Articles by author: jlarone

  • Joyce Khouzam Masters Project Presentation: Friday, June 5, 3:00 PM

    Wednesday, June 03, 2026 | By

    Joyce Khouzam, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Project titled Linear Forms in Logarithms and the Extendibility of a D(4)-Pair of Pell Numbers on Friday, June 5, 2026 at 3:00 PM.

    The examination committee includes Supervisor Dr. Omar Kihel and Supervisory Committee Member Dr. Hichem Ben-El-Mechaiekh.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the meeting can be found here: Join the meeting.

    Keywords: Linear forms in logarithms, Diophantine equations, Pell numbers

    Abstract:  This paper introduces linear forms in logarithms and determines how it can be used to resolve a concrete problem in number theory. We start by reviewing the tools needed throughout the paper such as: how well rational numbers can approximate real numbers, how continued fractions can make those approximations systematic, and how the Pell equation connects both ideas. From there, Pell numbers are central to the paper.

    Next, we look at Baker’s 1966 theorem and explain why a nonzero expression of the form b_1 log(a_1) + … + b_N log(a_N) cannot be made arbitrarily small and we show the more practical bounds that are due to Matveev and Laurent. We also describe the Dujella-Petho lemma, which uses continued fractions to bring large theoretical bounds down to a range small enough to check by hand or computer.

    As the main application, we walk through the proof of the answer to the question “which Pell numbers P_k can be added to the pair {P_{2n+4}, 4P_{2n+2}} to form a D(4)-triple?”. By reducing the problem to a Pellian equation, parametrizing its solutions, and applying Matveev’s theorem, Laurent’s theorem, and the Dujella-Petho lemma, we see that P_{2n} is the only answer.

  • Thomas Wolf Memorial Event

    Monday, May 04, 2026 | By

    We look forward to gathering tomorrow to remember Thomas Wolf. We will meet at 9:30 a.m. outside the J Block entrance to Pond Inlet, where Dean Berg, colleagues, and Thomas’s family will share a few words in his honour.

    In the event of rain, please proceed directly to the VPMI.

    A commemoration event for professor, friend and colleague of the Faculty of Mathematics and Science, Thomas Wolf will occur on May 5, 2026. The event follows the one-year anniversary of his passing on April 29th, 2025. We will begin the event outside by the entrance to Pond Inlet where a White Spruce tree has been planted in his honour. We are gathering in his memory to celebrate Professor Wolf and launch a new Mathematics and Statistics scholarship – The Thomas Wolf Mathematics Award.

    The event will take place from 9:30 a.m. to 10:30 a.m. meeting outside the entrance to Pond Inlet, where his tree is planted.  Thomas’ family will attend the event and speak to his lasting impact.

    To support the scholarship, a donation link has been created – http://brocku.ca/donate  Select the “In Memory of Thomas Wolf” option from the drop down menu under “Please select the designation of your gift.”  Please consider donating to help support the bright minds applying for the scholarship.

    In addition, we have created website which collects memories of Thomas. Please take a moment to share a photo or story of Thomas that will be included on the site –  https://brocku.ca/mathematics-science/thomas-wolf-tribute/ Approved stories will be read at the event to share in his memory.

  • Mathematics and Statistics Seminar, Dr. Takao Komatsu

    Monday, April 20, 2026 | By

    Students, faculty, and staff are invited to attend the upcoming Mathematics and Statistics Seminar with speaker Dr. Takao Komatsu on Tuesday, April 28, from 2:00 PM to 3:00 PM in GSB 307.  The talk is entitled Some Explicit Values of a q-Eulerian Multiple Zeta Value at Roots of Unity.

    Abstract

    In recent years, the theory of multiple zeta values has seen rapid development, with growing interest in their q-analogues—known as q-multiple zeta values—arising from q-generalizations. These q-analogues recover the classical multiple zeta values in the limit as q -> 1.

    As part of ongoing research into generalized Stirling numbers, Professor Komatsu has investigated finite q-multiple zeta values. In this talk, he will present results expressing these values using Eulerian numbers and derive explicit formulas in the case where q is a primitive root of unity.

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

    Monday, March 09, 2026 | By

    The Department of Mathematics and Statistics invites students, faculty, and staff to attend the upcoming colloquium with speaker Dr. Basil Nanayakkara on Tuesday, March 17, from 2:30 PM to 3:30 PM in MCJ404.  The talk is entitled The Zariski topology on the spectrum of a nil-clean ring.

    Abstract:

    We will show that the clopen subsets of the prime spectrum of a commutative nil-clean ring form a Boolean lattice. This is an interesting mix of topology and abstract algebra.

  • Math, Just Because with Dr. Jean-Jacques Rousseau

    Wednesday, February 04, 2026 | By

    In contribution to Black History Month events on campus, Dr. Jean-Jacques Rousseau will be delivering a math talk at the Black Student Centre on Monday, February 9, from 2:00 PM to 4:30 PM.

