Seminars
Winter 2025 |
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Friday, March 14th 12:30- 1:20pm |
Dr. Vaclav Linek Department of Mathematics and Statistics, University of Winnipeg |
Title: Skolem Sequences: A Monograph Project Abstract: An order n Skolem sequence consists of numbers 1, 2, . . . , n (the differences), each occurring twice, with the two occurrences of j exactly j positions apart. So 4, 1, 1, 3, 4, 2, 3, 2 is an order 4 Skolem sequence: the 1s are one position apart, 2s are two positions apart, 3s are three positions apart, and 4s are four positions apart. Similarly, 3, 4, 5, 3, 2, 4, 2, 5, 1, 1 is an order 5 Skolem sequence. |
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Friday, March 7th 12:30- 1:20pm |
Dr. Mehdi Dagdoug Department of Mathematics and Statistics, McGill University |
Title: Statistical Learning for Finite Population Sampling Abstract: Predictive models are frequently incorporated into survey strategies. Some examples of their use include model-based estimators, model-assisted estimators, and handling nonresponse through imputation and reweighting. In recent decades, the statistical community has shown growing interest in statistical learning, leading to significant advancements both theoretically and computationally. Statistical learning thus provides survey statisticians with new highly flexible tools. However, it also introduces new challenges, such as model selection and variance estimation. In this seminar, we will present a review of the literature on the use of predictive methods in survey sampling. We will detail their usual properties and discuss their advantages and limitations based on theoretical and empirical results. Finally, we will explore potential ways to address these limitations. |
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Friday, February 14th 12:30- 1:20pm |
Hermie Monterde PhD candidate at University of Manitoba |
Title: Fundamentals of quantum state transfer Abstract: A network of interacting qubits (usually subatomic particles) can be modelled by a connected weighted undirected graph $G$. The vertices and edges of $G$ represent the qubits and their interactions in the network, respectively. Quantum mechanics dictate that the evolution of the quantum system determined by $G$ over time is completely described by the unitary matrix $U(t)=\exp(itA)$, where $A$ is the adjacency matrix of $G$. Here, we interpret the modulus of the $(u,v)$ entry of $U(t)$ as the probability that the quantum state at vertex $u$ is found in $v$ at time $t$. In particular, if this modulus is equal to 1, then we say that perfect state transfer occurs between $u$ and $v$. In this talk, we discuss the role of the underlying graphs in the study of quantum state transfer. |
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Friday, February 7th 12:30- 1:20pm |
Dr. Saman Muthukumarana University of Manitoba, Department of Statistics
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Title: Advanced SMOTE Techniques for Addressing Class Imbalance in Real-World and High-Dimensional Classification Tasks Abstract: Class imbalance is a general challenge in machine learning, particularly in critical applications like medical diagnosis, fraud detection, and industrial anomaly detection, where minority classes are often underrepresented. Traditional classification models struggle to predict minority classes, leading to suboptimal outcomes. We introduce and evaluate advanced Synthetic Minority Over-sampling Technique (SMOTE) extensions to address this issue. These include four novel methods: Distance ExtSMOTE, Dirichlet ExtSMOTE, FCRP SMOTE, and BGMM SMOTE which enhance synthetic sample quality using weighted averages of neighboring instances and mitigate the impact of outliers. Building on these innovations, Deep-ExtSMOTE integrates autoencoder-based dimensionality reduction with an extended SMOTE framework to address both class imbalance and the curse of dimensionality. Autoencoders capture complex, non-linear relationships and reduce data dimensionality, while advanced resampling techniques improve the representation of minority classes.
