

2) What is the size of the largest monotone general position subset of the n x n grid?

3) Given n points in the plane, how many triangles can be approximate congruent to equilateral triangles?

The results presented are partially joint work with Balogh, Dumitrescu and Liu.

(Zoom link Meeting ID: 893 7295 9263 Password: 033409)

Abstract: An highly active research area is concerned with finding conditions on sparse sets that ensure the existence of many geometric patterns. I will present some results in this direction connecting Newhouse thickness and its generalizations to higher dimensions, games of Schmidt type and the existence of an abundance of homothetic copies of small sets.

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Meeting ID: 699 6049 3994
Passcode: 900153

The field of DNA Topology includes the study of DNA geometry (supercoiling) and topology (knots and links) and their effects on DNA in vitro and in vivo. Statistical mechanics-based polygonal models of DNA have proved useful for addressing many questions arising from DNA topology experiments. Of these, lattice polygon models have played a fundamental mathematical/computational role in addressing the open questions. In this talk, I will start by giving an overview of DNA topology experiments and open questions, along with examples of polygonal models used to study DNA topology.This will be followed by a review of recent advances we have made using lattice polygon models to address questions related to the knot and link statistics of DNA in vitro either subject to varying salt conditions or under nanochannel-like confinement.

Abstract: In how many ways can an m x n chessboard be tiled using 2 x 1 tiles? The solution is given by the number of perfect matchings in a related graph. Although computationally difficult in general, in this circumstance we are able to efficiently count these matchings.

Originally shown by P.W Kastelyn in 1961, I shall present an adapted solution given by Jiří Matoušek in his book "Thirty-three Miniatures: Mathematical and Algorithmic Applications of Linear Algebra" published in 2010.

I will discuss a problem that appeared on MathOverflow and its solution by the user “Fedja”. The result we will demonstrate is that if T is subset of the reals with Hausdorff dimension exceeding ½, then there is a positive probability that a standard Brownian Motion has a zero at some time t belonging to T.

The beautiful proof relies on the second moment method, which I will discuss along the way.

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Collection of genetic capture-recapture data can be paired with another field data collection method that collects presence-absence data, such as camera traps. Since the individual identification might not be possible for all the data captured in the first source, the second source can offer valuable information about the species. Both these data can be used in integrated modelling to estimate wildlife density and usually this method provides estimates more precise than single data source estimates. We applied two integrated models to estimate the population density of grizzly bears of the central Rocky Mountains of Alberta, Canada using capture-recapture data from hair traps and presence-absence data from camera traps. We found that these models did not provide estimates more precise than the single data source-models. One of the reasons could be the violation of the assumption that the data sources need to be independent. Often this assumption restricts the application of integrated models since in most cases these data sources are not independent. We formulated a model which can accommodate information from both capture-recapture and presence-absence data to estimate wildlife abundance when these data sources are dependent. This model can accommodate more than one season by considering parameters for survival, fecundity, and movement. Capture-recapture data are modelled with a spatially explicit capture-recapture approach while the presence-absence data are modelled conditional on the latent capture recapture information. We applied this model to a simulated data and estimated the population abundance to check the model accuracy.

Registration:
Participants register once on Zoom and may 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 each event date.

I will discuss a result with Bonatti and Crovisier from 2009 showing that the C^1 generic diffeomorphism f of a closed manifold has trivial centralizer; i.e. fg = gf implies that g is a power of f. I’ll discuss features of the C^1 topology that enable our proof (the analogous statement is open in general in the C^r topology, for r>1). I’ll also discuss some features of the proof and some recent work, joint with Danijela Damjanovic and Disheng Xu that attempts to tackle the non-generic case.

Location: Zoom (https://uvic.zoom.us/j/89372959263?pwd=q7IPZKueYMnaAxLaVmlwVqHfW0H0AR.1 Meeting ID: 893 7295 9263 Password: 033409)

Abstract :
In this talk, we consider a notion of stability for solutions of random optimization problems based on small perturbations of the input data and inspired by the technique for proving CLT using Stein's method as illustrated with examples by Chatterjee (2008). This notion of stability is closely related with the size of near-optimal solution sets for those optimization problems. We establish this notion of stability for a number of settings, such as branching random walk, the Sherrington--Kirkpatrick model of mean-field spin glasses, the Edwards--Anderson model of short-range spin glasses, the Wigner and Wishart ensemble of random matrices and combinatorial optimization problems like TSP / MST / MMP on weighted complete graphs and Euclidean spaces.

Abstract: Particle Swarm Optimization (PSO) algorithm is based on swarm intelligence and widely used in the field of Artificial Intelligence. Like many other nature-inspired metaheuristic algorithms, it is already widely used to tackle all sorts of hard optimization problems across disciplines, particularly in engineering and computer science. Interestingly, it is less used in the statistical sciences. Their meteoric rise in popularity is due to their ease of use, speed, availability of codes across different platforms and above all, their apparent lack of technical assumptions for them to work reasonably well. I focus on an exemplary algorithm PSO and, as examples, present some of the recent applications of PSO to find challenging optimal designs in the biomedical sciences. They include extensions of Simon’s two-stage designs to multiple stages, and theory-based dose response designs for estimating the optimal biological dose in early phase clinical trials. If time permits, I will also discuss applications of PSO and its variants for tackling non-design optimization problems in statistics.

