Events
All upcoming and recent events from the past six months:
Title: The Prediction of Random Effects and Model Selection
Speaker: Wenxue Ge, University of Victoria
Date and time:
20 Aug 2018,
1:30pm -
2:30pm
Location: DSB C114
Event type: Graduate dissertations
Read full description
The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
Wenxue Ge
BSc (Purdue University, 2015)
“The Prediction of Random Effects and Model Selection”
Monday, August 20, 2018 1:30 P.M.
DSB C114
Supervisory Committee:
Dr. Mary Lesperance, Department of Mathematics & Statistics, University of Victoria (Supervisor)
Dr. Xuekui Zhang, Department of Mathematics & Statistics, UVic (Member)
Chair of Oral Examination:
Dr. Julie Zhou, Department of Mathematics & Statistics, UVic
Title: Steiner triple systems with few parallel classes
Speaker: Daniel Horsley, Monash University, Melbourne
Date and time:
08 Aug 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Discrete math seminar
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A \emph{Steiner triple system} of order $v$ (or STS$(v)$) is a pair $(V,\mathcal{B})$ where $V$ is a $v$-set and $\mathcal{B}$ is a set of $3$-subsets of $V$ (called triples) such that each pair of elements of $V$ occurs in exactly one triple in $\mathcal{B}$. Such a system exists if and only if $v=6k+1$ or $v=6k+3$ for some integer $k$. A \emph{parallel class} of an STS$(6k+3)$ is a set of its triples that forms a partition of its point set.
In 2015, Darryn Bryant and I constructed the first known infinite family of STS$(6k+3)$s without parallel classes. More recently, together with Charles Colbourn and Ian Wanless, we were able to use similar methods to find, for all $k$, STS$(6k+3)$s with ``few'' (sublinearly many in $k$) disjoint parallel classes. This talk will discuss these results and their context.
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Title: Decomposing complete multigraphs into stars of varying sizes
Speaker: Daniel Horsley, Monash University, Melbourne
Date and time:
30 Jul 2018,
2:30pm -
3:20pm
Location: DSB C126
Event type: Discrete math seminar
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In 1979 Tarsi showed that an edge decomposition of a complete multigraph into stars of size $k$ exists whenever the obvious necessary conditions hold. In 1996 Lin and Shyu gave necessary and sufficient conditions for the existence of an edge decomposition of a (simple) complete graph into stars of sizes $m_1,\dots,m_t$.
I will discuss the common generalisation of these problems: when does a complete multigraph admit an edge decomposition into stars of sizes $m_1, \dots ,m_t$? This problem exhibits more complicated and interesting behaviour than either of its specialisations.
Title: Stability of the Euler and Lagrange relative equilibria in the curved 3–body problem
Speaker: Ernesto Perez Chavela, ITAM Dpto. de Matemáticas, Mexico
Date and time:
24 Jul 2018,
3:00pm -
3:50pm
Location: DSB C124
Event type: Applied math seminar
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In this talk we generalize the well known Euler and Lagrange rela- tive equilibria of the classical Newtonian three body problem, to spaces of constant curvature. We also study the liner stability of them.
Title: SUMS mini-conference
Date and time:
24 Jul
to
26 Jul 2018,
3:00pm -
5:00pm
Location: CLE C112
Event type: Conferences and workshops
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SUMS is running a mini-conference this week from July 24th-26th, 3-5pm in CLE C112. Short, accessible talks on a variety of subjects will be delivered by students and a few professors. The intended audience is math undergrads, but the rest of the department is welcome, and encouraged, to attend. Refreshments will be available. Speakers and abstracts (PDF)
Title: The Replicator Dynamics for Multilevel Selection in Evolutionary Games and Indelible Signatures of Individual-Level Selection
Speaker: Daniel Cooney, Princeton University
Date and time:
19 Jul 2018,
1:30pm -
2:20pm
Location: DSB C126
Event type: Applied math seminar
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We consider a stochastic model for evolution of group-structured populations in which selection operates at two organization levels: individuals compete with other individuals in their group, while groups also compete with other groups. Individuals obtain payoff from playing a two-strategy game, either a generalized version of the Prisoner's Dilemma or of the Hawk-Dove game, against members of their group. Individual-level competition depends on individual payoff, while group-level depends on average payoff of group members. This creates a tension between the two levels of selection, as defectors are favored by at the individual level, whereas groups with cooperators outperform groups of defectors at the between-group level. In the limit of infinite group size and infinite number of groups, we derive a non-local PDE that describes the probability distribution of group compositions in the population. For special families of payoff matrices, we characterize the long-time beha!
vior of solutions of our equation, with particular emphasis placed on understanding the average and most frequent group compositions at steady state. We observe, regardless of how weak within-group selection is relative to between-group selection, that the most prevalent group composition will contain more defectors than the type of group which maximizes average group payoff if, and only if, maximum average payoff is not achieved by full cooperator groups. In such cases, the conflict between the two levels of selection cannot be decoupled, and we even observe cases in which cooperation cannot be sustained even when between-group competition favors perfect coexistence of cooperators and defectors.
