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Abstract: A famous result of Rado characterises those integer matrices $A$ which are partition regular, that is, for which any finite colouring of $[n]:=\{1,2,\dots,n\}$ (for $n$ sufficiently large) gives rise to a monochromatic solution to the equation $Ax=0$. The probability threshold for when the binomial random set $[n]_p$ has the property above was established via results of R\"odl and Ruci\'nski (for the 0-statement), and Friedgut, R\"odl and Schacht (for the 1-statement). Collectively these results form the Random Rado Theorem.

There has also been interest in Rado-type results in the setting of abelian groups. In this talk we prove an analogue of the Random Rado Theorem in the setting of sequences of (subsets of) abelian groups.

Joint work with Andrea Freschi and Andrew Treglown.

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

MIKAYLA HOLMES
BSc (University of Victoria, 2021)

Background Connectivity: Understanding the brain's functional organization

Department of Mathematics and Statistics

Friday, May 19, 2023 10:00 A.M.
David Strong Building Room C128

Supervisory Committee:
Dr. Michelle Miranda, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Jodie Gawryluk, Department of Psychology, UVic

Chair of Oral Examination:
Dr. Raad Nashmi, Department of Biology, UVic

Abstract
Task-state fMRI (tfMRI) and rest-state fMRI (rfMRI) surface data from the Human Connectome Project (HCP) was examined with the goal of better understanding the nature of background activation signatures and how they compare to the functional connectivity of a brain at rest. In this paper we use a hybrid-decomposition and seed-based approach to calculate functional connectivity of both rfMRI data and the estimated residual data from a Bayesian spatiotemporal model. This model accounts for local and global spatial correlations within the brain by applying two levels of data decomposition methods. Moreover, long memory temporal correlations are taken into account by using the Haar discrete wavelet transform. Motor task data from the HCP is modelled, followed by an analysis of the residuals, which provide details regarding the brain's background functional connectivity. These residual connectivity patterns are assessed using a manual procedure and through studying the induced covariance matrix of the model's error term. When we compare these activation signatures to those found for the same subject at rest we found that regions within the subcortex displayed strong connections in both states. Regions associated with the default mode network also displayed statistically significant connectivity while the subject was at rest. In contrast, the pre-central ventral and mid-cingulate regions had strong functional patterns in the background activation signatures that were not present in the rest-state data. This modelling technique combined with a hybrid approach to assessing functional activation signatures provides valuable insights into the role background connections play in the brain. Moreover, it is easily adaptable which allows for this research to be extended across a variety of tasks and at a multi-subject level.

Abstract: I will discuss finite-time blowup for a model of the 3D Euler equation where the Helmholtz projection is replaced by a projection onto a more restrictive constraint space. The model preserves the structure of the self-advection nonlinearity entirely, and also conserves energy and helicity.

Abstract: The COVID-19 pandemic has placed an unprecedented strain on healthcare systems worldwide, making it difficult to accurately predict demand surge for acute care and allocate resources effectively. This paper proposes a novel predictive learning model that combines a differential equation model with delays and a multi-objective learning genetic algorithm to forecast hospitalizations and intensive care admissions based on predicted infections in a given population. Using data from Canada, Alberta, and Edmonton, we demonstrate the effectiveness of our model in significantly improving the ability to predict acute care capacity and manage resources during emergent infectious disease outbreaks such as COVID-19. Our approach is tailored to different population segments and considers various factors, such as variant strains of the virus and vaccination campaigns. Our model represents a significant contribution to the field, providing healthcare managers and decision-makers with a powerful tool to plan resources in the face of epidemics and major disasters. We contribute to the conversation on how we respond to public health emergencies, enabling more accurate predictions of demand for care and allocation of resources, ultimately saving lives and limiting the impact of these crises on our communities.

This is a joint work with Y. Bahri, N. Gilani, S. Ibrahim, A. Park and O. Chakroun

The Final Oral Examination
for the Degree of

Master of Science
(Department of Mathematics and Statistics)

Jianping Yu
Phd in Math, Chinese Academy of Sciences

“Hierarchical Model for Evaluation of Physician Care in the ICU”

April 26th, 2023
10:00am
On zoom

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

Chair of Oral Examination:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic

Abstract: One of the challenges of the accurate simulation of turbulent flows is that initial data is often incomplete, which is a significant difficulty when modeling chaotic systems whose solutions are sensitive to initial conditions. If one instead has snapshots of a system, i.e. data, one can make a better guess at the true state by incorporating the data via data assimilation. Many of the most popular data assimilation methods were developed for general physical systems, not just turbulent flows or chaotic systems. However, in the context of fluids, data assimilation works better than would be anticipated for a general physical system. In particular, turbulent fluid flows have been proven to have the property that, given enough perfect observations, one can recover the full state irrespective of the choice of initial condition. This property is unique to turbulent fluid flows, a consequence of their finite dimensionality. In this presentation, we will discuss the continuous data assimilation algorithm that was used to prove the convergence in the original, perfect data setting, present various robustness results of the continuous data assimilation algorithm, and discuss how continuous data assimilation can be used to identify and correct model error. Moreover, we will highlight the efforts of our other current research into long-standing problems in the stability of fluid flows, and how we have discovered some very interesting connections to our data assimilation research.

See announcement (pdf).

Abstract: Negative amphicheiral knots provide torsion elements in the knot concordance group, and torsion elements are less well understood than infinite-order elements. In this talk, I will introduce an equivariant version of the Alexander polynomial for strongly negative amphicheiral knots called the half-Alexander polynomial, focusing on its applications to knot concordance. In particular, we will show how understanding the geography behavior of the half-Alexander polynomial led to the construction of the first examples of non-slice amphichiral knots of determinant 1. This talk is based on joint work with Keegan Boyle.

