A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in numerous and often surprising contexts in both fields. But, perhaps, we should start with a few words about graphs in general. They are, of course, one of the prime objects of study in Discrete Mathematics. However, graphs are among the most ubiquitous models of both natural and human-made structures. In the natural and social sciences they model relations among species, societies, companies, etc. In computer science, they represent networks of communication, data organization, computational devices as well as the flow of computation, and more. In mathematics, Cayley graphs are useful in Group Theory. Graphs carry a natural metric and are therefore useful in Geometry, and though they are “just” one-dimensional complexes, they are useful in certain parts of Topology, e.g. Knot Theory. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. The study of these models calls, then, for the comprehension of the significant structural properties of the relevant graphs. But are there nontrivial structural properties which are universally important? Expansion of a graph requires that it is simultaneously sparse and highly connected. Expander graphs were first defined by Bassalygo and Pinsker, and their existence first proved by Pinsker in the early ’70s. The property of being an expander seems significant in many of these mathematical, computational and physical contexts. It is not surprising that expanders are useful in the design and analysis of communication networks. What is less obvious is that expanders have surprising utility in other computational settings such as in the theory of error correcting codes and the theory of pseudorandomness. In mathematics, we will encounter e.g. their role in the study of metric embeddings, and in particular in work around the Baum-Connes Conjecture. Expansion is closely related to the convergence rates of Markov Chains, and so they play a key role in the study of Monte-Carlo algorithms in statistical mechanics and in a host of practical computational applications. The list of such interesting and fruitful connections goes on and on with so many applications we will not even
Using computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of collaboration between scientists in each of these disciplines. In these networks two scientists are considered connected if they have coauthored one or more papers together. Here we study a variety of nonlocal statistics for these networks, such as typical distances between scientists through the network, and measures of centrality such as closeness and betweenness. We further argue that simple networks such as these cannot capture variation in the strength of collaborative ties and propose a measure of collaboration strength based on the number of papers coauthored by pairs of scientists, and the number of other scientists with whom they coauthored those papers.
Daniyaal Farooqi, Gavin Pu, Shreyasha Paudel
et al.
The emerging widespread usage of AI has led to industry adoption to improve efficiency and increase earnings. However, a major consequence of this is AI displacing employees from their jobs, leading to feelings of job insecurity and uncertainty. This is especially true for computer science students preparing to enter the workforce. To investigate this, we performed semi-structured interviews with (n = 25) students across computer science undergraduate and graduate programs at the University of Toronto to determine the extent of job replacement anxiety. Through thematic analysis, it was determined that computer science students indeed face stress and anxiety from AI displacement of jobs, leading to different strategies of managing pressure. Subfields such as software engineering and web development are strongly believed to be vulnerable to displacement, while specialized subfields like quantum computing and AI research are deemed more secure. Many students feel compelled to upskill by using more AI technologies, taking AI courses, and specializing in AI through graduate school. Some students also reskill by pursuing other fields of study seen as less vulnerable to AI displacement. Finally, international students experience additional job replacement anxiety because of pressure to secure permanent residence. Implications of these findings include feelings of low security in computer science careers, oversaturation of computer science students pursuing AI, and potential dissuasion of future university students from pursuing computer science.