Networks play a vital role in our society. All over the world, people depend on large-scale networks for communication, information, traffic, transport, finance and energy. These networks also contain a lot of information. Understanding, modelling, controlling and optimising networks is a huge challenge, especially when the architecture of the network is unknown. Complex networks also play a central role within nature. Think of chaotic dynamic systems such as the climate, the brain and the cell. These networks pose pressing questions around complexity, sustainability, biodiversity, self-organisation, emergence and uncertainty.
Connecting character
In finding answers to fundamental questions concerning structure, behaviour and universality of complex systems, mathematics in close interaction with other disciplines is a powerful tool. Challenges lie in diverse areas, from statistical methods to be developed for empirically evaluating network models and determining margins of confidence in inferences from complex data sets, to graph theory, algorithm analysis, and matrix operations. Practical questions about the reducibility of a network structure based on limited observations, about the future of a chaotic system like Earth in terms of sustainability, human influence, climate change, or biodiversity, and determining tipping points to new coherent or emergent behaviour, also need new mathematical models. For instance, can we develop neural networks that spontaneously exhibit new behaviour, or in other words, computers with consciousness? Of a philosophical nature is the question of why both natural and non-natural complex systems seemingly naturally become increasingly complex. Applied research translates models into algorithms for understanding and controlling complex networks. Questioners cite: underpinning choices for future energy supply; avoiding peak loads in traffic, of the internet, of the energy grid; modelling regulation in biological networks such as brains and thus predicting diseases such as Alzheimer's and Parkinson's; or predicting rare events that have enormous impact on our society, such as a financial crisis or a flood.
