News and events

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

    The Department of Mathematics and Statistics invites students, faculty and staff to attend a talk given by Dr. Basil Nanayakkara on Thursday, February 1st, 2024 from 1:00 PM to 2:00 PM. The talk is entitled The Brauer group.

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

    Abstract:

    Let k be a field. The set of all isomorphism classes of finite dimensional central division algebras over k can be endowed with a group structure using the tensor product of k algebras. We will discuss this group, called the Brauer group Br(k) of k and its many ramifications/properties.

  • Madiha Ahmed Masters Thesis Defence Thursday, February 1st, 1:00 PM.

    Madiha Ahmed, a Master of Science (in Statistics) candidate in the Department of Mathematics and Statistics, will defend her M.Sc. Thesis titled Attention-Based Generative Model in Deep Evolutionary Learning: A Multi-Objective Approach to Multi-Target SMILES Fragment-Based Drug Design for Cancer on Thursday, February 1st, 2024 at 1:00 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 the teams link.

    Abstract:

    Cancer remains a global health challenge, necessitating novel drug discovery methods. This graduate thesis introduces two innovative computational frameworks for multitarget drug design in cancer therapy firstly, by integrating Deep Evolutionary Learning (DEL) with a Transformer-based model. Departing from the traditional use of Variational Autoencoder (VAE), this research employs a Transformer-based generative model, capitalizing on its superior ability to capture long-range dependencies within molecular sequences to develop an understanding of the complex molecular grammar. Secondly, the research further evaluates the efficacy of a more granular fragmentation method than the one originally employed in DEL. These two proposed modifications of DEL: (i) Transformer-based model integrated in the original DEL framework and (ii) a fragmentation technique in finer granularity incorporated in the original DEL framework, are each evaluated and compared against the original DEL framework, the benchmark, in their molecular generative capabilities of targeting multiple proteins in cancer progression. In essence, the Transformer’s parallel processing capabilities enhance the drug design efficiency in terms of enhancing the diversity of novel and valid population samples produced and generating the highest-ranked novel molecule with the most optimal set of protein-ligand binding affinities. By optimizing the fragmentation technique, it is observed that it also performs well in maintaining a high novelty and validity of molecular compounds and interestingly, in drug design tasks involving specification of the off-targets, it produces a higher number of novel compounds that satisfy the objective thresholds compared to the benchmark. Overall, we believe that these are two groundbreaking approaches that can be explored for developing efficient cancer treatments, and can also offer potential solutions for other diseases requiring multi-target interventions.

    The examination committee includes Melanie Pilkington, Chair; S. Ejaz Ahmed and Yifeng Li, Co-Supervisors; Jinqiang Hou, External Examiner (Lakehead University); and Tianyu Guan and Betty Ombuki-Berman, Committee Members.

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

    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

    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

    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

    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

    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

    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

    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

    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