Articles by author: nmarshall

  • Sachini Abeysekara Masters Project Presentation Thursday, December 21, 2:00 PM.

    Thursday, December 07, 2023 | By

    Sachini Abeysekara, a Master of Science candidate in the Department of Mathematics and Statistics, will present her Masters Research Project (MATH 5P99) titled Fixed Point Methods in Convex Minimization for Large Data on Thursday, December 21, 2023 from 2:00 pm – 3:00 pm 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.

    Keywords: Machine Learning Data, Convex Optimization, Gradient Descent, Banach Fixed Point Principle

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

    Friday, May 12, 2023 | By

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Friday, May 19th, 2023 from 2:00 pm to 3:00 pm in Mackenzie Chown J-block room 404. The talk is entitled Crossed product algebras and Galois cohomology

    Abstract:

    Given a Galois extension K/k with Galois group G and a 2-cocycle f : G × G → K∗ , we will construct a k-algebra A = (K/k, f) called a crossedproduct algebra. We will show that A is central over k and simple, and that K is a self-centralizing subfield of A. Thus, A determines an element in the relative Brauer group Br(K/k) of the extension K/k. The similarity class [A] of A depends only on the cohomology class [f] of f. Therefore, the map [f] 7→ [A] from H2 (G, K∗ ) to Br(K/k) is well-defined. It can be shown that this map is a group isomorphism, giving the relation between Galois cohomology and the theory of Brauer groups. We will proceed at a pace comfortable for everyone without paying attention to the time. If time runs out, we will complete the remainder in a future talk.

  • Raymond Romaniuk Masters Project Presentation Friday April 21 at 2:00 PM

    Monday, April 17, 2023 | By

    Raymond Romaniuk, a Master of Science candidate in the Department of Mathematics and Statistics, will present his Masters Research Project (STAT 5P99) titled Combatting Imbalanced Data with the Introduction of Synthetic Data with Applications in College Basketball on Friday, April 21, 2023 from 2:00 pm – 3:00 pm in-person in MCJ 404.

    Abstract:

    Data imbalance is an important consideration when working with real world data. Over/undersampling approaches allow us to gather more insight from the limited data we have on the minority class; however, there are many proposed methods. The goal of our study is to identify the optimal approach for over/undersampling to use with Adaptive Boosting (AdaBoost). Based on a simulation study, we’ve found that combining AdaBoost with various sampling techniques provides an increased weighted accuracy across classes for progressively larger data imbalances. The three Synthetic Minority Oversampling Technique’s (SMOTE) and Jittering with Over/Undersampling (JOUS) performed the best, with the JOUS approach being the most accurate for all levels of data imbalance in the simulation study. We then applied the most effective over/undersampling methods to predict upsets (games where the lower seeded team wins) in the March Madness College Basketball Tournament.

    Keywords: Imbalanced data, Boosting Methods, AdaBoost, Over/Undersampling, College Basketball

  • Brittany Perry Masters Project Presentation Friday April 21 at 1:00 PM

    Monday, April 17, 2023 | By

    Brittany Perry, a Master of Science candidate in the Department of Mathematics and Statistics, will present her Masters Research Project (STAT 5P99) titled Boosting Methods for Classification with Small Sample Size on Friday, April 21, 2023 from 1:00 pm – 2:00 pm in-person in MCJ 404.

    Abstract:

    AdaBoost is an ensemble method that can be used to boost the performance of machine learning algorithms by combining several weak learners to create a single strong learner. The most popular weak learner is a decision stump (low depth decision tree). One limitation of AdaBoost is its effectiveness when working with small sample sizes. This work explores variants to the AdaBoost algorithm such as Real AdaBoost, Logit Boost, and Gentle AdaBoost. These variants all follow a gradient boosting procedure like AdaBoost, with modifications to the weak learners and weights used. We are specifically interested in the accuracy of these boosting algorithms when used with small sample sizes. As an application, we study the link between functional network connectivity (as measured by EEG recordings) and Schizophrenia by testing whether the proposed methods can classify a participant as Schizophrenic or healthy control based on quantities measured from their EEG recording.

    Keywords: AdaBoost , decision trees, small sample size, gradient boosting, Schizophrenia

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

    Wednesday, February 08, 2023 | By

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Thursday, February 16th, 2023 from 2:30 pm to 3:30 pm in Mackenzie Chown D-block room 303. The talk is entitled Category Theory — Yoneda’s lemma.

    Abstract:

    We will discuss the notions of category theory (representable functors, natural transformations, functor of points, etc.) until such time that we can state Yoneda’s lemma. Then we will state and prove the lemma. In algebraic geometry, the lemma is mostly used in its contravariant form. As such, we will state and prove the contravariant form of the lemma. The lemma can be used to embed the category of schemes over a field k, in the category of functors (k-algebras) to (sets). This embedding may be a stepping stone to solve some of the open problems in algebraic geometry.

  • Tian Zhao Masters Project Presentation Wed Feb 8 at 3:00 PM

    Friday, February 03, 2023 | By

    Tian Zhao, a Master of Science candidate in the Department of Mathematics and Statistics, will present his Masters Research Project (MATH 5P99) titled When does the sum of 4 Fibonacci numbers equal a power? on Wednesday, Feb. 8, 2023 at 3 pm in TH149.