Professor Wong has been a faculty member at the Fielding School of Public Health at UCLA since 1990. His early work includes rheumatology (scleroderma, lupus, rheumatoid arthritis), dentistry, environmental health science, cancer control and prevention, and intervention trials to fight obesity. His main methodological work is in finding efficient designs for the biomedical sciences. He has received multiple NIH grant awards, including serving as PI on several of them. He has given about 260 scientific presentations worldwide, including a 1-week short course at the Centre of Toxicology Center in Dortmund Technical University, Germany, and as an invited speaker, at the 16th Annual Conference on Statistical Issues in Clinical Trials, University of Pennsylvania, and at the 45th Annual Meeting of the Society of Clinical Trials. Prof. Wong is a fellow of the American Statistical Society, the Institute of the Mathematical Sciences, the American Association for the Advancement of Science, Elected Member of International Statistical Institute and a full member of the Sigma Xi, The Scientific Research Honor Society. He currently holds a Yushan Scholarship Award from the Ministry of Education in Taiwan.

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Empirical evidence shows that evolution may take place during species range expansion. Indeed, dispersal ability tends to be selected for at the leading edge of invasions, ultimately increasing a species' spreading speed. However, for organisms across many different taxa, higher dispersal comes at the cost of fitness, producing evolutionary trade-offs at the leading edge. Using reaction-diffusion equations and adaptive dynamics, we provide new insights on how such evolutionary processes take place. We show how evolution may drive phenotypes at the leading edge to maximize the asymptotic spreading speed, and conditions under which phenotypic plasticity in dispersal is selected for under different dispersal-reproduction trade-off scenarios. We provide some possible future research directions and other systems where the framework can be applied.

An (m, n)-mixed graph consists of a set of vertices, any two of which may be joined by either an edge of one of m colours or an arc of one of n colours, or not be joined at all. The operation of switching at a vertex v of an (m, n)-mixed graph with respect to an element of a subgroup \Gamma of S_m x S_n x S_2 permutes the colours of the edges incident with v, the colours of the arcs incident with v, and the orientation of the arcs incident with v. Switching defines an equivalence relation on the set of all (m, n)-mixed graphs: (m, n)-mixed graphs G and H are \Gamma-switch-equivalent if there exists a sequence of switches that transform G into H.

We consider the following problems and their solutions. For a fixed subgroup \Gamma of S_m x S_n x S_2:

* determine the number of equivalence classes of k vertex (m, n)-mixed graphs under switching with respect to \Gamma.
* how hard is it to determine whether to given (m, n)-mixed graphs G and H are \Gamma-switch equivalent?
* for a fixed (m, n)-mixed graph H, how hard is it to determine whether a given (m, n)-mixed graph G can be switched with respect to \Gamma so that there is a homomorphism of the transformed (m, n)-mixed graph G’ to H? (A homomorphism is a mapping of V(G) to V(H) that preserves edges, arcs and colours.)

(joint work with C. Eagle, I. Goldbring, and R. Miller)

Abstract: I will discuss recent work on the effective (computable) content of K-theory for operator algebras. I will explain at least the architecture of the proofs of the following theorems. 1) If $A$ is a computably presentable unital $C^*$-algebra, then the Abelian group $K_0(A)$ has a c.e. (a.k.a recursive) presentation. 2) If $A$ is a computably presentable uniformly hyperfinite algebra, then $K_0(A)$ has a computable presentation; moreover, the trace of $A$ is computable and its supernatural number is lower semi-computable. 3) UHF algebras are computably categorical; that is any two of their computable presentations are computably *-isomorphic.

Location: Zoom (https://uvic.zoom.us/j/89372959263?pwd=q7IPZKueYMnaAxLaVmlwVqHfW0H0AR.1
Meeting ID: 893 7295 9263
Password: 033409)

Abstract: Bounded density shifts are examples of hereditary subshifts. Bounded density shifts are defined by disallowing words whose sum of entries exceeds a value depending on the length of the word. After presenting some examples and reviewing the concepts of topological entropy and measure-theoretic entropy, we will provide sufficient conditions for bounded density shifts to have a unique measure of maximal entropy.

This is a joint work with Felipe García-Ramos and Ronnie Pavlov.

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High vaccine acceptance is key to achieving high vaccination coverage. While many studies explore factors influencing vaccine acceptance, the role of individual decision-making strategies is often overlooked. To address this, we developed a mechanistic model categorizing vaccine recipients into two main groups: myopic rationalists, who choose to vaccinate only when it maximizes their immediate benefit, and success-based learners, who follow those they perceive as most successful. By fitting the model to COVID-19 vaccine uptake data, we estimated the proportions of these decision-making types across American and Canadian jurisdictions. We further generalized the model to account for variations in individuals' perceived payoff gains from vaccination and analyzed the identifiability of group proportions and perceived payoff gains—determining whether these parameters can be uniquely recovered from error-free cumulative vaccination data. Sufficient conditions for identifiability were derived, paving the way for reliable estimation of group proportions and their perceived payoffs.

Abstract: Topological full groups arise from dynamical systems. Their main interest is for group theorists. But they first appeared from considerations in operator algebras. I'll will explain these topics. No background is needed.

