Articles by author: nmarshall

  • Learning Centre renamed to honour Dr. Eric Muller

    Tuesday, October 08, 2024 | By

    At a celebration on Thursday, October 3, 2024, the Department of Mathematics and Statistics renamed its Mathematics Learning Centre after Professor Emeritus Eric Muller. Dr. Muller is a former chair and longtime member of the Department. He was instrumental in its growth during its first years, implemented service courses for non-math majors at Brock, developed the concurrent education program for future math teachers, and lead the creation of the innovative Mathematics Integrated with Computers and Applications program. He has been recognized, provincially, nationally and internationally for his contributions to mathematics education.

    The newly named Eric Muller Math and Stats Learning Centre will continue his mission to continue to promote a rich mathematics and statistics learning experience to Brock students.

    Further details about Dr. Muller and the renaming can be found in this Brock News article.

    Dr. Muller in the Eric Muller Math and Stats Learning Centre

    Dr. Muller next to a new plaque recording his acheivements in the Eric Muller Math and Stats Learning Centre

  • Department of Mathematics and Statistics Colloquium Talk: Dr. Bernard Hodgson

    Monday, September 23, 2024 | By

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Bernard Hodgson from Université Laval (Québec) on Friday, October 4, 2024 from 2:00 PM to 3:00 PM. The talk is entitled History of mathematics as a component of university mathematics education

    For information, contact: Chantal Buteau: cbuteau@brocku.ca

    Abstract:

    I wish in my presentation to discuss the role that history of mathematics could, or should, play in university mathematics education, including in the preparation of schoolteachers. I will support my comments with original documents from the past, so to emphasize the wit of great mathematicians of earlier times as well as the ingenuity of methods they used when solving various problems, before the arrival of modern symbolism. I will present among others approaches developed by Archimedes for “squaring” a circle or a segment of a parabola; the resolution by al Khwarizmi of the second-degree trinomial, without the algebraic notations nowadays standard; or good old Pythagoras as revisited by Euclid.

    Biography:

    Bernard R. Hodgson is Professeur titulaire in the Department of Mathematics and Statistics at Université Laval. His research and teaching interests include mathematical logic and theoretical computer science, mathematical education (in particular the mathematical preparation of primary and secondary school teachers), history of mathematics education, and history of mathematics. He was an invited regular lecturer at the International Congress of Mathematicians-ICM (1990 and 1998) and at International Congress on Mathematical Education – ICME (1992 and 2016), and a plenary lecturer at ICME-12 (2012).

  • Reza Miry Masters Thesis Defence Monday, September 23, 9:30 AM

    Thursday, September 19, 2024 | By

    Reza Miry, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters thesis titled Time Series Prediction: HMMs with TAN and Bayesian Network Observation Structures on Monday, September 23, 2024 at 9:30 AM online on Microsoft Teams.

    The examination committee includes Stephen Anco, Chair; Pouria Ramazi and Tianyu Guan, Co-Supervisors; Rahul G. Krishnan, External Examiner (University of Toronto); and William Marshall and Xiaojian Xu, Committee Members.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at nmarshall@brocku.ca for a link to the Team.

    Abstract: This thesis addresses key challenges in time series classification, focusing on enhancing predictive accuracy through innovative modeling techniques. First, we introduce TAN-HMM, an extension of the traditional Hidden Markov Model (HMM) that incorporates Tree-Augmented Naive Bayes (TAN) to account for correlated features, significantly improving classification performance on complex datasets like MSRC-12. Next, we propose the Bayesian Network Hidden Markov Model (BN-HMM), which combines the temporal dynamics of HMMs with the structural flexibility of Bayesian Networks, achieving superior accuracy and feature relationship discovery. Finally, we tackle the problem of robust early warning signals for disease outbreaks, utilizing cutting-edge deep learning models to predict emerging disease behavior from simulated and real-world noisy datasets. Together, these contributions push the boundaries of time series classification and offer practical solutions for real-world applications, from human activity recognition to disease outbreak prediction.

  • Lasith Chamindu Pranath Pussella Masters Thesis Presentation Monday, September 16 11:00 AM

    Thursday, September 12, 2024 | By

    Lasith Chamindu Pranath Pussella, a Master of Science candidate in the Department of Mathematics and Statistics, will defend his thesis titled Simulation for Cricket: A Machine Learning Approach on Monday, September 16 at 11:00 AM in person in the Department of Mathematics and Statistics.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at nmarshall@brocku.ca for the room location.

