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Abstract: The stochastic heat equation (driven space-time white noise) arises from interface growth dynamics via the Kardar-Parisi-Zhang equation and from the theory of disordered systems via continuum directed random polymers. Despite these physical relations, many fundamental questions for the stochastic heat equation above one dimension remain open. In particular, two dimensions are the critical dimensions for the stochastic heat equation and are known for much more subtle properties.

In this talk, I will begin with an overview of the stochastic heat equation. Then I will turn to the setting of two dimensions and explain connections between (1) the moments of certain solutions from renormalizing the noise and (2) a solvable quantum mechanical system given by the many-body Bose gas with delta-function potentials. Accordingly, the last part of the talk will concentrate on related constructions of the Bose gas dynamics, with an emphasis on a Euclidean, probabilistic analytic view.

Abstract: In this talk, we will investigate the extensions of the cycle matroid of a complete graph. I will show that the number of these extensions is surprisingly large.

Please contact the organizer for the Zoom link.

Abstract: I will review the definition of the universal Toeplitz C*-algebra Tu(P) associated to a submonoid P of a group. Tu(P) is given by a presentation based on Xin Li’s semilattice of constructible ideals with an extra condition. After briefly mentioning faithful representations and a uniqueness theorem for the reduced Toeplitz algebra Tλ(P), I will concentrate on the associated universal boundary quotient ∂Tu(P) and its reduced version ∂Tλ(P), and give sufficient conditions for the latter to be purely infinite simple. I intend to discuss some new applications, mainly to monoids arising from non-maximal orders in number fields but also to right LCM monoids with nontrivial units. This is joint work with Camila F. Sehnem.

Abstract: Network analysis is one of the prominent multivariate techniques used to study structural and functional connectivity of the brain. In a network model of the brain, vertices are used to represent voxels or regions of the brain, and edges between two nodes represent a physical or functional relationship between the two incident regions. Network investigations of connectivity have produced many important advances in our understanding of brain structure and function, including in domains of aging, learning and memory, cognitive control, emotion, and disease. Despite their use, network methodologies still face several important challenges. In this talk, I will focus on a particularly important challenge in the analysis of structural and functional connectivity: how does one jointly model the generative mechanisms of structural and functional connectivity with other modalities? I propose and describe a statistical network model, called the generalized exponential random graph model (GERGM), that flexibly characterizes the network topology of structural and functional connectivity and can readily integrate other modalities of data. The GERGM also directly enables the statistical testing of individual differences through the comparison of their fitted models. In applying the GERGM to the connectivity of healthy individuals from the Human Connectome Project, we find that the GERGM reveals remarkably consistent organizational properties guiding subnetwork architecture in the typically developing brain. We will discuss ongoing work of how to adapt these models to neuroimaging cohorts associated with the ADRC at the University of Pittsburgh, where the goal is to relate the dynamics of structural and functional connectivity with tau and amyloid – beta deposition in individuals across the Alzheimer’s continuum.

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

I will describe variational problems whose solutions imply statements about dynamical systems, as well as how relaxations of these variational problems often can be solved computationally using tools of polynomial optimization. The talk will be an informal overview, focusing on the ODE case and including both deterministic and stochastic ODEs. In addition to showing computational results for particular systems, I will describe some theoretical results and open questions.

The lectures will be available via zoom and also will be projected live in a classroom. Please register (for both the zoom sessions and the classroom session) here:https://uvic.zoom.us/meeting/register/tZ0qdeutqTwoGtQF4_F8zJLxOovazzLI7APa

In 2016, Tao introduced the slice rank polynomial method as a reformulation of a technique that first appeared in work of Croot, Lev and Pach, and was the basis of a breakthrough of Ellenberg and Gijswijt on the upper bound for the famous cap-set problem. The cap-set problem asks about the maximum size of a subset of F_3^n not containing a three-term arithmetic progression. In this series of three lectures, we will discuss the slice rank polynomial method, various applications, and some of its limitations.

In the first lecture, we will give some background and show (following Tao) how the slice rank polynomial method can be used to show the Ellenberg-Gijswijt bound for the cap-set problem. The second lecture will discuss more applications, in particular a result of Naslund and Sawin on the so-called Erdös-Szemeredi sunflower problem (which is a problem in extremal set theory), as well as an upper bound for the maximum size of a subset of F_p^n that does not contain p distinct vectors summng to zero. The problem of determining the maximum size of such a subset is closely related to the Erdös-Ginzburg-Ziv problem in discrete geometry. In the third lecture, we will continue to discuss this problem, showing a much better upper bound by combining the slice rank polynomial method with with additional combinatorial ideas.

Lisa also says: I will do my best to make the lecture accessible to final year undergraduates (the first two lectures should definitely be accessible; the third might be a little bit more technical, but I hope that it will also still be accessible).

Lisa is the recipient of a UVic DWS award. The Distinguished Women Scholars (DWS) Awards and Lecture Series were established by the Provost to highlight and honour outstanding research and creative achievements by female-identifying scholars. The purpose of these awards is to celebrate, recognize and share the impact of outstanding research and creative achievements by women at any stage of their careers.

To celebrate PIMS 25th Anniversary we have convened a special Network Wide Colloquium featuring distinguished speakers with mathematical connections throughout the PIMS network. Join us as we continue this fall with a lecture from Rafe Mazzeo, Professor at Stanford University. Registration is open.

Z_2 Harmonic Spinors in Gauge Theory Rafe Mazzeo, Stanford University

Gauge-theoretic moduli spaces are often noncompact, and various techniques have been introduced to study their asymptotic features. Seminal work by Taubes shows that in many situations where the failure of compactness for sequences of solutions is due to the noncompactness of the gauge group, diverging sequences of solutions lead to what he called Z_2 harmonic spinors. These are multivalued solutions of a twisted Dirac equation which are branched along a codimension two subset. This leads to a number of new problems related to these Z_2 harmonic spinors as interesting geometric objects in their own right. I will survey this subject and talk about some recent work in progress with Haydys and Takahashi to compute the index of the associated deformation problem.