Title: Mathematical model of influenza A evolution with HA protein stability
Speaker: Chadi Saad-Roy, Princeton University
Date and time:
17 Jul 2018,
1:30pm -
2:20pm
Location: DSB C126
Event type: Applied math seminar
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Influenza A H3N2 displays a tremendous capacity to adapt and evolve in response to pressure from host immune systems. The mutations that aid in immune system evasion are thought to occur largely in the viral antigen hemagglutinin (HA). Nucleoprotein (NP) is another protein of influenza A that is under significantly less selection pressure than HA. It has been shown that substitutions in NP are constrained by NP stability. That is, certain substitutions that decrease stability, but otherwise increase fitness, only occur in tandem with others that increase NP stability. In this project, we formulate a phylodynamics model of viral evolution for influenza A that incorporates HA protein stability. Our model tracks host individuals that are, respectively, infected, have strain-transcending immunity, or have lifelong antibodies against each specific strain. Our formulation also includes salient biological features such as cross-immunity between closely related strains. We!
show that important novel features emerge due to the inclusion of HA protein stability in our model. We characterize these properties through multiple approaches, illustrating the significance of protein stability in influenza A models.
Title: Optimal Regression Design under Second-Order Least Squares Estimator: Theory, Algorithm and Applications
Speaker: Chi-Kuang Yeh, University of Victoria
Date and time:
13 Jul 2018,
1:00pm -
2:00pm
Location: Clearihue Building Room B346
Event type: Graduate dissertations
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Notice of the Final Oral Examination for the Degree of Master of Science
of
CHI-KUANG YEH
BSc Hons (University of Victoria, 2016)
“Optimal Regression Design under Second-Order Least Squares Estimator: Theory, Algorithm and Applications”
Department of Mathematics and Statistics
Friday, July 13, 2018 1:00 P.M. Clearihue Building Room B346
Supervisory Committee:
Dr. Julie Zhou, Department of Mathematics and Statistics, University of Victoria (Supervisor) Dr. Xuekui Zhang, Department of Mathematics and Statistics, UVic (Member)
External Examiner:
Dr. Xiaodai Dong, Department of Electrical and Computer Engineering, UVic
Chair of Oral Examination:
Dr. Adam Ritz, Department of Physics and Astronomy, UVic
Abstract
In this thesis, we first review the current development of optimal regression designs under the second-order least squares estimator in the literature. The criteria include A- and D-optimality. We then introduce a new formulation of A-optimality criterion so the result can be extended to c-optimality which has not been studied before. Following Kiefer's equivalence results, we derive the optimality conditions for A-, c- and D-optimal designs under the second-order least squares estimator. In addition, we study the number of support points for various regression models including Peleg models, trigonometric models, regular and fractional polynomial models. A generalized scale invariance property for D-optimal designs is also explored. Furthermore, we discuss one computing algorithm to find optimal designs numerically. Several interesting applications are presented and related MATLAB code are provided in the thesis.
Title: TBA
Speaker: Jo Cai, University of Victoria
Date and time:
24 Apr 2018,
2:30pm -
3:20pm
Location: DSB C108
Event type: Statistics seminar
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Title: Sequence representation in the brain, a brain imaging study
Speaker: Danesh Shahnazian, University of Victoria
Date and time:
17 Apr 2018,
2:30pm -
3:20pm
Location: DTB A104
Event type: Statistics seminar
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The neural correlates of sequence representation has been of interest to neuroscientists for some time. While past studies have employed univariate methods to study sequence production, many scientists now agree that this phenomenon can be better studied via multivariate methods. In this study, we used a multivariate statistical technique called representational similarity analysis to analyze brain imaging data recorded as our research participants engaged in performing four different sequences of actions. The results show that the medial prefrontal cortex a brain area located in the medial frontal lobe of the brain is involved in sequence production. Our study demonstrates the utility of representation similarity analysis in the analysis of sequence production.
Title: Some results in Ergodic Optimization
Speaker: Juliano dos Santos Gonschorowski, University of Victoria
Date and time:
16 Apr 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: In this seminar we will talk about variations of the following
problem: Given the functional P:M(T)\rightarrow \R, P(\mu)= \int f d\mu,
defined over the set M(T) of Borel invariant probabilities for some
dynamic T:X \rightarrow X, what are the measures that maximize the
functional? We also will talk about the motivation of that problem, some
classical and new results on this subject.
