Economics had its critics even before the financial crisis of a decade ago. Since then doubt has grown over how much economists really know. Much of economics rests on analyses of how individuals – as consumers, or in managing a business, for example – make supposedly optimal decisions in uncertain situations.
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.
High-profile data horror stories are becoming increasingly common, from Facebook’s relationship with Cambridge Analytica to the leak of UK diplomatic cables and massive security breaches at some of the world’s biggest companies.
Some of the strongest challenges for numerical weather prediction come from the unsteady nature of certain flows, in particular nocturnal and stable boundary layers.
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.
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.
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.
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.
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.
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.
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