The Final Oral Examination for the Degree of

Master of Science
(Department of Mathematics and Statistics)

Farbod Esmaeili
Shahid Beheshti University, B.Sc. in Statistics (2022)

“A Comparative Review of Stock Market Forecasting Models with a Simulation Study on GARCH Dynamics”

December 12, 2024
3:00 pm
Zoom: https://uvic.zoom.us/j/83893006823

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. Peter Dukes, Department of Mathematics and Statistics, UVic

The Final Oral Examination for the Degree of Master of Science

(Department of Mathematics and Statistics)

Naresh Neupane
MA, University of Victoria (2020)
BSc, Southeastern Louisiana University (2016)

“Optimal Designs for Quadratic, Cubic, Quartic and Quintic Polynomial Models in Balls”

December 13, 2024
1:30 pm
DTB A203

Supervisory Committee:
Dr. Julie Zhou, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Min Tsao, Department of Mathematics and Statistics, UVic (Member)

Chair of Oral Examination: Dr. Junling Ma, Department of Mathematics and Statistics, UVic

Zoom link: https://uvic.zoom.us/j/89993647116?pwd=QJTWUCoT9laxGYReeRo3mwlbOnLyrM.1

Abstract
Radiogenomics integrates medical imaging and (multiomic) genomic data to address clinical challenges, aiming to identify non-invasive biomarkers linked to genomic features and clinical outcomes. Deep learning (DL) has advanced this field, but limitations such as data incompleteness and low interpretability remain. This talk will present a novel framework for breast cancer (BC) prognostic biomarker identification using DL for image feature extraction and Bayesian tensor factorization (BTF) for multi-genomic data processing. The framework overcomes data limitations and improves upon traditional biomarker discovery. Furthermore, we introduces a Conditional Probabilistic Diffusion Model (CPDM) to generate synthetic magnetic resonance images (MRIs) from (multiomic) genomic profiles, addressing the challenge of unpaired data. The generated MRIs showed strong predictive capabilities for clinical outcomes, including gene mutations, receptor statuses, and patient survival. This research highlights the potential of AI-based models to enhance radiogenomics for precision oncology research.

Short Bio
Dr. Pingzhao Hu is a tenured Associate Professor and Tier 2 Canada Research Chair in Computational Approaches to Health Research in the Department of Biochemistry (Primary) and the Department of Computer Science (Cross-appointed) at Western University. Dr. Hu also has an Associate Professor (Status-Only) appointment in Division of Biostatistics, Dalla Lana School of Public Health, University of Toronto. Dr. Hu received his PhD in computer science from York University in 2012. His research program focuses on developing and applying machine leaning and statistical techniques for integrative analysis of multimodal health data for precision medicine.

Examining Committee

Supervisory Committee
Dr. Rod Edwards, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)

External Examiner
Dr. Bastien Fernandez, Laboratoire de Probabilités Statistique and Modélisation, French National Centre for Scientific Research

Chair of Oral Examination
Dr. Eva Kwoll, Department of Geography, UVic

Meeting link: https://uvic.zoom.us/j/87448763654

Abstract
Electronic circuitry based on chaotic Glass networks, a type of piecewise smooth dynamical system, has recently been proposed as a potential design for true random number generators. Glass networks are good designs due to their potential for chaotic behaviour and because their analytic tractability allows us here to propose a method for approximating their entropy, a measure of irregularity in dynamical systems. We discuss some of the historical developments that led to the interest in the model that we consider within the context of random number generation. Additionally, we discuss a method for converting a Glass network’s governing piecewise-smooth differential equations into discrete-time dynamical systems, and then into symbolic dynamical systems. We also detail how the symbolic entropy of the given Glass network is bounded above by the entropy of the symbolic dynamical system formed from its transition graph, a type of directed graph that represents the possible transitions in phase space between regions not containing discontinuities. We then extend previous results by detailing our new method of refining the transition graph to be a more accurate depiction of the true system’s dynamics, making use of more specific information about trapping regions in phase space. Refinements come in the form of splitting nodes and duplicating/partitioning edges on the transition graph and removing those that are never realized by the continuous dynamics. We show that refinements can be done to arbitrary levels and in the limit as the level of refinement goes to infinity, the entropy of the refined transition graphs converges to the true entropy of the system. Along with this, since it is not possible to calculate the limiting value, approximation is necessary. Doing this by hand is tedious and difficult, so as a result, we also detail here an algorithm we devised that automates the refinement process, allowing for approximation (from above) of symbolic entropy. Various examples are considered throughout and we also discuss how numerical simulation can be used to non-rigorously estimate symbolic entropy, as an independent (approximate) verification of our results. Finally, we detail some unfinished and future work which could extend our results further, along with alternative methods to achieve similar and potentially even stronger results. With our results and algorithm, using upper bounds on a Glass network’s symbolic representation’s entropy is now a viable method for assessing the irregularity of its dynamics.

We thank PIMS for their generous contribution which makes this in person event possible.

Abstract: Recent interactions between probability and number theory proved fruitful. In particular, random multiplicative functions (RMFs) are random models for partial sums of the Möbius function and Dirichlet characters, which are related to L-functions like the Riemann zeta function. In this talk, I will present the past, present, and future of RMFs: their history, known results, and current work on the moments and distribution of these partial sums of RMFs, as well as a look at the connections with random matrices that are likely to lead to major breakthroughs in the upcoming years.

Join Zoom Meeting https://umanitoba.zoom.us/j/66960493994?pwd=xahlt1zaWR3DTgL0eDsdoMbMu0JC7Q.1
Meeting ID: 669 6049 3994
Passcode: 900153

Pandemic preparedness needs modelling preparedness because during the COVID-19 pandemic there was high demand for modelling to provide short-term forecasts, counterfactual scenarios, quantities that summarize risk, and to inform decisions. To model COVID-19 in Newfoundland and Labrador, the cautionary tales of the 'atto-fox' and the 'island of Transmithica' informed our approach. These tales, as well as overgeneralization, have a role in explaining why travel measure recommendations were updated during the pandemic. To highlight the consequences of overgeneralization, we revisit the epidemiology of Atlantic Canada and the territories during the COVID-19 pandemic, and argue that the types of models needed to support decision-making in small jurisdictions are different, harder, and under-resourced. When modelling aims to support public health decision-making, the impact of modellers occurs within the context of colleagues and other experts. The aim of this talk is to have us consider: given what we have learned from the COVID-19 pandemic, how can modellers prepare to best support the public health response to future pandemics?