Speaker Biography: Rafe Mazzeo is an expert in PDEs and Microlocal analysis. He did his Ph.D. at MIT and was then appointed as Szegő Assistant Professor at Stanford University, where he is now Professor and Chair of the Department of Mathematics. He has served the mathematical community in many important ways, including as Director of the Park City Mathematics Institute.

Abstract: I will review the definition of the universal Toeplitz C*-algebra Tu(P) associated to a submonoid P of a group. Tu(P) is given by a presentation based on Xin Li’s semilattice of constructible ideals with an extra condition. After briefly mentioning faithful representations and a uniqueness theorem for the reduced Toeplitz algebra Tλ(P), I will concentrate on the associated universal boundary quotient ∂Tu(P) and its reduced version ∂Tλ(P), and give sufficient conditions for the latter to be purely infinite simple. I intend to discuss some new applications, mainly to monoids arising from non-maximal orders in number fields but also to right LCM monoids with nontrivial units. This is joint work with Camila F. Sehnem.

Abstract: We use a generic two-stage population model to derive an adaptive dynamical system for the evolution of reproduction age, and study how this evolution is driven by the harvest of adults. We consider the tradeoffs between maturation rate and fecundity, juvenile mortality, and adult mortality. We analyze the benefit and cost of faster maturation under each tradeoff that drives the evolution. We found that harvesting adults affects the evolution of maturation by affecting the benefit. For the tradeoff between maturation and juvenile mortality, harvesting adults does not affect the benefit, and thus does not affect optimal maturation strategy. For the other two tradeoffs, harvesting adults affects the benefit through the equilibrium adult/juvenile ratio, which is determined by the density dependence of juveniles. Harvesting adults causes a slower maturation only if it significantly reduces this ratio, which can only happen with very strong adult protection to juveniles. Otherwise, harvesting adults always causes a faster maturation.

Abstract: In this work, improved swarm intelligent algorithms, namely, Salp Swarm Optimization algorithm, whale optimization, and Grasshopper Optimization Algorithm are proposed for data clustering. Our proposed algorithms utilize the crossover operator to obtain an improvised version of the existing algorithms. The performance of our suggested algorithms is tested by comparing the proposed algorithms with standard swarm intelligent algorithms and other existing algorithms in the literature. Non-parametric statistical test, the Friedman test, is applied to show the superiority of our proposed algorithms over other existing algorithms in the literature. The performance of our algorithms outperforms the performance of other algorithms for the data clustering problem in terms of computational time and accuracy.

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

The lectures will be available via zoom and also will be projected live in a classroom. Please register (for both the zoom sessions and the classroom session) here:https://uvic.zoom.us/meeting/register/tZ0qdeutqTwoGtQF4_F8zJLxOovazzLI7APa

In 2016, Tao introduced the slice rank polynomial method as a reformulation of a technique that first appeared in work of Croot, Lev and Pach, and was the basis of a breakthrough of Ellenberg and Gijswijt on the upper bound for the famous cap-set problem. The cap-set problem asks about the maximum size of a subset of F_3^n not containing a three-term arithmetic progression. In this series of three lectures, we will discuss the slice rank polynomial method, various applications, and some of its limitations.

In the first lecture, we will give some background and show (following Tao) how the slice rank polynomial method can be used to show the Ellenberg-Gijswijt bound for the cap-set problem. The second lecture will discuss more applications, in particular a result of Naslund and Sawin on the so-called Erdös-Szemeredi sunflower problem (which is a problem in extremal set theory), as well as an upper bound for the maximum size of a subset of F_p^n that does not contain p distinct vectors summng to zero. The problem of determining the maximum size of such a subset is closely related to the Erdös-Ginzburg-Ziv problem in discrete geometry. In the third lecture, we will continue to discuss this problem, showing a much better upper bound by combining the slice rank polynomial method with with additional combinatorial ideas.

Lisa also says: I will do my best to make the lecture accessible to final year undergraduates (the first two lectures should definitely be accessible; the third might be a little bit more technical, but I hope that it will also still be accessible).

Lisa is the recipient of a UVic DWS award. The Distinguished Women Scholars (DWS) Awards and Lecture Series were established by the Provost to highlight and honour outstanding research and creative achievements by female-identifying scholars. The purpose of these awards is to celebrate, recognize and share the impact of outstanding research and creative achievements by women at any stage of their careers.

The lectures will be available via zoom and also will be projected live in a classroom. Please register (for both the zoom sessions and the classroom session) here:https://uvic.zoom.us/meeting/register/tZ0qdeutqTwoGtQF4_F8zJLxOovazzLI7APa

In 2016, Tao introduced the slice rank polynomial method as a reformulation of a technique that first appeared in work of Croot, Lev and Pach, and was the basis of a breakthrough of Ellenberg and Gijswijt on the upper bound for the famous cap-set problem. The cap-set problem asks about the maximum size of a subset of F_3^n not containing a three-term arithmetic progression. In this series of three lectures, we will discuss the slice rank polynomial method, various applications, and some of its limitations.

In the first lecture, we will give some background and show (following Tao) how the slice rank polynomial method can be used to show the Ellenberg-Gijswijt bound for the cap-set problem. The second lecture will discuss more applications, in particular a result of Naslund and Sawin on the so-called Erdös-Szemeredi sunflower problem (which is a problem in extremal set theory), as well as an upper bound for the maximum size of a subset of F_p^n that does not contain p distinct vectors summng to zero. The problem of determining the maximum size of such a subset is closely related to the Erdös-Ginzburg-Ziv problem in discrete geometry. In the third lecture, we will continue to discuss this problem, showing a much better upper bound by combining the slice rank polynomial method with with additional combinatorial ideas.

Lisa also says: I will do my best to make the lecture accessible to final year undergraduates (the first two lectures should definitely be accessible; the third might be a little bit more technical, but I hope that it will also still be accessible).

