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Publications

Ensemble clustering for graphs: comparisons and applications by Dr. François Théberge and Valérie Poulin recently appeared in Vol 4, Issue 51 of Applied Network Science.

In May 2019, Dr. Adam Logan, along with co-authors Drs. Martin Bright and Ronald van Luijk (both University of Leiden), published Finiteness results for K3 surfaces over arbitrary fields in the European Journal of Mathematics.

Dr. Colin Weir, and co-author Dr. David Thomson (Carleton University) published a paper on Artin–Schreier extensions of normal bases in the September 2018 edition of Finite Fields and Their Applications.

Valérie Poulin and Dr. François Théberge recently published two papers. The first was on Ensemble Clustering for Graphs in Complex Networks and Their Applications VII.  The code for the algorithm described in the paper is available on code ocean. The second paper, entitled Comparing Graph Clusterings: Set partition measures vs. Graph-aware measures, is to appear in COMPLEX NETWORKS 2018 Book of Abstracts.

John Healy and Dr. Leland McInnes are co-authors on two recent papers, wherein they provided their expertise in dimension reduction and the application of their UMAP algorithm in the fields of biotechnology and materials science. The first paper Dimensionality reduction for visualizing single-cell data using UMAP appeared in Nature Biotechnology, while the second, entitled Manifold learning of four-dimensional scanning transmission electron microscopy, appeared in Nature’s partner journal Computational Materials.

Dr. Colin Weir, with co-authors Dr. Beth Malmskog (Colorado College) and Dr. Rachel Pries (Colorado State University), published a paper on The de Rham cohomology of the Suzuki curves in Arithmetic Geometry: Computation and Applications, proceedings from the 16th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory.

Dr. Megan Dewar, Dr. John Proos, and co-author Dr. David Pike (Memorial University) recently published a paper on Connectivity in Hypergraphs in the June 2018 edition of the Canadian Mathematical Bulletin.

Events

August 19-23, 2019: Summer School on Data Science Tools and Techniques for Modelling Complex Networks

Dr. Francois Théberge, along with co-presenters Dr. Pawel Pralat, Dr. Bogumil Kaminski and Dr. Przemyslaw Szufel are presenting a week-long summer school on representing and analyzing relational data at the Fields Institute for Research in Mathematical Sciences. In a relational data set, an observation involves two or more entities. Such data sets are often modeled via graphs or hypergraphs. A graph is a collection of vertices representing the entities, connected via edges, each of which represents a relationship between two vertices. Hypergraphs are used to model relations involving an arbitrary number of entities. Exploratory data analysis over relational data can be challenging. Slicing or sampling a relational data set tends to destroy its structure and not much can be learned from it. The missing or noisy data problem is also more problematic with relational data. For example, the addition or removal of an edge in a graph can considerably change properties such as the diameter.

The course will explore various theoretical and practical aspects of relational data representation and mining. The format of the course will be a mix of lectures and demonstrations of various techniques over relational datasets using Python, Julia and Jupyter Notebooks.

July 8-14, 2019: SciPy 2019

TIMC was a Silver level sponsor of the 18th annual Scientific Computing with Python (SciPy) conference, held in Austin, Texas from July 8 - 14, 2019. SciPy brings together over 800 participants from industry, academia, and government to showcase their latest projects, learn from skilled users and developers, and collaborate on code development.

July 8-14, 2019: SciPy 2019 Session Co-Chair

The Data-Driven Discoveries track of the SciPy 2019 conference was co-chaired by Tutte Institute researchers Dr. Leland McInnes and Reshama Shaikh. They had the challenging task of narrowing down the almost 60 submissions from leading scientists and researchers into a selection of 20 talks for the conference. While the selections were difficult, the end result -- as evidenced by the final program -- was an exceptional series of talks.

To find out more, visit the SciPy 2019 schedule of events and presentations.

June 7-10, 2019: Canadian Mathematical Society Summer Meeting 2019

Dr. Megan Dewar was an invited speaker in the mini-course on Building Your Career in Mathematics. Dr. Dewar spoke about what it is like working at a government research institute and what graduate students might think about when considering such a career. She also spoke about some of the research recently produced by TIMC.

TIMC believes in contributing to the health of the wider Canadian mathematics community. Dr. Megan Dewar sits on the CMS Board of Directors as a Member for Ontario, as well as holding a position on the CMS Nominating Committee.