Abstract: Many fundamental problems in extremal combinatorics can be expressed as inequalities in graph homomorphism densities. In this talk, I will introduce some new results on this topic. Our research involves Sidorenko's conjecture, Kohayakawa-Nagle-R{\"o}dl-Schacht conjecture and common graphs. Moreover, I will share some recent advancements in problems of homomorphism densities for tournaments.

Abstract: It is not possible by looking at its K-theory to see if a C*-algebra is commutative or not, since every C*-algebra is KK-equivalent to a commutative C*-algebra. By contrast, there are, rather surprisingly, K-theory obstructions to commutativity if one works in the category of T-C*-algebras, where T is the circle group. In these 2 talks I will describe some special algebra-geometric structure in T-equivariant KK-theory, where T is a torus, and offer an open question or two.

Abstract: In the early stages of an outbreak, changes in the exponential growth rate of cases serve as crucial indicators for evaluating the effectiveness of control measures. Establishing a suitable likelihood function is essential for accurate growth rate estimation. To address this, we derive the probability generating function for new cases using a linear stochastic SEIR model and obtain formulas for its mean and variance. We approximate its distribution as a negative binomial and, by comparing this approximation with the probability distribution of simulated data, find that the negative binomial distribution fits the data well. Although the negative binomial distribution provides a good approximation for the distribution of new cases, selecting the most appropriate model for estimating the growth rate remains a challenge. We evaluate the performance of the negative binomial regression model and the hidden Markov model (HMM) in estimating the initial epidemic growth rate. Using simulated daily new cases with known parameters, we fit these models via the Markov Chain Monte Carlo (MCMC) method. Our results show that the confidence intervals generated by the HMM exhibit better coverage probabilities and narrower widths.

ZOOM: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09

We thank PIMS for their generous contribution which makes this in person event possible.

Abstract: This talk will present a novel discretization scheme for Wasserstein gradient flows (i.e. curves of steepest descent for functions of probability measures) based on the successive computation of Schrödinger bridges with equal marginals. In doing so, we develop a small-time approximation of same-marginal Schrödinger bridges using Langevin diffusion. This talk will begin with an introduction to entropic regularized optimal transport, introducing all the notions essential for understanding this scheme. Based on joint work with Medha Agarwal, Zaid Harchaoui, and Soumik Pal.

Abstract: The solution to the heat equation with non-negative, non-zero initial data is strictly positive. This property generalizes to most parabolic PDEs, but not necessarily to stochastic PDEs. The solution to a heat equation with multiplicative noise may be a compactly supported function, depending on the regularity of the noise coefficient. I will first discuss some classical theorems of this type when the equation has white Gaussian noise, and then discuss a recent result which proves the compact support property for solutions to a class of stochastic heat equations with white stable noise. Along the way we will develop some heuristics for why this property holds, sketch some proof techniques, and discuss connections with superprocesses.

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Attention-Deficit/Hyperactivity Disorder (ADHD) is a neurodevelopmental disorder common in both adults and children. Resting-state functional Magnetic Resonance Imaging (rs-fMRI) is an important tool for investigating brain function in neurological and psychiatric disorders including ADHD. Evidence suggests that there is an association between altered brain activity patterns and ADHD symptoms. We develop an analysis that first explores the fractal properties of rs-fMRI time series through examination of the scale-free power spectrum properties of rs-fMRI estimating the long-memory (LM) parameter at many spatial locations across the brain. We study the associations between the LM parameter and phenotypic covariates including age and medication status of ADHD patients. We estimate fractal complexity using the LM parameter and observe variations in the fractal complexity maps of the brain across different study groups. We find strong evidence that participants with ADHD who are on medication exhibit a negative correlation with the LM parameter within cerebellar regions. These findings shed further light on previous neuroimaging studies of ADHD reporting associations between alterations in brain shape structure and medication in the cerebellum. Our findings provide an important link between brain function and structure in the relationship between medication for ADHD and the cerebellar regions.

Abstract: A classical question in extremal (hyper)graph theory asks for tight minimum degree conditions which force the existence of certain spanning structures in large graphs, generalising Dirac's theorem from 1952. One aspect of this concerns tiling graphs with identical vertex disjoint copies of a small subgraph. For example, asking for tight minimum codegree conditions in a k-uniform hypergraph which force a perfect matching (under the obvious additional necessary condition that the number of vertices is divisible by k). Whilst there has been a lot of interest in these types of tiling problem, still very few results are known. We share a new result in this area, which is joint work with Amarja Kathapurkar, Natasha Morrison and Richard Mycroft.

Abstract: It is not possible by looking at its K-theory to see if a C*-algebra is commutative or not, since every C*-algebra is KK-equivalent to a commutative C*-algebra. By contrast, there are, rather surprisingly, K-theory obstructions to commutativity if one works in the category of T-C*-algebras, where T is the circle group. In these 2 talks I will describe some special algebra-geometric structure in T-equivariant KK-theory, where T is a torus, and offer an open question or two.

