First passage and first hitting times of Lévy flights and Lévy walks

In many areas of science and applied mathematics, important events often get initiated when a stochastic variable crosses a threshold value. Financial assets may be sold at a particular price, or a chemical reaction initiated when two particles come close enough. Read more

Seismological investigations of induced earthquakes near the Hutubi underground gas storage facility

Earth scientists have long known that fluid injected into the Earth’s crust can induce earthquakes. In principle, seismic activity may also be triggered through gas extraction through the mechanism of poroelastic stress perturbation, although such events have been observed less frequently. Read more

Minimal dynamical systems model of the Northern Hemisphere jet stream via embedding of climate data

Jet streams are narrow, fast-flowing westerly air currents located near the tropopause, the tropospheric boundary with the higher stratosphere. These jets play a major role in driving the large-scale atmospheric circulation and modulate the frequency, severity and persistence of weather events at middle latitudes. Read more

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