Articles from:September 2024

  • 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: [email protected]

    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 [email protected] 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 [email protected] 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 [email protected] 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.