Title: Bootstrap Calibration for Empirical Likelihood Methods
Speaker: Peng Tang, University of Victoria
Date and time:
13 Apr 2018,
4:00pm -
5:00pm
Location: CLE B017
Event type: Graduate dissertations
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The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
Peng TANG
2016 Xiamen University B.Econ
“Bootstrap Calibration for Empirical Likelihood Methods”
April 13th, 2018 4pm
CLE B017
Supervisory Committee:
Dr. Mary Lesperance, Department of Mathematics & Statistics, UVic (Co-supervisor)
Dr. Min Tsao, Department of Mathematics & Statistics, UVic (Co-supervisor)
Chair of Oral Examination:
Dr. Xuekui Zhang, Department of Mathematics & Statistics, UVic
Title: Comparisons of Outlier Detection Methods in Regression Model with Economic Data
Speaker: Yunfan Ma, University of Victoria
Date and time:
13 Apr 2018,
10:00am -
11:00am
Location: Clearihue Building Room B315
Event type: Graduate dissertations
Read full description
The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
YUNFAN MA
B.Sc (University of Victoria, 2016)
“Comparisons of Outlier Detection Methods in Regression Model with Economic Data”
Friday, April 13, 2018 10:00 A.M. Clearihue Building Room B315
Supervisory Committee:
Dr. Julie Zhou, Department of Mathematics & Statistics, UVic (Supervisor)
Dr. Laura Cowen, Department of Mathematics & Statistics, UVic (Member)
Chair of Oral Examination:
Dr. Christopher Eagle, Department of Mathematics & Statistics, UVic
Title: Multivariate Frailty Models for Two Types of Recurrent Events with A Dependent Terminal Event
Speaker: Grace Li, University of Victoria
Date and time:
12 Apr 2018,
2:00pm -
3:00pm
Location: Cornett A317
Event type: Graduate dissertations
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The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
Zhuolin (Grace) LI
B.Sc. (Xi’an Jiaotong University, 2011)M.A. (Xi’an Jiaotong University, 2014)
“Multivariate Frailty Models for Two Types of Recurrent Events with A Dependent Terminal Event: Application to Marital Dissolution and Retirement”
Thursday, April 12, 2018 2:00 P.M. Cornett Building Room A317
Supervisory Committee:
Dr. Mary Lesperance, Department of Mathematics & Statistics, UVic (Co-supervisor)
Dr. Zheng Wu, Department of Mathematics & Statistics, Department of Sociology, UVic (Co-supervisor)
Chair of Oral Examination:
Dr. Margaret Penning, Department of Sociology, UVic
Title: Uniqueness and nondegeneracy of ground states to nonlinear scalar field equations involving the Sobolev critical exponent in the
Speaker: HIroki Kikuchi, Tsuda University
Date and time:
11 Apr 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Applied math seminar
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Abstract:
In this talk, we consider the uniqueness and nondegeneracy of positive ground state solutions to semilinear elliptic equations with combined power-type nonlinearities involving the Sobolev critical exponent. This study is of great importance because of the resulting energy landscape and its implications for the dynamics.
We shall show that the positive radial ground state is unique and nondegenerate if the frequency is sufficiently large.
If time permits, we shall discuss about several future works.
This talk is based on a joint work with T. Akahori (Shizuoka), S. Ibrahim(Uvic), N. Ikoma(Keio), and H. Nawa(Meiji).
Title: Two projects
Speaker: Yan Xu, University of Victoria
Date and time:
10 Apr 2018,
2:30pm -
3:20pm
Location: DSB C108
Event type: Statistics seminar
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Title 1: Aggregating Analysis of Multiple Genomic Studies by Voting
Abstract 1: Aggregating analysis of multiple studies is an important research tool for studies involving genomic data. It becomes so popular in these days mainly due to two reasons. 1. The huge amount of genomic data from various past studies are available online to help researchers answer their new research questions. 2. Due to the curse of dimensionality and cost of experiments related to the whole genome biomarkers, many studies are underpowered after multiple testing adjustment. Meta-analysis, with history of more than a century, is the most popular statistical method to aggregate analyses from multiple studies. But results of meta-analysis can be misleading if some biomarkers in genomic data have some problems, or if bad studies are not excluded by the selection criteria due to undiscoverable confounding issues. To address this problem, we propose a new algorithm as an alternative to meta-analysis. A simulation study is conducted to compare the performance of our approach with meta-analysis, and show that our method is robust to the analysis of studies with abnormal signals.
Title 2: A Model-Based Clustering to Identify Disease-Associated SNPs
Abstract 2: Genome-wide association studies (GWASs) aim to detect genetic risk factors for complex human diseases by identifying disease-associated single-nucleotide polymorphisms (SNPs). The most commonly-usedGWAS method is the SNP-wise-test approach, in which an association test is performed for each SNP, and then the p-values are adjusted for multiple testing. However, this approach is often lack of power after multiple testing adjustments due to a huge number (> 1 million) of tests in GWAS. To address this problem, we propose a model-based clustering via a mixture of Bayesian hierarchical models, which could borrow information across SNPs to group SNPs to different clusters having different mean genotype levels between cases and controls. Simulation studies and real data studies showed that the proposed model-based clustering outperformed SNP-wised-test approach.
Title: Automorphisms of the shift: entropy and the dimension representation
Speaker: Scott Schmieding, Northwestern University
Date and time:
09 Apr 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: For a shift of finite type $(X,\sigma)$, the automorphism group
$Aut(\sigma)$
consists of all homeomorphisms from $X$ to $X$ which commute with the
shift map $\sigma$.
The group $Aut(\sigma)$ is known to contain a rich structure, and has
been heavily studied
over the years. To analyze a particular automorphism, one may consider its
action on the
dimension group, an ordered abelian group associated to the system
$(X,\sigma)$. We
will describe what this dimension group is, and discuss relationships
between various
dynamical properties of an automorphism and its action on the associated
dimension group.
We'll focus on connections between the topological entropy of an
automorphism and spectral
data coming from its action on the dimension group, and how this relates
to an entropy
conjecture for shifts of finite type in the spirit of Shub's classical
entropy conjecture.
Title: PIMS Undergraduate Event - Twist and Turn: the Story of the Game of Hex
Speaker: Ryan Hayward, University of Alberta
Date and time:
06 Apr 2018,
3:00pm -
4:00pm
Location: David Strong Building, room C116
Event type: PIMS lectures
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(pre-lecture refreshments in DTB A514 @ 2:30 pm)
In 1942, the Danish engineer, poet, and designer Piet Hein invented a new board game and --- with a little help from his friends --- introduced it to readers of the Danish newspaper Politiken. The game became popular: within a year, 50,000 game pads sold.