    Those interested in the event can find the full details and RSVP on ExperienceBU here.

    Math, Just Because is not a lecture, not a workshop, and certainly not a test! It’s a conversation, an exchange and a math-along. It will touch on how math can help get our money right, explain why we each have unique social media feeds, and show how music is really hearing mathematics.

    But this isn’t “Math, Because It’s Useful.” It’s Math, Just Because: the value of math for its own sake: math for edification, for self-transformation, and ultimately, math for being our best selves. This Black History Month, let’s walk tall knowing that math is ours, and be reminded of how powerful that makes you.

    Dr. Jean-Jacques Rousseau is a community math educator whose MATH4AI learning experiences build confidence in non-technical learners through problem-posing, “silly” questions, and real-world applications. He holds a PhD (IHPST, University of Toronto) and an MBA (Schulich School of Business, York University) and completed a three-year postdoc in AI & Trust at York University’s Lassonde School of Engineering. Jean-Jacques is a former Innovation Advisor to the President of Haiti and currently serves as EDID Advisor in the Office of the Vice-President Research at Brock University.

  • Congratulations to Billy Marshall for Major Research Prize

    Wednesday, November 26, 2025 | By

    Dr. Billy Marshall (Department of Mathematics and Statistics) and his team were recently awarded the 2025 Linda G. O’Bryant Noetic Sciences Research Prize (https://noetic.org/prize/).  They share the $100,000 prize with two other groups, all working on conscious AI.

    Of the 56 applicants and 8 finalists, the team lead by Dr. Marshall was selected for contributions in Evaluating Artificial Consciousness through Integrated Information Theory.  Over 3,000 researchers from around the world attended the online awards ceremony.

    We extend our congratulations to Dr. Marshall and his colleagues on their significant achievement.

  • Joshua Mac Intyre Masters Project Presentation: Thursday, November 27, 11:00 AM

    Wednesday, November 19, 2025 | By

    Joshua Mac Intyre, a Master of Science candidate in the Department of Mathematics and Statistics, will virtually present the Masters Research Project titled Nil Clean Group Rings over Metacyclic Groups on Thursday, November 27, 2025 at 11:00 AM.

    The examination committee includes Supervisor Dr. Yuanlin Li and Supervisory Committee Member Dr. Henryk Fukś.

    Students (both graduate and undergraduate) as well as other members of the Brock Community are invited to attend. A Microsoft Teams link to the meeting can be found here: Join the meeting.

    Keywords: Idempotent; group rings; nilpotent; nil clean; Peirce decomposition; Wedderburn-Artin; Metacyclic groups; Fermat numbers

    Abstract:  A ring is called nil clean if each element can be expressed as the sum of an idempotent and nilpotent. This presentation expounds on our work published in Nil clean group rings over metacyclic groups. We will assume at least an undergraduate understanding of group and ring theory but will provide some preliminary information on nil clean rings, group rings, and metacyclic groups. We will justify our comparison between the nil cleanness of ℤ2G, and any group ring RG, where R is a commutative ring and G is a finite group. This comparison will lead to an analysis of ℤ2G, for G up to an order of 20. Then, when considering a nil clean group ring RG over a metacyclic group G, we were able to reduce to the case where G = < a, b | a^{n} = b^{m} = 1, b^{-1}ab = a^{r} >, with m = 2k, n odd, and the center being trivial. We try to break it down a little further to when n is a prime power, calculating n for each m up to 16, and we verify whether most of these candidate group rings are indeed nil clean. Finally, we discuss the results of our investigation and a connection to Fermat numbers.

  • Mathematics and Statistics Seminar Series, Dr. Bernhard Spangl

    Wednesday, November 05, 2025 | By

    Students, faculty, and staff are invited to attend the upcoming event in the Mathematics and Statistics Seminar Series with speaker Dr. Bernhard Spangl on Tuesday, November 11, from 1:00 PM to 2:00 PM.  The talk is entitled Active learning: blending design of experiments and supervised learning

    Abstract

    In this talk I will focus on two research topics: (i) sample size estimation in balanced ANOVA models and (ii) query-by-committee active learning in regression scenarios. Their common aim is to minimize the sample size.

    First, we consider balanced one-way, two-way, and three-way ANOVA models to test the hypothesis that the fixed factor A has no effect. The other factors are fixed or random. We determine the noncentrality parameter for the exact F-test, describe its minimal value by a sharp lower bound, and thus we can guarantee the worst-case power for the F-test. These results allow us to compute the minimal sample size, i.e. the minimal number of experiments needed. Additionally, we provide a structural result for the minimal sample size that we call “pivot” effect (cf. also Spangl et al., 2021).

    Second, we discuss the problem of active learning in regression scenarios. In active learning, the goal is to provide criteria that the learning algorithm can employ to improve its performance by actively selecting data that are most informative. Active learning is usually thought of as being a sequential process where the training set is augmented one data point at a time. We restrict ourselves to a pool-based sampling scenario and investigate a committee-based approach as query strategy for actively selecting instantiations of the input variables x that should be labelled and incorporated into the training set using a real chemometric data set.