Lisa is the recipient of a UVic DWS award. The Distinguished Women Scholars (DWS) Awards and Lecture Series were established by the Provost to highlight and honour outstanding research and creative achievements by female-identifying scholars. The purpose of these awards is to celebrate, recognize and share the impact of outstanding research and creative achievements by women at any stage of their careers.

Abstract: One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. A new approach to data assimilation known as the Azouani-Olson-Titi algorithm (AOT) introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. In 2014, the solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this talk, I will present our work on parameter recovery, well-posedness for the sensitivity equations, a nonlinear version of the AOT algorithm, and real-world applications in ocean models, as well as new ideas based off of these investigations.

Abstract:
In 1975, Pippenger and Golumbic instigated the study of the maximum number of induced copies of a small graph H which can be contained in an n-vertex graph G. This problem has received considerable attention over the years, yet there remain many small graphs H for which the maximum is not known asymptotically, including the path on four vertices and many graphs on five vertices. The case where H is a cycle is of particular interest and was solved for 5-cycles for large enough n by Balogh, Hu, Lidický, and Pfender in 2016.

In this talk we will discuss recent progress on the analogous problem in the setting where the graphs G and H are planar. In particular, for sufficiently large n we determine exactly the maximum numbers of induced 4-, 5-, and 6-cycles that can be contained in a planar graph on n vertices and we classify the graphs which achieve these maxima.

Please contact the organizer if you need the Zoom link.

Abstract: In 1967, Haag, Hugenholtz, and Winnink introduced the KMS condition in a seminal paper as a condition for equilibrium in quantum statistical mechanics, since it survives, in some sense, to the procedure known as the thermodynamic limit. In the following years, many results were proved that vindicated this point of view, such as the variational principle. Some years later, Lanford and Ruelle, and Dobrushin independently, introduced another condition for equilibrium states better suited for classical systems, known today as the DLR equations, that nowadays are ubiquitous in classical statistical mechanics. In these two talks, I will briefly introduce both notions, discuss the apparent differences between them, and will sketch a proof that they are equivalent in some cases where both can be defined. I will also review some properties of the KMS states for the Ising model.

Abstract: Spatio-temporal counts of infectious disease cases often contain an excess of zeros. Existing zero inflated Poisson models applied to such data do not adequately capture the switching of the disease between periods of presence and absence overtime. As an alternative, we develop a new zero-state coupled Markov switching Poisson Model, under which the disease switches between periods of presence and absence in each area through a series of partially hidden nonhomogeneous Markov chains coupled between neighboring locations. When the disease is present, an autoregressive Poisson model generates the cases with a possible 0 representing the disease being undetected. Bayesian inference and prediction is illustrated using spatio-temporal counts of dengue fever cases in Rio de Janeiro, Brazil. This is joint work with Dirk Douwes-Schultz.​

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

Abstract: The knot signature demonstrates an important connection between knots and 4-manifolds. In this talk we will recall the construction of this invariant and discuss a new extension, the equivariant signature, to knots with certain symmetries. We will include a brief overview of symmetries of knots and some geometric applications of the equivariant signature.

Register here.

Recent progress in model theory is changing our understanding of how the finite and infinite interact. One aspect of this story has to do with the emerging appearance of complexity in so-called simple unstable theories, which provide a model theoretic framework for studying certain families of "random" objects, such as the theories of random graphs or hypergraphs or pseudofinite fields.

Speaker Biography: Maryanthe Malliaris received her Ph.D. from the University of California at Berkeley in model theory, and is currently Professor of Mathematics at the University of Chicago. She was a winner of the 2010 Kurt Gödel Research Prize Fellowship, and in 2017 was awarded the Hausdorff medal for joint work with Saharon Shelah. Malliaris was an invited speaker at the 2018 International Congress of Mathematicians.

Abstract: A knot K in the 3-sphere is slice if it bounds a disk in the 4-ball. If the knot K has a symmetry (e.g. K is periodic), we say that K is equivariantly slice if it bounds a disk in the 4-ball where the symmetry of the knot extends to a symmetry of the disk in the 4-ball. I'll discuss some joint work with Keegan Boyle on trying to understand equivariant sliceness.

Abstract: In 1967, Haag, Hugenholtz, and Winnink introduced the KMS condition in a seminal paper as a condition for equilibrium in quantum statistical mechanics, since it survives, in some sense, to the procedure known as the thermodynamic limit. In the following years, many results were proved that vindicated this point of view, such as the variational principle. Some years later, Lanford and Ruelle, and Dobrushin independently, introduced another condition for equilibrium states better suited for classical systems, known today as the DLR equations, that nowadays are ubiquitous in classical statistical mechanics. In these two talks, I will briefly introduce both notions, discuss the apparent differences between them, and will sketch a proof that they are equivalent in some cases where both can be defined. I will also review some properties of the KMS states for the Ising model.

Abstract: A two-stage enrichment design is a type of adaptive design, which extends a stratified design with a futility analysis on the marker negative cohort at the first stage, and the second stage can be either a targeted design with only the marker positive stratum, or still the stratified design with both marker strata, depending on the result of the interim futility analysis.

In this talk we consider the situation where the marker assay and the classification rule are possibly subject to error. We derive the sequential tests for the global hypothesis as well as the component tests for the overall cohort and the marker-positive cohort. We discuss the power analysis with the control of the type-I error rate and show the adverse impact of the misclassification on the powers. We also show the enhanced power of the two-stage enrichment over the one-stage design, and illustrate with examples of the recent successful development of immunotherapy in non-small-cell lung cancer.​

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

Abstract: In this talk I will discuss activated random walk (ARW) and the stochastic sandpile (SSM), two interacting particle systems that exhibit a phase transition on infinite domains and self-organized criticality on finite domains. ARW and SSM both consist of identical particles that perform simple random walk, initially with average density μ particles per site, but they follow different local interaction rules. Depending on the value of μ, particles may eventually stop moving, or remain active forever. Current research is focused on determining where the transition between these two phenomena occurs, and many questions still remain – even on Z. I will present some recent results and discuss the novel tools involved.