    Abstract:

    The aim of this work is the study of Diophantine equations using linear forms in logarithms and algebraic techniques. I was  particularly interested in solving the Diophantine equation of when a sum of 4 Fibonacci numbers equal a power of an integer. I will begin my talk by establishing some preliminary results. I will show how using linear forms in logarithms and techniques from algebraic number theory to solve Fn_1 + Fn_2 + Fn_3 + Fn_4 = 6^a.

  • Katia Benseba Masters Project Presentation Tues Feb 7th at 4:00 PM

    Friday, February 03, 2023 | By

    Katia Benseba will present her Math 5P99 Masters Research Project entitled Permutation Polynomials over Finite Fields and their application to Cryptography on Tuesday, February 7th, 2023 at 4:00 PM in MCG 310.

    Abstract:

    The aim of the paper is the study of Permutation Polynomials over finite fields and their application to
    cryptography. In my talk, I will begin by a brief review of finite fields, define permutation polynomials over finite fields and their properties. I will present old results such as Hermite-Dickson’s Theorem as well as some most recent ones. After introducing cryptography, I will give a historical overview, by  explaining some cryptosystems such as RSA and ElGamal. Finally, I will present some cryptographical protocols based on Permutation Polynomials over Finite Fields.

  • Colloquium Talk on Mathematics for Public Health by Dr. Pouria Ramazi

    Monday, June 20, 2022 | By

    Dr. Pouria Ramazi of the Department of Mathematics & Statistics will be giving a talk as part of a Colloquium on Mathematics for Public Health offered by the Field’s Institute for Research in Mathematical Sciences. The talk will take place online on Tuesday, June 21st, 2022 from 2:00 PM – 3:00 PM and is entitled Mathematical modeling of diseases spread: the dexterous use of simple machine-learning tools. 

    Abstract:

    Two main approaches exist in modeling diseases spread. First, the interactive dynamics of all variables that are assumed to be influential in the disease spread are specified explicitly, resulting in mechanistic models, such as the well-known susceptible-infected-removed (SIR). These models have proven to be successful in predicting the short-term future and providing insight into the disease dynamics. However, they are based on our prior understanding of the world, and hence, are only as “good” as that prior understanding, and do not extend to situations where the underlying mechanisms are unknown. Second, simple to advanced machine-learning models are developed fully from data and without incorporating prior human expert knowledge. Some of these models have shown an exceptional forecasting power; however, they often provide no intuition about the dynamics — the reason why they are often questioned and even avoided by mathematicians. A natural bridging between the two approaches would be to take a mechanistic modelling approach for those compartments of the disease spread whose governing dynamics are well-understood and a machine-learning approach for those other yet not-well understood compartments, and this is what I will be discussing in this talk.

    For information on how to register for the talk as well as information on other talks offered as part of this Colloquium, please see the following link: http://www.fields.utoronto.ca/activities/21-22/public-health-colloquium

  • Brock Math Education Seminar Series 2021-22: Dr. Steven Floyd

    Wednesday, June 01, 2022 | By

    As part of this year’s Brock Math Education Seminar Series, Dr. Steven Floyd will give an online talk on Thursday, June 16, 2022 from 2:00 PM – 3:00 PM. The talk will be entitled The Past, Present, and Future Direction of Computer Science Curriculum in K-12 Education. 

    Abstract:

    Once implemented only in optional courses at the secondary level, CS concepts and skills are now being integrated into other subject areas such as mathematics, science, and technology and other grades including K-8. This new state of K-12 CS education is explored through an analysis of 1) related theory reflected in the literature, 2) historical secondary school CS curriculum, 3) enrolment data and important issues related to equity, diversity, and inclusion, and 4) K-8 CS-related curriculum approaches currently being implemented in educational jurisdictions across Canada. Thematic Analysis is used to examine the goals and rationale of historical curriculum documents from Ontario and Document Analysis is used to compare various K-8 curriculum documents from across Canada. Together, the analysis provides a comprehensive look at K-12 CS education that supports educators, policy makers, and researchers in the field during a transformative time.

    Biography of Dr. Floyd:

    Steven Floyd recently completed his PhD at Western University with a focus on Curriculum Studies. Since 2003, Steven has been a high school computer science teacher, resource developer, e-learning course writer, and educational consultant. He has worked with school boards in Canada and the US in supporting computer science education in the K-12 grades, and was awarded the 2017 Computer Science Teachers Association Award for Teaching Excellence in Computer Science and the 2019 Canadian Research Centre on Inclusive Education Research Award. Steven is currently an Education Officer with Ontario’s Ministry of Education.

    For information, including how to access the Lifesize meeting where the talk will take place, please contact: Chantal Buteau: cbuteau@brocku.ca or Steven Khan: skhan6@brocku.ca

  • Information Session on Academic Exchange

    Friday, May 20, 2022 | By

    Prof. Dr. Markus Neuhäuser from the Department of Mathematics and Statistics, Koblenz University of Applied Sciences (Remagen, Germany) will give a session on Academic Exchanges between Brock University and the RheinAhrCampus Remagen (Koblenz University of Applied Sciences) in Germany. This session will take place on Tuesday, May 24th from 3:00 PM – 4:00 PM in PLZ 410.  Any students or faculty who are interested in academic exchange are encouraged to attend.

    Abstract:

    Brock University and the RheinAhrCampus Remagen (Koblenz University of Applied Sciences) in Germany are partner universities. In this talk the campus in Remagen as well as details on possible exchange programs are described. Subjects in Remagen are business and social sciences, mathematics and technology. Scholarships from the German Academic Exchange Service (DAAD) are available for Canadian students. Moreover, an academic internship is also possible in Remagen.

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