In this talk I will introduce three paradoxes in the spatial ecology of predators and prey (1) Buffer Zone Paradox: Why do wolves maintain stable buffer zones for prey, even though they may be only saving prey for the neighboring packs? (2) Road Use Paradox: Why are wolves attracted to roads and related linear features, even though that can mean higher chances of dying? (3) Path Less Travelled Paradox: Why do wolves preferentially travel to places they haven’t been recently, even if it means fewer prey? To help solve these paradoxes, I will start with the Fokker-Planck equation, which describes the probability density function for an individual undergoing a random walk. I will then employ a mixture of mathematical approaches including nonlinear advection-diffusion, differential games, first passage time theory and stochastic processes. All of the resulting models will be fit to data before drawing scientific conclusions.

Participants register once on Zoom and may 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 each event date.

Abstract: In defining colouring of oriented graphs via homomorphism one finds an easily checkable necessary condition for a valid colouring — vertices at directed distance at most two must receive different colours. With this idea in mind we extend the definition of quasi-transitive digraph to mixed graphs. In this talk we explore a full characterisation of quasi-transitive mixed graphs of degree at most three and find that the general problem of deciding if a graph admits a mixed orientation as a quasi-transitive mixed graph is NP-complete.

Abstract: Let $G$ be a graph with $n$ vertices. Let $A(G)$ be its adjacency matrix. Let $\lambda_1(G), \lambda_2(G)$ denote the largest and second largest eigenvalues of the adjacency matrix. Bollob\'{a}s and Nikiforov (2007) conjectured that for any graph $G \neq K_n$ with $m$ edges \[\lambda_1^2+\lambda_2^2\le \bigg( 1-\frac{1}{\omega(G)}\bigg)2m,\] where $\omega(G)$ denotes the clique number of $G$. In this talk, we prove this conjecture for graphs with not so many triangles, using the method of triangle counting. This is a joint work with Hitesh Kumar.

This seminar takes places across multiple time zones: 9:30 AM PT/ 10:30 AM MT / 11:30 AM CT Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

A matrix is called totally positive if all of its minors are positive. These matrices are important in mathe- matics, but checking whether a large matrix is totally positive can be challenging. In this talk, we explore whether certain matrices associated with a totally positive matrix, such as its compounds or those obtained through Dodgson condensation, also remain totally positive. In general, we find that this is not the case. However, we provide some helpful sufficient conditions that make it easier to verify when a matrix is totally positive using these techniques. This is joint work with Shaun Fallat and Charles R. Johnson.

Abstract: Short-term wind forecasting is essential for effectively utilizing wind energy. This talk presents an overview of research projects aimed at improving short-term wind speed forecasting. Initially, the benefits of incorporating atmospheric information using traditional time series models are discussed. Building on this foundation, a new modelling framework is introduced, along with several novel correlation functions designed to account for space- and time-asymmetry in empirical cross-correlations. Several case studies are presented to demonstrate the advantages of the proposed models.

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Sometimes in statistics we encounter challenges fitting a likelihood due to the number of unobserved variables that need to be marginalized before we perform maximization of the likelihood. Alternatively, we can use Markov chain Monte Carlo (MCMC), but this can end up being extremely slow. This is true for surveys (such as a camera trap study) that do not observe animal identities but wish to estimate density using methods like spatial capture-recapture (SCR). In this talk, we tackle two related problems: 1) a unique number of individual animals are counted at each detector, but animal identities are unknown between nearby correlated detectors (e.g. a point count survey of birds), 2) at each detector, only a count of the number of species-specific detections are made (e.g. camera trap studies). We use the spatial autocorrelation between the counts and assumptions about home range to estimate density from these data in a SCR framework. However, the problem is that we have an unknown number of animals in the population combined with an unknown home range parameter in space for each unobserved animal. This results in an infinite dimensional integration problem that is currently solved through MCMC and data augmentation. In this talk, we propose a pairwise composite likelihood construction where we write the probability of each count at each pair of detectors and reduce the dimension of the integration problem. Model fitting goes from hours (or in some cases days) to seconds or minutes. The maximum composite likelihood estimator has similar properties to the maximum likelihood estimator, and we show that our estimates are unbiased via a simulation study.

Abstract: An edge mapping of a graph is a function f:E(G) -> E(G) where f(e) \neq e for all e in E(G). A subgraph H of G is called f-free if for every e in E(H) f(e) \notin E(H). A graph G is called unavoidable for a graph H if every edge mapping of G has at least one f-free copy of H and minimally unavoidable if no proper subgraph of G also satisfies this property. In this talk, we will discuss the set of all minimally unavoidable graphs for a graph H for several different types of graphs H.

Abstract: The majority of work in the model theory of von Neumann algebras to date has been done entirely in the tracial setting. This is, in part, due to the lack of a user-friendly axiomatization that includes non-tracial von Neumann algebras. After a quick review of the prerequisite material, we will discuss computable axiomatizations and their utility. We will sample some of the key theoretical hurdles to a working computable model theory of non-tracial von Neumann algebras and how they were overcome. We will then consider some directions for future work. Joint work with Isaac Goldbring, Bradd Hart, and Thomas Sinclair.