Abstract: In this talk I will discuss activated random walk (ARW) and the stochastic sandpile (SSM), two interacting particle systems that exhibit a phase transition on infinite domains and self-organized criticality on finite domains. ARW and SSM both consist of identical particles that perform simple random walk, initially with average density μ particles per site, but they follow different local interaction rules. Depending on the value of μ, particles may eventually stop moving, or remain active forever. Current research is focused on determining where the transition between these two phenomena occurs, and many questions still remain – even on Z. I will present some recent results and discuss the novel tools involved.

Aaron will talk about the (classic) paper "Domination in Graphs with Minimum Degree Two" by William McCuaig and Bruce Shepherd (Journal of Graph Theory, 1989).

Notice of the Final Oral Examination for the Degree of Master of Science of

BRITTANY HALVERSON-DUNCAN
MSc (University of Victoria, 2014)
BSc (Queen’s University, 2011)

“A Multistate Extension of the Jolly Seber Model: Combining Adult Mark-recapture data with Juvenile data”

Department of Mathematics and Statistics

Thursday, October 21, 2021 9:00am (PDT)
David Strong Building Room A518

Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Simon Bonner, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner:
Dr. Wendell Challenger, LGL Ltd.

Chair of Oral Examination:
Prof. Conrad Alexandrowicz, Department of Theatre, UVic

Abstract

The Laskeek Bay Conservation Society has been collecting data on the East Limestone Island population of Ancient Murrelets since 1989. For the first 15 years of this decades-long study, mark-recapture data was collected annually on the adult population using one method while chicks were captured and tagged each year soon after their birth using another method. We developed a Jolly-Seber type model that integrates the adult and chick data. Using a multi-state framework, our model separates the ‘alive’ state of the JS model into several age-related states, allowing for different survival and capture parameters between states. In the Ancient Murrelet case study we found that a 6-state model with constant adult survival and capture parameters best fit the data. We determined that, since the detected chicks are rarely seen again, including these individuals in the model does not result in estimates which greatly differ from that of the standard Jolly Seber model but in a population in which juveniles have high survival and re-capture probabilities, the MSJS model is able to reduce the bias in estimates of population parameters.

Abstract: In these two talks I will give a brief introduction to \'etale groupoids and their C*-algebras, and present examples of factor groupoids which arise from quotients of path spaces of Bratteli diagrams, and examples that arise from certain extensions of Cantor minimal systems constructed by Robin Deeley, Ian Putnam, and Karen Strung. I will also describe how to compute the K-theory of these algebras, and how they fit into the Elliott classification scheme.

Abstract: We consider numerical strategies to handle two-dimensional Euler equations and 2D water waves in a fully non-linear regime. The free-surface is discretized via lagrangian tracers and the numerical strategy is constructed carefully to include desingularizations, but no artificial regularizations. We present a rigorous analysis of the singular kernel operators involved in these methods.

Zoom link: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09 Please login with your UVic ID.

I will present new, non-asymptotic bounds on the heights of random combinatorial trees and conditioned Bienaymé trees, as well as stochastic inequalities relating the heights of combinatorial trees with different degree sequences. The tool for most of the proofs is a new approach to coding rooted trees by sequences, based on a new proof of Cayley's formula.

3:00 pm Coffee Meet and Greet
3:30 pm Lecture

Abstract: Recursive distributional equations (RDEs) are ubiquitous in probability. For example, the standard Gaussian distribution can be characterized as the unique fixed point of the following RDE

X = (X_1 + X_2)/sqrt(2),

among the class of centered random variables with standard deviation of 1. (The equality in the equation is in distribution; the random variables X,X_1 and X_2 must all be identically distributed; and X_1 and X_2 must be independent.)

Recently, it has been discovered that the dynamics of certain recursive distributional equations can be solved using by using tools from numerical analysis, on the convergence of approximation schemes for PDEs. In particular, the framework for studying stability and convergence for viscosity solutions of nonlinear second order equations, due to Crandall-Lions, Barles-Souganidis, and others, can be used to prove distributional convergence for certain families of RDEs, which can be interpreted as tree-valued stochastic processes. I will survey some of these results, as well as the (current) limitations of the method, and our hope for further interplay between these two research areas.

Based on joint work with Erin Beckman, Hannah Cairns, Luc Devroye, Celine Kerriou, Jessica Lin, and Rivka Maclaine Mitchell.​

Download poster (PDF)

Abstract: Generating functions are an invaluable tool in many areas of discrete mathematics. In this talk we view generating functions as a data structure for combinatorial sequences and ask how efficiently we can determine properties such as asymptotics. This naturally leads us to consider the new field of analytic combinatorics in several variables (ACSV). The methods of ACSV rely on advanced results from complex analysis in several variables, topology, and algebraic and differential geometry -- giving the field a reputation for powerful methods which can be difficult for new researchers to get a firm grasp on. This talk aims to "demystify" ACSV by surveying some of its main results, software implementations, and recent applications of the theory.

Please contact the organizer for the Zoom link.

Abstract: In these two talks I will give a brief introduction to \'etale groupoids and their C*-algebras, and present examples of factor groupoids which arise from quotients of path spaces of Bratteli diagrams, and examples that arise from certain extensions of Cantor minimal systems constructed by Robin Deeley, Ian Putnam, and Karen Strung. I will also describe how to compute the K-theory of these algebras, and how they fit into the Elliott classification scheme.

Abstract: In this talk I will present an existence result for two-dimensional steady solitary water waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. The particularity of these waves is that they may have internal stagnation points and overhanging wave profiles. The proof relies on a novel reformulation of the problem as an elliptic system for two scalar functions in a fixed domain: one describing the conformal map of the fluid region and the other the flow beneath the wave. This is a joint work with Miles. H. Wheeler (University of Bath).

Zoom link: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09 Please login with your UVic ID.