In 1949 John Nash introduced the game to the Princeton math community, and in 1957 Martin Gardner passed it on to readers of Scientific American.
In this talk for a general audience, I will sketch some big moments in Hex history, ending with an outline of the ideas that make a nearly-superhuman computer Hex program tick.
---
Ryan Hayward received his B.Sc. and M.Sc. in mathematics from Queen's University (Kingston) in 1981 and 1982 and his Ph.D. in computer science from McGill University in 1987. His doctoral thesis, Two Classes of Perfect Graphs, was supervised by Vaclav Chvatal. From 1986 through 1989 he was assistant professor in the Department of Computer Science at Rutgers University, after which he held an Alexander von Humboldt fellowship at the Institute for Discrete Mathematics in Bonn for 1989-90.
From 1990 through 1992 he was assistant professor in the Department of Computing Science at Queen's University. From 1992 he was assistant and then associate professor in the Department of Mathematics and Computer Science at the University of Lethbridge, until in 1999 joining the Department of Computing Science at the University of Alberta, where he was promoted to professor in 2004.
He has supervised 13 graduate and 29 undergraduate students, some of whom later became university professors. His current research interests include algorithms for two-player games. His group (including at times Yngvi Bjornsson, Michael Johanson, Broderick Arneson, Philip Henderson, Jakub Pawlewicz, Chao Gao and Aja Huang --- later lead programmer of AlphaGo) has built the world's strongest computer Hex player, and has solved two 1-move 10x10 Hex openings and all smaller-board openings. With Bjarne Toft, he is writing a book on the history of Hex, to be published in 2018.
Many years ago, Ryan rode his bicycle from Vancouver to Lethbridge.
Download poster (PDF)
Title: Universality of the dimer model
Speaker: Gourab Ray, University Victoria
Date and time:
04 Apr 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Applied math seminar
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Abstract: A dimer model is a model of perfect matching and is an extremely popular subject motivated from problems in statistical mechanics. In this talk, I will outline the basics of this model along with our ongoing project aimed at showing that these models exhibit a large scale universal behaviour (with respect to graphs, underlying surface or boundary conditions) in a certain sense.
Ongoing Joint work with Nathanael Berestycki and Benoit Laslier.
Title: Elliptic operators and K-Homology (part 2 of 2)
Speaker: Anna Duwenig, University of Victoria
Date and time:
04 Apr 2018,
3:30pm -
4:45pm
Location: CLE D 132
Event type: Operator theory seminar
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Abstract: Any symmetric, elliptic differential operator on a smooth
manifold gives rise to a K-Homology class for said manifold. In these
talks, we will first provide the necessary background to understand this
Theorem by introducing Kasparov's K-Homology and the notion of
differential operators. We will then sketch a proof for the case of
compact manifolds.
Title: Ergodic optimization, bounds, and semidefinite programming
Speaker: David Goluskin, University of Victoria
Date and time:
03 Apr 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Dynamics seminar
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Abstract: I will discuss the estimation of infinite-time averages in
discrete and continuous dynamical systems. In particular, I will consider
upper bounds on the maximum such averages among all initial conditions --
in other words, the maximum expectations among invariant measures. Often
the search for a minimal upper bound can be posed as a polynomial
optimization problem, which in turn can be formulated as a semidefinite
program. The latter is a standard type of convex optimization problem that
can be solved with computer assistance.
Title: Gas meters and the Rao-Blackwell Theorem
Speaker: Mary Lesperance, University of Victoria
Date and time:
03 Apr 2018,
2:30pm -
3:20pm
Location: DSB C108
Event type: Statistics seminar
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When teaching the Rao-Blackwell Theorem in Stat450 this term, I was reminded that I encountered the theorem while working on a Statistical consulting contract which involved assessing the accuracy of gas meters.
The objectives of the consulting contract were: (i) to statistically evaluate Acceptance Sampling Plans used in the monitoring of household gas meter accuracy by the Ministry of Consumer and Corporate Affairs Canada, and (ii) to propose a new and fair methodology. In this seminar, I will introduce Acceptance Sampling theory and review the interesting statistical issues raised by the consulting application. En route, I will discuss a multivariate estimator used in Acceptance Sampling which was derived with the Rao-Blackwell Theorem.
Our work on this problem is published in The Canadian Journal of Statistics, the Journal of Statistical Computation(2 articles) and Simulation and Technometrics.
