Improving the art of earthquake prediction
In Southern California, Japan, Indonesia or other areas around the world prone to earthquakes, people at risk face vast uncertainty about when, where, and how strong the next one will be. Read more →
Quantification of systemic risk from overlapping portfolios in the financial system
Systemic risk in the financial system is risk tied not to one specific firm, but to the interactions between firms – for example, through possible avalanches of spreading financial distress. One important form of systemic risk arises from indirect links between financial institutions, created when financial institutions invest in the same assets. Read more →
Studying language evolution in the age of big data
The availability of large digital corpora of cross-linguistic data is revolutionizing many branches of linguistics, triggering a shift of study from detailed questions about individual features to more global patterns amenable to statistical analyses. Read more →
Phase transition, scaling of moments, and order-parameter distributions in Brownian particles and branching processes with finite-size effects
Random walks provide precise mathematical models for diffusion processes, while rooted trees offer a geometric representation of branching processes. Both are of broad importance in probability theory and statistical physics, and some important mathematical results establish links between the two. Read more →
Predicting chaos with an optimal combination of data and prior knowledge
Early in the 20th century, experts tried to forecast the weather by noting current conditions, patterns of winds, temperatures and air pressures, and looking into historical records to find previous moments when similar conditions prevailed. Looking a few days forward in the records, they could then make predictions by assuming the atmosphere would evolve as it had in the past. Read more →
Synchronisation and Extreme Value Theory for Coupled Map Lattices
Coupled Map Lattices (CML) are discrete time and space dynamical systems often used as simplified models for the study of spatially-extended non-linear systems. Read more →
Weak Galilean invariance as a selection principle for coarse-grained diffusive models
Galileo Galilei famously stated the principle of Galilean invariance, which links the equations of motion of closed systems as viewed in distinct inertial frames translating relative to one another at a constant velocity. Read more →
Universal behavior of the full particle statistics of one-dimensional Coulomb gases with an arbitrary external potential
Random matrix theory is central to the study of the properties of strongly correlated systems in condensed matter physics and related fields, where important physical quantities are surprisingly well reflected by the joint probability density of the eigenvalues of random matrices. Read more →
Intermittent dynamics in complex systems driven to depletion
From earthquakes driven by continental drift to businesses altering their strategies in response to customers’ behaviour, many complex systems exhibit highly unpredictable dynamics, fluctuating episodically between periods of relative quiescence and bursts of activity. Read more →
Heteroclinic networks – probing the hidden influence of unstable fixed points
The stable fixed points of a dynamical system attract obvious interest as potential resting points, or final states. Without continued forcing, for example, a physical pendulum will ultimately end up hanging motionless in the downward position. Read more →
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London Mathematical Laboratory
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