Articles by author: nmarshall

• FMS Research Colloquium Series #4 Indigenous Mathematics: A Survival Kit (May 13 12 PM)

  Thursday, April 25, 2024 | By nmarshall

  As part of the Faculty of Mathematics and Science Colloquium Series, Dr. Edward Doolitle, Associate Dean, Research and Associate Professor Mathematics in the Department of Indigenous Knowledge & Science, First Nations University of Canada has been invited to give a talk entitled Indigenous Mathematics: A Survival Kit. 

  Students, Faculty, Staff and members of the Brock Community are invited to join us on May 13th, 2024 from 12:00 PM – 1:00 PM in Rankin Family Pavilion room RFP (214/215), Everyone is welcome.

  Brock Community Members can register free with ExperienceBU -Doolittle

  Description:
  The fourth installment of the FMS Colloquium Series with Dr. Edward Doolittle Associate Dean, Research and Associate Professor, Mathematics, Department of Indigenous Knowledge & Science, First Nations University of Canada

  Serving as part four of the FMS Colloquium Series on the theme of The Anthropocene, Brock University is pleased to host Dr. Edward Doolittle who will present on Indigenous Mathematics: A Survival Kit.

  Edward Doolittle will speak about the mathematics that we can carry with us – not in books or journals – but in our own minds, perhaps with a small amount of material culture which can also be carried on the person. “It is mathematics consistent with Indigenous oral traditions, which might be appreciated by our ancestors before the Anthropocene, and also important again when the Anthropocene draws to a close,” said Doolittle.

  Speaker Biography:
  Edward Doolittle is Kanyen’kehake (Mohawk) from Six Nations in southern Ontario. He earned a PhD in pure mathematics (partial differential equations) from the University of Toronto in 1997. From then until 2001 he worked for Queen’s University’s Aboriginal Teacher Education Program, helping to administer the program and teaching Indigenous Mathematics Education, and from 2000 to 2001 he studied the Mohawk language in immersion with Onkwewenna Kentsyohkwa (Our Language Group) on Six Nations. From 2001 he has been on the faculty of First Nations University and the University of Regina, currently as Associate Professor of Mathematics and Associate Dean, Research. He is a recipient of a Governor General’s Gold Medal and of an honourable mention on the William Lowell Putnam Competition.

   

• Seminar Series: Dr. Henryk Fukś Thursday, April 4th 1:00 PM – 2:00 PM

  Tuesday, April 02, 2024 | By nmarshall

  As part of the Department of Mathematics and Statistics Seminar Series, Professor of Mathematics Henryk Fukś will present a lecture on the theme of the upcoming total solar eclipse, entitled “Solar and lunar cycles in the construction of the Gregorian Calendar.” Students, Faculty, Staff and members of the Brock community are invited to attend. The talk will take place in South Block, room STH 216 from 1:00 PM – 2:00 PM on Thursday, April 4th, 2024.

  Abstract
  On February 24, 1582, Pope Gregory XIII issued the bull “Inter gravissimas” introducing the new calendar, later called Gregorian. It is well known that the calendar reform corrected the average length of the year to make it closer to the astronomical solar year, but it is not so widely known that the Gregorian reform also corrected the way moon phases are calculated for the purpose of determining the day of Easter and for other liturgical purposes.

• Seminar Series: Jianhua Hu Thursday, March 28th 2:00 PM – 3:00 PM

  Tuesday, March 26, 2024 | By nmarshall

  The Department of Mathematics and Statistics invites students, faculty and staff to attend a seminar given by Jianhua Hu on Thursday, March 28th, 2024 from 2:00 PM to 3:00 PM. The talk is entitled Response best-subset selector for multivariate regression with high-dimensional response variables.

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

  Abstract:

  This talk is about investigating the statistical problem of response-variable selection with high-dimensional response variables and a diverging number of predictor variables with respect to the sample size in the framework of multivariate linear regression. A response best-subset selection model is proposed by introducing a 0-1 selection indicator for each response variable, and then a response best-subset selector is developed by introducing a separation parameter and a novel penalized least-squares function. The proposed procedure can perform response-variable selection and regression-coefficient estimation simultaneously, and the response best-subset selector has the property of model consistency under mild conditions for both fixed and diverging numbers of predictor variables. Also, consistency and asymptotic normality of regression-coefficient estimators are established for cases with a fixed dimension, and it is found that the Bonferroni test is a special response best-subset selector. Finite-sample simulations show that the response best-subset selector has strong advantages over existing competitors in terms of the Matthews correlation coefficient, a criterion that aims to balance accuracies for both true and false response variables. An analysis of real data demonstrates the effectiveness of the response best-subset selector in an application involving the identification of dosage-sensitive genes.

  This Seminar is part of the seminar series organized by the Department of Mathematics and Statistics

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

  Thursday, January 25, 2024 | By nmarshall

  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.

  Wednesday, January 24, 2024 | By nmarshall

  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.

  Thursday, December 07, 2023 | By nmarshall

  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 nmarshall

  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 nmarshall

  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 nmarshall

  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 nmarshall

  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.