June 3-7, 2019: The 14th International Conference on Finite Fields and their Applications

TIMC supported the 14th International Conference on Finite Fields and their Applications (Fq14) which was held from June 3-7, 2019 in Vancouver, BC. This biannual conference series began in 1991 and has become the foremost finite fields conference worldwide in both reputation and size. The principal topics of interest of the Fq conference series are theoretical, computational, and application-driven. Theoretical topics include the structure of finite fields, primitive elements, normal bases, polynomials, number-theoretic aspects of finite fields, character sums, function fields, and almost perfect nonlinear functions. Computational topics include algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, and sequences and functions. Application-driven topics include algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, and quantum information science.

May 29, 2019: Annual Tutte Lecture given by Dr. Lorena Barba

The Tutte Lecture, hosted annually in celebration of Dr. William Tutte’s birthday (May 14), is given by a distinguished mathematician to a broad CSE audience. This year’s lecture was given by Dr. Lorena Barba, Professor of Mechanical and Aerospace Engineering at the George Washington University.

Title: Next in reproducibility: standards, policies, infrastructure, and human factors

Abstract: The National Academies of Science, Engineering and Medicine released a consensus study report on “Reproducibility and Replicability in Science” on May 7, 2019. The report provides definitions of reproducibility and replicability accounting for the diversity of fields in science and engineering. It assesses the state of reproducibility and replicability across science, and it offers recommendations for researchers, agencies, policy makers, journals, professional societies, and more. In its definitions, the committee emphasized the ubiquity and importance of computing and the data-intensive processes in modern science. Reproducibility was defined as obtaining consistent computational results using the same input data, computational steps, methods, code, and conditions of analysis as an original study. Although this may sound straightforward, the report describes how a number of systematic efforts to reproduce computational results have failed in more than half of the attempts made, mainly due to insufficient detail on digital artifacts, such as data, code and computational workflow. In the wake of this comprehensive report, what is next for reproducibility?

Biography: Lorena A. Barba is an international leader in computational science and engineering and a long-standing advocate of open source software for science and education. Dr. Barba is chair of the Board of Directors for NumFOCUS, a charity in the United States that supports and promotes world-class, innovative, open-source scientific software. She is also an expert in research reproducibility, and was a member of the National Academies study committee on Reproducibility and Replicability in Science, which released its report in May 2019.

May 28, 2019: TIMC and Shopify present a public lecture by Dr. Lorena Barba

Title: One step forward, two steps back: the frustration of diversity efforts in STEM

Abstract: Two years ago, a Google engineer attended a diversity program. He had such an adverse reaction to it, that he proceeded to write a 10-page anti-diversity manifesto that he circulated on internal channels. It later became public, furore ensued, and the engineer was fired. Far from being the end of the story, this engineer played the victim of political correctness and became a darling of conservative media outlets. What happened here? One tech company’s attempts to educate its employees and improve the internal culture mightily backfired and as a result the cause for women in STEM was choked back. While a general sense that moving toward gender parity is desirable (though some still disagree with this premise), what actions to take remains unclear. Diversity training programs have been scarcely evaluated, and when they have, they seem to change awareness but not behavior. Sometimes, they create a backlash. More assertive action, like quotas, engender open resentment. Women in science and technology are underestimated by peers and teachers, pressed by stereotypes, disadvantaged in hiring and career progression, sexually harassed, disheartened as their expertise is ignored…and now they are resented for diversity initiatives. Science and technology needs its leaders to be fully committed to diversity and in full understanding of the social-justice underpinnings. Two vehicles for change are: male leaders who are allies and more women in leadership. The recent DataCamp debacle shows that a whole community’s action was needed to right the wrongs of one harasser and one company’s reticence to make him accountable. I aim to elicit your commitments to hire and promote women affirmatively, and to get educated and empower activism with evidence.

May 18, 2019: NSF-CBMS Conference and Software Day on Topological Methods in Machine Learning and Artificial Intelligence

Dr. Leland McInnes attended the software day and ran a code sprint at the NSF-CBMS Conference and Software Day on Topological Methods in Machine Learning and Artificial Intelligence in Charleston, South Carolina.

May 2-5, 2019: Topological Data Analysis, with Applications Workshop

TIMC provided funding to the University of Western Ontario for a workshop on Topological Data Analysis, with Applications organized by Dr. Rick Jardine and Dr. Matt Davison. Topological data analysis is an area of great interest to TIMC researchers, and we have a wish to see more developments in this field as well as encourage new researchers to join the effort. Dr. Leland McInnes was an invited speaker at the workshop, presenting a talk on Using Topological Data Analysis for Unsupervised Learning.

March 21, 2019: Computational Mathematics Seminar at University of Waterloo

Dr. Leland McInnes was an invited speaker at the University of Waterloo’s Computational Mathematics Seminar.  He discussed bringing topological and category theoretic tools to bear on computational problems in machine learning.