    Abstract:

    Cricket is the second most popular sport in the world with a significant presence in Commonwealth countries. Despite its popularity, cricket is underrepresented in the literature, especially in the domain of simulation. Simulation in cricket is challenging because of its complexity, dynamic nature, and data scarcity. In this research, we develop a simulation mechanism for cricket using machine learning techniques. The construction of the simulator is based on the availability of a detailed dataset from Cricket Australia. We employ machine learning to predict the outcome of a “delivery”, the core element of gameplay, which can further be utilized for scorecard generation and match simulations. Our simulator’s potential is demonstrated by employing it to determine the optimal batting position of a given batter in a team in Twenty20 cricket. Additionally, we develop an interactive web platform to enable the end users to directly interact with the simulator.

    Keywords: Cricket; machine learning; simulation; random forests; neural networks; T20 cricket;

    The examination committee includes Yifeng Li, Chair; S. Ejaz Ahmed and Tianyu Guan, Co-Supervisors; Taylor McKee, External Examiner (Department of Sport Management, Brock University); and William Marshall, Committee Member.

  • Anuththara Lekamalage Masters Thesis Presentation Wednesday, September 11 9:30 AM

    Monday, September 09, 2024 | By

    Anuththara Sarathchandra Lekamalage, a Master of Science candidate in the Department of Mathematics and Statistics, will defend her thesis titled Identifiability of Linear Threshold Decision Making Dynamics on Wednesday, September 11 at 9:30 AM. in person in the Department of Mathematics and Statistics.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at nmarshall@brocku.ca for the room location.

    Abstract:

    The binary-decision dynamics of two types of individuals; coordinators who tend to choose the more common option among others and anti-coordinators who avoid the common option can be modeled using the linear (anti-)threshold model. Each individual has a time-invariant threshold and decides whether to choose an option by comparing his threshold with the proportion of the population who have already chosen that option. The resulting decision-making dynamics can be predicted and controlled, provided that the thresholds are known. In practice, however, the thresholds are unknown, and often only the evolution of the total number of individuals who have chosen one option is known. The question then is whether the thresholds are identifiable given this quantity over time, which can be considered as the output of the decision-making dynamics. Identifiability investigates the recoverability of the unknown parameters given the error-free outputs, inputs, and the developed equations of the model. Different notions of and methods to test identifiability exist for dynamical systems defined in the continuous state space. However, the decision dynamics of the linear threshold model is defined in the discrete state space. We develop the identifiability framework for discrete space systems and highlight that this is not an immediate extension of the continuous space framework. Then, we investigate the threshold identifiability of both coordinators and anticoordinators in the linear threshold model. For both the synchronous and asynchronous dynamics, we find necessary and sufficient conditions for the identifiability of coordinating and anticoordinating populations. The results open the door for reliable estimation of the thresholds and in turn prediction and control of the decision-making dynamics using real-world data.

    The examination committee includes Ke Qiu, Chair; Pouria Ramazi, Supervisor; Tianyu Guan, External Examiner (York University); and Henryk Fuks and Stephen Anco, Committee Members.

  • Samiha Tasnim Masters Project Presentation Monday, August 19, 10:30 AM

    Tuesday, August 13, 2024 | By

    Samiha Tasnim, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters Research Project (STAT 5P99) titled The Impact of Exchange Rate Data on Canadian Inflation: An FPCA and Group LASSO Approach on Monday, August 19, 2024 at 10:30 AM online on Microsoft Teams.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at nmarshall@brocku.ca for a link to the Team.

    Abstract: This study investigates the temporal dynamics of exchange rates between various international currencies and the Canadian dollar, with a focus on understanding how these rates influence Canadian inflation. The Functional Principal Component Analysis (FPCA) is applied to effectively reduce the dimensionality of exchange rate data and capture important modes of variation. The extracted functional principal components (FPCs) were then used in a Group LASSO regression model to identify which currencies most significantly impact inflation rates in Canada. Our analysis includes exchange rates from nine countries. The results show that the U.S. Dollar (USD), Mexican Peso (MXN), and Swedish Krona (SEK) are the most influential currencies in predicting Canadian inflation rates. By employing these advanced statistical techniques, this study provides a comprehensive assessment of how fluctuations in global currencies can affect the domestic economic environment, offering valuable insights for policymakers and financial analysts. This study contributes to the broader understanding of currency exchange impacts on inflation and highlights the importance of specific international currencies in economic forecasting.