Title: Irreversible k- Threshold Conversion Processes on Graphs
Speaker: Jane Wodlinger, University of Victoria
Date and time:
03 Apr 2018,
1:30pm -
2:30pm
Location: Clearihue Building B017
Event type: Graduate dissertations
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Notice of the Final Oral Examination for the Degree of Doctor of Philosophy
of
JANE WODLINGER
MSc (Simon Fraser University, 2012) BSc (University of Victoria, 2009)
“Irreversible k- Threshold Conversion Processes on Graphs” Department of Mathematics and Statistics
Tuesday, April 3, 2018 1:30 P.M. Clearihue Building Room B017
Supervisory Committee:
Dr. Kieka Mynhardt, Department of Mathematics and Statistics, University of Victoria (Supervisor) Dr. Peter Dukes, Department of Mathematics and Statistics, UVic (Member)
Dr. Venkatesh Srinivasan, Department of Computer Science, UVic (Outside Member)
External Examiner:
Dr. Nancy Clarke, Mathematics and Statistics, Acadia University
Chair of Oral Examination:
Dr. Simon Devereaux, Department of History, UVic
Abstract
Given a graph G and an initial colouring of its vertices with two colours, say black and white, an irreversible k-threshold conversion process on G is an iterative process in which a white vertex becomes permanently coloured black if at least k of its neighbours are coloured black at time t − 1. A set S of vertices is an irreversible k-threshold conversion set (k-conversion set) of G if the initial colouring in which the vertices of S are black and the others are white results in the whole vertex set becoming black eventually. In the case where G is (k + 1)-regular, it can be shown that the k- conversion sets coincide with the so-called feedback vertex sets, or decycling sets.
In this dissertation we study the size, ck(G), and structure of minimum k-conversion sets in several classes of graphs, G. We examine conditions that lead to equality and inequality in existing bounds on ck(G) for k- and (k+1)-regular graphs. Furthermore, we derive new sharp lower bounds on ck(G) for regular graphs of degree ranging from k+1 to 2k−1 and for graphs of maximum degree k+1, and we determine exact values of ck(G) for certain classes of trees.
We show that every (k + 1)-regular graph has a minimum k-conversion set that avoids certain structures in its induced subgraph. These results lead to new proofs of several known results on colourings and forest partitions of (k + 1)-regular graphs and graphs of maximum degree k + 1.
Title: The A4-structure for a Graph
Speaker: Fay Ye, University of Victoria
Date and time:
29 Mar 2018,
10:00am -
11:00am
Location: HSD A264
Event type: Discrete math seminar
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Title: Elliptic operators and K-Homology" (part 1 of 2)
Speaker: Anna Duwenig, University of Victoria
Date and time:
28 Mar 2018,
3:30pm -
4:45pm
Location: CLE D 132
Event type: Operator theory seminar
Read full description
Abstract: Any symmetric, elliptic differential operator on a smooth
manifold gives rise to a K-Homology class for said manifold. In these
talks, we will first provide the necessary background to understand this
Theorem by introducing Kasparov's K-Homology and the notion of
differential operators. We will then sketch a proof for the case of
compact manifolds.
Title: Modeling, analysis and control of biological systems
Speaker: Ismail Belgacem, University of Victoria
Date and time:
28 Mar 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Applied math seminar
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Abstract: These systems can be: continuous or discrete, depending on the modeling approach: ODE or piecewise affine systems (hybrid: PWA). Generally they are also nonlinear, of large dimensions, with different time-scales and complex to analyze. First, we present the modeling of metabolic reactions (biochemical or enzymatic), e.g. Michaelis-Menten. Then we present the classical model of gene expression which only involves concentrations of mRNAs and of proteins and compared to a detailed model of genetic machinery within the cell involving the main actors of the transcription-translation process, such as RNA polymerase and ribosomes. We study the reduction and stability analysis of a transcription-translation model of RNA polymerase where we have a closed loop from the produced RNA polymerase (end-product) to the transcription step (RNA polymerase is needed to transcribe its own gene). Using model parameters given by biologists, we separate the full system into fast and slow subsystems and we reduce the full system using singular perturbations (Tikhonov Theorem). The reduced system consists of ordinary differential and algebraic equations. We perform a dynamical study of this system using theory of monotone and compartmental systems or monotone and concave systems. We present also the control of small genetic networks systems for example qualitative control for PWA systems or sliding mode control for negative (inhibition) feedback loops (ODE).
Title: Mallow Permutations, Stable Matchings and Scaling Limits
Speaker: Omer Angel, University of British Columbia
Date and time:
26 Mar 2018,
3:30pm -
4:20pm
Location: MacLaurin Building, room D110
Event type: PIMS lectures
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We present a new representation of the Mallows permutations to stable matchings on a random bi-partite graph. We also derive new results for the scaling limits of the cycles in the Mallows permutations in terms of the Ethier-Kurtz diffusion.
Joint with Ander Holroyd, Tom Hutchcroft and Avi Levy.
(pre-lecture refreshments @2:45pm in DTB A514)
Download poster (PDF)
Title: 28th Coast Combinatorics Conference
Date:
24 Mar
to
25 Mar 2018
Location: David Turpin Building Room A102
Event type: Conferences and workshops
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The Coast Combinatorics Conferences are low-key meetings that welcome 30-minute (or so) talks on any topic in discrete mathematics and/or theoretical computer science. They are informal and largely "self-serve", meaning that there is no registration fee, no main speaker, and you may be on your own for coffee etc. at a nearby cafe. Sometimes you may even need to introduce yourself when it is your time to speak.
Everyone is welcome to attend the CCC. Please let us know if you are coming by sending email to Gary MacGillivray: gmacgill at UVic dot ca. It makes planning easier.
We are in the process of arranging a lunch booking for Saturday, a social event (happy hour) for Saturday evening. Details are not available yet.
