Oxford Mathematician Neave O’Clery recently moved to Oxford from the Center for International Development at Harvard University where she worked on the development of mathematical models to describe the processes behind industrial diversification and economic growth. Here she discusses how network science can help us understand the success of cities, and provide practical tools for policy-makers.
A resting frog can deform the lily pad on which it sits. The weight of the frog applies a localised load to the lily pad (which is supported by the buoyancy of the liquid below), thus deforming the pad. Whether or not the frog knows it, the physical scenario of a floating elastic sheet subject to an applied load is present in a diverse range of situations spanning a spectrum of length scales. At global scales the gravitational loading of the lithosphere by mountain ranges and volcanic sea mounts involve much the same physical ingredients.
The classic picture of how spheres deform (e.g. when poked) is that they adopt something called 'mirror buckling' - this is a special deformation (an isometry) that is geometrically very elegant. This deformation is also very cheap (in terms of the elastic energy) and so it has long been assumed that this is what a physical shell (e.g. a ping pong ball or beach ball) will do when poked. However, experience shows that actually many shells don’t adopt this state - instead, beach balls wrinkle and ping pong balls crumple.
Cancer is a complex and resilient set of diseases and the search for a cure requires a multi-strategic approach. Oxford Mathematicians Lucy Hutchinson, Eamonn Gaffney, Philip Maini and Helen Byrne and Jonathan Wagg and Alex Phipps from Roche have addressed this challenge by focusing on the mathematical modelling of blood vessel growth in cancer tumours.
New methods for localising radiation treatment of tumours depend on estimating the spatial distribution of oxygen in the tissue. Oxford Mathematicians hope to improve such estimates by predicting tumour oxygen distributions and radiotherapy response using high resolution images of real blood vessel networks.
Systemic risk, loosely defined, describes the risk that large parts of the financial system will collapse, leading to potentially far-reaching consequences both within and beyond the financial system. Such risks can materialize following shocks to relatively small parts of the financial system and then spread through various contagion channels. Assessing the systemic risk a bank poses to the system has thus become a central part of regulating its capital requirements.