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

HANS OERI

MSc (Simon Fraser University, 2018)
BSc (Simon Fraser University, 2016)

“Convex Optimization Methods for Bounding Lyapunov Exponents”

Department of Mathematics and Statistics

Friday, April 14, 2023
10:00 A.M.
Virtual Defence

Supervisory Committee:
Dr. David Goluskin, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)
Dr. Nishant Mehta, Department of Computer Science, UVic (Outside Member)

External Examiner:
Dr. Milan Korda, Laboratoire d'analyse et d'architectures des systèmes, Centre national de la recherche scientifique, France

Chair of Oral Examination:
Dr. Daniela Constantinescu, Department of Mechanical Engineering, UVic

Abstract
In dynamical systems, the stability of orbits is quantified by Lyapunov exponents, which are computed from the average rate of divergence of trajectories. We develop techniques for computing sharp upper bounds on the maximal LE using methods from convex optimization, which have previously been used to compute sharp bounds on the time averages of scalar quantities on bounded orbits of dynamical systems. For discrete-time dynamics we develop an optimization-based approach for computing sharp bounds on the geometric mean of scalar quantities. We therefore express LEs as infinite-time averages and as geometric means in continuous-time systems and discrete-time systems, respectively, and then derive optimization problems whose solutions give sharp bounds on LEs. When the system’s dynamics is governed by a polynomial vector field, the problems can be relaxed to computationally tractable SOS programs whose solutions also give sharp bounds on LEs. An approach for the practical implementation of a sequence of SOS feasibility problems whose solutions converge to the maximal LE of discrete systems is provided. We explain how symmetries can be used to simplify and generalize the optimization problems in both continuous-time and discrete-time systems. We conclude by discussing the extension of the techniques developed here to the problem of bounding the sum of the leading LEs. Tractable SOS programs are derived for some special cases of this problem.

The applicability of all the techniques developed here is shown by applying them to various explicit examples. For some systems we numerically compute sharp bounds that agree with the the maximal LEs, and for some we prove analytic bounds on maximal LEs by solving the optimization problems by hand.

See announcement (pdf)

The aim of this talk is to present some theoretical and numerical results concerning Beltrami fields, called force-free fields in solar and fusion physics. The talk will be divided into three parts. In the first part, we will recall the physical context of the appearance of these fields, i .e. essentially the modeling of magnetic equilibria in solar physics. In the second part, we will recall some mathematical theoretical results concerning the existence and properties of fields in any three-dimensional domain. In the third and last part, we will expose some methods to compute these 3D fields and the associated physical equilibria, as well as some numerical results obtained with our codes.

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

Jack THOMAS
BSc (University of Victoria, 2019)

"Response to Improving abundance estimation by combining capture-recapture and presence-absence data: example with a large carnivore"

Tuesday, April 11, 2023
9:30 A.M.
David Strong Building C128

Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Simon Bonner, Department of Statistical and Actuarial Sciences, UWO (Co-Supervisor)

Chair of Oral Examination:
Dr. Farouk Nathoo, Department of Mathematics and Statistics, UVic

Given that Apr. 7th is a holiday, if the room in DSB is locked, we will have the seminar in the Math department.

Abstract: Cerf gave a not-well-known re-interpretation of Smale's proof that the diffeomorphism group of the 2-sphere has the homotopy-type of the isometry group. It fits into a family of proofs that allow for a partial description of the homotopy-fibres of the `scanning' maps Emb(D^{n-1}, S^1 x D^{n-1}) --> \Omega^j Emb(D^{n-1-j}, S^1 x D^{n-1}), as well as a proof that the monoid of co-dimension one spheres \pi_0 Emb(S^{n-1}, S^n) is a group, under the connect-sum operation. When n isn't 4 this is a well-known result due to the resolution of the generalized Schoenflies problem, but it would appear to be a new result when n=4. I will outline these observations.

Abstract: The Manickam-Miklós-Singhi Conjecture states that for positive integers n and k with n > (4k - 1), a multi-set X = {x_1,x_2, … ,x_n} with real entries and nonnegative sum has at least \binom{n-1}{k-1} subsets of size k with nonnegative sum.

Abstract: In the theory of harmonic analysis, one considers unitary representations of groups bearing some geometric significance. These may give rise to summable representations of an appropriate convolution algebra, and the trace can be computed either spectrally (in terms of irreducible factors) or geometrically, resulting in a "trace formula" that relates these two perspectives. Hallmark examples of this method include the Poisson summation formula and the Selberg trace formula. The work of Connes (1996, 1999) and Meyer (2004, 2007) considers geometric representations of groups arising from number theoretic data, and the trace formulas in their examples recover the explicit formulas of Weil relating prime numbers (or ideals) to the zeros of L-functions. In this talk, I will provide some background on trace formulas for groups, including one of the examples of Meyer, and introduce the group and representation that I am considering in my research.

For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic in the first talk, and discuss more details about proof techniques in the second talk. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

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

Meifan LIN
BMath, University of Waterloo, 2021

“On linear models selected by the constrained minimum criterion”

April 5th 10:00 a.m.
Conducted Virtually

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

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

Register via Zoom to receive the link for this event and the rest of the series.

ABSTRACT: Stochastic parameterizations (SMCM) are continuously providing promising simulations of unresolved atmospheric processes for global climate models (GCMs). One of the features of earlier SMCM is to mimic the life cycle of the three most common cloud types (congestus, deep, and stratiform) in tropical convective systems. In this present study, a new cloud type, namely shallow cloud, is included along with the existing three cloud types to make the model more realistic. Further, the cloud population statistics of four cloud types (shallow, congestus, deep, and stratiform) are taken from Indian (Mandhardev) radar observations. A Bayesian inference technique is used here to generate key time scale parameters required for the SMCM as SMCM is most sensitive to these time scale parameters as reported in many earlier studies. An attempt has been made here for better representing organized convection in GCMs, the SMCM parameterization is adopted in one of the state-of-art GCMs namely the Climate Forecast System version 2 (CFSv2) in lieu of the pre-existing simplified Arakawa–Schubert (default) cumulus scheme and has shown important improvements in key large-scale features of tropical convection such as intraseasonal wave disturbances, cloud statistics, and rainfall variability. This study also shows the need for further calibration the SMCM with rigorous observations for the betterment of the model’s performance in short term weather and climate scale predictions.