February 22-24, 2019: Machine Learning Prague

Dr. Leland McInnes was an invited speaker at Machine Learning Prague 2019. Leland’s talk was on topological approaches to unsupervised learning; discussing both the UMAP algorithm for dimension reduction, and how such techniques can be extended to other problems including metric learning, word embedding, clustering and even anomaly detection.

January 10-11, 2019: Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting

Dr. Adam Logan was invited to the annual meeting of the Simons Collaboration on Arithmetic Geometry, Number Theory and Computation. The meeting was attended by many of the leading North American researchers in these fields. This collaboration is the framework in which the Simons Foundation sponsors researchers and conferences, promotes collaboration, and supports access to extensive databases of mathematical objects arising in these fields. It has already had a substantial impact on the landscape of research and is expected to continue to do so. TIMC intends to continue its engagement with the Simons Collaboration in the future.

December 15 – 19, 2018: West Coast Number Theory

As in previous years, TIMC is providing financial assistance to the West Coast Number Theory (WCNT) Conference.  In its 49th year, WCNT is one of the longest standing conferences in number theory.  It is a uniquely collaborative meeting where participants present results, pose problems, and team up to tackle open questions in number theory.  Two TIMC researchers are co-organizing the meeting.

December 11 – 13, 2018: Complex Networks 2018

Francois Theberge will be presenting joint work with Valerie Poulin on two separate topics: (1) “Comparing Graph Clusterings: Set partition measures vs. Graph-aware measures” and (2) “Ensemble Clustering for Graphs” at the 7th International Conference on Complex Networks and their Applications.  Both works will also appear in conference proceedings publications.

The Complex Networks meeting aims to bring together researchers from different scientific communities working on areas related to complex networks. Two types of contributions are welcome: theoretical developments arising from practical problems, and case studies where methodologies are applied. Both contributions are aimed at stimulating the interaction between theoreticians and practitioners.

December 7 – 10, 2018:  Canadian Mathematical Society (CMS) Winter Meeting 2018

Dr. Megan Dewar is co-organizing a scientific session on Discrete Math in Communications and Computation.  She will also give a presentation in the session entitled “Connectivity in Hypergraphs”.  The session includes a diversity of speakers from academia and industry from across Canada.

TIMC believes in contributing to the health of the wider Canadian mathematics community.  Dr. Megan Dewar and Dr. Gary Walsh both sit on the CMS Board of Directors as Members for Ontario.

Oct 18 – 26, 2018:  GeekWeek Support

GeekWeek is an annual workshop run by the Canadian Cyber Incident Response Centre (CCIRC) – now part of CSE under the Canadian Centre for Cyber Security -- that brings together key players in the field of cyber security for nine days of intensive research and development. Tech enthusiasts are presented with the necessary time and resources to devise and implement innovative solutions to prevent, analyze or mitigate cyber-attacks. 

GeekWeek offers a unique environment for participants to transform the craziest ideas into reality: advanced tools, millions of samples of spam emails, malware, and analysis reports available for testing, and of course, access to other cyber experts. 

John Healy led a support group -- consisting of several TIMC and CSE data scientists -- tasked with providing participants with the tools and skills necessary to analyze the data they were working with.  The team relied heavily on the TIMC implementation of HDBSCAN for clustering and their recently developed UMAP technique for dimension reduction.

Oct 17 - 19, 2018:  PyData NYC Talks and Tutorial

TIMC’s presence at PyData NYC 2018 was strong.  Two researchers gave talks:  Dr. Leland McInnes presented “A Bluffer’s Guide to Dimension Reduction” and John Healy presented “HDBSCAN, fast density based clustering, the how and the why.”  Two other researchers – Dr Amy Wooding and Dr Kjell Wooding – gave a tutorial on Reproducible Data Science entitled “Up your bus number: A reproducible Data Science Workflow.”

Oct 12, 2018: Natural Language Processing Group at NRC

John Healy was invited to give a talk on “Word Embeddings” to the Natural Language Processing Group at the National Research Council.  John’s talk compared various word embedding algorithms, including word2vec, GloVe and FastText, as well as the work that TIMC has been doing in applying the dimension reduction techniques employed by UMAP to words.

September 13, 2018 : The Fields Institute for Research in Mathematical Sciences: Commercial and Industrial Mathematics Program

Dr. Leland McInnes has been invited by the Commercial and Industrial Mathematics Program to give a talk on Topological Methods for Unsupervised Learning. Leland’s talk will describe his very popular UMAP algorithm, and how theory can be extended to other unsupervised learning problems including clustering and anomaly detection.  See the poster for more information.