This is based on joint work with Dr. Surani Matharaarachchi and Dr. Mike Domaratzki. |
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Friday, January 24th 12:30- 1:20pm |
Dr. Amin Abed University of Manitoba, Department of Community Health Sciences |
Title: Individual Level Modeling of Infectious Disease Transmission with Reinfection Dynamics: Tuberculosis in Manitoba Abstract: Recent advancements in stochastic modeling of infectious disease transmission have increasingly incorporated spatial factors, significantly enhancing the accuracy of disease spread predictions and public health interventions. For many infectious diseases, reinfection is a key factor that significantly impacts disease dynamics, epidemic progression, prevalence and control efforts, complicating management strategies. Therefore, accurately incorporating reinfection into disease modeling is essential for developing effective interventions. To this end, our study expands upon the previously proposed Geographically Dependent Individual Level Models (GD-ILMs) of infectious diseases by integrating them within a Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) compartmental framework, termed GD-ILM SEIRS, to consider reinfection. A Monte Carlo Expectation Conditional Maximization algorithm was employed to estimate the parameters of the proposed model. The GD-ILM SEIRS was applied to Tuberculosis data from Manitoba, Canada, covering the period from 2011 to 2018. It considers spatial dependencies, as well as individual and regional risk factors that influence susceptibility to initial infection and reinfection, as well as infectivity. The examination of Manitoba's health authority districts highlights particular risk factors associated with susceptibility to initial infection and reinfection, and infectivity. Additionally, the fitted model enables the calculation of infection probabilities at high-resolution geographic scales. The results allow for targeted interventions and optimized resource allocation by detecting high-risk areas and vulnerable populations to reduce transmission rates, prevent reinfection, and enhance health outcomes in Manitoba. Moreover, a simulation study across different grid configurations demonstrates that the model performs effectively and provides accurate estimates for the model parameters. Our study highlights the critical need to integrate reinfection dynamics into infectious disease models to strengthen the impact of public health interventions and disease control strategies. |
Fall 2024 |
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Friday, November 15 12:30- 1:20pm |
Dr. Iian Smythe Department of Mathematics and Statistics, University of Winnipeg |
Title: Matrix groups and their orbit equivalence relations Abstract: One of the truisms of modern mathematics is that "groups act". For example, the symmetric groups act by permutations on sets of letters, while the dihedral groups act by symmetries on regular polygons. Any time we have an action of a group on a set, we can consider the resulting orbit equivalence relation; two elements of the set are equivalent if one can be sent to the other by an element of the acting group. In this talk, I will discuss certain actions by groups of invertible matrices and their relationships to actions by countable discrete groups. These actions arise from symmetries of hyperbolic space and have implications for the classification of hyperbolic manifolds. This talk is meant to be accessible to students familiar with the definition of a "group" (from MATH-3202), the notion of an "equivalence relation" (from MATH-1401), and some linear algebra (at the level of MATH-2203). |
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Friday, November 1 12:30- 1:20pm |
Dr. Matthew Wiersma Department of Mathematics and Statistics, University of Winnipeg |
Title: Random walks on groups Abstract: A random walk, sometimes colloquially known as a drunkard's walk, describes a process of successive random steps on a mathematical structure. We will consider random walks on groups in this talk. We will learn about different notions of entropy, which measure how random the process is, and how the entropy of a random walk is related to the underlying properties of the group. Time permitting, I will describe some new results relating Furstenberg entropy to the dynamical properties of the corresponding group action. These new results are based on joint work with Benjamin Anderson-Sackaney, Tim de Laat and Ebrahim Samei.
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Friday, October 11 12:30- 1:20pm |
Guanhong Xiao
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Title: Efficient estimation of Cox frailty models with application to lung cancer Abstract: It is a critical issue in survival analysis when studying diseases with treatment differences, especially when analyzing data from individuals whose observations are correlated due to shared environments. These data arise from various fields of biomedical research, such as multi-center clinical trials, group randomized trials, recurrent events, and environmental studies. The Cox proportional hazards (PH) model is the one that is most widely used to analyze survival data. Owing to its broad applicability, we explore the pretest and shrinkage estimation methods for the Cox PH model for right-censored clustered survival data when some of the covariates in the model may not be relevant for accurately predicting survival times. In order to address this, we employ two models: an unrestricted model that encompasses all covariates, and a restricted model that includes a smaller set of covariates. We optimally combine estimators from both models to establish pretest and shrinkage estimators. Mean squared error (MSE) and relative MSE are calculated to assess the performance of these estimators. By conducting extensive simulation studies and applying the proposed methods to a lung cancer data, we demonstrate that the shrinkage estimators exhibit lower risk compared to the estimators derived from the full model when the shrinkage dimension exceeds two. |