Kumar Roy is now working as a PIMS Postdoctoral Fellow with Prof. Boualem Khouider at Department of Mathematics and Statistics, University of Victoria. His current research topic is in the area of climate change modelling focusing on Stochastic models for clouds and tropical convection parameterization. He completed his PhD degree in Meteorology and Oceanography from Andhra University, India in March 2022 and his research has been carried out at Indian Institute of Tropical Meteorology (IITM), Pune, India. His research focuses on the development and application of sub-grid scale cloud models in numerical weather prediction (NWP) models, as well as how these models affect the forecasting abilities of NWP models.

Abstract: Probabilistic zero-forcing can be thought of as a model for rumour spreading, where a person is more likely to spread a rumour if several of their friends already believe it . We start with a graph that has one infected vertex. At each time step an infected vertex infects an uninfected neighbour with probability proportional to how many of its neighbours are already infected. I will focus in this talk on probabilistic zero-forcing on hypercubes and grids, and demonstrate tight bounds on how long it takes for every vertex to be infected (asymptotically almost surely). This is joint work with Trent Marbach and Pawel Pralat.

For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a "threshold." Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic in the first talk, and discuss more details about proof techniques in the second talk. Based on joint work with Keith Frankston, Jeff Kahn, Bhargav Narayanan, and Huy Tuan Pham.

Abstract: In 2017, Ron Aharoni proposed the following generalization of the Caccetta-Häggkvist conjecture: if G is a simple n-vertex edge-colored graph with n color classes of size at least r, then G contains a rainbow cycle of length at most the ceiling of n/r.

I will begin with a summary of recent progress on Aharoni's conjecture based on a new survey article of Katie Clinch, Jackson Goerner, Freddie Illingworth, and myself. I will then sketch a proof that Aharoni's conjecture holds up to an additive constant for each fixed r. The last result is joint work with Patrick Hompe.

Abstract: In noncommutative geometry, a spectral triple is a set of data which encodes a geometric phenomenon in an analytic way. The authors Butler, Emerson, and Schulz introduced a method of producing such spectral triples using the annihilation and creation operators of quantum mechanics. Their construction produced the Heisenberg cycle, a 2-dimensional spectral triple over the C*-algebra crossed-product of uniformly continuous, bounded functions on the real line crossed with the discretely topologized reals. In this talk, I will discuss a higher dimensional analogue of this Heisenberg cycle, properties of its zeta functions, as well as some promising examples of pullbacks for which the corresponding zeta functions can be meromorphically extended to the complex plane.

Abstract: A momentous legacy of twentieth-century mathematics is the realisation that deterministically evolving systems frequently exhibit, when observed for sufficiently extended periods of time, a statistical behaviour akin to the limiting behaviour of independent random variables. We shall explore a geometric incarnation of this surprising phenomenon, overviewing various kinds of statistical limit theorems for the free motion of a particle on a negatively curved surface. In order to emphasise the richness of possible asymptotic behaviours, as well as the variety of sources of randomness, we will further compare the free-motion dynamics with a closely related evolution on the same phase space, known as the horocycle flow.

In this talk, I will share our work on Single Cell RNA-Sequencing and cell-type annotation based on two recent projects. I'll start by introducing our BAL Single Cell RNA-seq data. Bronchoalveolar lavage (BAL) is a procedure that is sometimes done during a bronchoscopy. BAL is used to collect a sample from the lungs for testing, different from traditional lung tissue samples. After Covid-19, BAL has gotten more attention. However, it lacks significant consensus on annotating BAL scRNA-seq samples. The previous research mainly focused on annotating lung tissue samples. Consequently, we plan to construct an auto-annotation method for the BAL scRNA-seq sample, which can aid with the general cell type annotation. After that, I want to talk about exploring the Macrophages' and Alveolar macrophages' substructure. We want to identify their subtypes and how they affect the disease (COPD).

Description:
  The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is smooth outside a set of singular points. However, explicit examples show that the singular set could be, in general, as large as the regular set. This talk aims to introduce this beautiful problem and describe some classical and recent results on the regularity of the free boundary.

Speaker Biography:
Alessio Figalli is a leading figure in the areas of Optimal Transport, partial differential equations and the calculus of variations. He received his Ph.D. from the Scuola Normale Superiore di Pisa and the Ecole Normale Superieur de Lyon and has held positions in Paris and Austin, Texas. He is currently a Professor at ETH Zurich. His work has been recognized with many awards including the Prize of the European Mathematical Society in 2012 and the Fields Medal in 2018.

Time:
All network wide colloquia take place at 1:30pm Pacific Time with a few exceptions.

Registration:
To attend this event please register here to receive the meeting link. Talks will be recorded and posted on the PIMS resource page www.mathtube.org.

Abstract: A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= j$ for which some $F_i \in \F_i$ is comparable to some $F_j \in \F_j$. Two natural measures of the `size' of such a family are the sum $\sum_{i = 1}^k |\F_i|$ and the product $\prod_{i = 1}^k |\F_i|$. We prove upper and lower bounds on the sum measure for general $n$ and $k \ge 2$. In the process, we consider minimizing the number of sets comparable to a family $\F \subseteq \mathcal{P}([n])$ of a given size.

Abstract: Étale groupoid C*-algebras are ubiquitous and it is useful to have concrete methods for verifying that a given C*-algebra is isomorphic to a groupoid C*-algebra. It is a result, essentially due to Brown, Clark, Farthing, and Sims, that a Hausdorff second countable étale groupoid that is topologically principal and minimal has a simple reduced C*-algebra. This makes verifying faithfulness of its representations trivial. Removing the minimality condition one obtains an older result stating that faithfulness of a representation can be verified on the canonical commutative subalgebra of the groupoid. In this talk I will discuss the notion of an étale groupoid which is relatively topologically principal with respect to an open subgroupoid, as well as the consequences of this condition for representations of the groupoid C*-algebra.

