Mathematical random graph models for real world dynamical networks
Networks are all around us and hugely affect us: the neurons in our brain, COVID-19 spreading through the population, or computer viruses attacking digital infrastructure via computer networks. Experts estimate that in the US alon...
Networks are all around us and hugely affect us: the neurons in our brain, COVID-19 spreading through the population, or computer viruses attacking digital infrastructure via computer networks. Experts estimate that in the US alone, their government faced costs over 13.7 billion dollars due to cyberattacks in 2018. Insight into the structure and vulnerability of computer networks can help strengthen our defences against cyberattacks, reducing future cost and disruption. Analysing mathematical models of real-world networks can provide such insight. The abstract level of mathematics also makes such analyses widely applicable in various settings like hacking of computer networks and viral pandemics. Most networks change over time. They grow, shrink, and gain and lose connections, like neural plasticity, friendships made and lost, and computers breaking down. Many mathematical models, however, do not incorporate such realistic dynamics of evolving real-world networks. They only allow for network growth, not for removal of nodes and connections. This creates a gap between the theoretical knowledge and the practical use thereof.
I aim to close this gap by analysing properties of two models for real-world networks that incorporate realistic dynamics: Preferential attachment with vertex and edge removal and first-passage percolation on weight-dependent random connection models. The outcomes of this research can influence policy discussions around protecting digital infrastructure and our response to viral pandemics, tying in with the European Commission’s current priorities regarding digitalisation and health within NextGenerationEU.
The research through training provided within this fellowship will provide me with leadership skills and more experience in writing grant proposals and supervising students. Combined with its scientific training, it will help me solidify my potential as an early-career researcher and obtain a tenure-track position at a top European university.ver más
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