Winter 2024 |
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Friday, March 22nd 12:30- 1:20pm |
Dr. Leann Lac |
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Friday, March 15th 12:30- 1:20pm |
Dr. Janet Page North Dakota State University |
Title: Gorenstein rings and the Chicken McNugget problem Abstract: If chicken nuggets were only sold in packs of 6, 9, and 20 (as they originally were), then you could order 12 (6+6) or 15 (6+9) nuggets, but it’d be impossible to order exactly 7, 8, 10, 11, or 13 nuggets. What is the largest number of nuggets that it’d be impossible to order exactly? In this talk, we'll delve into the world of commutative algebra and learn about a special class of algebraic objects called "Gorenstein rings," which turn out to be deeply connected to this problem. We'll discuss some of their algebraic and geometric properties, and time permitting, we’ll discuss some combinatorial examples coming from rings defined by finite partially ordered sets along with some recent results. You may even be able to solve the Chicken McNugget problem before the talk! |
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Friday, January 19th 12:30- 1:20pm |
Dr. Shakhawat Hossain Department of Mathematics and Statistics, University of Winnipeg |
Title: Parametric regression models can be a viable alternative to the Cox proportional hazards model Abstract: In the realm of medical sciences, researchers often prefer the Cox proportional hazards model for survival analysis due to its fewer assumptions. However, a parametric model offers several significant advantages, including improved efficiency, estimations with straightforward and meaningful interpretations, and improved prediction accuracy. This paper investigates the usefulness of parametric survival models (Weibull, lognormal and log-logistic) in contrast to the Cox proportional hazards model. We explore specific aspects in which parametric survival models demonstrate advantages over the Cox model. Motivated by the use of normal-deviate residuals, we first asses the goodness of fit of both the Cox and parametric models, and then once the most effective model is identified, we employ efficient estimation methods, including pretest and shrinkage estimation, to improve the unrestricted model estimators. To evaluate the performance of these estimation strategies numerically, we conduct a simulation study and apply them to three real data sets. Our research shows that certain parametric models are comparable to the Cox model in terms of normal-deviate residuals and mean squared error criteria of efficient estimator. |
Fall 2023 |
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Friday, November 24th 12:30- 1:20pm |
Dr. Payman Eskandari Department of Mathematics and Statistics, University of Winnipeg |
Title: Special values of the Riemann zeta function - a journey from concrete to abstract Abstract: Number theory is the area of mathematics that concerns with the study of integers. It is one of the oldest branches of mathematics. A broken clay tablet from around 1800 BC includes a list of Pythagorean triples. The early Pythagoreans around 500 BC had discovered that the square root of 2 is irrational. One of the fascinating features of number theory is that it is a rich source of problems that are easy to state, and yet turn out to be astonishingly difficult to solve. Some of these innocent-seeming questions turn out to be at the surface level of highly deep, abstract and convoluted theories. An example of this is Fermat’s last theorem, a problem posed in the 17th century by Fermat that was finally solved in 1995 by Andre Wiles after development of highly abstract machinery over the previous two centuries. This talk aims to take the audience through a number-theoretic journey from the concrete to the abstract. The story begins with Euler's fascinating formula for the value of the infinite sum of the reciprocals of squares. Euler proved similar formulas for the sums of the reciprocals of the 4-th powers, 6-th powers, and so on. However, the situation for the sums of the reciprocals of the 3rd powers, 5-th powers, etc. seems very different and remains highly mysterious to date. We will overview the more concrete aspects of this picture, and then explain how they are related to highly abstract theories and conjectures: the theory of motives and the celebrated conjectures of Beilinson-Bloch and Grothendieck. In the end, I hope to also be able to say a few words about some more recent developments. |
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Friday, October 20th 12:30- 1:20pm |
Dr. Adam Clay University of Manitoba |
Title: Groups of homeomorphisms of R^n Abstract: When studying a group, it can be very helpful to realize the group as something other than an abstract object---e.g. is it isomorphic to a group of permutations, a group of matrices, perhaps a group of functions? In this talk, I'll discuss the question of when a given group is isomorphic to a group of homeomorphisms of Euclidean space. I'll first discuss the special case of groups of linear maps, using this special case to come up with some "expected results" that will likely hold true in the general case when we consider groups of homeomorphisms. The general case proves quite tricky, however, and I will outline a few recent results and current open problems. |
