Spectral theory for the stability of dynamical systems on large oriented locally tree-like graphs

The linear stability of large complex systems around their stationary points can be studied with random matrix theory. In one common model, the i.i.d. random matrix model, one assumes a simple statistical form for the interactions between distinct elements of a network. Read more

Bayesian approach for network adjustment for gravity survey campaign: methodology and model test

Variations in the strength of gravity over the Earth’s surface reflect underlying geophysical changes such as groundwater change, surface vertical deformation, tectonic events, earthquakes and other processes. To study such processes, so-called gravity survey campaigns collect observations made repeatedly at fixed stations. Read more

Scale interactions and anisotropy in stable boundary layers

Some of the strongest challenges for numerical weather prediction come from the unsteady nature of certain flows, in particular nocturnal and stable boundary layers. Read more

Condensation of degrees emerging through a first-order phase transition in classical random graphs

When steam condenses from vapour into liquid, the water molecules move closely together and the system, from a mathematical point of view, comes to reside in an extremely small portion of the conceptually available phase space. Read more

Effective bandwidth of non-Markovian packet traffic

Telecommunications engineers and operations researchers aim to manage complex and fluctuating traffic flows through extended networks. Among other techniques, they have exploited results from the theory of large deviations to estimate the likelihood that a demand in service will overflow the available resources. Read more

Thermodynamic uncertainty for run-and-tumble type processes

Systems out of equilibrium typically carry macroscopic currents of particles, mass or energy. Thermodynamic uncertainty relations offer universal bounds linking such currents and their statistical fluctuations to other system properties, especially entropy production. Read more

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