See poster (png)

Abstract: Non-local interaction plays a crucial role in various biological systems, ranging from the behaviour of individual cells to the movements of entire organisms. In recent years, there has been a growing focus on mathematically modelling these non-local interactions, often employing advection-diffusion equations with integral terms capturing non-local effects. In this presentation, we propose a natural extension of existing models by introducing a reaction term, specifically addressing birth and death processes in biological systems. We first present some results regarding the well-posedness of this non-local reaction-advection-diffusion model. Then, we will shift our focus to travelling wave solutions, which exemplify biological invasions. We use a combination of perturbation methods, exponential dichotomy, Fredholm operator theory and fixed point argument to prove the existence of travelling wave solutions. Finally, we will end our presentation with some numerical investigations.

Joint work with Dr. Slim Ibrahim and Dr. Mark Lewis.

Zoom link.

Abstract: The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an idea from computer science and fits on one page.

Our new approach resolves a conjecture of Babson of Benjamini from 1999 and provides a simpler proof of the celebrated result of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that percolation on any non-one-dimensional transitive graph undergoes a non-trivial phase transition.

Join Zoom Meeting https://uvic.zoom.us/j/89270000801

In the study of any population, its lifetime, or the time until it becomes extinct, is of prime interest. Very disquieting is the possibility that the population appears to be stable at a healthy level but then soon plummets to extinction. This behaviour may be exhibited by deterministic models that, for instance, incorporate a "strong Allee effect". The bifurcation parameter may cross a critical value that signals the change of the system dynamics from bistable, the stable states being the origin and a non-trivial equilibrium, to a system with one globally asymptotically stable equilibrium, the origin. Details of the dynamics may cause a considerable delay to extinction. Such delay, or long transient, is commonly known as a "ghost" and has been extensively studied. In this talk, we show that such transients may be considerably extended or shortened by environmental noise. This is joint work with Luis Gordillo of Utah State University.

The Cascadia Combinatorial Feast (formerly known as the Combinatorial Potlatch) is an annual, floating, one-day conference. It has been held for many years at various locations around Puget Sound and southern British Columbia, and is an opportunity for combinatorialists in the region to gather informally for a day of invited talks and conversation. While most who attend work in, or near, the Puget Sound basin, all are welcome. Typically there are three talks given by speakers who are visiting or new to the area, along with breaks for coffee and lunch. Many participants remain for dinner at a local restaurant or pub.

See the CCF 2024 event page for more information.

This seminar takes places across multiple time zones: 9:30 AM PT/ 10:30 AM MT / 11:30 AM CT Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

For more information see PIMS site.

Abstract: The notions of noise sensitivity and stability were recently extended for the voter model, a well-known and studied interactive particle system. In this model, vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend sensitivity and stability results to a different class of perturbations when the nearest neighbor exclusion process is performed in the collection of edge selections. Under a rate depending on the underlying graph, we prove that the consensus opinion of the voter model is “exclusion stable” when the dynamics above run for a short amount of time. This is done by analyzing the expected size of the pivotal set.

We thank PIMS for their generous contribution which makes this in person event possible.

This presentation will review the covariate measurement error in regression analysis, focusing on its impact on parameter estimation and inference. Specifically, we address this problem in the context of biomarker research, where discrete-valued biomarkers follow a conditional Poisson distribution, modeled by a Poisson process that captures the spatial distribution of marker-positive cells. To correct the bias introduced by such measurement errors, we propose a novel Poisson-based version of the simulation extrapolation method (SIMEX). We theoretically demonstrate that the POI-SIMEX estimator achieves strong consistency within a linear regression model. We further evaluate the performance of POI-SIMEX through simulation studies, comparing it against naive methods and an alternative corrected likelihood approach in linear regression and survival analysis settings. Finally, we apply POI-SIMEX to a high-grade serous ovarian cancer study, investigating the association between patient survival and the presence of CD8 Tregs.

Participants register once on Zoom and may 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 each event date.

When particles interacts with attractive-repulsive dynamics, which can model birds flocking, space dust, or a variety of other phenomena, they tend to form a nice distribution. Understanding these distributions is an active area of applied analysis that is highly related to the classical concept of equilibrium measures that arises in approximation theory and random matrix theory. In this talk we discuss the numerical computation of such measures via new results on power law kernels applied to orthogonal polynomials that facilitate exploration of regimes where analysis is not yet available.

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Abstract: I will present a coupling between a massive planar Gaussian free field (GFF) and a random curve in which the curve can be interpreted as the level of the field. This coupling is constructed by reweighting the law of the standard GFF-SLE_4 coupling. I will then show that in this coupling, the marginal law of the curve is that of a massive version of SLE_4, called massive SLE_4. This law on curves was orignally introduced by Makarov and Smirnov to describe the scaling limit of a massive version of the harmonic explorer.

ABSTRACT: A network of interacting qubits (usually subatomic particles) can be modelled by a connected weighted undirected graph $G$. The vertices and edges of $G$ represent the qubits and their interactions in the network, respectively. Quantum mechanics dictate that the evolution of the quantum system determined by $G$ over time is completely described by the unitary matrix $U(t)=\exp(itA)$, where $A$ is the adjacency matrix of $G$. Here, we interpret the modulus of the $(u,v)$ entry of $U(t)$ as the probability that the quantum state at vertex $u$ is found in $v$ at time $t$. In this talk, we discuss how the algebraic and spectral properties of a graph influence its ability to perform quantum state transfer.

