FCacioli Blog

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

Big data blog image

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

Mapping Blog Image

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

Prediciting Chaos Blog Image

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

Coupled Map Lattices Blog Image LML

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 Blog Image

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

Local energy transfers blog image

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 Blog Picture

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

Dynamics Blog image

Using Extreme Value Theory to Characterize Chaotic Dynamics

In the analysis of dynamical systems, the correlation dimension is a useful indicator describing the fractal structure of invariant sets. Other measures, such as the Lyapunov exponents and the entropy, provide complementary information on the time scale of predictability of the system. Read more

Energy Cascades Blog Image

Characterizing local energy transfers in atmospheric flows

Computational models employed for simulations of weather and climate have limited spatial resolution, currently around 2 km for regional weather models and 100 km for global climate models. Read more