Confirmed Speakers (so far)
Andrei Bulatov (Simon Fraser)
Patrick Fowler (University of Sheffield)
Leslie Hogben (Iowa State University and American Institute of Mathematics)
Sean McGuinness (Thompson Rivers)
Bojan Mohar (Simon Fraser)
Richard Nowakowski (Dalhousie)
Farzaneh Piri (Semnan University)
Hal Sudborough (University of Texas at Dallas)
Boting Yang (Regina)
For more information see the conference website.
Title: The Inverse Eigenvalue Problem of a Graph
Speaker: Leslie Hogben, Iowa State University and American Institute of Mathematics
Date and time:
22 Mar 2018,
3:30pm -
4:20pm
Location: HSD A264
Event type: PIMS lectures
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Inverse eigenvalue problems appear in various contexts throughout mathematics and engineering, and refer to determining whether or not there is a matrix with a prescribed structure (e.g., tridiagonal) and prescribed spectral property (e.g., having a given nullity, or having few distinct eigenvalues). For a given graph G, the associated matrices are real, symmetric, and have off-diagonal nonzero entries exactly where G has edges. The inverse eigenvalue problem of G (abbreviated by IEPG) is to determine the collection of all possible spectra (multisets of eigenvalues) for such matrices. Inverse eigenvalue problems and the background of this problem will be described, together with techniques such as the fundamental work of Colin de Verdière and the Strong Arnold Property. Two recent extensions of the Strong Arnold Property that target a better understanding of all possible spectra and their associated multiplicities will be presented; these are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Applications of these properties to the inverse eigenvalue problem of a graph will be discussed, including the solution of IEPG for all graphs of order at most five.
Download poster (PDF)
Title: A local Formula for the Dolbeault Operator on the Sphere
Speaker: Dan Hudson, University of Victoria
Date and time:
21 Mar 2018,
3:30pm -
4:45pm
Location: CLE D 132
Event type: Operator theory seminar
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ABSTRACT: The Dolbeault operator is a differential operator canonically associated to a complex manifold. In this talk we will develop the background on complex manifolds needed to give the definition of the Dolbeault operator, talk briefly about the Hodge star operator, and find a formula for the adjoint of the Dolbeault operator. We will then restrict our attention to the sphere S2 to derive a local formula for the Dolbeault operator and its adjoint. Finally, we will compute the index of the Dolbeault operator. If time permits, we will conclude by mentioning some instances where this operator makes an appearance.
Title: Conservative methods for dynamical systems
Speaker: Andy Wan, McGill University
Date and time:
21 Mar 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Applied math seminar
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We present a new class of conservative method, called the multiplier method, which enables systematic construction of conservative schemes for general dynamical systems. Specifically, the multiplier method can preserve arbitrary forms of conserved quantities and is applicable to systems without a symplectic or variational structure, such as dissipative systems. We illustrate this method on a variety of dynamical systems and discuss a connection between conservative methods and long-term stability.
This is joint work with Alexander Bihlo at Memorial University of Newfoundland and Jean-Christophe Nave at McGill University.
Title: Imaginary Geometry
Speaker: Gourab Ray, University of Victoria
Date and time:
19 Mar 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: I will give an informal overview of the an interconnection
between the Gaussian free field and SLE (Schramm Loewner Evolution) curves
which is given the name "imaginary geometry" by its creators Miller and
Sheffield. No previous knowledge of either Gaussian free field or SLE will
be assumed.
Title: Quantifier Elimination in C*-algebras
Speaker: Todd Schmid, University of Victoria
Date and time:
15 Mar 2018,
10:00am -
11:20am
Location: Mac D010
Event type: Operator theory seminar
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Abstract: Generally speaking, model theory seeks to measure the
complexity of the formulas of modern mathematics.
The study was initially restricted to discrete structures, but
contributions from Chang and Kiesler in the 1960s, and in the past two
decades from Ben Yaacov, Berenstein, and many others, led to a
continuous logic suitable for metric structures.
During this talk, we will discuss applications of continuous logic to
C*-algebras, how one measures the complexity of formulas from the theory
of C*-algebras, and an explicit measurement of this complexity in the
finite-dimensional case.
Title: An introduction to graphons (from a layman)
Speaker: Peter Dukes, University of Victoria
Date and time:
15 Mar 2018,
10:00am -
11:00am
Location: HSD A264
Event type: Discrete math seminar
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Title: Equilibrium, social welfare and optimal structure in hierarchical Public goods games
Speaker: Yifen Mu, University of Victoria
Date and time:
14 Mar 2018,
3:30pm -
4:20pm
Location: DSB C130
Event type: Applied math seminar
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Abstract: Game theory is a powerful tool to formulate the conflict and cooperation between self-interested people and to predict individual or social human behavior. Therein hierarchical games study the games with possibly general hierarchical structures between players, which can naturally arise from the non-symmetry in time or space of players and thus exist widely in many kinds of scenarios. The equilibrium becomes Stackelberg-Nash equilibrium in such games. In this talk we will investigate two specific hierarchical games, i.e., the discrete and continuous Public goods games with discrete and continuous actions respectively. Public goods game models the profound phenomenon of “Tragedy of the Commons” and is a standard model in experimental economics. We will give the explicit solution of the Stackelberg-Nash equilibrium of the games by solving optimization problems. The equilibrium results show counterintuitive phenomena in hierarchical games and reveal the significant influence of hierarchical structure to the system. Then based on the solution of equilibrium, we will consider the inverse problem and obtain the optimal hierarchical structure which can reach the best optimal social welfare.