Winter 2023 |
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Friday, March 24 12:30- 1:20 |
Dr. Kumar Murty University of Toronto and the Fields Institute for Research in Mathematical Sciences. |
Title: Factorization and modular forms Abstract: Factoring natural numbers has intrigued professional and amateur mathematicians alike for many centuries. Nowadays, we know that it also has practical implications, for the computational difficulty of factoring holds the key to the security of several encryption algorithms. In this talk, we show how the theory of modular forms, a topic from number theory, gives a new approach to the problem of factoring. We describe some results which are joint work with Aaron Chow. |
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Friday, February 10 12:30 - 1:20 |
Dr. Daniel Gabric Post-Doctoral Fellow Department of Mathematics and Statistics, University of Winnipeg |
Title: Asymptotic bounds for the number of closed and privileged words Abstract: A word w has a border u if u is a non-empty proper prefix and suffix of u. A word w is said to be closed if w is of length at most 1 or if w has a border that occurs exactly twice in w. A word w is said to be privileged if w is of length at most 1 or if w has a privileged border that occurs exactly twice in w. Let C_k(n) (resp. P_k(n)) be the number of length-n closed (resp. privileged) words over a k-letter alphabet. In this talk we present improved upper and lower bounds on C_k(n) and P_k(n). We completely resolve the asymptotic behaviour of C_k(n). We also nearly completely resolve the asymptotic behaviour of P_k(n) by giving a family of upper and lower bounds that are separated by a factor that grows arbitrarily slowly. |
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Friday, January 20 12:30- 1:20 |
Jeffrey Peitsch Undergraduate Student Department of Mathematics and Statistics, University of Winnipeg |
Title: Ensemble Learning Methods of Inference for Spatially Stratified Infectious Disease Systems Abstract: Individual level models (ILMs) are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information to account for population heterogeneity, and are generally fitted using Bayesian Markov chain Monte Carlo (MCMC) techniques. However, for large and spatially heterogeneous disease systems, the Bayesian MCMC framework is computationally intensive requiring large computing resources. In this study we propose to use ensemble learning methods to infer the disease transmission dynamics over spatially clustered populations, considering the clusters as natural strata. We compare the performance of three ensemble learning techniques: random forest, gradient boosting, and a deep forest. The methods are evaluated using simulated data and applied to the 2001 foot-and-mouth disease epidemic in the U.K. We show that natural stratification can help to predict the epidemic generating models more accurately than global data. |
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Friday, January 13 12:30- 1:20 |
Markus Bunge Data Scientist Sunlife Financial |
Title: Your Career in Data Science - Setting yourself up for success Abstract: When Googling "Getting started with your Data Science career" the familiar theme throughout the blogs is that by getting degrees, additional certifications, and submitting enough job applications, you will eventually get a job in the field. While this may work for some, the reality is that following this blueprint does not guarantee success, and even getting an interview can seem like a fairy tale. This talk will explore what tools you need, why soft skills are important, and other insights, to set yourself up for success in your Data Science journey. |
Fall 2022 |
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Friday, December 2 12:30-1:20
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Dr. Iian Smythe Department of Mathematics and Statistics, University of Winnipeg
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Title: Maximality, cardinality, and definability Abstract: Often in mathematics, we want to find objects which are maximal with respect to a certain property, meaning they have the property in question but any attempt to enlarge them will cause that property to be violated. This is what may be termed an "extremal" condition and examples include maximal ideals in rings, maximal linearly independent sets (i.e., bases) in vector spaces, or maximal acyclic subgraphs (i.e., spanning forests) in graphs. One important example arising in set theory is a maximal almost disjoint (or MAD) family of infinite subsets of the natural numbers; such families may be thought of as partitions of the natural numbers which allow for finite error. This talk will be a survey on MAD families, how we obtain them, how big they can be, and whether we can ever hope to explicitly construct them. |
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Friday, November 18 12:30-1:20 |
Dr. Razvan Romanescu Assistant Professor Department of Community Health Sciences, University of Manitoba