Abstract: For this talk I will discuss a conjectured duality result, expressed in terms of $KK$-theory and $E$-theory, between certain pairs of crossed product $C^*$-algebras obtained from two transverse subspaces of $\R^n$ acting by translation on the $n$-torus $\T^n$. Specifically, given subspaces $U$ and $V$ of $\R^n$ satisfying $\R^n = U \oplus V$, the natural translation actions of $U$ and $V$ on $\T^n$ induce crossed products $A_U := C(\T^n) \rtimes U$ and $A_V := C(\T^n) \rtimes V$ which, under some mild regularity conditions on $U$ and $V$, we propose are dual in the sense of $KK$-theory and $E$-theory. After a brief introduction to $KK$-theory, $E$-theory, and crossed products, I will outline how a duality between $A_U$ and $A_V$ would, up to Morita equivalence, generalize an instance of the Baum-Connes conjecture that is already known to be true. For the final portion of the seminar, I will summarize progress made towards constructing candidate duality classes in both the $KK$-theoretic and $E$-theoretic frameworks; the definitions of which seem to require, in part, a formal square root of the harmonic oscillator analysed in my M.Sc. thesis.

See abstract (PDF).

Zoom meeting.

Programme for the Degree of Master of Science

(Department of Mathematics and Statistics)

Yingjie HOU

BSc. (University of Liverpool, 2013)
MSc. (Imperial College London, 2014)

"A literature review of batch effect removal methods for scRNA-seq Data Analysis"

Tuesday, October 15, 2024
1:00 P.M.

Virtual Defence

Supervisory Committee:
Dr. Xuekui Zhang, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Ke Xu, Department of Economics, UVic (Member)

Chair of Oral Examination:
Dr. Min Tsao, Department of Mathematics and Statistics, UVic

Abstract: We show that \((n,d,\lambda)\)-graphs with \(\lambda=O(d/log^3n)\) are universal with respect to all bounded degree spanning trees. This significantly improves upon the previous best bound due to Han and Yang, and makes progress towards a problem of Alon, Krivelevich, and Sudakov from 2007. The key new idea in our proof relies on the existence of sorting networks of logarithmic depth, as given by a celebrated construction of Ajtai, Koml\'{o}s and Szemer\'{e}di, with further applications to the vertex disjoint paths problem. Joint work with Joseph Hyde, Alp M\"{u}yesser, and Matías Pavez-Signé.

Abstract: For this talk I will discuss a conjectured duality result, expressed in terms of $KK$-theory and $E$-theory, between certain pairs of crossed product $C^*$-algebras obtained from two transverse subspaces of $\R^n$ acting by translation on the $n$-torus $\T^n$. Specifically, given subspaces $U$ and $V$ of $\R^n$ satisfying $\R^n = U \oplus V$, the natural translation actions of $U$ and $V$ on $\T^n$ induce crossed products $A_U := C(\T^n) \rtimes U$ and $A_V := C(\T^n) \rtimes V$ which, under some mild regularity conditions on $U$ and $V$, we propose are dual in the sense of $KK$-theory and $E$-theory. After a brief introduction to $KK$-theory, $E$-theory, and crossed products, I will outline how a duality between $A_U$ and $A_V$ would, up to Morita equivalence, generalize an instance of the Baum-Connes conjecture that is already known to be true. For the final portion of the seminar, I will summarize progress made towards constructing candidate duality classes in both the $KK$-theoretic and $E$-theoretic frameworks; the definitions of which seem to require, in part, a formal square root of the harmonic oscillator analysed in my M.Sc. thesis. 

https://uvic.zoom.us/j/89372959263?pwd=q7IPZKueYMnaAxLaVmlwVqHfW0H0AR.1
Meeting ID: 893 7295 9263
Password: 033409

Abstract: Spin glasses are disordered statistical physics system with both ferromagnetic and anti-ferromagnetic spin interactions. The Gibbs measure belongs to the exponential family with parameters, such as inverse temperature $\beta>0$ and external field $h\in R$. Given a sample from the Gibbs measure of a spin glass model, we study the problem of estimating system parameters. In 2007, Chatterjee first proved that under reasonable conditions, for spin glass models with $h=0$, the maximum pseudo-likelihood estimator for $\beta$ is $\sqrt{N}$-consistent. However, the approach has been restricted to the single parameter estimation setting. The joint estimation of $(\beta,h)$ for spin glasses has remained open. In this talk, I will present a joint work with Wei-Kuo Chen, Arnab Sen, which shows that under some easily verifiable conditions, the bi-variate maximum pseudo-likelihood estimator is indeed jointly $\sqrt{N}$-consistent for a large collection of spin glasses, including the Sherrington-Kirkpatrick model and its diluted variants.

This seminar takes places across multiple time zones: 9:30 AM PT/ 10:30 AM MT / 11:30 AM CT Register via Zoom to receive the link (and reminders) for this event and the rest of the series.

In this talk, I will discuss recent progress on the directed Oberwolfach problem. A directed variant of the famous Oberwolfach problem, the directed Oberwolfach problem considers the fol- lowing scenario. Given m people and t round tables of size m1,m2 ...,mt such that mi ⩾ 2, does there exist a set of m − 1 seating arrangements such that each person is seated to the right of every other person precisely once? First, I will demonstrate how this problem can be formulated as a type of graph-theoretic problem known as a cycle decomposition problem. Then, I will discuss a partic- ular style of construction that was first introduced by R. Häggkvist in 1985 to solve several cases of the original Oberwolfach problem. Lastly, I will show how this approach can be adapted to the directed Oberwolfach problem, thereby allowing us to obtain solutions for previously open cases. Results discussed in this talk arose from collaborations with Andrea Burgess, Peter Danziger, and Daniel Horsley.