Abstract: Reproductive value is the relative expected number of off-springs produced by an individual in its remaining lifetime. It is also an invariant function for population processes with birth and death rates independent of the time except in cases when they are periodic. In this study, we prove that the limiting ratio of the survival probability of two branching processes starting from distinct state-time positions is equal to the relative reproductive value. Moreover, we developed a method to obtain the reproductive value for continuous time general branching population models with state-dependent rates and a renewal state. We are using size-biased birth rates for constructing the spinal representation of the branching process, which establishes the relation between survival probability and the Martingale of the process. Further, we provide sufficient conditions for a successful coupling to compare the survival probabilities of two branching population models.

Abstract: I highlight what I consider to be the two major contributions of topology to economic theory: the application of algebraic topology to social choice theory and the application of differential topology to general equilibrium theory. Interesting, but not surprisingly, both of these were directly influenced by the Bourbaki group.

Coffee and muffins at 2:15pm

Abstract: How many lines are spanned by a set of planar points?. If the points are collinear, then the answer is clearly "one". If they are not collinear, however, several different answers exist when sets are finite and "how many" is measured by cardinality. I will discuss a bit of the history of this problem and present a recent extension to the discretized and continuum settings, obtained in collaboration with T. Orponen and H. Wang. No specialized background will be assumed.

Pablo is a leader in the area of fractal geometry. He is a recent speaker at the International Congress of Mathematicians; and a Canada Research Chair at UBC.

Abstract: An $(m,n)$-generalized bent function is a function from $\mathbb{Z}_2^n$ to $\mathbb{Z}_m$ so that its associated Fourier transformations have constant absolute value. It is known that an $(m,n)$-generalized bent function exists whenever one of the following holds:

1. both $m$ and $n$ are even.
2. $4 \mid m$.

Abstract: We address the question: when does a purely infinite, simple, separable classifiable C*-algebra have a groupoid model? The answer was given up to stable isomorphism by Jack Spielberg and later in the unital case by L.O. Clark, J. Fletcher and A. an Huef. We will describe an alternate approach. This first requires a construction of Deaconu and Renault which I will describe. We further need a construction of mine into dynamical systems which I call 'binary factors' and finally an idea of orbit-breaking for Deaconu-Renault groupoids. This is joint work with Robin Deeley and Karen Strung.

Abstract: This talk is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies. This result is derived from a representation formula informing about the momentum spread, showing that the domain of influence in momentum is controlled by mild information in the sense that derivatives are not (or less than before) implied. In doing so, we develop a Radon Fourier analysis on the RVM system, which leads to the study of a class of singular weighted integrals. The end of my talk, I show how this method is applied in order to construct smooth solutions to the RVM system in the regime of hot, dense and strongly magnetized plasmas. This is a joint work with C. Cheverrey.

Abstract: Quantifying the relationship between daily changes in air pollution and short-term effects on mortality and hospitalisations is a complex task with many steps. Air pollution data contains missing values and outliers. Uncertainty in exposures should be reflected in uncertainty in effect sizes. Inference must account for the multitude of factors unrelated to air pollution that can influence mortality. Exposure-response effects are non-linear. Analyses across multiple cities and regions must take into account possible city-level variation in effects.

This talk will describe ongoing work undertaken in under contract from Health Canada to estimate health effects from pollution in 50 Canadian cities. A key feature of the project is the case-crossover model, a form of partial likelihood which adjusts for most changes in time using control days.

Abstract: I will present our recent methodology for integrating functional data into deep neural networks. The model is defined for scalar responses with multiple functional and scalar covariates. A by-product of the method is a set of dynamic functional weights that can be visualized during the optimization process. This visualization leads to a greater interpretability of the relationship between the covariates and the response relative to conventional neural networks. The model is shown to perform well in a number of contexts including prediction of new data and recovery of the true underlying relationship between the functional covariate and scalar response; these results were confirmed through real data applications and simulation studies. An R package (FuncNN) has also been developed on top of Keras, a popular deep learning library—this allows for general use of the approach.

Abstract: If a tricky devil challenged you to complete a Sudoku puzzle of their design, what restrictions could you place on their design to guarantee it was impossible for them to thwart your attempts? More specifically, if you could dictate exactly how many times that devil could use each symbol or pre-fill any one row, column, or box, could you safely bet that their deviously designed puzzle was still completable? This notion of seeking out guaranteed completability conditions for Sudoku drives the discussion as we delve into various graph and matrix representations of the Sudoku, explore relaxed notions of completability such as fractional completability, and use these tools to approach an answer. Due to the ongoing nature of this research, this talk is designed to serve as an introduction to the machinery of the argument being employed but does not conclude with a definitive answer.

Abstract: We address the question: when does a purely infinite, simple, separable classifiable C*-algebra have a groupoid model? The answer was given up to stable isomorphism by Jack Spielberg and later in the unital case by L.O. Clark, J. Fletcher and A. an Huef. We will describe an alternate approach. This first requires a construction of Deaconu and Renault which I will describe. We further need a construction of mine into dynamical systems which I call 'binary factors' and finally an idea of orbit-breaking for Deaconu-Renault groupoids. This is joint work with Robin Deeley and Karen Strung.

The Pacific Institute for the Mathematical Sciences will host an evening of

Math Mania

This "Girls in Math" event will take place
6:30-8:00 p.m. Tuesday, March 7, 2023 at
St. Margaret's School
1080 Lucas Ave.
Victoria, B.C.

"Fun" methods to teach math and computer science concepts to children (and adults!) by games and art will be demonstrated. Lots of hands-on activities!

• A Sorting Network
• An Impossible Balancing Act
• Bubbles
• Mathematical Puzzles
• The Guessing Game
• Sudoku
• The Penny Game
• The Set Game
• and lots more!

For more information contact:

PIMS UVic Site Office, Department of Mathematics and Statistics, University of Victoria
at (250) 472-4271
email: pims@uvic.ca

Zoom link.

joint work with E. Lesigne, A. Quas, J. Rosenblatt.

Abstract: Let S= (s_1<s_2<\dots) be a strictly increasing sequence of positive integers. We say S is good if for every real \alpha the sequence

\left(\frac1N\sum_{n\le N}e^{2\pi is_n\alpha}\right)_N

of complex numbers is convergent. Equivalently, the sequence S is good if for every real \alpha the sequence (s_n\alpha) has asymptotic distribution modulo 1. We are interested in finding out what the limit probability measure

\mu_{S,\alpha}=\lim_N \frac1N\sum_{n\le N}\delta_{s_n\alpha}

can be. It turns out that for an irrational \alpha the limit measure must be continuous. So now the main question is can it be any continuous measure? An affirmative answer would also affirm Furstenberg's x2x3 conjecture. What we can prove is that the limit measure can be any absolutely continuous measure.