Bio: Cedric Beaulac has recently received his PhD in Statistical Sciences from the University of Toronto and was awarded a CANSSI Distinguished Postdoctoral Fellowship in 2021. He is currently a postdoctoral fellow at Simon Fraser University and the University of Victoria where he studies neuroimaging genetics problems under the supervision of Farouk Nathoo, Jiguo Cao, and Mirza Faisal Beg. His research interests lie at the intersection of statistical sciences and machine learning.​

Abstract: In this presentation, we discuss the Variational AutoEncodeur (VAE): a latent variable model emerging from the machine learning community. To begin, we introduce the theoretical foundations of the model and its relationship with well-established statistical models. Then, we discuss how we used VAEs to solve two widely different problems. First, we tackled a classic statistical problem, survival analysis, and then a classic machine learning problems, image analysis and image generation. We conclude with a short discussion of our latest research project where we establish a new metric for the evaluation or regularization of latent variable models such a Gaussian Mixture Models and VAEs.​

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

Abstract: Joint work with: Omer Angel, Yinon Spinka

We prove that a well-known graphical expansion of the Ising model, known as the Loop O(1) model, is a factor of i.i.d. on unimodular random rooted graphs under various boundary conditions and in the presence of a non-negative external field. As an application we show that the gradient of the free Ising model is a factor of i.i.d. on unimodular planar maps. The key idea is to develop an appropriate theory of local limits of uniform even subgraphs with various boundary conditions and prove that they can be sampled as a factor of i.i.d. Another key tool we prove and exploit is that the wired uniform spanning trees on unimodular transient graphs are factors of i.i.d. This partially answers some questions posed by Tom Hutchcroft.

Abstract:

It was shown recently by Delcourt and Postle that any sufficiently large graph G of order n with minimum degree at least 0.827n has a fractional triangle decomposition, i.e. an assignment of weights to the triangles in G such that for every edge e, the total of all weights of triangles containing e is exactly one.

In this talk, I will consider a variant on this problem for 3-partite host graphs. This setting is a bit trickier, because triangle weights are typically moved around in the dense setting using cliques of order 4 or 5, and these are unavailable in 3-partite graphs. Using a different method, an analogous minimum degree threshold is computed for a balanced 3-partite graph to admit a fractional triangle decomposition.

One motivation is that the problem of completing partial Latin squares can be cast in terms of triangle-decomposition of 3-partite graphs. Applying a result of Barber, Kühn, Lo, Osthus and Taylor, our fractional threshold implies an honest-to-goodness threshold, and hence a result on completing sparse partial Latin squares of large order.

This is based on joint work with Flora Bowditch.

Abstract: In 2007 Kechris and Rosendal showed that there is a unique dense $G_\delta$ conjugacy class in the group of homeomorphisms of the Cantor set. An explicit construction of a member of this class, along with a characterization of members of the class, was given by Akin, Glasner, and Weiss shortly thereafter. A homeomorphism in this conjugacy class is knowns as a "generic" homeomorphism of the Cantor set. In this talk I will describe another context, arising from model theory, in which one can make sense of the notion of a "generic" structure quite generally, and in particular of a generic homeomorphism. I will explain why in this model-theoretic context there is a generic homeomorphism of the Cantor set, but the homeomorphism constructed by Akin, Glasner, and Weiss is not generic in this sense. No prior knowledge of model theory will be necessary.

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

Abstract: In longitudinal studies, we measure the same variables at multiple time-points to track their change over time. The exact data collection schedules (i.e., time of participants' visits) are often pre-determined to accommodate the ease of project management and compliance. Therefore, it is common to schedule those visits at equally spaced time intervals. However, recent publications based on simulated experiments indicate that the power of studies and the precision of model parameter estimators is related to the participants' visiting scheme. So, in this work, we investigate how to schedule participants' visits to better study the accelerated cognitive decline of senior adults, where a broken-stick model is often applied. We formulate this optimal design problem on scheduling participants' visiting into a high- dimensional optimization problem and derive its approximate solution by adding reasonable constraints. Based on this approximation, we propose a novel design of the visiting scheme that aims to maximize the power (i.e. reduce the variance of estimators) in identifying the onset of accelerated decline. Using both simulation studies and evidence from real data, we demonstrate that our design outperforms the standard equally-spaced one when we have strong prior knowledge on the change-points. This novel design helps researchers plan their longitudinal studies with improved power in detecting pattern change without collecting extra data. Also, this individual-level scheduling system helps monitor seniors' cognitive function and, therefore, benefits the development of personal level treatment for cognitive decline, which agrees with the trend of the health care system.

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

Abstract: Joint work with Christophe Garban. The discrete Coulomb gas is a model where an integer amount of charged particles are put on the $d$-dimensional grid. In this talk, I will discuss the basic properties of the Coulomb gas, its connection with other statistical physics models and the scaling limit of the potential of the discrete Coulomb gas at high enough temperature.

If you are local, please use your UVic SSO credentials so we don’t have to hand-admit you. Zoom link: https://uvic.zoom.us/j/98731132367?pwd=SzJKOWlKanZNaEVYMXRQQ0RpbGxJdz09

Abstract: We discuss a construction applying to any smooth flow on a smooth compact manifold M yielding an \(\R\)-equivariant spectral triple over the *-algebra of smooth functions on M. The case of Krönecker flow on the 2-torus determines a spectral triple over C^\infty (T^2)\rtimes \Gamma for an appropriate dense countable subgroup of the real line, inducing a Poincaré duality for the irrational rotation algebra. If time allows we discuss the problem of extending this result to higher genus surfaces.

Abstract: Nonlinear scalar field theories on the line such as the phi^4 model or the sine-Gordon model feature soliton solutions called kinks. They are expected to form the building blocks of the long-time dynamics for these models. In this talk I will survey recent progress on the asymptotic stability problem for kinks and I will present a recent result (joint work with W. Schlag) on the asymptotic stability of the sine-Gordon kink under odd perturbations.