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In this talk, I’ll take a birds-eye view of mathematical modelling. What is it? Is a model “a theory”? Is it “just a theory”? What can it accomplish, and how can it fail? I will outline an array of roles of (mechanistic) modelling in science, and outline some less-well-known uses of modelling. I will also describe some weaknesses of modelling, as I see them. I will argue that modelling can fail to be good science, and that modelling can even do harm in some contexts. I will propose that the onus is at least partly on modellers to prevent this, and I will make some comments and initiate discussion about how this might be approached. There will be cartoons.

Abstract: A combinatorial object is said to be quasirandom if it exhibits certain properties that are typically seen in a truly random object of the same kind. It is known that a permutation is quasirandom if and only if the pattern density of each of the twenty-four 4-point permutations is close to 1/24, which is its expected value in a random permutation. In other words, the set of all twenty-four 4-point permutations is quasirandom-forcing. Moreover, it is known that there exist sets of eight 4-point permutations that are also quasirandom-forcing. Breaking the barrier of linear dependency of perturbation gradients, we show that every quasirandom-forcing set of 4-point permutations must have cardinality at least five.

Abstract: A geometric graph $G$ is a graph $G$ whose vertices are drawn in the plane such that no three vertices are collinear, and each edge of G is a straight line segment. A geometric homomorphism from geometric graph $G$ to geometric graph $H$ is a homomorphism that preserves crossings. Similar to the regular chromatic number, the geochromatic number of a geometric graph $G$ is the smallest integer $n$ such that there is a geometric homomorphism from $G$ to a geometric clique $K_n$.

In this talk, we will particularly discuss the relation between chromatic numbers and geochromatic numbers. Even for a bipartite graph, its geochromatic number can be unbounded. However, if the graph is not too "dense", for example, every pair of crossing has distance at least $2$, then its geochromatic number is bounded by a constant.

Abstract: I will speak about Toeplitz-Pimsner algebras of product systems of Hilbert bimodules over group-embeddable monoids. Given a product system $\E$ over a submonoid of a group $G$, with coefficient algebra $A$, we show that, under technical assumptions, the fixed-point algebra $\Toepr(\E)^G$ of the gauge action of $G$ is nuclear if and only if $A$ is nuclear. Assuming in addition that $G$ is amenable, we conclude that the Toeplitz algebra is nuclear if and only if $A$ is nuclear.

I will also discuss exactness results and applications to product system over abelian monoids, $ax+b$-monoids of integral domains and Baumslag--Solitar monoids $BS^+(m,n)$ that admit an amenable embedding, which we provide when $m$ and $n$ are relatively prime. This is recent joint work with Elias Katsoulis and Camila Sehnem.

Abstract: In the talk exchangeability appears in two different meanings. In the first part, the determination of the phase diagram of the Curie-Weiss model relies on De Finetti’s Theorem. The Curie-Weiss distribution will be expressed as a random mixture of Bernoulli distributions. The competition between the Gaussian randomness in the CLT of Bernoulli’s and the randomness in their mixture replaces the standard energy-entropy competition. In the second part, we study a mean-field spin model with three- and two-body interactions. In a recent paper by Contucci, Mingione and Osabutey, the equilibrium measure for large volumes was shown to have three pure states, two with opposite magnetization and an unpolarized one with zero magnetization, merging at the critical point.

The aim is to apply the exchangeable pair approach due to Stein to prove (non-uniform) Berry-Esseen bounds, a concentration inequality, Cramér-type moderate deviations and a moderate deviations principle for the suitably rescaled magnetization.

Abstract: Strong cocomparability graphs are the reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01, 10. Strong cocomparability graphs form a subclass of cocomparability graphs (i.e., the complements of comparability graphs) and can be recognized in polynomial time.

In his seminal paper, Gallai characterized cocomparability graphs in terms of a forbidden structure called asteroids. Gallai proved that cocomparability graphs are precisely those reflexive graphs which do not contain asteroids.

In this talk, I will present a characterization of strong cocomparability graphs which is analogous to Gallai's characterization for cocomparability graphs. More precisely, I will show that strong cocomparability graphs are precisely those reflexive graphs which do not contain weak edge-asteroids (a weaker version of asteroids). The characterization also leads to a polynomial time recognition algorithm for strong cocomparability graphs.

Abstract: I will speak about Toeplitz-Pimsner algebras of product systems of Hilbert bimodules over group-embeddable monoids. Given a product system $\E$ over a submonoid of a group $G$, with coefficient algebra $A$, we show that, under technical assumptions, the fixed-point algebra $\Toepr(\E)^G$ of the gauge action of $G$ is nuclear if and only if $A$ is nuclear. Assuming in addition that $G$ is amenable, we conclude that the Toeplitz algebra is nuclear if and only if $A$ is nuclear. I will also discuss exactness results and applications to product system over abelian monoids, $ax+b$-monoids of integral domains and Baumslag--Solitar monoids $BS^+(m,n)$ that admit an amenable embedding, which we provide when $m$ and $n$ are relatively prime. This is recent joint work with Elias Katsoulis and Camila Sehnem.

Abstract: Double dimers are superimposition of two perfect matchings. Such superimpositions can be decomposed into disjoint simple loops. The question we address is: as the graphs become large, in a 'typical' double dimer sample, do some of the loops diverge to an infinite loop (or a bi-infinite path)? It is known that in the square lattice, this is not the case. In this talk, I will address the same question, but on planar hyperbolic graphs. (I will not spoil the answer in the abstract! )

The answer involves elements from the theory of hyperbolic geometry, circle packings, spanning trees, random walks and unimodular random graphs.