Abstract: We propose to estimate modal regression with spatial data observed over a rectangular domain by assuming that the conditional mode of the response variable given covariates follows a nonparametric regression structure. We study the newly developed spatial modal regression utilizing the local linear approximation augmented with shrinking bandwidths. The asymptotic normal distributions of the resultant modal estimators are established and the explicit formulas for their asymptotic biases and variances are derived under mild regularity assumptions. The selection of optimal bandwidths in theory and practice are discussed. We also show that the targeted spatial modal regression can be utilized as an alternative to a nonparametric spatial robust regression when the data are symmetrically distributed. The asymptotic distributions for such modal-based robust estimators are derived with appropriate choices of bandwidths, which demonstrate that the suggested estimators can achieve the full asymptotic efficiency of the mean estimators when there are no outliers and the error distribution is normal. Monte Carlo simulations and a real data analysis on soil data are presented to illustrate the good finite sample performance of the estimators. We in the end generalize the propounded spatial modal regression to an additive sum of the form to avoid the curse of dimensionality and develop a kernel-based backfitting algorithm for estimating. We substantiate that the proposed modal estimator of each additive component is asymptotically normal and converges at the univariate nonparametric modal optimal rate.

Abstract: Persistent Homology (PH) is an active research area in Algebraic Topology, especially in Topological Data Analysis, that concerns capturing structural information of data. It arises in critical applications such as machine learning, neuroscience, cosmology, medicine and biology among others. One of the primary challenges in TDA is distinguishing between signal (meaningful structures) and noise (arising from local randomness or other inaccuracies). A key tool of PH is the persistence diagram, which captures the birth and death of various features in a filtration of a dataset. Characterizing the distribution of these diagrams is an open problem in the field. This talk will introduce the open problem, address some fundamental results, and discuss our results so far on a given approach to the problem.

Abstract: Suppose we have a set P of n points in the plane, and another set S of n^{1/3} points in convex position. What can we say about the structure of this arrangement if P contains many translates of the set S? I will discuss a recent result showing that if P contains around n translates of S, then the translation vectors must come from a generalized arithmetic progression of low dimension.

The motivation for this problem comes from incidence geometry, where many constructions for strictly convex curves having many incidences with pointsets follow this general outline. In particular, I will discuss applications to the Erdos unit distance conjecture. This is joint work with Jozsef Solymosi and Ethan White.

Abstract: I will discuss four applications of statistics to COVID-19 research. 1) The disease COVID-19 is caused by infection by the SARS-CoV-2 virus. However, variation in human genetics can modulate the severity of the disease, or susceptibility to infection. HostSeq is a resource of ~10,000 DNA sequences of COVID-19+ Canadians. I will discuss statistical challenges and polygenic risk scores with HostSeq data. 2) Due to asymptomatic infection, and underreporting, the burden of COVID-19 is greater than indicated by confirmed case counts. I will discuss methods to estimate the true burden of COVID-19, and to combine confirmed case counts with serology surveys to provide more accurate estimates of prevalence. 3) I will discuss a statistical operationalization of SIR models to determine the lag between changes in non-pharmaceutical interventions and statistically significant changes in confirmed case count trajectories. 4) I will discuss evidence for neurological manifestation of COVID-19 in brain imaging. These applications are joint work with MAGPIE, UVic, SickKids and Oxford.

Abstract: I will describe the large-scale behavior of a random growth model (Internal DLA) on random planar maps which approximate a random fractal surface embedded in the plane (Liouville quantum gravity, LQG). No prior knowledge of these objects will be assumed. Joint work with Ewain Gwynne.

Math Challengers is a math competition for grades 8-10 students. Please see https://www.mathchallengers.ca/events.htm to sign up for the in-person version of the event at Camosun College.

Abstract: The concordance group of virtual knots is known to be nonabelian but still somewhat mysterious. Using the Gordon-Litherland form, we introduce new invariants of virtual knots defined in terms of non-orientable spanning surfaces for the knot. The associated mock Seifert matrices lead to a new algebraic concordance group, which is abelian but not finitely generated. This talk is based on joint work with Homayun Karimi.

Note that you need to register in advance at this web site.

The past twenty-five years have heralded an unparalleled increase in understanding of cancer. At the same time, mathematical modelling has emerged as a natural tool for unravelling the complex processes that contribute to the initiation and progression of tumours, for testing hypotheses about experimental and clinical observations, and assisting with the development of new approaches for improving its treatment. In this talk I will reflect on how increased access to experimental data is stimulating the application of new theoretical approaches for studying tumour growth. I will focus on two case studies which illustrate how mathematical approaches can be used to characterise and quantify tumour vascular networks, and to understand how microstructural features of these networks affect tumour blood flow.

Abstract: It is well known that a maximal planar graph of order at least 3 is 3-colourable if and only if it is Eulerian. It is also known that if a maximal planar graph of order at least 3 has exactly two vertices of odd degree, then these vertices are nonadjacent. I will show that these two results are equivalent.

The talk should be accessible to undergraduate students with a basic knowledge of graph theory.

Abstract: We consider a family of Pimsner algebras associated to correspondences constructed from self-similar group actions and we investigate the equilibrium states (the KMS states) for the natural time evolution on these algebras. For all inverse temperatures above a critical value, the KMS states on the Toeplitz algebra are given in a very concrete way by traces on the full group algebra of the group. At the critical inverse temperature, the KMS states factor through states of the Cuntz-Pimsner algebra; if the self-similar group is contracting, then the Cuntz-Pimsner algebra has only one KMS state. We apply these results to a number of examples, including self-similar actions associated to integer dilation matrices, and the canonical self-similar actions of the basilica group and the Grigorchuk group.