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Title: An R_t- based model for predicting multiple epidemic waves in a heterogeneous population Abstract: Most models of infectious disease based on ordinary differential equations assume that spread occurs through a homogeneous population. This produces poor fits to real data, because individuals vary in their number of epidemiologically-relevant contacts, and hence in their ability to transmit disease. In particular, network theory suggests that super-spreading events tend to happen more often at the beginning of an epidemic, and this spread dynamic requires different modeling assumptions. In this paper we argue that introducing a flexible decay shape for the effective reproductive number (Rt) better captures the progression of disease incidence over a network. This, in turn, produces better retrospective fits, as well as more accurate prospective predictions of observed epidemic curves. We extend this framework to fit multi-wave epidemics, and to accommodate public health restrictions on mobility. We demonstrate the performance of this model by doing a prediction study over two years of the SARS-CoV2 pandemic. |
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Friday, October 28 12:30-1:20
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Dr. Matthew Wiersma Department of Mathematics and Statistics, University of Winnipeg |
Title: Group C*-algebras, amenability, and failure of lifting properties Abstract: C*-algebras were introduced by von Neumann in the 1930s to model phenomena occurring in quantum physics and have since developed into a major field of study within pure mathematics. I will explain what a C*-algebra is, how to construct C*-algebras from groups, what an amenable group is, and how the amenability of a group is reflected in its C*-algebras. Towards the end of the talk, I will present joint work with A. Ioana and P. Spaas on the failure of lifting properties for certain group C*-algebras. |
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Wednesday, October 19 12:30-1:20 |
Dr. Nico Spronk University of Waterloo |
Title: A survey of amenability properties of Banach Abstract: Amenability for groups was first discovered by von Neumann, the failure of which is a critical element of Banach-Tarski paradox. Johnson devised the suitable analogue for Banach algebras in terms of structure of certain derivations, and proved it is the correct concept by showing that an L^1-group algebra is ameanable if and only if the underlying group itself is amenable. This has proved to be a valuable property for Banach algebras. It admits at least 2 essential relaxations, weak amenability (mainly for commutative Banach algebras), and Connes amenability for dual algebras, named in honour of Connes’s contributions to the theory of von Neumann algebras. |
Fall 2021 |
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Friday, Dec 3 12:30-1:20 |
Dr. Julien Arino Department of Mathematics, University of Manitoba |
Title: Considerations about case importations in the context of COVID-19 Abstract: The spatio-temporal spread of infectious diseases between human jurisdictions can be viewed as the repetition of several process-es, namely, transportation, importation, amplification and exportation. These processes operate differently depending on the scale at which they are considered. Taking the example of the current COVID-19 cris-is, top-level national jurisdictions imported the infection quickly and have, for the most part, remained with the infection since. However, zooming in at the level of local jurisdictions, there have been many phases of importation and amplification followed by periods without any transmission. As a consequence, understanding the importation process, how to lower its probability of success and its overall contrib-ution to local infection is important. I will present data concerning this process, then will discuss models that were developed to represent the process as well as evaluate some measures taken to alleviate importa-tion risks.
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Friday, Nov 12 12:30-1:20 |
Dr. Blake Madill Department of Pure Mathematics, University of Waterloo |
Title: From UW(innipeg) to UW(aterloo): Advice for future graduate students. Abstract: In this short and informal talk, I will discuss some of thelessons learned from my experiences as a Winnipeg undergraduate student and a Waterloo graduate student. Emphasis will be placed on the strengths of UWinnipeg and the unique opportunities it affords its students. This talk will be particularly interesting to third and fourth year undergraduate students who are considering graduate studies. |
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Friday, Oct 22 12:30-1:20 |
Dr. Narad Rampersad Department of Mathematics and Statistics, University of Winnipeg |
Title: Computer proofs of some combinatorial congruences Abstract: The classical congruence result of Lucas (1878) for the binomial coefficients "n choose m" modulo a prime p shows that looking at the base-p representations of n and m is often an efficient way to determine divisibility properties of the binomial coefficients modulop. Many authors have studied divisibility properties of famous combinatorial sequences along these lines. For instance, Alter and Kubota (1971) studied the Catalan numbers modulo p. Deutsch and Sagan (2006) looked at the Motzkin numbers, central Delannoy numbers, Apery numbers, etc., mod p. Rowland and Yassawi (2015) and Rowland and Zeilberger (2014) used finite automata to describe congruence properties of these types of sequences. We show how to combine the method of Rowland and Zeilberger with the software Walnut, which can prove many properties of so-called "automatic sequences", to give very quick, fully automated proofs of some of these congruence properties. |
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Friday, Sept 24 12:30-1:20 |
Dr. Aasaimani Thamizhazhagan Department of Mathematics and Statistics, University of Winnipeg |