July 29 – Aug 4, 2018: Oberwolfach workshop

Adam Logan was invited to participate in the Oberwolfach Research Institute for Mathematics Workshop on Explicit Methods in Algebraic Number Theory.  While there he presented a talk on “Three modular fivefolds of level 8.”

The Oberwolfach Research Institute for Mathematics is an international research centre situated in the German Black Forest. Leading experts from all over the world meet at the Institute in order to pursue their research activities, to discuss recent developments in their field with others, and to generate new ideas.

July 12, 2018 : SciPy 2018 Presentation

Dr. Leland McInnes presented a talk at the SciPy 2018 Conference (Scientific Computing with Python) which was held in Austin, Texas from July 9 – 15.   The talk, entitled UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, introduced the audience to a new approach to dimension reduction called UMAP. UMAP is grounded in manifold learning and topology, making an effort to preserve the topological structure of the data.  You can view Leland’s talk or read more on the UMAP fact sheet.

July 9 – 15, 2018:  SciPy 2018 Session Co-Chair

At this year’s SciPy 2018 conference (Scientific Computing with Python) the Machine Learning session was co-chaired by Tutte Institute researcher Dr. Leland McInnes, and Dr. Michelle Gill of BenevolentAI.

The Machine Learning track at SciPy received 31 excellent submissions, and selecting the best of those submissions was a challenging task. The end result was an extremely strong and well attended series of talks for this year’s SciPy.

To find out more, you can visit the SciPy schedule of events and presentations.

July 9 – 13, 2018 : Canadian Number Theory Association Conference

The Tutte Institue for Mathematics and Computing (TIMC) is providing funding to the Canadian Number Theory Association (CNTA) for its 15th conference in Quebec City, Quebec, at Laval University.

The CNTA was founded in 1987 for the purpose of enhancing and promoting learning and research in number theory, particularly in Canada.

June 12, 2018 : PyData Ann Arbor Meetup

Dr. Leland McInnes will be giving an invited talk on PCA, t-SNE, and UMAP: modern Approaches to Dimension Reduction.

June 4, 2018 : The Field Institute for Research in Mathematical Sciences: Commercial and Industrial Mathematics Program

Dr. Francois Theberge has been invited by the Commercial and Industrial Mathematics Program to give a talk on Hypergraph Modularity and Clustering.

June 1 – 4, 2018 : Canadian Mathematical Society Summer Meeting 2018

Dr. Gary Walsh is co-organizing a session on Computational and Diophantine Number Theory and Dr. Colin Weir is giving a talk titled Diophantine equations counting supersingular hyperelliptic curves.

May 17, 2018 : Annual Tutte Lecture : Dr. Kristin Lauter

The Tutte Lecture, hosted annually in celebration of Dr. William Tutte’s birthday (May 14), is given by a distinguished mathematician to a broad CSE audience. This year’s lecture was given by Dr. Kristin Lauter, Principal Researcher and Research Manager for the Cryptography Group at Microsoft Research.

Abstract: This talk will describe a mathematical solution for securely handling outsourced computation in the cloud, using homomorphic encryption.  One application is to provide private storage and computation on genomic data, to protect the long-term privacy of the data.  Many other applications in the health, financial, and public sectors can make use of homomorphic encryption techniques to securely and privately store and compute on encrypted data.  Current solutions for Homomorphic Encryption are based on hard problems in number theory related to lattices.  This talk will survey the theory and practice of homomorphic encryption today.

Biography:  Dr. Kristin Lauter is Principal Researcher and Research Manager for the Cryptography group at Microsoft Research.  Her research areas are number theory and algebraic geometry, with applications to cryptography.  She is particularly well known for her work on homomorphic encryption and elliptic curve cryptography.

Other news

The TIMC-developed UMAP algorithm has seen some high profile use in 2019. A recent collaboration between researchers from Google Brain and OpenAI produced a paper on how to better understand deep neural networks through a technique they refer to as the activation atlas. UMAP plays a central role in the approach, providing a map of the internal state space of the neural network. Looking beyond its use in artificial intelligence research, UMAP was also used in several high profile papers in Nature (1, 2, 3). The diversity of use helps to underline the importance of developing foundational mathematical techniques that can be applied to a very wide range of problems.  See the UMAP fact sheet for further details on the algorithm.

Fact sheet

Uniform Manifold Approximation and Projection (UMAP)

HDBSCAN (Hierarchical Density-Based Spatial Clustering of Applications with Noise)

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