    Keywords: Functional Principal Component Analysis, Group LASSO, inflation rate, exchange rates, economic indicators, predictive modeling, advanced statistical techniques

  • Department of Mathematics and Statistics Colloquium Talk: Dr. Basil Nanayakkara

    Friday, August 09, 2024 | By

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Thursday, August 22nd, 2024 from 2:00 PM to 3:00 PM. The talk is entitled Quaternion algebras and the Frobenius theorem – Part 2.

    For location room number, please email Neil Marshall (nmarshall@brocku.ca).

    Abstract:
    (This is a continuation of the seminar on July 25th. However, you will be able to understand this, even if you didn’t attend Part 1, as we will be discussing mainly the Frobenius theorem).

    Given a field k and nonzero elements a, b in k, we’ll construct a quaternion algebra over k associated with a and b. We’ll show that it is a central simple algebra, and hence determines an element in the Brauer group of k. Moreover, we’ll see that this quaternion algebra is a division algebra iff the norm function admits a nontrivial zero.

    A related result is the Frobenius theorem, which states that the finite dimensional division algebras over R are R, C and H only, thereby proving that the Brauer group of R is the cyclic group of order 2.

    The geometric counterpart of a quaternion algebra is a one-dimensional Brauer-Severi variety. If time permits, we’ll discuss this notion as well.

  • Congratulations to Pranath Pussella

    Monday, June 24, 2024 | By

    Earlier in June, Pranath Pusella a M.Sc. (Statistics) candidate in the Department of Mathematics and Statistics attended the 2024 Statistical Society of Canada (SSC) annual meeting in St. John’s, Newfoundland and Labrador. Pranath presented his recent work titled Simulation in Cricket: A Machine Learning Approach and was awarded a Honorable Mention for his presentation. The Department of Mathematics and Statistics would like to extend its congratulations
    to Pranath for his significant achievement at the conference.

    Below: An image of Pranath and his poster from the conference.

    Congratulations Pranath!

  • Congratulations to Dorothy Levay

    Wednesday, June 19, 2024 | By

    The Department of Mathematics and Statistics would like to congratulate Dorothy Levay, Instructor and Manager of Academic Support, who is the recipient of the 2024 Faculty of Mathematics and Science’s Distinguished Staff Award. Dorothy was recognized for her exceptional service beyond expected duties to enrich the experience of students across campus and her essential role in maintaining the operations of the department amid a period of great transition.

    Further details, including the recipients of other awardees given out by the Dean of the Faculty of Mathematics and Science this year, can be found in this Brock News Article.

    Congratulations Dorothy!

  • Siqin Zhao Masters Project Presentation Friday, June 14, 3:00 PM.

    Wednesday, June 05, 2024 | By

    Siqin Zhao, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters Research Project (STAT 5P99) titled Review of Lapse and Reentry Behavior and Its
    Impact on the Design of Variable Annuities on Friday, June 14, 2024 from 3:00 pm – 4:00 pm online on Microsoft Teams.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. If you are interested in the presentation, please contact Neil Marshall at nmarshall@brocku.ca for a link to the Team.

    Abstract: This project explores the role of Variable Annuities (VAs) and Registered Index-Linked Annuities (RILAs) within contemporary financial planning, emphasizing how they adapt to evolving market conditions. A comprehensive analysis of these products is provided, including their protective mechanisms, pricing models, and risk characteristics, to explain why they effectively meet investor needs. The evolution from traditional annuities to VAs is traced, and the further development of RILAs from VAs is discussed. The study particularly focuses on the behavior of policyholders who often choose to surrender their policies for more favorable options, thereby maximizing their benefits. Through qualitative and quantitative analysis, the paper illustrates how these products respond to market developments.

    Keywords: Variable Annuities, Registered Index-Linked Annuities, Policyholder Behavior, Insurance Product Design

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