Speaker: Prof. Lewi Stone
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. Read more
Title: From quadratic equations to neural networks—the story of Hilbert’s 13th Problem.
A beautiful theorem but totally useless!
Date and time: Friday 19 May 2017, 3:00–4:00pm Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: I will chart the history of Hilbert’s 13th Problem and connect it to recent theoretical research in neural networks and statistical regression. The focus will be a remarkable theorem of Kolmogorov and Arnold to the effect that continuous functions of many dimensions do not really exist. Specifically, any continuous function defined on the unit cube in N dimensions can be written as a continuous function of one variable acting on the sum N continuous functions of each of the coordinate variables separately. I will discuss where the problem came from, deep in the history of mathematics, and going back to the solution of polynomial equations, and how its solution might (or might not) be relevant to neural networks.
Title: A Mixed Integer Programming approach to the spatio-temporal problem of fragmenting high fuel load areas in the landscape while considering the availability and connectivity of faunal habitat
Date and time: Friday, 5 May 2017, 3:00–4:00pm Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: Wildfires are a threat to communities in many parts of the world and there is general consensus that this threat will be aggravated by climate change. Prescribed burning is a method used to reduce fuel loads in the landscape and hence the risk of large wildfires. But these actions impact on the habitat needs of fauna. Flora also have limited tolerances to such disturbances while fire-dependent species require a certain frequency of burning. Further, given constraints on resources to accomplish fuel-reduction tasks the question of ‘where and when to burn’ becomes complex. A spatio-temporal mixed integer programming model will be presented and illustrated to deal with this problem. The model attempts to maximise the spatial fragmentation of high fuel load while maximising connectivity of habitat.
Title: Recent advances in domain reconstruction from electrical impedance tomography data
Date and time: Friday, 21 April 2017, 3:00–4:00pm Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: Electrical impedance tomography is an emerging budget-priced, non-invasive medical imaging technique that is very likely to complement computerised tomography in important applications such as pulmonary function control and breast cancer screening in the future. The main difficulty associated with this technology is that the arising inverse problem is strongly ill-posed.
In this talk, I will discuss an alternative approach to domain reconstruction from electrical impedance tomography data, which is based on the concept of the convex source support introduced by Kusiak and Sylvester, as well as an appropriate numerical discretisation of the resulting problem.
Title: Classifying bent functions by their Cayley graphs
Date and time: Friday, 28 April 2017, 3:00–4:00pm Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: Bent Boolean functions are fascinating and useful combinatorial objects, whose applications include coding theory and cryptography. The number of bent functions explodes with dimension, and various concepts of equivalence are used to classify them. In 1999 Bernasconi and Codenotti noted that the Cayley graph of a bent function is strongly regular. This talk describes the concept of extended Cayley equivalence of bent functions, discusses some connections between bent functions, designs, and codes, and explores the relationship between extended Cayley equivalence and extended affine equivalence. SageMath scripts and SageMathCloud worksheets are used to compute and display some of these relationships, for bent functions up to dimension 8.
Bio: Paul Leopardi is a computer scientist and mathematician who works to support scientific applications at the Bureau of Meteorology in Melbourne. His academic career has included stints at UNSW, the University of Sydney, ANU and the University of Newcastle. He is an honorary Fellow at the University of Melbourne. His research interests have included high performance numerical computing, computations with Cifford algebras, constructive approximation, and bioinformatics and well as combinatorics. He was enticed to study Hadamard matrices by Judy-Anne Osborn, Jennifer Serberry and Kathy Horadam, amongst others. This led to the present study.
Title: Fast Extraction of the backbone of projected bipartite networks
Date and time: Friday, 7 April 2017, 3:00–4:00pm Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: The study of complex networks has received much attention over the past few decades, presenting a simple, yet efficient means of modelling and understanding complex systems. The majority of network science literature focuses on simple one-mode networks. In the real world, however, we often find systems that are best represented by bipartite networks that are commonly analysed by examination of their one-mode projection. One-mode projections are naturally very dense and noisy networks and hence the most relevant information may be hidden. One way to reveal hidden information is the extraction of significant edges, forming the backbone of the projection. Existing methods are computationally expensive. In this talk, I will introduce a computationally inexpensive method for extracting the backbone of projected bipartite networks. I will demonstrate that the edge weights of projections follow a Poisson binomial distribution and that finding the expected weight distribution of a random bipartite projection only requires knowledge of the bipartite degree distributions.
Bio: Jessica Liebig received her PhD in January 2017 from RMIT University. Her primary research interest lies in the area of network science and is directed toward the study of large, complex bipartite data. The work presented in her thesis examines bipartite networks with the aim of uncovering significant behaviour in real world networks.
Speaker: Dr Luc Doyen
Centre National de la Recherche Scientifique (CNRS)
Title: The tragedy of open ecosystems
Date and time: Thursday, 23 March 2017, 3:00–4:00pm (note this is a joint seminar with Lauriane Mouysset, 30+30 mins) Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus
Abstract: This paper investigates the role played by cooperation for the sustainable harvesting of an ecosystem. To achieve this, a bio-economic model based on a multi-species dynamics with interspecific relationships and multi-agent catches is considered. A comparison between the non-cooperative and cooperative optimal strategies is carried out. Revisiting the Tragedy of Open Access and over-exploitation issues, it is first proved analytically how harvesting pressure is larger in the non-cooperative case for every species. Then it is examined to what extent gains from cooperation can also be derived for the state of the ecosystem. It turns out that cooperation clearly promotes the conservation of every species when the number of agents is high. When the number of agents remains limited, results are more complicated, especially if a species-by-species viewpoint is adopted. However, we identify two metrics involving the state of every species and accounting for their ecological interactions which exhibit gains from cooperation at the ecosystem scale in the general case. Numerical examples illustrate the mathematical findings.