Zoom link: https://uvic.zoom.us/j/5826187847?pwd=RlVrb0RoU0xDWTlLUDVkZW54ZThyQT09. Please login with your UVic ID

Abstract:
We investigate a class of minimax optimal regression designs for models with heteroscedastic errors, and the resulting designs are robust against possible misspecification of the error variance. Since we never know the error variance exactly in practice, it is important to allow small deviations from the assumed error variance and construct robust optimal designs. In this talk, we discuss minimax design criteria, properties of minimax designs, and an effective algorithm to solve challenging non-convex optimization problems for finding those minimax designs on a discrete design space. Examples are given to illustrate minimax optimal designs and their properties. This is a joint work with Hanan Abousaleh.

Join Zoom Meeting https://uvic.zoom.us/j/87235877567

For more information and to register see https://www.pims.math.ca/scientific-event/210929-tppfsec.

Abstract: Closely motivated by financial considerations, we develop an integration theory which is not classical i.e. it is not necessarily associated with a measure. The base space, denoted by $\mathcal{S}$ and called a trajectory space, substitutes the set $\Omega$ in probability theory and provides a fundamental structure via conditional subsets $\mathcal{S}_{(S,j)}$ that allows the definition of conditional integrals. The setting is a natural by-product of no arbitrage assumptions that are used to model financial markets and games of chance (in a discrete infinite time framework). The constructed conditional integrals can be interpreted as required investments, at the conditioning node, for hedging an integrable function, the latter characterized a.e. and in the limit as we increase the number of portfolios used. The integral is not classical due to the fact that the original vector space of portfolio payoffs is not a vector lattice. In contrast to a classical stochastic setting, where price processes are associated with conditional expectations (with respect to risk neutral measures), we uncover a theory where prices are naturally given by conditional non-lattice integrals. One could then study analogues of classical probabilistic notions in such a non-classical setting, we enumerate some of the possible results such as Doob's martingale convergence theorem and indicate an analogy with a dynamical system setting and the ergodic theorem.

For more information and to register see https://www.pims.math.ca/scientific-event/210923-pnwcan.

Abstract: We discuss a construction applying to any smooth flow on a smooth compact manifold M yielding an \(\R\)-equivariant spectral triple over the *-algebra of smooth functions on M. The case of Krönecker flow on the 2-torus determines a spectral triple over C^\infty (T^2)\rtimes \Gamma for an appropriate dense countable subgroup of the real line, inducing a Poincaré duality for the irrational rotation algebra. If time allows we discuss the problem of extending this result to higher genus surfaces.

Abstract

The intrinsic infinite-dimensional nature of functional data creates a bottleneck in the application of traditional classifiers to functional settings. These classifiers are generally either unable to generalize to infinite dimensions or have poor performance due to the curse of dimensionality. To address this concern, we propose building a distance-weighted discrimination (DWD) classifier on scores obtained by projecting data onto one specific direction. We choose this direction by minimizing, over a reproducing kernel Hilbert space, an empirical risk function containing the DWD classifier loss function. Our proposed classifier avoids overfitting and enjoys the appealing properties of DWD classifiers. We further extend this framework to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate. Through simulation studies and a real-world application, we demonstrate that the proposed classifier performs favourably relative to other commonly used functional classifiers in terms of prediction accuracy in finite-sample settings.

https://uvic.zoom.us/j/87235877567

Abstract:

Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.

In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics.

Notice of the Final Oral Examination for the Degree of Master of Arts of

CHANGHAO GUO MA
(University of Victoria, 2013)

“The Spatial Dependence between Hypoxia and Cytotoxic T Cells in Tumor Microenvironment”

Department of Mathematics and Statistics

Monday, September 20, 2021 at 10:30 (PDT)
Remote Defence

Supervisory Committee:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic (Member)
Dr. Julian J. Lum, Department of Biochemistry and Microbiology, UVic (Outside Member)

External Examiner:
Dr. Cindy Feng, Department of Community Health and Epidemiology, Dalhousie University

Chair of Oral Examination:
Dr. Lynne Siemens, School of Public Administration, UVic

Abstract
The objective of this thesis is to examine the relationship between CAIX (a biomarker for insufficient oxygen in tumor microenvironment) and CD8+ T cells (the immune cells for killing cancer cells) for ovarian cancer. We approach the problem from two perspectives. The first approach is to set up count models such as Poisson, negative binomial, and zero-inflated Poisson models to examine the cell counts between CAIX and CD8+ T cells in the tumor microenvironment. The second approach is to apply the cross-K function, which is a second-order property of the point pattern process. We find that the tissue microarray (TMA), which is a technique to assemble hundreds of tissue samples on one TMA block, has a fixed effect on the CD8+ T cell counts. There are two TMA blocks A2 and B1. The relationship between CAIX and CD8+ T cells highly depends on TMAs. On TMA B1 stroma, a negative relationship between CAIX and CD8+ T cell counts is observed in the negative binomial models. When taking the spatial domain into accounts and comparing the estimated cross-K function of CAIX and CD8+ T cells to the simulated envelopes generated by a homogeneous Poisson process, we discover that CAIX and CD8+ T cells are regulated and repel each other on TMA B1. Tissue category also plays an influential role. The estimated cross-K function of CAIX and CD8 + T cells is more dispersed on tumors than on stroma.

