Advancing computational power has encouraged the analysis of large, high-dimensional data sets with machine learning and data mining techniques, as well as the use of algorithms to compute dynamical indicators such as Lyapunov exponents or generalized dimensions.
Geophysicists still lack a comprehensive understanding of the mechanisms and stochastic dynamics behind the earthquake generation process, and so also lack an ability to make reliable predictions of the likelihood of extreme events.
Efforts to control epidemics rely on mathematical and computational models of how infectious agents spread. Such models help to find ways to deter transmission – through vaccination and quarantine, for example, or information campaigns to alter human behaviour.
Mathematical models of Lévy Walks have found many recent applications to physical and biological systems, and such applications have generally approached Lévy Walks from the traditional perspective of discrete models for random walks.
In Western Europe, several recent summers have been exceptionally warm, especially the summers of 2003 and 2015. Based on observations over the past century, meteorologists have come to see such major heat events as typically stemming from anticyclonic atmospheric circulation and a lack of spring rainfall in Southern Europe.
Economists routinely model how people choose between different options. For example, a common issue is time delay: would you choose to receive £100 today, or prefer £200 next month?
Any fractal set possesses a unique dimension, which characterises its self-similar behaviour under a change of scale. The attractors of many dynamical systems are more complex multifractals, which possess a spectrum of dimensions, or “generalized” dimensions.
The interaction of noise and non-linearity can cause sharp dynamical transitions, as appear in phenomena such as stochastic resonance or noise-induced synchronization or chaos.
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.
Climate events linked to extremes of temperature (heatwaves/cold spells) have severe impacts on human health and natural ecosystems. Over the past few decades, the frequency and intensity of heatwaves have increased in Europe.
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