Title: A tight excess risk bound via a new complexity based on a unification of PAC-Bayesian, normalized maximum likelihood, and Radema
Speaker: Nishant Mehta, University of Victoria, Computer Science
Date and time:
13 Mar 2018,
2:30pm -
3:20pm
Location: DSB C108
Event type: Statistics seminar
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I will talk about a new notion of complexity, COMP, that interpolates between (and generalizes) some existing complexity notions from statistical learning theory. I will first derive COMP as a generalization of the Shtarkov sum, the normalizer in the normalized maximum likelihood (NML) distribution. When the NML distribution exists, the logarithm of the Shtarkov sum is precisely equal to the minimax regret for individual sequence prediction under log loss. Next, via a PAC-Bayesian analysis, I will show how COMP can be used to obtain tight upper bounds on the excess risk for randomized estimators (which include generalized Bayesian estimators). This excess risk bound will be in terms of COMP itself. Under a certain specialization, further upper bounding COMP leads to a standard PAC-Bayesian excess risk bound whose right hand side is the information complexity (essentially the empirical excess risk plus an additional complexity term involving the KL divergence from the posterior distribution to the prior distribution). Under a different specialization, the special case of empirical risk minimization with VC-type classes and large classes whose empirical L2 entropy exhibits polynomial growth, we will see how COMP is upper bounded in a way which yields optimal rates of convergence of the excess risk for such classes. Along the way, we will see connections to Rademacher complexity, and, in particular, we will recover bounds based on local Rademacher complexity while completely avoiding complicated local Rademacher complexity-based arguments. This is joint work with Peter Grünwald at CWI (in Amsterdam) and Leiden University.
Title: Stability results for non-autonomous dynamical systems
Speaker: Cecilia Gonzalez Tokman, University of Queensland
Date and time:
12 Mar 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: In this talk we discuss recent developments concerning stability
properties of non-autonomous dynamical systems, motivated by the ergodic
theoretical study of random, forced or time-dependent systems and their
coherent structures. In the setting of random interval maps we present
results about stability of random absolutely continuous invariant
measures. In the context of multiplicative ergodic theory, we discuss
results on stability of Lyapunov exponents and Oseledets spaces in finite
and infinite-dimensional settings. This is based on joint works with Gary
Froyland, Rua Murray and Anthony Quas.
Title: Doubly Lexical Orderings of Matrices
Speaker: Jing Huang, University of Victoria
Date and time:
08 Mar 2018,
10:00am -
11:00am
Location: HSD A264
Event type: Discrete math seminar
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Title: Bratteli diagrams and flat surfaces (Part 2 of 2)
Speaker: Ian Putnam, University of Victoria
Date and time:
07 Mar 2018,
3:30pm -
4:45pm
Location: CLE D 132
Event type: Operator theory seminar
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Abstract: Flat surfaces (also translation surfaces) are specific types
of dynamical systems which have received a great deal of attention, I
will give an outline of their construction in the finite genus case.
Bratteli diagrams are combinatorial objects, initially introduced to
describe approximately finite-dimensional (AF) C*-algebras and have also
been used for models of actions on Cantor sets. I will describe recent
work of Kathryn Lindsey and Rodrigo Trevino to construct examples of
flat surfaces in the infinite genus case from a Bratteli diagram. The
first talk will be entirely dynamical (and will likely have more
constructions than theorems). The second will focus on the rather
mysterious relationship between the AF-algebras and the C*-algebras
associated with the flat surface dynamics. (Joint work, in progress,
with Rodrigo Trevino.)
Title: Host Contact Structure is Important for the Recurrence of Influenza A
Speaker: Juan Jaramillo, UVic Computer Science
Date:
07 Mar 2018
Location: DSB C130
Event type: Applied math seminar
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Abstract: An important characteristic of influenza A is its ability to escape host immunity through antigenic drift. A novel influenza A strain that causes a pandemic confers full immunity to infected individuals, yet because of antigenic drift, these individuals have decreased immunity to drifted strains. We compute the required decrease in immunity so that a recurrence is possible. Models for influenza A must make assumptions on the contact structure on which the disease spreads. By determining the local stability of the disease free equilibrium via the reproduction number, we show that the classical random mixing assumption predicts an unrealistically large decrease of immunity before a recurrence is possible. We improve over the classical random mixing assumption by incorporating a contact network structure. A complication of contact networks is correlations induced by the initial pandemic. Thus in this presentation, I share joint work with P. van den Driessche and Junling Ma where we provide a novel analytic derivation of such correlations and show that contact networks may require a dramatically smaller drop in immunity before recurrence. Hence, the key new insight in our work is that on contact networks the establishment of a new strain is possible for much higher immunity levels of previously infected individuals than predicted by the commonly used random mixing assumption. This suggests that stable contacts like classmates, coworkers and family members are a crucial path for the spread of influenza in human population.
Title: Projections of a random walk on a space of binary trees
Speaker: Noah Forman, University of Washington
Date and time:
05 Mar 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: Consider the Markov process in the space of binary trees in
which, at each step, you delete a random leaf and then grow a new leaf in
a random location on the tree. In 2000, Aldous conjectured that it should
have a continuum analogue, which would be a continuum random tree-valued
diffusion. We will discuss a family of projectively consistent Markov
chains that are projections of this tree, and discuss how these
representations can be passed to the continuum. This is joint work with
Soumik Pal, Douglas Rizzolo, and Matthias Winkel.