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy of

EUGENE AFIAMOAH OPOKU BSc (Brock University, 2015)
BSc (University of Ghana, 2013)

“Statistical Methods for Imaging Data, Imaging Genetics and Sparse Estimation in Linear Mixed Models”

Department of Mathematics and Statistics

Friday, September 17, 2021 at 12:30pm (PDT)
Remote Defence

Supervisory Committee:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Ejaz Syed Ahmed, Department of Mathematics, Brock University (Co-Supervisor)
Dr. Dr .Mary Lesperance, Department of Mathematics and Statistics, UVic (Member)
Dr. Xuekui Zhang, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Zeny Feng, Department of Mathematics, University of Guelph

Chair of Oral Examination:
Dr. Simon Devereaux, Department of History, UVic

This thesis presents research focused on developing statistical methods with emphasis on techniques that can be used for the analysis of data in imaging studies and sparse estimations for applications in high-dimensional data. The first contribution addresses the pixel/voxel-labeling problem for spatial hidden Markov models in image analysis. We formulate a Gaussian spatial mixture model with Potts model used as a prior for mixture allocations for the latent states in the model. Jointly estimating the model parameters, the discrete state variables and the number of states (number of mixture components) is recognized as a difficult combinatorial optimization. To overcome drawbacks associated with local algorithms, we implement and make comparisons between iterated conditional modes (ICM), simulated annealing (SA) and hybrid ICM with ant colony system (ACS-ICM) optimization for pixel labelling, parameter estimation and mixture component estimation. In the second contribution, we develop ACS-ICM algorithm for spatiotemporal modeling of combined MEG/EEG data for computing estimates of the neural source activity. We consider a Bayesian finite spatial mixture model with a Potts model as a spatial prior and implement the ACS-ICM for simultaneous point estimation and model selection for the number of mixture components. Our approach is evaluated using simulation studies and an application examining the visual response to scrambled faces. In addition, we develop a nonparametric bootstrap for interval estimation to account for uncertainty in the point estimates. In the third contribution, we present sparse estimation strategies in linear mixed model (LMM) for longitudinal data. We address the problem of estimating the fixed effects parameters of the LMM when the model is sparse and predictors are correlated. We propose and derive the asymptotic properties of the pretest and shrinkage estimation strategies. Simulation studies is performed to compare the numerical performance of the Lasso and adaptive Lasso estimators with the pretest and shrinkage ridge estimators. The methodology is evaluated through an application of a high-dimensional data examining effective brain connectivity and genetics. In the fourth and final contribution, we conduct an imaging genetics study to explore how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer's disease. We develop an analysis of longitudinal resting-state functional magnetic resonance imaging (rs-fMRI) and genetic data obtained from a sample of 111 subjects with a total of 319 rs-fMRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. A Dynamic Causal Model (DCM) is fit to the rs-fMRI scans to estimate effective brain connectivity within the DMN and related to a set of single nucleotide polymorphisms (SNPs) contained in an empirical disease-constrained set. We relate longitudinal effective brain connectivity estimated using spectral DCM to SNPs using both linear mixed effect (LME) models as well as function-on-scalar regression (FSR).

Abstract: One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete. Data assimilation circumvents this issue by continually incorporating the observed data into the model. A new approach to data assimilation known as the Azouani-Olson-Titi algorithm (AOT) introduced a feedback control term to the 2D incompressible Navier-Stokes equations (NSE) in order to incorporate sparse measurements. The solution to the AOT algorithm applied to the 2D NSE was proven to converge exponentially to the true solution of the 2D NSE with respect to the given initial data. In this research, we test the robustness, improve, and implement the AOT algorithm, as well as generate new ideas based off of these investigations. First, we apply the AOT algorithm to the 2D NSE with an incorrect parameter and prove it still converges to the correct solution up to an error determined by the error in the parameters. This led to the development of a simple parameter recovery algorithm. The implementation of this algorithm led us to provide rigorous proofs that solutions to the corresponding sensitivity equations are in fact the Frechet derivative of the solutions to the original equations. Next, we present a proof of the convergence of a nonlinear version of the AOT algorithm in the setting of the 2D NSE, where for a portion of time the convergence rate is proven to be double exponential. Finally, we implement the AOT algorithm in the large scale Model for Prediction Across Scales - Ocean model, a real-world climate model, and investigate the effectiveness of the AOT algorithm in recovering subgrid scale properties.

For more information and to register see https://www.pims.math.ca/scientific-event/210915-tppfshh.

Abstract (PDF)

The Final Oral Examination for the Degree of

Master of Science
(Department of Mathematics and Statistics)

Yuying HUANG B. Sc., Sun Yat-sen University, 2019

“Novel Modelling of High-frequency Stock Trading Data”

Wednesday, August 25, 2021
2:00 pm PDT
Conducted Virtually

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

See announcement and abstract (PDF file).

See the announcement and abstract (PDF)

Notice of the Final Oral Examination for the Degree of Master of Science of

JEREMY HUME
HBSc (University of Toronto, 2019)

“Renormalization procedures for C*-algebras”

Department of Mathematics and Statistics

Thursday, August 12, 2021
10:00am (PDT)
Remote Defence

Supervisory Committee:
Dr. Ian F. Putnam, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Marcelo Laca, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Dana P. Willliams, Department of Mathematics, Dartmouth College

Chair of Oral Examination:
Dr. John Burke, Department of Biochemistry and Microbiology, UVic

Abstract
Renormalization procedures for families of dynamical systems have been used to prove many interesting results. Examples of results include that the bifurcation rate for the attractors of an analytic one-parameter family of quadratic-like maps is universal for all such families, unique ergodicity for almost every interval exchange mapping, a unique ergodicity criterion for the vertical translation ow of a at surface in terms of its "renormalization dynamics", known as Masur's criterion, and the classification of circle diffeoeomorphisms up to C∞ conjugation. We introduce renormalization procedures for C*-algebras and étale groupoids using the concepts of C0(X)-algebras and Morita equivalence for the former, and groupoid bundles and groupoid equivalence, in the sense of Muhly, Renault and Williams, for the latter. We focus on proving analogs to Masur's criterion in both cases using C*-algebraic methods. Applying our criterion to our examples of renormalization procedures provides a unique trace criterion for unital AF algebras extending the one provided by Treviño in the setting of at surfaces and the one provided by Veech in the setting of interval exchange mappings. Also, we recover the old fact that rotation of the circle by an irrational angle is uniquely ergodic, and the new fact that interesting groupoids associated to certain iterated function systems, recently introduced by Korfanty, have unique invariant probability measures whenever they are minimal. Lastly, we show how an étale groupoid renormalization procedure arises from an étale groupoid which factors down onto a groupoid associated to its renormalization dynamics, whenever it is a local homeomorphism.