Abstract: DNA methylation is an epigenetic mark intrinsically involved in regulating the activity of DNA, and methylation levels are known to change with age, exposures, and disease status. DNA methylation can be measured with a sequencing technique that gives methylated and unmethylated counts at each targeted position in the genome, but the data are very noisy. I will describe an over-dispersed quasi-binomial model with functional smoothing to model DNA methylation patterns in small genomic regions, and how these patterns depend on covariates. Results will be illustrated with an analysis of DNA methylation and a biomarker strongly associated with rheumatoid arthritis.

Math Challengers is a math competition for grades 8-10 students. Please see https://www.mathchallengers.ca/events.htm to sign up for the online version of the event.

Abstract: Farrell and Jones proved that the automorphism groups of compact hyperbolic manifolds in dimensions n≥1 do not have the homotopy-type of finite CW complexes. Here "automorphism group" means groups of diffeomorphisms, PL-homeomorphisms, and homeomorphisms respectively, i.e. we are not discussing homotopy-equivalences or isometries. Farrell and Jones primarily used the machinery of "Higher Simple Homotopy Theory", which reduces the problem of computing homotopy groups of automorphism groups (in a range) to that of the group of automorphisms of S^1 x D^{n-1}, which was worked-out by Hatcher and Wagoner, plus a good amount of K-theory. With David Gabai we found an alternate route to such theorems, that avoids Higher Simple Homotopy Theory entirely. For us the results occur in dimensions n≥4. I will describe how these kinds of arguments work.

This event is part of the PIMS sponsored Seminar Series: Mathematics of Ethical Decision-making Systems

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Speakers:

• Midori Ogasawara, Assistant Professor, UVic Sociology
• Patricia Cochran, Associate Professor, UVic Law
• Freya Kodar, Associate Professor, UVic Law
• Jentery Sayers, Associate Professor, UVic English

AGENDA:

• 3:00 pm Dr. Midori Ogasawara will speak on the social consequences of surveillance and data collection.
• 3:30 pm Break for refreshments
• 4:00 pm Dr. Patricia Cochran and Dr. Freya Kodar
  Title: Technology, access to justice and narratives of law in an unequal society In this presentation, we will share some information about our ongoing research collaborations about the relationship between access to justice and technologically-mediated decision-making (including algorithmic credit-scoring and the online Civil Resolution Tribunal). We will discuss some of the critical questions we think require interdisciplinary attention given the growing significance of technology in legal processes, and the challenges that such processes pose for important legal ideas such as equality.
• 4:30 pm Dr. Jentery Sayers
  Title: Modelling Games as Activity Systems to Evaluate the Generative Contradictions between Play and Work I’ll talk about the articulation of genre studies with cultural-historical activity theory to consider conflicting motives in video games. I’m hoping to focus on contradictions related to labour (e.g., between dev teams and players; between types of players), metagaming (e.g., between social norms and player activities that may be considered cheating), and genre (between storytelling and mechanics, or “ludonarrative dissonance”). I’ll ground the talk in the model of activity theory rather than the particulars of these contradictions and conflicts.
• 5:00 -5:30 pm Panel Discussion

**For those unable to attend in person, there will be a virtual component - e-mail Kristina at pims@uvic.ca for this ‘virtual attendance’ information.**

Abstract: Products of permutations are used to model problems in fields ranging from representation theory and algebraic geometry to topological graph theory. I will show how probability can be used to study such problems, with a focus on how graphs may be embedded on different surfaces.

Abstract: We introduce a model of a controlled random process. In this model, the vertices of a hypergraph are ordered randomly and then revealed, one by one, to an algorithm. The algorithm must decide, immediately and irrevocably, whether to keep each observed vertex. Given the total number of observed vertices ("time"), the algorithm's goal is to succeed - asymptotically almost surely - in completing a hyperedge by keeping ("purchasing") the smallest possible number of vertices.

We analyse this model in the context of random graph processes, where the corresponding hypergraph defines a natural graph property, such as minimum degree, connectivity, Hamiltonicity and the containment of fixed-size subgraphs.

Joint work with Alan Frieze and Michael Krivelevich.

Abstract: In single-cell RNA-sequencing studies, researchers often model the variation between cells with a latent variable, such as cell type or pseudotime, and investigate associations between the genes and the latent variable. As the latent variable is unobserved, a two-step procedure seems natural: first estimate the latent variable, then test the genes for association with the estimated latent variable. However, if the same data are used for both of these steps, then standard methods for computing p-values in the second step will fail to control the type I error rate.

In my talk, I will introduce two different approaches to this problem. First, I will apply ideas from selective inference to develop a valid test for a difference in means between clusters obtained from the hierarchical clustering algorithm. Then, I will introduce count splitting: a flexible framework that enables valid inference after latent variable estimation in count-valued data, for virtually any latent variable estimation technique and inference approach.

This talk is based on joint work with Jacob Bien (University of Southern California), Daniela Witten and Anna Neufeld (University of Washington), as well as Alexis Battle and Joshua Popp (Johns Hopkins University).

Abstract
The 15-puzzle which acts as an inspiration for this talk is a simple game consisting of 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically. Like the popular Rubik's cube, the sliding puzzle is often ‘jumbled up‘ and the goal of the puzzle is to place the tiles in numerical order from left to right and top to bottom with the empty tile in the bottom right corner. In the late 1880’s a famous American puzzler named Sam Loyd offered $1000 to anyone who could provide him with a series of moves that would swap only the tiles labelled 14 and 15 while leaving all other positions in their standard numerical order. In this talk we will discuss which mathematical principles guaranteed that Sam Loyd would keep his money and discuss how the mathematician Richard Wilson used graph theory ‘inception’ to generalize this notion to all sliding puzzles, determining exactly which solutions were possible and which could never be obtained.

Abstract: C*-algebras are often said to resemble `noncommutative spaces.' One way of making this idea precise makes use of the idea of Morita Equivalence. This is an introductory talk on Morita equivalence and its role in K-theory, representation theory (of groups), and group actions.

