CMT Group Meeting
This event is part of the Condensed Matter Theory Seminar Series.
"Building Landau-Ginzburg-type effective Lagrangians for Dynamic Networks."
Some networks are highly dynamic and weighted. Networks such as Economic, financial, and power grids have the properties that: 1) The links are weighted and highly dynamic; 2) Nodes have dynamical functions as attributes e.g. financial capital, value, or electric power generation capacity, etc.; 3) The nodes and the links are trying to optimize something e.g. increase profitability, avoid risk and loss, or load balancing, power delivery efficiency and avoiding blackouts; 4) They seem to have “healthy” and “unstable” phases i.e. market crash, blackout etc.. Similar things can be claimed about social networks, where people have “social capital” and are optimizing certain “social benefit” or happiness. This optimization suggests that there may be a classical action principle at work here, and indeed the use of Lagrangians in finance and control theory is common practice. It is however much less common to use it with random networks as input. I will first briefly present a phase transition observed in a phenomenological model, in which we are able to predict financial crises. Then I will show how using basic physical Landau-Ginzburg model building methods one can build a very general dynamical model for such systems and derive the phase transition from stable to unstable phase analytically in some cases.