Title: On the structure of invertible elements in certain Fourier-Stieltjes algebras Abstract: Let G be a locally compact group. The Fourier-Stieltjes B(G) is defined as a dual object to the measure algebra M(G) in a sense that generalizes Pontryagin duality from the theory of abelian locally compact groups. Hence there is natural expectation that properties of M(G) ought to be reflected in B(G). In this talk, we characterize the invertible elements of B(G) for certain non-abelian Lie groups G. This can be viewed as a dual result to Taylor's characterization of invertible elements in M(G) for abelian G and provides partial verification to a conjecture of Illie and Spronk. |
Winter 2021 |
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Friday, April 9 12:30-1:20 via Zoom |
Dr. Zeinab Mashreghi Department of Mathematics and Statistics, University of Winnipeg |
Details TBA |
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Friday, March 19 12:30-1:20 via Zoom |
Prof. Jim Stallard Department of Mathematics and Statistics, University of Calgary |
Details TBA |
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Friday, January 29 12:30-1:20 via Zoom |
Dr. Melissa Huggan Department of Mathematics, Ryerson University |
Title: Combinatorial Game Theory Abstract: Two player, perfect information games of no chance have beautiful mathematics underpinning their study. These are called combinatorial games. I will give a gentle introduction to combinatorial game theory. We will go on a journey via rulesets, including NIM, HACKENBUSH, and DOMINEERING, to illustrate several of the main theoretical results within this area of mathematics. |
Fall 2020 |
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Friday, December 4 12:30-1:20 via Zoom |
Dr. Gyanendra Pokharel Department of Mathematics and Statistics, University of Winnipeg |
Title: Likelihood-based model classification and prediction of spatial epidemics Abstract: In an emerging epidemic, public health officials must move quickly to control the spread. Information obtained from statistical disease transmission models often informs the development of control strategies. Inference procedures such as Bayesian Markov chain Monte Carlo (MCMC) allow researchers to estimate parameters of such models, but are computationally expensive. Pokharel and Deardon (2014) introduced an approach for inference on infectious disease data based on the idea of supervised statistical and machine learning method. Their method involves simulating epidemics from various infectious disease models, and using classifiers built from the epidemic curve-based summary statistic to predict which model were most likely to have generated observed epidemic curves. In this work, I propose to replace epidemic curve-based summary statistic by a likelihood-based summary statistic calculated over a design matrix constructed over the pre-defined parameter space. Then, thus built classifier is used to detect the disease transmission kernel and model parameters for the observed data. This approach may perform better than the epidemic curve-based classification approach assuming that the likelihood-based summary statistic provides better information to the model. |
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Friday, November 20 12:30-1:20 via Zoom |
Dr. Shakhawat Hossain Department of Mathematics and Statistics, University of Winnipeg |
Title: An efficient estimation approach to joint modelling of longitudinal and survival data Abstract: The joint models for longitudinal and survival data have recently received a significant amount of attention in medical and epidemiological studies. Joint models typically combine linear mixed effects models for repeated measurement data and Cox models for survival time. When we are jointly modelling the longitudinal and survival data, variable selection and efficient estimation of parameters are especially important for performing reliable statistical analyses, which are lacking in the literature. In this paper we discuss the pretest and shrinkage estimation methods for jointly modeling longitudinal data and survival time data, when some of the covariates in both longitudinal and survival components may not be relevant for predicting the individuals' survival times. In this situation, we fit two models: the full model that contains all the covariates and the subset model that contains a reduced number of covariates. We combine the full model estimators and the estimators that are restricted by a linear hypothesis to define pretest and shrinkage estimators. We provide their numerical mean squared errors (MSE) and relative MSE . We show that if the shrinkage dimension exceeds two, the risk of the shrinkage estimators is strictly less than that of the full model estimators. Our proposed methods are illustrated by extensive simulation studies and by a real-data example. This is the joint work with Jody Krahn (U of Winnipeg) and Dr. Shahedul Khan (University of Saskatchewan). |
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Friday, November 13 12:30-1:20 via Zoom |
Dr. Ortrud Oellermann Department of Mathematics and Statistics, University of Winnipeg |