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Abstract: The Perceptron model was proposed as early as the 1950's as a toy model of a one-layer neural network. The basic model consists of a set of solutions (either the Hamming cube or the sphere of dimension n) and a set of constraints given by independent n-dimensional Gaussian vectors. The constraints are that the inner product of a solution vector with each constraint vector scaled by sqrt{n} must lie in some interval on the real line. Probabilistic questions about the model include the satisfiability threshold (or the "storage capacity") and questions about the typical structure of the solution space. Algorithmic questions include the tractability of finding a solution (the learning problem in the neural network interpretation). I will describe the model, the main problems, and recent progress.

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Abstract: Nonlinear mixed effects (NLME) models are commonly used in modelling many longitudinal data such as pharmacokinetics and HIV viral dynamics. These models are often derived based on the underlying data generation mechanisms, so the parameters in these models often have meaningful physical interpretations and natural restrictions such as some parameters being positive. Hypothesis testing for these parameters should incorporate these restrictions, leading to one-sided or constrained tests. Motivated from HIV viral dynamic models, in this article we propose multi-parameter one-sided or constrained tests for NLME models with censored responses, e.g., viral dynamic models with viral loads below detection limits. We propose approximate likelihood-based tests which are computationally efficient. We evaluate the tests via simulations and show that the proposed tests are more powerful than the corresponding two-sided or unrestricted tests. We apply the proposed tests to an AIDS dataset with new findings.

The Helly number of a set in the plane is the smallest N such that the following is true. If any N members of a finite family of convex sets contains a point of S, then there is a point of S which is contained in all members of the family. An exponential lattice with base x consists of points whose coordinates are positive integer powers of x. We prove lower and upper bounds on Helly numbers of exponential lattices in terms of x, and we determine their values exactly in some cases. We also consider asymmetric exponential lattices, and characterise those that have finite Helly numbers.

Joint work with Gergely Ambrus, Martin Balko, Attila Jung and Márton Naszódi.

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Abstract: It is common in probability theory and statistics to study distributional convergences of sums of random variables conditioned on another such sum. In this talk I will present a novel approach using Stein’s method for exchangeable pairs that allows to derive a conditional central limit theorem of the form $(X_n|Y_n = k)$ with explicit rate of convergence as well as its extensions to a multidimensional setting. We will apply these results to particular models including pattern counts in a random binary sequence and subgraph counts in Erdös-Rényi random graph. This talk is based on joint work with Partha S. Dey.

Abstract:Gene co-expression network analysis is widely used in microarray and RNA sequencing data analysis. It groups genes based on their co-expression network. And genes within a group infer similarity in function or coregulation in the pathway.

In literature, the approaches to group genes are mainly unsupervised, which may introduce instability and variation across different datasets. Inspired by ensemble learning, we propose a novel approach that ensemble supervised and unsupervised learning techniques and simultaneously works on two tasks, gene module identification and phenotype prediction, during the data analysis process. The identified gene modules from this approach could suggest more candidate genes to the original pathway, and those genes are potential biomarkers for pathway-related diseases. In addition, the novel approach also improves the prediction accuracy for phenotypes. The algorithm can be used as a general prediction algorithm. And, as it is specially designed to handle large samples, it is suitable for handling single-cell data with many cells. We showcased the use of the algorithm in single-cell cell-type auto-annotation.

Abstract: I'll show an algorithm for 3 colouring triangle free graphs embedded on the Klein bottle that runs in polynomial time if most of the faces are 4 faces. Joint work with Jean-Sebastian Sereni and Zdenek Dvorak.

Abstract: Verifying nonlinear stability of a laminar fluid flow against all perturbations is a classic challenge in fluid dynamics. All past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. This "energy method" cannot show global stability of any flow in which perturbation energy may grow transiently. For the many flows that allow transient energy growth but seem to be globally stable (e.g. pipe flow and other parallel shear flows at certain Reynolds numbers) there has been no way to mathematically verify global stability. After explaining why the energy method was the only way to verify global stability of fluid flows for over 100 years, I will describe a different approach that is broadly applicable but more technical. This approach, proposed in 2012 by Goulart and Chernyshenko, uses sum-of-squares polynomials to computationally construct non-quadratic Lyapunov functions that decrease monotonically for all flow perturbations. I will present a computational implementation of this approach for the example of 2D plane Couette flow, where we have verified global stability at Reynolds numbers above the energy stability threshold. This energy stability result for 2D Couette flow had not been improved upon since being found by Orr in 1907. The results I will present are the first verification of global stability – for any fluid flow – that surpasses the energy method. This is joint work with Federico Fuentes (Universidad Católica de Chile) and Sergei Chernyshenko (Imperial College London).

Abstract: Take an Ising model with very low temperature. What is the largest p such that the Ising model dominates Bernoulli percolation with parameter p ? We will show that the answer to this question depends drastically on the geometry of the graph. We also obtain similar results for for two Ising models at very low, but close temperatures. A process is a finitary factor of iid if it can be written as a measurable and equivariant function of an iid process. As an application of the domination results, we show that the very low temperature Ising model on a nonamenable graph is a finitary factor of iid. This is in stark contrast with the amenable setting, where it is known through a celebrated result of Van Den Berg and Steif that the low temperature Ising model is not a finitary factor of iid. Joint work with Yinon Spinka.

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

Supervisory Committee
Dr. Slim Ibrahim, Department of Mathematics and Statistics, University of Victoria (Co-Supervisor)
Dr. Boualem Khouider, Department of Mathematics and Statistics, UVic (Co-Supervisor)

External Examiner
Dr. David Muraki, Department of Mathematics, Simon Fraser University

Chair of Oral Examination
Dr. Graham Voss, Department of Economics, UVic

Abstract
In this thesis, we discuss several numerical methods to approximate singular solutions for some partial differential equations such as Burgers’ equation, Prandtl’s equations, and the inviscid primitive equations. The numerical solutions we obtain for Burgers’ equation and Prandtl’s equations are compared with the existing analytical and numerical solutions in the literature. We observe the singularity formation in the numerical solutions to Burgers’ equation and Prandtl’s equations in finite time. For the inviscid primitive equations with the initial data are close to a suitable rescale of a smooth blowup profile proven by Collot, Ibrahim, and Lin, we compare the numerical solution to the theoretical blowup profile. The solution we obtain from the numerical scheme follows the profile, but the difference between the numerical and analytical profiles is quite significant closer to the blowup time. We then examine the stability of the numerical solutions by considering a small perturbation for the initial data. The gap between the perturbed and unperturbed solutions reduces as we choose smaller perturbation. However, this gap grows as it approaches the blowup time, and the stability of the numerical solutions remains in doubt.