Title: Minimum Chi-square Method for Estimating Population Size with Application to Capture-Recapture White Stork Data
Speaker: Sophia Zheng, University of Victoria
Date and time:
02 Mar 2018,
3:30pm -
4:30pm
Location: Clearihue Building B017
Event type: Graduate dissertations
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The Final Oral Examination for the Degree of
Master of Science (Department of Mathematics & Statistics)
Sophia (Yuyan) ZHENG
B.Sc., University of Victoria, 2016
“Minimum Chi-square Method for Estimating Population Size with Application to Capture-Recapture White Stork Data”
March 2, 2018 3:30pm Clearihue Building B017
Supervisory Committee:
Dr. Laura Cowen, Department of Mathematics & Statistics, UVic (Co-supervisor)
Dr. Min Tsao, Department of Mathematics & Statistics, UVic (Co-supervisor)
Chair of Oral Examination:
Dr.Xuekui Zhang, Department of Mathematics & Statistics, UVic
Title: Generalized Opposition Graphs
Speaker: Fay Ye, University of Victoria
Date and time:
01 Mar 2018,
10:00am -
11:20am
Location: HSD A264
Event type: Discrete math seminar
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Title: Bratteli diagrams and flat surfaces (Part 1 of 2)
Speaker: Ian Putnam, University of Victoria
Date and time:
28 Feb 2018,
3:30pm -
4:45pm
Location: CLE D 132
Event type: Operator theory seminar
Read full description
Abstract: Flat surfaces (also translation surfaces) are specific types
of dynamical systems which have received a great deal of attention, I
will give an outline of their construction in the finite genus case.
Bratteli diagrams are combinatorial objects, initially introduced to
describe approximately finite-dimensional (AF) C*-algebras and have also
been used for models of actions on Cantor sets. I will describe recent
work of Kathryn Lindsey and Rodrigo Trevino to construct examples of
flat surfaces in the infinite genus case from a Bratteli diagram. The
first talk will be entirely dynamical (and will likely have more
constructions than theorems). The second will focus on the rather
mysterious relationship between the AF-algebras and the C*-algebras
associated with the flat surface dynamics. (Joint work, in progress,
with Rodrigo Trevino.)
Title: Machine Learning Challenges in Music Technology
Speaker: George Tzanetakis, UVIc Computer Science
Date and time:
27 Feb 2018,
2:30pm -
3:20pm
Location: DSB C108
Event type: Statistics seminar
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The computer analysis of music is particularly challenging because of the multi-faceted and hierarchical nature of musical information. During the last 13 years techniques from machine learning have been leveraged in the field of music information retrieval to solve problems such as automatic genre classification, mood prediction and music recommendation. In most of these cases standard techniques from machine learning such as supervised classification and unsupervised clustering were utilized.
In this talk I will talk about two music analysis problems for which more advanced machine learning approaches are required. The first problem is automatic tag annotation and I will describe stacking which is an layered classifier architecture for solving this problem. The second problem is the hierarchical analysis of music into segments, chords and keys and I will describe the use of Markov Logic Networks to solve this problem. Markov Logic Networks are a rich formalism that combines the expressiveness of first-order logic for representing relations with the statistical learning abilities of data mining. The third problem I am going to discuss is the use of a machine learning approach to enable expressive bowing control of a virtual physical violin model, work that connect sound synthesis with music information retrieval.
Title: Ergodic Optimization: An overview
Speaker: Anthony Quas, University of Victoria
Date and time:
26 Feb 2018,
3:30pm -
4:20pm
Location: DSB C126
Event type: Dynamics seminar
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Abstract: As a prelude to a reading group being organized by David Goluskin, I will introduce the subject of ergodic optimization, and talk about the questions, the paradigms, and some results in the field.
Title: Traveling waves of bacteria at the mesoscopic scale
Speaker: Vincent Calvez, ENS, Lyon-France
Date and time:
22 Feb 2018,
3:30pm -
4:20pm
Location: DSB C124
Event type: Applied math seminar
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Abstract: Concentration waves of swimming bacteria Escherichia coli were described
in his seminal paper by Adler (Science 1966). These experiments gave
rise to intensive PDE modelling and analysis, after the original model
by Keller and Segel (J. Theor. Biol. 1971), and the work of Alt (J.
Math. Biol. 1980) and his co-authors. Together with Bournaveas,
Perthame, Raoul and Schmeiser, we have revisited this old problem from
the point of view of kinetic transport equations. This framework is very
much adapted to the so-called run-and-tumble motion, in which bacteria
modulate the frequency of reorientation (tumble) -- and thus the
duration of free runs -- depending on chemical variations in the
environment. I will present some recent analytical and numerical results
about the existence of traveling wave solutions for a coupled
kinetic-parabolic system describing concentration waves of bacteria in a
micro-channel. The parabolic-parabolic problem obtained in the diffusive
limit admits unique traveling wave solutions without any restriction on
the parameters. This is in opposition to the kinetic-parabolic system
for which solutions may be not unique, or may not exist for some extreme
range of parameters.