     

    Registration link 

    Mathematics and Statistics Seminar Series: Active learning: blending design of experiments and supervised learning with Dr. Bernhard Spangl – ExperienceBU

  • Srushti Desai Masters Project Presentation: Tuesday, November 4, 11:30 AM

    Wednesday, October 29, 2025 | By

    Srushti Dhavalkumar Desai, a Master of Science candidate in the Department of Mathematics and Statistics, will present the Masters Research Project titled Graph-Theoretical Analysis of Resting-State Functional Connectivity in the Human Brain: Weighted vs. Binary Representations on Tuesday, November 4, 2025 at 11:30 AM.

    The examination committee includes Supervisor Dr. William Marshall and Supervisory Committee Member Dr. Xiaojian Xu.

    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 [email protected] for the room location.

    Keywords: Functional connectivity; resting-state fMRI; graph theory; small-world propensity; weighted networks; binary networks; resilience; ADHD

    Abstract: The brain is always active, even during rest, as different regions continuously interact and exchange information. Understanding these patterns of interaction is essential for exploring how the brain functions as a networked system. When regions exhibit consistent and statistically significant coactivation over time, they are considered functionally connected. Functional Magnetic Resonance Imaging (fMRI) allows researchers to study these connections and construct functional connectivity networks. Graph theory provides a powerful framework for analyzing such networks, where brain regions are represented as nodes and their interactions as edges. Through measures such as small worldness, graph analysis can characterize how efficiently information is processed, reflecting networks that are both highly clustered and globally integrated. However, most graph theoretical metrics were originally designed for binary networks, where connections are treated as either present or absent. Preserving the continuous weights of functional connectivity can provide a more nuanced representation of connection strength and potentially yield deeper insights into brain organization. The present study aimed to determine which representation, binary or weighted, better estimates Small World Propensity (SWP), a measure that quantifies how strongly a network exhibits small world characteristics, and to examine whether SWP is associated with resilience, defined as the capacity to adapt and recover from adversity. Results indicated that weighted graphs performed better for dense networks, while selecting appropriate thresholds improved binary representations for sparse networks. No significant relationship was found between resilience and small worldness within the ADHD group, suggesting that small world organization alone may not account for individual differences in resilience in this dataset.

  • Sambavi Arulnandhy Master Thesis Defence: Tuesday, July 15, 2025 at 9:30 AM

    Thursday, July 10, 2025 | By

    Sambavi Arulnandhy, a Master of Science candidate in the Department of Mathematics and Statistics, will defend the Statistics thesis titled Enhanced EEG Spectral Decomposition with Applications to Neurodevelopmental Changes in ADHD on Tuesday, July 15, 2025 at 9:30 AM.

    The examination committee includes Chair Melanie Pilkington, Supervisor William Marshall, External Examiner (Brock University) Stephen M. Emrich, and Committee Members Jan Vrbik and S. Ejaz Ahmed.

    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 [email protected] for the room location.

    Keywords: ADHD, Aperiodic Activity, Customized Loss Function, EEG Spectral Decomposition, Modified Specparam

    Abstract:
    Aperiodic activity in electroencephalogram (EEG) signals, typically modeled as a 1/f-like trend in the power spectrum, reflects the brain’s excitation-inhibition balance, and provides valuable insights into neurodevelopment and cognitive function. This thesis focuses on two main goals: (a) to propose algorithmic improvements to EEG spectral decomposition methods; and (b) to apply the most effective method to investigate age- and sex-related differences in aperiodic EEG activity among children with and without Attention-Deficit Hyperactivity Disorder (ADHD). A comparative simulation study evaluated four spectral decomposition algorithms — Better Oscillation Detection Method (BOSC), Irregular Resampling Auto-Spectral Analysis (IRASA), Specparam and modified Specparam — on simulated EEG-like signals. BOSC and IRASA consistently underestimated components in multi-peak contexts. Specparam and modified Specparam demonstrated the highest accuracy with the modified version introducing a customized loss function that penalizes localized spectral dips differently than peaks and uses subgradient descent for adaptive fitting. This led to more stable parameter estimates and reduced mean squared error across simulations. The second objective is addressed in a registered report, applying Specparam to resting-state EEG data from the Healthy Brain Network. This study includes children aged 5-18 years, grouped by sex and ADHD diagnosis. Notably, it aims to address the long-standing underrepresentation of girls in ADHD research by analyzing aperiodic EEG activity in both sexes. The aperiodic estimates will be analyzed as functions of age, sex, and ADHD status, controlling for socioeconomic status, IQ, and the use of psychiatric medications. Statistical hypothesis testing will include Analysis of Variance (ANOVA) or non-parametric equivalents, with adjustments for group imbalance. These contributions enhance EEG spectral analysis techniques and offer insights into sex- and age-related neurodevelopmental differences in ADHD.

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