Abstract: The arboricity \Gamma(G) of an undirected graph G = (V,E) is the minimal number such that E can be partitioned into \Gamma(G) forests. Nash-Williams' formula states that \Gamma(G) = \ceil{ \gamma(G) }, where \gamma(G) is the maximum of |E_H|/(|V_H|-1) over all subgraphs (V_H, E_H) of G with |V_H| ≥ 2.

The Strong Nine Dragon Tree Conjecture states that if \gamma(G) ≤ k + d / (d+k+1) for natural numbers k, d, then there is a partition of the edge set of G into k+1 forests such that one forest has at most d edges in each connected component.

We settle the conjecture for d ≤ k + 1. For d ≤ 2(k+1), we cannot prove the conjecture, however we show that there exists a partition in which the connected components in one forest have at most d + \ceil{kd/(k+1)} - k edges.

As an application of this theorem, we show that every 5-edge-connected planar graph G has a 5/6-thin spanning tree, a spanning trees whose edges fill up at most 5/6 of every cut. This theorem is best possible, in the sense that we cannot replace 5-edge-connected with 4-edge-connected, even if we replace 5/6 with any positive real number less than 1. This strengthens a result of Merker and Postle which showed 6-edge-connected planar graphs have a 18/19-thin spanning tree. This is joint work with Benjamin Moore.

Abstract: Schrödinger operators with delta potentials are of longstanding interest for admitting closed analytic solutions, and they receive renewed attention for connections to the Kardar–Parisi–Zhang equation. Along with a review of this background, the talk will discuss a standard model of the operators in 2D and its counterpart in Feynman–Kac formulas.

We provide a brief motivational overview of recent developments of extensions of stochastics tools to deal with uncertainty. These are: Peng's nonlinear expectations and Ito's calculus without probabilities. We then describe a non-probabilistic version of a supermartingale theory closely motivated by financial considerations of no-arbitrage. The basic object replacing the classical filtered probability space is a structured trajectory set which allows the definition of conditional outer integrals as well as null sets. The conditional outer integrals are non linear functionals that allow to circumvent the linearity of the classical conditional expectations in proofs and definitions. Integrability notions emerge in our setting through non-classical conditional integral operators that lead to the special case of non-probabilistic martingales.

One can define non-probabilistic supermartingales and prove analogous of classical results like: Doob's optional sampling theorem, Dubin's upcrossing inequalities and Doob's a.e. convergence for non-negative supermartingales. All constructions and results have a hedging and superhedging interpretation and there is a direct way in which the new results generalize the classical case. Null sets appearing in the results have a financial interpretation and are handled in a more concrete way than in the classical theory.

See announcement and abstract (PDF)

See announcement and abstract PDF.

Interested students, please contact Peter Dukes at dukes@uvic.ca or register directly via the MAA website.

The William Lowell Putnam Mathematical Competition is the preeminent mathematics competition for undergraduate college students in the United States and Canada. The Putnam Competition takes place annually on the first Saturday of December. The competition consists of two 3-hour sessions, one in the morning and one in the afternoon. During each session, participants work individually on 6 challenging mathematical problems.

The Putnam began in 1938 as a competition between mathematics departments at colleges and universities. Now the competition has grown to be the leading university-level mathematics examination in the world. Although participants work independently on the problems, there is a team aspect to the competition as well. Prizes are awarded to the participants with the highest scores and to the departments of mathematics of the five institutions, the sum of whose top three scores is the greatest.

Abstract: Given a graph H, an edge-coloured graph G is H-rainbow saturated if it does not contain a rainbow copy of H, but the addition of any non-edge in any colour creates a rainbow copy of H. The rainbow saturation number, denoted by rsat(n,H), is the minimum number of edges among all H-rainbow saturated edge-coloured graphs on n vertices. We prove that, for any non-empty graph H, the rainbow saturation number is linear in n. This confirms a recent conjecture of Girão, Lewis, and Popielarz. Based on joint work with Natalie Behague, Tom Johnston, Shoham Letzter, and Natasha Morrison.

Abstract: Imprimitivity theorems establish the Morita equivalence between C*-algebras arising from certain group/groupoid dynamics. For example, Green's imprimitivity theorem arises when two groups act on a space by commuting free and proper actions. Recently, we introduced the notion of self-similar actions (also known as Zappa-Szep product) of groupoids on other groupoids and Fell bundles. These self-similar actions encode two-way actions between the groupoids, in contrast to the one-way action encoded by the classical group/groupoid actions. We prove a generalized imprimitivity theorem arising from such self-similar actions, which establishes a new way of constructing Morita equivalent groupoid and Fell bundles. This is joint work with Anna Duwenig.

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Abstract: The log-rank test is considered the criterion standard for comparing 2 survival curves in pivotal registrational oncology trials. However, with novel immunotherapies that often violate the proportional hazards assumptions over time, log-rank can lose power and may fail to detect treatment benefit. We performed systematic review and meta-analysis of 63 studies between the log-rank, maxcombo and dRMST. The findings of this review show that MaxCombo may provide a pragmatic alternative to log-rank when departure from proportional hazards is anticipated. Both tests resulted in the same statistical decision in most comparisons. Discordant studies had modest to meaningful improvements in treatment effect. The dRMST test provided no added sensitivity for detecting treatment differences over log-rank.

Bio: Jiabu Ye is principal scientist of Biostatistics at MSD. He is endometrial indication lead statistician over see several endometrial late phase clinical trials. Before joining MSD, Jiabu worked at late development trial statistician in AstraZeneca and lead multiple late phase trial development. He is also a member of NPH cross-pharma working group. He received PhD in biostatistics from University of Texas Health Science Center at Houston.