Lyapunov exponents play a central role in dynamical systems theory, and offer a measure of the local instability that lies behind deterministic chaos and the sensitive dependence of trajectories on initial conditions.
About Mark Buchanan
This author has yet to write their bio.Meanwhile lets just say that we are proud Mark Buchanan contributed a whooping 48 entries.
Entries by Mark Buchanan
Earthquake statistics follow an approximate scaling law – the famous Gutenberg-Richter law – which states that the number of earthquakes having magnitude m larger than some value M falls off as a power law with an exponent b. The value of b can be estimated from recorded data in earthquake catalogues.
The Dutch scientist Christiaan Huygens famously observed in 1665 that two pendulum-clocks situated in the same room would, over time, come to be synchronized. The explanation? The two clocks were actually interacting very weakly through movements of the floor.
According to current international regulation, financial institutions are obliged to calculate the risk in their trading book on the basis of expected shortfall (ES), a risk measure which aims to capture risk from rare, low-probability events more effectively than earlier measures.
A leading model in earthquake forecasting is the epidemic-type aftershock sequence model, which takes the times and locations of future aftershocks to depend on previous earthquakes, with more recent earthquakes exerting more influence than older events.
LML is delighted to announce that Yonatan Berman joins the Ergodicity Economics research programme as a Postdoctoral Fellow. Yonatan joins us from Paris School of Economics and has a PhD from Tel Aviv University.
Criminologists try to predict crime with a number of methods, such as “hot-spotting” – making maps of locations where crimes tend to occur – and epidemiological techniques based on the assumption that the local risk of crime rises temporarily after a crime occurs.
In 1975, Yoshiki Kuramoto introduced a simple model to describe the collective dynamics of a set of interacting oscillators. In the model, each oscillator has a natural frequency, and is coupled equally to all other oscillators.
How do animals move through their environment as they search for resources, or try to satisfy other natural goals? Over the past two decades, researchers have examined this question using real world data for organisms such as albatross, marine predators and bees, often finding a pattern of many short or mid-scale movements punctuated by occasional […]
Here are links to a few recent articles by LML Fellow Mark Buchanan.
London Mathematical Laboratory
8 Margravine Gardens
The Advent of Ergodicity Economics. An Overview of (Some) Results.
MPI MIS, Leipzig
7 January 2020
Pather Panchali + Presentation from Sunetra Gupta
Science on Screen
4 February 2020
Ergodicity Economics School
23 March to 3 April 2020
LML Summer School 2020
6 July to 31 July 2020