The Final Oral Examination
for the Degree of
Master of Science
(Department of Mathematics and Statistics)

Chi Kou
MBA (University of Calgary, 1996)
B. Sc (University of Victoria, 1989

“Implementation of CVXR to Estimate Mixture Distributions ”

August 11, 2021
10:30am PDT
Conducted Virtually

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

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

The Final Oral Examination
for the Degree of Master of Science
(Department of Mathematics and Statistics)

Jingyi WU
B.Sc., Nanjing University of Posts and Telecommunications, 2019

“Estimable group effects in generalized linear models”

Tuesday, August 10, 2021 2:00 P.M.
Conducted Virtually

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

Chair of Oral Examination:
Dr. Julie Zhou, Department of Mathematics and Statistics, UVic

Notice of the Final Oral Examination for the Degree of Master of Science of

TINGZHOU YU
BSc (Hebei Normal University, 2019)

“The coupling of uniform spanning trees and quantitative Russo–Seymour–Welsh for random walk on random graphs”

Department of Mathematics and Statistics

Tuesday, August 10, 2021
9:00am (PDT)
Remote Defence

Supervisory Committee:
Dr. Gourab Ray, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Benoit Laslier, Laboratoire de Probabilités, Statistique et Modélisation, Université de Paris

Chair of Oral Examination:
Dr. Ben Nadler, Department of Mechanical Engineering, UVic

Abstract
The central concern of this thesis is the study of the Russo-Seymour-Welsh (RSW) theory. The first contribution of this thesis is the a macroscopic decorrelation result for uniform spanning trees (USTs) on random planar graphs based on the RSW assumption. The similar result was established on a fixed graph in [BLR20, Theorem 4.21]. We extend this result to USTs on random graphs. In particular, we show that a similar coupling can be obtained for a collection of graphs, which has high probability. This is the key missing step in the application of the proof strategy in [BLR20] for random graphs, which established the scaling limits of height function of dimer model to a Gaussian free field on a fairly general class of fixed graphs. The second contribution of this thesis is the RSW type results for random walks on two concrete and natural examples: the unique infinite cluster of supercritical bond percolation in z2 and the Poisson-Delaunay triangulation in R2. We show that random walks crossing a rectangle without exiting holds with a stretched exponentially high in the scale. The proof employs a heat kernel estimate method for random walks on the supercritical bond percolation. The proof of RSW for bond percolation is a quick application of a combination of Barlow's results. However, we cannot apply Barlow's results for the Poisson-Delaunay triangulation directly since there is no uniform bound on degree. A key input is a quantitative isoperimetric inequality for Voronoi triangulation, which we consider to be another novel contribution of this thesis.

The Final Oral Examination for the Degree of Master of Science (Department of Mathematics and Statistics)

Yangming Li

B.Mathematics(University of Waterloo, 2018)

“Simulations with N-mixture models to understand the COVID-19 pandemic ”

July 30th,2021 2:30pm
Conducted Virtually

Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic (Supervisor)
Dr. Junling Ma, Department of Mathematics and Statistics, UVic (Member)

Chair of Oral Examination:
Dr. Michelle Miranda, Department of Mathematics and Statistics, UVic

Notice of the Final Oral Examination for the Degree of Master of Science of

YANG GUO

BEng (Huazhong Agricultural University, 2019)

“Learning COVID-19 Network from Literature Databases Utilizing Core Decomposition”

Department of Mathematics and Statistics

Tuesday, July 13, 2021 1:00 P.M. Conducted Virtually

Supervisory Committee:
Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Li Xing, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Venkatesh Srinivasan, Department of Computer Science, UVic (Outside Member)

External Examiner:
Dr. Lin Cai, Department of Electrical and Computer Engineering, UVic

Chair of Oral Examination:
Dr. Erin Kelly, Department of English, UVic

Abstract
The SARS-CoV-2 coronavirus is responsible for millions of deaths around the world. To help contribute to the understanding of crucial knowledge and to further generate new hypotheses relevant to SARS-CoV-2 and human protein interactions, we make use of the information abundant Biomine probabilistic database and extend the experimentally identified SARS-CoV- 2-human protein interaction (PPI) network in silico. We generate an extended network by integrating information from the Biomine database and the PPI network. To generate novel hypotheses, we focus on the high-connectivity sub-communities that overlap most with the PPI network in the extended network. Therefore, we propose a new data analysis pipeline that can efficiently compute core decomposition on the extended network and identify dense subgraphs. We then evaluate the identified dense subgraph and the generated hypotheses in three contexts: literature validation for uncovered virus targeting genes and proteins, gene function enrichment analysis on subgraphs, and literature support on drug repurposing for identified tissues and diseases related to COVID-19. The majority type of the generated hypotheses are proteins with their encoding genes and we rank them by sorting their connections to known PPI network nodes. In addition, we compile a comprehensive list of novel genes, and proteins potentially related to COVID-19, as well as novel diseases which might be comorbidities. Together with the generated hypotheses, our results provide novel knowledge relevant to COVID-19 for further validation.

Abstract: In this talk, I will discuss several Turán-type results for point-line incidences. It will be based on joint works with Istvan Tomon and Mozhgan Mirzaei.

This is part of the Round the World Relay in Combinatorics.

Abstract:
Russo-Seymour-Welsh's theory is a key concept in two-dimensional statistical physics models. A version of Russo--Seymour--Welsh type assumption for random walks was exploited by Berestycki, Laslier and Ray to study the decorrelation of uniform spanning trees (UST) in a planar graph. This ultimately led to a universality result about convergence of the dimer model. I will discuss an extension of this decorrelation theorem to USTs on random planar graphs. The major example we consider is the infinite cluster of supercritical bond percolation in the square lattice. This is joint work with my supervisor Gourab Ray.

Please contact the organizer if you need the Zoom link.