Comment on D. Bernoulli (1738)

Probability theory emerged in the second half of the 17th century as a way to think about monetary gambles, and how to choose wisely when facing uncertainty. Early thinking suggested that people would act so as to maximise the expected change in wealth – an average over all possible outcomes. Read more

Detection and replenishment of missing data in marked point processes

Point processes offer a convenient mathematical representation of earthquakes, volcanic eruptions, crimes and many other processes which occur at random times and locations. The data available in these fields has exploded with modern recording technology, and yet many data sets suffer from significant incompleteness. Read more

Can Signal Delay Be Functional? Including Delay In Evolved Robot Controllers

Signals travel at finite speeds within the nerves of living organisms, between satellites and the Earth, or in computers and other technological devices. As a result, they incur delays in moving from one point to another, which engineers, roboticists, control-theorists and neuroscientists typically consider as a source of error. Read more

Anomalous Diffusion in Random Dynamical Systems

Brownian motion has long been the standard paradigm for modelling random, diffusive motion, such as the haphazard movement of a dust particle floating in a fluid. This is considered to be “normal” diffusion, in which the mean square particle displacement – calculated as an average over an ensemble of particles – increases linearly in the long-time limit. Read more

Noisy network attractor models for transitions between EEG microstates

Electroencephalography (EEG) provides a direct measure of neuronal activity as reflected in the scalp electrical field. Empirically, global measures of EEG topography remain stable in so-called EEG microstates for brief periods (50–100 ms) before switching to another quasi-stable state. Read more

Normal and Anomalous Diffusion in Soft Lorentz Gases

Engineered nanoscale structures known as artificial graphene exhibit the properties of real graphene but in a setup where it is easy to tune features such as the electronic density, lattice constant, geometry or coupling with the environment. Read more

On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis

In the 1980s, most researchers approached empirical analysis of low-dimensional dynamical systems through the famous Takens embedding theorem, which guarantees that the attractor of any dynamical system can be reconstructed from samples of the values of key variables. Read more

The hammam effect or how a warm ocean enhances large scale atmospheric predictability

Will climate change make weather forecasting harder than it currently is? Or, could a warmer planet make prediction easier? The answer isn’t obvious. Because atmospheric dynamics are chaotic, there are practical limits to predictability, regardless of data precision and available computing power. Read more

Common Trajectories for Urban Economies

Large cities play a disproportionate role in global economic productivity and innovation. Their productivity advantage rests on specialization and the concentration of many diverse skills and capabilities in one place, multiplying economic opportunities and efficiencies. Even so, cities do not appear to develop along one predictable trajectory. Read more

Conditioned Lyapunov exponents for random dynamical systems

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. Read more