Articles by author: nmarshall

  • Mo Ahsan Ahmad Masters Project Presentation Friday, December 20, 10:30 AM

    Tuesday, December 17, 2024 | By

    Mo Ahsan Ahmad, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters project titled Advancing Generative Modeling and Applications with Boltzmann Machines, Restricted Boltzmann Machines, and Sum-Product Networks on Friday, December 20, 2024 at 10:30 AM online on Microsoft Teams.

    The examination committee includes supervisors Dr. Ejaz Ahmed and Dr. Yifeng Li and Supervisory Committee Member Dr. Pouria Ramazi.

    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. Please join with your microphones and camera turned off.

    Keywords: Probabilistic Models, Boltzmann Machines, Restricted Boltzmann Machines, SPNs, FMNIST Dataset, Model Performance

    Abstract:
    We live in the era of advanced machine learning methodologies with promising applications in generative probabilistic modeling. This study explores advanced machine learning methodologies with promising applications in probabilistic modeling and real-world problem-solving. The investigation focuses on Boltzmann Machines (BMs), Restricted Boltzmann Machines (RBMs), and Sum-Product Networks (SPNs), emphasizing their ability to analyze complicated data distributions and reconstruct meaningful outcomes. BMs and RBMs, as energy-based probabilistic models, provide a strong foundation for capturing patterns in a variety of datasets. SPNs, with their hierarchical structure, allow for scalable probabilistic inference and efficient data representation. Using the Fashion MNIST dataset as a benchmark, this work demonstrates the practical performance of these models, highlighting reconstructed images, and precise predictions, alongside quantitative performance metrics. These findings are relevant for a variety of applications, such as image synthesis, object detection, and pattern recognition in domains like healthcare diagnostics and scientific research. The results highlight the distinct strengths of each strategy: the scalability and inference effectiveness of SPNs, as well as the capacity of BMs and RBMs to efficiently reconstruct and model data distributions. By providing a comparative analysis of these approaches, the study provides practical insights for both researchers and developers, demonstrating generative models’ revolutionary capability in developing machine learning and deep learning applications.

  • Congratulations to Dorothy Levay winner of the 2024 Brock President’s Distinguished Staff Award

    Friday, December 13, 2024 | By

    The Department of Mathematics and Statistics would like to congratulate our staff member, Dorothy Levay who is the recipient of the 2024 Brock President’s Distinguished Staff Award. This award is to recognize staff who, in addition to their normal duties:

    • Demonstrated exemplary service and/or make a significant contribution in his/her unit

    • Done something exceptional to advance Brock’s reputation

    • Made a significant contribution to the University and/or community

    • Provided a valuable service to the broader community at Brock University outside his/her own unit 

    Photo of Dorothy Levay and her award

    Dorothy has for many years contributed to the success of the Department of Mathematics and Statistics and Brock University. She voluntarily took on a leadership role for the Department of Mathematics and Statistics’ teaching assistants years before it was officially added to her job description. She mentors the Department’s part-time instructors and teaching assistants, including observing lectures for first-time instructors and serving as chair of the Department’s Sessional and ILTA Teaching committee. As part of this, Dorothy reviews applications, makes recommendations to other committee members, conducts interviews and provides workplace references to part-time instructors and teaching assistants as requested.

    She also steps up when needed to assist with the the Department’s teaching, including rearranging her teaching deployment on short notice when, for example, sudden enrollment required a second section of Math 1P06 (Calculus II for Scientists). While regular teaching is a part of her job description, Dorothy goes above and beyond to provide exceptional instruction to our students, as recognized by her recipient of the 2015 FMS Distinguished Teaching Award as well as the 2001 Making a Difference Award, by the Brock Centre for Students with disABILITIES (now called Student Accessibility Services)

    Dorothy has contributed to advancing Brock’s reputation, by being the principal organizer of the tribute event in recognition of Professor Emeritus Eric Muller on October 3rd, 2024, officially announcing the newly renamed ‘Eric Muller Math & Stats Learning Centre.’ She also served as the co-chair of the local organizing committee of a 4-day Professional Development and Symposium, titled Coding, Computational Modeling, & Equity in Mathematics Education from April 26-29th 2023.

    She has served the university and the community by participating on the external Best Practices Recognition Advisory committee from 2001 to 2010. Dorothy also coordinated from 1996 to 2000 the First Nations Science Camp  during summers.

    She has been involved for many years with the Department of Mathematics and Statistics’ continuous development of its large service courses Math 1P97 and Stat 1P98, which serve close to 3000 students annually. As part of this, she volunteered to join the team responsible for updating the online course modules for both courses. Dorothy took the initiative to consult client departments such as Business, Health Sciences, Biology, Computer Science and Economics) to create program-focused examples as way to make the course contents explicitly more relevant to students. She has also lead the Department’s Service Course Committee when it redeveloped the assignments for Stat 1P98 to include a group case study including real-world data. She has been involved in the creation of the original online modules for the Math 1P97 online course. This commitment to these courses dates back to much earlier times, when she supported the (at the time, innovative) integration of Minitab in STAT 1P98 and of Maple in MATH 1P97.

    We are so happy that Dorothy’s exceptional contributions to the student experience and the Brock Community have been recognized by President Lesley Rigg and the University. Congratulations again Dorothy!

  • Azar Taheri Tayebi Masters Thesis Defence Wednesday, December 18, 2:00 PM

    Thursday, December 12, 2024 | By

    Azar Taheri Tayebi, a Master of Science candidate in the Department of Mathematics and Statistics, will present their Masters thesis titled Use of citizen-reports on angler behavior on Wednesday, December 18, 2024 at 2:00 PM in-person on campus.

    The examination committee includes Stephen Anco, Chair; Pouria Ramazi, Supervisor; Brett van Poorten, External Examiner (Simon Fraser University); and Yifeng Li and William Marshall, Supervisory 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 the room location.

    Abstract:
    Traditional methods for collecting angler behavior data, such as creel and aerial surveys, are costly, while modern alternatives like online platforms and smartphone apps offer cost-effective solutions. Previous studies identified correlations between citizen-reported data and conventional surveys but did not investigate direct relationships between the two or the role of intermediate variables. Using Bayesian networks, we examined these relationships for two key metrics—daily catch rate and fishing pressure—based on data from Alberta and Ontario, Canada. Our analysis included meteorological factors and day types as intermediates, with Bayesian model averaging to assess variable connections. Results indicated moderate direct links between webpage views and aerial boat counts in Ontario and low-probability links between creel survey catch rates and citizen-reported data in Alberta, with indirect links mediated by temperature and solar radiation. We also compared expert-based, ChatGPT-driven, and data-driven Bayesian network models for predicting aerial survey boat counts. All models showed similar predictive accuracy and identified the number of webpage visits as a key predictor of boat activity. These findings highlight the comparable performance of expert, AI-assisted, and data-driven approaches when key variables are considered.

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

    Monday, November 25, 2024 | By

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Monday, December 2nd, 2024 from 2:00 PM to 3:00 PM. The talk is entitled Co-induced modules and their cohomology: Shapiro’s lemma

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

    Abstract:
    Co-induced modules and their cohomology: Shapiro’s lemma
    Let H be a subgroup of a group G. Given an H-module, we will enhance it functorially to a G-module called the co-induced module. We will find the relation between the cohomology of the H-module and that of the co-induced G-module. This is the essence of Shapiro’s lemma.

  • 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

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