Random matrices and the stability of complex biological networks

Speaker: Prof. Lewi Stone
Mathematical Sciences
RMIT University

Title: Random matrices and the stability of complex biological networks

Date and time: Friday 23 June 2017, 3:00–4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: Network models have become indispensable tools for exploring the profound complexity of the living world. Intuitively, rich highly interconnected biological networks are expected to be the most stable, and are thus likely to better withstand the loss of a link, or to cope in the presence of external environmental perturbations. In the 70’s, Robert May exploited random matrix theory, and the famous “circular law” for matrix eigenvalue distributions (as used in atomic physics), to challenge this paradigm. He demonstrated convincingly that more complex and connected biological systems are in fact more fragile and less likely to be stable, in terms of their ability to recover after some small external perturbation. Since then, the random matrix framework has proved extremely useful for identifying those factors that beget stability in large biological communities of randomly interacting species. Moreover, in recent years, the random matrix approach has successfully spread to other disciplines, ranging from systems biology, neurosciences, HIV vaccine development, through to wireless, finance and banking, making this an exciting and vibrant contemporary research discipline. Here I outline how random matrices can be useful for dealing with these sorts of questions, and discuss some new results.

Bio: Prof Lewi Stone completed his university education at Monash University, worked 20-years at Tel Aviv University in Biomathematics and is now a member of RMIT School of Mathematical and GeoSpatial Sciences.

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