Title: The threshold dimension and threshold strong dimension of a graph Abstract: Let G be a connected graph and u,v and w vertices of G. Then w is said to resolve u and v if the distance from u to w does not equal the distance from v to w. If there is either a shortest u-w path that contains v or a shortest v-w path that contains u, then we say that w strongly resolves u and v. A set W of vertices of G is a resolving set (strong resolving set), if every pair of vertices of G is resolved (respectively, strongly resolved) by some vertex of W. A smallest resolving set (strong resolving set) of a graph is called a basis (respectively, a strong basis) and its cardinality, the metric dimension (respectively, the strong dimension) of G. The threshold dimension (respectively, threshold strong dimension) of a graph G, is the smallest metric dimension (respectively, strong dimension) among all graphs having G as a spanning subgraph. Graphs that are not spanning subgraphs of graphs with smaller metric dimension (or smaller strong dimension) are irreducible relative to the metric dimension (respectively, strong dimension). We present geometric characterizations for both the threshold dimension and threshold strong dimension of a graph and demonstrate the utility of these characterizations. We highlight some similarities and differences between these two invariants and show that they are not equal. We describe several bounds for these two invariants and discuss the existence of irreducible structures of a given order and dimension (strong dimension). [This is collaborative work of two research groups: Group 1: Lucas Mol, Matthew Murphy, Ortrud Oellermann; Group 2: Nadia Benakli, Novi Bong, Shonda Dueck, Linda Eroh, Beth Novick and Ortrud Oellermann.] |
Winter 2020 |
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Friday, March 13 12:30-1:20 3M62 |
Dr. Aynslie Hinds Institute of Urban Studies, University of Winnipeg |
Title: Applying Your Statistics Knowledge and Skills in the Non-Profit Sector Abstract: In this talk, I will discuss how I am using my statistics knowledge and skills to support community organizations with their research, evaluation, and information needs. Additionally, I will describe how students can apply their knowledge and skills to do similar work in a volunteer capacity with the support of Community Hub - Information and Research Partnerships (CHIRP). |
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Friday, February 28 12:30-1:20 Room 1L11 |
Dr. Vida Dujmović School of Computer Science and Electrical Engineering, University of Ottawa |
CANCELLED Title: Graph colourings Abstract: Graphs are mathematical structures used to model networks that arise in all areas of human endeavour. Graph colouring is among the most studied and most applicable topics in graph theory. In this talk, I will introduce several graph colouring problems, starting with the famous four colour theorem for colouring maps. I will then talk about a graph colouring problem that arises in the study of pattern-avoiding sequences. Finally, I will present a recent breakthrough at the intersection of the two previous topics, where colleagues and I solved a 20-year old open problem. |
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Friday, February 14 12:30-1:20 Room 3M62 |
Dr. Maxime Turgeon Department of Statistics, University of Manitoba |
Title: Principal Component of Explained Variance: an optimal and efficient dimension reduction method Abstract: Recent technical advances in genomics and neuroimaging have led to an abundance of high dimensional and correlated data. In this context, dimension-reduction techniques can be used to summarize high-dimensional signals, to further test for association with the covariates of interest. We revisit one such approach, renamed here as Principal Component of Explained Variance (PCEV). This method seeks a linear combination of outcomes by maximising the proportion of variance explained by the covariates of interest. In the first half of this talk, we propose a general high-dimensional analytical framework that is conceptually simple and free of tuning parameters. We provide a computational strategy for high-dimensional outcomes that relies on an assumption of block-independence that is natural in the context of genomics and neuroimaging. We also investigate the robustness of our approach when this assumption is not met. In the second half, using random matrix theory, we propose an empirical estimator that provides a fast way to compute valid p-values to test the significance of a high-dimensional multivariate association. We illustrate these different concepts using DNA methylation data and neuroimaging data. |
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Friday, January 31 12:30-1:20 Room 2M74 |
Dr. Melody Ghahramani Department of Mathematics and Statistics, University of Winnipeg |
Title: Time series regression for zero-inflated and overdispersed count data: a functional response model approach Abstract: Count time series data feature prominently in epidemiology, business, and environmental sciences. Often, such data exhibit zero-inflation and overdispersion in addition to serial dependence. Parametric models such as the zero-inflated negative binomial distribution are employed to account for zero-inflation and overdispersion. In practice, the conditional variance structure may be unknown or may not be negative binomial. In this talk, I develop a distribution-free approach for estimation of regression parameters of conditionally overdispersed and zero-inflated time series models. Model parameters are optimal in the Godambe-information sense. Simulation studies indicate that our method is robust to model misspecification with small relative bias and nearly the same efficiency as that of the MLE for some observation-driven count time series processes. A case study comparing our method with fully parametric methods using weekly syphilis counts from 2007--2010 in Virginia, USA illustrates the benefit of our method. This is joint work with Scott White (UWinnipeg statistics major graduate). |