What makes networks tick
October 22, 2015
In the field of mathematics, some researchers study theories while other researchers explore applications. Pawel Pralat, meanwhile, tries to do both.
A faculty member in Ryerson's Department of Mathematics, Pralat investigates the probability of certain events occurring in real-world networks and studies the fast-growing area of random graph theory. With applications as diverse as target-marketing, online dating and urban planning, graph theory tries to make better sense of our world by studying how complex networks behave and change.
For example, Pralat has recently begun to collaborate with the Tutte Institute for Mathematics and Computing. The Ottawa-based organization conducts classified research in order to improve the security of Canada and its allies. Pralat's work is supported by a $100,000 grant from the institute, but because they deal with classified problems, he won't have access to the full details in each project. Instead, he'll explore hypothetical questions that can be applied to multiple scenarios.
For example, how do you model email interactions between people? Current tools use graphs in which a directed arc from X to Y is used to indicate that person X sent an e-mail to Y. But what if X sends the same e-mail simultaneously to many people? Unfortunately, there are no tools and algorithms available to deal with this situation. "A general framework that we are trying to develop could be used, for instance, by search engines to identify important webpages on the Internet as well as to identify leaders and dangerous people in a network of e-mails," says Pralat.
In addition to enhancing national security, his work has also benefitted business. To that end, Pralat has received seven Engage grants – more than any other Canadian mathematician – from the Natural Sciences and Engineering Research Council of Canada. Typically held by engineers and computer scientists, Engage grants support short-term R&D projects that bring post-secondary researchers on board to find solutions to companies’ specific challenges.
Through a partnership with the Globe and Mail, Pralat combined “big data” (huge, complex data sets) with advanced algorithms to create a system that recommends personalized content to online readers. He also completed a project for BlackBerry, which aimed to better understand mobile users' interests. These initiatives also involved Ryerson Data Science Lab director Ayse Bener and her team.
Since social networks help to shape human behaviour, knowing how networks evolve provides insight into what we do and why we do it. "Who talks to whom in a network?" asks Pralat. "We wanted to understand how often we cut links with people whose interests are different than ours and make links with people who have similar interests. How do we change our behaviour and tastes as a result of interaction between users in the network? One would expect that social influence processes cause individuals to adopt the attributes of others they share ties with. Our probabilistic models and experiments lend insights into how social network structures evolve along with people’s attributes."
Pralat's work can also be used in the non-profit sector and to support research on social issues. Last month, for instance, he embarked on a project with Charter Press to help charities identify potential donors. Says Pralat, "In every situation, we're basically trying to understand the underlying micro-processes that shape the network we are analyzing. As a result, we not only observe important features and properties of a network, but we also understand why they occur and where the process is heading, even if the future behaviour is different from the past."